The article is concerned with the propagation of uncertainties in the values of turbulence model coefficients and parameters in turbulent flows. These coefficients and parameters are obtained through experiments performed on elementary flows, and they are subject to uncertainty. In this work, the widely used $k-ɛ$ turbulence model is considered. It consists of model transport equations for the turbulence kinetic energy and the rate of turbulent dissipation. Both equations involve various model coefficients about which adequate knowledge is assumed known in the form of probability density functions. The study is carried out for a flow over a 2D backward-facing step configuration. The Latin Hypercube Sampling method is employed for the uncertainty quantification purposes as it requires a smaller number of samples compared to the conventional Monte Carlo method. The mean values are reported for the flow output parameters of interest along with their associated uncertainties. The results show that model coefficient variability has significant effects on the streamwise mean velocity in the recirculation region near the reattachment point and turbulence intensity along the free shear layer. The reattachment point location, pressure, and wall shear are also significantly influenced by the uncertainties of the coefficients.

References

References
1.
Faragher
,
J.
, 2006, “
The Implementation of Probabilistic Methods for Uncertainty Analysis in Computational Fluid Dynamics Simulations of Fluid Flow and Heat Transfer in a Gas Turbine Engine
,”
Defense Science and Technology Division, Victoria, Australia, Tech. Rep. No. DSTO-TR-1830
.
2.
Pope
,
S. B.
, 2000,
Turbulent Flows
,
Cambridge University Press
,
Cambridge, UK
.
3.
Jones
,
W.
, and
Launder
,
B.
, 1972, “
The Prediction of Laminarization With a Two-Equation Model of Turbulence
,”
Int. J. Heat Mass Transfer
,
15
(
2
), pp.
301
314
.
4.
Platteeuw
,
P.
Loeven
,
G.
and
Bijl
,
H.
, 2008, “
Uncertainty Quantification Applied to the k - ɛ Model of Turbulence Using the Probabilistic Collocation Method
,”
49th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference
.
5.
Lucor
,
D.
Meyers
,
J.
, and
Sagaut
,
P.
, 2007, “
Sensitivity Analysis of Large-Eddy Simulations to Subgrid-Scale-Model Parametric Uncertainty Using Polynomial Chaos
,”
J. Fluid Mech.
,
585
, pp.
255
279
.
6.
Jouhaud
,
J.-C.
,
Sagaut
,
P.
Enaux
,
B.
, and
Laurenceau
,
J.
, 2008, “
Sensitivity Analysis and Multiobjective Optimization for LES Numerical Parameters
,”
ASME J. Fluids Eng.
,
130
, p.
021401
.
7.
McKay
,
M.
,
Beckman
,
R.
, and
Conover
,
W.
, 1979, “
A Comparison of Three Methods for Selecting Values of Input Variable in the Analysis of Output from a Computer Code
,”
Technometrics
,
21
(
2
), pp.
239
245
.
8.
Iman
,
R.
,
Helton
,
J.
, and
Campbell
,
J.
, 1981, “
An Approach to Sensitivity Analysis of Computer Models. I. Introduction, Input Variable Selection and Preliminary Variable Assessment
,”
J. Quality Technol.
,
13
(
3
), pp.
174
183
.
9.
Helton
,
J.
, and
Davis
,
F.
, 2003, “
Latin Hypercube Sampling and the Propagation of Uncertainty in Analyses of Complex Systems
,”
Reliability Eng. Syst. Safe.
,
81
(
1
), pp.
23
69
.
10.
Stein
,
M.
, 1987, “
Large Sample Properties of Simulations Using Latin Hypercube Sampling
,”
Technometrics
,
29
(
2
), pp.
143
151
.
11.
Swiler
,
L. P.
, and
Wyss
,
G. D.
, 2004, “
A User’s Guide to LHS: Sandia’s Latin Hypercube Sampling Software: LHS UNIX Library/Standalone Version
,”
Sandia National Laboratories, Albuquerque, NM., Tech. Rep. No. SAND2004–2439
.
12.
Cheng
,
J.
, and
Druzdel
,
M.
, 2000, “
Latin Hypercube Sampling in Bayesian Networks
,”
Proceedings of the 13th International Florida Artificial Intelligence Research Symposium Conference
,
AAAI Press and Menlo Park
,
CA
pp.
287
292
.
13.
von Kármán
,
T.
, 1931, “
Mechanical similitude and turbulence
,”
Technical Memorandums of National Advisory Committee for Aeronautics
, NACA-TM-611.
14.
Launder
,
B.
, and
Sharma
,
B.
, 1974, “
Application of Energy–Dissipation Model of Turbulence to the Calculation of Flow Near a Spinning Disc
,”
Lett. Heat Mass Transfer
,
1
, pp.
131
138
.
15.
Massey
,
F. J.
, 1951, “
The Kolmogorov–Smirnov Test for Goodness of Fit
,”
J. Am. Stat. Assoc.
,
46
(
253
), pp.
68
78
.
16.
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
.
17.
Mohamed
,
M.
, and
Larue
,
J.
, 1990, “
The Decay Power Law in Grid–Generated Turbulence
,”
J. Fluid Mech.
,
219
, pp.
195
214
.
18.
Biswas
,
G.
,
Breuer
,
M.
, and
Durst
,
F.
, 2004, “
Backward–Facing Step Flows for Various Expansion Ratios at Low and Moderate Reynolds Numbers
,”
ASME J. Fluids Eng.
,
126
, pp.
362
374
.
19.
Kim
,
J.
,
Kline
,
S.
, and
Johnston
,
J.
, 1980, “
Investigation of a Reattaching Turbulent Shear Layer: Flow Over a Backward–Facing Step
,”
ASME J. Fluids Eng.
,
102
, pp.
302
308
.
20.
Thangam
,
S.
, and
Hur
,
N.
, 1991, “
A Highly–Resolved Numerical Study of Turbulent Separated Flow Past a Backward–Facing Step
,”
Int. J. Eng. Sci.
,
29
(
5
), pp.
607
615
.
21.
Driver
,
D.
, and
Seegmiller
,
H.
, 1985, “
Features of a Reattaching Turbulent Shear Layer in Divergent Channel Flow
,”
AIAA J.
,
23
, pp.
163
171
.
22.
,
E.
, and
Eaton
,
J.
, 1988, “
An LDA Study of the Backward–Facing Step Flow, Including the Effects of Velocity Bias
,”
ASME J. Fluids Eng.
,
110
, pp.
275
282
.
23.
Nie
,
J.
, and
Armaly
,
B.
, 2003, “
Reattachment of Three Dimensional Flow Adjacent to Backward–Facing Step
,”
ASME J. Heat Transfer
,
125
(
3
), pp.
422
428
.