COMPUTATIONAL FLUID DYNAMICS

UNSTRUCTURED MESH OPTIMIZATION FOR

THE SIEMENS 4TH GENERATION DLE BURNER

Dejan Koren

Master’s thesis

School of Engineering Sciences, Department of mechanics,

KTH, Royal Institute of Technology

Master’s thesis

Computational Fluid Dynamics unstructured mesh optimization for the Siemens 4rd generation DLE

burner

Dejan Koren

Industrial Supervisors: Dr. Daniel Lörstad

Dr. Darioush Gohari Barhaghi

Siemens Turbomachinery AB, Finspång, Sweden

Academic Supervisor: Dr. Bernhard Semlitsch

KTH, Royal Institute of Technology

Examiner: Dr. Mihai Mihaescu

KTH, Royal Institute of Technology

Finspång, October 2015

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This work is dedicated to dr. Marta Klanjšek Gunde

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ABSTRACT

Every computational fluid dynamics engineer deals with a never ending story – limited computer resources. In computational fluid dynamics there is practically never enough computer power. Limited computer resources lead to long calculation times which result in high costs and one of the main reasons is that large quantity of elements are needed in a computational mesh in order to obtain accurate and reliable results.

Although there exist established meshing approaches for the Siemens 4th generation DLE burner, mesh dependency has not been fully evaluated yet. The main goal of this work is therefore to better optimize accuracy versus cell count for this particular burner intended for simulation of air/gas mixing where eddy-viscosity based turbulence models are employed. Ansys Fluent solver was used for all simulations in this work. For time effectivisation purposes a 30° sector model of the burner was created and validated for the mesh convergence study. No steady state solutions were found for this case therefore time dependent simulations with time statistics sampling were employed. The mesh convergence study has shown that a coarse computational mesh in air casing of the burner does not affect flow conditions downstream where air/gas mixing process is taking place and that a major part of the combustion chamber is highly mesh independent. A large reduction of cell count in those two parts is therefore allowed. On the other hand the RPL (Rich Pilot Lean) and the pilot burner turned out to be highly mesh density dependent. The RPL and the Pilot burner need to have significantly more refined mesh as it has been used so far with the established meshing approaches. The mesh optimization has finally shown that at least as accurate results of air/gas mixing results may be obtained with 3x smaller cell count. Furthermore it has been shown that significantly more accurate results may be obtained with 60% smaller cell count as with the established meshing approaches.

A short mesh study of the Siemens 3rd generation DLE burner in ignition stage of operation was also performed in this work. This brief study has shown that the established meshing approach for air/gas mixing purposes is sufficient for use with Ansys Fluent solver while certain differences were discovered when comparing the results obtained with Ansys Fluent against those obtained with Ansys CFX solver. Differences between Fluent and CFX solver were briefly discussed in this work as identical simulation set up in both solvers produced slightly different results. Furthermore the obtained results suggest that Fluent solver is less mesh dependent as CFX solver for this particular case.

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ACKNOWLEDGEMENTS

This work was carried out as the final part of the Master’s program in Engineering Mechanics at KTH, Royal Institute of Technology in Stockholm. Since everything started there I would like to thank this great institution with dr. Gunnar Tibert as, at that time, the Engineering Mechanics program director for giving me the honor of exploring a challenging but very interesting field of Fluid mechanics at the Department of Mechanics.

The project was carried out exclusively at Siemens Industrial Turbomachinery AB in Finspång therefore I would like to thank the Combustion group with Anders Häggmark as its manager for giving me the honor of performing my master thesis at their division.

I would like to express special gratitude to my first supervisor at Siemens, dr. Daniel Lörstad, whose expertise, understanding, patient guidance and all time positive energy added considerably to my master thesis project experience. I appreciate his vast knowledge and experience in Computational Fluid Dynamics and besides that also his strong pedagogic skills.

Furthermore I would like to thank my second supervisor dr. Darioush Gohari Barhaghi for helping me with his kind guidance. I would also like to thank Daniel Moëll and Anders Ljung for providing me with technical help regarding setting up simulations and meshing procedures.

I would like to thank Charlotte Eklöf for being a great project manager in the group.

I wish to acknowledge also my master thesis colleague Johan Sjölander for a great project collaboration and for being a great residence company during my stay in Finspång.

A very special thank goes to my girlfriend Polona Gunde for her love and endless support especially during critical phases of my studies and this thesis work.

My gratitude goes out as well to dr. Marta Klanjšek Gunde and dr. Jasmina Kožar Logar for giving me a great deal of motivation boost to pursue a Master’s Degree in this challenging branch of classical mechanics.

I would also like to thank my supervisor dr. Bernhard Semlitch and examiner dr. Mihai Mihaescu at KTH for helping me with the final shaping of this work.

Lastly I wish to thank my family for supporting me in my desire to broaden my views and horizons abroad through my studies and this work.

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CONTENTS Abstract .............................................................................................................................................................. iv Acknowledgements .............................................................................................................................................v Contents ............................................................................................................................................................. vi List of Figures ................................................................................................................................................... viii List of Tables ...................................................................................................................................................... ix 

1 INTRODUCTION ........................................................................................................................................ 1 

1.1 BACKGROUND ................................................................................................................................................ 1 1.2 OBJECTIVE ..................................................................................................................................................... 1 1.3 SIEMENS AND GAS TURBINES ............................................................................................................................. 2 

1.3.1 A brief history of Siemens establishment ........................................................................................... 2 Gas turbines at Siemens ..................................................................................................................................... 2 From STAL to Siemens in Finspång, Sweden ...................................................................................................... 2 

1.4 GAS TURBINES ................................................................................................................................................ 3 1.4.1 Combustion chambers ....................................................................................................................... 6 

Multiple Combustion Chamber .......................................................................................................................... 7 Can‐annular Combustion Chamber .................................................................................................................... 7 Annular Combustion Chamber ........................................................................................................................... 8 

1.5 THE DRY LOW EMISSIONS COMBUSTORS ............................................................................................................. 9 1.5.1 The Siemens SGT‐800 and 3rd generation DLE burner ...................................................................... 10 1.5.2 The Siemens SGT‐750 and 4th generation DLE burner ...................................................................... 11 

2 THEORETICAL BACKGROUND .................................................................................................................. 13 

2.1 GOVERNING EQUATIONS IN FLUID MECHANICS ................................................................................................... 13 2.1.1 Mass Conversation Equation ........................................................................................................... 13 2.1.2 Momentum Conservation Equation ................................................................................................. 13 2.1.3 Conservation of energy .................................................................................................................... 14 2.1.4 Equation of state .............................................................................................................................. 14 

2.2 TURBULENCE ............................................................................................................................................... 14 2.3 TURBULENCE MODELLING ............................................................................................................................... 15 

2.3.1 Raynolds Averaged Navier‐Stokes equations .................................................................................. 15 2.3.1.1 Eddy viscosity models ................................................................................................................................ 16 

Algebraic models or zero equation models ...................................................................................................... 17 One equation models ....................................................................................................................................... 17 Two equation models....................................................................................................................................... 17 2.3.1.1.1 The standard K‐ε eddy viscosity model............................................................................................. 17 2.3.1.1.2 The K‐ω eddy viscosity model .......................................................................................................... 18 2.3.1.1.3 The SST K‐ω model ........................................................................................................................... 18 The SST turbulence model in Ansys CFX and Fluent ......................................................................................... 19 Ansys CFX ......................................................................................................................................................... 19 Ansys Fluent ..................................................................................................................................................... 20 

2.3.2 Reynolds stress models (RSM) ......................................................................................................... 21 2.3.3 Large Eddy Simulation (LES) ............................................................................................................. 21 

2.4 SPECIES TRANSPORT ...................................................................................................................................... 21 2.4.1 Mass diffusion in turbulent flows ..................................................................................................... 21 2.4.2 Species transport in the energy equation ........................................................................................ 22 2.4.3 Equivalence ratio ............................................................................................................................. 22 

2.5 NUMERICAL METHODS ................................................................................................................................... 22 2.5.1 Discretization ................................................................................................................................... 22 

2.5.1.1 Cell‐centered and vertex‐centered Finite Volume Methods ..................................................................... 23 Basic differences .............................................................................................................................................. 23 Flux integration ................................................................................................................................................ 25 testing of cell‐centered and vertex‐centered scheme ..................................................................................... 25 

2.5.1.2 Spatial discretization ................................................................................................................................. 26 Ansys CFX ......................................................................................................................................................... 26 Ansys Fluent ..................................................................................................................................................... 26 

2.5.1.3 Gradient evaluation ................................................................................................................................... 27 2.5.2 Temporal discretization ................................................................................................................... 27 

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2.5.3 Continuity and momentum equation coupling ................................................................................ 27 2.5.4 Calculation procedures at periodic boundaries................................................................................ 29 

3 METHODOLOGY ..................................................................................................................................... 30 

3.1 GEOMETRY AND MESH CREATION ..................................................................................................................... 30 3.2 MODELS AND SOLUTION METHODS ................................................................................................................... 31 

3.2.1 Monitoring convergence progress ................................................................................................... 31 3.2.1.1 Steady state runs ....................................................................................................................................... 31 3.2.1.2 Transient runs with transient statistics ..................................................................................................... 32 

3.3 COMPUTATIONAL MESH OPTIMIZATION ............................................................................................................. 33 3.4 REPRESENTATION OF RESULTS ......................................................................................................................... 34 

Geometrical features ....................................................................................................................................... 34 Cell sizes ........................................................................................................................................................... 34 Velocity values ................................................................................................................................................. 34 Simulation Time ............................................................................................................................................... 34 Mass flow ......................................................................................................................................................... 34 

4 A SHORT STUDY OF THE 3RD GENERATION DLE BURNER .......................................................................... 35 

4.1 GEOMETRICAL MODEL ................................................................................................................................... 35 4.2 COMPUTATIONAL MESH ................................................................................................................................. 35 4.3 BOUNDARY CONDITIONS AND SOLUTION METHODS .............................................................................................. 36 4.4 RESULTS...................................................................................................................................................... 39 4.5 CONCLUSION REMARKS FOR THE SHORT 3RD

 GENERATION DLE BURNER STUDY .......................................................... 44 

5 THE 4TH GENERATION DLE BURNER COMPUTATIONAL MESH OPTIMIZATION .......................................... 45 

5.1 GEOMETRICAL MODEL ................................................................................................................................... 45 5.2 BOUNDARY CONDITIONS AND TIME STEP SIZE ...................................................................................................... 47 5.3 THE REFERENCE MESH .................................................................................................................................... 48 5.4 VALIDATION OF THE 30° SECTOR MODEL ........................................................................................................... 49 

5.4.1 Monitor points data ‐ 30° versus 90° sector model .......................................................................... 49 5.4.2 Results – comparison between 30° and 90° sector model ............................................................... 51 

5.5 THE MESH OPTIMIZATION ............................................................................................................................... 54 5.5.1 “The three meshes” .......................................................................................................................... 54 

Additional meshes ............................................................................................................................................ 55 5.5.2 Additional monitor points ................................................................................................................ 55 5.5.3 The mesh study ................................................................................................................................ 57 

5.5.3.1 Comparison of velocity and equivalence ratio distribution ....................................................................... 58 5.5.3.2 Quantitative assessment of the meshes along evaluation lines ................................................................ 59 

5.5.4 The optimized mesh – OPT1.4M ...................................................................................................... 61 5.5.5 Verification of the optimized mesh .................................................................................................. 62 

5.5.5.1 The monitor points .................................................................................................................................... 62 5.5.5.2 Assessment of the three meshes including the optimized mesh on interfaces downstream specific passages of the burner .......................................................................................................................................... 63 5.5.5.3 Comparison of time averaged velocity and equivalence ratio distribution ............................................... 65 5.5.5.4 Quantitative assessment of the optimized mesh along evaluation lines .................................................. 66 5.5.5.5 The pilot tip ............................................................................................................................................... 69 

5.5.6 Refining the pilot mesh –OPT1.8M .................................................................................................. 69 5.5.7 Conclusion remarks for the 4th generation DLE burner mesh optimization ..................................... 71 

6 DISCUSSION AND SUGGESTIONS FOR FUTURE WORK ............................................................................. 72 

The short 3rd generation DLE burner study ...................................................................................................... 72 The 4th generation DLE burner mesh optimization .......................................................................................... 73 

REFERENCES ............................................................................................................................................. 75 

APPENDIX ................................................................................................................................................. 77 

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LIST OF FIGURES Figure 1: The portfolio of Siemens gas turbines [34] ........................................................................................... 3 

Figure 2: Two‐shaft gas turbine [6] ...................................................................................................................... 4 

Figure 3: Brayton cycle pressure‐volume diagram for a unit mass of working fluid [6] ...................................... 4 

Figure 4: Examples of gas turbine configurations: (1) turbojet, (2) turboprop, (3) turboshaft, (4) high‐bypass turbofan, (5) low‐bypass turbofan with afterburner [8] ............................................................................ 5 

Figure 5: Two‐shaft gas turbine Siemens SGT‐700 [9] ......................................................................................... 5 

Figure 6: An early combustion chamber [12] ....................................................................................................... 6 

Figure 7: Flame stabilizing and general airflow pattern [12]................................................................................ 6 

Figure 8: Multiple combustion chambers [12] ..................................................................................................... 7 

Figure 9: Tubo‐annular combustion chamber [12] .............................................................................................. 8 

Figure 10: Annular combustion chamber [12] ..................................................................................................... 8 

Figure 11: A schematic comparison of a typical DLE combustor and a conventional combustor ........................ 9 

Figure 12: The SGT‐800 [35] ............................................................................................................................... 10 

Figure 13: The Siemens 3rd generation DLE burner [2] ...................................................................................... 10 

Figure 14: The SGT‐750 [37] ............................................................................................................................... 11 

Figure 15: The 4th generation DLE burner [38] ................................................................................................... 11 

Figure 16: Illustration of cell‐centered (left) and vertex‐centered (right) type control volume constructions [23] ............................................................................................................................................................ 24 

Figure 17: Dual median grid construction [24] ................................................................................................... 24 

Figure 18: Median dual control volume constructed at sharp edge corner [22] ............................................... 24 

Figure 19: Solution reconstruction for vertex‐centered and cell‐centered formulation in 2D unstructured mesh [22] ............................................................................................................................................................ 25 

Figure 20: Flowchart illustrating Fluent solver algorithms [25] ......................................................................... 28 

Figure 21: Cutting the geometry through the air casings damp holes ............................................................... 30 

Figure 22: Normalized velocity in two different monitor points ........................................................................ 32 

Figure 23: Splitting a tetrahedron [30] ............................................................................................................... 33 

Figure 24: Geometrical model of the 3rd generation DLE burner computational domain ................................ 35 

Figure 25: Comparison of the original and splitted surface computational mesh ............................................. 36 

Figure 26: Monitor points locations for the 3rd generation DLE burner ............................................................. 37 

Figure 27: Monitoring velocity in the Point 1, 3 and 5 and monitoring methane mass fraction in Point 1 ....... 37 

Figure 28: Comparison of the time averaged velocity field results between the two meshes on the Plane 1 .. 39 

Figure 29: The planes on which the evaluation lines can be seen ..................................................................... 39 

Figure 30: Comparison of the time averaged velocity field results between the two meshes .......................... 40 

Figure 31: Comparison of the predicted velocity field between Fluent and CFX ............................................... 40 

Figure 32: Comparison of the predicted turbulence kinetic energy distribution between Fluent and CFX ....... 41 

Figure 33: Time averaged equivalence ratio distribution for all four cases ....................................................... 42 

Figure 34: Time averaged velocity distribution along the lines for all cases ...................................................... 43 

Figure 36: The geometric model of the 90° sector of the burner ...................................................................... 46 

Figure 37: The geometric model of the 30° sector of the burner ...................................................................... 47 

Figure 38: Boundary conditions ......................................................................................................................... 47 

Figure 39: The reference computational mesh for the 30° sector model (SIT4.2M). The inflation layer is marked with the red line. ......................................................................................................................... 49 

Figure 40: Positions of the monitor points used for validating the 30° sector model (data obtained from the points shaded with red color can be seen in the Figure 41) ..................................................................... 49 

Figure 41: Monitoring velocity and methane mass fraction in the chosen points ............................................. 50 

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Figure 42: Positions of the evaluation lines for all cases .................................................................................... 51 

Figure 43: Comparison of the time averaged velocity field between the 30° and 90° sector model ................ 51 

Figure 44: Comparison of the time averaged equivalence ratio field between the 30° and 90° sector model . 52 

Figure 45: Comparison of the time averaged velocity and equivalence ratio between the models along the lines which are illustrated in the combustor cross section view .............................................................. 53 

Figure 46: The original generated mesh with 0.55 million cells – 0.55M mesh ................................................. 54 

Figure 47: Positions of the new monitor points ................................................................................................. 56 

Figure 48: Monitored velocity and methane mass fraction in “the three meshes” in the points shown in the cross section view of the combustor and additionally also remaining two meshes in the Point 16 (the My1.9M and the SIT4.2M mesh) .............................................................................................................. 57 

Figure 49: Comparison of time averaged velocity field in the whole domain and instantaneous axial velocity field in the RPL burner obtained with the four meshes ........................................................................... 58 

Figure 50: Comparison of time averaged equivalence ratio field in the whole domain obtained with the four meshes ...................................................................................................................................................... 58 

Figure 51: Velocity and equivalence ratio distribution along the lines obtained from different meshes .......... 60 

Figure 53: Monitored velocity and methane mass fraction in the same chosen points as shown in the Figure 48 but with included monitored data obtained from the optimized mesh (OPT1.4M) ........................... 62 

Figure 54: Positions of the interfaces at which the data in the Table 4 is extracted (shaded with red color). .. 63 

Figure 56: Comparison of the time averaged velocity field in the whole domain and instantaneous axial velocity field in the RPL burner obtained with the optimized mesh (OPT1.4M), the reference mesh (SIT4.2M) and the fine mesh (35M) .......................................................................................................... 65 

Figure 58: Velocity and equivalence ratio distribution along the lines obtained from different meshes with added results obtained from the optimized mesh ................................................................................... 67 

Figure 59: Velocity and equivalence ratio distribution along the line marked in the bottom picture and corresponding scatter diagram of node values on the plane the line is lying on. The scatter diagram of two‐dimensional data recreates the lines almost exactly and thereby confirms that there is nearly no variation of velocity and equivalence ratio on this plane in the tangential direction. ............................. 68 

Figure 60: Time averaged velocity and equivalence ratio distribution at the pilot tip ...................................... 69 

Figure 61: The region in which the grid cells are adapted (splitted) .................................................................. 69 

Figure 62: Equivalence ratio distribution directly downstream the pilot exit obtained with the OPT1.8M mesh and the 35M mesh .................................................................................................................................... 70 

Figure 63: Equivalence ratio distribution discrepancy along Line 1 corrected with the OPT1.8M mesh ........... 70 

Figure 64: Predicted time averaged equivalence ratio distribution at the pilot tip obtained with the OPT1.8M and the 35M mesh .................................................................................................................................... 71 

 

LIST OF TABLES Table 1: Model coefficients values [16] ............................................................................................................. 20 

Table 2: Boundary conditions for all runs  ......................................................................................................... 48 

Table 3: The main meshes for the mesh study and normalized physical simulation time (= number of flow‐throughs) of the time dependent runs with the corresponding mesh. .................................................... 55 

Table 4: Comparison of time and area averaged normalized velocity, instantaneous mass flow, time and area averaged equivalence ratio and mass flow averaged equivalence ratio on the crucial interfaces between specific passages in the domain. The values are compared against the 35M mesh. The differences are max 2% except in the cells shaded with green or red color. ........................................... 63 

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NOMENCLATURE

specific heat capacity at constant volume / ∙ internal energy per unit volume / body force per unit mass vector / enthalpy per unit volume / length scale mass flow / normalized mass flow

normal vector pressure fluctuation part of pressure / heat flux vector / vector pointing from vertexjto vertex j m time flow-through time velocity component in xdirection / , velocity vector / fluctuation part of velocity vector / spatial coordinate non-dimensional wall distance turbulent model constant turbulent model constant turbulent model constant arbitrary spatial discretization turbulent diffusivity / total energy per unit volume / convective flux terms viscous flux terms diffusion flux of species / kinetic energy per unit mass / length meanpressure kinetic energy production term / external heat source per unit volume / specific gas constant / ∙ surface area turbulent Schmidt number mean flow strain rate tensor user defined source term for turbulence kinetic energy user defined source term for turbulent frequency temperature ° conservativevariablesterms mean velocity vector / left state for upwind discretization right state for upwind discretization velocityscale / volume mass fraction of species

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Greek letters

turbulent model constant smoothing constant for exponential moving average turbulent model constant nonlinear blending function for High resolution scheme in CFX Cronecker delta function

turbulence kinetic energy dissipation rate / lengthscale dynamic viscosity / ∙ (dynamic) turbulent viscosity / ∙ kinematic viscosity / (kinematic) turbulent viscosity / invariant of the mean flow strain rate tensor viscous stress tensor

density / average density / turbulent model constant turbulent model constant turbulent model constant

arbitrary quantity general turbulent model coefficient equivalence ratio – limiter function at vertexj turbulence frequency

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LIST OF ABBREVIATIONS AND ACRONYMS

CFD Computational Fluid Dynamics DBCS Density Based Coupled Solver DLE Dry Low Emissions EMA Exponential Moving Average HRIC High Resolution Interface Capturing IP Integration Point LES Large Eddy Simulation MMA Modified Moving Average MUSCL Monotone Upstream-Centered Schemes for Conservation Laws PBCS Pressure Based Coupled Solver QUICK Quadratic Upstream Interpolation for Convective Kinematics RANS Reynolds Averaged Navier-Stokes Equation RPL Rich Pilot Lean RSM Reynolds Stress Model SGT Siemens Gas Turbine SIMPLE Semi-Implicit Method for Pressure-Linked Equations SIT Siemens Industrial Turbomachinery SST Shear Stress Transport STAL Svenska Turbinfabriks Aktiebolaget Ljungström WLE Wet Low Emissions

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1 INTRODUCTION

1.1 Background Design and operation of today’s modern gas turbines and their combustion systems face the need to combine high efficiency with low emissions, good flame stability and at the same time to reduce development and production costs. Computational Fluid Dynamics (CFD) implemented with different combustion models has become a powerful tool to address this issue. Combustion modelling using CFD has certainly reduced costs of developing a combustion chamber of a gas turbine. Although available computer power is continuously on the rise so are also the turbulence models and combustion models more and more advanced. Consequently our demand for computer resources is also constantly on the rise. In fact in the case of Computational Fluid Dynamics there is never enough computer power. Every CFD engineer eventually faces the fact that there is always a limited computer power available and if a commercial CFD code is used there is also a limited number of costly parallel licences available.

There is always a need to make a consensus. How detailed has to be the physical model? Which part of the combustor is a point of interest? Computer resources are often associated with the choice of turbulence model. Which level of details is needed when resolving the turbulence? More detailed models always need considerably more computer resources but detailed models are not always of engineering interest. One solution to reduce demanding computer power is to optimally choose the level of details and the other important aspect in Computational Fluid Dynamics is also to choose an optimum computational mesh. The resolution of a computational mesh greatly affects computer power demands. Higher mesh resolution in most cases contribute to better results but there is, however, often some room to reduce mesh resolution in order to save some solution time and still obtain acceptable results.

1.2 Objective This thesis work deals mainly with a computational mesh study for the combustor of the new Siemens gas turbine SGT-750. One of the most important contributions to achieve desired quality of combustion is effective mixing of fuel and oxidant. As an efficient combustion process always starts with efficient mixing of reactants the mesh study is conducted on the basis of merely fuel and oxidant mixing. There already exists an established meshing approach for the new 4th generation DLE burner but due to highly complex geometry relatively high amount of grid cells are needed. The primary objective of this thesis is consequently to answer to the question if it is possible to reduce the number of grid cells for the burner and still obtain acceptable results and thereby reduce solution times or with other words – solution costs. A side objective in this work was also to present the main differences between commercial CFD codes Ansys CFX and Ansys Fluent with application of the codes on the combustor which is employed in the older Siemens gas turbine, the SGT-800.

Summarizing the main objectives of this thesis would thus be:

Computational mesh optimization for the 4th generation DLE burner with the main goal to minimize the cell count using Ansys Fluent software

Show the differences in results between CFD codes Ansys Fluent and Ansys CFX with application on the ignition stage of the 3rd generation DLE burner

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1.3 Siemens and gas turbines

1.3.1 A brief history of Siemens establishment

The global company Siemens has evolved from a small back building workshop in Berlin in 1847 known then as the Telegraphenbauanstalt von Siemens & Halske. Within a few decades the small precision-engineering and electrical telegraph systems primarily producing workshop developed into one of the world’s largest companies in electrical engineering and electronics. The founder Werner Siemens, who was known as Werner von Siemens after 1888, had discovered the dynamoelectric principle in 1866 and after that the potential applications for electricity were limitless. With the help of Siemens innovations, heavy-current engineering began to evolve at a breath taking pace. The first electric railway operated at the Berlin Trade Fair in 1879 together with the first electric streetlights installation in the Kaisergalerie. In 1880 the first electric elevator was built in Mannheim and in 1881 the world’s first electric streetcar went into operation in Berlin-Lichterfelde. The name of Siemens had then become synonymous with electrical engineering. After Werner von Siemens’ death in 1892 his successors followed the course he had set and constantly advancing the company. Lighting, medical engineering, wireless communication, and in the 1920s household appliances were introduced. After World War II those were followed by components, data processing systems, automotive systems and semiconductors. The goal was apparent – to cover the whole electrical engineering, both light- and heavy-current electrical engineering. [1]

In spite of the difficult political and economic conditions after World War I and after World War II when the company was nearly completely destroyed had Siemens again regained its former leading position in the world marketplace. The year 1966 represented a milestone in the company’s development when the various activities and competences of the company, Siemens & Halske AG, Siemens-Schuckertwerke AG and Siemens-Reiniger-Werke AG merged to form Siemens AG. [1]

GAS TURBINES AT SIEMENS

As in 1866 Werner von Siemens discovered the dynamo-electric principle and thus enabled to convert mechanical energy into electrical energy in an economical way, the invention gave obvious means to manufacture also steam and gas turbines. Experimental gas turbines had been however around in different forms since the early 1900s [4]. The first successful gas turbine using rotary compressor and turbine was built by a Norwegian Aegidius Elling in 1903. It produced excess power of about 8kW [7]. Siemens established the first commercial gas turbine power plant in Switzerland in the year of 1939 and then the year 1972 represents the start of series production of a gas turbine with power output of 62.5 MW at the Berlin plant. In 1980 was at the same site produced the world’s largest gas turbine (125 MW). The record is still being held by Siemens as in 2011 the world record was set by the SGT5-8000H which has a power output of mighty 400 MW. [3]

FROM STAL TO SIEMENS IN FINSPÅNG, SWEDEN

Roots of the industry in Finspång go all the way back to 1400s. The serious industry started in 1631 when the Dutchman Louis De Geer bought Finspongs Bruk from the royal family and after that was Finspång one of the biggest cannon manufacturers in the world for a few centuries. [5]

Swedish turbine history goes back to 1893 when Gustav De Laval starts De Laval Ångturbin AB in Stockholm. In 1913 start brothers Birger och Fredrik Ljungström manufacture their

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counter rotating radial steam turbine in Finspång under the name Svenska Turbinfabriks Aktiebolaget Ljungström - STAL. With the end of 1950 the two companies unite under the name Stal-Laval and develop steam turbine powered boats with great success. Already in 1944 begins development in the area of gas turbines. Under commission of Swedish Air Forces development of three different jet engines was performed but at the end the Air Forces choose a foreign engine. STAL quickly turns the knowledge into stationary turbines. In 1955 the turbine GT35 was presented which was based on the intended jet engine. The turbine had originally output of 10MW and is today in its fourth generation and gives 17 MW – the model is in fact SGT-500. The company has had many names but today is it known as Siemens Industrial Turbomachinery AB since 2003 when the concern Siemens bought the company then known as Alstom Power Sweden AB. [5]

Figure 1: The portfolio of Siemens gas turbines [34]

The Figure 1above shows the complete portfolio of the gas turbines produced by Siemens. The wide gas turbine range has been designed and tailored to meet the challenges of the dynamic market environment. With capacities ranging from 4 to 400 MW those models fulfill the high requirements of a wide spectrum of applications in terms of efficiency, reliability, flexibility and environmental compatibility. [34]

1.4 Gas turbines A gas turbine is a type of internal combustion engine which in its most basic form consists of an upstream rotating compressor coupled to a downstream turbine with a combustion chamber in between. In the Figure 2 it can be seen the more advanced two-shaft gas turbine similar to in the thesis mainly studied the new model SGT-750. The most simple single shaft turbine is on the other hand without the power turbine shown in the Figure 2 (no 3’- 4 stage). An example of a single shaft engine combustor is also briefly studied in this work, more particularly the burner of the model SGT-800.

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Figure 2: Two-shaft gas turbine [6]

As opposed to the internal combustion piston engine, gas turbine combustion is a continuous process. For a turbine to produce a useful power, it must have a higher inlet pressure than the pressure at the exit. To achieve this compressor is used to compress the ambient air to a higher pressure (stage 1-2), energy is then added in the combustor by adding fuel in the air and igniting it so that the combustion process generates a high-temperature flow (stage 2-3). This high temperature and high pressure gas then enters the turbine which produces shaft work output (stage 3-3’). The turbine shaft work is in the first place used to drive its own compressor (approximately two thirds) and the net produced power (indicated by curve 3’- 4 in Figure 3) can finally be used for many different applications although gas turbines are generally associated with aircraft jet propulsion systems. [7]

Figure 3: Brayton cycle pressure-volume diagram for a unit mass of working fluid [6]

The Figure 4 summarizes the basic applications of the net produced power and thereby the basic types of gas turbine configurations. If the net power is not transferred further we can basically speak about a turbojet engine where hot high-speed exhaust gases exit the turbine and consequently push usually an aircraft in the opposite direction. If the shaft is coupled to a propeller then we usually speak about turbo propeller or shortly turpoprop.

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Figure 4: Examples of gas turbine configurations: (1) turbojet, (2) turboprop, (3) turboshaft, (4) high-bypass

turbofan, (5) low-bypass turbofan with afterburner [8]

Instead of a propeller a larger ventilator can be installed and so we get a (high-bypass) turbofan engine which is nowadays mostly used by commercial passenger aircraft. Low-bypass turbofans with afterburner are generally used by supersonic military aircraft. When a turbine is employed to produce mechanical power we usually refer to a turboshaft engine and in this group of gas turbines we can also find industrial turbines employed to drive various loads such as electric generators, process compressors, pumps etc. [7]

As illustrated in the Figure 2 the hot gases exiting the main turbine (usually referred as the compressor turbine) can drive another turbine (power turbine) which is disconnected from the main shaft and this way we get two-shaft gas turbine. Gas turbines operating with a power turbine are often used when there is a significant variation in the speed needed for the load. Examples are pipelines compressors or pumps where conditions can demand a low speed load but with high power demand. In those situations the gas turbine can operate at its maximum speed (to achieve maximum power) and the power turbine can run at the speed of the load. [7]

Figure 5: Two-shaft gas turbine Siemens SGT-700 [9]

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1.4.1 Combustion chambers

Let us start with the introduction to the main topic of this work – combustion chambers or combustors. Combustor design is a complex task, often referred to as a “black art”, as it is among all gas turbine engines’ components usually perceived as the least understood. Discharged air from the engine compressor exits at a very high velocity. In order to avoid unnecessary losses the first thing to after the compressor exit is to decelerate velocity – to diffuse it and raise its static pressure. After the reduction of the dynamic pressure, the air then enters the combustor burner and/or cooling system. [2] [10]

Figure 6: An early combustion chamber [12]

Since the speed of burning air and fuel mixture is usually only of the order of a few meters per second the flame would still be blown away even in the diffused air stream. Therefore a region of low or even negative axial velocity has to be created in the chamber and this is achieved by swirl vanes. The flow from the swirl blades creates a region of low velocity recirculation and it takes the form of a toroidal vortex (similar to a smoke ring). The vortex thereby stabilizes and anchors the flame as seen in the Figure 7. It could for example be arranged that the fuel injection from the nozzles intersects the recirculation vortex where the fuel is together with general turbulence effectively mixed. [12]

Figure 7: Flame stabilizing and general airflow pattern [12]

A typical combustion process releases gases with temperature at about 1800-2000°C which is far too hot for entry to the guide vanes of the turbine. Some portion of compressed air is therefore not used for combustion but is on the other hand progressively introduced into the flame tube. Another portion of the compressor air can be used for cooling the walls of the

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flame tube. Certainly the design of a combustion chamber can vary considerably, but the airflow distribution used to affect and maintain combustion is always very similar to the described. [12]

There are, however, three main types of combustion chamber in use for gas turbines. These are the multiple chamber (Figure 8), the tubo-annular chamber (Figure 9) and the annual chamber (Figure 10). The former type is often used in industrial gas turbine engines and so is in the case of SGT-750.

MULTIPLE COMBUSTION CHAMBER

The chambers at multiple chambers combustor are arrayed around the engine. Compressor air is directed by ducts to pass into the individual chambers where each chamber has an inner flame tube around which there is an air casing. In the Figure 8 the flame tubes are all interconnected which allows each tube to operate at the same pressure. This also allows combustion to propagate around the flame tubes during engine starting but this is, however, not the case for the SGT-750. The former has air casings interconnected instead and to be able to ignite the chambers has each chamber its own ignitor. [12]

Figure 8: Multiple combustion chambers [12]

CAN-ANNULAR COMBUSTION CHAMBER

The can-annular combustion chamber is an example of an evolution link between the multiple chamber and the annular type of chamber. A number of flame tubes are arrayed inside a common air casing. Airflow in the flame tube is similar to the flow of the multiple chambers already described. This configuration combines the easiness of maintenance and overhaul with the compactness of the annular system. [12]

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Figure 9: Tubo-annular combustion chamber [12]

ANNULAR COMBUSTION CHAMBER

The annual combustion chamber consists of a single flame tube which is completely in annular form and contained in an inner and outer casing. The liner consists of continuous, circular, inner and outer shrouds with distinctive holes in the shrouds which allow secondary air to enter the combustion chamber and thereby keeping the flame away from the shrouds. Fuel is introduced through a series of nozzles or burners equipped with swirler vanes at the upstream end of the liners so that the airflow through the flame tube is still similar to the already described. [12] [13]

Figure 10: Annular combustion chamber [12]

The main advantage of the annular chamber is that it is able to use the limited space most effective. The construction itself is relatively simple but still permits high quality air and fuel mixing. Because in comparison with a comparable tubo-annular chamber the wall area is much higher, the amount of cooling air required to prevent flame tube overheating is less. This reduction of cooling air raises the combustion efficiency to greatly eliminate unburned

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fuel and oxidizes the carbon monoxide to carbon dioxide and thus reducing air pollution. Another advantage is that the turbine inlet flow and temperature distribution in tangential direction is more even which results in easier optimization of a turbine for high efficiency. This type of combustion chamber has many advantages and at the same time considerably saves weight and production costs but employing and developing this type of combustor has two distinctive disadvantages – maintenance and testing. The construction does not allow simple assembly, disassembly and inspection of the combustor chambers as the other two types do. From testing point of view can combustors may be easily tested in single burner high pressure combustion tests rigs without compromising the hat side design, while drastic simplifications are required for basic tests of annular systems. A consequence of this downside is that annular combustion system development projects have a larger risk of a delay to fulfil project goals. This types of combustors are obviously the best candidates to be employed in aircraft engines but not always in large industrial gas turbines. [12] [13]

1.5 The Dry Low Emissions Combustors In the middle of the 1970s increased focus on environmental issues led to increased research on new and better gas turbines with water and steam cooling methods which was called “Wet Low Emission” (WLE). The best technology was in 1980s able to reduce NOx emissions to 42ppm and later to 25ppm. In the late 1980s the gas turbine producers started to develop “Dry Low Emission” technology (DLE) to be able to avoid the technology that demanded water or steam injection. The technology was then in the next ten years developed leading to a reduction of NOx emissions less than 25ppm. [15]

This approach is to burn most (at least 75%) of the fuel at cool and fuel lean conditions to prevent any major production of NOx. The principal strategy of such combustion systems is to premix fuel and air before the mixture enters combustion chamber and to have a lean mixture in order to lower the flame temperature and thus reduce NOx emission. Figure 11 shows a schematic comparison of a typical DLE combustor parallel with a conventional combustor. Both are equipped with a swirler to create required flow conditions to stabilize the flame but DLE burner has on the other hand much larger injector because it contains the fuel/air premixing chamber. [15]

Figure 11: A schematic comparison of a typical DLE combustor and a conventional combustor

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The DLE injector has (at least) two fuel circuits: main fuel and pilot fuel. Generally is most of the fuel (the main fuel) injected into the airstream immediately downstream of the swirler at the inlet to the premixing chamber. The pilot fuel is on the other hand injected directly into the combustion chamber with little or no premixing. As the flame temperature is now closer to the lean limit than in the conventional combustion system, the flame is now much more prone to combustion instabilities and flame out. This tends to happen often when the engine load is reduced and it would happen if no action was taken. The mixture would at this point become either too lean to burn or would lead to combustion instabilities. A small proportion of the fuel is therefore always burned richer to provide a stable “piloting” zone and the remainder is burned lean. [15]

1.5.1 The Siemens SGT-800 and 3rd generation DLE burner

In this work the new gas turbine SGT-750 is mainly discussed but beside this there is also a brief mesh study and a comparison of the CFD results between two different solvers used (Ansys CFX and Ansys Fluent) to simulate fuel and air mixing of the 3rd generations DLE burner during the ignition stage.

Figure 12: The SGT-800 [35]

The SGT-800 is available in three versions with power output of 47.5, 50.5 and 53.0 MW respectively. The main design features of the most powerful version of the single shaft turbine are 15-stage axial compressor with pressure ratio of 21.4:1, annular combustion chamber with thirty 3rd generation DLE burners and a 3-stage turbine design. It is used for electrical power generation with possibility for combined heat and power generation. Electrical efficiency is rated at 39 % and NOx emissions are kept below 15 ppm. [36]

Figure 13: The Siemens 3rd generation DLE burner [2]

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1.5.2 The Siemens SGT-750 and 4th generation DLE burner

The new Siemens SGT-750 is a low-weight industrial gas turbine designed to incorporate size and weight advantages whilst maintaining the robustness, flexibility and longevity of the traditional heavy-duty industrial gas turbine. The two-shaft gas turbine has a power output of 37 MW for power generation, or of 38.2 MW for mechanical drive. [37]

Figure 14: The SGT-750 [37]

The turbine was specifically designed for long operation times with extended overhaul intervals and features easy maintenance. Its main design features are 13-stage axial compressor, a two stage air cooled compressor turbine and a two-stage counter rotating non-cooled axial flow power turbine. The combustion chamber (see Figure 15) system consists of eight tubular combustion chambers. The design has been developed with focus on high reliability and easy maintenance. Individual combustion chambers can be simply replaced from the compressor side without disassembling the turbine module. [37]

Figure 15: The 4th generation DLE burner [38]

The dual fuel option has DLE capability on gas and for liquid fuel operation water injection can be used to reduce NOx emission. The 4th generation DLE burner is specifically designed for extremely low emissions over a wide operation range of the turbine. A compressor discharge air bleed is also available to further reduce the emissions at very low loads. Further important improvements over the older DLE burner are optimized aerodynamics and fuel/air mixing. Expected values for NOx and CO are below 15 ppm. [38]

RPL burner

Pilot burner

Main 1 gas Main 2 gas

Quarl

Convective combustor cooling

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This system is thus designed to operate in the lean premixed combustion mode. The aerodynamics of the burner is designed so that a well-defined recirculation zone is formed and is bounded by the quarl and aerodynamically anchored at the pilot tip to minimize axial movement. The burner design features four independently controlled fuel lines for maximum flexibility, see Figure 15. The burner is based on central stabilization technique which means that the separate fuel lines feed the centrally located RPL (Rich-Pilot-Lean) burner, the pilot burner and the two main passages (Main 1 and Main 2). [33]

The RPL burner represents a small pre-combustion chamber that is operated mostly in the fuel rich regime at slightly higher temperature than the main flame. This small device has two major purposes:

it plays a role of an ignition burner, like a small torch that ignites the pilot and the main flames

it supports the main flame and widens the operating window of the main burner

The pilot burner features swirler wings with an internal gas supply. Its location provides that the hot exhaust gases from the RPL burner are in close contact with oncoming fresh gas/air mixture. This central stabilization technique gives the possibility to optimize the fuel profiles of the main stages where the majority of the fuel is injected. [33]

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2 THEORETICAL BACKGROUND This chapter is intended to present the basic theoretical background used in the CFD simulations performed within this project. Not are details are given here therefore a more interested reader is advised to refer to literature that will be pointed out.

2.1 Governing equations in Fluid Mechanics The set of governing equations used in fluid mechanics is based on conservation laws which are conservation of mass, momentum and energy. These partial differential equations are also known as the Navier-Stokes equations as they were derived independently by Claude-Louis Navier and George Gabriel Stokes in the early nineteenth century. They have no known general analytical solution but can be discretized and solved numerically. Equations describing other processes such as combustion or fuel/air mixing can also be solved in conjunction with the Navier-Stokes equations. [16] Details about derivation of the following conservation laws can be found in Ansys Documentation [17].

2.1.1 Mass Conversation Equation

The general equation for conservation of mass or known also as the continuity equation can be written as follows:

∙ 0 (2.1)

The first term describes the rate of change of density in an (infinitesimally small) control volume and the second term describes the mass flux rate through the surface of the control volume.

2.1.2 Momentum Conservation Equation

Conservation of momentum in an inertial reference frame can be derived from the Newton’s second law and combining it with the continuity equation it can be written as:

∙ Π (2.2)

where the substantial derivative is defined as:

∙ 2.3

If we expand the equation (2.2) with help of (2.3) we get:

∙ ∙ 2.4

The first term on the left hand side describes the rate of change of momentum in a control volume and the second term on the left hand side describes the momentum flux through the surface of a control volume. The first term on the right hand side represents the body force per unit volume and the second term on the right hand side describes the surface force per unit volume applied on a fluid element. It consists of shear and normal stresses and the so called viscous stress tensor Π for a Newtonian fluid is given by:

23

2.5

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To get the final form of the momentum equation or the Navier-Stokes equation we combine the Equations (2.4) and (2.5):

23

2.6

2.1.3 Conservation of energy

The conversation of energy equation can be derived by the first law of thermodynamics on an infinitesimal fixed control volume to yield the equation with being the total energy per unit volume:

∙ ∙ ∙ ∙ 2.7

The left hand side terms describe the rate of change of total energy in a control volume and the total energy flux through the boundaries of a control volume respectively. On the right hand side we have the rate of heat from external sources, heat flux through the boundaries, work done on a control volume by body and surface forces respectively. The in the second term can written as

2.8

which is known as Fourier’s law for heat transfer where is thermal conductivity.

2.1.4 Equation of state

To close the equation system formed by Equations (2.1), (2.6) and (2.7) we use the equation of state. If we consider a compressible flow and disregard external heat addition or body forces and use Equation (2.1) for the mass conservation equation, the momentum equation (2.6) separated into three scalar equations and the energy equation (2.7) we have five scalar equations. They contain, however, seven unknowns , , , , , . The perfect gas equation of state is valid for gases whose intermolecular forces are negligible:

2.9

where is the specific gas constant. For low temperatures the specific heat capacity at constant volume is constant therefore the internal energy can be defined as:

2.10

Now we have additional two equations that make seven equations with seven unknowns and hence a closed system.

2.2 Turbulence Nearly all flows in the nature and engineering practice are turbulent. Winds and currents in the atmosphere and ocean or flows past transportation devices (vehicles, aircraft, ships …), flows through all sorts of engines or in our case flow through the combustion chamber are all turbulent. Turbulence is an enigmatic state of fluid flow which involves unpredictable fluctuations that can be both beneficial and problematic. Both can be encountered in a combustion chamber –turbulence is exploited for mixing of air and fuel but within the same device it can lead to noise and efficiency losses. A summary of some of the most characteristic features of turbulent flows would be: [18]

Chaotic fluctuations in space and time A wide spectrum of scales of swirling flow structures (eddies)

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High diffusivity High Reynolds number Dissipation of kinetic energy into heat

One of the most important numbers in fluid mechanics, commonly used for description of the turbulent flow regime, is the non-dimensional Reynolds number which is defined as a ratio between the inertial and viscous forces:

2.11

Density , characteristic velocity and characteristic length scale represent the inertial forces while the viscous forces are represented by dynamic viscosity . A high Reynolds number therefore states the dominance of inertial forces over viscous forces in a turbulent flow. At high Reynolds number a separation of flow scales occurs. The highly energetic large scales (integral scales) limited by the geometrical restrictions break up and the energy is then successively transferred to smaller and smaller eddies in a process known as the energy cascade. At the final stage the molecular viscosity is effectively dissipating the kinetic energy of the smallest eddies into heat. [19]

If we consider a turbulent flow not undergoing any rapid changes in the mean flow, the turbulence can be assumed to be in a state of quasi-equilibrium. That is in the sense that the dissipation occurring at the smallest scales is in balance with the kinetic energy transfer from the large scales. This important assumption is a basis for turbulence modeling. [20] [21]

2.3 Turbulence modelling Turbulent flow is fully governed by the Navier-Stokes equations and can be solved numerically by Direct Numerical Simulation (DNS). The DNS simulation is three-dimensional and time dependent but the range of time and length scales are large and increase rapidly with the Reynolds number. To cover the ranges we need very fine computational meshes and small time step sizes which lead to extremely high demand of computer resources. An alternative to solving for all scales exists in form of solving the mean flow characteristics averaged in time. [20] [21]

2.3.1 Raynolds Averaged Navier-Stokes equations

There are, however, several ways to model turbulent flow but the most widely used and also used in this work is the Reynolds Averaged Navier Stokes equation approach abbreviated and known as RANS or Reynolds averaging. It is obtained by splitting the total velocity and pressure fields into a mean and a fluctuating part. This is called the Reynolds decomposition and can be written as i.e.: [20] [21]

2.12

and

2.13

where the mean components are denoted by capital letters and the fluctuation parts with a prime. Inserting the decompositions into continuity and momentum equation and averaging the whole equations yields Reynolds averaged continuity equation and Reynolds averaged momentum equation. A similar procedure can be applied to the energy equation where the total enthalpy can be decomposed into average and fluctuating part. All the derivations can be found in [21] where the subject of turbulence is well covered. [20] [21]

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The mean flow equation is usually referred to as the Reynolds equation. For simplicity a simpler Reynolds equation which is valid for incompressible flows will be presented here. We start with the incompressible version of the Navier-Stokes equation:

1

2.14

and after applying the Reynolds decomposition (2.12) we get the mean flow incompressible Reynolds equation:

1

2.15

We can see that the Equations (2.14) and (2.15) look quite similar where the “turbulence interaction term” takes a role similar to that of the viscous stress tensor. Hence there is defined the turbulent stress or so called Reynolds stress tensor as:

2.16

This tensor represents the turbulence closure problem since the continuity (1) and Reynolds equation (3) make up four equations while after averaging we have ten unknowns. These are the mean velocity and pressure , i.e. four unknowns and the six Reynolds stress tensor components. To be able to close the system of equations the Reynolds stress tensor is the subject of modeling. [20] [21]

2.3.1.1 Eddy viscosity models

Similarly as we can isolate the isotropic part (pressure) of the stress tensor for a Newtonian fluid we can also isolate isotropic part of the Reynolds stress tensor which is in this case kinetic energy (per unit mass) of the turbulent fluctuations: [20] [21]

12

2.17

with which we can rewrite the Reynolds stress as (for the details about derivation please refer to Pope [21]):

23

23

2.18

This expression is often referred to as Bousinesq expression. In analogy with the contribution from pressure, 2/3 times the kinetic energy of the fluctuations gives an isotropic contribution to the Reynolds stress. The second part represents the anisotropic part and this is the part that is primarily described when an eddy viscosity concept is used to model turbulence. The isotropic part is on the other hand usually included in a modified pressure term. The eddy viscosity model, directly analogous to the Newtonian fluid stress description, can be written: [20] [21]

23

2.19

or for a simple shear flow

2.20

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In the expressions (2.19) and (2.20) the eddy viscosity is a property of the flow while the molecular viscosity is a property of fluid. The eddy viscosity is not considered constant but is governed by length scale (Λ) and velocity scale (V): [20] [21]

~ 2.21

In most turbulent flows the momentum mixing is prevailed by large energetic eddies. Modeling of Reynolds stress tensor with six components in general three-dimensional flow is so reduced to model the large eddy length and velocity scales. This is a large reduction in complexity and therefore very suitable for implementation in CFD codes for general flows. [20] [21]

Eddy viscosity models can be classified into three main groups:

ALGEBRAIC MODELS OR ZERO EQUATION MODELS

In algebraic or zero equation models length and velocity scales are related to the mean flow velocity field and geometry of the flow via for example velocity gradient or distance to the wall etc. These models work relatively well for specific cases they are designed for, like attached boundary layers for example but they are, however, not very general. [20] [21]

ONE EQUATION MODELS

Here one is typically solving the transport equation for kinetic energy, , or the eddy viscosity, . These models work also well for specific cases like attached boundary layers and other thin shear flows, but are not well suited for complex flows. A good example is the Spalart-Allmaras model which solves for eddy viscosity. This model has been used extensively for aeronautical applications. [20] [21]

TWO EQUATION MODELS

In two equation models two transport equations for two quantities are solved that can be used for determining length and velocity scales needed to determine eddy viscosity. Most common quantities are the turbulence kinetic energy ( ), its dissipation rate ( ) and the turbulence frequency ( ). No additional global information is generally needed thus such models are referred to as complete. Therefore they are most widely used and they have also been chosen to employ in this work. [20] [21]

2.3.1.1.1 The standard eddy viscosity model

The turbulence kinetic energy ( ) and its dissipation rate ( ) are computed from the two model transport equations which are solved together with RANS equations for the mean flow. The model equations which can be derived from transport equation for turbulent kinetic energy read

2.22

2.23

where is turbulent kinetic energy production term,

2 and 2.24

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For details please refer to Pope [21] or any other good book about modeling turbulence. However the values , , , , are model coefficients with standard values which are usually not changed. II is invariant of the mean flow strain rate tensor which reads [20] [21]

2.25

where the mean flow strain rate tensor is

12

2.26

2.3.1.1.2 The eddy viscosity model

Other alternatives to the eddy dissipation, , as the length scale determining quantity have been proposed. One of the advantages of the model is near wall treatment for low Reynolds number flows. The model does not involve complex nonlinear damping functions that need to be applied to the model for near wall treatment. Therefore the turbulence model developed by Wilcox is generally more accurate and robust for such flow conditions. [16][20]

In most models the turbulence frequency is defined as [20]

2.27

The furthermore assumes that the turbulence viscosity is linked to the turbulence kinetic energy and dissipation with relation:

2.28

Similarly as in molecular viscosity there is a relation

2.29

The model equations read

2.30

2 2.31

where , , , , and are again model constants with standard values.

A major problem with the standard is turbulence interfaces treatment. An example would be the boundary layer edge where the use of this model leads to unphysical sensitivity to free-stream values of kinetic energy and turbulence frequency . In practice this results for example in over prediction of computed turbulence energy in the stagnation region of an airfoil and general sensitivity to the conditions in the free stream. There are some different proposals to correct the problematic behavior, however, the best known and very popular solution was proposed by Menter. [20] [21]

2.3.1.1.3 The SST model

Menter proposed basically a hybrid model which combines advantages of both models. is thus used in the free stream and blends with help of a blending function to a

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formulation near the wall. In the Menter model, which is known as the Shear Stress Transport turbulence model, the blending between those two models is achieved by transforming the

model into equations based on and . This leads to introduction of a cross-diffusion term added to the equation: [20][21]

2 11

2.32

Both combined models still fail to properly predict the onset and amount of flow separation from smooth surfaces where the main reason is that both models do not account for the transport of the turbulent shear stress. This results in overprediction of turbulent viscosity. The proper behavior of the transport of shear stress is thus obtained by a limiter function to the formulation of the turbulent viscosity . [16]

THE SST TURBULENCE MODEL IN ANSYS CFX AND FLUENT

Let us take a look little closer at how the SST model is implemented in Ansys CFX and in Fluent, but however, more interested reader should refer to Ansys documentation [16] where all the details are thoroughly explained. Although the basic model formulation is very similar in both solvers, the implementation of the model differs slightly, which may besides different discretization approaches contribute to slightly different results. The turbulence model equations are presented in a slightly different form in the software documentation therefore they have been rewritten in a new form to be able to more easily compare the equations.

ANSYS CFX

,

2.33

,2 1

1

2.34

The first right hand side terms in both equations represent effective diffusivities where , and , are the turbulent Prantl number for and respectively. The third term on the right hand side in the Equation (2.33) represents the dissipation of . The second term in the Equation (2.34) may be already recognized as the cross-diffusion term where F is the first blending function based on the distance to the nearest surface and on the flow variables. The second blending function F , similar to F , is included in the formulation for calculation of turbulent viscosity which restricts the already mentioned limiter function to the wall boundary layer. Formulations for blending functions are not given here so for details please refer to Ansys documentation [16]. The third right hand side term in the Equation (2.34) represents the production of and the fourth term represents dissipation of . [16]

and are additional buoyancy production terms which are turned on in CFX only when buoyancy is modelled. All coefficients of the new model are in CFX simply a linear combination of the corresponding coefficients of the underlying models ( and ): [16]

1 2.35

where the coefficients are listed in the Table 1. [16]

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ANSYS FLUENT

,

2.36

,2 1

1

2.37

The SST turbulence model in Fluent rewritten in a form suitable for comparison seems to be almost identical to the formulation in CFX. The terms S , S , are user defined source terms that can among others also be used to model buoyancy turbulence as in CFX. However, note that the production term is evaluated differently and although most of the model coefficients are the same, they are treated slightly differently in Fluent. The coefficient can be for example even dependent on and speed of the sound when compressibility correction is turned on but in this work has been, however, turned off as this function is not recommended for general use. The coefficients and are otherwise dependent on ,

, , , and , , , respectively, but are with the standard values of the named coefficients almost identical to those used in CFX as seen in the Table 1. [16]

Table 1: Model coefficients values [16]

, , , ,

CFX 0.09 0.555 0.075 2 2 0.44 0.0828 1 1.168Fluent 0.09 0.553 0.075 1.176 2 0.44 0.0828 1 1.168

Blending of the coefficients and is accomplished in the same manner as in CFX, that is according to the Equation (2.35) while there is noticeable difference in blending of the coefficients , and , . Fluent uses here nonlinear recipe which can be written as: [16]

1

2.38

On the first sight identical SST turbulence model in both solvers can therefore in practice contribute to slightly different results when comparing CFX and Fluent calculations. However, if the coefficients and are manually changed in both solvers so that

, , , 2.39

and

, , , 2.40

then we can obtain a new turbulence model which is theoretically identical in both solvers and can be valid for comparison between Fluent and CFX results. This statement holds if the relation (2.28) can be used in the production term in the Equation (2.37) which makes the model equations identical for both solvers. There is an uncertainty how the production term is evaluated in Fluent therefore this issue will be addressed to Ansys customer support.

The details about blending functions, production limiters, wall scale and near wall treatment employed in the Menter SST model can be found in Ansys documentation [16]. This turbulence model is becoming more and more popular as it can be used for wide variety of flows especially when dealing with flow separation. It is the Airbus standard turbulence model and also exclusively used in this thesis work. [20]

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2.3.2 Reynolds stress models (RSM)

The eddy viscosity turbulence models rely on the Bussinesq assumption which is a major simplification. Some of the deficits of these models are the modeling of the production term where the model production is insensitive to rotation, has incorrect asymptotic behavior for large shear rates. In the Reynolds stress model the production is exact as it includes the rotation rate tensor and not only the strain rate tensor as in Equation (2.24). However, as the Reynolds stress tensor has six independent components we need here six additional partial differential equations to solve together with a length scale determining property such as the dissipation rate . Thus we end up with seven additional equations. This approach gives better results but is computationally expensive and not as robust and easy to implement into CFD codes as the eddy viscosity models. [20] [21]

2.3.3 Large Eddy Simulation (LES)

There exist many other different turbulent models which are often hybrids between different formulations but they will not be presented here as they are not associated with this thesis work. However, it might be interesting to briefly present Large Eddy Simulation approach. As the name itself suggests it resolves large eddies. It resolves the large scale turbulence and models only the smallest scales. The smallest scale tend to be more isotropic and more in the equilibrium than the large scales and are therefore easier to model. As already mentioned most of the turbulence kinetic energy is contained in the large scales which means that resolving the smallest scales is not that critical for the complete simulation. LES is still rather expensive compared to eddy viscosity models but it is being gradually introduced also in the industry. [20]

2.4 Species transport In this work we are dealing with air/gas mixing which also needs a certain model to employ. Most of the calculations in this work are done in Ansys Fluent therefore equations for species transport employed by Fluent are presented here. The software predicts the local mass fraction of each species through the solution of convection-diffusion equation for the ith species which takes the following form:

∙ ∙ 2.41

In the above equation is the net rate of production of species i by chemical reaction. This term is applicable when we are dealing with simulation of combustion together with which is the rate of creation by addition from the dispersed phase plus any eventual user defined sources. [16]

2.4.1 Mass diffusion in turbulent flows

In case of turbulent flows the mass diffusion term J in the Equation (2.41) is solved by

, , 2.42

In the above equation is the turbulent Schmidt number which is defined as

2.43

where is turbulent viscosity and is turbulent diffusivity. The dimensionless number describes thus the ratio between the turbulent transport of momentum and the turbulent

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transport of mass or eventually any other passive scalar. The Schmidt number may be adjusted to increase or decrease mixing to compensate for turbulence model errors, however, in this work the default value of 0.7 has been used. [16]

2.4.2 Species transport in the energy equation

For multicomponent mixing flow the transport of enthalpy due to species diffusion is included in the energy equation: [16]

∙ 2.44

2.4.3 Equivalence ratio

Solution of the species transport equation is a mass fraction or eventually a molar fraction of a specific species. However, a very useful parameter in internal combustion engines is fuel to oxidant equivalence ratio or also reciprocal parameter oxidant to fuel equivalence ratio . In this work fuel-oxidant equivalence ratio will be used as it is commonly used in gas turbine industry. It is defined as:

/

/ 2.45

This means that when 1 there is an excess of oxidant present in the mixture or the mixture is “lean” and when 1 there is an excess of fuel or the mixture is “rich”. When

1 then the actual mixture is equal to an ideal or stoichiometric mixture which theoretically means that the amount of oxidant present in the mixture is just enough to completely burn all the fuel. [26]

2.5 Numerical methods There exist different numerical approaches for solving the set of partial differential equations describing the behaviour of fluid flow like finite differences, finite elements, Boltzmann method etc. All approaches have certain advantages and disadvantages but, however, for fluid flow the finite volume method is the most suitable and natural method as it involves directly the approximation of conservation laws and is robust also in complex geometries. [19]

Most of commercial and in-house CFD codes implement finite volume method although discretization of the governing equations may differ. In this work was mainly used Ansys Fluent solver but a brief comparison of results using both Ansys Fluent and CFX was made therefore in the next section the main differences between those two solvers are also presented.

2.5.1 Discretization

The governing equations need to be discretized on discrete mesh grid points and evaluated at discrete times when dealing with time dependent flows. The set of equations can be practically ordered accordingly to their characteristic behaviour and can thereby be written in the following form: [19]

2.46

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where represents conservative variables, contain convective fluxes, contains viscous fluxes and are source terms, e.g. gravity. The mentioned flux terms can be written as:

,3

,

0

2.47

Equation (2.46) represents a differential equation but in order to be able to discretize governing equation using the fine volume method we have to write it in conservative form or integral form. Using Gauss divergence theorem we rewrite the Equation (2.46) for each control volume outlined by surface elements as: [19]

2.48

In the Equation (2.48) is the normalized normal vector on a surface element which we get after applying the Gauss divergence theorem. For a discretized finite volume the surface integrals can be transformed into algebraic expressions as discrete sums: [19]

, , , , , 2.49

where index 0 refers to the current control volume and is the total number of bounding surfaces of the control volume which is six in an example of hexahedral volume element. Furthermore the index refers to an individual surface of the current control volume. [19]

The flux terms in the governing equations are grouped according to their physical behaviour as seen in the Equation (2.47) so that different appropriate discretization schemes can be used for each term category. [19]

2.5.1.1 Cell-centered and vertex-centered Finite Volume Methods

Both cell-centered and cell-vertex discretization are successfully used in finite volume codes but it is still very difficult to draw a conclusion which one is a better choice for a CFD code discretized on an unstructured grid. In this work Ansys Fluent represents the first choice and Ansys CFX the other one. It has been debated for a long time which commercial code is a better choice but, however, generally speaking Fluent has a reputation that it is more difficult to achieve satisfactory convergence but when converged it gives slightly better results. Ansys CFX is on the other hand more forgiving in sense of robustness and efficiency.

Measuring performances using above discretization approaches highly depend on the computational environments, such as programming languages, operating systems and so on, therefore it is necessary to assess cell-centered and vertex-centered discretizations in identical working environments. G. Whang in the article [22] presents an interesting study of comparing and evaluation of both approaches using the DLR TAU code which offers both finite volume formulations within its solver. [22]

BASIC DIFFERENCES

The basic difference between the formulations lies in the construction of control volumes. In the cell-centered (Fluent) approach the control volumes are identical with primarily generated grid cells as shown on the left side of the Figure 16 where we can see both formulations applied on the same part of a two-dimensional grid. The unknowns are thus defined at the cell

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Figure 18: Median dual control volumeconstructed at sharp edge corner [22]

centroids while in the vertex-centered approach solution variables are located at the primal grid vertices and the control volumes are reformed around each primal grid node. This is achieved by a median dual mesh construction which connects the centroids of primal cells with surrounding midpoints of faces and edges. The dual-median grid construction is shown in the Figure 17.

Figure 16: Illustration of cell-centered (left) and vertex-centered (right) type control volume constructions [23]

The Figure 16 shows only an illustration to show the basic difference between the approaches as there exist different approaches even within the same vertex-centered discretization category. The control volume construction shown in the right side of the Figure 16 represents more precisely a Voronoi volume [24] while Ansys CFX employs the more popular dual median construction shown in the Figure 17.

Another important difference between the cell-centered and vertex-centered grid approach relates to the number of control volumes or degrees of freedom which is determined by the number of primary grid cells and vertices for the respective formulation. The ratio between number of grid cells and vertices varies with grid topology and so for pure three-dimensional tetrahedral mesh it is in the range of 5 to 6 while in pure structured meshes this ratio closes to one. This fact leads to the argument that the cell-centered scheme should be more accurate on the same unstructured grid. On the other hand has a control volume in the cell-centered grid formulation a smaller number of neighbor cell comparing to a control volume in the vertex-centered grid formulation which can affect accuracy of the linear reconstruction of gradients as the gradient of a flow variable is approximated at each control volume center taking into account the neighboring control volumes.

It is perhaps worth to point out that the construction of the median dual mesh can produce control volumes of bad quality. This can happen especially for grids with large distortions. A typical example is when a prism layer is generated at some sharp boundary like a trailing edge of an airfoil (see Figure 18). In this case an arrow-shaped control volumes will be formed which can greatly decrease performance of a solver. [22]

For details about differences in flux integration, gradient evaluation and boundary treatment please refer to G. Wang [22] and/or Ansys documentation [16]. In the next section flux integration and with respect to the two finite volume methods will be briefly presented.

Figure 17: Dual median gridconstruction [24]

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FLUX INTEGRATION

One characteristic of the cell-vertex approach is that the edges of the dual mesh always cross the midpoints of the face connected with two corresponding vertices while in the cell-centered approach this property generally cannot be achieved. This advantage brings a lot of benefits in surface flux computing, especially for central discretization. Therefore Ansys CFX uses central discretization as default spatial discretization. The upwind discretization is on the other hand better choice for Fluent solver.

a) Vertex-centered b) Cell-centered

Figure 19: Solution reconstruction for vertex-centered and cell-centered formulation in 2D unstructured mesh [22]

Just in order to briefly present the basic difference between approaches shown in the Figure 19 an example with Roe flux splitting scheme extracted from the article [22] is considered. The convective flux over the control volume face with edge can be written as:

,12

| | 2.50

If we assume that the solution has piecewise linear reconstruction over the control volume then the left and right states for vertex-centered formulation can be reconstructed as:

12

∙ 2.51

12

∙ 2.52

where is the gradient of and is the value of limiter function at vertex , represents the vector from vertex to vertex as seen in Figure 19. The factor ½ is a result from the midpoint property of median dual grid. [22]

For cell-centered approach the above formulation should be modified as

∙ 2.53

∙ 2.54

where and represent vectors pointing from cell centers to the barycenter of the control volume face.

TESTING OF CELL-CENTERED AND VERTEX-CENTERED SCHEME

G.Wang [22] conducted several test cases with three different airfoil designs at different flow conditions such as low and high Mach number flows. On a turbulent flat plate case he tested also performance when using structured grid. All comparisons were supported also with experimental results. His conclusions actually confirmed what has already been said about Ansys Fluent’s reputation.

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G. Wang’s results indicate that the cell-centered scheme and the cell-vertex scheme have nearly the same accuracy and efficiency for most of the structured grid test cases. This is expected as the number of degrees of freedom is the same. For the test cases with unstructured grid in general the cell-centered formulation is less efficient but more accurate compared to vertex-centered on the same mesh. [22]

2.5.1.2 Spatial discretization

ANSYS CFX

A number of spatial discretisation schemes have been developed either for specific flows or for more general application. Ansys CFX offers technically only two types of spatial discretization schemes. These are the 1st order upwind difference scheme and 2nd order central difference scheme. The default option used in CFX is the High Resolution Scheme which uses a special “recipe” shown in the expression below: [16]

∙ ∆ 2.55

In a discretised equation all the variables are stored at the nodes but several terms are evaluated on the surface of a control volume or in the integration point denoted as . The advective term for a quantity is now calculated using a mix of both available discretization schemes. If is equal to zero then a 1st order upwind scheme is obtained (which is robust but by its nature tend to smear out steep gradients and is therefore inaccurate) and for is equal to 1 then the scheme is fully second order accurate but may lead to unphysical oscillations. The value can be manually chosen but the default High Resolution Scheme uses a special nonlinear function for at each node computed to be as close to 1 as possible. [16]

ANSYS FLUENT

Fluent has many different spatial discretization schemes to choose from and they are generally

1st order upwind scheme Power law scheme 2nd order upwind scheme 2nd order central differencing scheme QUICK scheme 3rd order MUSCL scheme Modified HRIC scheme

The central differencing scheme can be, however, used only for LES calculations and offers similar blending as described by the Equation (2.55). Nevertheless the default scheme which can be used for accurate calculations of a wide variety of flows and mesh types is 2nd order upwind scheme. Blending between 1st and 2nd order upwind schemes is also possible for cases with problematic convergence and at a certain flow conditions when a converged solution to steady-state is not possible due to local flow fluctuations that can be both physical and numerical. Blending factor can be chosen manually as Fluent does not offer the “smart” blending function as described in the previous section. For details about specific numerical scheme please refer to Ansys documentation [16].

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2.5.1.3 Gradient evaluation

Gradients are needed for constructing values of a scalar at the control volume boundaries and on the other hand for computing secondary diffusion terms and velocity derivatives. Ansys CFX employs the standard finite element approach to accomplish both with use of shape functions. Ansys Fluent offers three methods to compute gradients: Green-Gauss Cell-Based, Green-Gaus Node-Based and Least Squares Cell-Based. The default method which is also used for all the calculations in this work is the latter choice as it is both accurate and computationally relatively inexpensive. [16]

2.5.2 Temporal discretization

For time dependent simulations the governing equations must be discretized in both space and time. In this work a steady-state solution was needed but none of the calculations with intermediate mesh density and more that 1st order accuracy in space converged to a steady-state solution due to local transient behaviour which can be either physical or numerical. The solution was then to run transient calculations with time statistics sampling in order to obtain a time average of the time dependent converged solution. [16]

Both Ansys CFX and Fluent offer 1st and 2nd order accurate implicit backward Euler schemes. In this work the 1st order accurate scheme was used since the object of interest was time averaged solution therefore the typical steep temporal gradients diffusion behaviour has been taken advantage of. The implicit 1st order backward Euler scheme can be written as: [16]

2.56

where is a scalar quantity, 1 is value at the next time level, is value at the current time level and function D incorporates any spatial discretization. The implicit scheme is a good choice as it is unconditionally stable (does not have a time step size limitation). Fluent offers also explicit time integration which is available only with the density based solver. [16]

2.5.3 Continuity and momentum equation coupling

Since its initial release the Fluent solver has provided two basic solver algorithms. The first is density-based coupled solver (DBCS in the Figure 20) which solves all the governing fluid dynamics equations (continuity, momentum and energy) in a coupled manner. This solver is applicable when there is a strong coupling or interdependence between density, energy and species. Examples of such flow are high speed compressible flow with combustion, hypersonic flow and shock interactions. The second solver is pressure-based segregated solver that solves the equations in a segregated or uncoupled manner and it has proven to be successfully applicable to wide range of physical models. However in some applications the convergence rate is not satisfactory generally due to the need for coupling between the continuity and momentum equations. Those situations in which equation coupling can be beneficiary include rotating machinery flows and internal flows in complex geometries. The third, a new option in Fluent, is pressure-based coupled solver (PBCS) which is a similar solver as the Ansys CFX solver. This algorithm solves the continuity and momentum equations in a coupled fashion. This approach removes approximations due to isolating the equations and permits the dependence of momentum and continuity on each other. This results in more rapid and stable convergence rate and improved robustness so that errors associated with initial conditions, nonlinearities in physical models or deformed meshes do not affect stability of the solution process as much as with segregated algorithms. [16] [25]

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A flowchart illustrating the pressure-based and density based solvers is shown in Figure 20. As seen the segregated solver solves momentum equations for the unknown velocity components one at a time as scalar equations and after that it solves a separate equation for continuity and pressure. The pressure solution is here used to correct the velocity components such that continuity is satisfied. In the case when the flow equations are coupled together, the coefficients computed for each equation contain dependent variables from the other equations. [25]

Figure 20: Flowchart illustrating Fluent solver algorithms [25]

In the case of segregated solver these variables are supplied merely by using previously computed values and this introduces a decoupling error. This error can result in delaying convergence in cases where strong pressure-velocity coupling exists. As the pressure-based solver solves continuity and momentum equations in a fully coupled fashion this means that a single matrix equation is solved and for that it is needed about twice the memory per cell for the coupled solver. In practice this means that the coupled solver needs slightly more computer time per iteration but on the other hand it takes less iterations to converge to the final solution. [25]

Some of the facts about the two types of solvers have been confirmed in this project. In this work the geometry of the 4th generation DLE burner is extremely complex and the otherwise computationally less expensive segregated solver’s performance was inferior to the coupled solver. All attempted steady state runs were therefore run with coupled solver. However, for transient cases the performance of the segregated solver was superior to the coupled when simulating the 4th generation DLE burner. The reason lies in the fact that the segregated solver needs less computer time per iteration and that if the initial conditions do not differ significantly from the final solution then even the segregated solver advances towards converged solution efficiently. Most of the transient cases in this work were run with around 15 iterations per time step. The coupled solver needed about 1 to 2 more iterations to achieve convergence criteria but net computer time per time step was about 10 - 15 % lower than when using the segregated solver. On the other hand, when simulating the 3rd generation DLE burner in the ignition stage where there is compressible (choked) flow included, the coupled solver option was more time effective. Obviously because those flow conditions result in stronger coupling between pressure and velocity.

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2.5.4 Calculation procedures at periodic boundaries

All calculations in this work have been performed with help of cost effective 90° and 30° sector models instead of employing a full model. All periodic sides that come in pairs have to be specifically defined as rotationally periodic sides. A CFD solver treats the flow at a periodic boundary as though the opposing periodic plane (called a shadow zone in Fluent) is a direct neighbour to the cells adjacent to the first periodic boundary. This means that when calculating the flow through the periodic boundary adjacent to a fluid cell, the flow conditions at the fluid cell adjacent to the opposite periodic plane (the shadow zone) are used. Therefore the periodic sides of cut geometry have to be identical. When generating a computational mesh for a periodic model a special option in a mesh generation software has to be turned on which ensures that the nodes will line up along an axi-symmetric model and forces the nodes to be rotationally periodic with one another. [16]

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3 METHODOLOGY In this chapter the basic approach and methodology is briefly presented. All details about procedures and concepts will be discussed in the next sections.

3.1 Geometry and mesh creation An established meshing approach for a single SGT-750 burner demands between 40 and 75 million grid cells. Since this represents an extensive effort for the available computer resources some periodic 90° sector models have also been tested and they gave acceptable results in modelling both air/fuel mixing and combustion. A 90° sector model of the burner seems a reasonable choice for a mesh study as solution time is only approximately ¼ of the solution time needed for a full 360° model while the obtained results should be very close to the full model, moreover it should be fully valid for a mesh convergence study.

New 90° sector geometry was created where special care was taken to cut the full model so that all details of the complex geometry were correctly captured. At the same time any eventual sharp corners in the cut geometry have to be strictly avoided in order to be able to prevent creating sharp edged grid cells. An example is shown in the Figure 21. It can be seen that the air casing’s geometry is cut exactly through the middle of the damp holes so that the angle between a circular outline of an opening and cut line is 90°. This theoretically means that when meshing with unstructured tetrahedral mesh the angle of a tetrahedral (or a triangle on a surface mesh) is about 90° depending on the mesh density in that region. On the other hand if the geometry had been cut like the cutting line b) in the Figure 21 suggests then the cells in that area would have been sharp cornered.

Figure 21: Cutting the geometry through the air casings damp holes

Those cells are generally of bad quality and can greatly reduce performance of the flow solver. The new geometry was then firstly the basis for the reference computational mesh creation. Let us call the reference mesh the “SIT mesh”. The SIT mesh was created according to established meshing parameters and is considered as a “trustworthy” mesh so that other test meshes can be compared against it. For all generated meshes in this work the mesh quality was assessed with a general ICEM CFD quality where the lowest limit was 0.3 which in all cases resulted in only a few elements having the lowest value. Each generated mesh was smoothed even further to maximize the number of high quality elements.

Besides 90° sector model of the burner a 30° sector model was also created. The idea was to test the performance and accuracy of the 30° sector periodic model where additional assumptions were needed to take in account. This approach would greatly reduce computation time. However, as even the 90° sector model is still relatively computationally expensive and since no reliable steady state solution was found, most of the calculations were done using the 30° sector model. The 90° sector model was then used merely as a reference to validate the 30° sector model.

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3.2 Models and solution methods Material used in all simulations in this work was Methane Air Mixture which originally consists of CH4, O2, N2, CO2, H2O but as no combustion was modeled the last two components were of course not included in the simulations. Species modeling was performed by Species Transport equations and density was modeled using the ideal gas assumption. Throughout the whole thesis work only the SST turbulence model was used.

As already mentioned the pressure based solver option was used for all cases however for simulating the 3rd generation DLE burner the coupled solver was more stable and time effective while for simulating the 4th generation DLE burner the segregated solver was slightly more efficient. For all runs the default 2nd order upwind spatial discretization method was chosen and 1st order implicit transient formulation was employed for the time dependent simulations. 1st order accuracy was chosen as in this project the point of interest was not transient behavior but average value and therefore diffusive property of this scheme was taken advantage of.

3.2.1 Monitoring convergence progress

It is often of engineering interest to obtain steady state RANS solution and so it is also in this study. Steady state solutions give a good picture of the reality needed in industry and are at the same time very cost effective therefore a lot of effort was put into attempt to acquire a steady state solution. However, as already mentioned it is not always possible for some cases to converge to the final steady state solution due to physical or numerical unsteady behaviour. This unsteady behaviour results in oscillation of the solution field in the computational domain during convergence process. Oscillations are often of a local nature therefore a solution may still be valid in the stable parts of the domain. In fact even the unstable part is not necessarily incorrect. A legally unconverged solution may be used in some cases as a “snapshot” which can be treated as one of many possible solutions.

3.2.1.1 Steady state runs

To track the oscillations of velocity and methane mass fraction during convergence process a number of monitor points were allocated to specific parts of the domain. The idea was to keep the steady state convergence process until the oscillations statistically stabilize. If the oscillations are less than the differences of a monitored quantity obtained from computing using different meshes then the steady state solution may be valid even for mesh convergence study.

To be able to grasp a trend from the oscillations and thereby to tell if the monitored values have statistically stabilized the oscillations have to be “smoothed” somehow. There exist many methods for reducing the effect of variation. In industry and financial calculations an often used technique is using moving average or sometimes called running average. This technique reveals more clearly the underlying trend of a variating value. There are also a number of different types of moving averages, in this work a Modified Moving Average (MMA) or smoothed running average is used. MMA is technically a special case of Exponential Moving Average (EMA) written as: [28] [29]

1 ∙ ∙ 3.1

MMA is a type of EMA when the smoothing constant is equal to 1/ therefore after reordering of the expression (3.1) we get

1∙ ∙ 1 3.2

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where is current moving average value is previous moving average value and is current original value. On the basis of the equation (3.2) a simple MATLAB script was

written in order to calculate the trends in the oscillations. The code can be found in Appendix.

The Figure 22 shows two examples of MMA application. It shows comparison of velocity evolution in two different points when running a steady state case with three different meshes. The three meshes have 0.55, 4.3 and 35 million volume cells respectively (details about this approach are explained in one of the next sections). The left graph shows the desired situation. The oscillations are less than the (average) differences in velocity which means that comparison of the results is possible when taking in account deviation from the mean values. However, that was not the case for all points in the domain. The graph on the right side of the Figure 22 shows that in one point the oscillations are larger than the average differences in velocity.

Figure 22: Normalized velocity in two different monitor points

In this case the steady state solutions could still be useful if the frequency of the oscillations was the same or with other words if the oscillations were in phase. This way a “snapshot” of the steady state solution would still be valid for comparison. This was, however, not the case which is already obvious in the Figure 22.

After many other tests i.e. testing different numerical schemes, changing Courant number, adjusting under-relaxation factors, even removing part of the geometry which is not of essential importance for air/fuel mixing simulation (air casing) no stable steady state solution was found. The last resort was therefore to employ time consuming transient runs with transient statistics sampling.

3.2.1.2 Transient runs with transient statistics

When sampling statistical data during time dependent simulation one is interested in arithmetic average of the solution field. Sampling data occur every time step and this gives rise to an important question: For what amount of physical time should the simulation be run to collect enough data to sufficiently describe the average values? Established rule of thumb is that a fluid particle should flow from inlet to the outlet (a so called “flow-through”) of the domain 5 to 10 times. This can be called a “flow-through” and so we can define a “flow-through time” which can be estimated simply as [2]

∙

3.3

where is average density of a fluid in a domain through which a fluid flows, is the total mass flow and is total volume of a domain. Another approach to estimate the flow-through time is to use limits function for streamlines in CFX Post software. Both approaches give similar results, however, it is worth to mention that some fluid particles may theoretically

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never leave the domain due to a recirculating zone created for example by a highly swirling flow. [2]

For the 3rd generation DLE burner operating in the ignition phase the estimated flow-through time through the whole burner was long. For the 4th generation DLE burner it was shorter but still too long to achieve required number of flow-throughs with available computer resources. As the maximum time step size to get reliable transient formulation was between 5·10-5 and 10-5 s that would mean that we need to run the simulations for between 50,000 and 100,000 time steps or even more. This in reality means very long solution times and that is when taking in account available computer resources and number of grid cells unfeasible. Despite the existence of considerable limitations it is still possible to get acceptable time averaged results with smaller sample size. In industry it is often used only 1 to 2 flow-throughs. Moving average of values in monitor points gives us information about the trends during transient solution process and if we notice a static trend in oscillations we can eventually decide to stop the simulation even earlier. However, caution has to be taken when analysing results with small sample size. [2]

3.3 Computational mesh optimization Due to complex geometry of the 4th generation DLE burner the meshing process is rather time consuming even when meshing with tetrahedral mesh if a computational mesh of a good quality is desired. Grid generation was performed exclusively in Ansys ICEM CFD. However, when geometry as a basis for the grid generation is complex the grid generation algorithm creates many cells of bad quality that have to be manually corrected. This process has to be carried out for each grid generation and can be very time consuming especially when coarse grids are desired.

To avoid that to some degree Ansys Fluent offers a powerful Grid Adaption tool which can refine and in some cases coarsen a mesh. That can be done manually or even automatically. For details about mesh adaption tool please refer to Ansys Documentation [16]. Mesh adaption is carried out by splitting grid cells. A disadvantage of splitting tetrahedrons is that in order to split a tetrahedron into more tetrahedrons the only way is to split one tetrahedron into eight new tetrahedrons like shown in the Figure 23.

Figure 23: Splitting a tetrahedron [30]

This results in a drastic increase in grid cell count when splitting the whole domain but the advantage is that creating a new mesh is a matter of seconds while creating a new mesh in ICEM CFD can take one whole working day. Another advantage is also that the changed mesh has identical configuration, however, care has to be taken when dealing with surface mesh. It is not possible to “smooth” the surface mesh, i.e. rounded surfaces have edged appearance in a coarse mesh, or with other words – new surface grid nodes cannot attach to surface geometry. After splitting all cells the surfaces will remain identical where the difference will be only that every edge will then have more cells and this can consequently affect flow field. If we take for example 2D flow past a cylinder: In a coarse mesh the cylinder can be described as i.e. octagon. While that can be a good approximation for a flow past a cylinder it may not be after splitting the cells as now the simulated flow is actually a

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flow past an octagon. The Mesh Adaption tool offers also a Region Adaption tool which was exploited in this work as well. It is possible to split grid cells in an arbitrary region within domain where limitation is that available shapes of regions are limited to spherical, hexagonal and cylindrical shapes.

3.4 Representation of results Please note that due to the company’s secret policy the exact solutions are confidential therefore all results and geometrical measures are provided in non-dimensional form. The output data was normalized with reference values as follows:

GEOMETRICAL FEATURES

The geometrical features of the SGT-800 burner are normalized with the inner radius of the mixing tube while the geometrical features of the SGT-750 are normalized with the inner radius of the main combustion chamber.

CELL SIZES

Cell sizes in different parts of the mesh were presented with non-dimensional measure where the reference size 1 is the cell size inside the RPL burner in the reference mesh (the SIT4.2M).

VELOCITY VALUES

The velocity data is in the case of SGT-800 combustor normalized with the average velocity magnitude inside the burner while in the case of SGT-750 the velocity data is normalized with velocity which is analytically calculated according to expression below:

3.4

where is the sum of the mass flow (air and gas) defined as inlet boundary conditions, is average density of the mixture at operating pressure and temperature in the combustion chamber, and is cross-sectional area of the combustion chamber.

SIMULATION TIME

The simulation time is normalized with estimated flow-through time for each burner which is essentially equal to the number of flow-throughs.

MASS FLOW

The mass flow values are normalized with the mass flow through the Main 2 passage of the main burner.

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4 A SHORT STUDY OF THE 3RD GENERATION DLE

BURNER This chapter may be considered as a pre-study of the methodology used in this thesis work. This sub-project was a short introduction into modelling air/fuel mixing in a combustion chamber but it nevertheless gave valuable insight about the differences in results when using different simulation software, in this case Ansys CFX and Fluent. Ansys CFX is almost exclusively used to simulate all categories of flows related to gas turbines at Siemens. However, point of interest here was to compare the results obtained from both solvers, when simulating fuel/air mixing in the 3rd generation DLE burner in a specific phase of the burner operation. J. Sjölander namely simulated fuel/air mixing in his master thesis work [27] when the burner is in the ignition phase. Main objectives of his work were to employ, evaluate and validate prediction methodologies for ignition limits applicable to gas turbine conditions with help of cost effective CFD simulations. This special case was studied using CFD for the first time and therefore it may be interesting to compare the results from both solvers. Both simulations performed with Ansys CFX and mesh generation for this burner were accomplished by J. Sjölander. [27]

4.1 Geometrical model A picture of the simulated burner can be seen in the Figure 13 or in the Figure 12 where the turbine is also visible. The geometrical model for this particular case is a periodic 90° sector shown in the Figure 24 where air casing and the combustion chamber is included as the burner is fitted to Siemens single burner atmospheric combustion test rig in Finspång.

Figure 24: Geometrical model of the 3rd generation DLE burner computational domain

4.2 Computational mesh In the Figure 25 are shown the original and splitted surface meshes for the 90° sector of the 3rd generation DLE burner. The original mesh consists of 2.8 million grid cells while the fine mesh with splitted cells, consists of 22.7 million cells. Let us name the two meshes 2.8M and 22.7M respectively. Note that the whole mesh consists of tetrahedrons only which means for example that there is no prism elements to resolve boundary layers. Inflation layers would greatly increase the cell count therefore it is usually avoided. Resolving the boundary layer does not contribute considerably to the needed accuracy for general simulations but it is important when interest is focused to heat transfer. Boundary layer has to be properly resolved

Air inlet

Pressure outlet

Pilot fuel injection

Ignition point

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when simulating heat transfer through walls therefore the inflation layer is usually created only on the walls where heat transfer is taken into account. However, as cell sizes near the walls are relatively small the y+ values for those simulations are not very large. Despite no inflation layer used the maximum y+ value is equal to 130.

Figure 25: Comparison of the original and splitted surface computational mesh

4.3 Boundary conditions and solution methods The 3rd generation DLE burner’s fuel system consists of three independent injection systems: central, main and pilot (for details please refer to Figure 13 on page 10). As their names imply the central fuel is injected in the central point of the swirl cone and it represents the very beginning of the flow through the burner. The central fuel enters the swirl cone of the burner already partially premixed and if we move slightly downstream, the main fuel is injected directly into the burner through a series of injection holes that are built-in to the swirler blades where it mixes with the air coming from air casing. The pilot fuel is injected through a circular array of injectors positioned on the external side of the burner’s end part so that the pilot fuel is actually injected directly into the combustion chamber.

During normal operation of the turbine the total mass flow of the fuel is suitably divided to the three injection sub-systems but at the ignition stage all of the fuel mass flow is directed to the pilot fuel injectors. Prescribed boundary conditions are thus:

Flow boundary conditions:

Air inlet: mass flow inlet Pilot gas: inlet (methane): mass flow inlet Outflow: pressure outlet

All temperatures set to constant room temperature (inlet air and fuel)

Adiabatic physical walls

Rotationally periodic sides

Atmospheric pressure

As a unique steady state solution could not be found transient runs with time statistics sampling were employed with fixed time step size of 10-5s for the case with the refined mesh

2.8M

22.7M

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and for the case with the original mesh it could be safely increased to 5·10-5s although the maximum Courant number in a small area of high-speed flow coming from the pilot nozzle was equal to 300. Maximum Courant number in that area for the case with the fine mesh was on the other hand equal to 120. The implicit transient formulation is unconditionally stable for any time step size but excessively large time step size may affect calculation accuracy. The upper limit is otherwise case dependent therefore caution has to be taken when increasing the time step size. However, a brief time step size study has shown that such large maximum Courant number for this calculation does not affect simulation accuracy. Furthermore, areas of high Courant numbers were limited to a small portion of the domain consisting of only a few grid cells whereas in the majority of the domain the Courant number was significantly smaller. The Courant number was smaller by order of magnitude in low flow speed areas and approximately 5 times smaller in relatively high speed swirling flow in the burner. Employing a large time step size without compromising the accuracy of the calculation allowed significant reduction of calculation time. [17]

The convergence criterion for each time step was set to 10-4 of scaled residual which resulted in approximately 13 needed iterations per time step. Convergence was more stable and slightly more time effective with employing the coupled solver probably due to a stronger coupling between velocity and pressure in the high speed compressible pipe flow through the pilot injector.

Figure 26: Monitor points locations for the 3rd generation DLE burner

Figure 27: Monitoring velocity in the Point 1, 3 and 5 and monitoring methane mass fraction in Point 1

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For monitoring convergence 5 monitor points were used as shown in the Figure 26. For the case with the original mesh (2.8 million cells) approximately 1.6 flow-throughs were achieved while for the case with splitted cells (22.7 million cells) even that was not possible as computational time would extremely long especially if considering much smaller time step size for this case. Approximately 0.25 flow-throughs for the case with the refined mesh was therefore achieved. Even though the physical simulation time was short some idea about the tendency of the flow development can be extracted from studying the moving average of the velocity in the monitor points. The Figure 27 shows velocity development progress for both meshes in the three most important monitor points and also methane mass fraction progress in Point 1 which is in fact the ignition point and hence the most important point in this study.

As seen in the Figure 27 the moving average of velocity and methane mass fraction oscillations show stable tendency in Points 1 and 3 when considering the results from the original mesh. The moving average also reveals that sampling size for transient statistics is sufficient in those two points. However, this is not entirely true for the Point 5 which is located in the air casing where air velocity is relatively low with large low frequency oscillations. For a better time average representation of the velocity in the Point 5 the transient simulation would have been needed to be run for additional number of time steps. However, for engineering practice in industry the collected transient data is sufficient.

The case with refined mesh should have been run for a considerable number of additional time steps but that was computationally too expensive and therefore unfeasible. However, the data from monitor points and their moving averages show that the averaged values may still be valid for comparison as the moving average shows a clear tendency of the oscillations. Furthermore, from the Figure 27 we can conclude that the sampling size represents a minimum to collect useful time averaged values for comparison. The data from the points 1 and 3 obtained from the original mesh namely show that the simulation time with the refined mesh is sufficient assuming that a similar simulation time as with the original mesh is needed to collect a reasonable average value.

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4.4 Results Figure 28 and Figure 30 below show results of the computed time averaged velocity field when using both computational meshes. The cutting plane on which the velocity field is illustrated is located so that the plane cuts the model exactly through the center of the pilot injector (Plane 1 in the Figure 29) which is approximately in the midsection of the 90° sector model. In Figure 28 there are also marked the lines along which the velocity results are later evaluated more in detail. There was an additional line created (Line 1a on the Plane 2) as the Plane 1 does not cut through one of the air inlet openings in the air casing in order to be able to correctly study the jet formed by the inlet opening.

Figure 28: Comparison of the time averaged velocity field results between the two meshes on the Plane 1

Figure 29: The planes on which the evaluation lines can be seen

The result of velocity distribution along the marked lines is presented in continuation (Figure 34 on page 43) where all results are combined (results from both solvers and all meshes) for better comparison. Although the difference in cell count between the two meshes is considerable the obtained results of velocity are obviously very similar. Note that in the Figure 30 the velocity scale in the legend does not represent all velocity scales in the shown velocity field. The legend is optimized so that the highest velocities (red spectrum) correspond to velocity in the center of the burner. The reason is that in the ignition stage of the combustor operation, when all gas mass flow is directed to the pilot injection system, the flow through the pilot nozzles reaches choked flow conditions. The flow speed through the pilot nozzles thus reaches speed of the sound. Velocity through the pilot nozzles is therefore very high as speed of the sound in methane at atmospheric conditions is 446 m/s. [31]

2.8M - Fluent

Line 1

22.7M - Fluent

Line 2 Line 3 Line 4 Line 5 Line 1a

Line 1a

Plane 2 Plane 1

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Figure 30: Comparison of the time averaged velocity field results between the two meshes

The evaluation of the results along the lines is presented in continuation where all the results are collected in order to be able to more graphically illustrate the differences between the meshes and the different solvers used. Because all results of the velocity field are very similar near the outlet and because velocity field in the air casing is not of essential importance are all the figures showing flow details only in the burner and in the front part of the combustion chamber - in the same manner as in the Figure 30.

Let us take a closer look how the velocity field results differ when using different solvers. Both computations were performed on identical computational mesh with identical boundary conditions and flow models. Both transient calculations were also run for enough time to obtain sufficiently large sampling size for time averaged velocity field. Surprisingly there are some distinctive features that distinguish the obtained results from both solvers despite identical settings. The most obvious one is the position of the stagnation point. According to the results obtained from Fluent solver the stagnation point should lie approximately on the same plane as the outlet opening from the burner. Results obtained from CFX solver predict position of the stagnation point moved for 0.8 non-dimensional units downstream . Fluent solver actually predicts the stagnation point position to be inside the burner while CFX solver predicts the stagnation point to be well inside the combustion chamber.

Figure 31: Comparison of the predicted velocity field between Fluent and CFX

2.8M - Fluent

22.7M - Fluent

Stagnation point

2.8M - Fluent

2.8M - CFX

Line 2

Line 3 Line 4 Line 5

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It is hard to conclude which prediction is closer to reality as no experimental measurements were made for this particular feature. One explanation could be in the different finite volume method techniques employed by both solvers as briefly summarized in the section 2.5 on the page 22. The Figure 30 also suggests that the difference occurs due to the discretization error. A closer look at the position of the stagnation point reveals that the calculation with Fluent using the refined mesh predicts the stagnation point to be located slightly more towards the interior of the burner. The difference is about 0.19 non-dimensional units, but for such a relatively small difference it is too optimistic to state that this absolutely holds as the time average sampling size is small for the calculation using the fine mesh.

Another explanation for the difference can be due to a slightly different SST turbulence models behaviour in both solvers as discussed in chapter 2.3.1.1.3 on page 18. As seen in the Figure 32 the predicted turbulence kinetic energy is significantly higher than the prediction obtained by Fluent. Note that the legend does not include all the values as the turbulence kinetic energy in the jet coming from the pilot nozzle is much higher than in other parts of the illustrated turbulence kinetic energy field.

Figure 32: Comparison of the predicted turbulence kinetic energy distribution between Fluent and CFX

The difference in obtained turbulence eddy dissipation is also in the same order as the difference in turbulence kinetic energy, while the results of turbulent eddy frequency do not differ much. It is hard to speculate which factor in turbulence modelling contributes to so significant differences in turbulence modelling in both solvers. There may be some additional differences besides different threating of the standard model coefficients i.e. differences in behaviour of blending function or limiter functions. However, the turbulence model study is not the scope of this thesis but it is an interesting feature that can be challenged for further study.

For this simulation there was no refined computational mesh available for the calculations using CFX solver that would be identical to the refined mesh used with Fluent (22.7M). J. Sjölander has used a fine mesh with 15 million elements which has cell count approximately in a similar order as the one used in Fluent. The results obtained from CFX calculations with 15 million cells (let us name it 15M) can be assumed as a valid comparison to the calculations obtained from Fluent with 22.7M mesh. The following figures are thus showing collected information about the four simulations. We start with comparison of time averaged equivalence ratio in the Figure 33.

2.8M - Fluent

2.8M - CFX

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Figure 33: Time averaged equivalence ratio distribution for all four cases

There are differences in predicted time averaged equivalence ratio when applying both solvers. Part of the explanation may be that Fluent predicts slightly higher values of turbulent viscosity in the region of swirling flow. Mass diffusion in turbulent flow is namely directly dependent on turbulent viscosity as shown in the Equation (2.42) on page 21. Another, more possible, explanation may be associated with the discretization error. Species transport equations are relatively sensitive to grid resolution which will be shown more clearly in the next section of this thesis. As it is obvious from the Figure 33 the results obtained from Fluent solver do not differ a lot even though the fine mesh has approximately eight times the number of grid cells. However, results obtained from Ansys CFX show larger discrepancies. Note that the fine mesh used in CFX calculations is not eight times more refined but approximately five times and despite that the differences are more noticeable. This roughly suggests that the CFX solver is more sensitive to grid resolution especially when solving species transport equation. Explanation can be in the type of finite volume discretization employed by CFX. This is briefly discussed in chapter 2.5.1.1 on page 23 where the fundamental differences between different discretization techniques are explained. While the cell-centered discretization approach has the ratio of control volumes and vertices equal to one, has the vertex-centered approach only about 1/5 to 1/6. This may contribute to stronger grid resolution sensitivity for the CFX solver.

Similar tendency show results of velocity distribution along the marked evaluation lines, though not so noticeable as the values of equivalence ratio. However, all graphs in the Figure 34 show this tendency except in the case of the velocity distribution along the Line 2 where the results from different meshes using the CFX solver are nearly identical and where the results obtained from Fluent differ to a relatively large degree. This is obvious also in the Figure 30 which shows that the velocity inside the burner according to results obtained from the finer mesh is generally higher than that obtained from the original mesh. As this is the only part of the computational domain where mesh sensitivity of the Fluent calculations is evident, the explanation may be insufficient sample size for calculating time averaged velocity for the case with the fine mesh. To confirm that a monitor point monitoring velocity inside the burner would be needed.

2.8M - Fluent 22.7M - Fluent

15M - CFX2.8M - CFX

Line 3

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Figure 34: Time averaged velocity distribution along the lines for all cases

The last figure in this section shows distribution of (time averaged) equivalence ratio ϕ on the cross sectional plane with longitudinal coordinate equal to the position of the ignition point. This area was of the greatest interest in the work of J. Sjölander. Furthermore a volume averaged equivalence ratio in a sphere with radius 5mm is shown in the Figure 35. This figure shows mentioned differences as well.

Figure 35: Time averaged equivalence ratio ϕ distribution and volume averaged ϕ in a sphere with radius 5mm

located in the ignition point

Line 1&1a Line 2 Line 3 Line 4 Line 5

2.8M - Fluent 22.7M - Fluent

15M - CFX 2.8M - CFX

Ignition point

ϕ 0.48 ϕ 0.45

ϕ 0.41 ϕ 0.34

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4.5 Conclusion remarks for the short 3rd generation DLE burner study There exist both, differences in results between the solvers and the meshes used. There is an obvious difference in equivalence ratio distribution results obtained from the different solvers and they again suggest greater mesh sensitivity of CFX solver while differences between the meshes used with Fluent solver show mesh sensitivity in a much lesser extent.

It is hard to draw any firm conclusions whether the statement that results obtained from Fluent for this particular case are closer to reality and less mesh sensitive than the results obtained from CFX. However, considering this short study with reference to the work of G.Wang et al [22] (shortly reviewed in chapter 2.5.1.1, page 23) this might have some basis for discussion. Besides different discretization technique employed in both solvers seems even the same SST turbulence model used in all computations to be slightly more refined in Fluent which might also contribute to more accurate results. A more extended and detailed study of those properties may be encouraged to confirm this statement.

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5 THE 4TH GENERATION DLE BURNER

COMPUTATIONAL MESH OPTIMIZATION As already mentioned an established meshing approach does exist for the new 4th generation DLE burner though no more detailed mesh study had been done before this work. To create a mesh for the basic full 360° geometry of the burner it is needed from 40 to up to 75 million grid cells. The basic geometry refers to the burner with air casing and combustion chamber without inlet casing which connects air inlet with other burners in the system of eight burners installed in the SGT-750 gas turbine. Such amount of grid cells is computationally extremelly expensive especially if transient data is needed. Due to perfect axial symmetry of the burner some studies were performed using a rotational symmetric 90° sector model. Asymmetry of the flow in the burner does exist as visible in the work of D.G. Barhagi et al. [32] but those minor deviations are not of essential importance for general aerodynamic or gas/air mixing simulations. Those differences are, however, more noticeable in the air casing of the burner but they almost completely vanish when the flow becomes swirling. With use of 90° sector model it is therefore possible either to reduce computational time by approximately 4 times or to use 4 times more grid cells in the simulation to be able to resolve the general flow characteristics more in detail at the same computational costs. This mainly holds when using the general two equation turbulence models like k-ε or SST for example. When employing more advanced turbulence models like LES or SAS it is always better to use a full 360° model even in swirling flow areas. One reason is that those sophisticated turbulence models resolve turbulence scales in much greater detail and because turbulence as such is a three-dimensional occurrence a rotationally symmetric sector model would excessively restrict the degrees of freedom to properly describe behaviour of turbulent structures in the flow. [20]

A good opportunity to use rotational symmetric models is also when investigating mesh dependency of a numerical model. In this work 9 meshes were created but with help of Fluent region adaption function this number goes to a total of 17 different meshes. Using those meshes totally 56 cases were run (29 steady state and 17 transient cases). This could not be possible without employing rotational symmetric models. Certainly not all meshes or all cases were successful. Also all runs were not studied in detail and will therefore not be discussed here but they helped as a support for understanding of the flow behaviour when applying different meshes or different solution methods.

Two rotationally symmetric (or periodic) geometrical models were created in this study. As a reference a full 360° mesh was used that consisted of 56 million grid cells together with air inlet casing. Based on configuration of this mesh a new symmetric 90° sector mesh was created which reduced the number of grid cells to 12.1 million. As this is still relatively large number a 30° sector mesh of similar configuration was created for the main runs intended for the mesh optimization. The grid cell count was so further reduced to 4.2 million which is now a reasonable number with respect to available computer resources. As already mentioned the 90° sector model was then used merely for validating the 30° sector model.

5.1 Geometrical model All details of the geometry may unfortunately not be shown in this work due to confidentiality. If the following figures of the geometry might seem to appear distorted, that has been done intentionally. However some details of the geometry in the burner (i.e. position of the pilot and the RPL burner) may be seen in the Figure 15 on page 11. The given full 360° solid CAD (parasolid) model was already inverted by a CAD design engineer so that empty space was converted into a solid which can then be used as a fluid volume while the original

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solid parts were removed. The so called “air model” was then only needed to be cut to get the 30° and 90° sectors which is not an easy task if a computational mesh generation of high quality is desired. As already explained in the chapter 3.1 on page 30 any specialties in the geometry need to be cut so that eventual sharp corners can be avoided. Typical examples are many circular openings in the geometry that must be cut through the middle point. The problem here is that not all centers of the openings lie on the same plane therefore different parts of the geometry had to be cut on different planes. Cutting planes had to be rotated for a specific angle to cut a part of the geometric model so that eventual openings are cut exactly through the center on both sides. At the same time angle between pairs of planes had to be maintained by either 30 or 90 degrees.

The 90° sector model was cut exclusively using software Ansys Design Modeler which provides user friendly environment to work with solids. The full geometry was thus cut so that the periodic sides of the model lie on three different flat planes and one curved plane, see Figure 36. The pilot burner consists of an even number of swirl blades that are positioned at a certain angle looking from upstream direction of incoming flow. Because the space between consecutive blades is small the only option is to cut the swirler between two blades with a plane that follows the shape of the blade. This resulted in curved surfaces on both sides of the pilot that contain ¼ number of the swirler blades and they must be identical on both sides in order to be able to apply rotational periodicity.

Figure 36: The geometric model of the 90° sector of the burner

For the 30° sector model some assumptions were needed to take into account. Some specific geometrical features like the number of fuel injection pipes for the RPL burner, air feeding lines for the RPL and number of swirler blades in the pilot are not multiplications of 12. It was therefore not possible to create a perfectly correct geometrical representation of the full 360° model with a periodic 30° sector. Solution is to simply assume a different number of those geometrical features so that they are a multiplication of 12. This has a certain effect on flow characteristics of the RPL and pilot which will be shown in continuation but this, however, does not play an important role for a mesh independence study.

Cutting a 30° portion of the full model was significantly more difficult task comparing to the 90° sector therefore a combination of two software was used to accomplish that. The majority of the geometry was cut with Ansys Design Modeler as it is significantly simpler to cut solid CAD models. The model had to be cut on 5 flat planes and 2 curved planes at different angles so the Ansys Design Modeler was used to cut on 6 out of 7 planes as it offers also a simple angle measurement tool. The last curved plane which represents the periodic side enclosing the pilot’s swirler blade had to be created in ICEM (see “Pilot burner” in the Figure 37). When a solid CAD model is imported into ICEM CFD it is automatically converted to a

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surface model as ICEM is a surface based design modeller. It offers powerful tools to work with surfaces therefore the software’s advantages have been exploited to design two identical surfaces that are highly curved in all three dimensions in order to tightly enclose the curved swirler blade.

Figure 37: The geometric model of the 30° sector of the burner

The choice of cutting planes to cut the geometry of the Pilot and RPL burner was dictated by the RPL air feeding lines and the curvature of the pilot’s swirler blades. The optimal choice was thus to “rotate” the 30° slice of the RPL for 30° to one direction and the Pilot burner slice had to be cut rotationally to the opposite direction for as much as 90°. Both ends of these two small devices need to come together at a certain point hence a rather complicated geometric configuration in that part of the geometry.

5.2 Boundary conditions and time step size Defining specific boundary conditions for a mesh study is not of essential importance but it is anyway advisory to use typical boundary conditions that computations are going to be used with in future calculations. Typical values for the burner during normal operation were therefore used. All inlet boundary conditions were defined using uniform mass flow in the normal direction of the boundary condition. Positions of the boundary conditions can be seen in the Figure 38.

Figure 38: Boundary conditions

Dimensionless mass flow values (normalized with the mass flow rate through the Main 2 passage) for each boundary condition together with other prescriptions are collected in the Table 2. The table shows boundary conditions used for all cases including different values for 90° and 30° sector model. The only difference is that in the simulations used for comparison of the results between the 90° and the 30° sector model different air inlet temperature was defined. Comparison of the two models was a preliminary study where all incoming fluid

Pilot burnerRPL burner

RPL cooler

Pressure outlet

Air inlet

Main 1 gas Main 2 gas

RPL gas Pilot gas

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temperatures were set to a room temperature. Later, when calculations were run for the mesh study and the mesh optimization, the inlet air temperature was set to a typical temperature of incoming air to the burner during normal operation. There are certain differences in the results when applying different inlet air temperatures but tests have shown that the flow behaviour remains almost identical and does not affect the validation of the 30° sector model. Preliminary calculations were therefore sufficient and no additional calculations were needed.

Table 2: Boundary conditions for all runs

B.C. B.C. type

Air inlet Mass flow inlet (air)

Main 1 gas Mass flow inlet (methane)

Main 2 gas Mass flow inlet (methane)

Pilot gas Mass flow inlet (methane)

RPL gas Mass flow inlet (methane)

Outlet Pressure outlet - Relative pressure = 0 Pa

Pressure High (operating) pressure

Turbulence 10% turb. intensity and 1/20 length scale

Walls Adiabatic, no slip condition

There is only one outlet boundary condition defined as the pressure outlet with zero relative pressure. In case of backflow at the outlet air with room temperature was used as the backflow material. Operating pressure was set to a typical value during a normal turbine operation with reference pressure in the combustion chamber center. For all inlet boundary conditions the turbulence was defined using 10% turbulence intensity where turbulent length scale was set to 1/20 of the geometric length scale of the belonging boundary condition surface. All physical walls have no slip condition defined and as heat transfer was not studied in this work those walls were defined as adiabatic. Because in this work we are not dealing with a full geometric model the sides of each model have to be defined as periodic boundary conditions. As the domain is rotationally periodic all side wall pairs were defined as rotationally periodic boundaries.

Fixed time step size used for this study was 10-5s. It was chosen according to established and tested transient simulation approaches for this burner. A brief time step size study suggested that it could be slightly increased but as no firm conclusions could be made due to long calculation times the time step size was not changed. Corresponding maximal Courant number for simulations calculated using meshes with cell sizes according to established meshing approaches was 35. In continuation it will be presented a substantially refined mesh for the 30° sector model consisting 35 million cells where corresponding maximal Courant number was 103. As no influence of relatively large Courant number on simulation results was detected the same time step size was used also for simulation using this mesh in order to decrease calculation time.

5.3 The reference mesh The first two meshes for both 30° and 90° sector models were created according to established meshing approaches for this combustor at Siemens. In the Figure 39 the reference mesh for the 30° sector model is shown which may be named as SIT4.2M as it contains 4.2

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million elements. A very similar mesh was created for the 90° sector model that has 12.1 million elements. For both reference meshes even inflation layer was created at the walls where heat transfer calculations might be performed. As already explained, a properly resolved boundary layer is critically needed only when heat transfer through the walls is a point of interest. The SIT4.2M mesh therefore consists of 3.9 million tetrahedral and 0.3 million prism elements in 5 layers.

Figure 39: The reference computational mesh for the 30° sector model (SIT4.2M). The inflation layer is marked

with the red line.

5.4 Validation of the 30° sector model In this chapter similarities and differences between the results when applying 90° and 30° sector model will be presented as for the main mesh optimization study the latter will be used.

5.4.1 Monitor points data - 30° versus 90° sector model

Positions of monitor points for monitoring oscillations of velocity magnitude and methane mass fraction during time dependent calculations can be seen in the Figure 40. In all 10 points the velocity magnitude was monitored while in the Points 8 and 10 also methane mass fraction was monitored which makes 12 data points. Results from all data points are not shown here but only the most important which reveal typical oscillations in different parts of the domains. Those points are shaded with red colour in the Figure 40. The monitor points for both sector models were positioned so that they lie on the same plane at a tangential angle adjusted so that in both models the points capture the same area of interest. This way comparison between two different geometrical models is valid.

Figure 40: Positions of the monitor points used for validating the 30° sector model (data obtained from the points

shaded with red color can be seen in the Figure 41)

In the Figure 41 the results obtained from the chosen monitor points can be seen. The graphs showing the oscillations and the moving averages of the oscillations in the Figure 41 are representative for all monitor points since behavior in remaining points which are not shown here is very similar. From all shown points, except the Point 3, we can conclude that for both

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cases time averaging was sufficient even though simulations were run only for a portion of flow-through time.

Approximately 0.25 and 0.5 flow-throughs were reached for the 90° and 30° sector model simulation respectively. In most points the behavior of oscillations, their moving averages and differences between average values were very similar to that in the Point 2 in the Figure 41. Monitor point 3 shows, however, very different behavior. In the area around the Point 3 there are similar flow conditions as around the Point 5 in the case of 3rd generation DLE burner which is covered in chapter 4.3 on page 36. In vicinity of this point there is also an area of low air velocity with large low frequency oscillations that can be either of physical or numerical origin. Time average is therefore not sufficient in this portion of the domain but, as it will be shown later, those instabilities do not influence the flow downstream. Furthermore, because this portion of the domain does not play a very important role for air/gas mixing simulation in this work, more extensive time averaging was not needed.

Figure 41: Monitoring velocity and methane mass fraction in the chosen points

The Point 5 shows very well sampled time average in that area for the 30° sector model while for the 90° sector model the simulation should have been left run for a longer time to get a similar quality of time average but it is nevertheless sufficient as the tendency is clear. The difference between the average values is on the other hand quite large in the area, approximately 6%. This is the consequence of different pilot and RPL geometry in both models discussed earlier in the section 5.1. The details about changed flow conditions will be shown in continuation. Results of methane mass fraction obtained from the Monitor point 8 might not seem sufficient for a good time average but the differences between the values are negligible and the same holds also for the velocity in the Point 8 where the difference between average values are only 1%. There is slightly larger difference between average values obtained from the Point 9 but it is, however, in the order of only 2%. According to all monitored data and their moving averages it has been concluded that the sample size for time average is sufficient for comparison between the 30° and 90° sector models.

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5.4.2 Results – comparison between 30° and 90° sector model

Comparison of the results between two different sector models and all other cases in continuation of this thesis work has been performed thoroughly with help of the evaluation lines shown in the Figure 42. Some lines were furthermore moved if needed in order to track any important changes in values of variables in axial or radial direction when vertical or horizontal lines were used respectively. Variables investigated were for the most part time averaged velocity magnitude, time averaged equivalence ratio and in some cases also instantaneous values of those values. Note that results from all evaluation lines will not be shown here but only the most important and representative for the whole domain.

Figure 42: Positions of the evaluation lines for all cases

The Figure 43 shows comparison of the time averaged velocity field between the models. For more realistic visualisations of solution fields on the cutting planes the planes have been reflected over the longitudinal axis as though if the full 360° model would have been simulated. Obviously the velocity field in the combustion chamber, the Main 1 and Main 2 passages (areas of highly swirling flow where the air/gas mixing is taking place) is very similar. Even in the area of low frequency oscillations (monitored with the Monitor point 3), where time averaging was not sufficient, the flow field is very similar. This highly unstable behaviour originates from “swinging” jets of air exiting the largest damp holes which then enter the Main 2 passage. This area is marked in the Figure 43 where the jet is clearly visible. At this point it is hard to conclude whether this instability is physically or numerically induced.

Figure 43: Comparison of the time averaged velocity field between the 30° and 90° sector model

30° sector

90° sector

Area of low frequency oscillations

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As shown with the Monitor point 3 the pattern of oscillations differ between the models. The explanation may be that in the case of the 30° sector model there are fewer degrees of freedom for the jet to swing in all directions and that there are only 1/3 the number of damp holes so the interaction between respective jets is also different.

If we move from that area downstream towards RPL burner more noticeable differences in velocity field emerge as the assumptions made in construction of the 30° sector model are showing their effects. As already explained in the section discussing the geometry for the 30° sector model a larger number of swirler blades in the pilot burner is assumed which results in approximately 22% smaller effective flow area through the pilot. More restricted flow through the pilot causes that air mass flow incoming to the pilot burner is about 16% lower. However, this leads also to larger pressure drop and therefore for about 8% higher area averaged velocity of the mixture on the plane directly downstream of the pilot exit. Another assumption made was that the RPL burner in the 30° sector model has larger number of air inlet openings which leads to lower resistance of air flow incoming to the RPL burner. Those two assumptions furthermore result in about 28% higher air mass flow incoming to the RPL which has as a consequence a much leaner air/gas mixture in the RPL burner in the case of the 30° sector model as obvious from the Figure 44. Average value of equivalence ratio in the case of the 90° sector model is equal to 2 while in the case of the 30° sector model it is equal to 1.7.

Figure 44: Comparison of the time averaged equivalence ratio field between the 30° and 90° sector model

Some differences in equivalence ratio distribution inside the Main1 and Main 2 passages may also be noticed. The reason might be in insufficient sampling size to obtain a better time average value in that area. Only a velocity progress during the calculation was monitored near the exit of the Main 1 passage (Monitor point 1) but not equivalence ratio therefore it is hard to conclude anything about the quality of time averaging of methane mass fraction in that area. The importance of monitoring both velocity and equivalence ratio in many specific areas of the domain has been shown in this model study. Many more monitor points were therefore created for the simulations following in the next sections. However, distribution and average values of equivalence ratio at the exit of the Main 1 and Main 2 passages are nearly the same in both cases. Equivalence ratio distribution is namely most important specifically at the exit of both passages because downstream near the exits a flame is being fed with this mixture which is by then already well mixed in both model cases.

30° sector

90° sector

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Figure 45: Comparison of the time averaged velocity and equivalence ratio between the models along the lines

which are illustrated in the combustor cross section view

The velocity and equivalence ratio distributions in the combustion chamber are otherwise nearly identical which can be confirmed by the graphs in the Figure 45. The graphs show the velocity and the equivalence ratio distribution along some chosen lines that represent how both models compare to each other. Velocity distribution along the Line 1h shows discrepancies due to insufficient time averaging in that area but the differences vanish almost immediately after entering the Main 1 and Main 2 (the Line 2h) passages where the air velocity increases. Velocity distribution along the Line 1 shows a small part of large discrepancy between the models in the lower part of the graph. The lower part of the Line 1 is positioned near the exit opening from the pilot burner and due to the assumptions made for the 30° sector model the velocity is higher in that part of the burner as already explained. Velocity distribution along the Line 2 RPL shows more clearly the consequence of the assumptions made for the 30° sector model since the velocity in the RPL burner is clearly higher. The graphs showing velocity and equivalence ratio along the Line 4, which is well inside the combustion chamber, confirm that the differences between the models inside the combustion chamber are negligible. We may finally conclude that the 30° sector model describes flow properties very accurately taking in the account the assumptions that had to be made.

Line 2h

Line 1h Line 1 Line 4

Line 2 RPL

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5.5 The mesh optimization This chapter deals with the main part of this work that has objective to improve meshing approaches to better optimize accuracy of the results versus cell count for the 4th generation burner. The 30° sector model has been validated therefore all calculations in the following sections intended for the mesh study were performed using the smaller, much more time effective model. For the runs presented in continuation all boundary conditions used were the same except that the inlet air temperature was changed to a typical inlet air temperature during normal turbine operation.

5.5.1 “The three meshes”

The basic idea of the approach to find regions of high/low mesh dependency is to create only one very coarse mesh in order to be able to split all cells in the domain two times using the mesh adaption tool in Fluent. This tool has been already introduced in the section 3.3 on the page 33 with some of its advantages and dissadvantages. The target cell count for the coarse mesh was 0.5 million cells which still gives after the second splitting a reasonable cell count with respect to available computer resources.

The coarse mesh had to be created with caution especially when creating surface mesh on rounded surfaces or in tight areas such as in the pilot burner between the swirler blades. As already explained in the section 3.3 new surface grid nodes after splitting the cells do not attach to surface geometry therefore all rounded surfaces were meshed so that they do not have too sharp edges which could after splitting cells affect flow field. In the model there is also a substantial number of pipe flows where diameters of pipes can be very small in comparison with the combustion chamber external measures. Correct meshing of all the pipes in the geometry would always exceed the goal cell count and on the other hand classical pipe meshing with large surface elements can lead to a blockage in the flow. Cross-section of a pipe meshed with large elements is no longer a circle but a poligon enclosed in a circle. The effective area of this poligon is thereby smaller which leads to blocked flow in a pipe. To overcome this limitation special measures were taken. Akram Soroush has shown in his master thesis [39] that for 12 aligned nodes per 360° the blockage is approximatelly 5%, a value that can be accepted in this work. Most of the pipes were therefore meshed so that they have minimum 12 sides with aligned surface nodes as shown in the detail window in the Figure 46.

Figure 46: The original generated mesh with 0.55 million cells – 0.55M mesh

With help of this approach a mesh with only 0.55 million elements (the 0.55M mesh) was created. With the quick method of splitting all cells in Fluent using mesh adaption tool a new mesh was created with 4.3 million elements (the 4.3M mesh) and furthermore with another splitting a mesh with 35 million cells was created (the 35M mesh). However, no inflation

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layer was created. In the air inlet passage of the pilot burner there were originally small cooling ribs placed on the wall which were removed. Removing cooling ribs certainly affects the flow field and especially changed mass flow through the pilot was a reason for concern therefore a highest possible friction coefficient was defined on the corresponding wall. The difference between the mass flow with and without cooling ribs was then after defining the friction coefficient only approximately 3% which still allows comparison of the results using the three meshes against the reference SIT4.2M mesh. Although the mesh generation algorithm failed to create a high quality mesh on a number of areas in the geometry, which is very common for a creation of a coarse mesh in a complicated geometry, a thorough manual correction of the surface and volume elements resulted in desired ICEM CFD quality of minimum 0.3. After splitting the cells the mesh quality naturally remains the same.

The domain has been divided into 9 subdomains with interfaces between them in order to be able to conveniently measure the mass flow between different passages of the burner. It is often a point of interest what is mass flow through i.e. the pilot burner, the RPL burner the Main 1 and Main 2 passages etc. This is applicable also for a mesh study to detect any dependency of mass flow through the passages on the cell count.

Besides “the three meshes” two main additional meshes were also used for the mesh study. One of them is the reference mesh – SIT4.2M and the second one is an early proposal of a slightly coarser mesh with a similar meshing approach as used in the reference mesh though slightly larger cells were used so that the cell count for this mesh is 1.9 million. This mesh may be called My1.9M. Thus for the mesh study mainly five different meshes were carefully inspected. The meshes and normalized physical simulation time for corresponding calculation are collected in the Table 3. Among the five meshes only the reference mesh includes the inflation layer on specifically chosen walls. Values of y+ associated with the tested meshes are therefore large and are in the areas of high velocity in the order of 1000.

Table 3: The main meshes for the mesh study and normalized physical simulation time (= number of flow-throughs) of the time dependent runs with the corresponding mesh.

Mesh 0.55M 4.3M 35M My1.9M SIT4.2M

Physical time 0.52 0.61 0.28 0.38 0.36

ADDITIONAL MESHES

There was a number of additional meshes created and tested but the results using those meshes were not of such significant importance as with the above five meshes. A mesh with 1 million elements was created and it allowed one splitting of cells which offered a new mesh with around 8 million elements. Another version of the My1.9M mesh was also created with the same configuration except that it included inflation layer at the walls as shown in the Figure 39. This mesh was used to test importance of the inflation layer for general aerodynamics and air/fuel mixing. Two additional versions of the 0.55M mesh where region adaption tool in Fluent was used to refine only the RPL burner to test the mesh dependency of the RPL burner and another where only the centerline of the combustion chamber was refined. Studying those meshes in detail was abandoned as the five meshes in the Table 3 are the most representative for all different areas in the domain.

5.5.2 Additional monitor points

Preliminary studies, including the validation of the 30° sector model, have shown the importance of monitoring the solution process in many different areas of the domain therefore 8 new monitor points were created. All monitor points are thus monitoring also methane mass

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fraction, where applicable, which makes totally 28 data points to be processed externally using MATLAB software. Positions of all monitor points can be seen in the Figure 47. Results of all data points are not shown here therefore only the most important and representative points have been chosen to show the transient solution progress using different meshes and they can be seen in the Figure 48.

Figure 47: Positions of the new monitor points

Most of the monitor points show behaviour similar to the graph describing velocity solution progress in the Point 2. This the desired behaviour with clear tendencies from which it can be concluded that a sufficient time average values have been obtained. Solution progress in some areas, especially for the methane mass fraction values, was not completely satisfactory as for example the Point 2 showing methane mass fraction solution progress seen in the Figure 48. However, some information about the tendencies can be reported by the moving average and the differences between moving averages are evidently small. Comparing moving averages reveals that the difference between results using 0.55M and 4.3M is approximately 6% while the difference between 4.3M and 35M under 1%.

As with all cases there is a problematic area in vicinity of the Point 3. Simulations using the 0.55M and the 4.3M mesh show some tendency (though there is 10% difference in MMA between the meshes) while no clear tendency can be extracted for the simulation using the 35M mesh. However, this flow, characterized with large low frequency oscillations, always stabilize immediately after entering the Main 1 and Main 2 passages. For this reason it can be concluded, similarly as before, that this behaviour has no important effect on the flow downstream where air/gas mixing is taking place. Results from the Point 3 reveal also that the amplitude grows with the number of elements in a mesh. Explanation may be that the coarser the mesh is in that area, the more diffused the swinging jet coming from the large damp holes is. The shape of the jet is more defined in the fine mesh and therefore the Point 3 “feels” moving of the jet more strongly. In some areas of the domain the oscillations show behaviour like those revealed by the Point 8 in the Figure 48. The tendencies might not look good especially for the case with the 35M mesh but, however, the differences between the values are negligible.

A special behaviour can be observed inside the RPL burner which was monitored with the Point 16. The tendencies are clear but the values are changing very slowly so that time averaging is completely irrelevant in this area but a closer look at the graphs brings to light the fact that the solution progress inside the RPL burner is converging towards a steady state solution. For the runs with SIT4.2M and My1.9M meshes it can be already confirmed that the steady state solution has been reached. For the case with 35M mesh the tendency suggests that the steady state solution has already been reached and this will be confirmed in continuation.

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Figure 48: Monitored velocity and methane mass fraction in “the three meshes” in the points shown in the cross section view of the combustor and additionally also remaining two meshes in the Point 16 (the My1.9M and the SIT4.2M mesh)

Assuming that for the cases with the remaining meshes (0.55M and 4.3M) the solution progress has the same tendency as that with the 35M mesh, the results from all meshes inside the RPL burner may be studied using instantaneous results for the velocity field. Similar conclusions about methane mass fraction tendencies inside the RPL burner cannot be drawn. It would have been computationally too expensive to run simulations in order to obtain more clear solution development of methane mass fraction inside the RPL burner. However, even for studying equivalence ratio inside the RPL burner instantaneous solution field was used. While the differences in methane mass fraction results obtained with the “the three meshes” are small (up to 2%) in the Point 16, the differences in velocities in the same point are large (over 10%). And obviously the more fine mesh in the RPL the higher velocity is obtained in the Point 16. In the next section we will take a closer look at the reasons for those differences.

5.5.3 The mesh study

In this section the main comparison between the meshes will be presented. Similarities and differences will be illustrated with velocity and equivalence ratio fields on a plane and for more detailed comparison the results will be compared with help of solution distribution along the evaluation lines. Results obtained from all meshes were thoroughly scrutinized using the lines shown in the Figure 42 on page 51 where some of them were eventually moved in axial direction if needed. Not all results from the evaluation lines will be presented here as many of them are very similar therefore in a similar manner as in former sections the most important and most representative results will be presented here. As the results obtained with the My1.9M mesh are in many cases very similar to those obtained with the 4.3M or SIT4.2M mesh the former is excluded from comparison for more transparent comparison except in some specific cases. The comparison is therefore principally presented with “the three meshes” - 0.55M, 4.3M, 35M and the reference mesh SIT4.2M.

Point 3

Point 16

Point 2

Point 8

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5.5.3.1 Comparison of velocity and equivalence ratio distribution

The Figure 49 shows comparison of velocity field in the whole domain obtained with the four meshes. The figure is organized so that each half of the domain represents velocity field results obtained with corresponding mesh as marked in the figure. As obvious from the Figure 49 even the coarsest mesh with only 0.55 million cells gives surprisingly accurate results for general aerodynamics.

Figure 49: Comparison of time averaged velocity field in the whole domain and instantaneous axial velocity

field in the RPL burner obtained with the four meshes

Figure 50: Comparison of time averaged equivalence ratio field in the whole domain obtained with the four

meshes

0.55M

4.3M

SIT4.2M

35M

Instantaneous axial velocity in the RPL burner

0.55M

4.3M

SIT4.2M

35M

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Velocity field inside the RPL burner also seemed to be very similar between the meshes used on the first sight. Large differences in velocity suggested by the Monitor point 16 became visible only after isolating axial velocity field from the total velocity magnitude field as shown in the Figure 49. Obviously the RPL burner is very mesh sensitive and needs even more refined mesh than the reference mesh in order to more accurately resolve velocity field with respect to the fine 35M mesh. Maybe it is worth to mention that the reference mesh, the SIT4.2M in this work, has slightly more refined grid in the RPL burner as it had been proposed by the established meshing approaches.

On the first sight the Figure 50 shows similar differences between the meshes used but the differences are more distinct. The meshes 0.55M and 4.3M show strong diffusion of equivalence ratio both inside the Main 1 and Main 2 passages and at the exit of the passages when the mixture enters the combustion chamber. A closer look to the RPL burner shows also that the same two meshes are not fine enough to predict accumulation of gas at the root of the RPL burner as both the SIT4.2M and the 35M do.

5.5.3.2 Quantitative assessment of the meshes along evaluation lines

In the Figure 51 some quantitative differences will be shown. Time averaged velocity and time averaged equivalence ratio distribution have been thoroughly examined along all lines shown in the Figure 42 and some additional if needed. Here it will be shown results along some chosen lines that represent the most critical areas of the domain and at the same time the most representative for the whole domain. For better information how the three main meshes perform the results obtained with the reference mesh are added which are illustrated with dashed lines. On the basis of all data from the evaluation lines conclusions about mesh dependency in specific areas of the domain can be drawn. Finally a suggestion for a new mesh with optimized ratio between cell count versus accuracy may be given.

The graph a) shows again large differences in velocity field obtained with all meshes in the area of highly unstable flow in the air casing of the burner. If we continue downstream the differences become smaller as seen in the graph b). Already immediately after entering the Main 1 and Main 2 passages the differences almost completely vanish but they do get slightly larger near the exit of the passages but the differences are, however, small for all meshes used as shows the graph c). The differences in equivalence ratio are on the other hand larger especially inside the Main 2 passage where only the reference mesh gives similar distribution as the 35M mesh. Thus far we can conclude that the cell size in the Main 2 passage has to be similar as that in the reference mesh, while in the Main 1 passage only the lower part near the wall has to be slightly more refined to capture a peak in the velocity magnitude which can be seen in the bottom part of the graph c). As the unstable flow in the air casing obviously does not influence the flow downstream and as the differences in mass flow at the entrance of both passages are negligible for all meshes, it can be concluded that in the complete air casing area the mesh may be coarse with a similar cell size as in the 0.55M mesh.

The graph e) shows more in detail the large discrepancies in the velocity field inside the RPL burner. For this particular part of the domain the solution obtained from the My1.9M mesh was added. This mesh has only slightly more refined grid in the RPL burner as the 0.55M mesh hence velocity magnitude obviously grows with the fineness of the mesh in the RPL burner. The graph e) confirms that even the reference mesh is not refined enough to correctly predict velocity field in the RPL burner if compared against the fine 35M mesh. A similar conclusion can be made for the equivalence ratio in the RPL burner, as suggested by the graph f), which leads to requirement of having a very fine grid in this part of the domain.

Continuing downstream towards the pilot tip, where the Line 1 crosses the outlet from the pilot and the RPL burner, the graph g) shows very small differences in velocity. Even the

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0.55M mesh gives velocity results that are in good agreement with the other meshes used. However, this is not the case for the equivalence ratio as seen in the graph h) which suggests that even the reference mesh is not fine enough properly resolve concentration of methane in that area. This part of the domain needs therefore at least as dense mesh as the reference mesh has.

Figure 51: Velocity and equivalence ratio distribution along the lines obtained from different meshes

Moving downstream towards position of the Line 3 it can be seen that, again, even the coarsest mesh gives results that are in a good agreement with the others, while solving species transport equations in that area is more mesh dependent especially near the wall. If we move

Line 1(Air casing) Line 1h

Line 1(m1+m2)

Line 1 RPL

Line 1(RPL+Pilot out)

Line 5 (Chamber)

Line 3 (Chamber)

c)b) a)

f)e) d)

i)h) g)

l)k) j)

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downstream towards the Line 5 and beyond the differences for both variables become very small as seen in the graphs k) and l). A large part of the combustion chamber may therefore have relatively coarse mesh where only the walls need be more refined though no inflation layer is urgently needed. Only the SIT4.2M mesh includes inflation layer for a proper resolving of the boundary layer on the chamber wall but as obvious from the graphs i), j), k) and l) what is needed is only more refined mesh at the chamber wall.

5.5.4 The optimized mesh – OPT1.4M

On the basis of the detailed comparison between the results using a number of different meshes a new mesh with optimized cell count versus accuracy ratio in different parts of the domain has been proposed. Some parts of the domain needed to be refined (i.e. the RPL burner), some parts needed to have approximately the same resolution (i.e. combustion chamber wall, Main 1 and Main 2 exit area) and some parts could be made coarser (i.e. combustion chamber). A special category represents the parts of the domain which do not affect mixing process in the pilot burner, the RPL burner and the Main 1 and Main 2 passages. Those areas could therefore be made coarser even though the differences between the results obtained with different meshes are substantial. To this category belong almost all parts of the domain where no mixing of air and fuel is taking place, i.e. air inlet casing, main air casing. It was, however, important that low resolution grid in those parts does not affect mass flow through different passages of the domain – see Figure 54 on page 63. The proposed new mesh (OPT1.4M) with 1.4 million cells can be seen in the Figure 52. The optimized mesh consists of only 1/3 the elements used in the reference mesh therefore about 3 times shorter computation time may be expected to get similar results.

Figure 52: Comparison between the reference mesh (SIT4.2M) and the proposed optimized mesh (OPT1.4M) with important cell sizes in non-dimensional form (the part enclosed with the yellow dashed line could eventually have cell size equal to 6)

Note that the number of elements could have still been slightly lower but due to specific limitations in ICEM CFD software some areas could not be made coarser. The first example

4 4 2-4 4 2

2

2-4

1 0.125-0.25 1 0.125-0.25

6-12 3-12 3-6 12 3

3

3-7.5

0.75

0.375-0.75

0.75-0.375

0.1875

SIT4.2M

OPT1.4M

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is the air inlet casing. This part of the domain does not need a refined mesh but as the combustion chamber wall does indeed need to be refined this refinement influences also the air inlet casing due to a very small distance between them. Element size definition in this software affects elements in all directions so unintended refinement of air inlet casing could not be avoided. Another example is the area in the front part of the combustion chamber (downstream the Main 1 and Main 2 outlets) where a large portion of the domain has a cell size equal to 3. This area could be smaller but because ICEM CFD offers only one shape of density box (a shape of a cigar) this was at the moment the optimal configuration of the density box without compromising a slow gradual increasing of cell size in downstream direction.

5.5.5 Verification of the optimized mesh

In this section we will take a look at the performance of the proposed mesh generated on the basis of the mesh study presented in the previous sections.

5.5.5.1 The monitor points

For completeness the Figure 53 shows how the time dependent solution progress using the optimized mesh compares against previous simulations in the chosen monitor points. The graphs show similar tendencies except that the moving average values tend to have values being closer to the values obtained with the 35M mesh which is a good indication.

Figure 53: Monitored velocity and methane mass fraction in the same chosen points as shown in the Figure 48

but with included monitored data obtained from the optimized mesh (OPT1.4M)

Assumption from the section 5.5.2 on page 55 regarding velocity tendencies in the Point 16 (inside the RPL burner) may now be confirmed. We assumed that the case with the 35M mesh has reached a steady state. The SIT4.2M mesh has in this study a uniform size of 1 in the RPL burner while the 35M mesh has on the other hand size of 0.5 which slowly decreases to 0.25 at the wall. For the OPT1.4M mesh a compromise between those approaches has been chosen

Point 3

Point 16

Point 2

Point 8

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so that the main cell size of 0.75 more quickly decreases to 0.375 at the wall. The approach seems to be successful. Initial conditions for the simulation with the OPT1.4M mesh were interpolated from the final result with the 35M mesh. The simulation with the OPT1.4M mesh was consequently a continuation of the simulation with the 35M mesh inside the RPL burner which had already by then reached a steady state solution. And although the OPT1.4M mesh has less refined mesh in the RPL burner the Monitor point 16 suggests that velocity field remains unchanged. However, methane concentration tends to grow even further as suggested by the Monitor point 16 and it is difficult to account when and at which value it will stabilize. Obviously the longer the run the higher concentration is obtained in the RPL burner as it is indicated in the Figure 53 showing methane mass fraction in the Monitor point 16. For the case with the optimized mesh it has grown the most and that is the reason the equivalence ratio related to the RPL burner will be slightly higher in the following figures.

5.5.5.2 Assessment of the three meshes including the optimized mesh on interfaces downstream specific passages of the burner

Before examining the performance of the new mesh with help of the evaluation lines let us take a look at the mass flow values through some important passages of the domain and averaged values of velocity and equivalence ratio on interfaces between the passages for the simulations with “the three meshes” and the OPT1.4M mesh.

Table 4: Comparison of time and area averaged normalized velocity, instantaneous mass flow, time and area averaged equivalence ratio and mass flow averaged equivalence ratio on the crucial interfaces between specific passages in the domain. The values are compared against the 35M mesh. The differences are max 2% except in the cells shaded with green or red color.

Figure 54: Positions of the interfaces at which the data in the Table 4 is extracted (shaded with red color).

Pilot out

Main 2 out

Main 1 outPilot air in

Pilot out

Main 1 in Main 2 in

RPL air in

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The Table 4 shows, among other variables, comparison of mass flow through the most important interfaces. There are 13 interfaces in the domain but the 4 interfaces shown are of utmost importance as they represent outlets of each passage where main mixing is taking place before entering the combustion chamber where the mixture ignites by the main flame. Figure 54 additionally shows positions of those outlet interfaces (the names in the boxes shaded with red colour) and corresponding inlets to those passages (the names in the boxes shaded with blue colour).

As available variables for sampling time statistics in Fluent include neither mass flow nor density, instantaneous data for the mass flow had to be used for comparison. Instantaneous mass flow data may be misleading but as instantaneous pressure, temperature and velocity values were in good agreement with mass flow on the interfaces, it can be assumed that the instantaneous mass flow is valid for comparison. Furthermore, mass flow through one of the interfaces was monitored during one of the last simulations and it showed time dependent variation of max 3% around the average value. According to the Table 4 the differences in mass flow are in most cases small. Certainly nearly identical values were observed on the inlet side of each passage after subtracting mass flow of the added gas from the mixture. Larger deviations may be noticed when applying the coarse 0.55M mesh and they can exceed 5%. A very coarse mesh in those passages obviously tends to hamper the accuracy. Larger differences in average equivalence ratio associated with the RPL burner and the OPT1.4M mesh may be noticed and the reason has been already explained (refer to the Monitor point 16). Larger differences in equivalence ratio (up to 7%) associated with the pilot burner may be also noticed in the Table 4.

Figure 55: Distribution of time averaged velocity and time averaged equivalence ratio on the interfaces

Pilot out

Main 2 out

Main 1 outPilot air in

RPL out

Main 1 in Main 2 in

RPL air in

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The Table 4 shows only average values on the four interfaces therefore it might also be interesting to see how do the distributions of time averaged velocity and time averaged equivalence ratio look like on those planes. This is shown in the Figure 55 which illustrates distribution of time averaged velocity and time averaged equivalence ratio on the interfaces introduced in the Table 4. For illustrative purposes the 30° section of the interfaces has been reflected around the centerline as though a whole 360° model was studied. Velocity fields show very small difference in results obtained with the 4.3M, 35M and the new OPT1.4M mesh. There are, however, larger differences in distribution of equivalence ratio. While differences in equivalence ratio distribution on the Main 1 interface are hardly noticeable if comparing the results obtained with the OPT1.4M mesh against 35M, there are slightly larger differences on the Main 2 interface. The equivalence ratio obtained with the OPT1.4M mesh in that area is characterized with more diffused distribution which is naturally a consequence of less refined mesh in that area. The differences are, however, small therefore only if there is a specific need to have more refined equivalence ratio distribution in that area more refined Main 2 passage is advised. For general air/gas mixing studies the OPT1.4M mesh is sufficient in that area. On the other hand large differences may be seen on the Pilot out interface as already suggested by the Table 4. The reasons for those large deviations will be discussed in continuation.

5.5.5.3 Comparison of time averaged velocity and equivalence ratio distribution

In a similar manner as before the Figure 56 and the Figure 57 show velocity field and equivalence ratio field in the whole domain respectively. The differences between the results obtained with the new optimized mesh, the reference mesh and the fine mesh are now minimal if the disregarded air casing is not taken into account. Velocity field inside the RPL burner obtained with the new mesh is now much more similar to the velocity filed obtained with the fine mesh than with the reference mesh. The same goes for the equivalence ratio distribution except that in the case with the new mesh the equivalence ratio in the RPL burner is higher due to already explained reasons.

Figure 56: Comparison of the time averaged velocity field in the whole domain and instantaneous axial velocity field in the RPL burner obtained with the optimized mesh (OPT1.4M), the reference mesh (SIT4.2M) and the fine mesh (35M)

Instantaneous axial velocity in the RPL burner

OPT1.4M

SIT4.2M

35M

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Figure 57: Comparison of time averaged equivalence ratio field in the whole domain obtained with the optimized

mesh (OPT1.4M), the reference mesh (SIT4.2M) and the fine mesh (35M)

5.5.5.4 Quantitative assessment of the optimized mesh along evaluation lines

The new mesh performance was thoroughly examined by comparing the results of solution fields along the evaluation lines in the same manner as it has been done so far. Figure 58 shows the same graphs as the Figure 51 only that the data obtained with the OPT1.4M mesh were added in order to be able to see how the new mesh compares with the others.

Graphs a) and b) show accuracy of the results which is in the order of the accuracy obtained with the 0.55M mesh which was of course expected. Other graphs show that the results obtained with the optimized mesh are in good agreement with the results obtained with the reference mesh, or even more, in some parts the results are comparable to the results obtained with the 35M mesh. As already suggested by the Monitor point 16, monitoring velocity inside the RPL burner, the velocity field obtained with the new mesh is very similar to the one obtained with the 35M mesh as obvious from the graph g). Equivalence ratio in the RPL burner is much higher as it was also already suggested by the Monitor point 16. Differences shown by the graph l) might seem large but note that the differences are relatively very small. Comparing equivalence ratio at the wall obtained with the OPT1.4M mesh and the 35M mesh show namely that the maximal difference is less than 3%.

There is, however, one part of the domain that shows certain large deviations in equivalence ratio which has already been suggested by the mass flow averaged equivalence ratio on the Pilot out interface given in the Table 4 and the Figure 55. The graph f) in the Figure 58 shows that the new OPT1.4M mesh gives otherwise very similar results in the area near the outlet of the RPL and the Pilot burner as the reference mesh SIT4.2M gives. However, large differences are shown when comparing equivalence ratio obtained with the two meshes against the 35M mesh. This might be an interesting feature to be explored even further.

SIT4.2M

35M

OPT1.4M

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Figure 58: Velocity and equivalence ratio distribution along the lines obtained from different meshes with added

results obtained from the optimized mesh

When studying three-dimensional solution fields with help of two-dimensional evaluation lines a question may arise in this context. To what degree are those lines representative? In this particular case the values along the lines may change if the lines are moved in tangential direction. Velocity fields shown in the Figure 55 suggest very small deviations in the tangential direction while equivalence ratios reveal noticeable variations in tangential direction especially on the Pilot out interface.

Line 1(Air casing) Line 1h

Line 1(m1+m2)

Line 1 RPL

c)b) a)

f)e) d)

i)h) g)

l)k) j)

Line 1(RPL+Pilot out)

Line 5 (Chamber)

Line 3 (Chamber)

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A useful method to assess this is with exporting two-dimensional node values on a plane a line in question is lying on. A scatter diagram may be constructed then with all node values on one axis and all its coordinates in the direction the line is pointing at on the other axis. If there is no variation in transversal or, as in this case in tangential direction, the scatter diagram will recreate the graphs along the line in question like shown in the example in the Figure 59. Conversely the node values would have been scattered around the values suggested by the line in question. The planes which the data in the Figure 59 is based on can be seen in the Figure 60.

Figure 59: Velocity and equivalence ratio distribution along the line marked in the bottom picture and corresponding scatter diagram of node values on the plane the line is lying on. The scatter diagram of two-dimensional data recreates the lines almost exactly and thereby confirms that there is nearly no variation of velocity and equivalence ratio on this plane in the tangential direction.

Based on the figures seen so far including the Figure 60 we can conclude that the optimized mesh OPT1.4M gives results being at least as accurate as those obtained with the reference mesh in all critical parts of the domain with 3x times smaller cell count. Not only that, it has been confirmed also that the optimized mesh gives results in the RPL burner which are as accurate as those obtained with the 35M mesh despite slightly less refined mesh in the RPL burner.

Pilot tip & Main 1 out

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5.5.5.5 The pilot tip

The Figure 59 and the Figure 60 suggest that the optimized mesh gives results associated with the equivalence ratio in the pilot burner also as accurate as the reference mesh. However, equivalence ratio values in this area are not even near the values obtained with the 35M mesh. This suggests that besides the RPL burner the pilot burner is also very mesh sensitive in terms of calculating the species transport equations. The Figure 60 shows the influence of much higher equivalence ratio directly downstream the pilot burner obtained with the 35M mesh shown in the detail view in the Figure 55 on page 64. Comparison of the equivalence ratio distribution obtained with the 35M mesh and the OPT1.4M mesh shows a similar distribution with a distinct difference – “a ring” of much higher equivalence ratio given by the 35M mesh. Obviously if higher accuracy in the pilot burner than expected to be obtained with the reference meshing approach even the mesh in the pilot burner needs to be refined.

Figure 60: Time averaged velocity and equivalence ratio distribution at the pilot tip

5.5.6 Refining the pilot mesh –OPT1.8M

The characteristic geometry of the 30° sector model allows relatively simple refinement of the pilot burner, without a large amount of redundant cells, with use of region adaption tool in the Fluent software. The optimal shape of the region to enclose the pilot burner geometry was in this case a cylinder. The optimal radius and position coordinates were found in the ICEM CFD software and the needed data about the cylinder were then transferred to Fluent. The position of the cylinder can be seen in the Figure 61.

Figure 61: The region in which the grid cells are adapted (splitted)

Pilot tip & Main 1 out

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Splitting cells in this small area resulted in additional 0.4 million cells which sums up to 1.8 million cells for the second optimized mesh which may be called the OPT1.8M mesh. There are, however, still many redundant cells which were created unintentionally but unavoidable. Most of them may be found around the RPL outlet where the cells were relatively small already before splitting. Cell sizes in the pilot burner are thus in the range of 0.1875-0.375 instead of 0.375-0.75 as in the OPT1.4M mesh. The adaption of the pilot burner results also in slightly more refined mesh in the pilot burner together with the pilot outlet area than in the 35M mesh which affects the results even further.

Referring back to the Figure 55 on page 64 large differences in equivalence ratio distribution directly downstream the pilot exit were observed. This affected also equivalence ratio distribution at the pilot tip as shown in the Figure 60. After refining the OPT1.4M mesh in the pilot burner the resulting equivalence ratio downstream the pilot outlet can be seen in the Figure 61.

Figure 62: Equivalence ratio distribution directly downstream the pilot exit obtained with the OPT1.8M mesh

and the 35M mesh

The equivalence ratio distribution is due to even more refined mesh in that area comparing to the 35M mesh also more refined which suggests that even the 35M mesh was not refined enough in the area to reach mesh independent solution. This fact opens a question whether even smaller cells are needed in the pilot burner area to reach theoretical mesh independency in the area. Nevertheless, the problematic area illustrated by the graph f) in the Figure 58 found on page 67 is now corrected as seen in the Figure 63. Equivalence ratio distribution along Line 1 in that part of the domain is now almost identical to that obtained with the 35M mesh.

Figure 63: Equivalence ratio distribution discrepancy along Line 1 corrected with the OPT1.8M mesh

Pilot out

RPL out

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The Figure 60 showed the influence of equivalence ratio distribution directly downstream the pilot outlet on distribution at the pilot tip. It might be interesting to see what difference does the mesh refinement in the pilot burner do at the pilot tip. Figure 64 shows that in this area the differences in equivalence ratio obtained with the OPT1.8M and the 35M mesh are undistinguishable. No significant changes in equivalence distribution downstream the pilot tip were observed therefore no additional figures showing the performance of the OPT1.8M mesh are shown here.

Figure 64: Predicted time averaged equivalence ratio distribution at the pilot tip obtained with the OPT1.8M and

the 35M mesh

5.5.7 Conclusion remarks for the 4th generation DLE burner mesh optimization

With respect to assumptions made for this mesh study it can be concluded that the established meshing approaches for the 4th generation DLE burner can be improved to better optimize cell count versus accuracy of the air/gas mixing simulations. It has been shown that the first optimized mesh, the OPT1.4M with 1.4 million elements, gives at least as good or even slightly more accurate results than the mesh created according to established meshing approaches with 3x smaller cell count. The OPT1.4M mesh is especially characterized by superior performance in the RPL burner which turned out to be very mesh sensitive even for general aerodynamics calculations.

It is not too far-fetched to state that the second optimized mesh with a refined pilot burner, the OPT1.8M mesh with 1.8 million elements, gives results that can be compared with the mesh that has 35 million elements (the 35M mesh). This consequently means that comparable results can be obtained with almost 20x lower cell count.

Saving a large number of elements was possible due to demonstrated low mesh dependency in the combustion chamber and the shown fact that a coarse mesh in the complete air casing does not influence flow conditions downstream where the air/gas mixing process begins. On the other hand it has been shown that the RPL and the pilot burner are very mesh sensitive and they both needed to be substantially refined. However, despite that fact the net cell count increase was still negative which lead to a relatively large decrease in cell count.

Pilot tip & Main 1 out

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6 DISCUSSION AND SUGGESTIONS FOR FUTURE WORK

THE SHORT 3RD GENERATION DLE BURNER STUDY

The first shorter part of this work involved a brief mesh study of the Siemens’ 3rd generation DLE burner for industrial gas turbines in the ignition stage of the burner’s operation. Furthermore a comparison of the results obtained with two different CFD solvers, Ansys CFX and Ansys Fluent, was performed. Simulations involved gas/air mixing in the 90° sector model therefore velocity field and distribution of equivalence ratio in the domain were of main interest. The brief mesh study was performed with only two meshes where the original mesh consisted of 2.8 million elements and the control mesh was created with region adaption tool in Fluent software which resulted in 22.7 million elements.

The differences in both velocity field and equivalence ratio obtained with both meshes were found to be minimal which suggests that the original mesh has an optimal ratio cell count versus accuracy for simulations performed with Fluent solver. On the other hand the comparison of the results between the solvers showed large discrepancies in both velocity field and equivalence ratio distribution despite identical mesh, boundary conditions and turbulence model used in both solvers. Despite the same turbulence model (k-ω SST) used in both solvers large difference in turbulent kinetic energy and turbulent eddy dissipation values were discovered – Fluent solver predicted significantly higher values. In search for finding an explanation it has been discovered that the k-ω SST turbulence model is slightly differently “tuned up” in both solvers. While most of model coefficients have practically the same values they are treated slightly differently. Among others uses Fluent solver more sophisticated blending functions used for blending of certain coefficients between values related to k-ε and k-ω turbulence models. The first suggestion for further study is therefore to investigate more in detail the implementations of otherwise very popular k-ω SST turbulence model in both solvers (i.e. blending functions, production limiters, etc.) and try to find the reasons for such large discrepancies. Different behaviour of turbulent models may therefore also to some degree affect discrepancies between the predicted velocity and equivalence ratio distribution, not only that, it has also been shown that both solvers use different discretization techniques which may also contribute to the discrepancies.

Comparing velocity field and equivalence ratio distribution obtained with two differently refined meshes within CFX solver showed significant differences. This observation suggests that CFX solver is more grid resolution sensitive than Fluent. This property can be associated with different discretization techniques employed by solvers. It has been suggested namely that the vertex centered finite volume method (employed by CFX solver) should be less accurate than the cell centered finite volume method (employed by Fluent) on the same tetrahedral mesh. The second suggestion for further study is therefore to investigate more in detail whether the Fluent solver is indeed less grid resolution sensitive as this short study suggests. Furthermore, as relatively large differences in velocity field obtained with both solvers are characterized by different position of stagnation point in the burner naturally a question arises which result is closer to reality. This trait may be relatively simply investigated experimentally in the atmospheric combustion rig with finding the position of the stagnation point.

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THE 4TH GENERATION DLE BURNER MESH OPTIMIZATION

There exist established meshing approaches for the new 4th generation DLE burner but mesh dependency has not been fully evaluated yet. Therefore the main goal of this extended mesh study in the main part of this work was to answer to the question whether it is possible to improve meshing approaches to better optimize cell count versus accuracy for this particular burner for air/gas mixing simulations.

Because 90° sector model was still too demanding to perform a mesh study with respect to available computer resources a 30° sector model was created instead. Despite some small geometrical assumptions made, the 30° sector model turned out to be a good representation of the 90° sector model and thereby a good representation of the full model. This was shown with comparison of two different models where established meshing approaches were applied which yield 12.1 million elements and 4.2 million cells for the 90° and 30° sector model respectively. The latter was used as a reference mesh for further mesh study among other additional meshes with different levels of refinement.

It has been shown that already a very coarse mesh (0.55 million elements for the 30° sector) gives fairly good general aerodynamics results while for accurate species transport equations solving a significantly more refined mesh is needed. In order to be able to get accurate results it has been shown that the RPL burner is very mesh sensitive even for general aerodynamics studies and both the RPL and the Pilot burner are very mesh sensitive in terms of solving species transport equations. The RPL and the Pilot burner need to have therefore significantly more refined mesh as it has been used so far with the established meshing approaches.

However, if similar accuracy as with the established meshing approaches is desired it has been shown that an optimized mesh with 1.4 million cells gives slightly better results than the reference mesh (4.2 million cells) for studying mixing processes in the burner and combustion chamber. The answer to the question given as the main goal of this thesis is therefore positive. Similar results as those obtained with the established meshing approaches may namely be obtained with 3x smaller cell count.

Furthermore it has been shown that if the pilot burner is suitably refined, which resulted in additional 0.4 million elements for the new mesh with 1.8 million elements, the results can be compared with the finest mesh used in this work that has 35 million cells. With a slight exaggeration can therefore be stated that a similar results as those obtained with the finest mesh can be obtained with almost 20x smaller cell count.

The suggested meshing approaches can still be slightly more optimized with removing excess cells in the front part of the combustion chamber with better manipulation of density boxes in meshing software, and especially in the area around the RPL and the pilot burner outlet where the region adaption tool created some redundant elements. The first suggestion for further study is therefore to create a new mesh according to suggested approaches and if specified areas are optimized a new mesh should probably have between 1.4 and 1.6 instead of 1.8 million elements. In this context it might eventually be interesting to investigate to what degree the pilot burner must be refined to reach mesh independency.

A large portion of available time for this work was devoted to find a cost effective steady state solution which was unfortunately unsuccessful for this case. The only option was therefore to employ time dependent simulations with time statistics sampling. One of the main reasons that time dependent simulations for this case are so time consuming is a very small time step size needed (10-5s in this study). A brief time step size study showed that for resolving velocity field the time step size may be larger but no certain conclusion could be made concerning solving species transport equations. The second suggestion for further study is

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therefore to perform a time step study to investigate if it is possible to accelerate very time consuming transient calculations with raising the time step size.

The third suggestion for further study would be to test this meshing approach on a 90° sector model or on a full model. It would be also interesting to test the performance of the optimized mesh with Ansys CFX solver. Would CFX solver for this case show similar behaviour as observed in the first part of this work?

This mesh study and resulting optimized mesh is, maybe needless to say, applicable to simulations performed with Eddy viscosity based turbulence models only. For employing more sophisticated turbulence models like LES or SAS a new mesh study with slightly different approach (i.e. only full 360° model is applicable) needs to be performed. This may also be a good suggestion for further study.

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[21] Turbulent Flows, Stephen B. Pope, Cornell University, Cambridge university press, 2000

[22] Comparison and evaluation of cell-centered and cell-vertex discretization in the unstructured TAU code for turbulent viscous flow; Gang Wang, Axel Schwope, Ralf Heinrich; DLR, Institute of Aerodynamics and Flow Technology, Lilienthalplatz 7, 38108 Braunschweig, Germany. V European Conference on Computational Fluid Dynamics

[23] Concepts for Scientific Computing; R. Heinzl; http://www.iue.tuwien.ac.at/phd/heinzl/node25.html; accessed 2015/09

[24] A brief review of simple finite volume schemes using triangular meshes; Sanderson L., Gonzaga de Oliviera; DCC, UFLA, 37200-000, Lavras

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[27] Prediction of ignition limits with respect to fuel fraction of inert gases; Johan Sjölander; Master thesis, Umeå university and Siemens Industrial Turbomachinery, 2015

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[32] Experimental and numerical investigation of a combustor model; Darioush G Barhagi, Jacek Janczevski, Thomas Larsson; Siemens Industrial Turbomachinery AB; Proceedings of ASME Turbo Expo 2011,GT2011, June 6-10, 2011, Vancouver, British Columbia, Canada

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APPENDIX

MATLAB code for processing monitor points data

----------------------------------------------------------------------------------------------------------------- clear all close all %%%%%%%%%%%%%%----INSERT FILE NAMES-----%%%%%%%%%%%%%%%%% files=['point-1-main-1-vel.out ' %35 characters 'point-1-main-1-ch4.out ' 'point-2-main-2-vel.out ' 'point-2-main-2-ch4.out ' 'point-3-main-in-2-vel.out ' 'point-4-air-in-vel.out ' 'point-5-pilot-out-vel.out ' 'point-6-rpl-out-vel.out ' 'point-7-chamber-cent-fwd-vel.out ' 'point-8-chamber-cent-mid-ch4.out ' 'point-8-chamber-cent-mid-vel.out ' 'point-9-chamber-upp-bck-vel.out ' 'point-10-chamber-upp-fwd.out ' 'point-10-chamber-upp-fwd-ch4.out ' %%% New Points %%% 'point-11-m1-behind-rod-ch4.out ' 'point-11-m1-behind-rod-vel.out ' 'point-12-m2-behind-rod-ch4.out ' 'point-12-m2-behind-rod-vel.out ' 'point-13-m2-exit-ch4.out ' 'point-13-m2-exit-vel.out ' 'point-14-swirl-m1-vel.out ' 'point-15-swirl-m2-vel.out ' 'point-16-rpl-inside-ch4.out ' 'point-16-rpl-inside-vel.out ' 'point-17-rpl-throat-ch4.out ' 'point-17-rpl-throat-vel.out ' 'point-18-chamber-fillet-ch4.out ' 'point-18-chamber-fillet-vel.out ' ]; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% nfiles=size(files,1); cases=[1 2 3 5 6 7]; % Choose which cases to compare for i=cases for j=1:nfiles readData(:,j) = dlmread(fullfile... ('H:\My Documents\SGT-750\SGT-750_30d\30d-FLUENT\The3Meshes_TRANSIENT\'... ,num2str(i),num2str(files(j,:))),' ',2,1); dataCell{1,i}=readData; end clear readData end %% %%%%%% Calculating Running Average %%%%%%%% for k=cases it=length(dataCell{1,k}); for l=1:nfiles ra{1,k}(1,l)=dataCell{1,k}(1,l); % first entry for m=2:it ra{1,k}(m,l)=(ra{1,k}(m-1,l)*(m-1)+dataCell{1,k}(m,l))/m; end end end %%

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%%%%%%% Plotting %%%%%%%%%%%%%% C = {'r','b','g','k',[0.5 .2 0.1],'m',[.5 .6 .7]}; % Cell array of colors. autoLegend = {'0.55M', '4.3M','35M','My2M','SIT4.2M','OPT1.4M','OPT1.8M'}; % Names of the cases autoTitle = {'Point 1 - Velocity (Main 1)','Point 1 - CH4 (Main 1)','Point 2 - Velocity (Main 2)','Point 2 - CH4 (Main 2)',... 'Point 3 - Velocity (Main 2 In)','Point 4 - Velocity (Air In)','Point 5 - Velocity (Pilot Out)','Point 6 - Velocity (RPL Out)',... 'Point 7 - Velocity (Chamber Front Middle)','Point 8 - CH4 (Chamber Middle)','Point 8 - Velocity (Chamber Middle)',... 'Point 9 - Velocity (Chamber Outlet)','Point 10 - Velocity (Chamber Upper Front)','Point 10 - CH4 (Chamber Upper Front)',... 'Point 11 - CH4 (Behind Rod - Main 1)','Point 11 - Velocity (Behind Rod - Main 1)','Point 12 - CH4 (Behind Rod - Main 2)',... 'Point 12 - Velocity (Behind Rod - Main 2)','Point 13 - CH4 (Main 2 Exit)','Point 13 - Velocity (Main 2 Exit))',... 'Point 14 - Velocity (Main 1 - Swirler)','Point 15 - Velocity (Main 2 - Swirler)','Point 16 - CH4 (RPL Inside)',... 'Point 16 - Velocity (RPL Inside)','Point 17 - CH4 (RPL Throat)','Point 17 - Velocity (RPL Throat))',... 'Point 18 - CH4 (Chamber Wall Fillet)','Point 18 - Velocity (Chamber Wall Fillet)'}; autoYlabel = {'Velocity [m/s]','CH4 Mass Fraction','Velocity [m/s]','CH4 Mass Fraction','Velocity [m/s]','Velocity [m/s]',... 'Velocity [m/s]','Velocity [m/s]','Velocity [m/s]','CH4 Mass Fraction',... 'Velocity [m/s]','Velocity [m/s]','Velocity [m/s]','CH4 Mass Fraction',... 'CH4 Mass Fraction','Velocity [m/s]','CH4 Mass Fraction','Velocity [m/s]','CH4 Mass Fraction','Velocity [m/s]',... 'Velocity [m/s]','Velocity [m/s]','CH4 Mass Fraction','Velocity [m/s]',... 'CH4 Mass Fraction','Velocity [m/s]','CH4 Mass Fraction','Velocity [m/s]'}; for n=1:nfiles figure(n) for o=cases x=1:length(dataCell{1,o}); set(gca,'fontsize', 17); plot(x,dataCell{1,o}(:,n),'DisplayName',... ['Data - ' autoLegend{o}], 'Color',C{o} ); hold on plot(x,ra{1,o}(:,n),'LineWidth',2,'DisplayName'... ,['MMA - ' autoLegend{o}], 'Color',C{o}); grid on %title(num2str(files(n,:))) % Create title based on file name title(autoTitle{n}) xlabel('Time step') ylabel(autoYlabel{n}) end leg=legend(gca,'show','location','best'); set(leg,'FontSize',12); set(gcf,'PaperPositionMode','auto') print(figure(n),autoTitle{n},'-dpng','-r0') %%%Save to file end

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