Uncertainty Analysis of Turbulence Model Closure Coefficients for Wall-Bounded Attached and Separated Flows


The purpose of this paper is to present the results of an uncertainty analysis study for commonly used turbulence models in Reynolds-Averaged Navier-Stokes codes due to the epistemic uncertainty in closure coefficients for attached and separated wall-bounded flows. Sensitivity analysis is performed to rank the uncertainty contribution of each coefficient to various output quantities of interest. In particular, an uncertainty and sensitivity analysis focusing on determining the similarities and differences between the results based on the structure of the flow (i.e., attached vs. separated) is performed. Comparison between two wall-bounded flow cases is performed including low-speed attached flow over a 2D zero pressure gradient flat plate and a 2D NASA wall-mounted hump case with separated flow. In total, two turbulence models were considered in the analysis: the Spalart-Allmaras Model and Wilcox (2006) κ-ω Model. The flow solver used in the study is Fun3D, a code developed by NASA Langley Research Center. The uncertainty quantiflcation approach involves stochastic expansions based on non-intrusive polynomial chaos to efficiently propagate the uncertainty. Sobol indices are used to rank the relative contribution of each closure coefficient to the total uncertainty for several output flow quantities. The results of the current study identify a set of closure coefficients for each turbulence model which contribute most to the uncertainty for both attached and separated low speed flows. These major conclusions are also consistent with the flndings of a previous work focusing on transonic wall-bounded flows.

Meeting Name

19th AIAA Non-Deterministic Approaches Conference (2017: Jan. 9-13, Grapevine, TX)


Mechanical and Aerospace Engineering

Research Center/Lab(s)

Center for High Performance Computing Research


The authors would like to acknowledge the support for this research provided by the NASA Grant NNX14AN17A (technical monitor: Mujeeb Malik).

Keywords and Phrases

NASA; Navier Stokes equations; Reynolds equation; Sensitivity analysis; Stochastic systems; Turbulence models; Turbulent flow; Wall flow, Epistemic uncertainties; NASA Langley Research Center; Quantities of interests; Reynolds averaged navier stokes codes; Spalart-Allmaras model; Uncertainty and sensitivity analysis; Uncertainty contributions; Zero pressure gradient, Uncertainty analysis

International Standard Book Number (ISBN)


Document Type

Article - Conference proceedings

Document Version


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© 2017 American Institute of Aeronautics and Astronautics (AIAA), All rights reserved.

Publication Date

01 Jan 2017

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