A Study of Linear Waves Based on Extended Thermodynamics for Rarefied Polyatomic Gases

We study the dispersion relation for sound in rarefied polyatomic gases basing on the recently developed theory of extended thermodynamics (ET) for both dense and rarefied polyatomic gases. For hydrogen and deuterium gases in a wide temperature range where the rotational and vibrational modes in a molecule play a role, we compare the dispersion relations with those obtained in experiments and by the classical Navier–Stokes Fourier theory. From the comparison with experiments, we estimate the bulk viscosity and evaluate its temperature dependence. We study the characteristics of attenuation in a gas which has a larger relaxation time related to the dynamic pressure than the other relaxation times related to the shear stress and the heat flux by adopting the ET theory with 6 fields.     

Recent Developments in Extended Thermodynamics of Dense and Rarefied Polyatomic Gases

We summarize the recent results and current open problems in extended thermodynamics (ET) of both dense and rarefied polyatomic gases. (i) We review, in particular, extended thermodynamics with 14 independent fields (ET14), that is, the mass density, the velocity, the temperature, the shear stress, the dynamic pressure, and the heat flux. (ii) We explain that, in the case of rarefied polyatomic gases, molecular extended thermodynamics with 14 independent fields (MET14) basing on the kinetic moment theory with the maximum entropy principle can be developed. ET14 and MET14 are fully consistent with each other. (iii) We show that the ET13 theory of rarefied monatomic gases is derived from the ET14 theory as a singular limit. (iv) We discuss briefly some typical applications of the ET14 theory. (v) We study the simple case of ET theory with 6 independent fields (ET6). (vi) The METn theories (n>14) are presented briefly. We analyze, in particular, the dependence of the characteristic velocities for increasing number of moments.     

Transport Processes in a Polyatomic Gas

Linear energy and momentum fluxes are obtained in the gas dynamics approximation for nonequilibrium stationary states of a polyatomic gas in an external magnetic field. The transport coefficients are found for a gas of linear diamagnetic molecules.     

Flow Structure behind a Shock Wave in a Channel with Periodically Arranged Obstacles

We study the propagation of a pressure wave in a rectangular channel with periodically arranged obstacles and show that a flow corresponding to a discontinuity structure may exist in such a channel. The discontinuity structure is a complex consisting of a leading shock wave and a zone in which pressure relaxation occurs. The pressure at the end of the relaxation zone can be much higher than the pressure immediately behind the gas-dynamic shock. We derive an approximate formula that relates the gas parameters behind the discontinuity structure to the average velocity of the structure. The calculations of the pressure, velocity, and density of the gas behind the structure that are based on the average velocity of the structure agree well with the results of gas-dynamic calculations. The approximate dependences obtained allow us to estimate the minimum pressure at which there exists a flow with a discontinuity structure. This estimate is confirmed by gas-dynamic calculations.     

Expansion of a Rarefied Gas Cloud in a Vacuum: Asymptotic Treatment

The unsteady expansion of a rarefied gas of finite mass in an unlimited space is studied. The long-time asymptotic behavior of the solution is examined at Knudsen numbers tending to zero. An asymptotic analysis shows that, in the limit of small Knudsen numbers, the behavior of the macroscopic parameters of the expanding gas cloud at long times (i.e., for small density values) has nothing to do with the free-molecular or continuum flow regimes. This conclusion is unexpected and not obvious, but follows from a uniformly suitable solution constructed by applying the method of outer and inner asymptotic expansions. In particular, the unusual temperature behavior is of interest as applied to remote sensing of rocket exhaust plumes.     

Some Linear Effects of Rotation on the Heat Transfer Problem in Rarefied Gases and Rarefied Gas Mixtures

The linearized field equations of extended thermodynamics for rarefied monatomic gases and gas mixtures are used to describe two different stationary processes. The aim of the paper is to study the linear effects predicted for such phenomena. Comparison between classical and extended theory and between the solutions for a single gas and a gas mixture will be also presented.     

星系螺旋结构的气体激波理论

本文用星际气体自引力星系激波来解释星系的螺旋结构、恒星的扰动引力场并非必要条件.我们首先证明,即使扰动引力场为零,也可以存在局部的星系激波解.这种解要求|ω_η0|>α,而且只要气体的密度反差比较大,就只能用激波解来解释螺旋结构.用叠代的方法求出了星际气体的自引力激波宏图.对一种特定的扰动引力场模拟气体自引力,可以在速度平面上定性分析激波解的特性.初始原星系盘中的物质分布不均匀性,通过缠卷过程、不稳定性增长和波动叠加.可以发展成星系激波宏图.这样,对星系激波的起源,演化和维持给出一个完整的图象.利用这个图象,可以解释星系螺旋结构的大量观测结果和分类特性.     

管道内激波的不稳定性

本文将无限大激波阵面的激波不稳定性理论[1]推广到矩形截面管道内的激波不稳定性问题.首先,给出这个问题的数学提法,包括扰动方程与三类边界条件.其次,给出扰动方程的普遍解.上游和下游的普遍解分别含有5个待定常数.再次,在一类边界条件和一个假定下,证明了激波前扰动为0,激波后两个声扰动之一为0.边界条件是,X→±∞处扰动物理量为0.假定只讨论激波不稳定性问题,从而可先设ω=iγ,γ是不稳定性增长率,为正实数.另一类边界条件是管壁上法向速度扰动为0,它使波数只能取一组离散值.最后,用扰动激波上的5个守恒方程这一边界条件来决定激波后4个待定常数和扰动激波振幅这个未知量时,导出了色散关系.结果表明,正实数γ确是存在.不稳定激波有两种模式,一种模式为γ=-W·k(W<0)它代表激波的绝对不稳定性,是新得到的模式.另一种模式与过去工作中给出的[2,3]大体相同.本文则进一步给出了这种模式的激波不稳定性增长率,并指出j2((?V/?P)_H=1+2M为最不稳定点(即无量纲化的不稳定性增长率Г=∞).如果不假定ω是纯虚数,而是复数,其虚部为正实数Im(ω)≥0.本文也严格证明了其不稳定性判据仍有两种模式,ω仍为纯虚数.     

Shock Wave Structure of Multi-Temperature Euler Equations from Kinetic Theory for a Binary Mixture

A multi-temperature hydrodynamic limit of kinetic equations is employed for the analysis of the steady shock problem in a binary mixture. Numerical results for varying parameters indicate possible occurrence of either smooth profiles or of weak solutions with one or two discontinuities.     

稀相气固悬浮体越过沿平面匀速运动激波后的流动结构*

本文给出气固悬浮体中激波感生边界层的渐近数值分析,其中计及了作用于固体粒子的Saf-fman升力.研究结果表明粒子横越边界层的迁移导致了粒子轨道的交叉,因此对目前通用的含灰气体模型应做相应的修正.本文利用匹配渐近展开方法得到了匀速运动激波后方的两相侧壁边界层方程,详细描述了在Lagrange坐标下计算颗粒相流动参数的方法,并给出了粒子浓度很低情况下的数值结果.     

On Shock Structure in a Solid

The simplest form of longitudinal constitutive equation fora compressible solid which exhibits second order convectiveand dissipative effects is = Am+Bm²+m/t. A constant profile waveform, analogous to that discovered independentlyboth by Taylor and by Rayleigh in 1910 for a compressible fluid,can propagate in such a solid. It is shown that any monotonicwaveform ultimately adopts this profile; the width and timeof formation of the profile are found. The constant profilewaveform appropriate to transverse vibration in an incompressiblesolid is investigated. Both waveforms propagate at the velocitiesgiven by the Rankine-Hugoniot equations in the absence of dissipation.     

反射型激波风洞中激波与边界层的相互作用

本文研究了反射型激波风洞中由于非完全反射对激波与壁面边界层相互作用的影响,给出了在反射激波坐标系中计算边界层速度分布、温度分布和马赫数分布的计算方法.算例表明,在计及氮气的平衡真实气体效应的情形下,随着入射激波马赫数M_s的增大,边界层的最小马赫数从壁面处移到边界层内;随着喷管喉道面积的增大,边界层的最小马赫数、反射激波的分叉角α和分叉区后的射流速度均随之减小.计算结果与实验值相比是一致的.     

Mathematical and Physical Properties of an Extended Thermodynamics Multi-temperature Model for the Description of Gas Mixtures

In this paper, we analyze some mathematical and physical properties of a 13-moment extended thermodynamics model for gas mixtures with the multi-temperature assumption and Maxwellian productions. Starting from the 1960s, this model was derived independently by many authors and it was applied to different physical problems. Here, we verify the validity of the Shizuta-Kawashima condition and others mathematical properties. Moreover, we describe the stationary heat transfer and the acceleration waves predicted by these equations.     

一类一维的辐射流体力学方程组激波的存在性

该文主要讨论一维空间中一类辐射流体力学方程组的激波. 由Rankine-Hugoniot条件及熵条件得此问题可表述为关于辐射流体力学方程组带自由边界的初边值问题. 首先通过变量代换, 将其自由边界转换为固定边界, 然后研究关于此非线性方程组的一个初边值问题解的存在唯一性. 为此先构造了此问题的一个近似解, 然后分别通过Picard迭代与Newton迭代对此非线性问题构造近似解序列. 通过一系列估计与紧性理论得到此近似解序列的收敛性, 其极限即为原辐射热力学方程组的一个激波.     

Viscous Shock Wave to an Inflow Problem for Compressible Viscous Gas with Large Density Oscillations

Acta Mathematicae Applicatae Sinica, English Series - This paper is concerned with the inflow problem for one-dimensional compressible Navier-Stokes equations. For such a problem, Huang, Matsumura,...     

Generalization of the Crocco Invariant for 3D Gas Flows Behind Detached Bow Shock Wave

Russian Mathematics - We study a steady 3D flow of the ideal gas. In the flow between the bow shock wave and the nose part of the body streamlined by the uniform supersonic flow, we consider...