Development of Numerical Method for Unsteady Shock/vortex Interference Flow in Non-perfect Gas

1. 建立了考虑热化学非平衡效应的非定常高超声速激波/激波干涉流的数值计算方法。四阶紧凑的MUSCL TVD格式在空间上与AUSM_DV和时间上的最大二阶LU-SGS格式耦合，使我们能够相当稳定地捕获非定常高温激波-激波干涉流。建立了考虑相对湿度的非定常跨声速激波/涡相互作用流的数值计算方法。将经典冷凝理论应用于新导出的气液两相流基本方程。利用该方法成功地计算了在非常潮湿条件下大迎角翼型周围出现的非平衡冷凝现象。开发了高超声速三维非定常激波/激波干涉流的计算程序。计算了高超声速平板上钝肋的非定常流场，明确了其形成非定常流场的机理。开发了机翼周围三维凝结云的计算程序。成功地计算了湿润条件下三维机翼周围的非平衡凝结，即所谓的“凝结云”。开发了具有热化学非平衡效应的三维非定常高超声速激波/激波干涉流的计算程序。计算结果表明在三维情况下考虑化学反应的重要性。在高温条件下，冲击距离显著减小，加热速率有较大变化。开发了轴对称磁-等离子体粘性流动的计算程序。一种同时求解流动方程和磁场感应方程的有效隐式方法。

1. Numerical method of unsteady hypersonic shock/shock interference flows considering thermochemical nonequilibrium effect was developed. The fourth-order compact MUSCL TVD scheme coupled with AUSM_DV in space and maximum second-order LU-SGS scheme in time enable us to capture unsteady high-temperature shock-shock interference flows quite stably.2. Numerical method of unsteady transonic shock/vortex interaction flows considering relative humidity was developed. The classical condensation theory is applied to newly derived fundamental equations for gas-liquid two phase flows. Nonequilibrium condensations appear around a high angle of attack airfoil in very humid condition were successfully calculated using the present method.3. Computational code of unsteady three-dimensional hypersonic shock/shock interference flows was developed. Hypersonic flows around a blunted fin on the flat plate were calculated and the unsteady flow mechanism which indicates why they become unsteady flows is clearly explained.4. Computational code of three-dimensional condensation cloud around wing was developed. The nonequilibrium condensation around the 3-D wing in humid condition, so-called 'condensation cloud', was successfully calculated.5. Computational code of unsteady three-dimensional hypersonic shock/shock interference flows with thermochemical nonequilibrium effect was developed. The calculated results indicate the importance of considering the chemical reaction also in 3-D cases. The shock stand-off distance decreases dramatically and the heating rate is considerably changed in the high-temperature condition.6. Computational code of axisymmetric magnet-plasma viscous flows was developed. An efficient implicit method for solving flow equations and the induced equation of magnetic field simultaneously.