Numerical Calculation of the Hypersonic Rarefied Transverse Flow Past a Cold Flat Plate

The hypersonic rarefied transverse flow past a flat plate is considered over a wide Knudsen number range. The problem is formulated for a model kinetic equation and solved using an implicit finite-difference second-order method. The results presented demonstrate the Knudsen and Mach number effect on the aerodynamic characteristics of the plate and the flow pattern.     

Analytical solution of the problem of sphere rotation in a rarefied molecular gas

A problem of sphere rotation in a rarefied molecular gas is solved in an isothermal approximation. The particle velocity profile in the rarefied molecular gas entrained by the rotating sphere is obtained with a second-order correction in terms of the Knudsen number. For a rarefied molecular gas, in contrast to a monatomic gas, the particle velocity is demonstrated to depend substantially on the Prandtl number if rotational degrees of freedom of molecules are taken into account.     

Invariant submodels of the model of thermal motion of gas in a rarefied space

A model describing the thermal motion of a gas in a rarefied space is investigated. This model can be used in the study of the motion of gas in outer space, and the processes occurring inside the tornado, and the state of the medium behind the shock front of the wave after a very intense explosion. For a given initial pressure distribution, a special choice of mass Lagrange variables leads to a reduced system of differential equations describing this motion, in which the number of independent variables is one less than the original system. This means that there is a stratification of a highly rarefied gas with respect to pressure. Namely, in a strongly rarefied space for each given initial pressure distribution, at each instant of time all gas particles are localized on a two-dimensional surface moving in this space. At each point of this surface, the acceleration vector is collinear with its normal vector. The resulting system admits an infinite Lie transformation group. All significantly various submodels that are invariant with respect to the subgroups of its eight-parameter subgroup generated by the transfer, extension, rotation, and hyperbolic rotation operators (the Lorentz operator) are found. For invariant submodels of rank 1, the basic mechanical characteristics of the gas flow described by them are obtained. Conditions for the existence of these submodels are given. For invariant submodels of rank 2, integral equations describing these submodels are obtained. For some submodels, the problem of describing the gas flow from the initial location of its particles and the distribution of their velocities has been investigated.     

Magnetogasdynamic flow past an infinite porous flat plate in slip flow regime

This paper presents an exact solution for the flow of a rarefied ionized gas over an infinite porous plate in the presence of a transverse magnetic field, by using the well known continuum approach. An attempt is made to bring out the salient features of the interaction between the applied magnetic field and the flow of a rarefied conducting gas. The analysis reveals that the skin friction, and the heat transfer into the plate are reduced due to gas rarefaction.     

Asymptotic solutions of the two-dimensional equations for a thin viscous shock layer in a rarefied gas

Two-dimensional hypersonic rarefied gas flow around blunt bodies is investigated for the continuum to free-molecular transition regime. In [1], as a result of an asymptotic analysis, three rarefied gas flow regimes, depending on the relationship between the problem parameters, were detected and one of these regimes was investigated. In the present study, asymptotic solutions of the thin viscous shock layer equations at small Reynolds numbers are obtained for the other two flow regimes. Analytical expressions for the heat transfer, friction and pressure coefficients are obtained as functions of the incident flow parameters and the body geometry and temperature. As the Reynolds number tends to zero, the values of these coefficients approach their values in free-molecular flow. The scaling parameters of hypersonic rarefied gas flow around bodies are determined for different regimes. The asymptotic solutions are compared with the results of direct Monte Carlo simulation.     

Sound propagation through a rarefied gas. Influence of the gas–surface interaction

Acoustic waves propagating through a rarefied gas between two plates induced by both oscillation and unsteady heating of one of them are considered on the basis of a model of the linearized Boltzmann equation. The gas flow is considered as fully established so that the dependence of all quantities on time is harmonical. The problem is solved for several values of two main parameters determining its solution, namely, the gas rarefaction defined as the ratio of the distance between the plates to the equivalent free path of gaseous molecules, and the oscillation parameter given as the ratio of the intermolecular collision frequency to the wave frequency. The reciprocal relation for such flows is obtained and verified numerically. An influence of the gas–surface accommodation coefficients on the wave characteristics is analyzed by employing the Cercignani–Lampis scattering kernel to the boundary conditions.     

Asymptotic solution of the two-dimensional equations for a thin viscous rarefied shock layer on a cold surface

Hypersonic rarefied flow past blunt bodies is studied in the continuum-free-molecular transition regime. On the basis of an asymptotic analysis three rarefied gas flow patterns are established depending on the relation between the relevant parameters of the problem. In the first regime corresponding to a cold surface asymptotic solutions of the equations of a thin viscous shock layer are derived at low Reynolds numbers in the axisymmetric and plane cases. Simple analytical expressions for the pressure and the heat transfer and friction coefficients are obtained as functions of the freestream parameters and the body geometry. With decrease in the Reynolds number the coefficients approach the values corresponding to free-molecular flow. In this regime a similarity parameter for the hypersonic rarefied flow past bodies is determined. The asymptotic solutions are compared with numerical solutions and the results of direct statistical simulation by the Monte Carlo method.     

Exact solutions of a dipolar fluid flow

Exact solutions for three canonical flow problems of a dipolar fluid are obtained: (i) The flow of a dipolar fluid due to a suddenly accelerated plate, (ii) The flow generated by periodic oscillation of a plate, (iii) The flow due to plate oscillation in the presence of a transverse magnetic field. The solutions of some interesting flows caused by an arbitrary velocity of the plate and of certain special oscillations are also obtained.     

Solution of the problem of a flow of rarefied gas of constant density around a semiinfinite plate by the integral diffusion method

Several papers [1–4] have proposed approximate diffusion models which can be used to examine the transport process in a rarefied gas where the mean free path is large and transport is not determined by the local gradient of the particular quantity.In this paper the integral diffusion model [2] is used to solve the problem of determination of the friction stress and velocity of a flow of an incompressible gas around a plane semi-infinite plate in the whole range of Knudsen numbers. The obtained solution is compared with published solutions and experimental data [9].     

Rotating flow of a second-order fluid on a porous plate

A study is made of the unsteady flow engendered in a second-order incompressible, rotating fluid by an infinite porous plate exhibiting non-torsional oscillation of a given frequency. The porous character of the plate and the non-Newtonian effect of the fluid increase the order of the partial differential equation (it increases up to third order). The solution of the initial value problem is obtained by the method of Laplace transform. The effect of material parameters on the flow is given explicitly and several limiting cases are deduced. It is found that a non-Newtonian effect is present in the velocity field for both the unsteady and steady-state cases. Once again for a second-order fluid, it is also found that except for the resonant case the asymptotic steady solution exists for blowing. Furthermore, the structure of the associated boundary layers is determined.     

Supersonic Rarefied Flow Past a Cascade of Transverse Flat Plates

The results of numerical calculations of the supersonic rarefied flow through an infinite, periodic cascade of flat plates set transverse to the incident flow are presented. The flow in the vicinity of the cascade is described on the basis of the kinetic Boltzmann equation. The Knudsen numbers, based on the plate span, the distances between the plates and the scalelength of the flow under consideration, range from 0.2 to 0.003. Both steady-state regimes with a shock attached to the cascade and time-dependent ones with an upstream-traveling shock are investigated.     

Self-sustained oscillations of shear flow past a slotted plate coupled with cavity resonance

Shear flow past a slotted plate configuration can give rise to highly coherent, self-sustained oscillations when coupling occurs with a resonant mode of an adjacent cavity. The distinctive feature of these oscillations is that the wavelength of the coherent instability along the plate is of the order of the plate length. This observation is in contrast to previous investigations of flow past perforated or slotted surfaces, where the instability scales on the diameter of the perforation or the gap length of a slot. The present oscillations occur even when the inflow boundary layer is turbulent and an inflectional form of the shear flow cannot develop along the cavity opening, due to the presence of the slotted plate. Instigation of a resonant mode of the cavity, in conjunction with an inherent instability of the shear flow along the plate, gives rise to ordered clusters of instantaneous vorticity and instantaneous velocity correlation. During the oscillation, ejection of flow occurs from the cavity to the region of the shear flow; this ejection is in accord with the convection of the large-scale cluster of vorticity along the slotted plate. This oscillation can be effectively detuned by adjusting the inflow velocity, such that the inherent instability of the shear flow past the slotted plate is no longer coincident with the resonant frequency of the cavity. Certain features of this self-sustained oscillation are directly analogous to recent findings of oscillations due to shear flow past a perforated plate bounded by a cavity, but in the absence of cavity resonance effects.     

Steady Natural Convection Flow of a Particulate Suspension Through a Parallel-Plate Channel

A continuum model for two-phase (fluid/particle) flow induced by natural convection is developed and applied to the problem of steady natural convention flow of a particulate suspension through an infinitely long channel. The walls of the channel are maintained at constant but different temperatures. The two-phase model accounts for particle-phase viscous effects. Boundary conditions borrowed from rarefied gas dynamics are employed for the particle-phase wall conditions. Various closed-form solutions for different special cases are obtained. A parametric study of the physical parameters involved in the problem are performed to illustrate the influence of these parameters on the flow and heat transfer aspects of the problem.     

高超声速稀薄流中横向喷流干扰特性实验研究

喷流干扰是高超声速飞行高精度控制的一种有效手段,研究者们以往大部分都主要集中于连续流条件下喷流干扰效应的机理研究,并给出了喷流干扰流场的典型结构,而稀薄流条件下喷流干扰特性的实验数据还十分匮乏.本文利用JFX爆轰激波风洞产生高超声速稀薄自由流,基于平板模型开展不同喷流压力和自由来流参数对横向喷流干扰特性影响的实验研究,采用高速纹影成像及图像处理技术,获得稀薄流条件下喷流干扰流场演化过程及流场结构的变化规律.相比于无喷流条件形成的流场,横向喷流与稀薄自由流相互作用形成的流场结构更为复杂,喷流压力由于受到稀薄来流的扰动,斜激波会短暂穿透喷流干扰流场并延伸至楔形体上部.喷流干扰流场内桶状激波的影响范围随着喷流压力的升高而逐渐变宽,位于三波点上游的斜激波空间位置不会随喷流压力的变化而改变,而位于三波点下游的弓形激波则向上游移动,当喷流压力过低时,桶状激波不会与其他两种激波交汇形成三波点.高超声速稀薄来流压力的降低同样会使桶状激波的影响范围变宽,弓形激波同样也会向上游移动,但基本不会对斜激波空间位置产生任何影响.     

Steady Flow Generated by a Core Oscillating in a Rotating Spherical Cavity

Steady flow generated by oscillations of an inner solid core in a fluid-filled rotating spherical cavity is experimentally studied. The core with density less than the fluid density is located near the center of the cavity and is acted upon by a centrifugal force. The gravity field directed perpendicular to the rotation axis leads to a stationary displacement of the core from the rotation axis. As a result, in the frame of reference attached to the cavity, the core performs circular oscillation with frequency equal to the rotation frequency, and its center moves along a circular trajectory in the equatorial plane around the center of the cavity. For the differential rotation of the core to be absent, one of the poles of the core is connected to the nearest pole of the cavity with a torsionally elastic, flexible fishing line. It is found that the oscillation of the core generates axisymmetric azimuthal fluid flow in the cavity which has the form of nested liquid columns rotating with different angular velocities. Comparison with the case of a free oscillating core which performs mean differential rotation suggests the existence of two mechanisms of flow generation (due to the differential rotation of the core in the Ekman layer and due to the oscillation of the core in the oscillating boundary layers).     

Planar collisionless jet impingement on a specular reflective plate

This paper presents a fundamental gas-kinetic study on a high speed planar rarefied jet impinging on a flat plate of specular reflections. Based on previous collisionless planar free jet results, it is straightforward to obtain jet impingement flowfield solutions, and jet impingement for specular reflective plate surface properties. Several direct simulation Monte Carlo simulation results are provided and they validate these analytical solutions of rarefied planar jet flows. The results can find applications in many disciplines, such as materials processing, molecular beams, and space engineering.     

Slow gas flow around a nonuniformly heated plate

Slow flow of a rarefied gas over a nonuniformly heated plate is investigated numerically. The interaction of the oncoming stream with the flow due to the variable temperature of the gas near the body is considered.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 181–184, September–October, 1981.     

Steady natural convection flow of a particulate suspension through a circular pipe

A continuum model for two-phase (fluid/particle) flow induced by natural convection is developed and applied to the problem of steady natural convention flow of a particulate suspension through an infinitely long pipe. The wall of the pipe is maintained at a constant temperature. The particle phase is endowed by an artificial viscosity which may be used to model particle-particle interaction in dension suspensions. Boundary conditions borrowed from rarefied gas dynamics are employed for the particle-phase wall conditions. Closed-form solutions for the velocity and temperature profiles are obtained. For the assumptions employed in the problem, the temperatures of both phases in the pipe are predicted to be uniform. A parametric study of some physical parameters involved in the problem is performed to illustrate the influence of these parameters on the velocity profiles of both the fluid and particle phases.     

Oscillatory channel flow in a rotating system

Oscillatory channel flow in a rotating system is considered. The Navier–Stokes equations reduce to the Ekman equations that are solved exactly. The results show the interaction between oscillation frequency and rotation rate. Resonance occurs when the oscillation frequency is twice the rotation rate.