The paper presents novel developments in the DNS-based, turbulence modeling strategy of Lakehal et al. developed for calculating jets in crossflow. The particular features of the model include: 1) dynamic coupling of the high-Re kε with a one-equation model resolving the near-wall viscosity-affected layer; 2) inclusion of the anisotropy of turbulent transport coefficients for all transport equations; 3) near-wall variation of the turbulent Prandtl number as a function of the local Reynolds number. Most of the important aspects of the proposed model are based on known DNS statistics of channel and boundary layer flows. The model is validated against experiments for the case of film cooling of a flat plate, where coolant air is injected from a row of streamwise inclined jets. Excellent results were obtained for this configuration as compared to earlier numerical investigations reported in the open literature. The model is then extended to calculate film cooling of a symmetrical turbine blade by a row of laterally injected jets for various blowing rates. Comparison of the calculated and measured wall-temperature distributions show that only with this anisotropy eddy-viscosity/diffusivity model can the spanwise spreading of the temperature field be well predicted and the strength of the secondary vortices reduced. Furthermore, results of additional calculations show that combining the anisotropy eddy viscosity model with the DNS-based relation for turbulent Prandtl number promotes the eddy diffusivity of heat vis-a`-vis that of momentum further, leading to an enhanced spanwise spreading of the jet. The performance of this new approach improves with increasing blowing rate.

1.
Acharya
,
S.
,
Tyagi
,
M.
, and
Hoda
,
A.
,
2001
, “
Flow and Heat Transfer Predictions for Film Cooling
,”
Ann. N.Y. Acad. Sci.
,
934
, pp.
110
125
.
2.
Haven
,
B. A.
, and
Kurosaka
,
M.
,
1997
, “
Kidney and Anti-Kidney Vortices in Crossflow Jets
,”
J. Fluid Mech.
,
352
, pp.
27
64
.
3.
Haslinger, W., and Hennecke, D. K., 1997, “High Resolved Distribution of Adiabatic Film Cooling Effectiveness for Turbine Leading Edge Film Cooling,” ISABE Paper No. 97-7113.
4.
Ligrani
,
P. M.
,
Wigle
,
J. M.
, and
Jackson
,
S. W.
,
1994
, “
Film-Cooling from Holes with Compound Angle Orientations: Part 2—Results Downstream a Single Row of Holes with 6d Spanwise Spacing
,”
ASME J. Heat Transfer
,
116
, pp.
353
362
.
5.
Mehendale
,
A. B.
, and
Han
,
J. C.
,
1992
, “
Influence of Mainstream Turbulence on Leading Edge Film Cooling Heat Transfer.
ASME J. Turbomach.
,
114
, pp.
707
715
.
6.
Ardey, S., 1998, “3D-Messung des Stroemungsfeldes um die filmgekuehlte Vorderkante einer Referenzschaufe,” Abschlussbericht zum TURBOTHERM II-Verbundvorhaben 2.1.8.4 der Arbeitsgemeinschaft Hochtemperatur Gasturbine, Report LRT-Inst. 12-98/02, Universita¨t der Bundeswehr Mu¨nich, Germany.
7.
Beeck, A, 1992, “Stroemungsfelduntersuchungen zum aerodynamischen Verhalten eines hochbelasteten Turbinengitters mit Kuehlluftausblasung an der Vorderkante,” Ph.D thesis, Universita¨t der Bundeswehr Munich, Institut fuer Strahlantriebe, Germany.
8.
Findlay
,
M. J.
,
Salcudean
,
M.
, and
Gartshore
,
I. S.
,
1999
, “
Jets in a Crossflow—Effects of Geometry and Blowing Ratio
,”
ASME J. Fluids Eng.
,
121
, pp.
373
378
.
9.
Leylek
,
J. H.
, and
Zirkle
,
R. D.
,
1994
, “
Discrete-Jet Film Cooling: A Comparison of Computational Results with Experiments
,”
ASME J. Turbomach.
,
116
, pp.
358
368
.
10.
Walters, K. D., and Leylek, J. H., 1997, “A Detailed Analysis of Film-Cooling Physics, Part 1: Streamwise Injection with Cylindrical Holes,” ASME Paper No. 97-GT-269.
11.
Lakehal
,
D.
,
Theodoridis
,
G.
, and
Rodi
,
W.
,
1998
, “
Computation of Film Cooling of a Flat Plate by Lateral Injection from a Row of Holes
,”
Int. J. Heat Fluid Flow
,
19
, pp.
418
430
.
12.
Azzi
,
A.
, and
Lakehal
,
D.
,
2002
, “
Perspectives in Modeling Film Cooling of Turbine Blades by Transcending Conventional Two-Equation Turbulence Models
,”
ASME J. Turbomach.
,
124
, July, pp.
472
484
.
13.
Garg
,
V. K.
, and
Abhari
,
R. S.
,
1997
, “
Comparison of Predicted and Experimental Nusselt Number for a Film Cooled Rotating Blade
,”
Int. J. Heat Fluid Flow
,
18
, pp.
452
460
.
14.
Ferguson, D. J., Walters, K. D., and Leylek, J. H, 1998, “Performance of Turbulence Models and Near-Wall Treatments in Discrete Jet Film Cooling Simulations,” ASME Paper No. 98-GT-438.
15.
Garg
,
V. K.
, and
Ameri
,
A. A.
,
1997
, “
Comparison of Two-Equation Turbulence Models for Prediction of Heat Transfer on Film-Cooled Turbine Blades
,”
Numer. Heat Transfer, Part A
,
31
, pp.
347
371
.
16.
Bohn, D. E., Becker, V., Kusterer, K., Ardey, S., and Fottner, L., 1997, “The Influence of Slot Injection and Shower-Head Injection on the 3D Flow Field of a Film-Cooled Turbine Blade under Consideration of Side-Wall Effects,” AIAA Pap., No. 97/7162.
17.
Irmisch, S, 1995, “Simulation of Film-Cooling Aerodynamics with a 2-D Navier-Stokes Solver using Unstructured Grids,” ASME Paper No. 95-GT-024.
18.
Theodoridis
,
G.
, and
Rodi
,
W.
,
1999
, “
Calculation of the Flow Around a High-Pressure Turbine Blade with Cooling-Jet Injection from Slots at the Leading Edge
,”
Flow, Turbul. Combust.
62
, pp.
89
110
.
19.
Vogel, D. T., 1993, “Numerische Untersuchung des Mischungsverhaltens von Filmku¨hlstrahlen in Turbinenstro¨mungen,” Ph.D thesis, Ruhr-Universita¨t Bochum, Germany.
20.
Theodoridis
,
G.
,
Lakehal
,
D.
, and
Rodi
,
W.
,
2001
, “
3D Calculations of the Flow Field Around a Turbine Blade with Film Cooling Injection Near the Leading Edge
,”
Flow, Turbul. Combust.
,
66
, pp.
57
83
.
21.
Lakehal
,
D.
,
Theodoridis
,
G.
, and
Rodi
,
W.
,
2001
, “
Three Dimensional Flow and Heat Transfer Calculations of Film Cooling at the Leading Edge of a Symmetrical Turbine Blade Model
,”
Int. J. Heat Fluid Flow
,
22
, pp.
113
122
.
22.
Rodi, W., 1991, “Experience with Two-Layer Models Combining the k-ε Model with a One-Equation Model Near the Wall,” AIAA Pap. No. 91-0216.
23.
Kaszeta
,
R. W.
, and
Simon
,
T. W.
,
2000
, “
Measurement of Eddy Diffusivity of Momentum in Film Cooling Flows with Streamwise Injection
,”
ASME J. Turbomach.
,
122
, pp.
178
183
.
24.
Bergeles
,
G.
,
Gosman
,
A. D.
, and
Launder
,
B. E.
,
1978
, “
The Turbulent Jet in a Cross Stream at Low Injection Rates: a Three-Dimensional Numerical Treatment
,”
Numer. Heat Transfer
,
1
, pp.
217
242
.
25.
Sinha
,
A. K.
,
Bogard
,
D. G.
, and
Crawford
,
M. E.
,
1991
, “
Film-Cooling Effectiveness Downstream of a Single Row of Holes with Variable Density Ratio
,”
ASME J. Turbomach.
,
113
, pp.
442
449
.
26.
Rodi, W., Theodoridis G., and Lakehal, D., 1997, “Entwicklung eines geeigneten Turbulenz- und Waermeuebergangsmodells fuer ein 3D Berechnungsverfahren der Filmkuehlung an der Schaufelvorderkante,” Abschlussbericht Institut fuer Hydromechanik, University of Karlsruhe.
27.
Norris, L. H., and Reynolds, W. C., 1975, “Turbulent Channel Flow with a Moving Wavy Boundary,” Report No. FM-10, Stanford University, Department of Mechanical Engineering.
28.
Rodi
,
W.
,
Mansour
,
N. N.
, and
Michelassi
,
V.
,
1993
, “
One-Equation Near-Wall Turbulence Modeling with the Aid of Direct Simulation Data
,”
ASME J. Fluids Eng.
,
115
, pp.
196
205
.
29.
Gilbert, N., and Kleiser, L., 1991, “Turbulence Model Testing with the Aid of Direct Numerical Simulation Results,” Proc., 8th Symposium on Turbulent Shear Flows, Paper No. 26-1, Munich, Germany, September 9–11.
30.
Quarmby
,
A.
, and
Quirk
,
R.
,
1974
, “
Axisymmetric and Non-Axisymmetric Turbulent Diffusion in a Plain Circular Tube at High Schmidt Number
,”
Int. J. Heat Mass Transf.
,
17
, p.
143
143
.
31.
Kim
,
J.
,
Moin
,
P.
, and
Moser
,
R.
,
1987
, “
Turbulence Statistics in Fully Developed Channel Flow at Low Reynolds Number
,”
J. Fluid Mech.
,
177
, pp.
133
166
.
32.
Kays, W. M., and Crawford, M. E., 1993, Convective Heat and Mass Transfer, Third Edition, McGraw-Hill, New York, NY.
33.
Lu
,
D. M.
, and
Hetsroni
,
G.
,
1995
, “
Direct Numerical-Simulation of a Turbulent Open-Channel Flow with Passive Heat-Transfer
,”
Int. J. Heat Mass Transf.
,
38
, pp.
3241
3258
.
34.
Madavan, N. K, and Rai, M. M., 1995, “Direct Numerical-Simulation of Boundary Layer Transition on a Heated Flat Plate with Elevated Freestream Turbulence,” AIAA Pap. No. 95-0771.
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