Graphical Abstract Figure
Graphical Abstract Figure
Close modal

Abstract

Trailing edge cutback film cooling flows are ubiquitous in small and medium gas turbines, but they are difficult to predict accurately due to the inherent deterministic and stochastic unsteadiness that controls the effectiveness of the cooling system. To help develop accurate closure models for such flows, the characteristics of both types of unsteadiness and their effects on the mean flows are analyzed in this research. Zonal detached eddy simulation (ZDES) is performed on a trailing edge cutback flow model, and the numerical results are validated against the measured data. Then, by using spectral proper orthogonal decomposition (SPOD) reconstruction, the original dataset is segregated into deterministic and stochastic unsteadiness. The characteristics of the stress tensor and the heat flux of each type of unsteadiness are analyzed in detail, and notable differences between the two unsteadiness are identified in terms of the stress tensor anisotropy and distribution of unsteady kinetic energy and heat flux. By propagating the unsteadiness through the Reynolds-averaged Navier–Stokes (RANS) equations, the effect of different unsteadiness on the mean flow prediction is quantified. An accurate prediction of the total stress tensor reduces the prediction error in the velocity field by 79% and cooling effectiveness by 55%. An accurate prediction of the total heat flux vector reduces the prediction error in cooling effectiveness further by 37%. These findings provide valuable knowledge for the physical understanding, turbulence modeling, and aerothermal design of cutback trailing edge flows.

References

1.
Sandberg
,
R. D.
, and
Michelassi
,
V.
,
2022
, “
Fluid Dynamics of Axial Turbomachinery: Blade- and Stage-Level Simulations and Models
,”
Annu. Rev. Fluid Mech.
,
54
(
1
), pp.
255
285
.
2.
Han
,
J.-C.
,
Dutta
,
S.
, and
Ekkad
,
S.
,
2012
,
Gas Turbine Heat Transfer and Cooling Technology
,
CRC Press
,
Boca Raton, FL
.
3.
Sandberg
,
R. D.
, and
Michelassi
,
V.
,
2019
, “
The Current State of High-Fidelity Simulations for Main Gas Path Turbomachinery Components and Their Industrial Impact
,”
Flow Turbul. Combust.
,
102
(
4
), pp.
797
848
.
4.
Tucker
,
P.
,
2011
, “
Computation of Unsteady Turbomachinery Flows: Part 1—Progress and Challenges
,”
Prog. Aerosp. Sci.
,
47
(
7
), pp.
522
545
.
5.
Holloway
,
D. S.
,
Leylek
,
J. H.
, and
Buck
,
F. A.
,
2002
, “
Pressure-Side Bleed Film Cooling: Part I – Steady Framework for Experimental and Computational Results
,”
Proceedings of the ASME Turbo Expo 2002: Power for Land, Sea, and Air. Volume 3: Turbo Expo 2002, Parts A and B
,
Amsterdam, The Netherlands
,
June 3–6
.
6.
Schneider
,
H.
,
Von Terzi
,
D. A.
,
Bauer
,
H.-J.
, and
Rodi
,
W.
,
2015
, “
Coherent Structures in Trailing-Edge Cooling and the Challenge for Turbulent Heat Transfer Modelling
,”
Int. J. Heat Fluid Flow
,
51
, pp.
110
119
.
7.
Xu
,
Q.
,
Wang
,
P.
,
Wang
,
P.
,
Du
,
Q.
, and
Liu
,
J.
,
2023
, “
Experimental and Numerical Investigations on the Unsteady Flow and Film Cooling Characteristics of the Trailing Edge Cutback
,”
Appl. Therm. Eng.
,
224
, p.
120094
.
8.
Kacker
,
S.
, and
Whitelaw
,
J.
,
1969
, “
An Experimental Investigation of the Influence of Slot-Lip-Thickness on the Impervious-Wall Effectiveness of the Uniform-Density, Two-Dimensional Wall Jet
,”
Int. J. Heat Mass Transf.
,
12
(
9
), pp.
1196
1201
.
9.
Taslim
,
M. E.
,
Spring
,
S. D.
, and
Mehlman
,
B. P.
,
1992
, “
Experimental Investigation of Film Cooling Effectiveness for Slots of Various Exit Geometries
,”
AIAA J. Thermophys. Heat Transf.
,
6
(
2
), pp.
302
307
.
10.
Horbach
,
T.
,
Schulz
,
A.
, and
Bauer
,
H.-J.
,
2011
, “
Trailing Edge Film Cooling of Gas Turbine Airfoils–External Cooling Performance of Various Internal Pin Fin Configurations
,”
ASME J. Turbomach.
,
133
(
4
), p.
041006
.
11.
Holloway
,
D. S.
,
Leylek
,
J. H.
, and
Buck
,
F. A.
,
2002
, “
Pressure-Side Bleed Film Cooling: Part II – Unsteady Framework for Experimental and Computational Results
,”
Proceedings of the ASME Turbo Expo 2002: Power for Land, Sea, and Air. Volume 3: Turbo Expo 2002, Parts A and B
,
Amsterdam, The Netherlands
,
June 3–6
.
12.
Martini
,
P.
, and
Schulz
,
A.
,
2004
, “
Experimental and Numerical Investigation of Trailing Edge Film Cooling by Circular Coolant Wall Jets Ejected From a Slot With Internal Rib Arrays
,”
ASME J. Turbomach.
,
126
(
2
), pp.
229
236
.
13.
Martini
,
P.
,
Schulz
,
A.
,
Bauer
,
H. J.
, and
Whitney
,
C. F.
,
2005
, “
Detached Eddy Simulation of Film Cooling Performance on the Trailing Edge Cutback of Gas Turbine Airfoils
,”
ASME J. Turbomach.
,
128
(
2
), pp.
292
299
.
14.
Joo
,
J.
, and
Durbin
,
P.
,
2009
, “
Simulation of Turbine Blade Trailing Edge Cooling
,”
ASME J. Fluids Eng.
,
131
(
2
), p.
021102
.
15.
Ivanova
,
E.
,
Ledezma
,
G.
,
Wang
,
G.
, and
Laskowski
,
G. M.
,
2015
, “
Experimental and Numerical Investigations of the Heat Transfer and Flow Field in a Trailing Edge Cooling Geometry: Part 2—LES and Hybrid RANS/LES Study
,”
Proceedings of the ASME Turbo Expo 2015: Turbine Technical Conference and Exposition. Volume 5B: Heat Transfer
,
Montreal, Quebec, Canada
,
June 15–19
.
16.
Wissink
,
J.
,
Michelassi
,
V.
, and
Rodi
,
W.
,
2004
, “
Heat Transfer in a Laminar Separation Bubble Affected by Oscillating External Flow
,”
Int. J. Heat Fluid Flow
,
25
(
5
), pp.
729
740
.
17.
Lengani
,
D.
,
Simoni
,
D.
,
Pichler
,
R.
,
Sandberg
,
R. D.
,
Michelassi
,
V.
, and
Bertini
,
F.
,
2019
, “
On the Identification and Decomposition of the Unsteady Losses in a Turbine Cascade
,”
ASME J. Turbomach.
,
141
(
3
), p.
031005
.
18.
Lav
,
C.
,
Sandberg
,
R. D.
, and
Philip
,
J.
,
2019
, “
A Framework to Develop Data-Driven Turbulence Models for Flows With Organised Unsteadiness
,”
J. Comput. Phys.
,
383
, pp.
148
165
.
19.
Wang
,
R.
,
He
,
X.
, and
Yan
,
X.
,
2022
, “
Spectral Proper Orthogonal Decomposition Analysis of Trailing Edge Cutback Film Cooling Flow
,”
Phys. Fluids
,
34
(
10
), p.
105106
.
20.
Martini
,
P.
,
2008
, “
Filmkühlung hochbeanspruchter Turbinenschaufelhinterkanten: Wärmeübergang und Strömung im Nahfeld praxisbezogener Ausblasespalte
,” Ph.D. thesis,
Logos Verlag
,
Berlin
. https://d-nb.info/99075605X
21.
Schneider
,
H.
,
2013
, “
Zur Strömungsphysik Der Turbulenten Mischung An Filmgekühlten Turbinenschaufel-Hinterkanten
,” Ph.D. thesis,
Karlsruher Institut für Technologie
.
22.
Spalart
,
P. R.
,
Deck
,
S.
,
Shur
,
M. L.
,
Squires
,
K. D.
,
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
.
23.
Spalart
,
P.
, and
Allmaras
,
S.
,
1994
, “
A One-Equation Turbulence Model for Aerodynamic Flows
,”
Rech. Aerospatiale
,
1
, pp.
5
21
.
24.
He
,
X.
,
Zhao
,
F.
, and
Vahdati
,
M.
,
2022
, “
Detached Eddy Simulation: Recent Development and Application to Compressor Tip Leakage Flow
,”
ASME J. Turbomach.
,
144
(
1
), p.
011009
.
25.
Spalart
,
R.
,
2001
, “
Young-Person’s Guide to Detached-Eddy Simulation Grids
,”
NASA Langley Research Center
,
Hampton, VA
,
Technical Report No. NASA/CR-2001-211032
, https://ntrs.nasa.gov/citations/20010080473
26.
Reynolds
,
W.
, and
Hussain
,
A.
,
1972
, “
The Mechanics of an Organized Wave in Turbulent Shear Flow. Part 3. Theoretical Models and Comparisons With Experiments
,”
J. Fluid Mech.
,
54
(
2
), pp.
263
288
.
27.
van de Wall
,
A. G.
,
Kadambi
,
J. R.
, and
Adamczyk
,
J. J.
,
2000
, “
A Transport Model for the Deterministic Stresses Associated With Turbomachinery Blade Row Interactions
,”
ASME J. Turbomach.
,
122
(
4
), pp.
593
603
.
28.
Towne
,
A.
,
Schmidt
,
O. T.
, and
Colonius
,
T.
,
2018
, “
Spectral Proper Orthogonal Decomposition and Its Relationship to Dynamic Mode Decomposition and Resolvent Analysis
,”
J. Fluid Mech.
,
847
, pp.
821
867
.
29.
Nekkanti
,
A.
, and
Schmidt
,
O. T.
,
2021
, “
Frequency–Time Analysis, Low-Rank Reconstruction and Denoising of Turbulent Flows Using SPOD
,”
J. Fluid Mech.
,
926
, p.
A26
.
30.
He
,
X.
,
Fang
,
Z.
,
Rigas
,
G.
, and
Vahdati
,
M.
,
2021
, “
Spectral Proper Orthogonal Decomposition of Compressor Tip Leakage Flow
,”
Phys. Fluids
,
33
(
10
), p.
105105
.
31.
Emory
,
M.
, and
Iaccarino
,
G.
,
2014
, “
Visualizing Turbulence Anisotropy in the Spatial Domain with Componentality Contours
,” Annual Research Briefs, Center for Turbulence Research, https://web.stanford.edu/group/ctr/ResBriefs/2014/14_emory.pdfhttps://web.stanford.edu/group/ctr/ResBriefs/2014/14_emory.pdf
32.
Schmitt
,
F. G.
,
2007
, “
About Boussinesq’s Turbulent Viscosity Hypothesis: Historical Remarks and a Direct Evaluation of Its Validity
,”
Comptes Rendus Mécanique
,
335
(
9–10
), pp.
617
627
.
33.
Spalart
,
P. R.
,
2000
, “
Strategies for Turbulence Modelling and Simulations
,”
Int. J. Heat Fluid Flow
,
21
(
3
), pp.
252
263
.
34.
Hellsten
,
A.
,
2005
, “
New Advanced K-ω Turbulence Model for High-Lift Aerodynamics
,”
AIAA J.
,
43
(
9
), pp.
1857
1869
.
35.
Sandberg
,
R. D.
,
Tan
,
R.
,
Weatheritt
,
J.
,
Ooi
,
A.
,
Haghiri
,
A.
,
Michelassi
,
V.
, and
Laskowski
,
G.
,
2018
, “
Applying Machine Learnt Explicit Algebraic Stress and Scalar Flux Models to a Fundamental Trailing Edge Slot
,”
ASME J. Turbomach.
,
140
(
10
), p.
101008
.
36.
Reynolds
,
O.
,
1961
, “
On the Extent and Action of the Heating Surface of Steam Boilers
,”
Int. J. Heat Mass Transf.
,
3
(
2
), pp.
163
166
.
37.
Daly
,
B. J.
, and
Harlow
,
F. H.
,
1970
, “
Transport Equations in Turbulence
,”
Phys. Fluids
,
13
(
11
), pp.
2634
2649
.
38.
Abe
,
K.
, and
Suga
,
K.
,
2001
, “
Towards the Development of a Reynolds-Averaged Algebraic Turbulent Scalar-Flux Model
,”
Int. J. Heat Fluid Flow
,
22
(
1
), pp.
19
29
.
39.
Wu
,
J.
,
Xiao
,
H.
,
Sun
,
R.
, and
Wang
,
Q.
,
2019
, “
Reynolds-Averaged Navier-Stokes Equations With Explicit Data-Driven Reynolds Stress Closure Can Be Ill-Conditioned
,”
J. Fluid Mech.
,
869
, pp.
553
586
.
You do not currently have access to this content.