Development and testing of a numerical simulation method for thermally nonequilibrium dissociating flows in ANSYS Fluent

Various issues of numerical simulation of supersonic gas flows with allowance for thermochemical nonequilibrium on the basis of fluid dynamic equations in the two-temperature approximation are discussed. The computational tool for modeling flows with thermochemical nonequilibrium is the commercial software package ANSYS Fluent with an additional userdefined open-code module. A comparative analysis of results obtained by various models of vibration-dissociation coupling in binary gas mixtures of nitrogen and oxygen is performed. Results of numerical simulations are compared with available experimental data.     

Conservation laws for a vortex in a compressible nonequilibrium medium

The problem of conservation of magnitudes is considered for a vortex in a relaxing compressible medium. Heat release due to the relaxation of a nonequilibrium medium leads to the propagation of compression waves, which remove material. Traditional integrals of motion are inapplicable in this case. We pro-pose the concept of integral quantity, which is conserved with an arbitrary degree of accuracy despite the fact that waves cross the boundary of the integration domain. Based on this concept, a broad class of conservation laws is derived for axisymmetric disturbances of columnar vortices, including conservation of the circulation and total angular momentum of the vortex. For nonaxisymmetric disturbances, it is shown that the total angular momentum and properly defined energy integral are conserved. Numerical verification of the derived conservation laws is performed and the perspectives for using these conservation laws in numerical simulations are discussed.     

Stability and three-wave interaction of disturbances in supersonic boundary layer with mass exchange on the wall

The interaction of disturbances in a boundary layer of the compressible gas is considered in the linear and nonlinear approximation (the weakly nonlinear theory of stability) in the presence of mass exchange (gas blowing or suction) on the surface. The regimes of moderate (the Mach number M = 2) and high (M = 5.35) supersonic velocities of the flow are considered. The suction from the surface is shown to lead to a considerable variation of the linear evolution of disturbances: the vortex disturbances of the first mode and the acoustic disturbances of the second mode are stabilized, the rate of variation is determined by suction intensity. The nonlinear interactions in three-wave systems between the vortex waves in asymmetric triplets at M = 2 and between the waves of different nature (acoustic and vortex waves) ?? in the symmetric ones at M = 5.35 are considered. The planar acoustic wave is the excitation wave in the latter, which excites the three-dimensional subharmonic components of the vortex nature. It is shown that one can delay considerably the transition region with the aid of suction, thereby one can reduce the skin-friction drag. In the gas blowing regime, strong deformations of the mean fields of boundary layers occur, which lead to the destabilization of the vortex and acoustic waves in the linear region and activate the nonlinear processes in transition region. One can expect that this will lead to the acceleration of tripping in supersonic flow.     

Sound amplification in inhomogeneous flows of nonequilibrium gas

The conditions of the acoustic instability of flows of thermodynamically nonequilibrium gas are determined. It is shown that the growth increments of the velocity, temperature, pressure, and density disturbances are different. When the Mach numbers are small, only the velocity and temperature disturbances grow along the flow.     

考虑转动能的一维/二维Boltzmann-Rykov模型方程数值算法

研究考虑转动能的Boltzmann-Rykov模型方程,基于转动自由度对气体分子速度分布函数矩积分,引入约化速度分布函数,应用离散速度坐标法与数值积分技术,将气体运动论模型方程化为在离散速度坐标点处关于三个约化速度分布函数的联立方程组.应用拓展计算流体力学有限差分方法,数值计算考虑转动自由度的双原子气体一维、二维Boltzmann模型方程,得到高、低Knudsen数一维激波管内流动和二维竖直平板绕流问题的流场,分析验证考虑转动能的Boltzmann-Rykov模型方程全流域统一算法求解一维/二维气体流动问题的可靠性.结果表明,气体稀薄程度与分子内自由度对流场具有较大影响,且Knudsen数较高的稀薄气体流动呈现严重的非平衡流动特点.     

Multiple temperature model for the information preservation method and its application to nonequilibrium gas flows

The information preservation (IP) method has been successfully applied to various nonequilibrium gas flows. Comparing with the direct simulation Monte Carlo (DSMC) method, the IP method dramatically reduces the statistical scatter by preserving collective information of simulation molecules. In this paper, a multiple temperature model is proposed to extend the IP method to strongly translational nonequilibrium gas flows. The governing equations for the IP quantities have been derived from the Boltzmann equation based on an assumption that each simulation molecule represents a Gaussian distribution function with a second-order temperature tensor. According to the governing equations, the implementation of IP method is divided into three steps: molecular movement, molecular collision, and update step. With a reasonable multiple temperature collision model and the flux splitting method in the update step, the transport of IP quantities can be accurately modeled. We apply the IP method with the multiple temperature model to shear-driven Couette flow, external force-driven Poiseuille flow and thermal creep flow, respectively. In the former two cases, the separation of different temperature components is clearly observed in the transition regime, and the velocity, temperature and pressure distributions are also well captured. The thermal creep flow, resulting from the presence of temperature gradients along boundary walls, is properly simulated. All of the IP results compare well with the corresponding DSMC results, whereas the IP method uses much smaller sampling sizes than the DSMC method. This paper shows that the IP method with the multiple temperature model is an accurate and efficient tool to simulate strongly translational nonequilibrium gas flows.     

Evolution of a single vortex in a uniform nonequilibrium medium

The problem of the evolution of a single vortex in a nonequilibrium medium with a temperature-or density-dependent energy release was solved. In a medium that is stable against small perturbations, the vortex passes to a new stationary state, and no vortex breakdown occurs. For a temperature-dependent energy release, analytical solutions that define changes in the characteristics of the vortex were obtained for high and low relaxation times. The solutions were compared with the results of numerical simulation by the Godunov method.     

Evolution of disturbances in the shock layer on a flat plate in the flow of a mixture of vibrationally excited gases

The results of the numerical and experimental investigations of the evolution of the disturbances in a hypersonic shock layer on a flat plate streamlined by a flow of the mixture of vibrationally excited gases are presented. The experimental study was conducted in the hot-shot high-enthalpy wind tunnel IT-302 of the ITAM SB RAS. The numerical simulation was carried out with the aid of the ANSYS Fluent package using the solution of the unsteady two-dimensional Navier?Stokes equations with the incorporation of the user-created modules and enabling the consideration of the vibrational non-equilibrium of the carbon dioxide molecules within the framework of the model of the two-temperature aerodynamics. It was obtained that an increase in the carbon dioxide concentration in the mixture with air leads to a reduction of the intensity of pressure disturbances on the surface. The efficiency (up to 20 %) of the method of sound absorbing coatings in the vibrationally excited flows of the mixture of the carbon dioxide and air has been shown.     

Nonequilibrium effects of reactive flow based on gas kinetic theory

How to accurately probe chemically reactive flows with essential thermodynamic nonequilibrium effects is an open issue. Via the Chapman–Enskog analysis, the local nonequilibrium particle velocity distribution function is derived from the gas kinetic theory. It is demonstrated theoretically and numerically that the distribution function depends on the physical quantities and derivatives, and is independent of the chemical reactions directly as the chemical time scale is longer than the molecular relaxation time. Based on the simulation results of the discrete Boltzmann model, the departure between equilibrium and nonequilibrium distribution functions is obtained and analyzed around the detonation wave. In addition, it has been verified for the first time that the kinetic moments calculated by summations of the discrete distribution functions are close to those calculated by integrals of their original forms.     

Two-temperature hydrodynamics and multiple sound modes in disparate-mass gas mixtures

Gas mixtures of heavy plus light molecules can apparently support several different sorts of sound waves (the most recent such prediction is that of Campa and Cohen). The origin of the first such predictions is reviewed, along with the development of the two-temperature hydrodynamic equations which govern these mixtures at moderate wavenumbers and frequencies. Light scattering in the two-temperature regime is also discussed. Experiments in both sound propagation and light scattering are shown to confirm the existence of a two-temperature regime, and two simultaneous sound modes, in these disparate-mass gas mixtures.     

An analysis of ionization kinetics models in a hypersonic flow past a cylinder

A calculation-theoretical analysis of the possibility of using several chemical and ionization kinetics models accepted in aerophysics and models of the nonequilibrium dissociation of diatomic molecules in the interpretation of the results of experimental studies of transverse passage of molecular nitrogen past cylindrical models at a rate of 11.3 km/s was performed. The two-dimensional problem of transverse flow of a viscous heat-conducting chemically and physically nonequilibrium gas past a cylinder was solved. A comparison of experimental gas density and electron concentration distributions with calculation results was performed to discuss the sensitivity of calculations to various chemical and ionization kinetics models and nonequilibrium dissociation.     

可压涡卷空间演化的迎风紧致差分数值模拟

从数值算法的耗散和色散特征的时空全离散Fourier分析出发,通过直接求解二维非定常可压Navier Stokes方程,将发展的5阶迎风紧致差分格式用于无约束可压平面受迫剪切层中基频涡卷空间演化过程的数值模拟.采用被动守恒标量等方法显示了基频涡卷的饱和、一次对并、二次对并等现象,据此探讨了入口来流亚谐扰动引起的初值效应问题,表明可压大尺度涡结构空间演化形态与受迫扰动方式之间存在关联.     

Laser-induced gas vortices

Recently, several femtosecond-laser techniques have demonstrated molecular excitation to high rotational states with a preferred sense of rotation. We consider collisional relaxation in a dense gas of such unidirectionally rotating molecules, and suggest that due to angular momentum conservation, collisions lead to the generation of macroscopic vortex gas flows. This argument is supported using the Direct Simulation Monte?Carlo method, followed by a computational gas-dynamic analysis.     

Nonequilibrium states of the soft mode anharmonic phonons

A theory of the nonequilibrium state of the soft mode optical phonons in ferroelectrics exposed to the pumping electromagnetic field has been developed. The self-consistent field equation, which determines the phase transition temperature shift and the dielectric permeability change due to a deviation of the system from the equilibrium state is derived. A two-temperature model describing the energy transport in the presence of pumping is suggested. Analytic solutions of this model both for evolving in time and for stationary states are obtained. Spatial oscillations of the soft mode temperature are predicted for the observation time approximately equal to the energy relaxation time. It is shown that nonlinear effects can be a reason of forming of the bottleneck in the energy relaxation process. An exactly solvable model of a breather: the breather with the one-site non-linearity has been constructed and investigated.     

Physics of the amplification of vortex disturbances in shear flows

The physics of the linear mechanism of the amplification of vortex disturbances in shear flows, which is due to the nonorthogonality of the eigenfunctions of the problem in the linear dynamics, is described. To obtain the clearest and simplest picture, a parallel flow with a linear velocity shear is studied, and the vortex disturbances are represented in the form of plane waves — spatial Fourier harmonics. On this level our physical approach is consonant with the nonmodal mathematical analysis of linear processes in shear flows, which has been actively cultivated in the last few years. The physics presented explains the non-monotonic growth of vortex disturbances in time at the linear stage of evolution. Moreover, being universal, the “language” employed in this work can also be used to describe the amplification of potential (acoustic) disturbances. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 7, 517–522 (10 April 1996)     

Critical dynamics of gauge systems: spontaneous vortex formation in 2D superconductors

We examine the formation of vortices during the nonequilibrium relaxation of a high-temperature initial state of an Abelian-Higgs system. We equilibrate the scalar and gauge fields using gauge-invariant Langevin equations and relax the system by instantaneously removing thermal fluctuations. For couplings near critical, kappa(c) = square root[lambda]/e = 1, we observe the formation of large clusters of like-sign magnetic vortices. Their appearance has implications for the dynamics of the phase transition, for the distribution of topological defects, and for late-time phase ordering kinetics. We offer explanations for both the observed vortex densities and vortex configurations.     

采用态-态模型的热化学非平衡喷管流数值研究

数值求解耦合态-态模型的N₂/N准一维喷管非平衡流方程,获得驻室温度3 000 K~10 000 K,压力1 atm~10 atm条件下的流场参数分布和详细的振动能级分布,分析喷管流动中的宏观和微观特性,并对这类复合占优的流动考察双温度模型中假设的合理性.     

A new class of gas-kinetic relaxation schemes for the compressible Euler equations

Starting from the gas-kinetic model, a new class of relaxation schemes for the Euler equations is presented. In contrast to the Riemann solver, these schemes provide a multidimensional dynamical gas evolution model, which combines both Lax-Wendroff and kinetic flux vector splitting schemes, and their coupling is based on the fact that a nonequilibrium state will evolve into an equilibrium state along with the increase of entropy. The numerical fluxes are constructed without getting into the details of the particle collisions. The results for many well-defined test cases are presented to indicate the robustness and accuracy of the current scheme.     

Implosion of plasma liners in the presence of an axial magnetic field

Based on a radiative magnetohydrodynamic model, a numerical investigation is made of the implosion of single- and two-stage plasma liners with an initial axial magnetic field. The radiative magnetohydrodynamic model includes the equations of two-temperature hydrodynamics taking into account the electron and ion thermal conductivity, the electromagnetic field equations, and the equations of radiative transfer in a nonequilibrium medium. It is shown that in the case of a single-stage liner the implosion takes place in a subsonic regime, while the dynamics of a two-stage liner is determined by that of the propagation of shock waves of various intensities through the inner stage. Institute of High-Current Electronics, Siberian Branch of the Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 6–15. December, 1995.     

Vortex source flowing into vacuum under thermal crisis

Thermal crisis of a stationary vortex source flowing to vacuum is considered for air on the basis of the model of a diatomic gas with variable heat capacities due to the excitation of vibrational degrees of freedom of molecules. The versions with different heat supply laws are compared. The effect of the size of the heat-release region (from close-to-zero value to that exceeding the minimal radius of the vortex source by tens of times) as well as the effect of the circulation of the flow on the critical parameters determining thermal crisis are considered. A qualitative difference from the thermal crisis in a perfect (ideal) gas with constant heat capacities is demonstrated.