HLLE++格式在高马赫数空腔流动模拟中的应用

空腔流动存在剪切层运动、涡脱落与破裂,以及激波与激波、激波与剪切层、激波与膨胀波和激波/涡/剪切层相互干扰等现象,流动非常复杂,特别是高马赫数(M>2)时,剪切层和激波更强,激波与激波干扰更严重,对数值格式的要求更高,既需要格式耗散小,对分离涡等有很高的模拟精度,又需要格式在激波附近具有较大的耗散,可以很好地捕捉激波,防止非物理解的出现。Roe和HLLC等近似Riemann解格式在高马赫数强激波处可能会出现红玉现象,而HLLE++格式大大改善了这种缺陷,在捕捉高超声速激波时避免了红玉现象的发生,同时还保持在光滑区域的低数值耗散特性。本文在结构网格下HLLE++格式的基础上,通过改进激波探测的求解,建立了基于非结构混合网格的HLLE++计算方法,通过无粘斜坡算例,验证了HLLE++格式模拟高马赫数流动的能力,并应用于高马赫数空腔流动的数值模拟,开展了网格和湍流模型影响研究,验证了方法模拟高马赫数空腔流动的可靠性和有效性。

Application of HLLE++ scheme in the simulation of high Mach number cavity flow

Cavity flow is very complex,and there are phenomena such as shear layer motion,vortex shedding and rupture,as well as interaction between shock and shock,shock and shear layer,shock and expansion wave,shock wave,vortex and shear layer.Especially at high Mach number(M>2),the shear layer and shock wave are stronger,and the interaction between shock waves is more serious.Therefore,high Mach number cavity simulation requires higher-accuracy numerical schemes.It is necessary for the schemes to not only have low dissipation and high simulation accuracy for separated vortices,but also have large dissipation near the shock wave to better capture the shock wave and prevent the emergence of non-physical solutions.The approximate Riemann schemes such as Roe,HLLC and so on may cause the Ruby phenomenon at high Mach number strong shock wave,and the HLLE++ scheme greatly overcomes this defect.HLLE++ scheme avoids the occurrence of the Ruby phenomenon when capturing hypersonic shock wave,and maintains the low numerical dissipation in the boundary layer.Based on the HLLE++ scheme on the structured grid,the HLLE++ method on the unstructured hybrid grid is established by improving the solution method of shock detection.The ability of the HLLE++ scheme to simulate high Mach number flow is verified by the inviscid slope example.The HLLE++ scheme is applied to the numerical simulation of high Mach number cavity flow,and the effects of grids and turbulence model are studied.At the same time,the reliability and effectiveness of the method for simulating the flow of high Mach number cavity are verified.