Unsteady Film Cooling on HP Gas Turbine

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UNSTEADY 3D NAVIER-STOKES CALCULATION OFA FILM-COOLED TURBINE STAGE WITH DISCRETE

COOLING HOLES

Th. Hildebrandt, J. EttrichNUMECA Ingenieurbro, D-90530 Wendelstein, [email protected]

M. Kluge, M. Swoboda, A. Keskin, F. Haselbach, H.-P. SchifferROLLS ROYCE Deutschland, Eschenweg 11, D-15287 Dahlewitz, [email protected]

ABSTRACTEvery modern high-pressure turbine needs a highly sophisticated cooling

system. The most frequently used cooling method of to date is film cooling,characterized by a high degree of interaction between the main flow and thecooling flow. Therefore the effects of film cooling have to be taken into accountin the aerodynamic design of film cooled high-pressure turbines.

Using modern commercial turbomachinery oriented CFD-methods, themodeling of film cooling holes can be achieved by various numerical methodsof different complexity. The so-called source term modeling is fast and easy to

apply, but cannot provide very detailed flow information. In contrast, thediscretization of every single cooling hole represents a very complexapproach, but provides more in-depth information about the cooling pattern.The efforts of full-scale modeling need to be balanced against the moredetailed and accurate results. In addition to the complex geometries of filmcooled turbines, the flow phenomena are highly unsteady, thus requiring aCPU intensive time dependent numerical approach.

The present paper is focused on a detailed investigation of the unsteadyflow field in a film cooled high-pressure turbine stage. An unsteady 3D Navier-Stokes calculation is applied to the entire stage configuration including a fulldiscretization of all the cooling holes.

NOMENCLATURESymbols Subscripts; Abbreviations

M [ - ] Blowing rate c Coolingv [ m/s ] Velocity 1,2 Inlet, exit conditions

p [ Pa ] Pressure t total

Ma [ - ] Mach Number is isentropic

Re [ - ] Reynolds Number NGV Nozzle Guide Vane

[ kg/m3] Density


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INTRODUCTIONIn order to obtain maximum thermodynamic cycle efficiency a high temperature

level is required in the high pressure (HP) turbines of modern environmentallyfriendly gas turbines. The temperature level there is usually by far higher than themaximum allowable temperature of even the most advanced materials. Therefore,

every modern HP turbine needs a sophisticated cooling system. From a variety ofavailable cooling methods film cooling emerged as todays standard cooling method.Relatively cool compressor air is injected through numerous holes and slots on theblade and endwall surfaces of a HP-turbine. Apart from the desired influence of theinjected cooling air on the heat transfer coefficients of the blade and endwallsurfaces, the cooling jets have a considerable effect on the main flow as well (Benz(1994), Hildebrandt et.al. (2001), Vogel (1997)). As a consequence, the effects of filmcooling have to be taken into account in the aerodynamic design of a HP turbine.

Modern commercial Navier-Stokes solvers provide the designer in the turbo-machinery environment with a variety of options to simulate the flow inside the bladepassage of a film-cooled turbine. The CFD modeling of film cooling holes can be

achieved by various numerical methods of different complexity. The numericaltechnique of source term modeling is the fastest and least complex method tointroduce the effects of film cooling into a 3D Navier-Stokes calculation of a turbine.This method is computationally least expensive and easy to apply, making it wellsuitable for the fast turn-around times, which are required in the modern designprocesses. The cooling flow is taken into account by a distribution of various sourcesof mass, momentum and energy on the blade and endwall surfaces. In contrast, thefull modeling of every single cooling hole represents the most complex approach.Using this method every cooling hole, including the cooling air plenum is discretized.Obviously, turn-around times and engineering efforts are by far higher if compared tothe source term method. The reward of applying this method to a film-cooled turbine

is a high amount of very detailed flow information.

The complex flow phenomena of film cooling are apparently time dependentthemselves, and additionally, highly influenced by the unsteady rotor-statorinteraction of the adjacent blade rows. The impinging wakes of a preceding blade roware periodically altering the local cooling efficiency along the blade surfaces of thesucceeding turbine rotor. Vice versa, the circumferentially changing backpressureinduced by a succeeding blade row can lead to considerable fluctuations in bladepressure distribution and shock location. The local blowing rate

v

vM cc

= (1)

is a function of the local velocity ratio, hence depending strongly on the pressuregradient between the plenum and the local ejection position on the blade surface.Therefore, a periodically fluctuating blade pressure distribution leads directly to anequivalently fluctuating local film cooling efficiency. Therefore Unsteadiness is crucialif the focus is on very detailed cooling flow phenomena.

The present paper is focused on a detailed investigation of an unsteady flow fieldin a film cooled high-pressure turbine stage. The flow is simulated using an unsteady3D Navier-Stokes calculation of the entire turbine stage of a nozzle guide vane androtor configuration including a full modeling of all single cooling holes.


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COMPUTATIONAL METHODWithin the frame of the presented computations a commercial CFD systems has

been employed. FINE/Turbo, developed by NUMECA Int. S.A (NUMECA (2002)),is a specialized CFD package for all sort of turbomachinery applications. Thepackage includes grid generation, the flow solver and a post processing software. All

program modules are embedded into a turbomachinery specific environment.

The numerical scheme solves the 3D Reynolds-averaged Navier-Stokesequations (RANS) on general structured non-orthogonal multi-block grids. Theflexibility of the structured grids is greatly enhanced by use of so-called Full NonMatching Connections, a technique, which allows to arbitrarily connect grids block ofdifferent grid topologies or point numbers to each other.

The numerical algorithm incorporated into FINE/Turbo is an explicit four stageRunge-Kutta scheme (Jameson and Baker (1984)). A variety of convergenceacceleration techniques are employed, such as implicit residual smoothing, dual time

stepping and full multigrid. Space integration is performed using a second order cell-centered finite volume discretization with second and fourth order artificialdissipation. Coarse grid calculations can be carried out in an automatic way on everycoarser grid level.

A number of turbulence models are available within FINE/Turbo. In the scopeof the present work the algebraic turbulence model of Baldwin and Lomax (1978) hasbeen chosen. All solid walls have been treated as fully turbulent. The authors are wellaware that a simple turbulence model and the assumption of fully turbulent boundarylayers cannot capture sufficiently accurate the quite complex turbulent structurestypical for film cooling. With the main objectives of this study in mind comparing afully discretized film cooling geometry with a source term approach the use of asomewhat simpler model seemed justified and effective. Moreover, new experimentaldata suggest (Ardey (1998)) that in film cooling simulations the use of any eddyviscosity turbulence model is questionable due to the extreme anisotropic nature ofturbulence in these cases.

THE MT-1 SINGLE STAGE HP TURBINEThe MT-1 single stage HP-turbine, which had been investigated in the present

study, is described in detail in (Kluge et.al. (2003). Table 1 summarizes some basicgeometrical and aerodynamic specifications of the design data of the TATEF turbinestage.

Aero- /ThermodynamicsBlade Number NGV / Rotor n 32 / 60, 64* [ - ]Mass Flow, Inlet m1 17.49 [ kg/s ]Rotational Speed 9.500 [ RPM]

Exit Mach Number Ma2 0.98 [ - ]Reynolds Number Re2 2.8e6 [ - ]Gas-to-Wall Temperature Ratio 1.54

Table 1: Design Data of the MT-1 Turbine


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In order to carry out unsteady CFD simulations with an acceptable computationaleffort the domain scaling method had been applied. There, it is desirable to obtain asmall common integer factor as a blade number ratio between NGV and rotor. Theoriginal blade number of the rotor had been increased from 60 to 64 enabling toperform a time-dependent periodic computation with one stator passage and two

rotor passages meshed. Usually the error, which results from changing the solidity, isacceptable, if the change in blade pitch is less than 10%, which is the case herein.

NUMERICAL BOUNDARY CONDITIONS

Aero- /ThermodynamicsInlet, NGV pt1 461.000 [ Pa ]

Direction axialTt1 444.4 [ K ]

Inlet, Front cavity pt1 943.000 [ Pa ]

Direction axial into PlenumTt1 271 [ K ]

Inlet, rear cavity pt1 682.000 Pa ]Direction axial into Plenum

Tt1 272 [ K ]Outlet p2 (rad. eq.) 142.100 @ Hub [ Pa ]Walls: all NGV, rotor hub & blade Tw imposed 288.5 / 333 [ K ]Walls: all other Adiabatic

Table 2: Numerical Boundary Conditions

These types of inlet and exit boundary conditions are typical for turbomachinery

cases. There was some uncertainty about the specification of the wall boundaryconditions. As a best possible assumption, the thermal wall boundary conditions hadbeen set to a constant wall temperature inside the entire NGV as well as on the rotorblade surface and hub. All other walls within the domain were treated as adiabatic.Considering the very short measurement times (approx. 500ms) this simplificationseems justified.

COMPUTATIONAL GRID

The numerical domain was discretized using a structured multi-block grid.Compared to an unstructured tetrahedral approach structured grids usually provide ahigher numerical accuracy. Consequently, emphasis was laid on a high grid quality inorder to minimize numerical errors, particularly inside the cooling holes and theirimmediate vicinity. The grid in these regions is locally highly refined. This high levelof refinement would have led to an overall number of grid points, far beyond anyreasonable limits. In order to reduce the problem size coarser grid blocks are locatedaround the highly resolved grid regions. The coarse and fine grid areas areconnected by means of a non-congruent block-to-block connection using a fullyconservative interpolation technique. The application of this technique in film coolingconfigurations had been described by Hildebrandt (2001).


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Around the blades as well as in the front and rear plenum and inside the coolingholes HOH-topologies had been applied (Fig.1, Fig. 2). The grid is composed of 651grid blocks with a total number of 2.1 Mio. Grid points. About 75% of the grid pointsare located in the immediate vicinity of the cooling holes. The refined areas aroundthe rows of cooling holes are visible in Fig.2. These areas are resolved about four

times finer in each spatial direction than the surrounding regions of the main flow.

The non-dimensional wall distance y+ varies typically around 1 and 2, dependingon the local flow conditions. The laminar sub-layer, important for any prediction ofwall shear stress or heat transfer, is therefore well captured.

Figure 1: Numerical Grid Blade-to-Blade View / Plenum with Cooling Holes

Figure 2: Numerical Grid on NGV Surface


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COMPUTATIONAL PERFORMANCEAll computations were carried out on a single processor PC at 1800 MHz,

running under LINUX. Starting from a steady state solution the unsteady computationtook about 18 times to pass the rotor leading edge behind the NGV trailing edge inorder to achieve a satisfactory periodical behaviour. The unsteady mass flow was

taken as a convergence criteria (Fig.3). The total CPU time was in the order of 20days, requiring about 1 GB of RAM. The overall level of convergence was slightlyfluctuating around three orders of magnitude reduction in the total RMS residual.

Figure 3 Mass Flow Convergence History

The unsteady calculations were carried out using the domain scaling technique.The rotor pitch was brought from 60 to 64 blades, allowing to mesh two rotor bladeswith the same periodicity as one NGV pitch. For convergence acceleration dual time

stepping was used. The rotor turning was resolved by 32 discrete angular positionsfor one rotor pitch.

COMPARISON FULL DISCRETIZATION / SOURCE TERM APPROACH

Source Term Full Discretization

Iterations for full convergence ~ 6.200 ~ 10.000Grid points ~ 1.500.000 ~2.100.000Blocks 16 651Relative CPU time 1.0 ~2.4Relative RAM 1.0 ~1.55

Table 3: Resource requirements

Apart from the human effort of meshing 120 additional cooling holes, the sourceterm approach requires considerably less computational resources. The larger RAMrequirements are obvious, considering the higher number of grid cells and blocks. Inaddition, the CPU time increases over-proportionally since the coupling between themain flow and the cooling jets is much stronger in case of the fully discretizedapproach. Here, convergence is slowed down due to the slow propagation from the

main flow through the holes into the plenum.


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RESULTSBlade Pressure Distribution

The blade pressure distribution, given as isentropic Mach number (Fig. 4) in theNGV at 50% span compares the results of the steady and unsteady results of boththe source term approach and the fully discretized cooling holes as well as

experiments.Quite interestingly, although the unsteady results are fluctuating within a hardly

visible range, the time average deviates significantly from the steady calculationperformed by using a mixing plane approach. The differences occur mainly in threeareas.

First, all the pressure peaks around the emerging cooling jets are by far moredominant in the unsteady calculation than in the steady results. Here, any influencefrom the downstream rotor can be excluded since the location of the cooling holes isupstream of the sonic throat. The pressure peaks are particularly significant in caseof the fully meshed cooling holes, and less obvious in the source term results. Thesepressure over- and undershoots originate in a quasi stagnation of the main flow

immediately in front of the cooling jet. After a severe deceleration, the main flow isforced around the cooling jet resulting in a strong acceleration. In such a case thecooling jet behaves very much like a solid obstacle in the flow, characteristic forcylindrical cooling holes (Hildebrandt, Ganzert, Fottner (2000)). Strong interactionsbetween the emerging cooling jets and the main flow occur. These interactions leadto a complicated system of vortices (Vogel (1997)), which are prone to self-excitedunsteadiness.

Figure 4: Isentropic Mach Number Distribution NGV 50% Span

The second region of interest is around the exits of the second row of coolingholes located at the pressure side at around (x/lax = 0.5). The cooling holes on thepressure side are arranged in two double rows. In the steady calculation, a strongpeak occurs, which corresponds to the first set of holes of the second rows, while the

effects from the second part of the double row is barely visible. In contrast, the time


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accurate solution produces the dominant velocity peak around the position of thesecond set of cooling holes in the double row. The unsteadily computed jets of thefirst row are apparently by far stronger than their counterparts from the steadysolution. The strong peak visible for the first cooling hole row on the suction sidegives also evidence to this. Consequently, the stronger unsteady jet of the first line of

holes forces the main flow away from the blade surface, which results in a much lesssevere interaction between the main flow and the jets emerging from the second lineof holes. Again this effect is by far less pronounced, but still detectable in case of thesource term approach. Here, the cooling jets are always weaker than in case of thefully discretized holes. The steady source term calculation hardly shows any sign ofthe cooling jets in the isentropic Mach number distribution.

Third, the second row of cooling holes on the suction side have the most visibleeffect on the main flow, recognizable by a strong pressure under- and overshoot. Thelocation (x/lax = 0.7) is close to the peak Mach-Number of the main flow. Hence, thejets are emerging into a region of low pressure, resulting in a high local blowing rate.The succeeding shock (x/lax = 0.75) is less pronounced in the unsteady time-

averaged calculation. The unsteady shock fluctuations are smeared out by the time-averaging. Since there are hardly any differences between source term approachand the discretized cooling holes, it is obvious that this phenomena is not connectedto any film cooling effects.

Figure 5: Blade Pressure Distribution Rotor 50% Span

The blade pressure on the rotor surface is given for all the unsteady time steps,the unsteady time average and the steady computation (Fig. 5). Naturally, the timedependent fluctuations inside the rotor are by far more dominant, forced by theimpinging wakes from the upstream NGV. The differences between the timeaveraged and the steady results is largest at the rotor leading edge. It is this region,which suffers most form the numerical simplifications necessary for a mixing planeapproach. The range of the time dependent fluctuations is large throughout nearlythe complete blade. However, approaching the trailing edge, the fluctuations aredamped out, showing hardly any influence on the rotor exit Mach number.


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Heat Transfer CoefficientsThe heat transfer on the blade surfaces is expressed by the Nusselt number

Wg TT

q

k

LNu

= (2)

Similar to the blade pressure distribution the unsteady effects are less obvious inthe NGV. There, the most significant phenomena are taking place on the suction sideclose to the leading edge. The ejecting cooling flow interacts with the main flow,triggering time dependent separations of the main flow immediately behind the NGVleading edge. The obvious discontinuity at around 50% normalized axial distance(x/lax = 0.5) on the NGV suction surface is caused by the connection of a very finegrid to the relatively coarse surrounding grid. The high gradients of the quite sensitiveNusselt number are smeared out on the coarser grid, causing a discontinuity ifplotted along the blade surface.

Figure 6: Nusselt Number Distribution, NGV 50% Span

The overall level of the Nusselt number along the uncooled rotor blade surface isby far smaller compared to the cooled NGV. Unsteady effects are dominantthroughout the entire blade passage (Fig. 7). The range of the time dependentNusselt number can reach more than three times the level of the steady or timeaveraged calculation questioning the reliability of steady heat transfer calculations inmultistage configurations.

The hot streaks of uncooled flow and the cooling jets emerging from the NGVenter the rotor passage in an alternating way (Fig. 8). In cases where relatively coolair from the jets impinges on the rotor blade surface the Nusselt number changes itssign, indicating a heat flux from the rotor into the flow (Fig.7).


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Figure 7: Nusselt Number Distribution, Rotor 50% Span

.

Figure 8: Absolute Total Temperature Distribution, Rotor 50% Span

Flow DetailsIn contrast to a less labour- and CPU-intensive set-up with source terms (Kluge

et.al. (2003)) the meshing of every single cooling hole, including the plenum providesa much higher level of detailed information. Since the local flow conditions at thecooling hole exits are not longer a fixed boundary condition as in the source termapproach, the local blowing rate has the freedom to adapt itself according to the localflow conditions. Consequently, the local blowing rate varies from hole to hole,obvious in the distribution of the heat transfer coefficient in Figure 9.


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Figure 9: Heat Transfer Coefficient in NGV

The cooling flow enters the blade passage in a typical flow pattern (Fig. 10). Independence on the inclination angle, the local blowing rate and the shape of thecooling hole, the emerging jet acts much like a solid obstacle. The incomingboundary layer of the main flow rolls up into a horseshoe vortex, causing a counter-rotating kidney vortex behind the jet. (Hildebrandt et.al. (2002), Wilfert (1994)). Thisvortex configuration is responsible for the hot gas entrainment beneath the cool air, adistinct and undesired feature of cylindrical cooling holes.

Figure 10: Vortex Configuration at Cooling Flow Exit

CONCLUSIONSUnsteady calculations of a transonic film cooled turbine stage where the cooling

holes and the cold air plenum is discretized represent a high level of very detailedinformation from the flow. Clearly, on the downside of this approach are the highCPU requirements and the quite labour intense pre-processing. Both limitationsprohibit the use of such a method in the frame of the daily design work in industry,which is characterized by short turn around times. The source term approach,

presented in Kluge et. al. (2003) is more suitable in such an environment, but suffers


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not only from a lack of detailed flow information, but more important from anuncertainty in the specification of the correct boundary condition for the source terms.Here, a full discretization offers the advantage that no boundary conditions arenecessary on the exit surface of the cooling holes as long as the plenum is taken intoaccount. However, the boundary conditions for the plenum are relatively

straightforward to obtain. An option is proposed to combine these two approaches.First, a set of fully discretized simulations are conducted for typical configurationsand operating conditions. From these results, boundary conditions for the sourceterm approach can be derived in order to calibrate the source term boundaryconditions. But even then, the immediate vicinity of the cooling holes will be bettercaptured using a full discretization of holes and plenum.

ACKNOWLEDGEMENTThe reported work was carried out under the contract of the European Commission

as part of the BRITE EURAM project contract number BRPR-CT-97-0519, Projectnumber BE97-4440 (TATEF).The authors wish to acknowledge the financial support as

well as the contributions from ALSTOM POWER, FIAT AVIO, ITP, SNECMA, TURBO-MECA, MTU AeroEngines, ROLLS-ROYCE Plc. and ROLLS ROYCE DEUTSCHLAND.

REFERENCES[1] Ardey, S., (1998): Untersuchung der aerodynamischen Effekte von Vorder-

kanten-Khlluftausblasung an einem hochbelasteten Turbinengitter, Ph.D.Thesis, University of the German Armed Forces Munich, Germany

[2] Baldwin, B.S.; Lomax H., (1978): Thin Layer Approximation and AlgebraicModel for Separated Turbulent Flow, AIAA Paper 78-0257

[3] Benz, E. (1994): Entwicklung und Erweiterung von grundlegenden Anstzen

zur numerischen Berechnung turbulenter Unter- und berschallstrmungen inGasturbinen, Ph.D. Thesis, University Karlsruhe, Germany

[4] Hildebrandt, Th.; Ganzert, W., Fottner, L. (2000): Systematic Experimental andNumerical Investigations on the Aerothermodynamic of a Film Cooled TurbineCascade with Variation of the Cooling Hole Shape Part II, ASME Paper 00-GT-298

[5] Hildebrandt, Th.; (2001): CFD Simulation Filmgekhlter Turbinen, VDI-GET2001, Dsseldorf, Germany

[6] Jameson, A.; Baker, T.J.; (1984): Multigrid Solution of the Euler Equations forAircraft Configurations, AIAA Paper 84-0093

[7] Kluge, M.; Swoboda, M.; Keskin, A.; Haselbach, F.; Schiffer, H.-P.,

Hildebrandt, Th.; Ettrich, J. (2003): Unsteady 3D Navier-Stokes Calculation ofa Film-Cooled Turbine Stage, Cooling Flow Modeling via Source TermApproach

[8] NUMECA Int. S.A; (2002), FINE/Turbo User Manual, V. 5.3, Brussels, Belgium

[9] Vogel, D.T.; (1997): Numerische Untersuchung des Mischungsverhaltens vonFilmkhlstrahlen in Turbinenstrmungen, DLR-Report 96-35, Institut frAntriebstechnik, DLR Cologne, Germany

[10] Wilfert, G.; Fottner, L.; (1994): The Aerodynamic Mixing Effect of DiscreteCooling Jets with the Mainstream Flow on a Highly Loaded Turbine Cascade,ASME Paper 94-GT-235

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Unsteady Film Cooling on HP Gas Turbine