Gas-kinetic unified algorithm for computable modeling of Boltzmann equation and application to aerothermodynamics for falling disintegration of uncontrolled Tiangong-No.1 spacecraft

How to solve the hypersonic aerothermodynamics around large-scale uncontrolled spacecraft during falling disintegrated process from outer space to earth,is the key to resolve the problems of the uncontrolled Tiangong-No.1 spacecraft reentry crash.To study aerodynamics of spacecraft reentry covering various flow regimes,a Gas-Kinetic Unified Algorithm(GKUA)has been presented by computable modeling of the collision integral of the Boltzmann equation over tens of years.On this basis,the rotational and vibrational energy modes are considered as the independent variables of the gas molecular velocity distribution function,a kind of Boltzmann model equation involving in internal energy excitation is presented by decomposing the collision term of the Boltzmann equation into elastic and inelastic collision terms.Then,the gas-kinetic numerical scheme is constructed to capture the time evolution of the discretized velocity distribution functions by developing the discrete velocity ordinate method and numerical quadrature technique.The unified algorithm of the Boltzmann model equation involving thermodynamics non-equilibrium effect is presented for the whole range of flow regimes.The gas-kinetic massive parallel computing strategy is developed to solve the hypersonic aerothermodynamics with the processor cores 500~45,000 at least 80%parallel efficiency.To validate the accuracy of the GKUA,the hypersonic flows are simulated including the reentry Tiangong-1 spacecraft shape with the wide range of Knudsen numbers of 220~0.00005 by the comparison of the related results from the DSMC and N-S coupled methods,and the low-density tunnel experiment etc.For uncontrolling spacecraft falling problem,the finite-element algorithm for dynamic thermalforce coupling response is presented,and the unified simulation of the thermal structural response and the hypersonic flow field is tested on the Tiangong-1 shape under reentry aerodynamic environment.Then,the forecasting analysis platform of end-of-life largescale spacecraft flying track is established on the basis of ballistic computation combined with reentry aerothermodynamics and deformation failure/disintegration.

A Gas-Kinetic Unified Algorithm for Non-Equilibrium Polyatomic Gas Flows Covering Various Flow Regimes

In this paper,a gas-kinetic unified algorithm(GKUA)is developed to investigate the non-equilibrium polyatomic gas flows covering various regimes.Based on the ellipsoidal statistical model with rotational energy excitation,the computable modelling equation is presented by unifying expressions on the molecular collision relaxing parameter and the local equilibrium distribution function.By constructing the corresponding conservative discrete velocity ordinate method for this model,the conservative properties during the collision procedure are preserved at the discrete level by the numerical method,decreasing the computational storage and time.Explicit and implicit lower-upper symmetric Gauss-Seidel schemes are constructed to solve the discrete hyperbolic conservation equations directly.Applying the new GKUA,some numerical examples are simulated,including the Sod Riemann problem,homogeneous flow rotational relaxation,normal shock structure,Fourier and Couette flows,supersonic flows past a circular cylinder,and hypersonic flow around a plate placed normally.The results obtained by the analytic,experimental,direct simulation Monte Carlo method,and other measurements in references are compared with the GKUA results,which are in good agreement,demonstrating the high accuracy of the present algorithm.Especially,some polyatomic gas non-equilibrium phenomena are observed and analysed by solving the Boltzmann-type velocity distribution function equation covering various flow regimes.

求解Boltzmann模型方程高性能并行算法在航天跨流域空气动力学应用研究

对Boltzmann方程碰撞积分物理分析与可计算建模,得到适于描述航天再入从外层空间到近地面各流域统一Boltzmann模型方程,提出求解Boltzmann模型方程统一算法高性能并行计算数学模型.发展离散速度空间区域分解大规模并行计算技术,分析统一算法变量依赖关系,建立可扩展并行计算方案;研究数据并行分布与并行执行特征,开展大规模并行化程序设计,并在小、中、大规模256-512、4096-20 625CPU及异构计算机500-45 000、3125-112 500进程并行算法测试,建立稳定运行于国产千万亿次超级计算机高性能可扩展大规模并行算法与航天器再入跨流域复杂气动力/热绕流问题并行化软件应用平台.通过对稀薄流到连续流再入飞行不同高度可回收返回式卫星飞行器、近空间大尺度机动飞行器跨流域绕流环境不同粒度高性能计算与验证,揭示大尺度复杂结构飞行器跨流区飞行稀薄过渡流区热流系数比连续、近连续流区热流系数随物面变化剧烈得多、大得多,发现该类飞行器后端面热流最大值发生在水平舵外侧拐角处,达驻点热流六分之一量级,提供了一个可靠求解航天器再入各流域高超声速绕流问题统一算法高性能并行计算应用研究方向.

稀薄气体自由分子流到连续流跨流域气动力热绕流统一算法研究

研究描述各流域气体流动输运现象统一的Boltzmann模型方程及数值求解方法,发展气体分子运动论离散速度坐标法,建立直接求解分子速度分布函数耦合迭代数值格式;研究可用于高、低不同马赫数绕流问题的Gauss型离散速度数值积分法,建立模拟各流域高超声速气动力、热绕流问题气体运动论统一算法与并行计算技术。对稀薄气体自由分子流到连续流不同Knudsen数、高低不同马赫数球体、钝锥外形、飞船返回舱再入飞行环境等绕流问题并行计算与算法验证分析,证实统一算法用于高稀薄自由分子流到连续流高超声速飞行器气动力、热绕流问题求解的可靠性,揭示飞行器跨流区不同高度高超声速绕流现象与变化规律。

含转动非平衡效应Boltzmann模型方程统一算法与跨流域绕流问题模拟研究

通过对转动自由度松弛变化特性的研究,采用转动惯量描述气体分子自旋运动,利用分子总角动量守恒作为一个新的碰撞不变量,确立含转动非平衡效应各流域统一的Boltzmann模型方程。基于转动能量空间对分布函数进行守恒积分,得到计及转动非平衡效应的分子速度分布函数控制方程组,应用气体分子运动论离散速度坐标法对速度分布函数方程所依赖的速度空间离散降维,构造直接求解分子速度分布函数的气体动理论统一格式。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影响的气体分子运动论边界条件数学模型及数值处理方法。由此提出模拟高稀薄自由分子流到连续流各流域转动非平衡效应的Boltzmann模型方程统一算法。通过对高、低不同马赫数1.5≤Ms≤25考虑转动非平衡效应的氮气激波结构与不同Knudsen数9×10-4≤Kn!≤10再入竖直平板、Ramp制动器、尖双锥外形跨流域高超声速绕流问题模拟研究,将计算结果与有关实验数据、广义退化Boltzmann与ES椭球统计模型等研究结果对比分析,验证含转动非平衡效应Boltzmann模型方程统一算法求解自由分子流到连续流跨流域绕流问题可靠性。