Numerical modelling of unsteady high-speed compressible flows

本课题研究的是本质上非定常的高速多维可压缩流动，与定常现象相比，在可压缩流体动力学中对可压缩流动的探索要少得多，同样，准确有效的数值方法和代码也很少。新的数值方法和计算机代码专门针对非定常，多尺度，多流体流动的空间局域特征（激波，接触面，边界层，涡流等）将开发的基础上，由首席研究员的局部自适应非结构有限体积欧拉（无粘）解非反应气体混合物的工作。可以进行三个主要的推广：(1)对于高雷诺数的非定常粘性流动，其中粘性效应仅限于激波锋面、边界层和分离区、接触面；(2)具有不同状态方程的流体混合物（Tait， JWL等）(3)非均质介质中的非线性声学问题。该研究项目将包括以下应用领域：(I)冲击波反射的基础研究，特别是粘度和导热性对冲击波反射的影响；（二）高超声速吸气式发动机（超燃冲压发动机）进气道启动，包括最近提出的创新技术（隔膜破裂、加速启动）；（三）气体/爆炸系统的流动动力学。(a)通道效应问题（当炸药层在平面或轴对称通道内引爆时），在采矿、航空航天、高压物理等领域有许多应用；(b)超高速发射器的不同概念，利用高炸药的巨大能量密度将射弹加速到超高速，可用于高速冲击试验（例如测试卫星缓冲器护罩时）；（四）非均质介质中的非线性波。在这个领域，所开发的计算方法将用于声学中波相共轭的模拟，并在生物组织的超声成像、无损检测、磁声学等方面有实际应用。

The research program is concerned with essentially unsteady high-speed multi-dimensional compressible flows, which are much less explored in compressible fluid dynamics than steady phenomena and, likewise, accurate and efficient numerical methods and codes for them are few in number. New numerical methods and computer codes specifically tailored for unsteady, multi-scale, multi-fluid flows with spatially-localized features (shock waves, contact surfaces, boundary layers, vortices etc.) will be developed on the basis of the previous work by the principal investigator on locally adaptive unstructured finite-volume Euler (inviscid) solvers for non-reacting gas mixtures. Three major generalizations are to be undertaken: (1) For unsteady viscous flows at high Reynolds numbers in which viscosity effects are confined to shock fronts, boundary layers and separation zones, contact surfaces; (2) For mixtures of fluids with various equations of state (Tait, JWL etc.) (3) For nonlinear acoustics problems in heterogenous media. The research program will encompass the following application areas: (I) Basic studies of shock wave reflections, in particular on the influence of viscosity and heat conductivity on shock wave reflections; (II) Starting of air inlets of hypersonic air-breathing engines (scramjets), including recenlty proposed innovative techniques (diapgragm rupture, accelerative starting); (III) Flow dynamics in gas/explosive systems. (a) Channel effect problem (when an explosive layer is detonated inside a planar or axisymmetrical channel) which has many applications in mining, aerospace, high-pressure physics and other fields; (b) Different concepts of hypervelocity launchers in which the enormous energy densities of high explosives is used to accelerate projectiles to hypervelocities, which can be applied to high-speed impact tests (e.g. when testing satellite bumper shields); (IV) Non-linear waves in heterogenous media. In this area the developed computational method will be used for simulations of wave phase conjugation in acoustics with practical applications in echography of biological tissues, non-destructive testing, magneto-acoustics etc.