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壁面函数在超声速湍流模拟中的应用研究

王新光1,毛枚良2,何琨1,陈琦1,万钊1   

  1. 1. 中国空气动力研究与发展中心
    2. 中国空气动力研究与发展中心计算所
  • 收稿日期:2021-07-26 修回日期:2021-09-30 出版日期:2021-10-09 发布日期:2021-10-09
  • 通讯作者: 何琨
  • 基金资助:
    国家自然科学基金

Application research of the wall function in the supersonic turbulence simulation

  • Received:2021-07-26 Revised:2021-09-30 Online:2021-10-09 Published:2021-10-09

摘要: 本文通过子迭代的方式计算摩擦速度,更新虚拟点湍流粘性系数来实现对壁面剪切应力的修正,耦合两方程SST k-ω模型,在国家数值风洞软件平台上实现了壁面函数方法。通过压缩拐角和高速飞行器等典型算例进行考核,初步数值实验结果表明:(1)压缩拐角算例壁面函数在无量纲壁面距离y+≤200范围内,均准确预测湍流边界层速度分布,可显著提高粗网格上壁面湍流边界层和壁面摩擦系数的预测精度,且壁面函数使用粗网格最多可节约75%的计算时间;(2)对于复杂外形,附面层网格间距变宽,可使得整体网格减少约38%的网格总量,在相同的计算设置情况下可节约60%的计算时间。唇口附近出现明显的激波边界层干扰现象,使用壁面函数后稀网格和密网格得到流场中分离、激波反射相同,且分离区最高压力系数偏差从15%降低为2%。从粗网格和密网格全机轴向力系数比较来看,使用壁面函数后摩阻预测偏差可从40%下降到4%。整体来看,壁面函数的引入提供了一种高效的飞行器湍流流动气动力预测方法。

关键词: 壁面函数, 湍流粘性系数, SST k-ω模型, 壁面摩擦力, 高速飞行器

Abstract: The wall function approach has been implemented in the National Numerical Windtunnel software coupling the SST k-ω model through an iteration of the friction velocity and updating the turbulence viscosity in the virtual point to modify the wall shear stress. This approach has been verified by the compression corner and high-speed flight vehicle, which shows that: (1) The wall function approach with the coarse mesh (y+≤200) improves the velocity distribution of the turbulence boundary layer and skin-friction significantly with a decrease of 75% computation time compared with the fine mesh. (2) For the complex flight vehicle, the total mesh amount decrease about 38% when coarsen the wall distance in the wall layer, and the CPU time consumption decrease 60% with the same numerical setup. The shock/boundary layer interaction exist near the inlet, where the similar flow separation and shock reflection are obtained for the fine mesh and coarse mesh with the wall function approach. From the comparison of axial force variation, the wall function approach leads an decrease of the prediction error of skin-friction from 40% to 4%, and the whole axial force from 11% to 2%. Overall, the wall function approach is an efficient numerical method for the turbulence force prediction of flight vehicle.

Key words: Wall function, Turbulence viscosity, SST k-ω model, Skin friction, High-speed flight vehicle

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