Self-Similar Solution of Spherical Shock Wave Propagation in a Mixture of a Gas and Small Solid Particles with Increasing Energy under the Influence of Gravitational Field and Monochromatic Radiation

Similarity solution for a spherical shock wave with or without gravitational field in a dusty gas is studied under the action of monochromatic radiation. It is supposed that dusty gas be a mixture of perfect gas and micro solid particles. Equilibrium flow condition is supposed to be maintained and energy is varying which is continuously supplied by inner expanding surface. It is found that similarity solution exists under the constant initial density. The comparison between the solutions obtained in gravitating and non-gravitating medium is done. It is found that the shock strength increases with an increase in gravitational parameter or ratio of the density of solid particles to the initial density of the gas, whereas an increase in the radiation parameter has decaying effect on the shock waves.     

Self-Similar Solution of Spherical Shock Wave Propagation in a Mixture of a Gas and Small Solid Particles with Increasing Energy under the Influence of Gravitational Field and Monochromatic Radiation

Similarity solution for a spherical shock wave with or without gravitational field in a dusty gas is studied under the action of monochromatic radiation. It is supposed that dusty gas be a mixture of perfect gas and micro solid particles. Equilibrium flow condition is supposed to be maintained and energy is varying which is continuously supplied by inner expanding surface. It is found that similarity solution exists under the constant initial density. The comparison between the solutions obtained in gravitating and non-gravitating medium is done. It is found that the shock strength increases with an increase in gravitational parameter or ratio of the density of solid particles to the initial density of the gas, whereas an increase in the radiation parameter has decaying effect on the shock waves.     

Filtration combustion of a porous structure in a multicomponent gas environment

A mathematical model for describing the quasi-isobaric filtration combustion of porous materials with the formation of condensed reaction products in a multicomponent gas is developed. Two-stage combustion waves (control modes) at the counter filtration of gas mixture are examined. The effect of inert gas component on the structure of a two-stage filtration combustion wave is studied, and the critical conditions of the changeover between filtration combustion modes caused by inert gas concentration variation are determined. It is demonstrated the characteristics of the two-stage combustion front propagating in the control mode in a multicomponent gas flow depends on the porosity of the heterogeneous system.     

Generation of zonal flow in the Earth?s dissipative ionospheric F-layer

Generation of zonal flow in the Earth?s dissipative ionospheric F-layer is considered. Dissipation arises due to Pedersen conductivity acting as an inductive (magnetic) inhibition. It is shown that in contrast to previous investigations the zonal flow growth rate does not depend on small wave vector component of zonal flow mode, needs no instability condition and the spectral energy transferring (inverse cascade) process unconditionally takes place.     

Shock wave emission from laser-induced cavitation bubbles in polymer solutions

The role of extensional viscosity on the acoustic emission from laser-induced cavitation bubbles in polymer solutions and near a rigid boundary is investigated by acoustic measurements. The polymer solutions consist of a 0.5% polyacrylamide (PAM) aqueous solution with a strong elastic component and a 0.5% carboxymethylcellulose (CMC) aqueous solution with a weak elastic component. A reduction of the maximum amplitude of the shock wave pressure and a prolongation of the oscillation period of the bubble were found in the elastic PAM solution. It might be caused by an increased resistance to extensional flow which is conferred upon the liquid by the polymer additive. In both polymer solutions, however, the shock pressure decays proportionally to r⁻¹ with increasing distance r from the emission centre.     

A note on poroacoustic traveling waves under Forchheimerʼs law

Acoustic traveling waves in a gas that saturates a rigid porous medium is investigated under the assumption that the drag experienced by the gas is modeled by Forchheimer?s law. Exact traveling wave solutions (TWS)s, as well as approximate and asymptotic expressions, are obtained; decay rates are determined; and acceleration wave results are presented. In addition, special cases are considered, critical values of the wave variable and parameters are derived, and comparisons with predictions based on Darcy?s law are performed. It is shown that, with respect to the Darcy case, most of the metrics that characterize such waveforms exhibit an increase in magnitude under Forchheimer?s law.     

Numerical study of shock wave interaction in steady flows of a viscous heat-conducting gas with a low ratio of specific heats

Specific features of shock wave interaction in a viscous heat-conducting gas with a low ratio of specific heats are numerically studied. The case of the Mach reflection of shock waves with a negative angle of the reflected wave with respect to the free-stream velocity vector is considered, and the influence of viscosity on the flow structure is analyzed. Various issues of nonuniqueness of the shock wave configuration for different Reynolds numbers are discussed. Depending on the initial conditions and Reynolds numbers, two different shock wave configurations may exist: regular configuration interacting with an expansion fan and Mach configuration. In the dual solution domain, a possibility of the transition from regular to the Mach reflection of shock waves is considered.     

Self-similar Solution of a Cylindrical Shock Wave under the Action of Monochromatic Radiation in a Rotational Axisymmetric Dusty Gas

A self-similar flow behind a cylindrical shock wave is studied under the action of monochromatic radiation in a rotational axisymmetric dusty gas. The dusty gas is taken to be a mixture of small solid particles and perfect gas,and solid particles are continuously distributed in the mixture. The similarity solutions are obtained and the effects of the variation of the radiation parameter, the ratio of the density of solid particles to the initial density of the gas, the mass concentration of solid particles in the mixture and the index for the time dependent energy law are investigated.It is observed that an increase in the radiation parameter has decaying effect on the shock waves; whereas the shock strength increases with an increase in the ratio of the density of solid particles to the initial density of the gas or the index for the time dependent energy law. Also, it is found that an increase in the radiation parameter has effect to decrease the flow variables except the density and the azimuthal component of fluid velocity. A comparison is also made between rotating and non-rotating cases.     

On numerical solution of the shallow water equations with chemical reactions on icosahedral geodesic grid

The shallow water equations coupled to the set of reaction–advection–diffusion equations are discretized on a geodesic icosahedral mesh using the finite volume technique. The method of solution of this coupled system is based on the principle of semi-discretization. The algorithm is mass conserving and stable for advection with the Courant numbers up to 2.7. The important part of the methodology is the optimization of the node positions in the icosahedral grid. It is shown that a slight adjustment of the mesh is instrumental in improving the accuracy of the numerical approximation. The convergence of the approximation of the differential operators is evaluated and compared to the data published in the literature. Numerical tests performed with the shallow water solver include two advection experiments, steady and unsteady zonal balanced flow, mountain flow, and the Rossby wave. The mountain flow and the Rossby wave cases are used to test the transport properties of the method in the case of both passive and reactive scalar fields. The investigation of essential numerical characteristics of the method is concluded by the simulation of an unstable zonal jet. The numerical simulation is performed using the set of shallow water equations without dissipation as well as with the viscosity term added to the momentum equation. Results show that the behavior of the model is consistent with both the literature published on the subject and the general empirical evidence.     

The flow velocity distribution from the doppler information on a plane in three-dimensional flow

In order to observe and estimate the flow of fluid in three-dimensional space, the pulsed Doppler method has been used widely. However, the velocity information acquired is only the velocity component in the beam direction of the wave even if an observation plane is formed by beam scanning. Accordingly, it is difficult to know the velocity distribution in the observation plane in tree-dimensional flow. In this paper, the new idea for processing the velocity distribution in the beam direction on an observation plane for transposing to flux distribution (flow function method) has been introduced. Further, the flow in an observation domain is divided into two kinds of flows, viz., the base flow which indicates the directivity of the flow in the observation domain and the vortex which is considered a two-dimensional flow. By applying the theory of a stream function to the two-dimensional flow, and by using the physical feature of a streamline to the base flow, the velocity component v which intersects perpendicularly to the beam direction is estimated. The flow velocity distribution in a scanning plane (observation plane) can be known from these two components of velocity, viz., beam direction componentu and perpendicular component to the beam directionv. The principle was explained by an example of the blood flow measurement in normal and abnormal heart chamber, by the ultrasonic Doppler method.     

FDTD Simulation on the Interaction Between Gaussian Beam and Biaxial Anisotropic Metamaterial Slabs

The interaction between Gaussian beam and indefinite anisotropic metamaterial (AMM) slabs are simulated with auxiliary differential equation method in finite-difference time-domain method (FDTD). The directions of wave vector and energy flow densities in three types of AMM slabs are investigated. The field intensity distributions and phases of TE-polarized wave for the interaction between Gaussian beam and AMM slabs are given. Numerical results show that the sign of x component of relative permeability tensor of AMM determines the refraction is regular or anomalous, whereas the sign of z component of relative permeability tensor of AMM determines the energy flow is positively refracted or negatively refracted. Positive or negative Goos-H?nchen shift associated with Total Cutoff media are also shown. This work was supported by National Key Laboratory of Electromagnetic Environment fund (51486030305HT0101) and (9140C08060507ZCZJ18).     

Unstructured Adaptive Grid Flow Simulations of Inert and Reactive Gas Mixtures

Unstructured adaptive grid flow simulation is applied to the calculation of high-speed compressible flows of inert and reactive gas mixtures. In the present case, the flowfield is simulated using the 2-D Euler equations, which are discretized in a cell-centered finite volume procedure on unstructured triangular meshes. Interface fluxes are calculated by a Liou flux vector splitting scheme which has been adapted to an unstructured grid context by the authors. Physicochemical properties are functions of the local mixture composition, temperature, and pressure, which are computed using the CHEMKIN-II subroutines. Computational results are presented for the case of premixed hydrogen–air supersonic flow over a 2-D wedge. In such a configuration, combustion may be triggered behind the oblique shock wave and transition to an oblique detonation wave is eventually obtained. It is shown that the solution adaptive procedure implemented is able to correctly define the important wave fronts. A parametric analysis of the influence of the adaptation parameters on the computed solution is performed.     

Natural sloshing frequencies and modes in a rectangular tank with a slat-type screen

Being installed in tanks, screens play the role of slosh-suppressing devices which may strongly change resonant sloshing frequencies and yield an extra nonlinear damping due to cross-flow resulting in either flow separation or jet flow. Employing the linear sloshing theory and domain decomposition method, we construct an accurate analytical approximation of the natural sloshing modes in a rectangular tank with a slat-type screen at the tank middle. Two-dimensional irrotational flow of an ideal incompressible liquid is assumed. Because the considered flow model does not account for flow separation and jet flow at the screen, the velocity field is locally singular at the sharp edges. The constructed solution captures this singularity. Analyzing this solution establishes a complex dependence of the natural sloshing frequencies on the solidity ratio, the number of submerged screen gaps, the liquid depth, and the position of perforated openings relative to the mean free surface. Results are compared with experimental data. Natural surface wave profiles are discussed in the context of a jump of the velocity potential at the screen and the local inflow component to the screen.     

Shock waves and formation of carbon dioxide hydrate at an increased pressure in the gas-liquid medium

The processes of breaking, solution, and formation of hydrates behind a shock wave of moderate amplitude were studied experimentally in water with carbon dioxide bubbles under different initial static pressures. It is shown that an increase in the static pressure in a gas-liquid medium leads to reduction of critical relative amplitude of the shock wave, corresponding to starting development of Kelvin — Helmholtz instability and bubble splitting into small gas inclusions behind the shock wave front. It is shown that the rates of carbon dioxide solution and hydrate formation behind the shock wave front are close by the value; their dependences on medium and wave parameters are determined. Calculations by the model of gas hydration behind the shock wave are presented. The work was financially supported by the Russian Foundation for Basic Research (grants Nos. 06-01-00142 and 06-08-00657).     

微通道脉管非线性交变振荡微观机理的分子动力学研究

采用分子动力学方法,对He在微通道脉管内的非线性交变振荡的热力学响应进行仿真,研究气体振荡诱导管内轴向压力梯度、温度场的形成,并阐述微通道长径比对温差与相位的影响.结果表明：微通道内伴随压差驱动力在管内形成类似正弦函数压力波、速度波、质量流量波与半正弦的温度波.振荡周期随脉管管径的增大而缩短,随脉管长度的增加而增长,受直径影响很小;微通道两端的时均温差随长度的增加而增大,受直径的影响很小.预测针对不同的脉管直径存在一个最佳长径比与振荡周期,其数值随直径的增大而增大,为优化脉冲管的性能提供理论依据.     

Global Shock Waves¶for the Supersonic Flow Past a Perturbed Cone

We prove the global existence of a shock wave for the stationary supersonic gas flow past an infinite curved and symmetric cone. The flow is governed by the potential equation, as well as the boundary conditions on the shock and the surface of the body. It is shown that the solution to this problem exists globally in the whole space with a pointed shock attached at the tip of the cone and tends to a self-similar solution under some suitable conditions. Our analysis is based on a global uniform weighted energy estimate for the linearized problem. Combining this with the local existence result of Chen–Li [1] we establish the global existence and decay rate of the solution to the nonlinear problem. Received: 1 August 2001 / Accepted: 14 January 2002     

Hydrodynamic instability of premixed flame propagating in narrow planar channel in the presence of gas flow

The paper analyses the hydrodynamic instability of a flame propagating in the space between two parallel plates in the presence of gas flow. The linear analysis was performed in the framework of a two-dimensional model that describes the averaged gas flow in the space between the plates and the perturbations development of two-dimensional combustion wave. The model includes the parametric dependences of the flame front propagation velocity on its local curvature and on the combustible gas velocity averaged along the height of the channel. It is assumed that the viscous gas flow changes the surface area of the flame front and thereby affects the propagation velocity of the two-dimensional combustion wave. In the absence of the influence of the channel walls on the gas flow, the model transforms into the Darrieus–Landau model of flame hydrodynamic instability. The dependences of the instability growth rate on the wave vector of disturbances, the velocity of the unperturbed gas flow, the viscous friction coefficients and other parameters of the problem are obtained. It is shown that the viscous gas flow in the channel can lead, in some cases, to a significant increase in instability compared with a flame propagating in free space. In particular, the instability increment depends on the direction of the gas flow with respect direction of the flame propagation. In the case when the gas flow moves in the opposite direction to the direction of the flame propagation, the pulsating instability can appear.     

Transformation of atmospheric components near a spark discharge at the anode polarization of a metallic electrode hanging over a solution

The variation of the pressure of a gas phase activated by spark discharges between an aqueous electrolyte solution (liquid cathode) and a metallic electrode (anode) hanging over the solution is studied. A mathematical model of the proceeding reaction kinetics is constructed, and the variation of the partial pressures of all initial and produced components in the gas phase is calculated. Both the Faraday and non-Faraday mechanisms of gas component production from water are confirmed. It is found that a large overhanging drop responsible for additional supply of simultaneously produced H₂ and O₂ molecules forms rapidly at the end face of the anodically polarized electrode.     

稀薄气体二维外部柱体绕流特性研究

本文采用直接模拟蒙特卡罗方法对稀薄气体二维外部柱体绕流问题进行了数值模拟。结果表明:外部绕流问题,在特定情况下会产生激波,激波的产生,不仅与气体的稀薄程度有关,还与来流马赫数有关。而气流与壁面之间的换热,随来流马赫数增加而增加,随气体稀薄程度增加而减小。