Simulation of unsteady hypersonic combustion around projectiles in an expansion tube

The temporal evolution of combustion flowfields established by the interaction between wedge-shaped bodies and explosive hydrogen-oxygen-nitrogen mixtures accelerated to hypersonic speeds in an expansion tube is investigated. The analysis is carried out using a fully implicit, time-accurate, computational fluid dynamics code that we recently developed to solve the Navier-Stokes equations for a chemically reacting gas mixture. The numerical results are compared with experimental data from the Stanford University expansion tube for two different gas mixtures at Mach numbers of 4.2 and 5.2. The experimental work showed that flow unstart occurred for both the Mach 4.2 cases. These results are reproduced by our numerical simulations and, more significantly, the causes for unstart are explained. For the Mach 5.2 mixtures, the experiments and numerical simulations both produced stable combustion. However, the computations indicate that in one case the experimental data were obtained during the transient phase of the flow; that is, before steady state had been attained. Received 7 February 2000/ Accepted 20 February 2001     

Numerical simulation with a TVD–FVM method for circular cylinder wake control by a fairing

A water drop-shaped fairing is applied to control the wake behind a circular cylinder and to suppress the formation of Karman vortex street in this paper. The results are evaluated using high resolution CFD technique. A finite-volume total variation diminishing (TVD) approach based upon the recently proposed elemental velocity vector transformation (EVVT) method, which aims at solving the incompressible turbulent flow for irregular boundary conditions with renormalization group (RNG) turbulence model, is used to simulate the flow field around circular cylinder systems. The calculations are carried out with cylinder systems with and without fairings, while the fairings have different top shape angles within the range of $30°~90°$. The Reynolds number ranges from 1000 to 50 000. It is shown that the simulation results of present numerical method reaches good agreement with the available experimental and numerical simulation data of typical circular cylinder flow and a fixed fairing cylinder system flow. Compared with bare cylinder, the faired bluff structures can obviously reduce the lift and drag forces and alter the vortex shedding frequency. Overall, the mean drag coefficient can be reduced up to about (10–31)% and the RMS lift coefficient can be reduced up to (30–99)% for all faired systems at given Reynolds numbers. The influence of Reynolds number and attack angles on the flow field characters of bare cylinder and faired cylinders is also discussed. The faired structures with shape angles within $30°~45°$under zero-attack-angle-inflow case are considered as the optimal structures, with which the mean drag coefficient and the RMS lift coefficient can be reduced up to (26–31)% and (98–99)%, respectively. Considering the influence of attack angles on lift and drag coefficients reduction, 75° shaped faired structure may be taken as a proper option.     

非定常隐式TVD格式的基本理论和验证

用于非定常问题的时间二阶精度的隐式TVD格式的理论多年来一直是个空白。本文按新的途径构造了一种时间二阶精度的隐式TVD格式,以发展了的手段证明了其为无条件(任意时间步长)TVD的,且限量因子Φ不受传统上界的限制,具体构造了这样的新的Φ。所得理论结果均为计算所验证,格式显示了良好的稳定性和分辨率。     

TVD三阶和四阶格式求解渗流方程新方法

在使用显式格式计算含水率曲线过程中,如果空间步长太大,则会造成差分格式的不稳定.为了减弱空间步长带来的影响,建立了TVD三阶和四阶格式来计算两相流问题的含水率,与一点上游加权格式和两点上游加权格式进行比较,可以看出,用TVD格式计算的结果与实际结果更接近;该格式在稳定性方面也比上游加权格式稳定,Courant数的大小对格式的稳定性起决定作用.     

A High-Order NVD/TVD-Based Polynomial Upwind Scheme for the Modified Burgers' Equations

A bounded high order upwind scheme is presented for the modified Burgers' equation by using the normalized-variable formulation in the finite volume framework. The characteristic line of the present scheme in the normalized-variable diagram is designed on the Hermite polynomial interpolation. In order to suppress unphysical oscillations, the present scheme respects both the TVD (total variational diminishing) constraint and CBC (convection boundedness criterion) condition. Numerical results demonstrate the present scheme possesses good robustness and high resolution for the modified Burgers' equation.     

无波动,无自由参数,耗散的隐式差分格式

本文建立了求解NS方程和Euler方程无波动、无自由参数、耗散的隐式差分格式.该格式是TVD的和无条件稳定的.其隐式部分在1,2,3维情况下仅分别依赖于3,5,9个点,且系数矩阵是主对角占优的.计算例题表明,该方法可获得和显式方法相同的精度,能很好地捕捉激波和剪切层,且计算时间比显式有较多的节省.     

可压缩平面流中尖角处不定常涡产生的初始阶段的数值模拟

本文采用有限体积法结合高分辨率的ＴＶＤ（总变差不增）格式，对平面激波遇矩形、三角形障碍物问题进行数值模拟，采用Ｓｃｈｗａｒｚ变换生成计算网格，可使网格线在尖角处较密集且网格设置符合流场物理特性。初始阶段的流场复杂且粘性影响的尺度很小，模型中可以忽略流体的粘性。计算结果描述了平面无粘可压流中，由于弓形激波后熵与温度的不均匀性引起的尖角下游不定常集中涡的产生过程。数值计算与应我们要求所做激波管实验的光测结果相符合。     

两种TVD格式在跨音透平叶栅流场计算中的应用

两种ＴＶＤ格式在跨音透平叶栅流场计算中的应用黄伟光，刘建军（中国科学院工程热物理研究所北京１０００８０）关键词跨音速透平，Ｅｕｌｅｒ方程，ＴＶＤ格式１引言现代高负荷透平大都工作在跨音范围，研究发展能准确预测跨音速透平叶栅内部流场的激波位置与强度以及叶...     

非定常自由面流激波解的二阶守恒算法

将计算双曲型守恒律弱解的Lax-Wendroff型TVD格式推广到断面形状沿程任意变化的一般浅水方程组，构造了二阶精度的差分格式．新格式适用于模拟天然河道中溃坝洪水波的传播．提供了表明方法性能的算例，实际天然梯级水库溃坝问题的数值实验表明格式稳定，适应性强．     

Second order scheme for scalar conservation laws with discontinuous flux

Burger, Karlsen, Torres and Towers in [9] proposed a flux TVD (FTVD) second order scheme with Engquist–Osher flux, by using a new nonlocal limiter algorithm for scalar conservation laws with discontinuous flux modeling clarifier thickener units. In this work we show that their idea can be used to construct FTVD second order scheme for general fluxes like Godunov, Engquist–Osher, Lax–Friedrich, … satisfying (A, B)-interface entropy condition for a scalar conservation law with discontinuous flux with proper modification at the interface. Also corresponding convergence analysis is shown. We show further from numerical experiments that solutions obtained from these schemes are comparable with the second order schemes obtained from the minimod limiter.