转动非平衡玻尔兹曼模型方程统一算法与全流域绕流计算应用

基于过去开展稀薄自由分子流到连续流气体运动论统一算法框架,采用转动惯量描述气体分子自旋运动,确立含转动非平衡效应各流域统一玻尔兹曼模型方程.基于转动能量对分布函数守恒积分,得到计及转动非平衡效应气体分子速度分布函数方程组,使用离散速度坐标法对分布函数方程所依赖速度空间离散降维;应用拓展计算流体力学有限差分方法,构造直接求解分子速度分布函数的气体动理论数值格式;基于物面质量流量通量守恒与能量平衡关系,发展计及转动非平衡气体动理论边界条件数学模型及数值处理方法,提出模拟各流域转动非平衡效应玻尔兹曼模型方程统一算法.通过高、低不同马赫数1:5～25氮气激波结构与自由分子流到连续流全飞行流域不同克努森数（9×10-4～10）Ramp制动器、圆球、尖双锥飞行器、飞船返回舱外形体再入跨流域绕流模拟研究,将计算结果与有关实验数据、稀薄流DSMC模拟值等结果对比分析,验证统一算法模拟自由分子流到连续流再入过程高超声速绕流问题的可靠性与精度.      

稀薄流到连续流的气体运动论模型方程算法研究

通过引入碰撞松弛参数和当地平衡态分布函数对BGK模型方程进行修正，确定含流态控制参数可描述不同流域气体流动特性的气体分子速度分布函数的简化控制方程。发展和应用离散速度坐标法于气体分子速度空间，利用一套在物理空间和时间上连续而速度空间离散的分布函数来代替原分布函数对速度空间的连续依赖性。基于非定常时间分裂数值计算方法和无波动、无自由参数的NND耗散差分格式，建立直接求解气体分子速度分布函数的气体运动论有限差分数值方法。推广应用改进的Gauss-Hermite无穷积分法和华罗庚－王元提出的以单和逼近重积分的黄金分割数论积分方法等，对离散速度空间进行宏观取矩获取物理空间各点的气体流动参数，由此发展一套从稀薄流到连续流各流域统一的气体运动论数值算法。通过对不同Knudsen数下一维激波管问题、二维圆柱绕流和三维球体绕流的初步数值实验表明文中发展的数值算法是可行的。     

GAS-KINETIC UNIFIED ALGORITHM FOR BOLTZMANN MODEL EQUATION IN ROTATIONAL NONEQUILIBRIUM AND ITS APPLICATION TO THE WHOLE RANGE FLOW REGIMES

基于过去开展稀薄自由分子流到连续流气体运动论统一算法框架,采用转动惯量描述气体分子自旋运动,确立含转动非平衡效应各流域统一玻尔兹曼模型方程.基于转动能量对分布函数守恒积分,得到计及转动非平衡效应气体分子速度分布函数方程组,使用离散速度坐标法对分布函数方程所依赖速度空间离散降维;应用拓展计算流体力学有限差分方法,构造直接求解分子速度分布函数的气体动理论数值格式;基于物面质量流量通量守恒与能量平衡关系,发展计及转动非平衡气体动理论边界条件数学模型及数值处理方法,提出模拟各流域转动非平衡效应玻尔兹曼模型方程统一算法.通过高、低不同马赫数1：5～25氮气激波结构与自由分子流到连续流全飞行流域不同克努森数（9×10^-4～10）Ramp制动器、圆球、尖双锥飞行器、飞船返回舱外形体再入跨流域绕流模拟研究,将计算结果与有关实验数据、稀薄流DSMC模拟值等结果对比分析,验证统一算法模拟自由分子流到连续流再入过程高超声速绕流问题的可靠性与精度.     

高超声速非平衡流动-辐射特性数值模拟研究

飞行器高超声速飞行过程中所承受对流加热和辐射加热可能具有相当的量级,因此合理准确预测气动加热需要将二者进行综合考虑.文章发展了具有非玻尔兹曼电子能级分布和振动能级分布的高温空气碰撞辐射模型,并耦合一维激波后流动方程计算不同飞行条件下激波后的非平衡流动特性,采用逐线辐射输运模型计算获得激波后非平衡辐射特性、辐射强度和辐射输运通量,深入比较分析了不同飞行高度和马赫数对非平衡流动和辐射输运过程的影响.计算结果表明对于高空高马赫飞行条件,其波后流动存在显著的热力学非平衡、化学非平衡和能级非平衡特征,在近激波区域高振动能级和原子高束缚电子激发态明显低于玻尔兹曼分布.在高空高马赫条件下真空紫外辐射占据主导地位,主要是由高能原子束缚-束缚跃迁造成的.随着高度和马赫数的下降,激波层内气体解离和电离程度降低,原子辐射贡献下降,分子辐射贡献增加,导致红外、可见光和紫外波段的辐射输运增强,真空紫外辐射输运过程减弱.     

基于多块对接网格的隐式气体运动论统一算法应用研究

基于玻尔兹曼模型方程的气体运动论统一算法(gas kinetic unified algorithm,GKUA) 给出了一种能模拟从连续流到自由分子流跨流域空气动力学问题的途径. 该算法采用传统计算流体力学技术将分子运动和碰撞解耦处理,若采用显式格式将受格式稳定条件限制,在模拟超声速流动尤其是近连续流和连续流区的流动时计算效率较低. 为了提高计算效率,扩展其工程实用性,采用上下对称高斯-赛德尔(LU-SGS) 方法和有限体积法构造了求解玻尔兹曼模型方程的隐式方法,同时在物理空间采用能处理任意连接关系的多块对接网格技术. 通过模拟近连续过渡区并排圆柱绕流问题,计算结果与直接模拟蒙特卡洛方法模拟值吻合较好,验证了该方法用于跨流域空气动力计算的可靠性与可行性.      

三维复杂流场内能激发松弛的DSMC数值模拟

本文研究了带内能激发松弛和不同来流条件下的复杂外形高超声速飞行器过渡区三维流场特性.采用一种对飞行器物面网格与DSMC计算域网格分别标识的方法,通过判断模拟分子与表面碰撞来完成飞行器物面网格与DSMC计算域网格间的信息传递和信息存贮,对于复杂外形飞行器精确描述的物面网格不需做进一步处理,直接应用于不依赖于飞行器外形的DSMC计算的通用子程序中.采用L-B碰撞模型,分析了内能激发松弛的流场参数特性,从分子碰撞、分子与飞行器表面碰撞的角度,分析了不同来流条件下的流场参数的变化情况.     

基于多层分块算法的激波干扰流场预测

激波-激波干扰流场预测是超声速乃至高超声速流动中最具挑战性的问题之一. 特别地, 第IV类激波干扰由于其在壁面驻点附近产生极高的热载荷而备受关注. 本文针对圆柱诱导的弓形激波和入射斜激波的干扰问题, 分别基于量热完全气体模型和考虑振动激发的热完全气体模型, 数值求解有黏二维可压缩NS方程, 分析了高温气体效应对激波干扰流场结构, 以及第IV类激波干扰流场状态参数的影响. 接着, 本文基于一种具有广义可分离特性的遗传算法 (多层分块算法), 给出能够预测不同气体模型下第IV类激波干扰流场三波点的坐标位置、超声速射流的几何形状等特征性几何结构的数学模型, 进一步获得高温气体效应对激波干扰类型转变准则影响的定量化评估. 激波干扰类型转变准则面上的多组临界工况的激波干扰流场结构以及壁面压力和壁面热流分布的对比结果表明, 不同气体模型下的激波干扰类型和流场结构差异较为显著, 获得的定量化预测模型对工程中气动热环境的预测具有一定的参考价值.      

基于Boltzmann模型方程的气体运动论统一算法研究

模型方程出发,研究确立含流态控制参数可描述不同流域气体流动特征的气体分子速度分布函数方程; 研究发展气体运动论离散速度坐标法, 借助非定常时间分裂数值计算方法和NND差分格式, 结合DSMC方法关于分子运动与碰撞去耦技术, 发展直接求解速度分布函数的气体运动论耦合迭代数值格式; 研制可用于物理空间各点宏观流动取矩的离散速度数值积分方法, 由此提出一套能有效模拟稀薄流到连续流不同流域气体流动问题统一算法. 通过对不同Knudsen数下一维激波内流动、二维圆柱、三维球体绕流数值计算表明, 计算结果与有关实验数据及其它途径研究结果(如DSMC模拟值、N-S数值解)吻合较好, 证实气体运动论统一算法求解各流域气体流动问题的可行性. 尝试将统一算法进行HPF并行化程序设计, 基于对球体绕流及类``神舟'返回舱外形绕流问题进行HPF初步并行试算, 显示出统一算法具有很好的并行可扩展性, 可望建立起新型的能有效模拟各流域飞行器绕流HPF并行算法研究方向. 通过将气体运动论统一算法推广应用于微槽道流动计算研究, 已初步发展起可靠模拟二维短微槽道流动数值算法; 通过对Couette流、Poiseuille流、压力驱动的二维短槽道流数值模拟, 证实该算法对微槽道气体流动问题具有较强的模拟能力, 可望发展起基于Boltzmann模型方程能可靠模拟MEMS微流动问题气体运动论数值计算方法研究途径.      

复杂微通道气体流动的格子Boltzmann模拟

构建了一个模拟复杂微通道内气体流动的多松弛格子Boltzmann模型。该模型采用动力学曲面滑移边界,考虑了微尺度效应和努森层影响。此外,为了更准确地描述微通道内气体的滑移速度,在模型中引入孔隙局部Kn数来代替平均Kn数。之后采用Poiseuille流对模型进行验证,模拟结果与用直接模拟蒙特卡洛方法和分子模拟结果吻合较好,证明了该模型模拟微通道内处于滑移区和过渡区气体流动的有效性。最后,采用该模型模拟多孔介质内气体渗流过程。结果表明,随着孔隙平均Kn数的增加,多孔介质内的高渗区域增加,且优先从小孔隙中开始增加,这是由于小孔隙中微尺度效应更加明显,相对大孔隙流动阻力更小所致。     

快速颗粒流碰撞应力的动理模型

颗粒碰撞是快速颗粒流的动量传递,能量传递及耗散的主要机制。因此,碰撞应力是快速颗粒流研究的主要内容。本文基于大小均匀、光滑圆球颗粒的非弹性碰撞模型,类比气体分子动理论中的处理方法得出快速颗粒流积分形式的碰撞应力,能量传递通量及能量耗散率等关系。在颗粒速度分布函数的一级近似式符合Maxwell分布的假设下,对碰撞应力积分得出相应于Boltzmann方程二级近似解的碰撞应力表达式。在简单快速颗粒流动条件下,本文的理论结果与实验资料符合较好。     

Gas-kinetic description of shock wave structures by solving Boltzmann model equation

On the basis of the mesoscopic theory of Boltzmann-type velocity distribution function, the modified Boltzmann model equation describing the one-dimensional gas flows from various flow regimes is presented by incorporating the molecular interaction models relating to the viscosity and diffusion cross-sections, density, temperature and the dependent exponent of viscosity into the molecular collision frequency. The gas-kinetic numerical method for directly solving the molecular velocity distribution function is studied by introducing the reduced distribution functions and the discrete velocity ordinate method, in which the unsteady time-splitting method and the NND finite difference scheme are applied. To study the inner flows of non-equilibrium shock wave structures, the one-dimensional unsteady shock-tube problems with various Knudsen numbers and the steady shock wave problems at different Mach numbers are numerically simulated. The computed results are found to give good agreement with the theoretical, DSMC and experimental results. The computing practice has confirmed the good precision and reliability of the gas-kinetic numerical algorithm in solving the highly nonequilibrium shock wave disturbances from various flow regimes.     

Numerical investigation on performance of three solution reconstructions at cell interface in DVM simulation of flows in all Knudsen number regimes

In the conventional discrete velocity method (DVM), the local solution of collisionless Boltzmann equation with a piecewise constant distribution for the distribution function is utilized to reconstruct distribution function at the cell interface and then calculate numerical flux of Boltzmann equation for updating the distribution function at cell center. In this process, a numerical dissipation will be introduced into the solution due to neglecting of the collision effect at the cell interface. This numerical dissipation may deteriorate the solution accuracy of conventional DVM in the continuum flow regime, in which the particle collision happens frequently. To overcome this defect, two improved schemes are first presented in this work, in which the local discrete solution of Boltzmann equation with Shakhov model is adopted to evaluate the distribution function at the cell interface, while the equilibrium state of the local solution is computed by different ways. One of the improved schemes evaluates the equilibrium state exactly by the moments of distribution functions according to the compatibility condition, while the other computes the equilibrium state approximately by a simple average at the cell interface. Since the collision effect is incorporated in evaluation of numerical flux, the improved schemes can provide reasonable solutions in all flow regimes. On the other hand, they introduce some extra computational efforts for determining the collision term at the cell interface as compared with the conventional DVM. To assess the performance of different methods for simulation of flows in all flow regimes, a comprehensive study is then carried out in this work.     

Passive heat transfer in a turbulent channel flow simulation using large eddy simulation based on the lattice Boltzmann method framework

In this paper, a large eddy simulation based on the lattice Boltzmann framework is carried out to simulate the heat transfer in a turbulent channel flow, in which the temperature can be regarded as a passive scalar. A double multiple relaxation time (DMRT) thermal lattice Boltzmann model is employed. While applying DMRT, a multiple relaxation time D3Q19 model is used to simulate the flow field, and a multiple relaxation time D3Q7 model is used to simulate the temperature field. The dynamic subgrid stress model, in which the turbulent eddy viscosity and the turbulent Prandtl number are dynamically computed, is integrated to describe the subgrid effect. Not only the strain rate but also the temperature gradient is calculated locally by the non-equilibrium moments. The Reynolds number based on the shear velocity and channel half height is 180. The molecular Prandtl numbers are set to be 0.025 and 0.71. Statistical quantities, such as the average velocity, average temperature, Reynolds stress, root mean square (RMS) velocity fluctuations, RMS temperature and turbulent heat flux are obtained and compared with the available data. The results demonstrate great reliability of DMRT–LES in studying turbulence.     

Passive heat transfer in a turbulent channel flow simulation using large eddy simulation based on the lattice Boltzmann method framework

In this paper, a large eddy simulation based on the lattice Boltzmann framework is carried out to simulate the heat transfer in a turbulent channel flow, in which the temperature can be regarded as a passive scalar. A double multiple relaxation time (DMRT) thermal lattice Boltzmann model is employed. While applying DMRT, a multiple relaxation time D3Q19 model is used to simulate the flow field, and a multiple relaxation time D3Q7 model is used to simulate the temperature field. The dynamic subgrid stress model, in which the turbulent eddy viscosity and the turbulent Prandtl number are dynamically computed, is integrated to describe the subgrid effect. Not only the strain rate but also the temperature gradient is calculated locally by the non-equilibrium moments. The Reynolds number based on the shear velocity and channel half height is 180. The molecular Prandtl numbers are set to be 0.025 and 0.71. Statistical quantities, such as the average velocity, average temperature, Reynolds stress, root mean square (RMS) velocity fluctuations, RMS temperature and turbulent heat flux are obtained and compared with the available data. The results demonstrate great reliability of DMRT–LES in studying turbulence.     

Monte Carlo analysis of dissociation and recombination behind strong shock waves in nitrogen

Computations are presented for the relaxation zone behind strong, one-dimensional shock waves in nitrogen. The analysis is performed with the direct simulation Monte Carlo method (DSMC). The DSMC code is vectorized for efficient use on a supercomputer. The code simulates translational, rotational and vibrational energy exchange and dissociative and recombinative chemical reactions. A new model is proposed for the treatment of three body recombination collisions in the DSMC technique which usually simulates binary collision events. The new model represents improvement over previous models in that it can be employed with a large range of chemical rate data, does not introduce into the flow field troublesome pairs of atoms which may recombine upon further collision (pseudo-particles) and is compatible with the vectorized code. The computational results are compared with existing experimental data. It is shown that the derivation of chemical rate coefficients must account for the degree of vibrational nonequilibrium in the flow. A nonequilibrium chemistry model is employed together with equilibrium rate data to compute successfully the flow in several different nitrogen shock waves.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1990.     

A Bhatnagar–Gross–Krook kinetic model with velocity-dependent collision frequency and corrected relaxation of moments

We propose a Bhatnagar–Gross–Krook (BGK) kinetic model in which the collision frequency is a linear combination of polynomials in the velocity variable. The coefficients of the linear combination are determined so as to enforce proper relaxation rates for a selected group of moments. The relaxation rates are obtained by a direct numerical evaluation of the full Boltzmann collision operator. The model is conservative by construction. Simulations of the problem of spatially homogeneous relaxation of hard spheres gas show improvement in accuracy of controlled moments as compared to solutions obtained by the classical BGK, ellipsoidal-statistical BGK and the Shakhov models in cases of strong deviations from continuum.     

Prandtl number effects in MRT lattice Boltzmann models for shocked and unshocked compressible fluids

This paper constructs a new multiple relaxation time lattice Boltzmann model which is not only for the shocked compressible fluids, but also for the unshocked compressible fluids. To make the model work for unshocked compressible fluids, a key step is to modify the collision operators of energy flux so that the viscous coefficient in momentum equation is consistent with that in energy equation even in the unshocked system. The unnecessity of the modification for systems under strong shock is analyzed. The model is validated by some well-known benchmark tests, including thermal Couette flow, Riemann problem. The first system is unshocked and the latter is shocked. In both systems, the Prandtl number effects are checked. Satisfying agreements are obtained between new model results and analytical ones.     

认识稀薄气体动力学

以通俗易懂的方式介绍了空气动力学当气体间断分子效应显著时发展起来的特殊分文——稀薄气体动力学、讨论了非平衡现象与稀薄气体动力学的关系．通过与8速度气体模型的间断Boltzmann方程的对比，解释了Boltzmann方程碰撞项的物理意义和数学困难，简要综述了其一般解法、讨论了分子在物体表面的反射和问题的边界条件，着重介绍了直接模拟Monte Carlo(DSMC)方法和为克服低速稀薄流动(如MEMS中流动)中模拟困难的信息保存(IP)方法。