A review of the mathematical modeling of equilibrium and nonequilibrium hypersonic flows

This paper systematically reviews the mathematical modeling based on the computational fluid dynamics(CFD)method of equilibrium and nonequilibrium hypersonic flows.First,some physicochemical phenomena in hypersonic flows(e.g.,vibrational energy excitation and chemical reactions)and the flow characteristics at various altitudes(e.g.,thermochemical equilibrium,chemical nonequilibrium,and thermochemical nonequilibrium)are reviewed.Second,the judgment rules of whether the CFD method can be applied to hypersonic flows are summarized for accurate numerical calculations.This study focuses on the related numerical models and calculation processes of the CFD method in a thermochemical equilibrium flow and two nonequilibrium flows.For the thermochemical equilibrium flow,the governing equations,chemical composition calculation methods,and related research on the thermodynamic and transport properties of air are reviewed.For the nonequilibrium flows,the governing equations that include one-,two-,and three-temperature models are reviewed.The one-temperature model is applied to a chemical nonequilibrium flow,whereas the two-and three-temperature models are applied to a thermochemical nonequilibrium flow.The associated calculations and numerical models of the thermodynamic and transport properties,chemical reaction sources,and energy transfers between different energy modes of the three models are presented in detail.Finally,the corresponding numerical models of two special wall boundary conditions commonly used in hypersonic flows(i.e.,slip boundary conditions and catalytic walls)and related research,are reviewed.

Explicit Large Time Stepping with Third-Order Exponential Time Differencing Scheme for Hypersonic Chemical Non-Equilibrium Flow

In this paper, a third-order exponential time differencing scheme, named ETDRK3, was investigated for large time stepping in the computation of hypersonic non-equilibrium flow. The second-order Harten-TVD scheme was used for the spatial discretization. The efficient implementation of the scheme with diagonalization of Jacobin matrix was established and carried out for the semi-cylindrical around flow. Current observations showed that the numerical results were in good agreement with those obtained by the classical explicit three-stage Runge-Kutta scheme (RK3) and implicit LU scheme. Efficiency assessments promised the effectiveness of the ETDRK3 scheme. The rationality of the application of this scheme was proved by its preferable accuracy and efficiency.

NON-STATIONARY EFFECTS IN HYPERSONIC NONUNIFORM DUSTY-GAS FLOW PAST A BLUNT BODY

In the framework of the two-fluid model, a hypersonic flow of a nonuniform dusty gas with low inertial (non-depositing) particles around a blunt body is considered. The particle mass concentration is assumed to be small, so that the effect of particles on the carrier phase is significant only inside the boundary layer where the particles accumulate. Stepshaped and harmonic nonuniformities of the particle concentration ahead of the bow shock wave are considered and the corresponding nonstationary distributions of the particle concentration in the shock layer are studied. On the basis of numerical study of nonstationary two-phase boundary layer equations derived by the matched asymptotic expansion method, the effects of free-stream particle concentration nonuniformities on the thermal flux, and the friction coefficient in the neighborhood of stagnation point are investigated, in particular, the most “dangerous” nonuniformity periods are found.

On transition of type V interaction in double-wedge flow with non-equilibrium effects

The transition between regular reflection （RR） and Mach reflection （MR） of type V shock-shock interaction on a double-wedge geometry with high temperature non-equilibrium effects is investigated by extended shock-polar method and numerical simulation. First, the critical angles of transition from detachment criterion and yon Neumann criterion are determined by the extended shock-polar method considering the non-equilibrium effects. Then wave patterns and the transition process are numerically obtained. Results of the critical transition angles from shock-polar calculation and numerical simulation show evident disagreement, indicating transition mechanism between RR and MR of type V interaction is changed. By comparing with the frozen counterpart, it is also found that non-equilibrium effects lead to a larger critical wedge angle and a larger hysteresis interval.

Three-Dimensional Structure of Non-Equilibrium Homogeneous Condensation Flow in a Supersonic Rectangular Nozzle

Numerical simulations have been carried out for a supersonic three-dimensional rectangular arc nozzle, where a secondary flow toward the center of the curvature occurs due to the shape of the nozzle. It is known that secondary flow causes longitudinal vortices to form near the wall of the nozzle corner, making the nozzle outlet flow unstable and induces loss of transport energy. When the working fluid is a condensable gas with relatively large latent heat such as moist air or steam, rapid accelerated expansion in the nozzle causes non-equilibrium condensation due to supersaturation. After the release of latent heat during phase transition, nozzle flow continues expanding at an equilibrium saturation condition. In the absence of foreign particles, e.g. ions or dust particles, condensation nuclei are formed in the gas itself causing non-equilibrium homogeneous condensation. Supersonic nozzle flow properties vary considerably due to the occurrence of condensation phenomenon. The objective of this study is to investigate the effect of non-equilibrium homogeneous condensation on the longitudinal vortices which form in the range close to the corner of rectangular arc nozzle numerically.

Simulating high Reynolds number flow in two-dimensional lid-driven cavity by multi-relaxation-time lattice Boltzmann method

By coupling the non-equilibrium extrapolation scheme for boundary condition with the multi-relaxation-time lattice Boltzmann method, this paper finds that the stability of the multi-relaxation-time model can be improved greatly, especially on simulating high Reynolds number （Re） flow. As a discovery, the super-stability analysed by Lallemand and Luo is verified and the complex structure of the cavity flow is also exhibited in our numerical simulation when Re is high enough. To the best knowledge of the authors, the maximum of Re which has been investigated by direct numerical simulation is only around 50 000 in the literature; however, this paper can readily extend the maximum to 1000 000 with the above combination.

大尺寸自由活塞激波风洞自由流参数诊断方法

高焓激波风洞自由流具有一定程度的热化学非平衡,使得流场参数的确定存在困难。针对大尺寸自由活塞高焓激波风洞的总温2 700~4 700 K、总压5.6~20.3 MPa条件,采用非接触吸收光谱技术、接触测量技术等测试技术,结合多温度多组分数值模拟方法,共同诊断喷管名义马赫数10出口自由流的参数。结果显示,温度测量值与计算值最大偏差小于7.5%,速度测量值与计算值最大偏差小于5%,NO浓度测量值与计算中最大偏差小于12%。

闪沸喷雾孔几何形状对孔内流动特性影响的数值模拟

研究了汽车直喷汽油机喷嘴的几何形状对于闪沸喷雾孔内流动以及相变过程的影响机理。基于热不平衡假设建立了一维的两相相变流动模型,对于具有不同喷孔流道长度、直径、入口处圆角以及流道锥角的结构,分析了闪沸喷雾孔内流动的特性。将该模型结果与作者团队先前的实验结果进行了精度比对,验证了模型的准确性。结果表明:喷孔流道长度越长,孔径越小,从而孔内相变越剧烈。流道入口处圆角会减少喷孔内部蒸汽的生成。收缩型喷孔压降较小,孔内蒸汽相的生成也相应减少,从而扩张型喷嘴增大蒸汽产生速率。不同的喷孔结构,改变了流道内的压力以及速度分布;压力分布影响了气泡的生长速率,速度分布影响了气泡的生长时间,而两者共同作用影响了孔内的相变特性。

高超声速流场激光测速技术研究进展

高超声速气流条件下飞行器内/外部流动中存在强湍流及脉动、边界层转捩、激波-边界层干扰和高温真实气体效应等耦合效应,表征该非定常流动现象对飞行器气动力、气动热以及目标光电特性等产生的影响是高超声速流动研究中的前沿课题.速度作为表征流动过程最重要的参数之一,准确的速度测量对于深入理解上述复杂流动-传输机理以及高超声速飞行器设计具有重要指导意义.文章针对高超声速流场速度测量中几种常用的非接触式激光测试技术进行了综述,主要包括基于空间法的粒子图像测速,基于激光吸收光谱、激光诱导荧光和瑞利散射的多普勒测速,基于飞行时间法的分子标记测速,以及基于流场折射率的聚焦激光差分干涉测速技术.首先简要介绍每种激光测速技术的基本原理,然后进一步介绍该技术在高超声速自由流、层/湍流边界层、激波/边界层干扰、尾流或其他复杂流动区域的速度及其脉动度测量等方面的典型应用,分析各种技术环境适用性及面临的局限性和挑战.最后对基于激光技术的高超声速流场速度测量进行了总结及发展趋势展望.

R13/R26矩方法的介观尺度壁面边界条件

宏观尺度NSF(Navier-Stokes-Fourier)、R13/R26矩方程边界条件在中、大克努森数Kn来流条件下计算精度大幅度降低,也极易发散。针对这一难题,提出R13/R26矩方程的介观尺度边界条件,在靠近壁面处重构速度分布函数,并输入介观尺度Boltzmann模型方程;基于离散速度法求解宏观参数,所得到的宏观参数作为R13/R26矩方程的壁面边界条件。仿真结果表明:基于介观尺度边界条件的R13/R26矩方法相较原边界条件计算精度最大提高59.84%,同时,所提出的边界条件将矩方法对Kn的适用范围拓展到1.0。

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.

Hypersonic Shock Wave/Boundary Layer Interactions by a Third-Order Optimized Symmetric WENO Scheme

A novel third-order optimized symmetric weighted essentially non-oscillatory(WENO-OS3)scheme is used to simulate the hypersonic shock wave/boundary layer interactions.Firstly,the scheme is presented with the achievement of low dissipation in smooth region and robust shock-capturing capabilities in discontinuities.The Maxwell slip boundary conditions are employed to consider the rarefied effect near the surface.Secondly,several validating tests are given to show the good resolution of the WENO-OS3 scheme and the feasibility of the Maxwell slip boundary conditions.Finally,hypersonic flows around the hollow cylinder truncated flare(HCTF)and the25°/55°sharp double cone are studied.Discussions are made on the characteristics of the hypersonic shock wave/boundary layer interactions with and without the consideration of the slip effect.The results indicate that the scheme has a good capability in predicting heat transfer with a high resolution for describing fluid structures.With the slip boundary conditions,the separation region at the corner is smaller and the prediction is more accurate than that with no-slip boundary conditions.

基于阻力和伴流不均匀度的21万吨散货船线型优化

[目的]基于船体绕流场计算分析,以阻力和伴流不均匀度为优化目标,对21万吨散货船线型进行优化设计。[方法]首先,借助计算流体动力学(CFD)工具对初始线型进行数值评估并计算船体绕流场,得到波形、压力分布、速度分布等流场特征。其次,根据CFD计算结果,构建优化策略,形成改型方案,并对改型方案进行CFD计算,评估阻力和伴流不均匀度优化效果。最后,开展优化后船型快速性模型试验,验证优化效果。[结果]CFD计算结果表明,改型相较于原型,有效功率降低了2.46%,伴流不均匀度降低了8.48%。模型试验结果表明,改型相较于原型,螺旋桨收到功率降低了3.49%。[结论]研究显示,所提出的优化方法可以获得阻力性能优良、伴流场均匀性好的船体线型,具有较强的工程适用性。

基于客流博弈均衡的旅客列车双层开行方案优化

为提高旅客列车运行效益及旅客出行满意度,以铁路运营部门净收益、列车空座位走行公里最小化为上层0-1规划模型,以旅客出行满意度最大化为下层客流均衡模型,构建了纯整数非线性高速铁路旅客列车开行方案双层规划模型。针对下层客流均衡模型,通过划分博弈环境和分析旅客乘车出行选择行为,选取旅客同质群体作为局中人,构造各局中人合理赢得函数,对每个博弈环境均运用非合作博弈理论进行客流均衡分配。基于构建的模型特征分析,采用NSGA-Ⅱ算法求解上层停站方案模型,运用QPSO算法求解下层客流博弈均衡模型,并以兰新高速铁路为例验证了模型及算法的可行性。结果表明:该算法可获得使铁路运营部门与旅客双方均满意的Nash均衡解,由此得到的开行方案铁路旅客损失率为0%。

Effect of Nozzle Inlet Shape on Annular Swirling Flow with Non-Equilibrium Condensation

Recently,by combining a swirl flow with non-equilibrium condensation phenomena of condensate gas generated in a supersonic flow,a separating and extracting techniques of condensate gas have been developed.This technique can reduce the size of the device and don't use chemicals.In the present study,by using a non-equilibrium condensation phenomenon of moist air occurred in the supersonic flow in the annular nozzle composed of an inher body and an outer nozzle with a swirl,the possibility of separation of the condensable gas and the effect of shape of nozzle inlet on the flow field were examined numerically.

Passive Control of Transonic Flow Fields with Shock Wave Using Non-equilibrium Condensation and Porous Wall

When non-equilibrium condensation occurs in a supersonic flow field.the flow is affected by the latent heat released.In the present study.in order to control the transonic flow field with shock wave,a condensing flow was produced by an expansion of moist air on a circular bump model and shock waves were occurred in the supersonic parts of the fields.Furthermore,the additional passive technique of shock /boundary layer interaction using the porous wall with a cavity underneath was adopted in this flow .The effects of these methods on the shock wave characteristics were investigated numerically and experimentally.The result obtained showed that the total pressure loss in the flow fields might be effectively reduced by the suitable combination between non-equilibrium condensation and the position of porous wall.

Study on constant-pressure specific heat of non-equilibrium phase change process in gas-liquid two-phase flow system

In this paper,the air-water vapor-water system is taken as an example,and the formula of constant-pressure specific heat during non-equilibrium phase change process in the two-phase flow system is deduced using the theory of two-phase flow and thermophysics. The constant-pressure specific heat of non-equilibrium phase change process is calculated with the corresponding numerical model,and the numerical results are compared to those of the equilibrium phase change process. It is shown that in evaporation process,the variational rate of the non-equilibrium specific heat increases with increasing initial fluid temperature and particle mass fraction. The smaller particle radius is,the faster the varia-tional rate is. Meanwhile,the constant-pressure specific heat of equilibrium process is higher than that of the non-equilibrium process all the time.

Control of Transonic Flow Fields Using Local Occurrence of Non-Equilibrium Condensation

Control of supersonic flow fields with shock wave is important for some industrial fields. There are many studies for control of the supersonic flow fields using active or passive control. When non-equilibrium condensation occurs in a supersonic flow field, the flow is affected by latent heat released. Many studies for the condensation have been conducted and the characteristics have been almost clarified. Further, it was found that non-equilibrium condensation can control the flow field. In these studies, the condensation occurs across the passage of the flow field and it causes the total pressure loss in the flow field. However, local occurrence of non-equilibrium condensation in the flow field may change the characteristics of total pressure loss compared with that by the condensation across the passage of the nozzle and there are few for researches of locally occurred non-equilibrium condensation in supersonic flow field. The purpose in the present study is to clarify the effect of local occurrence of non-equilibrium condensation on the transonic flow field in a nozzle with a circular bump. As a result, local occurrence of non-equilibrium condensation reduced the shock strength and total pressure loss in the transonic flow field by flowing the moist air from trailing edge of the circular bump to the mainstream.

Effect of Non-Equilibrium Condensation of Moist Air on Flow Field in Ludwieg Tube

The time-dependent behavior of non-equilibrium condensation of moist air through a Ludwieg tube with a diaphragm downstream is investigated by using a computational fluid dynamics work. The two-dimensional, compressible, Navier-Stokes equations, fully coupled with the condensate droplet growth equations, are numerically solved by a third-order MUSCL type TVD finite-difference scheme with a second-order fractional time step. Baldwin-Lomax turbulence model is employed to close the governing equations. The present computations represent the experimental flows well. The results obtained show that for an initial relative humidity over 40 %, the periodic excursions of the condensation shock occurs in the Ludwieg tube, and the frequency increases with the initial relative humidity. It is also found that total pressure loss due to non-equilibrium condensation in the Ludwieg tube should not be ignored even for a very low initial relative humidity. Furthermore, the variations of condensation properties are also

Numerical Investigation on Wet Steam Non-equilibrium Condensation Flow in Turbine Cascade

Based on the two-phase wet steam flow with spontaneous condensation,experimental verification and flow analysis on nozzle and 2D cascade are carried out.The 3D Reynolds-Averaged gas-liquid two-phase flow control equation solver is explored with k ε k p turbulence model.Furthermore,3D flow numerical simulation on the last stage stator of the steam turbine is carried out.The results show that a sudden pressure rise on blade suction surface is mainly caused by the droplet growth in condensation flow.The more backward the condensation position is in cascade passage,the less the sudden pressure rise from condensation is,and the larger the nucleation rate is,the maximum under-cooling and the number of droplets per unit volume are.Interaction of condensation wave and shock wave has imposed greater influence on the parameters of the blade cascade outlet.