The purpose of this paper is to present results of an uncertainty and sensitivity analysis study of commonly used turbulence models in Reynolds-Averaged Navier–Stokes 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 NASA 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) $\kappa -\omega$ (W2006), and the Menter Shear-Stress Transport (SST) turbulence models are considered in the stochastic analyses of these flow problems, and the FUN3D code 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 uncertainty in various output quantities of interest for the set of canonical flow problems considered in this study. Mainly, the SA turbulence model is most sensitive to the uncertainties in the diffusion constant ($\sigma$), the log layer calibration constant ($\kappa$), and the turbulent destruction constant ($c_{w2}$). The predictive capability of the W2006 model is most sensitive to the uncertainties in a dissipation rate constant (${\sigma }_w$), the shear stress limiter ($C_{lim}$), and a turbulence-kinetic energy constant (${\beta }^{*}$). Likewise, the SST turbulence model was found to be most sensitive to the diffusion constants (${\sigma }_{w1}$ and ${\sigma }_{w2}$), the log layer calibration constant ($\kappa$), and the shear stress limiter ($a_1$).

本文的目的是展示雷诺平均纳维-斯托克斯码中常用湍流模型的不确定性和敏感性分析研究结果，这是由于一组湍流模型验证案例的闭合系数的认知不确定性，这些模型代表了几个典型流问题。该研究的重点是对 2D 零压力梯度平板、2D NASA 壁挂式驼峰和轴对称冲击波边界层相互作用的分析，所有这些都在 NASA 兰利研究中心湍流建模资源网站上有详细记录。斯帕拉特-阿尔马拉斯 (SA)、威尔科克斯 (2006)$\kappa -\omega$(W2006) 和 Menter Shear-Stress Transport (SST) 湍流模型在这些流动问题的随机分析中被考虑，并且 FUN3D 代码被用作流动求解器。不确定性量化方法涉及基于非侵入式多项式混沌的随机扩展，以有效地传播不确定性。使用 Sobol 指数执行敏感性分析，以对每个闭合系数对多个输出流量的总不确定性的相对贡献进行排序。结果概括了一组封闭系数，这些系数已被确定为对本研究中考虑的一组典型流问题的各种感兴趣的输出量的不确定性贡献最大。主要是 SA 湍流模型对扩散常数的不确定性最敏感（$\sigma$)，对数层校准常数 ($\kappa$)，以及湍流破坏常数 ($C_{瓦2}$）。W2006 模型的预测能力对耗散率常数 (${\sigma }_{瓦}$), 剪应力限制器 ($C_{升\mathrm{一世}米}$)，以及湍流动能常数 (${\beta }^{*}$）。同样，发现 SST 湍流模型对扩散常数最敏感（${\sigma }_{瓦1}$ 和 ${\sigma }_{瓦2}$)，对数层校准常数 ($\kappa$) 和剪切应力限制器 (${\mathrm{一种}}_1$）。