基于流场/声爆耦合伴随方程的超声速公务机声爆优化

Sonic boom optimization of supersonic jet based on flow/sonic boom coupled adjoint equations

基于自主研发的大规模并行结构化网格CFD求解器PMB3D以及并行化伴随方程求解器PADJ3D,开展了流场/声爆伴随方程的求解研究。首先采用标准算例,对内部CFD代码PMB3D软件和声爆预测代码进行了声爆计算可信度验证,以及声爆强度对近场声压梯度的校核。针对并行环境下多块对接网格的近场声压提取操作的复杂性,提出了"包围盒"的方法实现并行环境下近场声压装配单元编号、网格块编号以及对应的进程编号确定,基于声爆计算坐标将并行传递的数据进行一维排序,为声爆预测、伴随方程以及梯度求解提供输入条件。通过线性插值雅克比矩阵实现均匀坐标系梯度信息向非均匀坐标转换,并进一步根据结构化网格特征提出了插值原则,简化了近场声压转换雅克比矩阵的变分。通过装配单元记录,实现声爆强度对流场守恒变量的变分结果向各个进程装配,将装配结果作为流场伴随方程的右端项实现流场声爆耦合伴随方程的求解。此外,对小型超声速公务机开展了声爆优化,对比分析了设计前后的声压及其频谱特性。

Based on the PMB3 Dsolver for large-scale parallel structured CFD grid and the PADJ3 Dsolver for parallel adjoint equation(in-house code),a study of flow/sonic boom coupled adjoint equations is carried out.Firstly,the reliability of the sonic boom calculation for the PMB3 Dand the reliability of the sonic boom prediction are verified,and the precision of sonic boom signal to the gradient of the near-field input signal is validated.To address the complex extraction of near-field sonic boom signal in multi-block grid,a"sonic boom box"approach is proposed providing cell numbering of near-field sound pressure assembly,grid block numbering,and corresponding process number determination in parallel environment.Then based on the calculated coordinates of sonic boom,the data passed in parallel environment are one-dimensionally sorted,providing input conditions for sonic boom prediction,adjoint equations,and gradient solutions.The Jacobi matrix of linear interpolation is used to transform the gradient information of uniform coordinate system to non-uniform coordinates.Furthermore,the principle of improved interpolation is proposed in accordance to the features of the structural grid,simplifying the variation of the near-field transformation in Jacobi matrix.By recording the assembly unit,the derivative of the sonic boom signal on flow field variable is assembled to the grid cell,and the assembled result is used as the right term for the flow field adjoint equations to obtain the solution of the flow/sonic boom coupled adjoint equations.The level of sonic boom is optimized for small supersonic business jets,and the contours of typical cross-sectional flow field pressure before and after the design are compared and the differences between the two results are analyzed.