球坐标系下多介质混合物模型的数值模拟

利用多介质混合模型在求解球坐标系下的Riemann问题时，需要考虑界面处压力平衡性弱、奇点处理、状态方程复杂等多个难点。本文将原始基于体积分数的Mie-Grüneisen多介质混合模型扩展到球坐标系下，并对多个细节进行了修正和改进，包括:在界面处对热力学参数进行修正、采用质量分数导出新输送方程、利用质量分数加权计算偏导数、采用相邻网格点的物理量定义奇点等。经过改进后的计算模型，可以得到无振荡的数值解，而且可以准确捕捉到冲击波和界面的位置。另外，使用改进后的质量分数模型比原始的体积分数模型得到的计算结果更准确。     

欧拉流体力学数值方法中的界面计算

本文所提算法适用于二维和三维多介质流体力学两步欧拉数值方法中输运计算的混合网格(包括自由面网格)界面处理。在一个混合网格中，界面被近似地看作直线(二维)或平面(三维)。整个方法分为三步：(1)第一步，用混合网格周围的八个网格的介质面积份额(二维)或二十六个网格的介质体积份额(三维)确定界面的法线方向；第二步，用混合网格的本身的介质面积份额(二维)或体积份额(三维)确定界面的方程(位置)；第三步，用此直线方程求出通过网格边界的流以及下一时刻网格的面积份额(二维)或体积份额(三维)。最后给出了用此方法所做的一些数值计算及与SLIC算法的比较。     

多组份计算中封闭性模型研究

在使用单速度多组份方法计算多介质混合网格中的物理量时,需要给出一种封闭模型来使控制方程封闭。本文分析了压力增量相等封闭性模型存在基础遭到破坏的原因,之后在保证流场守恒性的前提下构造可以保证假设基础的可解方程组对压力增量相等封闭性模型进行修正,给出了一种改进方法。使用改进的模型进行了爆轰驱动飞片问题的计算,计算结果表明,改进的模型能很好的追踪物质界面和冲击波位置,同时较好的抑制界面处压力、内能震荡。     

材料微结构演化的相场模拟

材料的各种宏观性能与其内部的微观结构密切相关,如何通过控制材料微结构的分布来提高其性能指标一直是工程界与学术界广泛关注的课题。由于场变量在界面的突变,传统的基于局部理论的突变界面模型在描述材料微结构演化方面存在一定的困难。基于非局部理论的相场法采用扩散界面的概念来描述界面,避开了理论上描述突变界面的困难,在模拟材料内部任意的组织形态和复杂的微结构演化方面具有独特的优点。本文首先介绍相场法的热力学理论基础,包括自由移动边界问题、扩散界面模型、非局部能量泛函、相场动力学方程及其常用求解方法。然后重点介绍铁电、铁磁和多铁性材料微结构演化的相场模拟,同时简要介绍相场法在软物质和锂离子电池材料微结构演化模拟中的应用,最后给出总结和展望。     

上浮气泡与自由表面相互作用的ISPH-FVM耦合方法模拟

上浮气泡与自由表面相互作用的过程涉及复杂的界面拓扑演化,该过程一直是气泡流研究领域广为关注的问题之一.为探究上浮气泡与自由表面相互作用动力学行为,将不可压缩光滑粒子流体动力学(incompressible smooth particle hydrodynamics, ISPH)方法与有限体积法(finite volume method, FVM)相结合提出了一种ISPH-FVM耦合方法.在ISPH-FVM耦合方法中,粒子和网格之间的信息交互是通过核近似插值技术实现,并将连续表面应力模型(continuous surface stress, CSS)引入当前耦合框架中以评估相界面处表面张力效应.此外, CSS模型通过FVM网格上定义的体积分数进行离散和计算,并且网格上的体积分数是通过网格支持域内ISPH粒子的核近似插值获得的.随后,利用ISPH-FVM耦合方法模拟了平衡状态下圆形气泡振荡以及单气泡上升,并将模拟结果与其他数值方法结果进行比较,验证了当前耦合方法中表面张力模型的收敛性以及界面追踪的准确性.为测试ISPH-FVM耦合方法模拟涉及复杂拓扑变化气泡流的性能,对上浮气泡与自由表面相...     

燃烧室两相流场亚网格燃烧模型的研究

在三维任意曲线坐标系下采用不同的亚网格燃烧模型对环形燃烧室火焰筒气液两相湍流瞬态反应流进行大涡模拟．计算中所采用的数学度模型有：k方程亚网格尺度模型估算亚网格湍流黏性；热通量辐射模型估算辐射换热，分别采用亚网格EBU燃烧模型（E-A model）、亚网格二阶矩输运方程模型（SOM）和亚网格二阶矩代数模型（SOM-A）估算化学反应速率．并在非交错网格系统下气相采用SIMPLE算法和混合差分格式求解，液相采用Lagrange处理，并用PSIC算法对其进行求解．通过实验结果和计算结果的比较，表明在三维任意曲线坐标系下对燃烧室火焰简两相湍流油雾燃烧流场进行大涡模拟，3种不同的亚网格燃烧模型都能真实反映两相湍流化学反应流流动及实际燃烧过程，而采用亚网格二阶矩输运方程模型稍优于其他两种亚网格燃烧模型．     

基于非结构化同位网格的SIMPLE算法

通过基于非结构化网格的有限体积法对二维稳态Navier—Stokes方程进行了数值求解。其中对流项采用延迟修正的二阶格式进行离散；扩散项的离散采用二阶中心差分格式；对于压力-速度耦合利用SIMPLE算法进行处理；计算节点的布置采用同位网格技术，界面流速通过动量插值确定。本文对方腔驱动流、倾斜腔驱动流和圆柱外部绕流问题进行了计算，讨论了非结构化同位网格有限体积法在实现SIMPLE算法时，迭代次数与欠松弛系数的关系、不同网格情况的收敛性、同结构化网格的对比以及流场尾迹结构。通过和以往结果比较可知，本文的方法是准确和可信的。     

用混合网格及各向异性多重网格法求解三维可压紊流流动

采用混合网格求解紊流Navier Stokes方程。在物面附近采用柱状网格 ,其他区域则采用完全非结构网格。方程的求解采用Jamson的有限体积法 ,紊流模型采用两层Baldwin Lomax代数紊流模型。用各向异性多重网格法来加速解的收敛。数值算例表明 ,用混合网格及各向异性多重网格求解紊流流动是非常有效的     

非结构网格二阶有限体积法中黏性通量离散格式精度分析与改进

非结构网格二阶有限体积离散方法广泛应用于计算流体力学工程实践中,研究非结构网格二阶精度有限体积离散方法的计算精度具有现实意义. 计算精度主要受到网格和计算方法的影响,本文从单元梯度重构方法、黏性通量中的界面梯度计算方法两个方面考察黏性流动模拟精度的影响因素. 首先从理论上分析了黏性通量离散中的“奇偶失联”问题,并通过基于标量扩散方程的制造解方法验证了“奇偶失联”导致的精度下降现象,进一步通过引入差分修正项消除了“奇偶失联”并提高了扩散方程计算精度;其次,在不同类型、不同质量的网格上进行基于扩散方程的制造解精度测试,考察单元梯度重构方法、界面梯度计算方法对扩散方程计算精度的影响,结果显示,单元梯度重构精度和界面梯度计算方法均对扩散方程计算精度起重要作用;最后对三个黏性流动算例(二维层流平板、二维湍流平板和二维翼型近尾迹流动)进行网格收敛性研究,初步验证了本文的结论,得到了计算精度和网格收敛性均较好的黏性通量计算格式.      

欧拉坐标系下具有锐利相界面的可压缩多介质流动数值方法研究

可压缩多介质流动问题的数值模拟在国防和工业领域内均具有重要的研究价值,诸如武器设计、爆炸安全防护等,通常具有大变形、高度非线性等特点,是一项极具挑战性的研究课题. 本文提出了一种基于 Euler 坐标系的非结构网格、具有锐利相界面的二维和三维守恒型多介质流动数值方法,可用于模拟可压缩流体和弹塑性固体在极端物理条件下的大变形动力学行为. 利用分片线性的水平集函数重构出单纯形网格内分段线性的相界面,并在混合网格内构建出具有多种介质的相界面几何结构,理论上可以处理全局任意种介质、局部 3 种介质的多介质流动问题. 利用传统的有限体积格式来计算单元边界上同种介质间的数值通量,并通过在相界面法向上求解局部一维多介质 Riemann 问题的精确解来计算不同介质间的数值通量,保证了相界面上的通量守恒. 提出了一种非结构网格上的单元聚合算法,消除了由于网格被相界面分割成较小碎片、违反 CFL 条件,进而可能带来数值不稳定的问题. 针对一维多介质 Riemann 问题、激波与气泡相互作用问题、浅埋爆炸问题、空中强爆炸冲击波和典型坑道内冲击波传播问题开展了数值模拟研究,将计算结果与相关的理论、实验结果进行比对,验证了数值方法的正确性和可靠性.      

The use of Hugoniot analysis for the propagation of vapor explosion waves

Experimental studies have shown that a mixture of molten metal and water can support the propagation of a quasi-steady vapor explosion wave. Analysis of steadily propagating vapor explosion waves has been carried out by applying the one-dimensional conservation laws of mass, momentum and energy and appropriate equations of state to a homogeneous mixture of molten tin, water and steam. The effects of void fraction, melt/water volume fraction and melt temperature on the Hugoniot curves have been considered. For low temperature melts, the Hugoniot curve lies partially inside the saturation dome and a Chapman-Jouguet (CJ) detonation point occurs only for low void fractions. For high melt temperatures, the downstream states lie entirely outside the saturation region. Increasing the volatility of the coolant or the addition of chemical reactions increases the predicted CJ detonation pressure and velocity. CJ deflagration solutions were obtained in all cases. The existence of a CJ detonation or CJ deflagration for a multiphase fuel-coolant mixture has yet to be substantiated experimentally and nonequilibrium effects may play a role in the divergence between theory and experiments.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1990.     

基于液体碳氢燃料的旋转爆轰燃烧特性研究

为了探索液体碳氢燃料参与旋转爆轰所产生的不完全燃烧现象,采用守恒元与求解元方法,开展柱坐标系下的汽油/空气两相旋转爆轰燃烧室三维数值模拟研究,针对燃料喷注压力和反应物当量比对旋转爆轰流场结构及燃烧室性能的影响进行分析。分析结果表明:保持总当量比为1.00,随着燃料喷注压力的上升,燃烧室内燃料不均匀分布增强,产生局部富燃区,燃料在燃烧室未能完全反应,导致燃烧室燃料比冲下降;保持喷注压力不变,减小当量比,在贫燃工况下依然存在局部富燃区,导致燃烧室内出现不完全燃烧现象,降低燃烧室比冲性能。由此可知,反应物喷注方案对气液两相旋转爆轰的不完全燃烧有显著影响。     

Numerical analysis of oscillations of a gaseous cavity in a compressible liquid

The radial oscillations of a gas-filled spherical cavity in an infinite compressible ideal liquid are investigated. The numerical solution of the equation of motion of a gaseous sphere is used for the comparison of acoustic and energy characteristics of underwater trotyl explosion and small-amplitude explosion sound sources (detonation of explosive gaseous mixture, expansion of a compressed inert gas).Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 176–182, March–April, 1971.     

Diffuse interface model for high speed cavitating underwater systems

High speed underwater systems involve many modelling and simulation difficulties related to shocks, expansion waves and evaporation fronts. Modern propulsion systems like underwater missiles also involve extra difficulties related to non-condensable high speed gas flows. Such flows involve many continuous and discontinuous waves or fronts and the difficulty is to model and compute correctly jump conditions across them, particularly in unsteady regime and in multi-dimensions. To this end a new theory has been built that considers the various transformation fronts as ‘diffuse interfaces’. Inside these diffuse interfaces relaxation effects are solved in order to reproduce the correct jump conditions. For example, an interface separating a compressible non-condensable gas and compressible water is solved as a multiphase mixture where stiff mechanical relaxation effects are solved in order to match the jump conditions of equal pressure and equal normal velocities. When an interface separates a metastable liquid and its vapor, the situation becomes more complex as jump conditions involve pressure, velocity, temperature and entropy jumps. However, the same type of multiphase mixture can be considered in the diffuse interface and stiff velocity, pressure, temperature and Gibbs free energy relaxation are used to reproduce the dynamics of such fronts and corresponding jump conditions. A general model, based on multiphase flow theory is thus built. It involves mixture energy and mixture momentum equations together with mass and volume fraction equations for each phase or constituent. For example, in high velocity flows around underwater missiles, three phases (or constituents) have to be considered: liquid, vapor and propulsion gas products. It results in a flow model with 8 partial differential equations. The model is strictly hyperbolic and involves waves speeds that vary under the degree of metastability. When none of the phase is metastable, the non-monotonic sound speed is recovered. When phase transition occurs, the sound speed decreases and phase transition fronts become expansion waves of the equilibrium system. The model is built on the basis of asymptotic analysis of a hyperbolic total non-equilibrium multiphase flow model, in the limit of stiff mechanical relaxation. Closure relations regarding heat and mass transfer are built under the examination of entropy production. The mixture equation of state (EOS) is based on energy conservation and mechanical equilibrium of the mixture. Pure phases EOS are used in the mixture EOS instead of cubic one in order to prevent loss of hyperbolicity in the spinodal zone of the phase diagram. The corresponding model is able to deal with metastable states without using Van der Waals representation.     

Nucleation and flashing in nozzles—2. Comparison with experiments using a five-equation model for vapor void development

A quasi-one-dimensional, five-equation, homogeneous, nonequilibrium model has been developed and utilized on a microcomputer to calculate the behavior of flowing, initially subcooled, flashing water systems. Equations for mixture and vapor mass conservation, mixture momentum conservation, liquid energy conservation and bubble transport were discretized and linearized semi-implicitly, and solved using a successive iteration Newton method. Closure was obtained through simple constitutive equations for friction and spherical bubble growth, and a new nucleation model for wall nucleation in small nozzles combined with an existing model for bulk nucleation in large geometries to obtain the thermal nonequilibrium between phases. The model described was applied to choked nozzle flow with subcooled water inlets based on specified inlet conditions of pressure and temperature, and vanishing inlet void fraction and bubble number density. Good qualitative and quantitative agreement with the experiment confirms the adequacy of the nucleation models in determining both the initial size and number density of nuclei, and indicates that mechanical nonequilibrium between phases is not an important factor in these flows. It is shown that bulk nucleation becomes important as the volume-to-surface ratio of the geometry is increased.     

Coupled thermo-hygro-mechanical damage model for concrete subjected to high temperatures

Based on the theory of mixtures, a coupled thermo-hygro-mechanical (THM) damage model for concrete subjected to high temperatures is presented in this paper. Concrete is considered as a mixture composed of solid skeletons, liquid water, water vapor, dry air, and dissolved air. The macroscopic balance equations of the model consist of the mass conservation equations of each component and the momentum and energy conservation equations of the whole medium mixture. The state equations and the constitutive model used in the model are given. Four final governing equations are given in terms of four primary variables, i.e., the displacement components of soil skeletons, the gas pressure, the capillary pressure, and the temperature. The processes involved in the coupled model include evaporation, dehydration, heat and mass transfer, etc. Through the process of deformation failure and the energy properties, the mechanics damage evolution equations are established based on the principle of conversation of energy and the Lemaitre equivalent strain assumption. Then, the influence of thermal damage on the mechanical property is considered.     

Rapid detonation initiation by sparks in a short duct: a numerical study

Rapid onset of detonation can efficiently increase the working frequency of a pulse detonation engine (PDE). In the present study, computations of detonation initiation in a duct are conducted to investigate the mechanisms of detonation initiation. The governing equations are the Euler equations and the chemical kinetic model consists of 19 elementary reactions and nine species. Different techniques of initiation have been studied for the purpose of accelerating detonation onset with a relatively weak ignition energy. It is found that detonation ignition induced by means of multiple sparks is applicable to auto-ignition for a PDE. The interaction among shock waves, flame fronts and the strip of pre-compressed fresh (unburned) mixture plays an important role in rapid onset of detonation.     

Three-dimensional computer model of nonequilibrium aerophysics of the spacecraft entering in the Martian atmosphere

A three-dimensional computer model of nonequilibrium aerophysics of the spacecraft entering in the Martian atmosphere and landing on the planet surface is presented. The model is based on the system of Navier-Stokes equations, the energy conservation equation in the form of the Fourier-Kirchhoff equation for the translational temperature, the system of equations of vibrational kinetics for six vibrational modes of N₂, O₂, CO₂ and CO molecules, and the equation of selective thermal radiation transfer in the multigroup spectral approximation. The results of two-dimensional and threedimensional calculations of the nonequilibrium flowfield and the convective and radiative heating of the EXOMARS spacecraft surface are presented. The calculations are performed on regular multiblock curvilinear grids using the NERAT-2D and NERAT-3D computer codes developed in the Institute for Problems in Mechanics of the Russian Academy of Sciences.     

2021-08期封面

铝粉反应模型是对悬浮铝粉尘气-固两相爆轰进行数值模拟研究的关键。通过考虑铝粉燃烧产物氧化铝（Al₂O₃）在高温下的分解吸热反应,改进了铝粉的扩散燃烧模型。将该模型嵌入到三维的气-固两相爆轰数值计算程序中,分别对铝粉/空气混合物以及铝粉/氧气混合物的爆轰进行了数值模拟,计算得到的稳定爆轰波速度与实验结果、文献值均吻合较好,误差小于5.5%,表明改进的铝粉反应模型适用于不同氧化气体氛围中铝粉尘爆轰的模拟计算。此外,对两相爆轰参数及爆轰流场的物理量分布进行分析,获得了铝粉反应模型对爆轰波结构的影响规律。     

Analysis of coupled thermo-hydro-mechanical behavior of unsaturated soils based on theory of mixtures I

This paper analyzes a coupled thermo-hydro-mechanical behavior of unsaturated soils based on the theory of mixtures. Unsaturated soil is considered as a mixture composed of soil skeleton, liquid water, vapor, dry air, and dissolved air. In addition to the mass and momentum conservation equations of each component and the energy conservation equation of the mixture, the system is closed using other 37 constitutive （or restriction） equations. As the change in water chemical potential is identical to the change in vapor chemical potential, a thermodynamic restriction relationship for the phase transition between pore water and pore vapor is formulated, in which the impact of the change in gas pressure on the phase transition is taken into account. Six final govern- ing equations are given in incremental form in terms of six primary variables, i.e., three displacement components of soil skeleton, water pressure, gas pressure, and temperature. The processes involved in the coupled model include thermal expansions of soil skeleton and soil particle, Soret effect, phase transition between water and vapor, air dissolution in pore water, and deformation of soil skeleton.