Numerical simulation of hypersonic thermochemical nonequilibrium flows using nonlinear coupled constitutive relations

To predict aeroheating performance of hypersonic vehicles accurately in thermochemical nonequilibrium flows accompanied by rarefaction effect, a Nonlinear Coupled Constitutive Relations (NCCR) model coupled with Gupta’s chemical models and Park’s two-temperature model is firstly proposed in this paper. Three typical cases are intensively investigated for further validation, including hypersonic flows over a two-dimensional cylinder, a RAM-C II flight vehicle and a type HTV-2 flight vehicle. The results predicted by NCCR solution, such as heat flux coefficient and electron number densities, are in better agreement with those of direct simulation Monte Carlo or flight data than Navier-Stokes equations, especially in the extremely nonequilibrium regions, which indicates the potential of the newly-developed solution to capture both thermochemical and rarefied nonequilibrium effects. The comparisons between the present solver and NCCR model without a two-temperature model are also conducted to demonstrate the significance of vibrational energy source term in the accurate simulation of high-Mach flows.     

基于非线性耦合本构关系的改进边界条件

非线性耦合本构关系（NCCR）模型是在Eu的广义流体动力学方程（GHE）基础上,通过绝热假设、Eu封闭和Myong简化推导出的关于非守恒量（黏性应力与热流）的非线性代数方程,有效拓展了线性的纳维-斯托克斯-傅里叶（NSF）本构模型在非平衡流动中的模拟能力,为快速准确模拟连续与稀薄耦合流动问题提供了强有力的理论工具。针对该模型开展滑移边界条件研究,结合努森层内物理量非线性分布的特点,提出一套在物面处与模型精度相一致的非线性修正滑移边界条件。在有限体积框架下,采用AUSMPW⁺格式和LU-SGS方法以及NCCR的完整耦合求解算法,对不同稀薄程度的高超声速单原子氩气圆柱绕流和平板绕流问题进行数值模拟。研究结果表明,基于NCCR模型的修正边界条件准确刻画出物面努森层内流动的非线性特点,有效提高了固壁滑移边界的精度。采用非线性修正边界的NCCR模型准确预测了连续流、滑移流和过渡流域的物面压力、摩阻与热流系数。     

高超声速化学非平衡流动Navier-Stokes/DSMC耦合算法

基于相同的化学反应模型,在已有计算流体力学（CFD）和直接仿真蒙特卡罗（DSMC）方法及程序的基础上,采用Modular Particle-Continuum（MPC）耦合技术,建立了包含化学非平衡Navier-Stokes/DSMC耦合算法。算法结构中DSMC计算区域在CFD计算结果上根据当地克努森数自动选取。发展了适用于流场分区信息交换的亚松弛技术,抑制DSMC方法对CFD计算的影响。把DSMC方法和CFD的应用范围拓展到过渡流区,为复杂飞行器近连续过渡流区高超声速化学非平衡流动数值模拟研究提供了一种工程适用的预测分析手段。通过对二维圆柱高超声速化学非平衡绕流的算例与其他结果的比较研究,表明耦合算法不论在流场结构、流场非平衡现象,还是飞行器表面参数、整体气动力/热特性方面,都能够得到与全DSMC计算吻合的结果,证实了所建立的Navier-Stokes/DSMC耦合计算模型与方法的有效性和可靠性。仿真了某航天器解体碎片在过渡区的化学非平衡流动,得到碎片在过渡区的气动力/热特性,为碎片的陨落计算提供依据。     

非结构网格高超声速化学非平衡MHD流场数值模拟

 在非结构网格上对考虑化学非平衡效应的二维高超声速磁流体绕钝头体流动进行了数值模拟。控制方程由二维理想磁流体动力学（MHD）方程和组元连续方程两部分组成,化学动力学模型为5组元17反应模型。MHD方程空间离散采用AUSM格式,时间推进采用显式5步龙格-库塔格式,并通过弱耦合的方式与化学反应控制方程结合在一起。计算模型为二维钝头体,外加磁场为偶极子场,磁场源位于钝头体内部。在高超声速来流条件下,对有、无磁场干扰,是否考虑化学反应下的4种工况进行了数值计算,得到了满意的结果,并与有限的参考文献进行了对比。结果表明本文发展的方法能准确地模拟考虑化学非平衡效应的高超声速MHD流场。     

高超声速非平衡流场多个振动温度模型的数值研究

利用数值求解热化学非平衡Navier-Stokes方程的方法,建立了考虑一个和多个振动温度的高超声速热化学非平衡流场的CFD计算程序,并对半球模型和球锥模型进行了数值计算,研究结果表明:(1)各个分子组分的振动温度分布于考虑一个振动温度模型的振动温度周围,即一个振动温度模型的振动温度是多个振动温度模型的各个分子组分振动温度的一种平均值;(2)在模型身部,振动温度的峰值高于平动温度的峰值;在模型近尾出现振动温度冻结并高于平动温度。     

基于Reynolds平均的高超声速二方程湍流模型

 在Reynolds平均的框架下推导了可压缩湍流Reynolds应力方程和湍动能方程。根据一定的假设和尺度分析简化并封闭了所推导的湍动能方程。在均匀湍流假设下,湍动能耗散率可分解成可压缩性耗散和旋度耗散,并对其中的可压缩性耗散进行了封闭;同时认为旋度耗散不受可压缩性影响,直接引用传统的Reynolds平均不可压缩湍动能耗散率模型方程。由此构造了适用于高马赫数的二方程可压缩湍流模型。应用所发展的模型计算了高超声速平板绕流,并与若干现有模型的计算、实验与半经验公式的计算结果进行了对比,验证了所发展的模型。在此基础上,通过对压缩拐角的高超声速湍流的数值模拟,对所发展的湍流模型,以及若干现有模型进行了对比,显示了不同湍流模型及可压缩性修正在计算壁面压力分布和热流分布上的特点,说明了湍流模型可压缩修正的必要性,得到了所发展模型的计算结果最接近实验结果的结论。     

任意单元间断Galerkin有限元计算方法研究

基于龙格库塔间断Galerkin(RKDG)有限元法的构造思想,通过局部坐标变换,发展了非正交单元DG有限元计算方法;借鉴非结构网格有限体积隐式计算方法,发展了适应于DG有限元方法的隐式计算方法;借鉴一维和二维(三角形单元)DG有限元限制器构造方法,提出了非正交三棱柱单元限制器方法;利用上述方法数值模拟了球头和双椭球的高超声速粘性绕流,得到了清晰的流场结构,并得到了较好的压力和热流分布,表明该方法在复杂高超声速流动的数值模拟方面具有广阔的应用前景。     

高超声速飞行器表面温度分布与气动热耦合数值研究

针对高超声速飞行器热防护设计中的高温气体非平衡效应问题和气动热环境精确预测问题,基于流场的非平衡Navier-Stokes方程、表面的能量守恒方程和内部的热传导方程,考虑流场的非平衡效应、表面的热辐射效应、催化效应和烧蚀效应以及热防护层内部的热传导效应,建立了初步的表面温度分布与气动热的耦合计算方法,完善了高超声速飞行器气动物理流场计算软件(AEROPH_Flow)。在表面材料为碳-碳(C-C)条件下,对飞行高度为65km和飞行速度为8,10km/s的半球以及飞行高度为50km和飞行速度为8km/s的球锥模型,开展了表面温度分布与气动热的耦合计算,验证了计算方法和计算软件,分析了表面温度分布对气动热环境的影响。研究结果表明:表面温度分布对气动热的计算结果有较大影响,在气动热环境的预测中,不仅要考虑热化学非平衡效应和表面催化效应的影响,还要考虑表面温度分布的影响,最好是采用表面温度分布与气动热耦合计算的方法,以减小表面温度分布对气动热计算结果的影响。为此,需要发展完善非平衡流场/表面催化和烧蚀/热传导温度场(气/表/固)的计算模型、耦合求解技术和计算软件,实现对高超声速飞行器的真实飞行条件下高温气体非平衡效应和气动热环境的精确模拟。     

二维超／高超声速进气道流场数值模拟

对超／高超声速三级压缩进气道流场进行了数值模拟,来流马赫数为4、6,进气道内流动为层流状态,根据二维Navier-Stokes方程,采用二阶精度Roe格式进行离散。按照流场特点,合理地设计网格分布及调整不同黏性范围的熵修正,防止了壁面附近过大的数值耗散,使计算结果更加合理。在进气道模型的各级压缩折转角处,获得了清晰的激波结构,在进气道内部的各种波系的相交、反射和激波诱导的边界层分离等现象都得到合理的描述。计算得到的压力分布,在各级压缩斜板上同简单波理论结果十分接近。用本文方法计算了另一个二级压缩进气道,沿上、下壁面的压力分布与试验比较符合得较好。     

三维等离子体MHD气动热环境数值模拟

电磁流动控制技术是一个多学科交叉融合的重要研究方向,在高超声速飞行器气动特性优化、气动热环境减缓、边界层转捩和等离子体分布等流动控制方面显示出广阔的应用前景。考虑高超声速飞行器绕流流场中发生的离解、复合、电离和置换等化学反应,气体分子振动能激发以及化学非平衡效应,耦合电磁场作用并基于低磁雷诺数假设,通过数值模拟求解三维非平衡Navier-Stokes流场控制方程和Maxwell电磁场控制方程,建立磁场与三维等离子体流场耦合数值模拟方法及程序,采用典型算例进行考核。在此基础上,开展不同条件下磁场对再入三维等离子体流场以及气动热环境影响分析。研究表明:建立的高超声速飞行器的等离子体流场与磁场耦合计算方法及程序,其数值模拟结果与文献符合,外加磁场使飞行器头部弓形激波外推,磁场强度越强,激波面外推距离越大;不同磁场强度环境下,流场中温度峰值大小略有变化,变化幅度较小;磁场对绝大部分区域的热流有减缓作用,作用的大小与飞行高度、马赫数以及磁场的配置紧密相关;当前的计算条件下,飞行的高度越高,磁场的作用越明显。     

Numerical simulation of multi-dimensional inviscid compressible flows by using TV-HLL scheme

This paper deals with the numerical solution of inviscid compressible flows. The threedimensional Euler equations describing the mentioned problem are presented and solved numerically with the finite volume method. The evaluation of the numerical flux at the interfaces is performed by using the Toro Vazquez-Harten Lax Leer(TV-HLL) scheme. An essential feature of the proposed scheme is to associate two systems of differential equations, called the advection system and the pressure system. It can be implemented with a very simple manner in the standard finite volume Euler and Navier–Stokes codes as extremely simple task. The scheme is applied to some test problems covering a wide spectrum of Mach numbers, including hypersonic, low speed flow and three-dimensional aerodynamics applications.     

Optimal three-dimensional impact time guidance with seeker’s field-of-view constraint

This paper proposes a new three-dimensional optimal guidance law for impact time control with seeker’s Field-of-View (FOV) constraint to intercept a stationary target. The proposed guidance law is devised in conjunction with the concept of biased Proportional Navigation Guidance (PNG). The guidance law developed leverages a nonlinear function to ensure the boundedness of velocity lead angle to cater to the seeker’s FOV limit. It is proven that the impact time error is nullified in a finite-time under the proposed method. Additionally, the optimality of the biased command is theoretically analyzed. Numerical simulations confirm the superiority of the proposed method and validate the analytic findings.     

烧蚀对再入体绕流电子数密度影响的数值研究

从化学非平衡NS方程或其简化形式(粘性激波层方程、PNS方程)出发,采用分区求解的方法数值模拟含泰氟隆烧蚀产物的高超声速再入体流场.首先计算分析了RAM-C飞行试验状态和一个考核算例,对计算方法和程序作了初步验证.其次耦合烧蚀壁面边界条件和流体控制方程,采用19组分28个反应的化学反应模型,对有、无烧蚀情况下高超声速钝锥体再入绕流及底部流场进行了数值模拟,深入分析了烧蚀产物对再入流场电子数密度及温度分布的影响.     

DSMC量子动理学化学反应模型的数值模拟

为评估直接模拟蒙特卡罗（DSMC）方法中新近发展的一种量子动理学（QK）化学反应模型，在自研高超声速稀薄气体流动数值模拟软件RariHV中实现该模型，并进行了单个绝热单元内的热泳平衡/非平衡反应测试。结果表明，数值解与理论解吻合良好，QK模型具有很好的预测化学反应流动的能力。为进一步验证QK模型在真实流动中的表现，还计算了高超声速绕圆柱的化学反应流动，QK模型计算的驻点线上温度和组分分布都与总碰撞能（TCE）模型结果吻合良好。相较于TCE模型，QK模型的优势是不再依赖反应速率系数的实验数据，在深空探测等化学反应数据缺乏的领域具有一定的应用前景。     

Numerical analysis of hypersonic thermochemical non-equilibrium environment for an entry configuration in ionized flow

A theoretical methodology for thermochemical non-equilibrium flow combing with the HLLC (Harten-Lax-van Leer Contact) scheme was applied to study the hypersonic thermochemical non-equilibrium environment of an entry configuration in ionized flow. A two-temperature controlling model was utilized and the Gupta’s 11 species (N₂, O₂, NO, O, N, NO⁺, N₂⁺, O₂⁺, N⁺, O⁺, e^?) thermochemical non-equilibrium model was taken. Firstly, numerical calculations of hypersonic thermochemical non-equilibrium environments for different aerodynamic shapes were carried out to verify the reliability of the method above. Then, the method was used to research the effects of ionization and wall catalysis on the hypersonic thermochemical non-equilibrium environment of the entry configuration in ionized flow. The shock stand-off distance can be reduced by thermochemical reactions but doesn’t continue to decrease significantly when ionization occurs. The shock stand-off distance calculated by the 11 species model is 4.2% smaller than that calculated by the 5 species (N₂, O₂, NO, O, N) thermochemical non-equilibrium model without considering ionization. Ionization reduces wall heat flux but increases wall pressure a little. The effect of ionization on aerothermal loads is greater than that of aerodynamic loads. The thermochemical reactions of electrons and ions catalyzed at the wall increase wall heat flux significantly but make a small change in wall pressure. The maximum wall heat flux obtained by only considering the electrons and ions catalyzed at the partially catalytic wall condition is 11.8% less than that calculated at the super-catalytic wall condition.     

A quasi-one-dimensional model for hypersonic reactive flow along the stagnation streamline

This study proposes a quasi-one-dimensional model to predict the chemical non-equilibrium flow along the stagnation streamline of hypersonic flow past a blunt body. The model solves reduced equations along the stagnation streamline and predicts nearly identical results as the numerical solution of the full-field Navier-Stokes equations. The high efficiency of this model makes it useful to investigate the overall quantitative behavior of related physical-chemical phenomena. In this paper two important properties of hypersonic flow, shock stand-off distance and oxygen disso-ciation, are studied using the quasi-one-dimensional model with the ideal dissociating gas model. It is found that the shock stand-off distance is affected by both chemical and thermal non-equilibrium. The shock stand-off distance will increase when the flow conditions are changed from equilibrium to non-equilibrium, because the average density of the shock-compressed gas will decrease as a result of the increase in translational energy. For oxygen dissociation, the maximum value of its dis-sociation degree along the stagnation line varies with the flight altitude. It is increased at first and decreased thereafter with the altitude, which is due to the combination effect of the equilibrium shift and chemical non-equilibrium relaxation. The overall variation of the maximum dissociation is then plotted in the speed and altitude coordinates as a reference for engineering application.     

高超声速再入体烧蚀流场计算分析

从化学非平衡NS方程或其简化形式(粘性激波层方程、PNS方程)出发,求解高超声速再入体的绕流和底部尾流流场。首先讨论了碳基材料烧蚀壁面条件的确定方法,计算了包含和不包含碳-碳烧蚀产物的再入体半球的化学反应绕流流场,并和文献结果进行了对比。在此基础上,计算了两个高度条件下,包含和不包含碳-酚醛烧蚀产物的再入小钝锥的绕流和尾流流场,分析了烧蚀产物对流场电子数密度、温度等流动参数的影响。     

Theoretical investigation of shock stand-off distance for non-equilibrium flows over spheres

We derived a theoretical solution of the shock stand-off distance for a non-equilibrium flow over spheres based on Wen and Hornung’s solution and Olivier’s solution. Compared with previous approaches, the main advantage of the present approach is allowing an analytic solution without involving any semi-empirical parameter for the whole non-equilibrium flow regimes. The effects of some important physical quantities therefore can be fully revealed via the analytic solution. By combining the current solution with Ideal Dissociating Gas (IDG) model, we investigate the effects of free stream kinetic energy and free stream dissociation level (which can be very different between different facilities) on the shock stand-off distance.     

(高)超声速流动试验技术及研究进展

近年来,与高速飞行器相关的(高)超声速流动受到了极大的关注。这类流动所具有的非定常性、强梯度和可压缩性对试验方法和风洞设计技术提出了挑战。超声速纳米示踪平面激光散射(NPLS)技术是由作者所在团队研发的非接触光学测试技术。它能够以较高的空间分辨率来揭示超声速三维流场的一个瞬态剖面的时间解析的流动结构。介绍了NPLS技术以及基于NPLS开发的密度场测量、雷诺应力测量和气动光学波前测量等方法,并回顾了这些技术在超声速边界层、超声速混合层、超声速压缩拐角、激波/边界层相互作用和光学头罩绕流等流动中的应用,清晰地再现了边界层、混合层、激波等典型流场结构及其时空演化特性。另外,为了模拟和研究高空大气条件下边界层自然转捩和超声速混合层的转捩特性,介绍了高超声速静风洞、超-超混合层风洞的设计技术以及层流化喷管的设计方法。     

高超声速电离绕流的数值模拟

本文从三维N－S方程出发，采用稳式L－U分解算法和7组分15个反应的化学模型，数值模拟高超声速电离空气绕流。首先采用对称TVD格式、AUSMPW＋格式和Van Leer的矢通量分裂格式计算了高超声速球头绕流，并对它们的计算结果做了对比分析。然后用前两种格式，对RAM－C飞行试验模型三个再入高度（81km、71km、61km）的流场进行了数值模拟，计算的流场电子数密度值和试验测量数据符合较好。