广义Burgers方程声爆传播模型高阶格式离散  

High-order scheme discretization of sonic boom propagation model based on augmented Burgers equation

作　　者：王迪 钱战森[1,2] 冷岩 WANG Di;QIAN Zhansen;LENG Yan(AVIC Aerodynamics Research Institute,Shenyang 110034,China;Aviation Key Laboratory of Science and Technology on High Speed and High Reynolds Number Aerodynamic Force Research,Shenyang 110034,China)

机构地区：[1]中国航空工业空气动力研究院,沈阳110034 [2]高速高雷诺数气动力航空科技重点实验室,沈阳110034

出　　处：《航空学报》2022年第1期281-293,共13页Acta Aeronautica et Astronautica Sinica

基　　金：国家自然科学基金(11672280)。

摘　　要：声爆预测技术是研制新一代环保型超声速民机的关键技术之一。针对当前基于广义Burgers方程的声爆远场传播模型的数值求解格式精度较低的情况,开展了高阶格式离散方法研究。通过分析该模型中各效应项的物理性质,应用合适的高阶精度格式对各项分别进行离散求解,并采用经典几何声学射线法计算声爆传播路径,实现了对地面声爆波形的精准预测。通过对美国F-5E机型的声爆飞行试验和第二届国际声爆预测研讨会的典型算例进行数值模拟,验证了本文高阶离散方法的可靠性。进一步的结果分析表明,采用高阶离散格式的预测方法相比传统二阶精度预测方法具有明显的低耗散特性,在同等网格数目上可获得更高分辨率的计算结果,且其网格收敛性远优于传统二阶精度格式,同时在计算效率上也有一定优势;在Burgers方程的各效应项中,非线性项的影响更为明显,因而采用高阶离散格式时其优势更为突出;热黏性吸收项对数值结果影响较小,采用高阶离散格式对计算精度的提升效果也不明显,实际计算中仍可以采用传统离散格式,甚至忽略该项的贡献。The sonic boom prediction is one of the key technologies in the development of the new generation low-boom supersonic transport aircraft.In view of the low accuracy of the numerical scheme for the far-field propagation model of sonic boom based on the augmented Burgers equation,we study the discretization method for high-order scheme.After the physical properties of each effect term in the model is analyzed,an appropriate high-order accuracy scheme is used to discretize each term,and the classical geometric acoustic ray tracing method is adopted to calculate the propagation path of sonic boom,so as to realize the accurate prediction of ground waveform.The reliability of the high-order discrete method used in this paper is verified by the numerical simulation of the sonic boom flight test of F-5E aircraft and the standard numerical examples of the 2nd AIAA Sonic Boom Prediction Workshop on sonic boom prediction.Further results show that the high-order scheme has lower dissipation than the traditional second-order scheme,and thus can obtain higher resolution results with the same number of grids,with the grid convergence much higher than that of the traditional second-order scheme.Meanwhile,the high-order scheme also has advantages in computational efficiency.Among the effect terms of the augmented Burgers equation,the influence of the nonlinear term is more noticeable,explaining the prominence of the advantages of the adopted high-order scheme.The influence of the thermoviscous absorption term on the numerical results is small,and the improvement of calculation accuracy by using high-order scheme is not obvious.Therefore,the traditional discrete scheme can still be used in actual calculations,and the contribution of this term can even be ignored.

关 键 词：超声速民机 广义 BURGERS方程 声爆预测 高阶格式 计算流体力学 

分 类 号：V211.3[航空宇航科学与技术—航空宇航推进理论与工程]