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Research Papers: Techniques and Procedures

# Uncertainty Quantification of Turbulence Model Coefficients via Latin Hypercube Sampling Method

[+] Author and Article Information
Matthew C. Dunn

Assistant Professor Mem. ASMEmcd0002@uah.eduProfessor Mem. ASMEmcd0002@uah.eduDepartment of Mechanical and Aerospace Engineering,  The University of Alabama in Huntsville, Huntsville, AL 35899mcd0002@uah.edu

Babak Shotorban1

Assistant Professor Mem. ASMEbabak.shotorban@uah.eduProfessor Mem. ASMEbabak.shotorban@uah.eduDepartment of Mechanical and Aerospace Engineering,  The University of Alabama in Huntsville, Huntsville, AL 35899babak.shotorban@uah.edu

Assistant Professor Mem. ASMEkader.frendi@uah.eduProfessor Mem. ASMEkader.frendi@uah.eduDepartment of Mechanical and Aerospace Engineering,  The University of Alabama in Huntsville, Huntsville, AL 35899kader.frendi@uah.edu

1

Corresponding author.

J. Fluids Eng 133(4), 041402 (May 06, 2011) (7 pages) doi:10.1115/1.4003762 History: Received July 28, 2010; Revised February 26, 2011; Published May 06, 2011; Online May 06, 2011

## Abstract

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.

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## Figures

Figure 1

Backward-facing step geometry

Figure 2

Discretization errors

Figure 3

Streamwise velocity profiles at various x locations; —, computations with 6σ uncertainty error bars; ○, experiments of Kim [19]

Figure 4

Turbulence intensity profiles at various x locations; —, computations with 6σ uncertainty error bars; ○, experiments of Kim [19]

Figure 5

Pressure coefficient along (a) the top wall and (b) the bottom wall; —, computations with 6σ uncertainty error bars; ○, experiments of Kim [19]

Figure 6

Friction coefficient along the bottom wall; —, computations with 6σ uncertainty error bars; ○, experiments of Driver and Seegmiller [21]

Figure 7

The cumulative distribution function (CDF) of the reattachment point location

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