A Switch Function-Based Gas-Kinetic Scheme for Simulation of Inviscid and Viscous Compressible Flows

In this paper, a switch function-based gas-kinetic scheme (SF-GKS) is presented for the simulation of inviscid and viscous compressible flows. With the finite volume discretization, Euler and Navier-Stokes equations are solved and the SF-GKS is applied to evaluate the inviscid flux at cell interface. The viscous flux is obtained by the conventional smooth function approximation. Unlike the traditional gas-kinetic scheme in the calculation of inviscid flux such as Kinetic Flux Vector Splitting (KFVS), the numerical dissipation is controlled with a switch function in the present scheme. That is, the numerical dissipation is only introduced in the region around strong shock waves. As a consequence, the present SF-GKS can well capture strong shock waves and thin boundary layers simultaneously. The present SF-GKS is firstly validated by its application to the inviscid flow problems, including 1-D Euler shock tube, regular shock reflection and double Mach reflection. Then, SF-GKS is extended to solve viscous transonic and hypersonic flow problems. Good agreement between the present results and those in the literature verifies the accuracy and robustness of SF-GKS.     

Implicit preconditioned WENO scheme for steady viscous flow computation

A class of lower–upper symmetric Gauss–Seidel implicit weighted essentially nonoscillatory (WENO) schemes is developed for solving the preconditioned Navier–Stokes equations of primitive variables with Spalart–Allmaras one-equation turbulence model. The numerical flux of the present preconditioned WENO schemes consists of a first-order part and high-order part. For first-order part, we adopt the preconditioned Roe scheme and for the high-order part, we employ preconditioned WENO methods. For comparison purpose, a preconditioned TVD scheme is also given and tested. A time-derivative preconditioning algorithm is devised and a discriminant is devised for adjusting the preconditioning parameters at low Mach numbers and turning off the preconditioning at intermediate or high Mach numbers. The computations are performed for the two-dimensional lid driven cavity flow, low subsonic viscous flow over S809 airfoil, three-dimensional low speed viscous flow over 6:1 prolate spheroid, transonic flow over ONERA-M6 wing and hypersonic flow over HB-2 model. The solutions of the present algorithms are in good agreement with the experimental data. The application of the preconditioned WENO schemes to viscous flows at all speeds not only enhances the accuracy and robustness of resolving shock and discontinuities for supersonic flows, but also improves the accuracy of low Mach number flow with complicated smooth solution structures.     

钝锥再入飞行器黏性干扰效应建模

针对典型的钝锥外形, 采用统一气体动理学格式(UGKS)模拟了高度70~110 km下不同Mach数和攻角的流场, 进行了流场特性的分析, 并基于黏性干扰的理论成果, 将气动力特性与第3黏性干扰参数、攻角和Mach数等参数进行关联, 建立了气动力系数的黏性干扰模型, 给出了模型预测结果的相关性分析和准确性评估。经初步测试, 该模型预测结果与UGKS直接模拟结果具有良好的一致性, 对工程应用快速获取高空气动特性具有重要意义。      

Comparative study on aerodynamic heating under perfect and nonequilibrium hypersonic flows

In this study, comparative heat flux measurements for a sharp cone model were conducted by utilizing a high enthalpy shock tunnel JF-10 and a large-scale shock tunnel JF-12, responsible for providing nonequilibrium and perfect gas flows, respectively. Experiments were performed at the Key Laboratory of High Temperature Gas Dynamics(LHD), Institute of Mechanics, Chinese Academy of Sciences. Corresponding numerical simulations were also conducted in effort to better understand the phenomena accompanying in these experiments. By assessing the consistency and accuracy of all the data gathered during this study, a detailed comparison of sharp cone heat transfer under a totally different kind of freestream conditions was build and analyzed. One specific parameter, defined as the product of the Stanton number and the square root of the Reynold number, was found to be more characteristic for the aerodynamic heating phenomena encountered in hypersonic flight. Adequate use of said parameter practically eliminates the variability caused by the deferent flow conditions, regardless of whether the flow is in dissociation or the boundary condition is catalytic. Essentially, the parameter identified in this study reduces the amount of ground experimental data necessary and eases data extrapolation to flight.     

高速动能弹温度场数值模拟

随着兵器发射技术和空气动力学技术的发展,动能弹的发射初速和飞行状态正从超声速向高超声速发展,由此产生了气动热问题.准确预测动能弹温度场是其气动力和热防护设计的关键技术.采用CFD预测温度场的方法,包括平衡流流动控制方程及差分格式,构造平衡流通量Jacob矩阵,在差分格式矢通量分裂过程中嵌入平衡流真实气体模型模拟温度场,获得平衡流气体状态方程.对典型高速动能弹热环境进行验证,考察方法的合理性.对设计的一种新型高超声速动能弹温度场进行数值模拟,为其气动设计及热防护提供了较可靠的数据.     

混合通量差分格式的比较

系统研究了几种混合通量差分格式的构造方法和耗散模型,分别对低速平板绕流、二维跨音速喷管流动和高超音速钝头体无粘绕流进行了数值模拟,结合先进的EASM湍流模型对格式的粘性分辨率和激波稳定性进行了细致的比较分析.结果表明混合通量差分格式兼顾了FDS和FVS格式的优点,具有较高的间断分辨率和数值稳定性.     

基于遗传算法的升力体外形优化设计

升力体由于低热流率再入物理特性和高效的内部容积利用率，是高超声速飞行器气动外形的一种典型布局.文章对升力体飞行器进行参数化数值建模，并提取其表征外形的参数作为设计变量，综合考虑飞行器再入过程中的气动力、气动热、容积利用率及稳定性等性能指标.运用多目标混合遗传算法对升力体进行了多变量、多约束下的气动外形优化设计，获得了再入飞行器外形的最优Pareto解.数值模拟结果表明，典型状态下最优Pareto解与CFD结果相差12%，验证了优化结果的准确性.      

类前缘局部热防护的场协同问题初步分析

本文针对二维类前缘外形在带表面吹气情况下的高超声速流场进行了数值模拟,结果表明表面吹气能起到局部防热作用。本文应用场协同的概念,分析了流场中速度场与温度场的关系,从机理上进一步认识有关冷却的原理。     

Osher Flux with Entropy Fix for Two-Dimensional Euler Equations

We compare in this paper the properties of Osher flux with O-variant and P-variant (Osher-O flux and Osher-P flux) in finite volume methods for the two-dimensional Euler equations and propose an entropy fix technique to improve their robustness. We consider both first-order and second-order reconstructions. For inviscid hypersonic flow past a circular cylinder, we observe different problems for different schemes: a first-order Osher-O scheme on quadrangular grids yields a carbuncle shock, while a first-order Osher-P scheme results in a dislocation shock for high Mach number cases. In addition, a second-order Osher scheme can also yield a carbuncle shock or be unstable. To improve the robustness of these schemes we propose an entropy fix technique, and then present numerical results to show the effectiveness of the proposed method. In addition, the influence of grid aspects ratio, relative shock position to the grid and Mach number on shock stability are tested. Viscous heating problem and double Mach reflection problem are simulated to test the influence of the entropy fix on contact resolution and boundary layer resolution.     

面向高超声速飞行器的激波智能预测方法

高超声速飞行器激波位置的准确预测能够有效提升数值模拟的精度和效率。一方面, 对高超声速飞行器激波附近网格进行正交和加密处理, 可有效提升数值计算精度; 另一方面, 使用高超声速飞行器激波位置对计算网格进行修正, 能够加速CFD计算收敛过程。提出了一种基于机器学习的高超声速飞行器激波智能预测方法, 对典型高超声速飞行器外形进行激波位置的高效准确预测。首先, 针对典型高超声速飞行器外形和典型飞行状态, 使用数值模拟方法获得收敛的流场, 并采用基于Mach数等值线的激波提取方法, 从流场中判别激波面并提取构成激波面的关键点位置, 形成训练数据; 然后采用有监督学习算法, 学习关键点位置, 并利用二次曲线沿流向拟合关键点形成初步的激波线族; 最后, 基于剖面压力云图, 构造基于投影压力图像的智能预测神经网络, 对初步形成的激波线族进行修正, 并获得三维激波面。大量的实验结果表明, 激波预测模型能够对高超声速飞行器激波位置做出准确预测, 预测的激波面与CFD数值计算结果中提取的激波面误差在10-4量级。      

High-order shock-fitting methods for direct numerical simulation of hypersonic flow with chemical and thermal nonequilibrium

In recent years, much progress has been made in the direct numerical simulation of laminar-turbulent transition of hypersonic boundary layer flow. However, most of the efforts at the direct numerical simulation of transition previously have been focused on the idealized perfect gas flow or “cold” hypersonic flows. For practical problems in hypersonic flows, high-temperature effects of thermal and chemical nonequilibrium are important and cannot be modeled by a perfect gas model. Therefore, it is necessary to include the real gas models in the numerical simulation of hypersonic boundary layer transition in order to accurately predict flow field parameters. Currently most numerical methods for hypersonic flow with thermo-chemical nonequilibrium are based on shock-capturing approach at relatively low order of accuracy. Shock capturing schemes reduce to first-order accuracy near the shock and have been shown to produce spurious oscillations behind curved strong shocks. There is a need to develop new methods capable of simulating nonequilibrium hypersonic flow fields with uniformly high-order accuracy and avoid spurious oscillations near the shock. This paper presents a fifth-order shock-fitting method for numerical simulation of thermal and chemical nonequilibrium in hypersonic flows. The method is developed based on the state-of-the-art real gas models for thermo-chemical nonequilibrium and transport phenomena. Shock-fitting approach is used because it has the advantage of capturing the entire flow field with high-order accuracy and without any oscillations near the shock. The new method has been tested and validated for a number of test cases over a wide span of free stream conditions. The developed method is applied for the study of receptivity of free stream acoustic waves over a blunt cone for hypervelocity flow. Some preliminary results of the computations of the high order shock fitting method for the above mentioned study have also been presented.     

高精度格式WCNS-E-5计算物面热流

采用加权紧致非线性格式WCNS-E-5,四阶精度的二阶导数差分近似以及四阶精度的边界格式构造了高精度算法,对高超声速粘性流动的物面热流进行数值研究.首先考察了壁面网格雷诺数对驻点热流的影响,然后开展了边界格式对热流计算结果影响的研究,最后对大攻角钝锥绕流进行了数值模拟.研究结果表明:WCNS-E-5能降低边界层内网格分辨率,全场高精度的WCNS-E-5计算得到的流场图像清晰、真实、分辨率高,热流值准确、可靠.     

高超声速飞行器前缘流固耦合计算方法研究

对高超声速流场和结构温度场进行了耦合计算分析, 同时基于准静态假设对结构应力进行了分析. 流场部分采用基于非定常Navier-Stokes (N-S)方程的有限体积法, 湍流模型采用SST k-ω 模型, 固体部分采用基于非稳态热传导方程的有限元法, 同时基于准静态假设对固体结构的应力应变进行了分析. 在流固交界面处, 高速流体从固体结构得到温度边界条件, 固体结构从高速流体得到热流边界条件, 从而实现了流场和固体温度场的紧耦合计算.通过与超声速无限长圆管绕流试验结果进行对比, 验证了该方法的可靠性. 同时对二维圆管结构在气动加热过程中的温度、应力等的变化进行了比较详细的分析. 研究结果表明: 随着气动加热时间的推进, 由于圆管结构的高温区在不断扩大, 导致了结构的热变形在不断地增大; 圆管最小变形区出现在θ为60°处; 同时研究发现在计算时间内圆管热变形对外部流场的影响可以忽略不计.     

Flow characteristics of hypersonic inlets with different cowl-lip blunting methods

Under hypersonic flight conditions,the sharp cowl-lip leading edges have to be blunted because of the severe aerodynamic heating.This paper proposes four cowl-lip blunting methods and studies the corresponding flow characteristics and performances of the generic hypersonic inlets by numerical simulation under the design conditions of a flight Mach number of 6 and an altitude of 26 km.The results show that the local shock interference patterns in the vicinity of the blunted cowl-lips have a substantial influence on the flow characteristics of the hypersonic inlets even though the blunting radius is very small,which contribute to a pronounced degradation of the inlet performance.The Equal Length blunting Manner(ELM)is the most optimal in that a nearly even reflection of the ramp shock produces an approximately straight and weak cowl reflection shock.The minimal total pressure loss,the lowest cowl drag,maximum mass-capture and the minimal aeroheating are achieved for the hypersonic inlet.For the other blunting manners,the ramp shock cannot reflect evenly and produces more curved cowl reflection shock.The Type V shock interference pattern occurs for the Cross Section Cutting blunting Manner(CSCM)and the strongest cowl reflection shock gives rise to the largest flow loss and drag.The cowl-lip blunted by the other two blunting manners is subjected to the shock interference pattern that transits with an increase in the blunting radius.Accordingly,the peak heat flux does not fall monotonously with the blunting radius increasing.Moreover,the cowl-lip surface suffers from severe aerothermal load when the shear layer or the supersonic jet impinges on the wall.     

再入体头部粘性流场高分辨率格式数值模拟

TVD格式是目前数值研究以激波为主要特征之一的超声速、高超声速流场的最先进的算法之一。本文用二阶迎风TVD格式,对三种烧蚀外形的轴对称粘性流场和10°钝锥有攻角三维粘性流场进行了数值模拟,得到了高质量的头部脱体激波和与实验结果及直线推进法计算一致的物面压力分布,表明了TVD格式在再入体粘性绕流计算中的独特优势。     

A Hybrid Lattice Boltzmann Flux Solver for Simulation of Viscous Compressible Flows

In this paper, a hybrid lattice Boltzmann flux solver (LBFS) is proposed for simulation of viscous compressible flows. In the solver, the finite volume method is applied to solve the Navier-Stokes equations. Different from conventional Navier-Stokes solvers, in this work, the inviscid flux across the cell interface is evaluated by local reconstruction of solution using one-dimensional lattice Boltzmann model, while the viscous flux is still approximated by conventional smooth function approximation. The present work overcomes the two major drawbacks of existing LBFS [28–31], which is used for simulation of inviscid flows. The first one is its ability to simulate viscous flows by including evaluation of viscous flux. The second one is its ability to effectively capture both strong shock waves and thin boundary layers through introduction of a switch function for evaluation of inviscid flux, which takes a value close to zero in the boundary layer and one around the strong shock wave. Numerical experiments demonstrate that the present solver can accurately and effectively simulate hypersonic viscous flows.     

吸气式高超声速飞行器气动力气动热的数值模拟方法及应用

对吸气式高超声速飞行器而言,物面热流和摩阻的准确预测对飞行器设计及安全十分关键.介绍采用CFD准确预测气动力和气动热的方法,包括流动的控制方程、湍流模型及湍流的先进壁面函数边界条件,介绍流动的数值求解方法.对典型超声速层流和湍流流动的摩擦阻力和热流进行详细的验证与确认,考察CFD工具在使用先进壁面函数边界条件后,湍流计算的法向网格无关性能力.对设计的一种吸气式高超声速飞行器的气动力和气动热进行数值模拟,为飞行器的气动设计及热防护提供了可靠的数据.     

Theory of aerodynamic heating from molecular collision analysis

An aerodynamic heating model is derived from molecular collision analysis, in which the rising temperature of a hypersonic flying object as a function of the flying speed in a classical dense monoatomic gas environment is set up. The model predicts that the rising temperature of the hypersonic flying object is independent of the gas density but depends linearly on the gas atomic mass. A nonequilibrium molecular dynamics simulation is carried out to verify the theoretical model. Also, through analyzing the vibrational density of states in the flying objects, it is found that the excited phonon frequency is near the collision frequency, uncovering that the phonons are mainly excited by the face colliding gas atoms. Our study provides a new insight into understanding the intrinsic mechanism of aerodynamic heating and helps to develop the temperature-controllable hypersonic flying vehicle.     

高速飞行器磁控阻力特性

采用低磁雷诺数磁流体数学模型,对外加磁场下的高超声速半球体流场进行数值模拟.选取三种简单理想磁场(轴向、径向、周向均布磁场),分析了不同磁场类型对流场结构、气动阻力与洛伦兹阻力的影响及作用机理.研究发现,轴向磁场径向"挤压"效应使得激波外形凸出,且壁面静压存在"饱和现象";径向磁场存在轴向"外推"效应,较大的磁场强度会导致肩部形成高温区;周向磁场下感应电场的存在导致增阻效果很差.进而对比了两种相同驻点磁感应强度特殊分布磁场(偶极子磁场、螺线管磁场)下的流场,发现了不同于理想磁场的径向"扩张"效应.按增阻效果从大到小依次为径向磁场、螺线管磁场、轴向磁场、偶极子磁场、周向磁场.     

Variation character of stagnation point heat flux for hypersonic pointed bodies from continuum to rarefied flow states and its bridge function study

This paper is a research on the variation character of stagnation point heat flux for hypersonic pointed bodies from continuum to rarefied flow states by using theoretical analysis and numerical simulation methods. The newly developed near space hypersonic cruise vehicles have sharp noses and wingtips, which desires exact and relatively simple methods to estimate the stagnation point heat flux. With the decrease of the curvature radius of the leading edge, the flow becomes rarefied gradually, and viscous interaction effects and rarefied gas effects come forth successively, which results in that the classical Fay-Riddell equation under continuum hypothesis will become invalid and the variation of stagnation point heat flux is characterized by a new trend. The heat flux approaches the free molecular flow limit instead of an infinite value when the curvature radius of the leading edge tends to 0. The physical mechanism behind this phenomenon remains in need of theoretical study. Firstly, due to the fact that the whole flow regime can be described by Boltzmann equation, the continuum and rarefied flow are analyzed under a uniform framework. A relationship is established between the molecular collision insufficiency in rarefied flow and the failure of Fourier’s heat conduction law along with the increasing significance of the nonlinear heat flux. Then based on an inspiration drew from Burnett approximation, control factors are grasped and a specific heat flux expression containing the nonlinear term is designed in the stagnation region of hypersonic leading edge. Together with flow pattern analysis, the ratio of nonlinear to linear heat flux W _r is theoretically obtained as a parameter which reflects the influence of nonlinear factors, i.e. a criterion to classify the hypersonic rarefied flows. Ultimately, based on the characteristic parameter W _r , a bridge function with physical background is constructed, which predicts comparative reasonable results in coincidence well with DSMC and experimental data in the whole flow regime.