超声速流体Kelvin-Helmholtz不稳定性速度梯度效应研究

Velocity gradient in Kelvin-Helmholtz instability for supersonic fluid

利用加权本质上无振荡(WENO)方法模拟超声速流体Kelvin-Helmholtz(KH)不稳定性,研究速度梯度对KH不稳定性线性增长率和后期非线性演化的影响.模拟发现超声速流体中的速度梯度对KH不稳定性具有较强的致稳作用,给出了包含速度梯度致稳的线性增长率经验公式.数值模拟和经验公式符合得很好.模拟给出了清晰的流场密度等值线,这说明WENO方法模拟超声速流体KH不稳定性具有较好的界面变形捕捉能力.模拟结果表明速度梯度影响KH涡的演化,在给定密度梯度的情况下速度梯度越大KH涡的横向尺度越小.

Two-dimensional numerical calculations using weighted essentially non-oscillatory schemes（WENO） scheme were performed to study velocity gradient in the Kelvin-Helmholtz（KH） instability for supersonic fluid. It is found that the velocity gradient has a stabilization effect on the KH instability for supersonic fluid,and the linear growth rate empirical formula with velocity gradient stabilization effect is deduced. The empirical formula with velocity gradient stabilization effect agrees well will the simulation results. The sharp density contour is obtained,which indicates that the WENO finite difference scheme has good capturing ability in interface deformation. The evolution of KH vortex is influenced by the velocity gradient. When the density gradient is fixed,it is found that the larger the velocity gradient the smaller the transverse scale of the KH vortex.