Doctoral Dissertations

Keywords and Phrases

Computational Fluid Dynamics; Sensitivity Analysis; Shock Wave Boundary Layer Interaction; Turbulence Modeling; Uncertainty Quantification


"The purpose of this research is to present results of an uncertainty and sensitivity analysis study of commonly used turbulence models in Reynolds-Averaged Navier-Stokes (RANS) codes due to the epistemic uncertainty in closure coefficients for a set of turbulence model validation cases that represent the structure of several canonical flow problems. The study focuses on the analysis of a 2D zero pressure gradient flat plate, a 2D wall mounted hump, and an axisymmetric shock wave boundary layer interaction, all of which are well documented on the NASA Langley Research Center Turbulence Modeling Resource website. The Spalart-Allmaras (SA), the Wilcox (2006) k-ω (W2006), and the Menter Shear-Stress Transport (SST) turbulence models are considered in the stochastic analyses of these flow problems and the FUN3D Code of NASA was utilized as the flow solver. The uncertainty quantification approach involves stochastic expansions based on non-intrusive polynomial chaos to efficiently propagate the uncertainty. Sensitivity analysis is performed with Sobol indices to rank the relative contribution of each closure coefficient to the total uncertainty for several output flow quantities. The results generalize a set of closure coefficients which have been identified as contributing most to the various output uncertainty for the problems considered in this study. Mainly, the SA turbulence model is most sensitive to the uncertainties in the diffusion constant, the log layer calibration constant, and the turbulent destruction constant. The predictive capability of the W2006 model is most sensitive to the uncertainties in a dissipation rate constant, the shear stress limiter, and a turbulence-kinetic energy constant. Likewise, the SST turbulence model was found to be most sensitive to a diffusion constants, the log layer calibration constant, and the shear stress limiter. The results of this study are expected to guide the efforts on improving the accuracy of RANS predictions through validation experiments and data-driven modeling approaches for various flow problems by identifying the coefficients for refinement"--Abstract, page iii.


Hosder, Serhat

Committee Member(s)

Riggins, David W.
Isaac, Kakkattukuzhy M.
Han, Daoru Frank
Leifsson, Leifur


Mechanical and Aerospace Engineering

Degree Name

Ph. D. in Aerospace Engineering


The author thanks the NASA Grant NNX14AN17A for additional funding.


Missouri University of Science and Technology

Publication Date

Spring 2021


xiv, 99 pages

Note about bibliography

Includes bibliographic references (pages 94-98).


© 2021 Aaron James Erb, All rights reserved.

Document Type

Dissertation - Open Access

File Type




Thesis Number

T 11834