Menter SST湍流模型系数在高速流动模拟中的不确定度量化研究

Uncertainty quantification of Menter SST turbulence model coefficients in hypersonic flow simulations

Menter SST湍流模型系数的不确定性会对高速流动数值模拟的结果产生显著影响。本文针对二维压缩拐角、二维圆柱和三维双椭球体3个典型高速模型,定量评估湍流模型封闭系数不确定性对数值模拟的影响。首先,采用非嵌入多项式混沌方法量化由Menter SST湍流模型封闭系数不确定性导致的气动力/热数值模拟的不确定度;然后,依据Sobol敏感性指标对封闭系数的敏感性进行排序,辨识导致不确定度的关键因素。研究结果表明气动热的不确定度普遍大于气动力。在考察的9个封闭系数中,σ_(ω1)、β^(*)、κ、a_(1)是对数值模拟结果不确定度贡献较大的关键模型参数,其敏感性大小与当地流动特征相关:在流动的大部分区域内,生成项系数σ_(ω1)和κ是导致数值模拟结果不确定度的主要因素;而在流动发生分离或出现激波后的区域,数值模拟结果受耗散项系数β^(*)与剪切应力限制器参数a_(1)的影响更显著。

The precision of numerical simulations for hypersonic flows is significantly influenced by the uncertainties in the closure coefficients of the Menter SST turbulence model.This study conducts a quantitative assessment of these uncertainties across three canonical hypersonic models:the two-dimensional compression corner,the two-dimensional cylinder,and the three-dimensional double ellipsoid.Firstly,the non-intrusive polynomial chaos method is used to quantify the uncertainty in the numerical simulations of aerodynamic forces and heating caused by the uncertain closure coefficients of the Menter SST turbulence model.The sensitivities of the closure coefficients are then ranked based on the Sobol sensitivity index to identify the key factors contributing to the uncertainty.The results show that uncertainties in aerodynamic heating generally exceed those in aerodynamic forces.Among all the nine closure coefficients examined in this paper,σ_(ω1)、β^(*)、κ、a_(1) are the key model parameters that contribute significantly to the uncertainty of the simulation results.And the sensitivities of which are related to local flow characteristics.In most flow areas,the coefficients of production termσ_(ω1)and κ are the main factors contributing to the uncertainty of the numerical simulation results.While in regions of flow separation or behind shock waves,the simulation results are more significantly influenced the dissipation term coefficient β^(*)and the shear stress limiter a_(1).