Effusion cooling is one of the most effective and widespread techniques to prevent combustor liner from being damaged. However, most recent developments in combustion techniques, resulting from increasingly stricter air pollution regulations, have highlighted the necessity of reducing the amount of air available for effusion cooling while keeping an adequate level of protection. Adoption of compound angles in effusion cooling is increasingly recognized by jet engine manufacturers as a powerful solution to meet new combustor requirements. Therefore, understanding the flow behavior and developing methods able to provide accurate estimates of wall temperatures is of a major importance. This study assesses the capability of a high-level Reynolds-averaged Navier–Stokes (RANS) method, differential Reynolds stress model (DRSM), in conjunction with a generalized gradient diffusion hypothesis (GGDH), and of a hybrid RANS–large eddy simulations (LES) method, zonal detached eddy simulation (ZDES), to predict overall film effectiveness. Both approaches are compared with the experimental data from Zhang et al. (2009, “Cooling Effectiveness of Effusion Walls With Deflection Hole Angles Measured by Infrared Imaging,” Appl. Therm. Eng., 29(5), pp. 966–972) and with a classical well-known RANS model (k–ω shear-stress transport (SST) model). Despite the fact that some discrepancies are found, both approaches have proved suitable and reliable for predicting wall temperatures (relative errors of about 5%). Moreover, a new method to deal with ZDES length scales for unstructured grids is proposed. ZDES applicability and its general advantages and drawbacks are also discussed. Finally, an in-depth analysis of the film structure is carried out on the basis of the ZDES simulations. The principal structures are identified (an asymmetric main vortex (AMV) and a counter rotating vortex pair, CRVP), and the film formation mechanisms are presented. Significant spanwise-homogeneous distributions of surface overall film cooling effectiveness are observed.

References

References
1.
Zhang
,
C.
,
Lin
,
Y.
,
Xu
,
Q.
,
Liu
,
G.
, and
Song
,
B.
,
2009
, “
Cooling Effectiveness of Effusion Walls With Deflection Hole Angles Measured by Infrared Imaging
,”
Appl. Therm. Eng.
,
29
(
5
), pp.
966
972
.
2.
Ligrani
,
P.
,
Goodro
,
M.
,
Fox
,
M.
, and
Moon
,
H.-K.
,
2012
, “
Full-Coverage Film Cooling: Film Effectiveness and Heat Transfer Coefficients for Dense and Sparse Hole Arrays at Different Blowing Ratios
,”
ASME J. Turbomach.
,
134
(
6
), p.
061039
.
3.
Ligrani
,
P.
,
Goodro
,
M.
,
Fox
,
M. D.
, and
Moon
,
H.-K.
,
2015
, “
Full-Coverage Film Cooling: Heat Transfer Coefficients and Film Effectiveness for a Sparse Hole Array at Different Blowing Ratios and Contraction Ratios
,”
ASME J. Heat Transfer
,
137
(
3
), p.
032201
.
4.
Schmidt
,
D. L.
,
Sen
,
B.
, and
Bogard
,
D. G.
,
1996
, “
Film Cooling With Compound Angle Holes: Adiabatic Effectiveness
,”
ASME J. Turbomach.
,
118
(
4
), pp.
807
813
.
5.
Sen
,
B.
,
Schmidt
,
D. L.
, and
Bogard
,
D. G.
,
1996
, “
Film Cooling With Compound Angle Holes: Heat Transfer
,”
ASME J. Turbomach.
,
118
(
4
), pp.
800
806
.
6.
Ligrani
,
P.
, and
Ramsey
,
A.
,
1997
, “
Film Cooling From Spanwise-Oriented Holes in Two Staggered Rows
,”
ASME J. Turbomach.
,
119
(
3
), pp.
562
567
.
7.
Jung
, I
. S.
, and
Lee
,
J. S.
,
2000
, “
Effects of Orientation Angles on Film Cooling Over a Flat Plate: Boundary Layer Temperature Distributions and Adiabatic Film Cooling Effectiveness
,”
ASME J. Turbomach.
,
122
(
1
), pp.
153
160
.
8.
Ekkad
,
S.
,
Zapata
,
D.
, and
Han
,
J.
,
1997
, “
Heat Transfer Coefficients Over a Flat Surface With Air and CO2 Injection Through Compound Angle Holes Using a Transient Liquid Crystal Image Method
,”
ASME J. Turbomach.
,
119
(
3
), pp.
580
586
.
9.
McGovern
,
K.
, and
Leylek
,
J.
,
2000
, “
A Detailed Analysis of Film Cooling Physics: Part II—Compound-Angle Injection With Cylindrical Holes
,”
ASME J. Turbomach.
,
122
(
1
), pp.
113
121
.
10.
Aga
,
V.
,
Rose
,
M.
, and
Abhari
,
R. S.
,
2008
, “
Experimental Flow Structure Investigation of Compound Angled Film Cooling
,”
ASME J. Turbomach.
,
130
(
3
), p.
031005
.
11.
Aga
,
V.
, and
Abhari
,
R. S.
,
2011
, “
Influence of Flow Structure on Compound Angled Film Cooling Effectiveness and Heat Transfer
,”
ASME J. Turbomach.
,
133
(
3
), p.
031029
.
12.
Stratton
,
Z. T.
,
Shih
,
T. I.-P.
,
Laskowski
,
G. M.
,
Barr
,
B.
, and
Briggs
,
R.
,
2015
, “
Effects of Crossflow in an Internal-Cooling Channel on Film Cooling of a Flat Plate Through Compound-Angle Holes
,”
ASME
Paper No. GT2015-42771.
13.
McClintic
,
J. W.
,
Wilkes
,
E. K.
,
Bogard
,
D. G.
,
Dees
,
J. E.
,
Laskowski
,
G. M.
, and
Briggs
,
R.
,
2015
, “
Near-Hole Thermal Field Measurements for Round Compound Angle Film Cooling Holes Fed by Cross-Flow
,”
ASME
Paper No. GT2015-43949.
14.
Mayle
,
R.
, and
Camarata
,
F.
,
1975
, “
Multihole Cooling Film Effectiveness and Heat Transfer
,”
ASME J. Propul. Power
,
97
(
4
), pp.
534
538
.
15.
Kaszeta
,
R.
, and
Simon
,
T.
,
2000
, “
Measurement of Eddy Diffusivity of Momentum in Film Cooling Flows With Streamwise Injection
,”
ASME J. Turbomach.
,
122
(
1
), pp.
178
183
.
16.
Bianchini
,
C.
,
Andrei
,
L.
,
Andreini
,
A.
, and
Facchini
,
B.
,
2013
, “
Numerical Benchmark of Nonconventional RANS Turbulence Models for Film and Effusion Cooling
,”
ASME J. Turbomach.
,
135
(
4
), p.
041026
.
17.
Bergeles
,
G.
,
Gosman
,
A.
, and
Launder
,
B.
,
1978
, “
The Turbulent Jet in a Cross Stream at Low Injection Rates: A Three-Dimensional Numerical Treatment
,”
Numer. Heat Transfer
,
1
(
2
), pp.
217
242
.
18.
Lakehal
,
D.
,
2002
, “
Near-Wall Modeling of Turbulent Convective Heat Transport in Film Cooling of Turbine Blades With the Aid of Direct Numerical Simulation Data
,”
ASME J. Turbomach.
,
124
(
3
), pp.
485
498
.
19.
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
(
3
), pp.
472
484
.
20.
Cottin
,
G.
,
Laroche
,
E.
,
Savary
,
N.
, and
Millan
,
P.
,
2011
, “
Modeling of the Heat Flux for Multi-Hole Cooling Applications
,”
ASME
Paper No. GT2011-46330.
21.
Most
,
A.
,
Savary
,
N.
, and
Berat
,
C.
,
2007
, “
Reactive Flow Modelling of a Combustion Chamber With a Multiperforated Liner
,”
AIAA
Paper No. 2007-5003.
22.
Mendez
,
S.
, and
Nicoud
,
F.
,
2008
, “
Large-Eddy Simulation of a Bi-Periodic Turbulent Flow With Effusion
,”
J. Fluid Mech.
,
598
, pp.
27
65
.
23.
Rodebaugh
,
G.
,
Stratton
,
Z.
,
Laskowski
,
G.
, and
Benson
,
M.
,
2015
, “
Assessment of Large Eddy Simulation Predictive Capability for Compound Angle Round Film Holes
,”
ASME
Paper No. GT2015-43602.
24.
Spalart
,
P.
,
Jou
,
W.
,
Strelets
,
M.
, and
Allmaras
,
S.
,
1997
, “
Comments on the Feasibility of LES for Wings, and on a Hybrid RANS/LES Approach
,”
Adv. DNS/LES
,
1
, pp.
4
8
.
25.
Spalart
,
P. R.
,
Deck
,
S.
,
Shur
,
M.
,
Squires
,
K.
,
Strelets
,
M. K.
, and
Travin
,
A.
,
2006
, “
A New Version of Detached-Eddy Simulation, Resistant to Ambiguous Grid Densities
,”
Theor. Comput. Fluid Dyn.
,
20
(
3
), pp.
181
195
.
26.
Shur
,
M. L.
,
Spalart
,
P. R.
,
Strelets
,
M. K.
, and
Travin
,
A. K.
,
2008
, “
A Hybrid RANS-LES Approach With Delayed-DES and Wall-Modelled LES Capabilities
,”
Int. J. Heat Fluid Flow
,
29
(
6
), pp.
1638
1649
.
27.
Deck
,
S.
,
2012
, “
Recent Improvements in the Zonal Detached Eddy Simulation (ZDES) Formulation
,”
Theor. Comput. Fluid Dyn.
,
26
(
6
), pp.
523
550
.
28.
Kapadia
,
S.
,
Roy
,
S.
, and
Heidmann
,
J.
,
2003
, “
Detached Eddy Simulation of Turbine Blade Cooling
,”
AIAA
Paper No. 2003-3632.
29.
Martini
,
P.
,
Schulz
,
A.
,
Bauer
,
H.-J.
, and
Whitney
,
C.
,
2006
, “
Detached Eddy Simulation of Film Cooling Performance on the Trailing Edge Cutback of Gas Turbine Airfoils
,”
ASME J. Turbomach.
,
128
(
2
), pp.
292
299
.
30.
Chauvet
,
N.
,
Deck
,
S.
, and
Jacquin
,
L.
,
2007
, “
Zonal Detached Eddy Simulation of a Controlled Propulsive Jet
,”
AIAA J.
,
45
(
10
), pp.
2458
2473
.
31.
Kim
,
S. I.
, and
Hassan
,
I.
,
2010
, “
Unsteady Simulations of a Film Cooling Flow From an Inclined Cylindrical Jet
,”
J. Thermophys. Heat Transfer
,
24
(
1
), pp.
145
156
.
32.
Takahashi
,
T.
,
Funazaki
,
K.-I.
,
Salleh
,
H. B.
,
Sakai
,
E.
, and
Watanabe
,
K.
,
2012
, “
Assessment of URANS and DES for Prediction of Leading Edge Film Cooling
,”
ASME J. Turbomach.
,
134
(
3
), p.
031008
.
33.
Menter
,
F. R.
,
1994
, “
Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications
,”
AIAA J.
,
32
(
8
), pp.
1598
1605
.
34.
Wilcox
,
D. C.
,
1988
, “
Reassessment of the Scale-Determining Equation for Advanced Turbulence Models
,”
AIAA J.
,
26
(
11
), pp.
1299
1310
.
35.
Deck
,
S.
,
2005
, “
Zonal-Detached-Eddy Simulation of the Flow Around a High-Lift Configuration
,”
AIAA J.
,
43
(
11
), pp.
2372
2384
.
36.
Smagorinsky
,
J.
,
1963
, “
General Circulation Experiments With the Primitive Equations—I: The Basic Experiment
,”
Mon. Weather Rev.
,
91
(
3
), pp.
99
164
.
37.
Strelets
,
M.
,
2001
, “
Detached Eddy Simulation of Massively Separated Flows
,”
39th AIAA Aerospace Sciences Meeting and Exhibit
, Reno, NV.
38.
Fan
,
T. C.
,
Xiao
,
X.
,
Edwards
,
J. R.
,
Hassan
,
H. A.
, and
Baurle
,
R. A.
,
2002
, “
Hybrid LES/RANS Simulation of a Shock Wave/Boundary Layer Interaction
,”
AIAA
Paper No. 2002-0431.
39.
Sainte-Rose
,
B.
,
Bertier
,
N.
,
Deck
,
S.
, and
Dupoirieux
,
F.
,
2008
, “
Delayed Detached Eddy Simulation of a Premixed Methane-Air Flame Behind a Backward-Facing Step
,”
AIAA
Paper No. 2008-5134.
40.
Ritter
,
J.
,
1990
, “
An Efficient Bounding Sphere
,”
Graphics Gems
,
Academic Press Professional
, Cambridge, MA, pp.
301
303
.
41.
Speziale
,
C. G.
,
Sarkar
,
S.
, and
Gatski
,
T. B.
,
1991
, “
Modelling the Pressure-Strain Correlation of Turbulence: An Invariant Dynamical Systems Approach
,”
J. Fluid Mech.
,
227
, pp.
245
272
.
42.
Daly
,
B. J.
, and
Harlow
,
F. H.
,
1970
, “
Transport Equations in Turbulence
,”
Phys. Fluids
,
13
(
11
), pp.
2634
2649
.
43.
Refloch
,
A.
,
Courbet
,
B.
,
Murrone
,
A.
,
Villedieu
,
P.
,
Laurent
,
C.
,
Gilbank
,
P.
,
Troyes
,
J.
,
Tessé
,
L.
,
Chaineray
,
G.
,
Dargaud
,
J. B.
,
Quémerais
,
E.
, and
Vuillot
,
F.
,
2011
, “
CEDRE Software
,”
Aerosp. Lab
,
2
, pp.
1
10
.
44.
Marmignon
,
C.
,
Couaillier
,
V.
, and
Courbet
,
B.
,
2011
, “
Solution Strategies for Integration of Semi-Discretized Flow Equations in ELSA and CEDRE
,”
Aerosp. Lab
,
2011
, pp.
1
11
.
45.
Spalart
,
P. R.
,
2009
, “
Detached-Eddy Simulation
,”
Annu. Rev. Fluid Mech.
,
41
(
1
), pp.
181
202
.
46.
Hunt
,
J.
,
Wray
,
A.
, and
Moin
,
P.
,
1988
, “
Eddies, Stream, and Convergence Zones in Turbulent Flows
,” Center for Turbulence Research Report,
Report No. CTR-S88
, pp.
193
208
.
47.
Fric
,
T.
, and
Roshko
,
A.
,
1994
, “
Vortical Structure in the Wake of a Transverse Jet
,”
J. Fluid Mech.
,
279
, pp.
1
47
.
48.
Kelso
,
R. M.
,
Lim
,
T.
, and
Perry
,
A. E.
,
1996
, “
An Experimental Study of Round Jets in Cross-Flow
,”
J. Fluid Mech.
,
306
, pp.
111
144
.
49.
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
(
5
), pp.
418
430
.
50.
Shapiro
,
S. R.
,
King
,
J.
,
M'Closkey
,
R. T.
, and
Karagozian
,
A. R.
,
2006
, “
Optimization of Controlled Jets in Crossflow
,”
AIAA J.
,
44
(
6
), pp.
1292
1298
.
51.
Andreini
,
A.
,
Ceccherini
,
A.
,
Facchini
,
B.
, and
Coutandin
,
D.
,
2010
, “
Combined Effect of Slot Injection, Effusion Array and Dilution Hole on the Heat Transfer Coefficient of a Real Combustor Liner: Part 2—Numerical Analysis
,”
ASME
Paper No. GT2010-22937.
52.
Miron
,
P.
,
2005
, “
Etude Expérimentale des Lois de Parois et du Film de Refroidissement Produit par une Zone Multiperforée sur une Paroi Plane
,” Ph.D. thesis, University of Pau and Pays de l'Adour, Pau, France.
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