“定黏假设”对伴随系统求解和梯度精度影响  

Influence of “frozen viscosity assumption” on solution and gradient accuracy of adjoint system

作　　者：吴航空 王丁喜[1] 黄秀全[1] 徐慎忍 WU Hangkong;WANG Dingxi;HUANG Xiuquan;XU Shenren(School of Power and Energy,Northwestern Polytechnical University,Xi'an 710072,China)

机构地区：[1]西北工业大学动力与能源学院,西安710072

出　　处：《航空学报》2022年第7期205-221,共17页Acta Aeronautica et Astronautica Sinica

基　　金：国家科技重大专项(2017-Ⅱ-009-0023);西北工业大学博士论文创新基金(CX2022045)。

摘　　要：“定黏假设”的引入能简化伴随方程的推导及流场求解器的子程序微分过程,但同时会引起灵敏度计算误差,有时甚至导致求解的不稳定性。为了探讨层流和湍流黏性系数对伴随灵敏度计算精度的影响程度,分别研究了3种不同定黏方法:冻结层流黏性系数方法(FLV),冻结湍流黏性系数方法(FEV)和同时冻结层流及湍流黏性系数方法(FLEV)。首先基于代数形式的主方程和目标函数详细推导了完全湍流及3种不同定黏方法所对应的伴随方程;然后介绍如何利用自动微分软件开发相应离散伴随求解器并给出流程图;最后以跨声速NASA Rotor 67为研究对象,通过与线化求解器和完全湍流伴随求解器的结果进行对比,分析研究不同工况(最高效率点及近失速点)下“定黏假设”方法对离散伴随系统求解稳定性、灵敏度收敛性、灵敏度精度及残差的渐近收敛率的影响。The introduction of the “frozen viscosity assumption” can simplify the derivation of the adjoint equation and the differentiation of flow solver subroutines, but can also lead to computational errors of sensitivities and sometimes even solution instability. To investigate the effect of laminar viscosity and eddy viscosity on computational accuracy of sensitivities, this paper presents a study on three different frozen viscosity approaches: the Frozen Laminar Viscosity approach(FLV), Frozen Eddy Viscosity approach(FEV) and Frozen Laminar and Eddy Viscosity approach(FLEV). First, the adjoint equations corresponding to full turbulence and three different frozen viscosity approaches are derived based upon the nonlinear flow equations and the objective function in an algebraic form. Then, we introduce how to use the algorithm differentiation tool to develop the discrete adjoint solver and provide the corresponding flow charts. Finally, the transonic NASA Rotor 67 is used to study the effects of different frozen viscosity approaches on solution stability, sensitivity convergence, sensitivity accuracy and asymptotic convergence rate of residual at different operating points(a peak efficiency point and a near stall point) of the adjoint solver. The results are compared with those of the linear solver and the adjoint solver with full turbulence.

关 键 词：伴随方法 定黏假设 冻结层流黏性系数方法 冻结湍流黏性系数方法 冻结层流及湍流黏性系数方法 自动微分 

分 类 号：V231.3[航空宇航科学与技术—航空宇航推进理论与工程] O354[理学—流体力学]