cfd supercritical airfoils
TRANSCRIPT
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CFD ANALYSIS OF SUPERCRITICAL AIRFOIL OVER SIMPLE AIRFOIL
A Thesis Submitted in Partial Fulfilment of the
Requirements for the Degree
By
Shantanu Khanna
(R180207050)
Under the Guidence of
Dr. Ugur Guven
Professor of Aerospace Engineering (Ph.D)
Nuclear Science and Technology Engineer (M.sc)
College of Engineering
University of Petroleum and Energy Studies,
Dehradun
May, 2011
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CFD ANALYSIS OF SUPERCRITICAL AIRFOIL OVER SIMPLE AIRFOIL
A Thesis Submitted in Partial Fulfilment of the
Requirements for the Degree
By
Shantanu Khanna
(R180207050)
Under the Guidence of
Dr. Ugur Guven
Professor of Aerospace Engineering (Ph.D)
Nuclear Science and Technology Engineer (M.sc)
Approved
.......................................
Dean
College of Engineering
University of Petroleum and Energy Studies,
Dehradun
May, 2011
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CERTIFICATE
This is to certify that the work contained in this thesis titled “CFD Analysis of Supercritical Airfoil over Simple Airfoil” has been carried out by Shantanu Khanna under my supervision and has not been submitted elsewhere for a degree.
Dr.UGUR GUVEN
Professor of aerospace engineering
(April 15 2011)
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UNIVERSITY OF PETROLIUM AND ENTEGY STUDIES
CFD ANALYSIS OF SUPERCRITICAL AIRFOIL OVER SIMPLE AIRFOIL
Major Project by
Shantanu Khanna
Project Supervisor: Prof. Dr.Ugur GUVEN
Department: ASE
Program: B.Tech
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Forward I would like to express my deep appreciation and thanks for my advisor. This work is supported by Prof. Dr. Ugur GUVEN
April 2011
Shantanu Khanna
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Table of Contents
S.no Page no.
List of Tables.....................................................................................................3
List of Figures....................................................................................................4
Abstract..............................................................................................................6
Chapter 1: Introduction....................................................................................7
1.1 Supercritical Airfoil........................................................................................7
1.2 Features of Supercritical Airfoil.....................................................................8
1.2.1 Trailing Edge Thickness..................................................................8
1.2.2 Maximum Thickness.......................................................................8
1.2.3 Aft upper surface curvature.............................................................8
1.3 Airfoil Data....................................................................................................8
Chapter 2: CFD Literature.............................................................................10
2.1. CFD (Computational Fluid Dynamics).......................................................10
2.1.1. Discretization Methods in CFD ...................................................10
2.1.1.1. Finite difference method (FDM)...................................10
2.1.1.2. Finite volume method (FVM).......................................11
2.1.1.3. Finite element method (FEM).......................................11
2.1.2. How does a CFD code work? ......................................................12
2.1.2.1. Pre-Processing ..............................................................13
2.1.2.2. Solver ...........................................................................16
2.1.2.3 Post-Processing: ............................................................17
2.1.3. Advantages of CFD......................................................................17
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Chapter 3: Analysing flow in CFD...................................................................19
3.1 Create geometry in Gambit............................................................................19
3.1.1 Import edge.....................................................................................19
3.1.2 Crete Farfield Boundary.................................................................19
3.1.3 Create Face.....................................................................................20
3.2 Mesh geometry in Gambit............................................................................20
3.2.1 Mesh Edges...................................................................................20
3.2.2 Mesh Face.....................................................................................21
3.3 Specify Boundary Types in Gambit............................................................21
3.3.1 Define Boundary Types................................................................21
3.4 Set up problem in Fluent.............................................................................21
3.5 Solve...........................................................................................................24
Chapter 4: Analysis........................................................................................25
Chapter 5: Conclusion...................................................................................46
5.1 Pressure drag……………………………………………………………..46
5.2 Shock wave strength..................................................................................46
REFRENCE...................................................................................................47
APPENDIX....................................................................................................48
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List of Table
S.no Page no
Table 1.1: Specification of NACA SC(2) 0714.....................................................8
Table 1.2 : Specifications of NACA 4412 airfoil..................................................9
Table 5.1; Pressure Drag.....................................................................................46
Table 5.2: Strength of Shockwave......................................................................46
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List of Figures
S.no Page no.
Figure 1.1: Supercritical Airfoil..........................................................................7
Figure 2.1: Algorithm of numerical approach used by simulation softwares.......15
Figure 3.1: Import Edges......................................................................................19
Figure 3.2: Meshing..............................................................................................21
Figure 3.2: Model Solver......................................................................................23
Figure 3.4: Model Viscous...................................................................................24
Figure 3.5: Defining Boundary condition............................................................25
Figure 4.1: Contours of static pressure.................................................................25
Figure 4.2: Contours of dynamic pressure............................................................26
Figure 4.3: Contours of total pressure..................................................................26
Figure 4.4: Contours of static temperature...........................................................27
Figure 4.5: Contours of total temperature............................................................27
Figure 4.6: Contours of velocity magnitude........................................................28
Figure 4.7: Velocity vectors.................................................................................28
Figure 4.8: Contours of static pressure.................................................................29
Figure 4.9: Contours of dynamic pressure...........................................................29
Figure 4.10: Contours of total pressure...............................................................30
Figure 4.11: Contours of static temperature........................................................30
Figure 4.12: Contours of total temperature.........................................................31
Figure 4.13: Contours of velocity magnitude.....................................................31
Figure 4.14: Velocity vectors..............................................................................32
Figure 4.15: Contours of static pressure..............................................................32
Figure 4.16: Contours of dynamic pressure.........................................................33
Figure 4.17: Contours of total pressure................................................................33
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Figure 4.18: Contours of static temperature.........................................................34
Figure 4.19: Contours of total temperature..........................................................34
Figure 4.20: Contours of velocity magnitude.......................................................35
Figure 4.21: Velocity vectors................................................................................35
Figure 4.22: Contours of static pressure................................................................36
Figure 4.23: Contours of dynamic pressure...........................................................36
Figure 4.24: Contours of total pressure.................................................................37
Figure 4.25: Contours of static temperature..........................................................37
Figure 4.26: Contours of total temperature............................................................38
Figure 4.27: Contours of velocity magnitude........................................................38
Figure 4.28: Velocity vectors.................................................................................39
Figure 4.29: Contours of static pressure.................................................................39
Figure 4.30: Contours of dynamic pressure............................................................40
Figure 4.31: Contours of total pressure...................................................................40
Figure 4.32: Contours of static temperature............................................................41
Figure 4.33: Contours of total temperature..............................................................41
Figure 4.34: Contours of velocity magnitude...........................................................42
Figure 4.35: Velocity vectors...................................................................................42
Figure 4.36: Contours of static pressure...................................................................43
Figure 4.37: Contours of dynamic pressure..............................................................43
Figure 4.38: Contours of total pressure.....................................................................44
Figure 4.39: Contours of static temperature..............................................................44
Figure 4.40: Contours of total temperature...............................................................45
Figure 4.41: Contours of velocity magnitude............................................................45
Figure 4.42: Velocity vectors......................................................................................46
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ABSTRACT
In this project flow over supercritical airfoil and conventional airfoil is compared at
Mach number 0.6. Parameters which are observed are Pressure drag and Strength of
shockwave as they are one of the parameters which are prominent in transonic speed.
Software tools used are GAMBIT and FLUENT. Gambit is used for preparing the
geometry and meshing and FLUENT is used for analysing the flow. Computational
fluid dynamics is used because preparing a model of airfoil is a lengthy and difficult
process and wind tunnel capable of 0.6 Mach number is not available. CFD gives
99% accurate results.
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Chapter 1: INTRODUCTION
1.1 Supercritical Airfoil
Transonic Jet aircrafts fly at speed of .8-.9 Mach number. At these speeds speed of
air reaches speed of sound somewhere over the wing and compressibility effects start
to show up. The free stream Mach number at which local sonic velocities develop is
called critical Mach number. It is always better to increase the critical mach number
so that formation of shockwaves can be delayed. This can be done either by
sweeping the wings but high sweep is not recommended in passenger aircrafts as
there is loss in lift in subsonic speed and difficulties during constructions. So
engineers thought of developing an airfoil which can perform this task without loss
in lift and increase in drag. They increased the thickness of the leading edge and
made the upper surface flat so that there is no formation of strong shockwave and
curved trailing edge lower surface which increases the pressure at lower surface and
accounts’ for lift.
Figure 1.1: Supercritical Airfoil.
1.2 Features of Supercritical Airfoil
1.2.1 Trailing Edge Thickness
The design philosophy of the supercritical airfoil required that the trailing-edge
slopes of the upper and lower surfaces be equal. This requirement served to retard
flow separation by reducing the pressure recovery gradient on the upper surface so
that the pressure coefficients recovered to only slightly positive values at the trailing
edge. Increasing the trailing-edge thickness of an interim ll-percent-thick
supercritical airfoil from 0 to 1.0 percent of the chord resulted in a significant
decrease in wave drag at transonic Mach numbers; however, this decrease was
achieved at the expense of higher drag at subcritical Mach numbers.
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1.2.2 Maximum Thickness
For the thinner airfoil, the onset of trailing-edge separation began at an
approximately 0.1 higher normal-force coefficient at the higher test Mach numbers,
and the drag divergence Mach number at a normal-force coefficient of 0.7 was 0.01
higher. Both effects were associated with lower induced velocities over the thinner
airfoil.
1.2.3 Aft upper surface curvature
The rear upper surface of the supercritical airfoil is shaped to accelerate the flow
following the shock wave in order to produce a near-sonic plateau at design
conditions.
1.3 Airfoil Data
There are two airfoils chosen for this analysis one is supercritical and other is
conventional airfoil. Super critical airfoil chosen for this project is NACA SC(2)
0714 and NACA 4412 which is conventional airfoil.
Table 1.1: Specification of NACA SC(2) 0714
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Table 1.2 : Specifications of NACA 4412 airfoil
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Chapter 2: CFD Literature
2.1. CFD (Computational Fluid Dynamics)
CFD is one of the branches of fluid mechanics that uses numerical methods and
algorithms to solve and analyze problems that involve fluid flows. Computers are
used to perform the millions of calculations required to simulate the interaction of
fluids and gases with the complex surfaces used in engineering. However, even with
simplified equations and high speed supercomputers, only approximate solutions can
be achieved in many cases. More accurate codes that can accurately and quickly
simulate even complex scenarios such as supersonic or turbulent flows are an
ongoing area of research.
2.1.1. Discretization Methods in CFD
There are three discretization methods in CFD:
1. Finite difference method (FDM)
2. Finite volume method (FVM)
3. Finite element method (FEM)
2.1.1.1. Finite difference method (FDM)
A finite difference method (FDM) discretization is based upon the differential form
of the PDE to be solved. Each derivative is replaced with an approximate difference
formula (that can generally be derived from a Taylor series expansion). The
computational domain is usually divided into hexahedral cells (the grid), and the
solution will be obtained at each nodal point. The FDM is easiest to understand when
the physical grid is Cartesian, but through the use of curvilinear transforms the
method can be extended to domains that are not easily represented by brick-shaped
elements. The Discretization results in a system of equation of the variable at nodal
points, and once a solution is found, then we have a discrete representation of the
solution.
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2.1.1.2. Finite volume method (FVM)
A finite volume method (FVM) discretization is based upon an integral form of the
PDE to be solved (e.g. conservation of mass, momentum, or energy). The PDE is
written in a form which can be solved for a given finite volume (or cell). The
computational domain is discretized into finite volumes and then for every volume
the 12 governing equations are solved. The resulting system of equations usually
involves fluxes of the conserved variable, and thus the calculation of fluxes is very
important in FVM. The basic advantage of this method over FDM is it does not
require the use of structured grids, and the effort to convert the given mesh in to
structured numerical grid internally is completely avoided. As with FDM, the
resulting approximate solution is a discrete, but the variables are typically placed at
cell centers rather than at nodal points. This is not always true, as there are also face-
centered finite volume methods. In any case, the values of field variables at non-
storage locations (e.g. vertices) are obtained using interpolation.
2.1.1.3. Finite element method (FEM)
A finite element method (FEM) discretization is based upon a piecewise
representation of the solution in terms of specified basis functions. The
computational domain is divided up into smaller domains (finite elements) and the
solution in each element is constructed from the basis functions. The actual equations
that are solved are typically obtained by restating the conservation equation in weak
form: the field variables are written in terms of the basis functions, the equation is
multiplied by appropriate test functions, and then integrated over an element. Since
the FEM solution is in terms of specific basis functions, a great deal more is known
about the solution than for either FDM or FVM. This can be a double-edged sword,
as the choice of basis functions is very important and boundary conditions may be
more difficult to formulate. Again, a system of equations is obtained (usually for
nodal values) that must be solved to obtain a solution.
Comparison of the three methods is difficult, primarily due to the many variations of
all three methods. FVM and FDM provide discrete solutions, while FEM provides a
continuous (up to a point) solution. FVM and FDM are generally considered easier to
program than FEM, but opinions vary on this point. FVM are generally expected to
provide better conservation properties, but opinions vary on this point also.
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2.1.2. How does a CFD code work?
CFD codes are structured around the numerical algorithms that can be tackle fluid
problems. In order to provide easy access to their solving power all commercial CFD
packages include sophisticated user interfaces input problem parameters and to
examine the results. Hence all codes contain three main elements: 13
1. Pre-processing.
2. Solver
3. Post-processing.
2.1.2.1. Pre-Processing
This is the first step in building and analyzing a flow model. Preprocessor consist of
input of a flow problem by means of an operator –friendly interface and subsequent
transformation of this input into form of suitable for the use by the solver. The user
activities at the Pre-processing stage involve:
• Definition of the geometry of the region: The computational domain.
• Grid generation the subdivision of the domain into a number of smaller, non-
overlapping sub domains (or control volumes or elements Selection of physical or
chemical phenomena that need to be modeled).
• Definition of fluid properties
• Specification of appropriate boundary conditions at cells, which coincide with or
touch the boundary. The solution of a flow problem (velocity, pressure, temperature
etc.) is defined at nodes inside each cell. The accuracy of CFD solutions is governed
by number of cells in the grid. In general, the larger numbers of cells better the
solution accuracy. Both the accuracy of the solution & its cost in terms of necessary
computer hardware & calculation time are dependent on the fineness of the grid.
Efforts are underway to develop CFD codes with a (self) adaptive meshing
capability. Ultimately such programs will automatically refine the grid in areas of
rapid variation.
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GAMBIT (CFD PREPROCESSOR) GAMBIT is a state-of-the-art preprocessor
for engineering analysis. With advanced geometry and meshing tools in a powerful,
flexible, tightly-integrated, and easy-to use interface, GAMBIT can dramatically
reduce preprocessing times for many applications. Complex models can be built
directly within GAMBIT‘s solid geometry modeler, or imported from any major
CAD/CAE system. Using a virtual geometry overlay and advanced cleanup tools,
imported geometries are quickly converted into suitable flow domains. A
comprehensive set of highly-automated and size function driven meshing tools
ensures that the best mesh can be generated, whether structured, multiblock,
unstructured, or hybrid. 14
2.1.2.2. Solver
The CFD solver does the flow calculations and produces the results. FLUENT,
FloWizard, FIDAP, CFX and POLYFLOW are some of the types of solvers.
FLUENT is used in most industries. FloWizard is the first general-purpose rapid
flow modeling tool for design and process engineers built by Fluent. POLYFLOW
(and FIDAP) are also used in a wide range of fields, with emphasis on the materials
processing industries. FLUENT and CFX two solvers were developed independently
by ANSYS and have a number of things in common, but they also have some
significant differences. Both are control-volume based for high accuracy and rely
heavily on a pressure-based solution technique for broad applicability. They differ
mainly in the way they integrate the fluid flow equations and in their equation
solution strategies. The CFX solver uses finite elements (cell vertex numerics),
similar to those used in mechanical analysis, to discretize the domain. In contrast, the
FLUENT solver uses finite volumes (cell centered numerics). CFX software focuses
on one approach to solve the governing equations of motion (coupled algebraic
multigrid), while the FLUENT product offers several solution approaches (density-,
segregated- and coupled-pressure-based methods)
The FLUENT CFD code has extensive interactivity, so we can make changes to the
analysis at any time during the process. This saves time and enables to refine designs
more efficiently. Graphical user interface (GUI) is intuitive, which helps to shorten
the learning curve and make the modeling process faster. In addition, FLUENT's
adaptive and dynamic mesh capability is unique and works with a wide range of
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physical models. This capability makes it possible and simple to model complex
moving objects in relation to flow. This solver provides the broadest range of
rigorous physical models that have been validated against industrial scale
applications, so we can accurately simulate real-world conditions, including
multiphase flows, reacting flows, rotating equipment, moving and deforming objects,
turbulence, radiation, acoustics and dynamic meshing. The FLUENT solver has
repeatedly proven to be fast and reliable for a wide range of CFD applications. The
speed to solution is faster because suite of software enables us to stay within one
interface from geometry building through the solution process, to post-processing
and final output. 15
The numerical solution of Navier–Stokes equations in CFD codes usually implies a
discretization method: it means that derivatives in partial differential equations are
approximated by algebraic expressions which can be alternatively obtained by means
of the finite-difference or the finite-element method. Otherwise, in a way that is
completely different from the previous one, the discretization equations can be
derived from the integral form of the conservation equations: this approach, known
as the finite volume method, is implemented in FLUENT (FLUENT user‘s guide,
vols. 1–5, Lebanon, 2001), because of its adaptability to a wide variety of grid
structures. The result is a set of algebraic equations through which mass, momentum,
and energy transport are predicted at discrete points in the domain. In the freeboard
model that is being described, the segregated solver has been chosen so the
governing equations are solved sequentially. Because the governing equations are
non-linear and coupled, several iterations of the solution loop must be performed
before a converged solution is obtained and each of the iteration is carried out as
follows:
(1) Fluid properties are updated in relation to the current solution; if the calculation is
at the first iteration, the fluid properties are updated consistent with the initialized
solution.
(2) The three momentum equations are solved consecutively using the current value
for pressure so as to update the velocity field.
(3) Since the velocities obtained in the previous step may not satisfy the continuity
equation, one more equation for the pressure correction is derived from the
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continuity equation and the linearized momentum equations: once solved, it gives the
correct pressure so that continuity is satisfied. The pressure–velocity coupling is
made by the SIMPLE algorithm, as in FLUENT default options.
(4) Other equations for scalar quantities such as turbulence, chemical species and
radiation are solved using the previously updated value of the other variables; when
inter-phase coupling is to be considered, the source terms in the appropriate
continuous phase equations have to be updated with a discrete phase trajectory
calculation.
(5) Finally, the convergence of the equations set is checked and all the procedure is
repeated until convergence criteria are met. (Ravelli et al., 2008) 16
Figure 2.1: Algorithm of numerical approach used by simulation softwares
The conservation equations are linearized according to the implicit scheme with
respect to the dependent variable: the result is a system of linear equations (with one
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equation for each cell in the domain) that can be solved simultaneously. Briefly, the
segregated implicit method calculates every single variable field considering all the
cells at the same time. The code stores discrete values of each scalar quantity at the
cell centre; the face values must be interpolated from the cell centre values. For all
the scalar quantities, the interpolation is carried out by the second order upwind
scheme with the purpose of achieving high order accuracy. The only exception is
represented by pressure interpolation, for which the standard method has been
chosen. Ravelli et al., 2008). 17
2.1.2.3 Post-Processing:
This is the final step in CFD analysis, and it involves the organization and
interpretation of the predicted flow data and the production of CFD images and
animations. Fluent's software includes full post processing capabilities. FLUENT
exports CFD's data to third-party post-processors and visualization tools such as
Ensight, Fieldview and TechPlot as well as to VRML formats. In addition, FLUENT
CFD solutions are easily coupled with structural codes such as ABAQUS, MSC and
ANSYS, as well as to other engineering process simulation tools.
Thus FLUENT is general-purpose computational fluid dynamics (CFD) software
ideally suited for incompressible and mildly compressible flows. Utilizing a
pressure-based segregated finite-volume method solver, FLUENT contains physical
models for a wide range of applications including turbulent flows, heat transfer,
reacting flows, chemical mixing, combustion, and multiphase flows. FLUENT
provides physical models on unstructured meshes, bringing you the benefits of easier
problem setup and greater accuracy using solution-adaptation of the mesh. FLUENT
is a computational fluid dynamics (CFD) software package to simulate fluid flow
problems. It uses the finite-volume method to solve the governing equations for a
fluid. It provides the capability to use different physical models such as
incompressible or compressible, inviscid or viscous, laminar or turbulent, etc.
Geometry and grid generation is done using GAMBIT which is the preprocessor
bundled with FLUENT. Owing to increased popularity of engineering work stations,
many of which has outstanding graphics capabilities, the leading CFD are now
equipped with versatile data visualization tools. These include
Domain geometry & Grid display.
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Vector plots.
Line & shaded contour plots.
2D & 3D surface plots.
Particle tracking.
View manipulation (translation, rotation, scaling etc.)
2.1.3. Advantages of CFD
Major advancements in the area of gas-solid multiphase flow modeling offer
substantial process improvements that have the potential to significantly improve
process plant operations. Prediction of gas solid flow fields, in processes such as
pneumatic transport lines, risers, 18
fluidized bed reactors, hoppers and precipitators are crucial to the operation of most
process plants. Up to now, the inability to accurately model these interactions has
limited the role that simulation could play in improving operations. In recent years,
computational fluid dynamics (CFD) software developers have focused on this area
to develop new modeling methods that can simulate gas-liquid-solid flows to a much
higher level of reliability. As a result, process industry engineers are beginning to
utilize these methods to make major improvements by evaluating alternatives that
would be, if not impossible, too expensive or time-consuming to trial on the plant
floor. Over the past few decades, CFD has been used to improve process design by
allowing engineers to simulate the performance of alternative configurations,
eliminating guesswork that would normally be used to establish equipment geometry
and process conditions. The use of CFD enables engineers to obtain solutions for
problems with complex geometry and boundary conditions. A CFD analysis yields
values for pressure, fluid velocity, temperature, and species or phase concentration
on a computational grid throughout the solution domain. Advantages of CFD can be
summarized as:
1. It provides the flexibility to change design parameters without the expense of
hardware changes. It therefore costs less than laboratory or field experiments,
allowing engineers to try more alternative designs than would be feasible otherwise.
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2. It has a faster turnaround time than experiments.
3. It guides the engineer to the root of problems, and is therefore well suited for
trouble-shooting.
4. It provides comprehensive information about a flow field, especially in regions
where measurements are either difficult or impossible to obtain.
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Chapter 3: Analysing flow in CFD
3.1 Create geometry in Gambit
3.1.1 Import edge
To specify the airfoil geometry we will import a file containing a list of vertices
along the surface and have GAMBIT join these vertices to create edge,
corresponding to the surface of the airfoil.
Main Menu >File >Input >ICEM input
Figure 3.1: Import Edges
3.1.2 Crete Farfield Boundary
We will create the farfield boundary by creating vertices and joining them
appropriately to form edges.
Operation Toolpad >Geometry Command Button >Vertex Command Button >Create
Vertex
Label X Y Z
A -12 12 0
B 12 12 0
C 12 -12 0
D -12 -12 0
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Operation Toolpad >Geometry Command Button >Edge Command Button >Create
Edge
Create edges AB, BC, CD, DA by selecting the vertices
3.1.3 Create Face
We will create the face by selecting the edges AB, BC, CD, DA naming the face
Farfield.
Operation Toolpad >Geometry Command Button >Face Command Button >Form
Face
By selecting the airfoil edges make an airfoil face naming Airfoil.
Before proceeding to the next step we will subtract the faces, subtracting face Airfoil
from Farfield.
Operation Toolpad >Geometry Command Button >Face Command Button
Click on the Boolean Operations Button and select Subtract Face Box select Farfield
in upper box and Airfoil in lower box click apply.
3.2 Mesh geometry in Gambit
3.2.1 Mesh Edges
Operation Toolpad >Mesh Command Button >Edge Command Button >Mesh Edges
Taking interval count 50 we mesh the edges AB, BC, CD, DA.
3.2.2 Mesh Face
Operation Toolpad >Mesh Command Button >Face Command Button >Mesh Faces
Taking interval count 100 we mesh the face Farfield
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Figure 3.2: Meshing
3.3 Specify Boundary Types in Gambit
3.3.1 Define Boundary Types
Operation Toolpad >Zone Command Button >Specify Boundary Types
Under entity select Edges and select AB, CD as Prssure_Farfield, DA as
Velocity_Inlet, BC as Peassure_Outlet.
Save the work and Export Mesh.
Main Menu >File >Save
Main Menu >File >Export >Mesh
3.4 Set up problem in Fluent
Import File
Main Menu >File >Read Case
Check Grid
Main Menu >Grid >Check
Define Properties
Define >Model >Solver
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Figure 3.2: Model Solver
Under Solver select Density based Solver and in Gradient option select Green-Gause
node based.
Define >Model >Viscous
Under Viscous select K-epsilon
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Figure 3.4: Model Viscous
Define >Model >Energy
Turn On the Energy equation
Define >Materials
Make sure that air is selected under Fluid Material and set Density to Ideal Gas
Define >Operating Conditions
Set Operating Pressure to be 101325 Pascal
Define >Boundary Conditions
Set the Velocity Magnitude to be 250 m/sec i.e around 0.6 Mach
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Figure 3.5: Defining Boundary condition
3.5 Solve
Solve >Control >Solution
Set Discretization to be Second Order Upwind for Flow, Turbulent Kinetic Energy,
Turbulent Dissipation Rate
Solve >Initialize >Initialize
Set Velocity_Inlet under compute form
Main Menu >File >Write >Case
Solve Iterate
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Chapter 4: Analysis
Supercritical airfoil at Zero degree
Figure 4.1 shows static pressure contour at 0.6 Mach number. From figure 4.1 it can be observed that there is high pressure of 35100 Pascal and at trailing edge pressure is -18200 Pascal. Resultant pressure is 53300 Pascal.
Figure 4.1: Contours of static pressure
Figure 4.2 shows dynamic contour at 0.6 Mach number. From figure 4.2 it can be observed that a weak shock is formed near the trailing edge of the airfoil. And at the lower surface of the trailing edge high pressure region is there which compensates for lift loss due to flat upper surface.
Figure 4.2: Contours of dynamic pressure
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Figure 4.3: Contours of total pressure
Figure 4.3 and figure 4.4 shows contours of total pressure and static temperature their behaviour is same as static pressure and dynamic pressure.
Figure 4.4: Contours of static temperature
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Figure 4.5: Contours of total temperature
Figure 4.6: Contours of velocity magnitude
Figure 4.6 shows velocity magnitude and figure 4.5 shows contour of total temperature. Figure 4.7 shows the velocity vectors over supercritical airfoil.
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Figure 4.7: Velocity vectors
Supercritical airfoil at Fifteen degree
Figure 4.8: Contours of static pressure
Figure 4.8 shows static pressure contour at 0.6 Mach number. From figure 4.8 it can be observed that there is high pressure of 35100 Pascal and at trailing edge pressure is -27700 Pascal. Resultant pressure is 62800 Pascal.
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Figure 4.9: Contours of dynamic pressure
Figure 4.9 shows dynamic contour at 0.6 Mach number. From figure 4.2 it can be observed that a weak shock is formed near the trailing edge of the airfoil. And at the lower surface of the trailing edge high pressure region is there which compensates for lift loss due to flat upper surface.
Figure 4.10: Contours of total pressure
Figure 4.10 shows contour of total pressure. Figure 4.11 and 4.12 shows contour of static temperature and total temperature the contours show same behaviour as static pressure and dynamic pressure.
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Figure 4.11: Contours of static temperature
Figure 4.12: Contours of total temperature
Figure 4.13 shows velocity magnitude and figure 4.14 shows velocity vectors. The contours behave same as contours of dynamic pressure.
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Figure 4.13: Contours of velocity magnitude
Figure 4.14: velocity vector
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Supercritical airfoil at Thirty degree
Figure 4.15 shows static pressure contour at 0.6 Mach number. From figure 4.15 it can be observed that there is high pressure of 71200 Pascal and at trailing edge pressure is -35000 Pascal. Resultant pressure is 106200 Pascal.
Figure 4.15: Contours of static pressure
Figure 4.16 shows dynamic contour at 0.6 Mach number. From figure 4.16 it can be observed that a weak shock is formed near the trailing edge of the airfoil. And at the lower surface of the trailing edge high pressure region is there which compensates for lift loss due to flat upper surface.
Figure 4.16: Contours of dynamic pressure
38
Figure 4.17: Contours of total pressure
Figure 4.18: Contours of static temperature
Figure 4.17 shows contours of total pressure this contour shows combined effect of static pressure and dynamic pressure. Figure 4.18 shows effect on static temperature and it shows same result as static pressure. Formation of shockwave leads to rise in temperature and total temperature also increases as shown in figure 4.19.
39
Figure 4.19: Contours of total temperature
Figure 4.20: Contours of velocity magnitude
Figure 4.20 shows velocity magnitude and 4.21 shows direction of velocity vectors the contours behave same as plots of dynamic pressure.
40
Figure 4.21: velocity vector
Simple airfoil at Zero degree
Figure 4.22: Contours of static pressure
Figure 4.22 shows static pressure contour at 0.6 Mach number. From figure 4.22 it can be observed that there is high pressure of 39200 Pascal and at trailing edge pressure is -18200 Pascal. Resultant pressure is 57400 Pascal.
41
Figure 4.23: Contours of dynamic pressure
Figure 4.23 shows dynamic contour at 0.6 Mach number. From figure 4.23 it can be observed that a weak shock is formed near the trailing edge of the airfoil. And at the lower surface of the trailing edge high pressure region is there which compensates for lift loss due to flat upper surface.
Figure 4.24: Contours of total pressure
Figure 4.24 shows contours of total pressure this contour shows combined effect of static pressure and dynamic pressure. Figure 4.25 shows effect on static temperature and it shows same result as static pressure. Figure 4.26 shows effect on dynamic temperature the formation of shockwave leads to rise in temperature and total temperature also increases as shown in figure 4.27.
42
Figure 4.25: Contours of static temperature
Figure 4.26: Contours of total temperature
Figure 4.27 shows velocity magnitude and 4.28 shows direction of velocity vectors the contours behave same as plots of dynamic pressure.
43
Figure 4.27: Contours of velocity magnitude
Figure 4.28: velocity magnitude
44
Simple airfoil at Fifteen degree
Figure 4.29 shows static pressure contour at 0.6 Mach number. From figure 4.29 it can be observed that there is high pressure of 41000 Pascal and at trailing edge pressure is -35100 Pascal. Resultant pressure is 76100 Pascal.
Figure 4.29: Contours of static pressure
Figure 4.30 shows dynamic contour at 0.6 Mach number. From figure 4.30 it can be observed that a weak shock is formed near the trailing edge of the airfoil. And at the lower surface of the trailing edge high pressure region is there which compensates for lift loss due to flat upper surface.
Figure 4.30: Contours of dynamic pressure
45
Figure 4.31 shows contours of total pressure this contour shows combined effect of static pressure and dynamic pressure. Figure 4.32 shows effect on static temperature and it shows same result as static pressure. The formation of shockwave leads to rise in temperature and total temperature also increases as shown in figure 4.33.
Figure 4.31: Contours of total pressure
Figure 4.31 shows contours of total pressure this contour shows combined effect of static pressure and dynamic pressure. Figure 4.32 shows effect on static temperature and it shows same result as static pressure. Figure 4.33 shows effect on dynamic temperature the formation of shockwave leads to rise in temperature and total temperature also increases as shown in figure 4.34.
Figure 4.32: Contours of static temperature
46
Figure 4.33: Contours of total temperature
Figure 4.34: Contours of velocity magnitude
Figure 4.34 shows velocity magnitude and 4.35 shows direction of velocity vectors the contours behave same as plots of dynamic pressure.
47
Figure 4.35: velocity vector
Simple airfoil at Thirty degree
Figure 4.36: Contours of static pressure
Figure 4.36 shows static pressure contour at 0.6 Mach number. From figure 4.36 it can be observed that there is high pressure of 41900 Pascal and at trailing edge pressure is -28800 Pascal. Resultant pressure is 70700 Pascal.
48
Figure 4.37: Contours of dynamic pressure
Figure 4.37 shows dynamic contour at 0.6 Mach number. From figure 4.37 it can be observed that a weak shock is formed near the trailing edge of the airfoil. And at the lower surface of the trailing edge high pressure region is there which compensates for lift loss due to flat upper surface.
Figure 4.38: Contours of total pressure
Figure 4.38 shows contours of total pressure this contour shows combined effect of static pressure and dynamic pressure. Figure 4.39 shows effect on static temperature and it shows same result as static pressure. The formation of shockwave leads to rise in temperature and total temperature also increases as shown in figure 4.40.
49
Figure 4.39: Contours of static temperature
Figure 4.40: Contours of total temperature
Figure 4.41 shows velocity magnitude and 4.42 shows direction of velocity vectors the contours behave same as plots of dynamic pressure.
50
Figure 4.41: Contours of velocity magnitude
Figure 4.42: velocity vector
51
Chapter 5: Conclusion
5.1 Pressure drag
Pressure Drag is calculated by taking difference in static pressure at leading edge and trailing edge. More difference means more pressure drag
Angle of Attack NACA 4412 NACA sc(2)0714
00 43130 Pascal 34995 Pascal
150 59600 Pascal 55400 Pascal
5.2 Shock wave strength
Strength of Shockwave is estimated by calculating the decrease in velocity.
Angle of Attack NACA 4412 NACA sc(2)0714
00 140 m/sec 113 m/sec
150 413 m/sec 148 m/sec
From above analysis I conclude that In case of Supercritical airfoil
at 00 angle of attack there is 18% decrement in pressure drag. at 150 angle of attack there is 7% decrement in pressure drag. at 00 angle of attack there is 19.2% decrement in strength of shockwave. at 150 angle of attack there is 64% decrement in strength of shockwave.
52
REFRENCE
Anderson, J.D(2001), Introduction to flight, New York, Tata Mc Grawhill
Anderson, J.D(2005), Introduction toAerodynamics, New York, Tata Mc Grawhill
URL:www.NASA.com
URL:www.cornelluniversitylectures.com
URL:www.aerospacelectures.co.cc
53
APPENDIX
A1: Airfoil data for NACA SC(2)0714
1.000000 -0.010400 0.990000 -0.007100 0.980000 -0.003900 0.970000 -0.000900 0.950000 0.004900 0.920000 0.013100 0.900000 0.018100 0.870000 0.025100 0.850000 0.029400 0.820000 0.035300 0.800000 0.038900 0.770000 0.043900 0.750000 0.046900 0.720000 0.050900 0.700000 0.053300 0.680000 0.055500 0.650000 0.058500 0.620000 0.061000 0.600000 0.062500 0.570000 0.064500 0.550000 0.065600 0.530000 0.066600 0.500000 0.067800 0.480000 0.068400
54
0.450000 0.069200 0.430000 0.069500 0.400000 0.069700 0.380000 0.069800 0.350000 0.069600 0.330000 0.069200 0.300000 0.068500 0.270000 0.067300 0.250000 0.066400 0.220000 0.064600 0.200000 0.063200 0.170000 0.060600 0.150000 0.058500 0.120000 0.054800 0.100000 0.051800 0.070000 0.046200 0.050000 0.041100 0.040000 0.038100 0.030000 0.034300 0.020000 0.029300 0.010000 0.021900 0.005000 0.015800 0.002000 0.009500 0.000000 0.000000 0.000000 0.000000
55
0.002000 -0.009300 0.005000 -0.016000 0.010000 -0.022100 0.020000 -0.029500 0.030000 -0.034400 0.040000 -0.038100 0.050000 -0.041200 0.070000 -0.046200 0.100000 -0.051700 0.120000 -0.054700 0.150000 -0.058500 0.170000 -0.060600 0.200000 -0.063300 0.220000 -0.064700 0.250000 -0.066600 0.280000 -0.068000 0.300000 -0.068700 0.320000 -0.069200 0.350000 -0.069600 0.370000 -0.069600 0.400000 -0.069200 0.420000 -0.068800 0.450000 -0.067600 0.480000 -0.065700 0.500000 -0.064400 0.530000 -0.061400
56
0.550000 -0.058800 0.580000 -0.054300 0.600000 -0.050900 0.630000 -0.045100 0.650000 -0.041000 0.680000 -0.034600 0.700000 -0.030200 0.730000 -0.023500 0.750000 -0.019200 0.770000 -0.015000 0.800000 -0.009300 0.830000 -0.004800 0.850000 -0.002400 0.870000 -0.001300 0.890000 -0.000800 0.920000 -0.001600 0.940000 -0.003500 0.950000 -0.004900 0.960000 -0.006600 0.970000 -0.008500 0.980000 -0.010900 0.990000 -0.013700 1.000000 -0.016300 A2: Airfoil data for NACA 4412
0.0000000 0.0000000 0
0.0005000 0.0023390 0
0.0010000 0.0037271 0
57
0.0020000 0.0058025 0
0.0040000 0.0089238 0
0.0080000 0.0137350 0
0.0120000 0.0178581 0
0.0200000 0.0253735 0
0.0300000 0.0330215 0
0.0400000 0.0391283 0
0.0500000 0.0442753 0
0.0600000 0.0487571 0
0.0800000 0.0564308 0
0.1000000 0.0629981 0
0.1200000 0.0686204 0
0.1400000 0.0734360 0
0.1600000 0.0775707 0
0.1800000 0.0810687 0
0.2000000 0.0839202 0
0.2200000 0.0861433 0
0.2400000 0.0878308 0
0.2600000 0.0890840 0
0.2800000 0.0900016 0
0.3000000 0.0906804 0
0.3200000 0.0911857 0
0.3400000 0.0915079 0
0.3600000 0.0916266 0
0.3800000 0.0915212 0
0.4000000 0.0911712 0
0.4200000 0.0905657 0
58
0.4400000 0.0897175 0
0.4600000 0.0886427 0
0.4800000 0.0873572 0
0.5000000 0.0858772 0
0.5200000 0.0842145 0
0.5400000 0.0823712 0
0.5600000 0.0803480 0
0.5800000 0.0781451 0
0.6000000 0.0757633 0
0.6200000 0.0732055 0
0.6400000 0.0704822 0
0.6600000 0.0676046 0
0.6800000 0.0645843 0
0.7000000 0.0614329 0
0.7200000 0.0581599 0
0.7400000 0.0547675 0
0.7600000 0.0512565 0
0.7800000 0.0476281 0
0.8000000 0.0438836 0
0.8200000 0.0400245 0
0.8400000 0.0360536 0
0.8600000 0.0319740 0
0.8800000 0.0277891 0
0.9000000 0.0235025 0
0.9200000 0.0191156 0
0.9400000 0.0146239 0
0.9600000 0.0100232 0
59
0.9700000 0.0076868 0
0.9800000 0.0053335 0
0.9900000 0.0029690 0
1.0000000 0 0
0.0000000 0.0000000 0
0.0005000 -.0046700 0
0.0010000 -.0059418 0
0.0020000 -.0078113 0
0.0040000 -.0105126 0
0.0080000 -.0142862 0
0.0120000 -.0169733 0
0.0200000 -.0202723 0
0.0300000 -.0226056 0
0.0400000 -.0245211 0
0.0500000 -.0260452 0
0.0600000 -.0271277 0
0.0800000 -.0284595 0
0.1000000 -.0293786 0
0.1200000 -.0299633 0
0.1400000 -.0302404 0
0.1600000 -.0302546 0
0.1800000 -.0300490 0
0.2000000 -.0296656 0
0.2200000 -.0291445 0
0.2400000 -.0285181 0
0.2600000 -.0278164 0
0.2800000 -.0270696 0
60
0.3000000 -.0263079 0
0.3200000 -.0255565 0
0.3400000 -.0248176 0
0.3600000 -.0240870 0
0.3800000 -.0233606 0
0.4000000 -.0226341 0
0.4200000 -.0219042 0
0.4400000 -.0211708 0
0.4600000 -.0204353 0
0.4800000 -.0196986 0
0.5000000 -.0189619 0
0.5200000 -.0182262 0
0.5400000 -.0174914 0
0.5600000 -.0167572 0
0.5800000 -.0160232 0
0.6000000 -.0152893 0
0.6200000 -.0145551 0
0.6400000 -.0138207 0
0.6600000 -.0130862 0
0.6800000 -.0123515 0
0.7000000 -.0116169 0
0.7200000 -.0108823 0
0.7400000 -.0101478 0
0.7600000 -.0094133 0
0.7800000 -.0086788 0
0.8000000 -.0079443 0
0.8200000 -.0072098 0
61
0.8400000 -.0064753 0
0.8600000 -.0057408 0
0.8800000 -.0050063 0
0.9000000 -.0042718 0
0.9200000 -.0035373 0
0.9400000 -.0028028 0
0.9600000 -.0020683 0
0.9700000 -.0017011 0
0.9800000 -.0013339 0
0.9900000 -.0009666 0
1.0000000 0 0