Abstract

Design for cooling effectiveness in turbine blades relies on accurate models for dynamic losses and heat transfer of internal cooling passages. Metal additive manufacturing (AM) has expanded the design space for these configurations, but can give rise to large-scale roughness features. The range of roughness length scales in these systems makes morphology resolved computational fluid dynamics (CFD) impractical. However, volumetric roughness models can be leveraged, as they have computational costs orders of magnitude lower. In this work, a discrete element roughness model (DERM), based on the double-averaged Navier–Stokes equations, is presented and applied to additively manufactured rough channels, representative of gas turbine blade cooling passages. Unique to this formulation of DERM is a generalized sheltering-based treatment of drag, a two-layer model for spatially averaged Reynolds stresses, and explicit treatment of dispersion. Six different AM rough surface channel configurations are studied, with roughness trough to peak sizes ranging from 15% to 60% nominal channel passage half-width, and the roughness Reynolds number ranges from Rek = 60 to 300. DERM predictions for spatially and temporally averaged mean flow quantities are compared to previously reported direct numerical simulation results. Good agreement in the mean velocity profiles, stress balances, and drag partitions are observed. While DERM models are typically calibrated to specific deterministic roughness morphologies at comparatively small roughness Reynolds numbers, the present more generalized DERM formulation has wider applicability. Here, it is demonstrated that the model can accommodate random roughness of large scale, typical of AM.

References

1.
Snyder
,
J. C.
,
Stimpson
,
C. K.
,
Thole
,
K. A.
, and
Mongillo
,
D.
,
2016
, “
Build Direction Effects on Additively Manufactured Channels
,”
ASME J. Turbomach.
,
138
(
5
), p.
051006
.
2.
Snyder
,
J. C.
,
Stimpson
,
C. K.
,
Thole
,
K. A.
, and
Mongillo
,
D.
,
2015
, “
Build Direction Effects on Microchannel Tolerance and Surface Roughness
,”
ASME J. Turbomach.
,
137
(
11
), p.
111411
.
3.
Stimpson
,
C. K.
,
Snyder
,
J. C.
,
Thole
,
K. A.
, and
Mongillo
,
D.
,
2016
, “
Roughness Effects on Flow and Heat Transfer for Additively Manufactured Channels
,”
ASME J. Turbomach.
,
138
(
5
), p.
051008
.
4.
Stimpson
,
C. K.
,
Snyder
,
J. C.
,
Thole
,
K. A.
, and
Mongillo
,
D.
,
2017
, “
Scaling Roughness Effects on Pressure Loss and Heat Transfer of Additively Manufactured Channels
,”
ASME J. Turbomach.
,
139
(
2
), p.
021003
.
5.
Kirsch
,
K. L.
, and
Thole
,
K. A.
,
2018
, “
Numerical Optimization, Characterization, and Experimental Investigation of Additively Manufactured Communicating Microchannels
,”
ASME J. Turbomach.
,
140
(
11
), p.
111003
.
6.
Hanson
,
D. R.
,
McClain
,
S. T.
,
Snyder
,
J. C.
,
Kunz
,
R. F.
, and
Thole
,
K. A.
,
2019
, “
Flow in a Scaled Turbine Coolant Channel With Roughness Due to Additive Manufacturing
,”
Proceedings of ASME Turbo Expo 2019
,
Phoenix, AZ
,
June 17–21
, pp.
1
12
.
7.
Flack
,
K. A.
, and
Schultz
,
M. P.
,
2014
, “
Roughness Effects on Wall-Bounded Turbulent Flows
,”
Phys. Fluids
,
26
(
10
), p.
101305
.
8.
Schultz
,
M. P.
, and
Flack
,
K. A.
,
2008
, “
Turbulent Boundary Layers on a Systematically Varied Rough Wall
,”
Phys. Fluids
,
21
(
1
), pp.
1
9
.
9.
Flack
,
K. A.
, and
Schultz
,
M. P.
,
2010
, “
Review of Hydraulic Roughness Scales in the Fully Rough Regime
,”
ASME J. Fluids Eng.
,
132
(
4
), p.
041203
.
10.
Bons
,
J. P.
,
McClain
,
S. T.
,
Wang
,
Z. J.
,
Chi
,
X.
, and
Shih
,
T. I.
,
2008
, “
A Comparison of Approximate Versus Exact Geometrical Representations of Roughness for CFD Calculations of Cf and St
,”
ASME J. Turbomach.
,
130
(
2
), p.
021024
.
11.
Schlicting
,
H.
,
1936
, “
Experimental Investigation of the Problem of Surface Roughness
,”
NACA TM823
.
12.
Taylor
,
R. P.
,
Coleman
,
H. W.
, and
Hodge
,
B. K.
,
1985
, “
Prediction of Turbulent Rough-Wall Skin Friction Using a Discrete Element Approach
,”
ASME J. Fluids Eng.
,
107
(
2
), pp.
251
257
.
13.
Taylor
,
R. P.
,
Coleman
,
H. W.
, and
Hodge
,
B. K.
,
1983
,
AFATL Technical Report 83-90
,
Harvard
,
Cambridge, MA
.
14.
Taylor
,
R. P.
,
Coleman
,
H. W.
, and
Hodge
,
B. K.
,
1989
, “
Prediction of Heat Transfer in Turbulent Flow Over Rough Surfaces
,”
ASME J. Heat Mass Trans.
,
111
(
2
), pp.
568
572
.
15.
McClain
,
S.
,
2002
, “
A Discrete-Element Model for Turbulent Flow Over Randomly Rough Surfaces
,” Ph.D. thesis,
Mississippi State University
,
MS
16.
McClain
,
S. T.
,
Hodge
,
B. K.
, and
Bons
,
J. P.
,
2004
, “
Predicting Skin Friction and Heat Transfer for Turbulent Flow Over Real Gas Turbine Surface Roughness Using the Discrete Element Method
,”
ASME J. Turbomach.
,
126
(
2
), pp.
259
267
.
17.
McClain
,
S. T.
, and
Brown
,
J. M.
,
2009
, “
Reduced Rough-Surface Parametrization for Use With the Discrete-Element Model
,”
ASME J. Turbomach.
,
131
(
2
), pp.
75
84
.
18.
Aupoix
,
B.
,
1994
, “
Modeling of Boundary Layers Over Rough Surfaces
,”
Advances in Turbulence V: Proceedings of the Fifth European Turbulence Conference
,
Siena, Italy
,
July 5–8
, pp.
16
20
.
19.
Whitaker
,
S.
,
1986
, “
Flow in Porous Media I: A Theoretical Derivation of Darcy’s Law
,”
Trans. Porous Media
,
1
(
3
), pp.
3
25
.
20.
Crapiste
,
G.
,
Rotstein
,
E.
, and
Whitaker
,
S.
,
1986
, “
A General Closure Scheme for the Method of Volume Averaging
,”
Chem. Eng. Sci.
,
41
(
2
), pp.
227
235
.
21.
Pedras
,
M.
, and
de Lemos
,
M.
,
2001
, “
Macroscopic Turbulence Modeling for Incompressible Flow Through Undeformable Porous Media
,”
Int. J. Heat Mass Transfer
,
44
(
6
), pp.
1081
1093
.
22.
Aupoix
,
B.
,
2016
, “
Revisiting the Discrete Element Method for Predictions of Flows Over Rough Surfaces
,”
ASME J. Fluids Eng.
,
138
(
3
), p.
031205
.
23.
Hanson
,
D. R.
,
2017
, “
Computational Investigation of Convective Heat Transfer on Ice-roughened Aerodynamic Surfaces
,” Ph.D. thesis,
Pennsylvania State University
,
PA
.
24.
Hanson
,
D. R.
,
Kinzel
,
M. P.
, and
McClain
,
S. T.
,
2019
, “
Validation of the Discrete Element Roughness Method for Predicting Heat Transfer on Rough Surfaces
,”
Int. J. Heat. Mass. Transfer.
,
136
(
6
), pp.
1217
1232
.
25.
Hanson
,
D. R.
, and
Kinzel
,
M. P.
,
2019
, “
Evaluation of a Subgrid-Scale Computational Fluid Dynamics Model for Ice Roughness
,”
AIAA J. Aircraft
,
56
(
2
), pp.
787
799
.
26.
Chedevergne
,
F.
, and
Forooghi
,
P.
,
2020
, “
On the Importance of the Drag Coefficient Modelling in the Double Averaged Navier-Stokes Equations for Prediction of the Roughness Effects
,”
J. Turbul.
,
21
(
8
), pp.
463
482
.
27.
McClain
,
S. T.
,
Hanson
,
D. R.
,
Cinnamon
,
E.
,
Snyder
,
J. C.
,
Kunz
,
R. F.
, and
Thole
,
K. A.
,
2021
, “
Flow in a Simulated Turbine Blade Cooling Channel With Spatially Varying Roughness Caused by Additive Manufacturing Orientation
,”
ASME J. Turbomach.
,
143
(
7
), p.
071013
.
28.
Stafford
,
G. J.
,
McClain
,
S. T.
,
Hanson
,
D. R.
,
Kunz
,
R. F.
, and
Thole
,
K. A.
,
2022
, “
Convection in Scaled Turbine Internal Cooling Passages With Additive Manufacturing Roughness
,”
ASME J. Turbomach.
,
144
(
4
), p.
041008
.
29.
Altland
,
S. J.
,
Zhu
,
X.
,
McClain
,
S. T.
,
Kunz
,
R. F.
, and
Yang
,
X. I. A.
,
2021
, “
Flow in Additively Manufactured Super Rough Channels
,”
J. Flow
,
2
, p.
E19
.
30.
Raupach
,
M.
,
1992
, “
Drag and Drag Partition on Rough Surfaces
,”
Boundary Layer Meteorol.
,
60
, pp.
1
25
.
31.
Yang
,
X. I. A.
,
Sadique
,
J.
,
Mittal
,
M.
, and
Meneveau
,
C.
,
2016
, “
Exponential Roughness Layer and Analytical Model for Turbulent Boundary Layer Flow Over Rectangular-Prism Roughness Elements
,”
J. Fluid Mech.
,
789
, pp.
127
165
.
32.
McClain
,
S. T.
,
Collins
,
S. P.
,
Hodge
,
B. K.
, and
Bons
,
J. P.
,
2006
, “
The Importance of the Mean Elevation in Predicting Skin Friction for Flow Over Closely Packed Surface Roughness
,”
ASME J. Fluids Eng.
,
128
(
3
), pp.
579
586
.
33.
Nikuradse
,
J.
,
1937
, “
Law of Flow in Rough Pipes
,”
NACA
,
WA
, Technical Memorandum 1292.
34.
Antonialli
,
I. A.
, and
Silveira-Neto
,
A.
,
2018
, “
Theoretical Study of Fully Developed Turbulent Flow in a Channel, Using Prandtl’s Mixing Length Model
,”
J. Appl. Mathe. Phys.
,
6
(
4
), pp.
677
692
.
35.
Launder
,
B. E.
, and
Spalding
,
D. B.
,
1974
, “
The Numerical Computation of Turbulent Flows
,”
Comput. Methods. Appl. Mech. Eng.
,
3
(
2
), pp.
269
289
.
36.
Kuwata
,
Y.
, and
Kawaguchi
,
Y.
,
2018
, “
Direct Numerical Simulation of Turbulence Over Systematically Varied Irregular Rough Surfaces
,”
J. Fluid Mech.
,
862
, pp.
781
815
.
37.
Jelly
,
T. O.
, and
Busse
,
A.
,
2019
, “
Reynolds Number Dependence of Reynolds and Dispersive Stresses in Turbulent Channel Flow Past Irregular Near-Gaussian Roughness
,”
Int. J. Heat Fluid Flow
,
80
, p.
108485
.
38.
Busse
,
A.
, and
Jelly
,
T. O.
,
2020
, “
Influence of Surface Anisotropy on Turbulent Flow Over Irregular Roughness
,”
Flow, Turbulence Combust.
,
104
, pp.
331
354
.
39.
Yang
,
X. I. A.
,
Zafar
,
S.
,
Wang
,
J. X.
, and
Xiao
,
H.
,
2019
, “
Predictive Large-Eddy-Simulation Wall Modeling Via Physics-Informed Neural Networks
,”
Phys. Rev. Fluids
,
4
, p.
034602
.
40.
Chung
,
D.
,
Hutchins
,
N.
,
Schults
,
M.
, and
Flack
,
K.
,
2021
, “
Predicting the Drag of Rough Surfaces
,”
Annu. Rev. Fluid Mech.
,
53
, pp.
439
471
.
41.
Xu
,
H.
,
Altland
,
S.
,
Yang
,
X.
, and
Kunz
,
K.
,
2021
, “
Flow Over Closely Packed Cubical Roughness
,”
J. Fluid Mech.
,
920
, pp.
1
24
.
42.
Levenberg
,
K.
,
1944
, “
A Method for the Solution of Certain Non-linear Problems in Least Squares
,”
Q. Appl. Math
,
2
(
2
), pp.
164
168
.
43.
Altland
,
S.
,
2022
, “
A Distributed Element Roughness Model Based on the Double Averaged Navier-Stokes Equations
,” Ph.D. thesis,
Pennsylvania State University
,
PA
.
44.
Kunz
,
R. F.
,
2001
, “
An Unstructured Two-Fluid Method Based on the Coupled Phasic Exchange Algorithm
,”
15th AIAA Computational Fluid Dynamics Conference
,
Anaheim, CA
,
June 11–14
, p.
2672
.
You do not currently have access to this content.