A discontinuous Galerkin immersed boundary solver for compressible flows: Adaptive local time stepping for artificial viscosity–based shock-capturing on cut cells

We present a higher-order cut cell immersed boundary method (IBM) for the simulation of high Mach number flows. As a novelty on a cut cell grid, we evaluate an adaptive local time stepping (LTS) scheme in combination with an artificial viscosity–based shock-capturing approach. The cut cell grid is optimized by a nonintrusive cell agglomeration strategy in order to avoid problems with small or ill-shaped cut cells. Our approach is based on a discontinuous Galerkin discretization of the compressible Euler equations, where the immersed boundary is implicitly defined by the zero isocontour of a level set function. In flow configurations with high Mach numbers, a numerical shock-capturing mechanism is crucial in order to prevent unphysical oscillations of the polynomial approximation in the vicinity of shocks. We achieve this by means of a viscous smoothing where the artificial viscosity follows from a modal decay sensor that has been adapted to the IBM. The problem of the severe time step restriction caused by the additional second-order diffusive term and small nonagglomerated cut cells is addressed by using an adaptive LTS algorithm. The robustness, stability, and accuracy of our approach are verified for several common test cases. Moreover, the results show that our approach lowers the computational costs drastically, especially for unsteady IBM problems with complex geometries.     

CH4/空气简化动力学机理数值验证

选择绕圆柱预混燃烧算例，验证CH₄/空气三种简化动力学机理（16s41r、15s19r和53s325r）.考虑均匀来流，忽略湍流和湍流与燃烧相互作用以及燃料扩散效应，假设层流有限反应速率，采用保自由流5阶WENO格式求解多组分Euler方程组，得到CH₄/空气预混燃烧流场温度等值线、沿驻点线压力和温度及其CH₄、CO和CO₂质量百分数分布.结果表明：三种简化动力学机理给出的流场均出现弓形激波和火焰面，弓形激波和火焰驻点距离及其形状、诱导区宽度和简化动力学机理相关.当圆柱直径增大，弓形激波和火焰向圆柱上游移动，对应的驻点距离均增大，诱导区宽度变短，点火延时变小，但火焰和弓形激波位置次序未变化.53s325r模型要比16s41r模型和15s19r模型精度要高，点火延时覆盖的压力和温度范围也较宽，所有简化机理均未完全反应，在较大圆柱直径下游达到化学平衡.     

Flow properties of a dusty-gas point source in a supersonic free stream

By using Lagrangian method, the flow properties of a dusty-gas point source in a supersonic free stream were studied and the particle parameters in the near-symmetry-axis region were obtained . It is demonstrated that fairly inertial particles travel along oscillating and intersecting trajectories between the bow and termination shock waves . In this region, formation of " mufti- layer structure" in panicle distribution with alternating low- and high density layers is revealed. Moreover, sharp accumulation of particles occurs near the envelopes of particle trajectories .     

An implicit-explicit upwind algorithm for the parabolized Navier-Stokes equations

In this paper, a second-order implicit-explicit upwind algorithm has been developed for three-dimensional Parabolized Navier-Stokes (PNS) equations. The agreement between the results of the new upwind algorithm and those of the implicit upwind algorithm and its ability in marching a long distance along the streamwise direction have been shown for the supersonic viscous flow past a sphere-cone body. The CPU time is greatly reduced. The project supported by the National Natural Science Foundation of China     

Direct Statistical Simulation of a Supersonic Flow of a Binary Mixture of Rarefied Gases around a Transversely Positioned Cylinder

A supersonic flow of a binary mixture of gases in a wide range of rarefaction (from a flow with a Knudsen number K _n = 0.1 to a free-molecular flow) around a cylinder is studied by means of direct statistical Monte Carlo simulations (DSMC method). The influence of a small fraction of heavy particles in a light gas flow on the region of significant nonequilibrium near the cylinder and on the heat flux is considered.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 5, pp. 53–59, September–October, 2005.     

Axisymmetric impingement of a hot jet on a flat plate: equilibrium flow analysis of high-temperature air

The flow structure of an underexpanded supersonic jet with high reservoir temperature impinging on a flat plate has been numerically investigated using a Total Variation Diminishing (TVD) scheme. When the temperature of the flow field is high enough to cause chemical reaction, the specific heat ratio,, is no longer equal to 1.4, nor constant. This explains the difference found in the literature between the flow properties of the calorically perfect gas and that of the chemically reacting flow. Under the equilibrium flow assumption the effect of high temperature gas on the impinging jet has been taken into account in the present paper by using specific heat ratio and speed of sound given by correlation polynomials of thermodynamic variables. The limiting case of cold jet calculation in the present numerical results agreed well with the existing experimental data. For the equilibrium jet with high reservoir temperature,T _o=1000K, qualitative support of the present result has been provided by means of the approximation theory.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

超声速平板圆台突起物绕流实验和数值模拟研究

高速飞行器表面不可避免的存在突起物并形成复杂流场, 从而引起飞行器气动特性和热载荷的变化; 同时, 突起物是流动控制的重要方法之一, 合适的突起物形状及安装位置对于改善冲压发动机进气道性能有重要意义. 本文采用基于纳米粒子的平面激光散射技术(NPLS)研究了马赫3.0来流边界层为层流的平板上三个不同高度圆台突起物绕流流场, 主要关注了突起物后方的尾迹边界层, 并采用高精度的显式五阶精度加权紧致非线性格式(WCNS-E-5)离散求解Navier-Stokes方程模拟了该流场. 获得了超声速圆台绕流精细流场结构, 观察到突起物后方尾迹区域边界层发展的过程. 结合实验和数值模拟结果可以发现, 当圆台高度接近或者小于当地边界层厚度时, 突起物对边界层的扰动非常弱, 圆台后方尾迹边界层能够维持较长距离的层流状态, 在边界层转捩阶段也有清晰的发卡涡结构出现; 反之, 边界层受到的扰动明显增大, 在突起物后方很快发展为湍流; 风洞噪声对本文研究圆台引起的边界层扰动有一定影响, 实验获得的边界层转捩位置要比数值结果靠前. 基于NPLS流场图像, 采用间歇性方法分析了圆台突起物后方边界层的特性, 对于高度大于边界层厚度的圆台其间歇性曲线较为接近并且更加饱满, 边界层的脉动也更为强烈.     

Initiation of Combustion in a Supersonic Hydrogen-Air Mixture Flow by CO<Subscript>2</Subscript>-Laser Radiation

Features of the ignition kinetics of an H₂/air mixture in the supersonic flow behind an inclined shock front are analyzed when asymmetric vibrations of a small amount (<1%) of O₃ molecules specially introduced into the initial mixture are excited by 9.7 μm wavelength radiation. It is shown that this radiation leads to intensification of the chain reactions and makes it possible to organize combustion at small distances from the front (of the order of 1 m) of even relatively weak shocks at small values of the laser radiation energies absorbed by the gas. This method of initiating combustion in a supersonic flow is 10–100 times more efficient than the thermal method.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, 2005, pp. 157–167.Original Russian Text Copyright © 2005 by Lukhovitskii, Starik, and Titova.     

带展向曲率的超音速混合层中扰动演化的研究

超音速混合层的流动不稳定性较之亚音速或不可压的混合层大大减弱，为了提高混合效率， 通过数值模拟的方法分别研究了展向曲率、展向速度、来流马赫数等因素对混合效率所 起的作用. 计算结果表明：在给定展向速度的情况下，带有展向曲率的三维混合层，曲率越 大三维扰动增长率越大，而且法向的卷起范围也越大. 当展向曲率不为零时，展向速度的增 大也能有效地增强混合能力. 由流场中的高频扰动波产生的涡，在向下游发展过程中会有破 碎、拉伸，低频扰动波没有发现这一现象. 对于有展向曲率和展向速度的混合层，提高来流 马赫数时，流场中最不稳定扰动的增长率仍很大. 因此，这是一种提高混合层混合效率的新 途径.     

Numerical modeling of the disturbances of the separated flow in a rounded compression corner

Numerical modeling of the time-dependent supersonic flow over a compression corner with different roundness radii is performed on the basis of the solution of the two-dimensional Navier-Stokes equations in the regimes corresponding to local boundary layer separation. The development of unstable disturbances generated by local periodic injection/suction in the preseparated boundary layer is calculated. The results are compared with those of similar calculations for a flat plate. It is shown that the natural oscillations of the boundary-layer second mode stabilize in the separation zone and grow intensely downstream of the reattachment point. The acoustic modes excited within a separation bubble are studied using numerical calculations and an asymptotic analysis.