cfd les of jets in cross flow and its application to a gas turbine burner.pdf

8/10/2019 CFD LES of Jets in Cross Flow and its Application to a Gas Turbine Burner.pdf

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LES of Jets in Cross Flow

and its Application to a Gas Turbine Burner

J. U. Schluter ([email protected]) and T. SchonfeldCERFACS, 42, Av. Gaspard Coriolis, 31057 Toulouse Cedex 1,http://www.cerfacs.fr

Abstract. LES computations of jets in cross flow (JICF) were performed. Exper-imental investigations reported in literature are reproduced with good agreementconcerning the momentum field and the mixing of a passive scalar. The resultsvalidate the ability of the present LES approach to compute fuel injection of thetype JICF. LES computations of fuel injection in an industrial gas turbine burnerare presented.

Keywords: LES, jet in cross flow, mixing, gas turbine burner

1. Introduction

The increasing demand in reducing pollutants in gas turbines [31] forcesgas turbine manufacturers to investigate possibilities to mix fuel andoxydizer in the best way possible before their ignition. It is well known,that fuel rich combustion leads locally to higher temperatures andhigher pollutant formations. Although Reynolds-averaged mean valuesmight suggest a perfect mixedness, the unsteady nature of turbulentcombustion may result in a temporally surplus of fuel in the combustionchamber. Gas turbine manufacturers seek to avoid these conditions in

their burners as from the design stage on.The motivation for this project originates in a demand from the

Siemens Power Generation (KWU) company to undertake a LargeEddy Simulation (LES) analysis of a gas turbine burner configurationand to explore possibilities for using LES as a design tool. Fig 1 showssuch a gas turbine burner. It is of swirl type, where the swirl is inducedby several circumferential vanes. The fuel (natural gas) is injected onthe surfaces of the vanes. In fig. 2 a close-up on the vane is shown,where air is coming from the left and the fuel is injected perpendicularto the airflow.

The objectives of this LES analysis are to determine the mixingquality of the burner and to track vortex developments around the

vane, which might disturb later on in the combustion chamber andpotentially lead to combustion instabilities. The problem met herein is,that measurements inside the burner are extremely difficult to achieveunder operating conditions because of the limited access of measure-

c2002 Kluwer Academic Publishers. Printed in the Netherlands.

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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 ofthe vanes. The air (from the left) and the fuel form a JICF.

ment probes and optical devices to the inner geometry of the burner.Measurements on the inlet and outlet of the burner have been made,but they are too far away from the fuel injection to give significantinsight to the flow around the vane.

For this reason, a direct comparison between LES and measurementis nearly impossible to validate the LES results. Hence, before applyingthe LES approach to the gas turbine burner, a validation of the LEStechnique and the underlying flow solver is done on simpler test cases.

The ability of the underlying flow solver to reproduce foil flows has beenshown previously [21], so that the discription of the vane itself did notpose a problem. However, the ability of the flow solver to reproducethe fuel injection still had to be done. As a simplified test case the jet

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in cross flow (JICF) has been chosen to investigate the fuel injection.Here, the vane is replaced by a plane wall.

The computation of the burner flow requires a high number of meshpoints to describe the principle flow features: the inlet flow, the vane

flow, the injector flow and the swirling flow at the outlet. The varietyand number of different flow problems encountered here will need each ahigh number of mesh points to describe the flow properly. It is desirableto know the minimum number of mesh points to describe the differentproblems in order to keep low the total number of mesh points in thefull 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: turbineblade cooling, V/STOL aircrafts, roll control of missiles or chimneyflows are examples of the wide field of applications, but most of theinterest in research has been focused on the application to combustors.

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

Investigations on the JICF have started in the 1930s [28] with themixing of chimney plumes. Since, there have been numerous investiga-

tions on the JICF leading to the perception, that the JICF, in contrastto other flow configurations like the jet and the mixing layer, cannotbe generalized in terms of self similarity and Reynolds dependence,due to strong nonlinear effects. The systematic analysis of the JICFstarted in the 1970s with the discovery and acceptance of coherentstructures [10],[9]. A clear definition of coherent structures cannot begiven. Hussain [15],[16] tries to define them as a connected, large scalefluid mass with a phase correlated vorticity over his spatial extend, butstill this definition is incomplete.

However, coherent structures are able to explain various non-lineareffects in the JICF. Up to now, at least four different types of coherentstructures are determined in the JICF. They are shown in Fig. 3. The

most dominant vortex system is the counter rotating vortex pair. Thethree other vortices, the jet shear layer vortices, the wake vortices andthe horseshoe vortex are often called secondary vortices, as they playa minor, although not neglectable role in the far field of the jet.

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Crossflow

Jet Shear Layer

Vorticies

Counter Rotating

Vortex Pair

Wake VorticiesHorseshoe

Vortex

Figure 3. Vortex system for a jet in cross flow (from Fric & Roshko [13])

In the following some recent developments in JICF research aresummarized. 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 momentumratior defined as:

r= jetv2jet

crossflowv2

crossflow(1)

In most cases the jet fluid and the crossflow fluid consist of the samespecies and have the same temperature, hence jet=crossflow. The

momentum ratio simplifies then to the velocity ratio:

r=vjet

vcrossflow(2)

Different flow regimes can be determined based on the velocity ratior. JICF withr


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

to the investigations. Dependent on the wall boundary layer thicknessthis flow regime can occur up to a velocity ratio of r = 1. This flowconfiguration is especially important for turbine blade coolings [7].

Velocity ratiosrbetween 1 and 10 are common flow regimes for com-bustion applications. The jet is then able to push through the boundarylayer, which plays a minor role. The JICF is now determined by freeturbulence characteristics and is easier reproducible. Andreopoulos [5]measured velocity profiles for JICF with velocity ratios from 0.5 to2, where the described transition from wall boundary layer to freeturbulence can be seen.

JICF with velocity ratios higher than 10 have additional effects asthey behave more and more like free jets with increasing velocity ratio.

2.3. Vortex Systems

The mechanism for the formation of the counter rotating vortex pair(CVP) is not fully understood. It can be taken as certain, that thevorticity of the CVP has its origin at the sidewalls of the jet. Haven[14] investigated different nozzle geometries for the jet. Rectangular jetswith a low aspect ratio (the edges at the sides of the jet are longer thanthe upstream and downstream edge) amplified the CVP. The longersidewalls produce more vorticity, which can be found later in the CVP.On the other side, jets with a high aspect ratio have a weaker CVP.

Toy [30] investigated two closely spaced jets issuing into a crossflow.The jets were either side-by-side or in-line. Hot-wire measurements onthe centerline of the jets were made. As a major feature found, only one

CVP, instead of two, was produced, when the jets were in a side-by-sidesetup. The data obtained, was not sufficient to give a reason for thisbehaviour. To the authors knowledge, a mechanism which leads to asingle CVP is not reported in literature.

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

The horseshoe vortex forms upstream of the jet at the crossflowwall. The adverse pressure gradient at the crossflow wall forces thewall boundary layer to separate and to form a vortex. It is then con-vected and stretched by the flow and wraps around the jet nozzle like anecklace. The same kind of vortices can be observed for flows where aboundary layer hits on an obstacle, e.g. a cylinder mounted on a wall [6].The vortex is in interaction with the upstream edge of the jet orifice,causing a separation bubble inside the jet (see also [20],[17]). Fig. 4shows a sketch of the horseshoe vortex and the separation bubble.

The existence of the separation bubble was first proposed by An-dreopoulos [2]. He measured the velocities in the interior of the jet-pipeand found non-symmetric profiles. In this investigation, the crossflowaffects the jet-pipe flow up to 2D upstream of the nozzle.

The wake vortices were first believed to be the consequence of ashedding process behind the jet, with the jet acting like a solid cylinderand the wake vortices behaving like a Karman vortex street. However,Perry [20] pointed out, that in an incompressible fluid no vorticitycan be produced inside the flow. The vorticity transport equation forincompressible fluids:

D

Dt = u+2 (3)

shows a convection term on the left hand side, a term which describes

the reorientation and stretching of the vorticity due to the velocitygradients and a viscous term on the right hand side, but no explicitproduction term. That means, in incompressible flows vorticity canonly enter a flow by initial conditions and imposed wall boundaries,but not be generated in the interior, which would be the case, if thewake vortices would be shed from the jet like from a solid cylinder. Fric& Roshko [13] connected the wake vortices to a separation event atthe cross flow wall at the sides of the jet nozzle. The end of the vortexstring, which is close to the nozzle is convected by the jet and followsthe jet trajectory, while the other end stays close to the wall, bringingthe 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].He simplified the calculation by using a slip wall as the crossflow wall.

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Hence, the crossflow boundary layer is neglected and the horseshoevortex and the wake vortices cannot be calculated. His results agreequalitatively with the measurements of Andreopoulos [3],[5], besides alarge error near the wall.

A numerical investigation from Chiu [11] tested the applicability ofdifferent algebraic turbulence models with the result, that the turbu-lence models do not improve the calculations compared with a laminarcalculation. It showed the limits of an eddy viscosity model applied tofree turbulence.

The investigation of Alvarez [1] used the k- model and a directclosure. The direct closure improved the calculations, but the errorwas still high.

The strong unsteady behaviour of the JICF leads to the conclusion,that an unsteady LES approach might be useful for reproducing andpredicting the JICF. Yuan [33], [32] made an LES calculation of aJICF. He calculated a JICF with a small Reynolds number (Re=2100)on meshes with 1.3 million mesh points. The results agree quite wellwith measurements, although no direct comparison is possible , becausethe Reynolds number is lower and the velocity ratio is not exactly thesame as in the experimental references.

He pointed out, that it is necessary to mesh the pipe which suppliesthe jet, in his case on a length of one diameter D upstream. But,as Andreopoulos [2] mentioned, there is an interaction between thecrossflow and the jet-flow. In the examined case (r = 2) the crossflowaffects the pipe-flow around two diameters upstream the pipe, so thathis extension was probably not sufficient. The high number of meshpoints and the low Reynolds number make it difficult to apply this

computation to industrial configurations.

3. Mathematical Formulation of LES

3.1. Governing Equations

The basic idea of LES is to resolve the larger scales of motion of theturbulence while approximating the smaller ones. To achieve this, a fil-ter is applied to the continuity equation and the transport equations ofmomentum, energy and species. For reacting flows, often Favre filteringis used, which is defined as:

Q= Q = +

Q (x, t) G

x x

dx (4)

leading to the following equations for momentum u i and species Yi:

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momentum (j= 1, 2, 3)

ui

t +

ui

uj

xi+

p

xi=

ijxj

+ Tijxj

(5)

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

Ykt

+uiYk

xi=

xi

Dk

Ykxi

+ k+ kj

xj(6)

3.2. Subgrid Scale Models

The termsTij and ik result from the convective termsuiuj andYkui,which are split into a resolved part on the left hand side of the equation,directly delivered by the LES calculation, and an unresolved part on

the right hand side, which needs to be modeled.We used an eddy viscosity approach for the subgrid scales:

Tij = 2tSij+1

3Tllij (7)

with

Sij =1

2

uixj

+ ujxi

(8)

Although the eddy viscosity approach is not valid for free turbulence,its simplicity allows faster computations and by this a higher spatialdiscretization and an increase of the resolved part of the spectrum.

Subgrid mixing is modeled by an eddy diffusity approach with a

turbulent diffusity based on the turbulent viscosity t of the subgridstress model and a constant Schmidt number S c:

kj = tSc

Ykxj

(9)

3.3. Present Implementation

For our LES calculations we used the AVBP parallel solver developed atCERFACS and the Oxford University [21], based on the parallel libraryCOUPL [22]. The program handles structured and unstructured meshesand is second-order accurate in space and time.

Two models were used to determine the eddy viscosity t. The firstone is the Standard Smagorinsky Model [23]:

t= (C1x)2

2SijSij (10)

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A

B

C

E

D

Figure 5. exploded view of grid blocks

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:

t= (C2x)2

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

and a constant C2 = 0.37. This model offers a better behaviour intransitional flows and was optimized to work in wall boundary layers.

4. Grid Resolution

The spatial discretisation of the flow is based on structured meshes.Although the AVBP solver allows unstructured meshes, the structuredmesh approach provides a better control of the point distribution in

the flow. Fig. 5 shows an exploded view of the mesh. At the bottomis the plenum chamber of the jet (A) passing over into a pipe (B).The jet nozzle is at the upper end of the pipe. An O-grid is put inthe jet trajectory and the vicinity of the nozzle (C). A block behind

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the nozzle (D) describes the flow downstream of the nozzle and severalcoarse blocks (E) are put around the jet trajectory to mesh the nearlyundisturbed outer flow.

Meshing the jet pipe flow is important. As already pointed out, there

is an influence of the crossflow to the jetflow in the pipe. The existenceof a recirculation zone at the edge of the jet nozzle (see fig. 4) makesthis area sensible to mesh point distribution. The mesh has to be fineenough to capture this recirculation zone.

In the LES computation of Yuan [33] the influence of an extensionof the mesh into the jet pipe was examined. He found out, that the flowbehaviour is much better reproduced with such a mesh extension.

We found out, that a simple extension might not be sufficient. Ourfirst calculations have been carried out with a 3D long pipe leadingto the jet nozzle and the velocity profile u was imposed at the entryof the pipe. This led to strong pressure oscillations in the pipe. Asa numerical artefact, the pipe acts as a Helmholtz resonator, becausethe inlet below the wall forms a velocity node. The frequency of theoscillations are determined by the length of the pipe. The jet shearlayer roll-up locks into the oscillations and the jet acts like a forced jet.Kelso [17] found, that the jet trajectory is affected by the forcing. Inour computations the trajectory is higher than in the case where theoscillations are suppressed.

In order to avoid pressure oscillations we use a combination of twocountermeasures. The first one is to impose the mass flux u instead ofthe velocity u as a boundary condition to change the acoustic wavereflections at the inlet. The second is to extend the jet pipe meshinto the plenum chamber in front of the jet pipe (Block A in fig. 5).

The sudden change in diameter between jet pipe and plenum chambermakes it more difficult for the system pipe/plenum chamber to act as aresonator. This approach is more expensive, but offers as a by-productmore certainty on the jet velocity profile.

Furthermore a refinement of the mesh in the low pressure regiondownstream of the jet nozzle is necessary. It influences the jet trajectoryand higher trajectories were obtained with a low resolution mesh. Thismesh is automatically fine enough to capture the wake vortices. But,additionally the wall region, where the wake vortices have their origin,has to be well resolved as well.

However, it turned out, that the number of mesh points was stilltoo high, when applied to a real configuration of the burner. To assess

the accuracy of even coarser meshes, additional computations wereperformed on an even simpler mesh. Here, the jet pipe is meshed by a6x6 H-mesh. The crossflow is meshed with one single block of H-type

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

topology. The plenum chamber stays part of the computed domain andis meshed by an H-block as well.

5. LES Validation Test Cases

In order to obtain meaningful statements on the validity of the LEScomputations of the injectors of the real burner geometry, test cases areneeded which are close to the real problem with respect to the Reynoldsnumber and the velocity ratio r. In the real problem the Reynoldsnumber is Re8000, based on the exit velocity of the injecting fuel andthe injector diameter, and the velocity ratior 2 at the nozzle.

Three cases have been chosen:

1. The first one is a series of experiments carried out by Andreopoulosand Rodi [2], [3], [5], [4]. They provide detailed hot wire mea-surements of the mean velocity components, the turbulent kinetic

energy, the Reynolds stresses and measurements on the turbulentkinetic energy budget. Furthermore they made measurements on aslightly heated jet to obtain statements on the mixing behaviourby measuring the temperature field.

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In the experiments the velocity ratio varys fromr = 0.5 (Re=20500)to r = 2 (Re=82000). Since the behaviour of the jet changes dra-matically for velocity ratios lower thanr = 1 the experiments witha velocity ratio r = 2 were chosen to be reproduced despite the

high Reynolds number.

2. Because the work on the gas turbine burner focuses on mixing, wehave chosen as a second test case the experiments by Smith andMungal [25], [24], [27], [26]. They seeded the jet air with acetone andmade LIF measurements of the mixing behaviour. Here, we havechosen to reproduce their measurement of a JICF with a Re=16400and a velocity ratio r = 5.

3. An additional problem in the gas turbine concerns the interactionbetween adjacent jets. Hence, the third test case is a measurementof a twin jet from Toy et al. [30]. He measured velocity profiles in

the far field of the jets with Re=31800 and a velocity ratio r = 6.Here the establishment of a single CVP in the far field of the jetsshall be reproduced.

Despite the requirements on the mesh, a dexterous point distributionin the mesh limits the number of points to 90.000 for the test cases ofAndreopoulos & Rodi and Smith & Mungal and 200.000 for the caseof Toy. Tests with coarser meshes have been done, but the results werepoor, so that it can be assumed, that this is a lower limit in terms ofmesh points. The first cell on the surface of the crossflow wall has athickness ofy+ = 90 in the case of Andreopoulos & Rodi and Toy anda thickness ofy+ = 50 in the case of Smith & Mungal.

6. Computational Results

6.1. Reproduction of General Flow Characteristics

All flow visualizations in this section have been made from the Reynolds-averaged flow field of the unsteady computation of the test case ofAndreopoulos & Rodi. The features shown can be found in all othercomputations as well.

Fig. 7 shows the streamlines computed by LES in the initial regionof the CVP. 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 theside walls of the jet pipe. It seems from the flow visualization of theLES computation, that this can be confirmed. The vortices start veryearly, right behind the orifice.

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Figure 7. Streamlines at the jet orifice, viewer is downstream of the orifice lookingupstream. The developing counter rotating vortex pair can b e seen. Streamlinescreated from Reynolds averaged flow field from the unsteady LES computation fromthe case of Andreopoulos & Rodi.

Figure 8. side view on the computed streamlines at the jet orifice from the case ofAndreopoulos & Rodi juxtaposed with the proposed streamline pattern of Perry &Kelso [20]. The horseshoe vortex system is not fully resolved by the LES computationand thus simpler. The recirculation zone at the upstream edge of the jet pipe canbe seen. Streamlines created from Reynolds averaged flow field from the unsteadyLES computation.

Fig. 8 juxtaposes the streamline pattern proposed by Perry & Kelso[20] with the computed streamlines. The resolution of the mesh up-stream is not fine enough to resolve all vortices in this region. Baker [6]showed that the two secondary vortices of a horseshoe vortex are weak.The weakness and the small size of these vortices make it difficult fora numerical investigation to capture these structures. Nevertheless asimplified horseshoe vortex develops upstream of the orifice.

Fig. 9 juxtaposes the streamline pattern in the x y plane on thecenterline of the jet found by Kelso [17] and the streamline patternof the LES computation of the case of Andreopoulos & Rodi. Thecomparison can be done only qualitatively, because of the different

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Figure 9. qualitative comparison of streamline patterns in the x y plane on thecenterline of the jet, left Kelso [17] with a vr = 2.2 and the LES computation ofSmith & Mungal with a vr = 5, Streamlines created from Reynolds averaged flowfield from the unsteady LES computation

Figure 10. qualitative comparison of streamline patterns in the x y plane on thecenterline of the jet, left Kelso [17] with vr = 2.2 and the LES computation ofAndreopoulos & Rodi with vr = 2, the half-circle denotes the position of the jetnozzle. Streamlines created from Reynolds averaged flow field from the unsteadyLES computation

experimental setups. In both flow fields a velocity node in the wake,close to the wall can be found.

In fig. 10 the side view and top view of the streamline patterns arecompared. The streamline patterns resemble, except for one importantdifference: the vortex in the x-z plane directly behind the jet nozzleturns in opposite direction. Kelso admitted in his investigation, that theresolution of his measurement grid is quite coarse in this region. Becauseof the higher resolution in the LES computation we believe, that theorientation of this vortex has to be clockwise. The direction of thevortex can be confirmed from fig. 7. The vortex pair developing directlybehind the nozzle is in a nearly upright position at the nozzle itself and

bends over with the jet. That means, the vortex seen behind the nozzlein fig. 10 must have the same orientation as the CVP. This is onlythe case, when the vortex behind the nozzle spirals out clockwise. Theorigin of this vortex is unclear. Neither the jet nor the wall boundary

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0.0 1.0 u/uc

0.00

1.00

2.00

3.00

4.00

5.00

y/D

x/D=4x/D=2 x/D=6 x/D=10 x/D=16

Figure 11. comparison of the momentum fields on the centerline of the jet, circles:measurements, solid line: LES Filtered Smag. Model, dashed line: LES StandardSmag. Model, averaging time 0.25s

layer of the crossflow carrys the vorticity of this sign. A computation,where the plane wall from the crossflow has been replaced by a slip wall,still showed this vortex. This indicates, that the origin of this vortex islocated in the pipe wall.

In the literature this vortex is unmentioned, with the exception from

the investigation of Kelso [17]. It seems, further investigation on theorigin and further history of this vortex is necessary, especially to shedlight into the development of the CVP.

6.2. Test Case of Andreopoulos & Rodi

6.2.1. Momentum FieldComparisons between the hot wire data obtained from Andreopoulos &Rodi and our LES computations were made to quantify the reproduce-ability. In order to show the ability of LES to simulate the experimenton low-resolved meshes, all LES computations are made on meshes with90000 mesh points. The u component of velocity is compared in Fig.

11 for different positions downstream on the jet centerline. Regardingthe profile at x/D = 2 the measurements and the LES computationwith the Filtered Smagorinsky model agree well. The LES computationusing the Standard Smagorinsky model shows a wrong trajectory, the

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0.00 0.05 0.10 TKE0.00

1.00

2.00

3.00

4.00

5.00

y/D

x/D=16x/D=10x/D=06x/D=04

Figure 12. comparison of the turbulent kinetic energy fields on the centerline ofthe jet. The graphs concerning LES contain only the resolved part of the turbulentmotion. circles: measurements, solid line: LES Filtered Smag. Model, dashed line:LES Standard Smag. Model, averaging time 0.25s

location of the velocity maximum is too high by 0.4D, but the rightorder of magnitude. As already mentioned, the Filtered Smagorinskymodel was optimized for boundary layers. Hence, the oncoming wall

boundary layer is better described and the momentum ratio close tothe wall is better predicted. This has an influence on the jet trajectory.Theuvelocity profiles downstream show, that the Filtered Smagorinskymodel has advantages over the Standard Smagorinsky model, althoughthe trajectory is slightly too high. The measured velocity deficit belowthe jet trajectory is leveled out in the LES computation too early.

The turbulent kinetic energy (TKE)k2 =u2+v2+w2 was chosen tocompare dynamic variables. The TKE of the LES calculations presentedhere represent only the TKE of the resolved spectrum of turbulence.This means, that the subgrid turbulence does not appear in the graphs.In regions, where the level of subgrid turbulence is high, the TKE ofthe LES computations is underestimated. This is especially the case in

wall boundary layers, where the high shear stress at the wall impliesa production of small scale structures, which are not captured by themesh resolution. In free turbulence far off the wall, the LES mesh isfine enough to allow comparisons with measurements.

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0.50 0.25 0.00 0.25 0.50

x/D

0.50

0.25

0.00

0.25

0.50

0.75

1.00

1.25

1.50

v/rrodi

Figure 13. comparison of the velocity profiles at the jet orifice, circles: measure-ments, solid line: LES, averaging time 0.25s

Fig. 12 shows a comparison of TKE. The profile atx/D = 4 shows agood agreement of the LES calculation with the Filtered Smagorinskymodel. The Standard Smagorinsky model shows a too high trajectory(which confirms the observation from fig. 11) and overestimates theTKE. Obviously the Standard Smagorinsky model is not dissipating

sufficiently the turbulent energy. The constant C1 of the StandardSmagorinsky model could be increased to adapt the model to the flow,but this would question the universal validity of the model. The down-stream profiles show a quite good agreement far off the wall, but close tothe wall the TKE of the LES computations is well below the measuredTKE. Here, as mentioned above, the level of subgrid turbulence is notneglectable.

A look at the measured velocity profile at the jet orifice (fig. 13) fromAndreopoulos & Rodi shows a major discrepancy in the recirculationbubble between the hot wire measurements and the LES computation,which can be explained as follows: although Andreopoulos already pro-posed the possibility of a temporal recirculation zone at this location for

very short time spans [2], he did not expect a steady recirculation zone.But the major limitation of hot wire measurements is, that they cannotmeasure the direction of the flow and thus always pretend to measurea positive velocity. This explains, that in the region of the recirculation

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0.00 0.25 0.50 mixture fraction & T/Tmax

0.0

1.0

2.0

3.0

4.0

5.0

y/D

x/D=4x/D=2 x/D=6 x/D=10 x/D=16

Figure 14. comparison of the mixture fraction of a passive scalar distribution (LES)with the non-dimensionalized temperature distribution on the centerline of thejet, circles: measurements, solid line: LES Filtered Smag. Model, dashed line: LESStandard Smag. Model, averaging time 0.25s

bubble Andreopoulos & Rodi still measure a positive velocity. The LEScomputations in contrast, show the recirculation zone and confirm theobservations of Perry & Kelso[20] (see also fig. 8).

6.2.2. Scalar FieldDue to the lack of reliable measurement techniques for mixing in the80ths, Andreopoulos heated the jet slightly by 4C and measured thetemperature field instead. The goal was to obtain information on themixing behaviour of a species injected by the jet with a Schmidt numberequal to the Prandtl number. The temperature difference had to bekept small in order to preserve nearly equal densities. This helped toleave the jet velocity unharmed while maintaining the impulse ratio rand to avoid additional effects by buoyancy in the far field of the jet.But accuracy problems arise when measuring the temperature with

thermo couples, especially in highly turbulent regions. An additionaleffect occurs close to the wall, which potentially heats up. For the LEScomputations the field of a passive scalar with a Schmidt number ofSc=0.72 equal to the Prandtl number was computed.

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With the knowledge of these problems, the comparison of the mea-sured temperature field with the computed mixture fraction of a passivescalar on fig. 14 has to be looked at carefully. At x/D = 2 the agree-ment is quite well, but downstream the profiles increasingly disagree,

especially close to the wall. This is explained with heating up of the wallin the experiment. However, we do not feel, that this bad agreementis of major importance, since the following test case from Smith &Mungal shows better agreement, so that the disagreement in the casefrom Andreopoulos & Rodi can be explained by different boundaryconditions.

6.3. Test Case of Smith & Mungal

6.3.1. Scalar FieldThe doubts in the comparability of the measured temperature field

with the computed mixing of a scalar led to further investigations ofthe JICF with regard to mixing. In the recent years LIF measurementsbecame a reliable tool to predict mixing behaviour in turbulent flows.Acetone seeded air is used to track the history of fluid particles in theflow.

Our LES computations that aim to reproduce the case of Smith& Mungal show basically the same behaviour as before: a CVP isdeveloping, the horseshoe vortex, wake vortices, jet shear layer vorticesand the recirculation zone at the leading edge of the jet nozzle appearas seen previously.

The field of a passive scalar with a Schmidt number Sc=1.0 wascomputed to compare it with the mixture fraction of acetone from the

experiment. Fig. 15 shows the comparisons between experiment andLES computations, which show an excellent agreement. The computa-tion using the Standard Smagorinsky model shows a slightly too hightrajectory. The better agreement compared to the previous case canbe explained by two facts. First, the Reynolds number is lower thanin the case of Andreopoulos & Rodi. This fact speaks for a sufficientaccuracy for the LES computations of an injector on the vane in thereal geometry, because the Reynolds number is even lower than in thecase of Smith & Mungal. Second, because of the higher velocity ratio,the boundary layer plays a minor role. The origin of the boundary layeron the vane is only slightly upstream of an injector, at the leading edgeof the vane, and is accelerated then. This means, the boundary layer

thickness is supposed to be very small at the height of the injectors andhas only little effect on the jet flow.

As model for the describtion of the subgrid mixing the eddy diffusitymodel was chosen. The results show, that even this simple model is able

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0.00 0.10 0.20 mixure fraction Y0.00

5.00

10.00

15.00

y/D

x/D = 5 x/D = 10 x/D = 20x/D = 15

Figure 15. comparison of the mixture fraction of a passive scalar distribution ofthe measured nondimensionalized mixture fraction of acetone seeded air with theLES computation on the centerline of the jet, circles: measurements, solid line: LESFiltered Smag. Model, dashed line: LES Standard Smag. Model, averaging time0.25s, mesh size: 90000 points

to reproduce the mixing behaviour of a JICF. Because of its simplicityand fast execution it was chosen for all other LES computations.

6.3.2. Influence of the Schmidt NumberThe LIF measurements with acetone seeded air and a Schmidt numberof Sc 1.0 are performed to simulate the mixing behaviour of methane(Sc 0.72). To determine the influence of the Schmidt number on themixing behaviour, an LES computation was performed with two passivescalars. One of the passive scalars posesses the Schmidt number Sc=1.0and the other Sc=0.72. Only one computation needed to be performed,because the passive scalars have no feedback on the momentum field.Here, the advantage of a numerical investigation is clear: both scalarsuse exactly the same momentum field. Fig. 16 shows the comparison of

the distribution of the scalars. The curves are very close together andshow nearly no deviation. As expected, the distibution of the scalarwith a Sc=0.72 diffuses slightly more. It can be concluded, that the LIFmeasurements simulate the mixing behaviour of methane accurately.

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0.00 0.10 0.20 mixure fraction0.00

5.00

10.00

15.00

y/D

x/D = 5 x/D = 10 x/D = 20x/D = 15

Figure 16. Influence of Schmidt number to mean mixture fraction distribution,LES computation of two passive scalars with different Schmidt number, solid line:Sc=0.72, dotted line: Sc=1.0

6.3.3. Influence of Mesh CoarseningIn order to assess the influence of grid resolution, tests on simpler,less problem adapted meshes were performed. Here, the mesh cell sizeand point distribution is comparable to meshes used in the gas turbine

burner. The meshes have approximately 30000 mesh points. Although itcannot be assumed that the LES computation reproduces exactly quan-titatively the measurements, we aim to reproduce the measurementqualitatively.

The comparison of the scalar fields (fig. 17) shows some disagree-ments. The results are worse than in previous computations, but sur-prisingly good given the fact, that they are performed on unsufficientmeshes where not all requirements of LES are met. The trajectory istoo high, which is probably due to the bad resolution of the boundarylayer. Furthermore the scalar quantity is not sufficiently diffused. Thiseffect results from the filtering of the small scale structures by thecoarse mesh and thus a worse description of the turbulent transport.

This could be improved by a more sophisticated subgrid mixing model,but this idea was dropped in favour of fast computation times.

In conclusion, the LES computation delivers reasonable qualitativesolutions even on coarse meshes and statements about mixedness can

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0.00 0.10 0.20 mixure fraction Y0.00

5.00

10.00

15.00

y/D

x/D = 5 x/D = 10 x/D = 20x/D = 15

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

be derived from these computations. But qualitative comparisons haveto be regarded carefully.

6.4. Test Case of Toy

To obtain information about the reproducibility of the merging mech-anism of two adjacent jets the experiments of Toy [30] were computed.Here, additional problems occur, because little is known about theinteractions of the jet. To the authors knowledge, no mechanism isreported to explain the behaviour of the two jets to form one singleCVP instead of two. The aim of the LES investigation is to reproducethis merging mechanism and to shed light into this phenomenon.

The quantitative comparison of the momentum field on the center-line between the two jets is shown in fig. 18. The results are not as goodas in the previous LES computations. It has to be mentioned, that the

interactions of the two jets leads to longer durations until a stationaryflow pattern is established. That means, the computed time span oft=0.235s might not be sufficient to obtain reliable mean values on thecenterline of the jet.

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0.0 0.5 1.0 1.5 u/uc

0.00

5.00

10.00

15.00

20.00

y/D

x/D=2.5 x/D=5 x/D=10 x/D=20

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

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

The knowledge of the whole velocity field (and hence the entirevorticity field) makes it possible to have a closer look at the mecha-

nism which leads to the development of a single CVP and the fate ofthe two other vortices. Fig 19 shows a series of streamwise vorticitydistributions downstream of the two jets. From fig. 19 a) and b) can beseen, 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 Coandaeffect normally occurs when a jet is close to a parallel wall. The entrain-ment of the jet is disturbed by the wall and, due to the impossibility toentrain the fixed wall, the jet bends towards the wall. With two paralleljets a similar behaviour can be seen. Here, in the zone between the twojets the entrainment is disturbed and the jets bend towards the otherone as each jet trys to entrain the other.

In the case of the twin jet in crossflow this causes a problem forthe two inner vortices. The two vortices are quenched (fig. 19 c) anddivided in two vortex pairs (fig. 19 d), one pair (2a and 3a) abovethe remaining two outer vortices (1 and 4) and one pair below,

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a)

1 4

32

1 4

32

b)

4

3

c)

1

2

1 4

2a 3a

2b 3b

d)

2b 3b

2a 3a

4

e)

1

3a2a

4

3b2b

f)

1

3b

g)

4

2b

2a 3a

1

3b

2a

4

h)

2b

3a

1

i)

4

3b2b

1

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

close to the wall (2b and 3b). The four small vortices spin fast tokeep the torque of the initial two (inner) vortices constant. The stronggradients in these small, fast spinning vortices lead to higher dissipationrates and a shorter life span of the vortices. In the far field (fig. 19 i) thetwo originally outer vortices survive and form one single CVP. Thereremains a pair of small vortices close to the wall, though.

7. LES of Fuel Injection in a Gas Turbine

The lack of measurements in a real burner geometry to determine the

accuracy were compensated by the investigation of the JICF. The sim-ilar flow conditions of the JICF and the fuel injectors on the vane inthe industrial application gave confidence, that the computations of theburner geometry predicts the flow behaviour with sufficient precision,

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Figure 20. fuel injection on a part of the vane, isosurface: mixture fraction, isocon-tours: pressure, black arrows: velocity vectors. Inside the vane is the fuel supplyleading to the upper and lower injector.

that allows to make statements about mixedness and vortex formationsinside the burner. A full analysis of our LES computation of the Siemensgas turbine burner is beyond the scope of this article, and we explainonly the main steps of the analysis.

Our first approach in examining the burner was to have a look at apair of injectors on the vane in a homogeneous outer air flow (Fig. 20).This gave us the possibility to determine fuel mass flux rates throughthe injectors and to investigate vortex formations around the vane,which interact with the fuel injecting jets. The computation of a fullvane in homogeneous surrounding flow (Fig. 21) gave insight aboutinteractions between adjacent jets, especially to the merging mechanismof adjacent jets, which lead to unmixedness.

The final step, the computation of a segment of the burner has beendone recently. But for reasons of confidentiality we are not able topresent results of this computation in this article.

Fig 22 show a probability density function (PDF) of mixture fraction

downstream of an injector. There is a peak at 0 (pure air) and anotherat 0.075. This means, there are pockets of air alternating with pocketsof fuel. The mean value does not give any useful information, becausethe probability that the fluid is in a state of the mean value is quite

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Figure 21. visualization of fuel injection on the vane

improbable. Furthermore the mean value suggests, that the fluid atthis position is perfectly mixed, which is certainly not the case at everyinstant. This sort of PDF in the combustion chamber causes problemsdue to the fuel-rich combustion at certain instances leading to higherNOx production. Visualizations of the LES computation gives insightinto the flow to correlate the unmixed pockets to vortex formationsaround the vane. The knowledge of the reasons for unmixedness in themixing section of the burner gives the possibility for designing engineersto improve the mixedness in the gas turbine burner.

8. Conclusions

The present LES computations have proven the ability of reproducingthe main features of jets in cross flow on reasonably coarse grids.

The necessity of including the jet pipe and the plenum chamber tothe computed domain became evident. The proper description of thewall boundary layer is required to obtain the correct jet trajectory.The low pressure region downstream of the nozzle influences the jettrajectory and needs a high spatial discretization as well.

The general flow characteristics, like the development of the counter-rotating vortex pair, the horseshoe vortex, the jet shear layer vorticesand the merging of two adjacent jets are reproduced. Furthermore somelight could be shed into the merging mechanism of two adjacent jets.

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0.000 0.025 0.050 0.075 0.100 0.125 0.150mixture fraction

0.00

0.05

0.10

0.15

0.20

0.25

probability

surplus of AIR surplus of FUEL

meanvalue

perfectlymixed

Figure 22. example of a proability density function of mixture fraction downstreamof an injector.

The subgrid turbulence model influences the jet trajectory. For flows,that are strongly affected by the wall boundary layer, the FilteredSmagorinsky model showed better results. The nature of the JICF,to be determined by large scale motions, makes it possible for the LESapproach to obtain results with a good agreement, even with simplesubgrid models.

The LES approach has been applied to a gas turbine burner toobtain informations about momentum field and mixing. The compu-tations gave valuable insight in the events in the burner. This showsthe capability of the LES approach to be used as research tool in thedesign process of an industrial gas turbine burner.

Acknowledgements

This work has been carried out with the support of the gas turbinedepartment of Siemens Power Generation KWU (Combustion).

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