cfd les of jets in cross flow and its application.pdf

Flow, Turbulence and Combustion65: 177–203, 2000.© 2001Kluwer Academic Publishers. Printed in the Netherlands.

177

LES of Jets in Cross Flow and Its Applicationto a Gas Turbine Burner

J.U. SCHLÜTER and T. SCHÖNFELDCERFACS, 42, Av. Gaspard Coriolis, 31057 Toulouse Cedex 1, France

Received 14 December 1999; accepted in revised form 12 April 2000

Abstract. LES computations of jets in cross flow (JICF) were performed. Experimental investiga-tions reported in literature are reproduced with good agreement concerning the momentum field andthe mixing of a passive scalar. The results validate the ability of the present LES approach to computefuel injection of the type JICF. LES computations of fuel injection in an industrial gas turbine burnerare presented.

Key words: LES, jet in cross flow, mixing, gas turbine burner.

1. Introduction

The increasing demand in reducing pollutants in gas turbines [31] forces gas tur-bine manufacturers to investigate possibilities to mix fuel and oxydizer in the bestway possible before their ignition. It is well known that fuel rich combustionleads locally to higher temperatures and higher pollutant formations. AlthoughReynolds-averaged mean values might suggest a perfect mixedness, the unsteadynature of turbulent combustion may result in a temporally surplus of fuel in thecombustion chamber. Gas turbine manufacturers seek to avoid these conditions intheir burners as from the design stage on.

The motivation for this project originates in a demand from the Siemens PowerGeneration (KWU) company to undertake a Large Eddy Simulation (LES) analysisof a gas turbine burner configuration and to explore possibilities for using LES as adesign tool. Figure 1 shows such a gas turbine burner. It is of swirl type, where theswirl is induced by several circumferential vanes. The fuel (natural gas) is injectedon the surfaces of the vanes. In Figure 2 a close-up on the vane is shown, where airis coming from the left and the fuel is injected perpendicular to the airflow.

The objectives of this LES analysis are to determine the mixing quality of theburner and to track vortex developments around the vane, which might disturb lateron in the combustion chamber and potentially lead to combustion instabilities. Theproblem met herein is that measurements inside the burner are extremely difficult toachieve under operating conditions because of the limited access of measurementprobes and optical devices to the inner geometry of the burner. Measurements on

178 J.U. SCHLÜTER AND T. SCHÖNFELD

Figure 1. A Siemens gas turbine burner currently under investigation at CERFACS.

Figure 2. Close-up on the vane of the burner. The fuel is injected on the surface of the vanes.The air (from the left) and the fuel form a JICF.

the inlet and outlet of the burner have been made, but they are too far away fromthe fuel injection to give significant insight to the flow around the vane.

For this reason, a direct comparison between LES and measurement is nearlyimpossible to validate the LES results. Hence, before applying the LES approachto the gas turbine burner, a validation of the LES technique and the underlyingflow solver is done on simpler test cases. The ability of the underlying flow solverto reproduce foil flows has been shown previously [21], so that the description ofthe vane itself did not pose a problem. However, the ability of the flow solver toreproduce the fuel injection still had to be done. As a simplified test case the jet incross flow (JICF) has been chosen to investigate the fuel injection. Here, the vaneis replaced by a plane wall.

The computation of the burner flow requires a high number of mesh pointsto describe the principle flow features: the inlet flow, the vane flow, the injectorflow and the swirling flow at the outlet. The variety and number of different flow

LES OF JETS IN CROSS FLOW 179

problems encountered here will need each a high number of mesh points to describethe flow properly. It is desirable to know the minimum number of mesh points todescribe the different problems in order to keep low the total number of meshpoints in the full burner computation. Hence, the present investigations of the JICFare limited to computations on relatively coarse meshes.

2. Flow Physics of the Jet in Cross Flow

2.1. INTRODUCTION

The JICF has attracted attention in fluid mechanics research: turbine blade cooling,V/STOL aircrafts, roll control of missiles or chimney flows are examples of thewide field of applications, but most of the interest in research has been focused onthe application to combustors.

The JICF is a very pleasant flow configuration with regard to mixing. It is oneof the most effective way to mix two fluids in a limited space, which is superior toother flow constellations like the mixing layer or the jet in coflow [8].

Investigations on the JICF have started in the 1930s [28] with the mixing ofchimney plumes. Since, there have been numerous investigations on the JICF lead-ing to the perception, that the JICF, in contrast to other flow configurations likethe jet and the mixing layer, cannot be generalized in terms of self similarity andReynolds dependence, due to strong nonlinear effects. The systematic analysis ofthe JICF started in the 1970s with the discovery and acceptance of coherent struc-tures [9, 10]. A clear definition of coherent structures cannot be given. Hussain[15, 16] tries to define them as a “connected, large scale fluid mass with a phasecorrelated vorticity over his spatial extend”, but still this definition is incomplete.

However, coherent structures are able to explain various nonlinear effects in theJICF. Up to now, at least four different types of coherent structures are determinedin the JICF. They are shown in Figure 3. The most dominant vortex system is thecounterrotating vortex pair. The three other vortices, the jet shear layer vortices,the wake vortices and the horseshoe vortex are often called secondary vortices, asthey play a minor, although not neglectable role in the far field of the jet.

In the following some recent developments in JICF research are summarized.Note, that there exists an extensive review from Margason [19] from 1993.

2.2. THE MOMENTUM RATIO

The most dominant quantity to characterize a JICF is the momentum ratior definedas:

r =√

ρjetv2jet

ρcrossflowv2crossflow

. (1)


Figure 3. Vortex system for a jet in crossflow (from Fric and Roshko [13]).

In most cases the jet fluid and the crossflow fluid consist of the same species andhave the same temperature, henceρjet = ρcrossflow. The momentum ratio simplifiesthen to the velocity ratio:

r = vjet

vcrossflow. (2)

Different flow regimes can be determined based on the velocity ratior. JICFwith r < 0.5 play a special role. The jet flow is weaker than the crossflow. It is notable to break through the wall boundary layer of the crossflow and plays more therole of an obstacle for the crossflow. The far field of the jet is primarily governedby the oncoming boundary layer. This fact introduces a large number of additionalparameters to the investigations. Dependent on the wall boundary layer thicknessthis flow regime can occur up to a velocity ratio ofr = 1. This flow configurationis especially important for turbine blade coolings [7].

Velocity ratios r between 1 and 10 are common flow regimes for combustionapplications. The jet is then able to push through the boundary layer, which playsa minor role. The JICF is now determined by free turbulence characteristics andis easier reproducible. Andreopoulos [5] measured velocity profiles for JICF withvelocity ratios from 0.5 to 2, where the described transition from wall boundarylayer to free turbulence can be seen.

JICF with velocity ratios higher than 10 have additional effects as they behavemore and more like free jets with increasing velocity ratio.


Figure 4. Left: jet shear layer vortices and trajectory of the horseshoe vortex, right: horseshoevortex and recirculation bubble at the upstream edge of the jet orifice (from Kelso [18]).

2.3. VORTEX SYSTEMS

The mechanism for the formation of the counterrotating vortex pair (CVP) is notfully understood. It can be taken as certain, that the vorticity of the CVP has itsorigin at the sidewalls of the jet. Haven [14] investigated different nozzle geome-tries for the jet. Rectangular jets with a low aspect ratio (the edges at the sides ofthe jet are longer than the upstream and downstream edge) amplified the CVP. Thelonger sidewalls produce more vorticity, which can be found later in the CVP. Onthe other side, jets with a high aspect ratio have a weaker CVP.

Toy [30] investigated two closely spaced jets issuing into a crossflow. The jetswere either side-by-side or in-line. Hot-wire measurements on the centerline ofthe jets were made. As a major feature found, only one CVP, instead of two,was produced, when the jets were in a side-by-side setup. The data obtained, wasnot sufficient to give a reason for this behaviour. To the authors’ knowledge, amechanism which leads to a single CVP is not reported in literature.

The jet shear layer vortices are produced directly at the jet orifice (Figure 4).The two streams (jet stream and crossflow) form a mixing layer with a Kelvin–Helmholtz instability, which causes a roll-up near the edges of the jet.

The horseshoe vortex forms upstream of the jet at the crossflow wall. Theadverse pressure gradient at the crossflow wall forces the wall boundary layerto separate and to form a vortex. It is then convected and stretched by the flowand wraps around the jet nozzle like a necklace. The same kind of vortices canbe observed for flows where a boundary layer hits on an obstacle, e.g. a cylindermounted on a wall [6]. The vortex is in interaction with the upstream edge of thejet orifice, causing a separation bubble inside the jet (see also [17, 20]). Figure 4shows a sketch of the horseshoe vortex and the separation bubble.

The existence of the separation bubble was first proposed by Andreopoulos [2].He measured the velocities in the interior of the jet-pipe and found non-symmetricprofiles. In this investigation, the crossflow affects the jet-pipe flow up to 2D up-stream of the nozzle.


The wake vortices were first believed to be the consequence of a sheddingprocess behind the jet, with the jet acting like a solid cylinder and the wake vorticesbehaving like a von Kármán vortex street. However, Perry [20] pointed out, that inan incompressible fluid no vorticity can be produced inside the flow. The vorticitytransport equation for incompressible fluids:

Dω

Dt= ω · ∇u+ ν∇2ω (3)

shows a convection term on the left-hand side, a term which describes the reori-entation and stretching of the vorticity due to the velocity gradients and a viscousterm on the right-hand side, but no explicit production term. That means, in incom-pressible flows vorticity can only enter a flow by initial conditions and imposedwall boundaries, but not be generated in the interior, which would be the case, ifthe wake vortices would be shed from the jet like from a solid cylinder. Fric andRoshko [13] connected the wake vortices to a separation event at the cross flowwall at the sides of the jet nozzle. The end of the vortex string, which is close tothe nozzle is convected by the jet and follows the jet trajectory, while the other endstays close to the wall, bringing the vortex in an upright position.

2.4. PREVIOUS NUMERICAL INVESTIGATIONS OF THE JICF

The first numerical investigation of a JICF has been made by Sykes [29]. Hesimplified the calculation by using a slip wall as the crossflow wall. Hence, thecrossflow boundary layer is neglected and the horseshoe vortex and the wake vor-tices cannot be calculated. His results agree qualitatively with the measurements ofAndreopoulos [3, 5], besides a large error near the wall.

A numerical investigation from Chiu [11] tested the applicability of differentalgebraic turbulence models with the result, that the turbulence models do notimprove the calculations compared with a laminar calculation. It showed the limitsof an eddy viscosity model applied to free turbulence.

The investigation of Alvarez [1] used thek–ε model and a direct closure. Thedirect closure improved the calculations, but the error was still high.

The strong unsteady behaviour of the JICF leads to the conclusion, that anunsteady LES approach might be useful for reproducing and predicting the JICF.Yuan [32, 33] made an LES calculation of a JICF. He calculated a JICF with asmall Reynolds number (Re= 2100) on meshes with 1.3 million mesh points.The results agree quite well with measurements, although no direct comparisonis possible , because the Reynolds number is lower and the velocity ratio is notexactly the same as in the experimental references.

He pointed out, that it is necessary to mesh the pipe which supplies the jet, in hiscase on a length of one diameterD upstream. But, as Andreopoulos [2] mentioned,there is an interaction between the crossflow and the jet-flow. In the examined case(r = 2) the crossflow affects the pipe-flow around two diameters upstream the


pipe, so that his extension was probably not sufficient. The high number of meshpoints and the low Reynolds number make it difficult to apply this computation toindustrial configurations.

3. Mathematical Formulation of LES

3.1. GOVERNING EQUATIONS

The basic idea of LES is to resolve the larger scales of motion of the turbulencewhile approximating the smaller ones. To achieve this, a filter is applied to thecontinuity equation and the transport equations of momentum, energy and species.For reacting flows, often Favre filtering is used, which is defined as:

ρQ = ρQ =+∞∫−∞

ρQ(x, t)G(x − x′)dx′, (4)

leading to the following equations for momentumui and speciesYi:

• momentum(j = 1,2,3)

∂ρui

∂t+ ∂ρui uj

∂xi+ ∂p

∂xi= ∂τij

∂xj+ ∂Tij∂xj; (5)

• species mass fraction(k = 1, . . . , N)

∂ρYk

∂t+ ∂ρui Yk

∂xi= ∂

∂xi

(ρDk

∂Yk

∂xi

)+ ˜ωk + ∂9kj

∂xj. (6)

3.2. SUBGRID SCALE MODELS

The termsTij and9ik result from the convective termsuiuj and Ykui , which aresplit into a resolved part on the left-hand side of the equation, directly delivered bythe LES calculation, and an unresolved part on the right-hand side, which needs tobe modeled.

We used an eddy viscosity approach for the subgrid scales:

Tij = 2νt Sij + 1

3Tllδij (7)

with

Sij = 1

2

(∂ui

∂xj+ ∂uj∂xi

). (8)


Although the eddy viscosity approach is not valid for free turbulence, its simplic-ity allows faster computations and by this a higher spatial discretization and anincrease of the resolved part of the spectrum.

Subgrid mixing is modeled by an eddy diffusity approach with a turbulent dif-fusity based on the turbulent viscosityνt of the subgrid stress model and a constantSchmidt number Sc:

9kj = νt

Sc

∂Yk

∂xj. (9)

3.3. PRESENT IMPLEMENTATION

For our LES calculations we used the AVBP parallel solver developed at CERFACSand the Oxford University [21], based on the parallel library COUPL [22]. Theprogram handles structured and unstructured meshes and is second-order accuratein space and time.

Two models were used to determine the eddy viscosityνt . The first one is theStandard Smagorinsky Model [23]:

νt = (C11x)2√

2Sij Sij (10)

with C1 = 0.18, which has the advantage of simplicity and speed.The second model is the Filtered Smagorinsky model [12] defined on a high-

pass filter HP:

νt = (C21x)2√

2HP(Sij )HP (Sij ) (11)

and a constantC2 = 0.37. This model offers a better behaviour in transitional flowsand was optimized to work in wall boundary layers.

4. Grid Resolution

The spatial discretization of the flow is based on structured meshes. Although theAVBP solver allows unstructured meshes, the structured mesh approach providesa better control of the point distribution in the flow. Figure 5 shows an explodedview of the mesh. At the bottom is the plenum chamber of the jet (A) passing overinto a pipe (B). The jet nozzle is at the upper end of the pipe. An 0-grid is put inthe jet trajectory and the vicinity of the nozzle (C). A block behind the nozzle (D)describes the flow downstream of the nozzle and several coarse blocks (E) are putaround the jet trajectory to mesh the nearly undisturbed outer flow.

Meshing the jet pipe flow is important. As already pointed out, there is an influ-ence of the crossflow to the jetflow in the pipe. The existence of a recirculation zoneat the edge of the jet nozzle (see Figure 4) makes this area sensible to mesh pointdistribution. The mesh has to be fine enough to capture this recirculation zone.


Figure 5. Exploded view of grid blocks.

In the LES computation of Yuan [33] the influence of an extension of the meshinto the jet pipe was examined. He found out, that the flow behaviour is much betterreproduced with such a mesh extension.

We found out, that a simple extension might not be sufficient. Our first calcula-tions have been carried out with a 3D long pipe leading to the jet nozzle and thevelocity profileu was imposed at the entry of the pipe. This led to strong pressureoscillations in the pipe. As a numerical artefact, the pipe acts as a Helmholtz res-onator, because the inlet below the wall forms a velocity node. The frequency ofthe oscillations are determined by the length of the pipe. The jet shear layer roll-uplocks into the oscillations and the jet acts like a forced jet. Kelso [17] found, thatthe jet trajectory is affected by the forcing. In our computations the trajectory ishigher than in the case where the oscillations are suppressed.

In order to avoid pressure oscillations we use a combination of two counter-measures. The first one is to impose the mass fluxρu instead of the velocityuas a boundary condition to change the acoustic wave reflections at the inlet. Thesecond is to extend the jet pipe mesh into the plenum chamber in front of the jetpipe (Block A in Figure 5). The sudden change in diameter between jet pipe andplenum chamber makes it more difficult for the system pipe/plenum chamber to act


Figure 6. Smoke visualization of the test case of Andreopoulos and Rodi,r = 2, Re= 81000.

as a resonator. This approach is more expensive, but offers as a by-product morecertainty on the jet velocity profile.

Furthermore a refinement of the mesh in the low pressure region downstreamof the jet nozzle is necessary. It influences the jet trajectory and higher trajectorieswere obtained with a low resolution mesh. This mesh is automatically fine enoughto capture the wake vortices. But, additionally the wall region, where the wakevortices have their origin, has to be well resolved as well.

However, it turned out that the number of mesh points was still too high, whenapplied to a real configuration of the burner. To assess the accuracy of even coarsermeshes, additional computations were performed on an even simpler mesh. Here,the jet pipe is meshed by a 6×6 H-mesh. The crossflow is meshed with one singleblock of H-type topology. The plenum chamber stays part of the computed domainand is meshed by an H-block as well.

5. LES Validation Test Cases

In order to obtain meaningful statements on the validity of the LES computationsof the injectors of the real burner geometry, test cases are needed which are closeto the real problem with respect to the Reynolds number and the velocity ratior.In the real problem the Reynolds number isRe ' 8000, based on the exit velocityof the injecting fuel and the injector diameter, and the velocity ratior ' 2 at thenozzle. Three cases have been chosen:


1. The first one is a series of experiments carried out by Andreopoulos and Rodi[2–5]. They provide detailed hot wire measurements of the mean velocitycomponents, the turbulent kinetic energy, the Reynolds stresses and measure-ments on the turbulent kinetic energy budget. Furthermore they made measure-ments on a slightly heated jet to obtain statements on the mixing behaviour bymeasuring the temperature field.In the experiments the velocity ratio varies fromr = 0.5 (Re = 20500) tor = 2 (Re= 82000). Since the behaviour of the jet changes dramatically forvelocity ratios lower thanr = 1 the experiments with a velocity ratior = 2were chosen to be reproduced despite the high Reynolds number.

2. Because the work on the gas turbine burner focuses on mixing, we have chosenas a second test case the experiments by Smith and Mungal [24–27]. Theyseeded the jet air with acetone and made LIF measurements of the mixingbehaviour. Here, we have chosen to reproduce their measurement of a JICFwith a Re= 16400 and a velocity ratior = 5.

3. An additional problem in the gas turbine concerns the interaction betweenadjacent jets. Hence, the third test case is a measurement of a twin jet fromToy et al. [30]. He measured velocity profiles in the far field of the jets withRe = 31800 and a velocity ratior = 6. Here the establishment of a singleCVP in the far field of the jets shall be reproduced.

Despite the requirements on the mesh, a dexterous point distribution in the meshlimits the number of points to 90.000 for the test cases of Andreopoulos and Rodiand Smith and Mungal and 200.000 for the case of Toy. Tests with coarser mesheshave been done, but the results were poor, so that it can be assumed, that this is alower limit in terms of mesh points. The first cell on the surface of the crossflowwall has a thickness ofy+ = 90 in the case of Andreopoulos and Rodi and Toy anda thickness ofy+ = 50 in the case of Smith and Mungal.

6. Computational Results

6.1. REPRODUCTION OF GENERAL FLOW CHARACTERISTICS

All flow visualizations in this section have been made from the Reynolds-averagedflow field of the unsteady computation of the test case of Andreopoulos and Rodi.The features shown can be found in all other computations as well.

Figure 7 shows the streamlines computed by LES in the initial region of theCVP. It can be seen, that the CVP starts to develop very early. Haven [14] showed,that the vorticity of the CVP has its origin at the side walls of the jet pipe. It seemsfrom the flow visualization of the LES computation, that this can be confirmed.The vortices start very early, right behind the orifice.

Figure 8 juxtaposes the streamline pattern proposed by Perry and Kelso [20]with the computed streamlines. The resolution of the mesh upstream is not fineenough to resolve all vortices in this region. Baker [6] showed that the two sec-


Figure 7. Streamlines at the jet orifice, viewer is downstream of the orifice looking up-stream. The developing counterrotating vortex pair can be seen. Streamlines created fromReynolds-averaged flow field from the unsteady LES computation from the case of An-dreopoulos and Rodi.

Figure 8. Side view on the computed streamlines at the jet orifice from the case of Andreopou-los and Rodi juxtaposed with the proposed streamline pattern of Perry and Kelso [20]. Thehorseshoe vortex system is not fully resolved by the LES computation and thus simpler. Therecirculation zone at the upstream edge of the jet pipe can be seen. Streamlines created fromReynolds-averaged flow field from the unsteady LES computation.

ondary vortices of a horseshoe vortex are weak. The weakness and the small sizeof these vortices make it difficult for a numerical investigation to capture thesestructures. Nevertheless a simplified horseshoe vortex develops upstream of theorifice.

Figure 9 juxtaposes the streamline pattern in thex–y plane on the centerline ofthe jet found by Kelso [17] and the streamline pattern of the LES computation ofthe case of Andreopoulos and Rodi. The comparison can be done only qualitatively,because of the different experimental setups. In both flow fields a velocity node inthe wake, close to the wall can be found.

In Figure 10 the side view and top view of the streamline patterns are compared.The streamline patterns resemble, except for one important difference: the vortexin the x–z plane directly behind the jet nozzle turns in opposite direction. Kelso


Figure 9. Qualitative comparison of streamline patterns in thex–y plane on the centerlineof the jet, left Kelso [17] with avr = 2.2 and the LES computation of Smith and Mungalwith avr = 5. Streamlines created from Reynolds-averaged flow field from the unsteady LEScomputation.

Figure 10. Qualitative comparison of streamline patterns in thex–y plane on the centerlineof the jet, left Kelso [17] withvr = 2.2 and the LES computation of Andreopoulos and Rodiwith vr = 2, the half-circle denotes the position of the jet nozzle. Streamlines created fromReynolds averaged flow field from the unsteady LES computation.

admitted in his investigation, that the resolution of his measurement grid is quitecoarse in this region. Because of the higher resolution in the LES computation webelieve, that the orientation of this vortex has to be clockwise. The direction of thevortex can be confirmed from Figure 7. The vortex pair developing directly behindthe nozzle is in a nearly upright position at the nozzle itself and bends over withthe jet. That means, the vortex seen behind the nozzle in Figure 10 must have thesame orientation as the CVP. This is only the case, when the vortex behind thenozzle spirals out clockwise. The origin of this vortex is unclear. Neither the jetnor the wall boundary layer of the crossflow carries the vorticity of this sign. Acomputation, where the plane wall from the crossflow has been replaced by a slipwall, still showed this vortex. This indicates, that the origin of this vortex is locatedin the pipe wall.


Figure 11. Comparison of the momentum fields on the centerline of the jet, circles: mea-surements, solid line: LES Filtered Smag. Model, dashed line: LES Standard Smag. Model,averaging time 0.25 s.

In the literature this vortex is unmentioned, with the exception from the investi-gation of Kelso [17]. It seems, further investigation on the origin and further historyof this vortex is necessary, especially to shed light into the development of the CVP.

6.2. TEST CASE OFANDREOPOULOS ANDRODI

6.2.1. Momentum Field

Comparisons between the hot wire data obtained from Andreopoulos and Rodi andour LES computations were made to quantify the reproducibility. In order to showthe ability of LES to simulate the experiment on low-resolved meshes, all LEScomputations are made on meshes with 90000 mesh points. Theu component ofvelocity is compared in Figure 11 for different positions downstream on the jetcenterline. Regarding the profile atx/D = 2 the measurements and the LES com-putation with the Filtered Smagorinsky model agree well. The LES computationusing the Standard Smagorinsky model shows a wrong trajectory, the location ofthe velocity maximum is too high by 0.4D, but the right order of magnitude. Asalready mentioned, the Filtered Smagorinsky model was optimized for boundarylayers. Hence, the oncoming wall boundary layer is better described and the mo-mentum ratio close to the wall is better predicted. This has an influence on the jettrajectory. Theu velocity profiles downstream show, that the Filtered Smagorinsky


Figure 12. Comparison of the turbulent kinetic energy fields on the centerline of the jet. Thegraphs concerning LES contain only the resolved part of the turbulent motion. Circles: mea-surements, solid line: LES Filtered Smag. Model, dashed line: LES Standard Smag. Model,averaging time 0.25 s.

model has advantages over the Standard Smagorinsky model, although the trajec-tory is slightly too high. The measured velocity deficit below the jet trajectory isleveled out in the LES computation too early.

The turbulent kinetic energy (TKE)k2 = u′2+v′2+w′2 was chosen to comparedynamic variables. The TKE of the LES calculations presented here represent onlythe TKE of the resolved spectrum of turbulence. This means, that the subgridturbulence does not appear in the graphs. In regions, where the level of subgridturbulence is high, the TKE of the LES computations is underestimated. This isespecially the case in wall boundary layers, where the high shear stress at the wallimplies a production of small scale structures, which are not captured by the meshresolution. In free turbulence far off the wall, the LES mesh is fine enough to allowcomparisons with measurements.

Figure 12 shows a comparison of TKE. The profile atx/D = 4 shows agood agreement of the LES calculation with the Filtered Smagorinsky model.The Standard Smagorinsky model shows a too high trajectory (which confirmsthe observation from Figure 11) and overestimates the TKE. Obviously the Stan-dard Smagorinsky model is not dissipating sufficiently the turbulent energy. TheconstantC1 of the Standard Smagorinsky model could be increased to adapt themodel to the flow, but this would question the universal validity of the model. Thedownstream profiles show a quite good agreement far off the wall, but close to the


Figure 13. Comparison of the velocity profiles at the jet orifice. Circles: measurements, solidline: LES, averaging time 0.25 s.

wall the TKE of the LES computations is well below the measured TKE. Here, asmentioned above, the level of subgrid turbulence is not neglectable.

A look at the measured velocity profile at the jet orifice (Figure 13) fromAndreopoulos and Rodi shows a major discrepancy in the recirculation bubblebetween the hot wire measurements and the LES computation, which can be ex-plained as follows: although Andreopoulos already proposed the possibility of atemporal recirculation zone at this location for very short time spans [2], he didnot expect a steady recirculation zone. But the major limitation of hot wire mea-surements is, that they cannot measure the direction of the flow and thus alwayspretend to measure a positive velocity. This explains, that in the region of the recir-culation bubble Andreopoulos and Rodi still measure a positive velocity. The LEScomputations in contrast, show the recirculation zone and confirm the observationsof Perry and Kelso [20] (see also Figure 8).

6.2.2. Scalar Field

Due to the lack of reliable measurement techniques for mixing in the 1980s,Andreopoulos heated the jet slightly by 4◦C and measured the temperature fieldinstead. The goal was to obtain information on the mixing behaviour of a speciesinjected by the jet with a Schmidt number equal to the Prandtl number. The tem-perature difference had to be kept small in order to preserve nearly equal densities.This helped to leave the jet velocity unharmed while maintaining the impulse ratior and to avoid additional effects by buoyancy in the far field of the jet. But accuracyproblems arise when measuring the temperature with thermocouples, especiallyin highly turbulent regions. An additional effect occurs close to the wall, which


Figure 14. Comparison of the mixture fraction of a passive scalar distribution (LES) withthe non-dimensionalized temperature distribution on the centerline of the jet. Circles: mea-surements, solid line: LES Filtered Smag. Model, dashed line: LES Standard Smag. Model,averaging time 0.25 s.

potentially heats up. For the LES computations the field of a passive scalar with aSchmidt number of Sc= 0.72 equal to the Prandtl number was computed.

With the knowledge of these problems, the comparison of the measured temper-ature field with the computed mixture fraction of a passive scalar on Figure 14 hasto be looked at carefully. Atx/D = 2 the agreement is quite well, but downstreamthe profiles increasingly disagree, especially close to the wall. This is explainedwith heating up of the wall in the experiment. However, we do not feel, that thisbad agreement is of major importance, since the following test case from Smithand Mungal shows better agreement, so that the disagreement in the case fromAndreopoulos and Rodi can be explained by different boundary conditions.

6.3. TEST CASE OFSMITH AND MUNGAL

6.3.1. Scalar Field

The doubts in the comparability of the measured temperature field with the com-puted mixing of a scalar led to further investigations of the JICF with regard tomixing. In the recent years LIF measurements became a reliable tool to predictmixing behaviour in turbulent flows. Acetone seeded air is used to track the historyof fluid particles in the flow.


Figure 15. Comparison of the mixture fraction of a passive scalar distribution of the measurednon-dimensionalized mixture fraction of acetone seeded air with the LES computation on thecenterline of the jet. Circles: measurements, solid line: LES Filtered Smag. Model, dashedline: LES Standard Smag. Model, averaging time 0.25 s, mesh size: 90000 points.

Our LES computations that aim to reproduce the case of Smith and Mungalshow basically the same behaviour as before: a CVP is developing, the horseshoevortex, wake vortices, jet shear layer vortices and the recirculation zone at theleading edge of the jet nozzle appear as seen previously.

The field of a passive scalar with a Schmidt number Sc= 1.0 was computedto compare it with the mixture fraction of acetone from the experiment. Figure 15shows the comparisons between experiment and LES computations, which showan excellent agreement. The computation using the Standard Smagorinsky modelshows a slightly too high trajectory. The better agreement compared to the previouscase can be explained by two facts. First, the Reynolds number is lower than in thecase of Andreopoulos and Rodi. This fact speaks for a sufficient accuracy for theLES computations of an injector on the vane in the real geometry, because theReynolds number is even lower than in the case of Smith and Mungal. Second,because of the higher velocity ratio, the boundary layer plays a minor role. Theorigin of the boundary layer on the vane is only slightly upstream of an injector,at the leading edge of the vane, and is accelerated then. This means, the boundarylayer thickness is supposed to be very small at the height of the injectors and hasonly little effect on the jet flow.

As model for the description of the subgrid mixing the eddy diffusity modelwas chosen. The results show, that even this simple model is able to reproduce the


Figure 16. Influence of Schmidt number to mean mixture fraction distribution, LES computa-tion of two passive scalars with different Schmidt numbers. Solid line: Sc= 0.72, dotted line:Sc= 1.0.

mixing behaviour of a JICF. Because of its simplicity and fast execution it waschosen for all other LES computations.

6.3.2. Influence of the Schmidt Number

The LIF measurements with acetone seeded air and a Schmidt number of Sc' 1.0are performed to simulate the mixing behaviour of methane (Sc' 0.72). To de-termine the influence of the Schmidt number on the mixing behaviour, an LEScomputation was performed with two passive scalars. One of the passive scalarspossesses the Schmidt number Sc= 1.0 and the other Sc= 0.72. Only one com-putation needed to be performed, because the passive scalars have no feedback onthe momentum field. Here, the advantage of a numerical investigation is clear: bothscalars use exactly the same momentum field. Figure 16 shows the comparison ofthe distribution of the scalars. The curves are very close together and show nearlyno deviation. As expected, the distribution of the scalar with a Sc= 0.72 diffusesslightly more. It can be concluded, that the LIF measurements simulate the mixingbehaviour of methane accurately.

6.3.3. Influence of Mesh Coarsening

In order to assess the influence of grid resolution, tests on simpler, less problemadapted meshes were performed. Here, the mesh cell size and point distribution iscomparable to meshes used in the gas turbine burner. The meshes have approxi-


Figure 17. Influence of mesh coarsening to mixing, solid line: LES computation, mesh size:30000 points, dashed line: LES computation, mesh size 90000 points, circles: measurements.

mately 30000 mesh points. Although it cannot be assumed that the LES computa-tion reproduces exactly quantitatively the measurements, we aim to reproduce themeasurement qualitatively.

The comparison of the scalar fields (Figure 17) shows some disagreements. Theresults are worse than in previous computations, but surprisingly good given thefact, that they are performed on insufficient meshes where not all requirements ofLES are met. The trajectory is too high, which is probably due to the bad resolutionof the boundary layer. Furthermore the scalar quantity is not sufficiently diffused.This effect results from the filtering of the small scale structures by the coarse meshand thus a worse description of the turbulent transport. This could be improved bya more sophisticated subgrid mixing model, but this idea was dropped in favour offast computation times.

In conclusion, the LES computation delivers reasonable qualitative solutionseven on coarse meshes and statements about mixedness can be derived from thesecomputations. But qualitative comparisons have to be regarded carefully.

6.4. TEST CASE OFTOY

To obtain information about the reproducibility of the merging mechanism of twoadjacent jets the experiments of Toy [30] were computed. Here, additional prob-lems occur, because little is known about the interactions of the jet. To the authors’knowledge, no mechanism is reported to explain the behaviour of the two jets


Figure 18. Test case of Toy [30], comparison of the momentum field on the centerline of thetwo jets. Circles: measurements, solid line: LES, averaging time 0.235 s.

to form one single CVP instead of two. The aim of the LES investigation is toreproduce this merging mechanism and to shed light into this phenomenon.

The quantitative comparison of the momentum field on the centerline betweenthe two jets is shown in Figure 18. The results are not as good as in the previousLES computations. It has to be mentioned, that the interactions of the two jets leadsto longer durations until a stationary flow pattern is established. That means, thecomputed time span oft = 0.235 s might not be sufficient to obtain reliable meanvalues on the centerline of the jet.

Nevertheless, some major flow characteristics can be reproduced. The two jetsmerge and form a single CVP (Figure 19) in the far field of the jets. This agreeswith the measurements of Toy [30].

The knowledge of the whole velocity field (and hence the entire vorticity field)makes it possible to have a closer look at the mechanism which leads to the de-velopment of a single CVP and the fate of the two other vortices. Fig 19 showsa series of streamwise vorticity distributions downstream of the two jets. FromFigures 19a and 19b it can be seen, that the two jets produce two CVPs, that means,four vortices. Further downstream the two jets attract each other and start to merge.

This attraction can be explained with the Coanda effect. The Coanda effectnormally occurs when a jet is close to a parallel wall. The entrainment of the jetis disturbed by the wall and, due to the impossibility to entrain the fixed wall, thejet bends towards the wall. With two parallel jets a similar behaviour can be seen.


Figure 19. Test case of Toy [30], vorticity distribution at different downstream positions:x = (a) 0 mm, (b) 20 mm, (c) 40 mm, (d) 60 mm, (e) 80 mm, (f) 100 mm, (g) 150 mm,(h) 200 mm, (i) 300 mm. Initially two counterrotating vortex pairs develop. Due to the Coandaeffect both jets attach each other. The two middle vortices are quenched and parted in foursmaller vortices, one pair above the main CVP, one below, close to the wall.

Here, in the zone between the two jets the entrainment is disturbed and the jetsbend towards the other one as each jet tries to entrain the other.

In the case of the twin jet in crossflow this causes a problem for the two innervortices. The two vortices are quenched (Figure 19c) and divided in two vortexpairs (Figure 19d), one pair (“2a” and “3a”) above the remaining two outer vortices(“1” and “4”) and one pair below, close to the wall (“2b” and “3b”). The four smallvortices spin fast to keep the torque of the initial two (inner) vortices constant. Thestrong gradients in these small, fast spinning vortices lead to higher dissipationrates and a shorter life span of the vortices. In the far field (Figure 19i) the twooriginally outer vortices survive and form one single CVP. There remains a pair ofsmall vortices close to the wall, though.


Figure 20. Fuel injection on a part of the vane, isosurface: mixture fraction, isocontours:pressure, black arrows: velocity vectors. Inside the vane is the fuel supply leading to the upperand lower injector.

7. LES of Fuel Injection in a Gas Turbine

The lack of measurements in a real burner geometry to determine the accuracywere compensated by the investigation of the JICF. The similar flow conditionsof the JICF and the fuel injectors on the vane in the industrial application gaveconfidence, that the computations of the burner geometry predicts the flow behav-iour with sufficient precision, that allows to make statements about mixedness andvortex formations inside the burner. A full analysis of our LES computation of theSiemens gas turbine burner is beyond the scope of this article, and we explain onlythe main steps of the analysis.

Our first approach in examining the burner was to have a look at a pair ofinjectors on the vane in a homogeneous outer air flow (Figure 20). This gave usthe possibility to determine fuel mass flux rates through the injectors and to in-vestigate vortex formations around the vane, which interact with the fuel injectingjets. The computation of a full vane in homogeneous surrounding flow (Figure 21)gave insight about interactions between adjacent jets, especially to the mergingmechanism of adjacent jets, which lead to unmixedness.

The final step, the computation of a segment of the burner has been done re-cently but for reasons of confidentiality we are not able to present results of thiscomputation in this article.


Figure 21. Visualization of fuel injection on the vane.

Figure 22 shows a probability density function (PDF) of mixture fraction down-stream of an injector. There is a peak at 0 (pure air) and another at 0.075. Thismeans, there are pockets of air alternating with pockets of fuel. The mean valuedoes not give any useful information, because the probability that the fluid is in astate of the mean value is quite improbable. Furthermore the mean value suggests,that the fluid at this position is perfectly mixed, which is certainly not the case atevery instant. This sort of PDF in the combustion chamber causes problems dueto the fuel-rich combustion at certain instances leading to higher NOx production.Visualizations of the LES computation gives insight into the flow to correlate theunmixed pockets to vortex formations around the vane. The knowledge of the rea-sons for unmixedness in the mixing section of the burner gives the possibility fordesigning engineers to improve the mixedness in the gas turbine burner.

8. Conclusions

The present LES computations have proven the ability of reproducing the mainfeatures of jets in cross flow on reasonably coarse grids.

The necessity of including the jet pipe and the plenum chamber to the com-puted domain became evident. The proper description of the wall boundary layeris required to obtain the correct jet trajectory. The low pressure region downstreamof the nozzle influences the jet trajectory and needs a high spatial discretization aswell.

The general flow characteristics, like the development of the counterrotatingvortex pair, the horseshoe vortex, the jet shear layer vortices and the merging of


Figure 22. Example of a probability density function of mixture fraction downstream of aninjector.

two adjacent jets are reproduced. Furthermore some light could be shed into themerging mechanism of two adjacent jets.

The subgrid turbulence model influences the jet trajectory. For flows, that arestrongly affected by the wall boundary layer, the Filtered Smagorinsky modelshowed better results. The nature of the JICF, to be determined by large scalemotions, makes it possible for the LES approach to obtain results with a goodagreement, even with simple subgrid models.

The LES approach has been applied to a gas turbine burner to obtain informa-tion about momentum field and mixing. The computations gave valuable insight inthe events in the burner. This shows the capability of the LES approach to be usedas research tool in the design process of an industrial gas turbine burner.

Acknowledgement

This work has been carried out with the support of the gas turbine department ofSiemens Power Generation KWU (Combustion).

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