基于新的经验关联公式的[γ-Reθ]转捩模型在高超声速流动中的应用

Application of [γ-Reθ] Transition Model in Hypersonic Flow Based on New Correlation Equation

关键词:  转捩模型  高超声速流动  间歇因子

Key words:  Transition model  Hypersonic flow  Intermittency factor

摘要:

为提高[γ-Reθ]转捩模型在高超声速流动下的转捩预测精度，参考部分高超声速风洞的实验数据对该模型进行改进，在原始经验关联公式的基础上提出了转捩动量厚度雷诺数基于马赫数、湍流度、压力梯度因子的经验关联公式；选取高超声速平板绕流、高超声速圆锥绕流等算例对提出的经验关联公式进行了验证，并将原始经验关联公式和提出的经验关联公式计算得到的重要参数进行对比，分析了提出的公式的作用机理。结果表明:基于低速不可压流动经验关联公式的[γ-Reθ]转捩模型在高超声速流动中计算得到的流场中[Reθt]分布偏低(一般只有真实值的40%～60%)，进而导致边界层内[Reθt]偏低而过早达到转捩触发准则，与实验值相比所预测的位置可能提前10%(以参考长度为基准)甚至更多。新的经验关联公式有效地改善了这一问题，计算结果与实验值符合得更好。

Abstract:

In order to improve the simulation accuracy of the original [γ-Reθ] transition model when applied to hypersonic flow calculation，a new correlation of the transitional moment thickness Reynolds number with Mach number，turbulence intensity and pressure-gradient correction-factor was proposed based on hypersonic wind tunnel data. Verification of the new correlation was conducted on hypersonic flows around the flat plate and cones. Comparison of the key parameters，which was computed by origin correlation and the new correlation，was performed，and mechanism of action of the new correlation was analyzed and elaborated. Results indicate that the [γ-Reθ] transition model based on the origin correlation of low speed incompressible flow experiments leads to much lower transitional moment thickness Reynolds number in the flow field(usually only 40%～60% of the actual value)，which cause early trigger of the transition，making transition position move upstream 10% or more(based on reference length). The proposed new correlation can improve the prediction of transition location and results agree better with experimental ones.