任意马赫数非定常流动数值模拟的统一算法

发展适用于从低速到高速任意马赫数非定常流动数值模拟的统一算法.通过引入一个伪时间导数项和一个新的预处理矩阵,得到双时间非定常预处理可压缩Navier-Stokes方程.方程的对流项采用三阶Roe通量近似差分格式离散,粘性项采用二阶中心差分格式离散.基于数值通量的线性化技术,实现伪时间步的隐式ADI-LU格式迭代,进而获得物理时间步的二阶推进精度.重点以低马赫数流动为例,求解了圆柱绕流和NACA0015翼型等速上仰动态失速问题.计算结果表明该统一算法能够较好地模拟低马赫数乃至任意马赫数非定常流动.     

基于低马赫数方法的内嵌边界数值算法研究

低马赫数方法通过对可压缩方程中的压力波进行过滤,得到的方程能够对于反应或者传热造成密度出现较大波动问题进行很好描述。此方面的研究大多数集中在多相反应等问题上,然而工程实际上普遍存在的流固耦合以及多场耦合问题却鲜有涉及。本文将低马赫数方法与内嵌边界方法进行结合发展出可以用来求解弱可压缩流动中的流固耦合以及传热问题的数值算法。本文对加热圆柱在封闭腔体内的自然对流进行研究,同时也对本文提出的算法的正确性以及准确性进行了验证。     

格子Boltzmann方法应用于气动声学研究

应用格子Boltzmann方法(LBM)对不同类型的气动声学问题进行数值研究.通过模拟一维平面声波和二维点源声波的传播,得到沿传播方向的声压脉动,其振荡幅值和衰减趋势与理论值相吻合.其次进行声波衍射和干涉现象的数值模拟.最后,模拟处于流场中运动声源辐射声场的多普勒效应.模拟结果说明LBM方法能较好地模拟低马赫数下的声学问题,包括声压脉动的传播,声波的波动特性以及流动与声波间的相互作用.     

水下低频振荡涡流场声散射调制机理与特性研究

水下涡流场对声波的散射问题是声波在复杂流场中传播的基本问题,在水下目标探测和流场声成像领域具有重要意义.针对水下低频振荡涡流场声散射调制问题建立了理论分析模型与数值计算方法,探究了其声散射调制声场的产生机理与时空频特性.首先,基于运动介质的波动方程,通过引入势函数将波动方程分解为流声耦合项和非耦合项,并对流声耦合项进行频域分析处理,揭示了水下振荡涡流场的声散射调制机理;其次,采用间断伽辽金数值方法对水下低频振荡涡流场中声传播过程进行了数值模拟,分析了低马赫数条件下,不同入射声波频率、涡流场的振荡频率和涡核尺度对涡流场声散射调制声场时空频特性的影响规律,并结合理论分析模型对其特性进行了解释.研究表明:低马赫数下,振荡涡流场对声波的散射可产生包含涡流场振荡频率双边带调制谐波的散射调制声场,且随着入射声波频率、涡核尺度的增大,散射调制声场强度增强,总散射声场空间分布具有对称性和明显主瓣,且主瓣方位角趋近于入射波传播方向;在频率比远大于1条件下,涡流场振荡频率对散射调制声场强度影响较小.     

气动声学中声传播问题的辛算法研究

引入辛算法对气动声学中的声传播问题进行了数值研究。采用Hamilton系统描述理想气体的声波方程,时间离散采用辛可分Runge-Kutta方法,空间离散采用近似解析方法,构造声波方程的保辛格式。将辛算法和有限差分算法分别在数值频散和计算效率等方面进行了对比分析,研究结果表明:辛算法能够有效地抑制数值频散,在计算效率方面具有明显的优越性。声传播特性模拟结果表明辛算法能够准确地模拟点源声辐射、声波干涉、反射及衍射现象。     

基于SIMPLE求解对流-扩散方程的一种新方法

针对SIMPLE系列算法,通过分别求解控制容积界面和节点两个位置的对流-扩散方程来提高数值计算精度,提出了一种流动与传热数值模拟的新方法。采用新的数值方法对顶盖驱动流与正方腔自然对流进行了数值模拟。数值模拟结果表明,在相同网格划分时,新的数值方法相对迎风格式、乘方格式、QUICK格式SIMLE算法的计算精度高;而在计算精度基本相同时,新方法有较高的计算效率。     

声波衰减的数值模拟

为了采用计算流体力学方法对热声制冷机进行数值模拟,以突破热声热机现有计算方法的限制,基于压力修正算法的基本思想开发了用于模拟非稳态小马赫数可压缩流动的数值程序,并将其应用于声波衰减的数值模拟.对一维及二维声波衰减过程的模拟显示,数值计算的结果与声学理论的预测符合良好,说明了方法的正确性.     

再入飞行器流场热辐射输运解算方法库研究

基于若干热辐射输运求解方法的一维辐射平衡和温度间断算例结果的对比分析,提出了一个由离散坐标法、P_1近似和光学厚度极限近似构建的热辐射输运解算方法库,该方法库可与再入飞行器热化学非平衡流场控制方程实现有效耦合模拟。利用该方法库模拟了60 km高空、马赫数35的球头算例,计算表明热辐射对高温流场具有显著的"冷却"作用;辐射传热与对流传热水平相当,流场非耦合热辐射计算的辐射热流将高出耦合计算值27%,此类飞行条件下的数值模拟研究应当考虑热辐射耦合效应。     

电子回旋波与快波协同效应的数值研究

在考虑了电子的反弹平均效应及高能电子的相对论效应下,通过数值求解电子的Fokker-Planck方程,研究了托卡马克等离子体中快波与电子回旋波电流驱动问题。采用九点差分法对方程进行离散,应用近似LU因子分解法对方程进行了数值求解。计算结果表明快波与电子回旋波联合电流驱动具有很强的协同效应,在两波联合电流驱动下,驱动电流大于单波电流驱动之和。     

两相湍流色噪声扩维法PDF模型及数值模拟

由颗粒运动的朗之万方程出发,对流体脉动速度采用扩维方法,得到两个不同层次的PDF输运方程.通过对颗粒运动方程求解和高斯分布假设,解决PDF方程的封闭问题,获得颗粒二阶矩模型,然后将颗粒应力方程简化成代数方程,建立代数应力模型.将对流扩散方程的有限分析法运用到求解两相流模型中,对壁面两相射流进行数值模拟,对比分析数值结果与实验结果.     

ON TRANSMISSION OF SOUND IN A NON-UNIFORM DUCT CARRYING A SUBSONIC COMPRESSIBLE FLOW

The differential equations governing the transmission of one-dimensional sound waves in a non-uniform duct carrying a subsonic compressible mean flow have been the subject of a recent debate [1, 2]. Of the two formulations presented, one is considered to be non-acoustical and the other as neglecting the spatial variation of the speed of sound. The present paper shows that both formulations are acoustical and represent valid approximations to correct conditions for isentropic sound propagation in a subsonic low Mach number duct. Each formulation is associated with an “error wave”, which is essentially a hydrodynamic wave when the mean flow Mach number is small. Three-port modelling is required, however, to capture this wave when the Mach number of the mean flow is relatively large and a numerical matrizant approach is described which can be used for this purpose.     

Rotational temperature and density measurements in a hypersonic flow by dual-line CARS

Rotational temperature and nitrogen number density are measured in the shock wave/boundary layer interaction region in the vicinity of a two-dimensional compression corner disposed in a low pressure, 55 K, Mach 10 hypersonic air flow. Spatially-resolved data are recorded using a nonlinear optical technique named dual-line coherent anti-Stokes Raman scattering (DLCARS). Averaged temperature and density profiles are compared with those predicted by a Navier-Stokes solver. Good agreement is found.     

超临界翼型的跨音速抖振特性

以二维非定常N-S方程为基本方程,计算跨音速翼型升力系数的时间历程.根据升力系数的脉动量急剧上升的起始点确定抖振起始边界,以超临界机翼DFVLR-R2和传统翼型NACA0012为研究对象,研究了两种翼型的抖振特性,计算结果表明,在超临界翼型的设计马赫数附近,超临界翼型具有良好的抖振特性.     

基于第二粘性的Navier-Stokes方程组求解正激波结构

为考察气体第二粘性（体积粘性）对正激波内部流动的影响机制，数值求解含第二粘性的一维Navier-Stokes方程组.结果表明：第二粘性对激波内部的密度、热流和能量分布等物理量具有抹平效应，导致热流和熵流的峰值减小、激波厚度增加，体积粘性耗散的增加使得一部分机械能转化为内能；考虑第二粘性所计算的密度分布和激波厚度大为改善，与实验数据吻合较好；当马赫数为1.2≤Ma≤10，激波内部的Knudsen数满足0.12≤Kn≤0.4，对于马赫数Ma≤4.0的激波内部流动，考虑第二粘性的连续流Navier-Stokes方程组能够准确地模拟正激波结构.     

高超音速进气道粘性流场的分块计算

本文采用一种隐式迎风型TVD格式求解二维Navier—Stokes方程，使用分块技术数值模拟了某超音速进气道在飞行马赫数2．291和2.557两种状态下的流动，给出了该进气道的内外流场结构、捕获面积比、表面压力分布、总压恢复系数等等。     

Exact solutions to one-dimensional acoustic fields with temperature gradient and mean flow

An exact solution for one-dimensional acoustic fields in ducts in the presence of an axial mean temperature gradient and mean flow is presented in this paper. The analysis is valid for mean Mach numbers such that the square of the mean Mach number is much less than one. The one-dimensional wave equation for ducts with axial mean temperature gradient and mean flow is derived. By appropriate transformations, the wave equation is reduced to an analytically solvable hypergeometric differential equation for the case of a linear mean temperature profile. The developed solution is applied to investigate the dependence of sound propagation in a duct on factors such as temperature gradient and mean flow. The results obtained using the analytical solution compare very well with the numerical results. The developed solution is also compared with an existing analytical solution.     

Stationary velocity and pressure gradients in a thermoacoustic stack.

The second-order time-averaged acoustics of a viscous, thermally conducting gas between closely spaced parallel plates is studied. The acoustic disturbance is studied by expanding the equations of fluid dynamics and heat transfer to second order in Mach number. The undisturbed state is allowed to have a nonzero temperature gradient. A set of coupled equations for the time-averaged pressure gradient, velocity, and temperature are obtained and solved. Particular attention is paid to the relation between the time-averaged mass flux and pressure gradient. An explicit expression is obtained relating the time-averaged pressure drop across a thermoacoustic stack to the time-averaged mass flux through the stack.     

Diffusive Limit of a Kinetic Model for Cometary Flows

A kinetic equation with a relaxation time model for wave-particle collisions is considered. Similarly to the BGK-model of gas dynamics, it involves a projection onto the set of equilibrium distributions, nonlinearly dependent on the moments of the distribution function. Under a diffusive and low Mach number scaling the macroscopic limit is a generalization of the incompressible Navier-Stokes equations, where the momentum equations are coupled to a diffusive equation for an energy distribution function. By a moment approximation, this system can be related to a low Mach number model of fluid mechanics, which already appeared in the literature. Finally, for a linearized version corresponding to Stokes flow an existence result for initial value problems is proved.     

Fully compressible simulations of the impact of acoustic waves on the dynamics of laminar premixed flames for engine-relevant conditions

Thermo-acoustic instabilities remain problematic in the design of propulsion systems such as gas turbine engines, rocket motors, and ramjets. They arise from the constructive interaction of heat release rate and acoustic pressure oscillations, and can result in increased noise and mechanical fatigue. In the present work, we are concerned with the flame response to the thermodynamic fluctuations that accompany an incident acoustic wave. The objective is to investigate the flame dynamics under engine-relevant conditions using high-fidelity numerical simulations and detailed chemical kinetics. The focus is placed on the combustion of hydrogen and n-heptane, as they are both of practical interest and behave very differently when subjected to acoustic waves. We extract the phase and gain of the unsteady heat release response, which are directly related to the Rayleigh criterion and thus the stability of the system. We highlight the differences between results obtained using the fully compressible Navier-Stokes equations and the low Mach number approximation. The two simulation frameworks agree very well for acoustic wavelengths much larger than the flame thickness. However, they differ significantly at high frequencies. The gain erroneously reaches a plateau under the low Mach number approximation, while it decays to zero using the fully compressible framework. This difference is attributed to the spatial variations in the acoustic pressure, which are not captured by the low Mach number approximation.