Rarefied MHD laminar radial channel flow

The steady axisymmetrical laminar flow of slightly rarefied electrically conducting gas between two circular parallel disks in the presence of a transverse magnetic field is analytically investigated. A solution is obtained by expanding the velocity and the pressure distribution in terms of a power series of 1/r. The effect of rare-faction is taken to be manifested by slip of the velocity at the boundary. Velocity, induced magnetic field, pressure and shear stress distributions are determined and compared with the case of no rarefaction.Nomenclature b outer radius of channel - C _f skin friction coefficient, _w /(Q ²/t ⁴) - H ₀ impressed magnetic field - H _r ^* induced magnetic field in the radial direction - H _r induced dimensionless magnetic field in the radial direction, H _r ^* /H ₀ - M Hartmann number, H ₀ t(/)^1/2 - P dimensionless static pressure, P*t ⁴/Q ² - P* static pressure - P _b dimensionless pressure at outer radius of channel - P ₀ reference dimensionless pressure - Q source discharge - R gas constant - Rm magnetic Reynolds number, Q/t - Re Reynolds number, Q/t - 2t channel width - T absolute gas temperature - u dimensionless radial component of the velocity, u*t ²/Q - u* radial component of the velocity - w dimensionless axial component of the velocity, w*t ²/Q - w* axial component of the velocity - z, r dimensionless axial and radial directions, z*/t and r*/t, respectively - z*, r* axial and radial direction, respectively - molecular mean free path - magnetic permeability - coefficient of kinematic viscosity - density - electrical conductivity     

Rarefied hypersonic flow in a plane channel with a surface glow discharge

The gasdynamic structure of a hypersonic molecular nitrogen flow in a plane channel whose opposite surfaces are segmented electrodes for generating a continuous surface glow discharge is investigated using a two-dimensional computational model. The electrodynamic structure of the surface glow discharge in the hypersonic rarefied gas flow (distributions of the charged particle concentrations, current density, and electric potential) is studied. A two-dimensional conjugate electrical-gasdynamic model consisting of the continuity, Navier-Stokes, and energy conservation equations and the chargedparticle continuity equations in the ambipolar approximation is proposed. The real thermophysical and transport properties of molecular nitrogen are taken into account. It is shown that using a surface glow discharge in a hypersonic rarefied gas flow makes it possible effectively to modify the shock-wave flow structure and hence to consider this type of discharge as additional tool for controlling rarefied gas flows.     

Rarefied gas flow into a vacuum from a plane long channel closed at one end

The time-dependent problem of rarefied gas flow into a vacuum from a plane long channel closed at one end is solved on the basis of the kinetic S-model. The effect of diffuse molecular reflection from the channel walls on the flow velocity and the process of channel cavity vacuumization is studied as a function of the channel length and the extent of gas rarefaction under the condition that the wall temperature is maintained to be constant. The kinetic equation is solved numerically using a conservative finite-difference method of the second order of accuracy in spatial coordinates. The possibility of simplification of the problem for long times by means of reduction to the diffusion process is considered.     

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.     

Rarefied Poiseuille flow in elliptical and rectangular tubes

An isothermal steady rarefied gas flow in a long channel (tube) of elliptical or rectangular cross-section under the action of a given pressure gradient (Poiseuille flow) is studied on the basis of the Bhatnagar-Gross-Krook model. The solution is obtained using a conservative higher-order method. The velocity field in a channel cross-section is investigated as a function of the rarefaction degree and the cross-section geometry parameters. The main calculated function is the gas flow rate through the tube. The solutions obtained are compared with the available results.     

Rarefied gas flow past a sphere with injection

Hypersonic rarefied gas flow over the windward face of a sphere is considered in the presence of distributed injection from the surface of the body. A similar problem was previously solved in [1–3] within the framework of continuum mechanics and in [4] on the basis of model kinetic equations. In the present study the calculations were carried out using the Monte Carlo method of direct statistical modeling [5, 6]. The injected gas was the same as the free-stream gas. A simple monatomic gas model with a rigid sphere interaction potential was employed. The reflection of the molecules from the surface of the body was assumed to be diffuse with total energy accommodation. The calculation procedure using weighting factors is described in [7]. The influence of injection on the mechanical and thermal effect of the gas flow on the body is investigated for various degrees of rarefaction of the medium and injection rates.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 175–179, July–August, 1990.     

Steady two-dimensional merging flow from two channels into a single channel

Two-dimensional steady symmetric merging flow from two channels into a single one is investigated. The geometry of the configuration has been chosen such that it can be mapped conformally onto a rectangular geometry, thus facilitating the numerical solution procedure for the governing Navier-Stokes equations. Computed velocity profiles and streamline patterns are presented in graphical form. Furthermore, results concerning the inlet length are given.     

Time periodic electroosmotic flow of micropolar fluids through microparallel channel

The time periodic electroosmotic flow of an incompressible micropolar fluid between two infinitely extended microparallel plates is studied.The analytical solutions of the velocity and microrotation are derived under the Debye-H(u|¨)ckel approximation.The effects of the related dimensionless parameters,e.g.,the micropolar parameter,the frequency,the electrokinetic width,and the wall zeta potential ratio of the upper plate to the lower plate,on the electroosmotic velocity and microrotation are investigated.The results show that the amplitudes of the velocity and the volume flow rate will drop to zero when the micropolar parameter increases from 0 to 1.The effects of the electrokinetic width and the frequency on the velocity of the micropolar fluid are similar to those of the Newtonian fluid.However,the dependence of the microrotation on the related parameters mentioned above is complex.In order to describe these effects clearly,the dimensionless microrotation strength and the penetration depth of the microrotation are defined,which are used to explain the variation of the microrotation.In addition,the effects of various parameters on the dimensionless stress tensor at the walls are studied.     

Rarefied gas flow in a triangular duct based on a boundary fitted lattice

The rarefied fully developed flow of a gas through a duct of a triangular cross section is solved in the whole range of the Knudsen number. The flow is modelled by the BGK kinetic equation, subject to Maxwell diffuse boundary conditions. The numerical solution is based on the discrete velocity method, which is applied for first time on a triangular lattice in the physical space. The boundaries of the flow and computational domains are identical deducing accurate results with modest computational effort. Results on the velocity profiles and on the flow rates for ducts of various triangular cross sections are reported and they are valid in the whole range of gas rarefaction. Their accuracy is validated in several ways, including the recovery of the analytical solutions at the free molecular and hydrodynamic limits. The successful implementation of the triangular grid elements is promising for generalizing kinetic type solutions to rarefied flows in domains with complex boundaries using adaptive and unstructured grids.     

Rarefied gas motion in a short planar channel over the entire knudsen number range

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 48–53, September–October, 1989.     

Implicit large-eddy simulation applied to turbulent channel flow with periodic constrictions

The subgrid-scale (SGS) model in a large-eddy simulation (LES) operates on a range of scales which is marginally resolved by discretization schemes. Accordingly, the discretization scheme and the subgrid-scale model are linked. One can exploit this link by developing discretization methods from subgrid-scale models, or the converse. Approaches where SGS models and numerical discretizations are fully merged are called implicit LES (ILES). Recently, we have proposed a systematic framework for the design, analysis, and optimization of nonlinear discretization schemes for implicit LES. In this framework parameters inherent to the discretization scheme are determined in such a way that the numerical truncation error acts as a physically motivated SGS model. The resulting so-called adaptive local deconvolution method (ALDM) for implicit LES allows for reliable predictions of isotropic forced and decaying turbulence and of unbounded transitional flows for a wide range of Reynolds numbers. In the present paper, ALDM is evaluated for the separated flow through a channel with streamwise-periodic constrictions at two Reynolds numbers Re = 2,808 and Re = 10,595. We demonstrate that, although model parameters of ALDM have been determined for isotropic turbulence at infinite Reynolds number, it successfully predicts mean flow and turbulence statistics in the considered physically complex, anisotropic, and inhomogeneous flow regime. It is shown that the implicit model performs at least as well as an established explicit model.      

On the behaviour of periodic disturbances introduced into a turbulent channel flow by an oscillating airfoil

This paper is on the propagation characteristics of disturbances in turbulent shear flow. Periodic disturbances are introduced into a fully developed turbulent channel flow by an airfoil executing pitching oscillations. Hot-wire measurements are done on the mean and fluctuating velocities, on the Reynolds stresses and their spectra. The spectral data are evaluated to obtain the decay characteristics of the induced disturbance in this flow. The results show that the disturbance propagation in this flow is characterised by different decay rates in the regions near and far from the disturbance source.     

Stability of periodic motion of fluid in a planar channel

The stability of periodic motion of a fluid in a planar channel was investigated experimentally. Two mechanisms of departure from stability of rectilinear motion — at high and low frequencies, respectively — were observed. The critical Reynolds number was found as a function of the pulsation frequency. The results of the quasistationary theoretical approach to the stability of periodic flows [1] agree with the experiment.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 114–118, November–December, 1979.I thank G. F. Shaidurov, under whose guidance this work was carried out.     

Hydromagnetic flow in a rotating channel

The steady flow in a parallel plate channel rotating with an angular velocity Ω and subjected to a constant transverse magnetic field is analysed. An exact solution of the governing equations is obtained. The solution in the dimensionless form contains two parameters: the Hartmann number, M ², and K ² which is the reciprocal of the Ekman number. The effects of these parameters on the velocity and magnetic field distributions are studied. For large values of the parameters, there arise thin boundary layers on the walls of the channel.     

Magnetohydrodynamic entrance flow in a channel

A MHD entrance flow in a channel is studied in the Prandtl approximation. It is shown that consistency with the approximation requires an appropriate change in the boundary conditions which hold for the original, unsimplified equations. The correct boundary conditions are established and used to repete the numerical calculations in a few cases studied by other authors with the unmodified boundary conditions. In the cases here considered the numerical differences do not amount in practice to more than 10%, though they grow with increasing Hartmann number. Gabinete de Aplicaciones Nucleares de O.P. and Centro Coordinado de Fisica (C.S.I.C.-U.A.M.). Present address: Departamento de Física, Facultad de Ciencias, Universidad Autónoma de Madrid.     

Density-stratified Sadovskii flow in a channel

Stably density-stratified and nonstratified flows in a channel past a pair of symmetrical closed-streamline vortices on the channel axis are considered. The numerical results obtained cover the whole range of subcritical stratification and eddy lengths. An asymptotic solution for a very long closed-streamline region is found. The results can be used directly in the asymptotic theory of separated flows at high Reynolds number. Sadovskii flows are plane potential inviscid flows past a pair of closed-streamline regions of uniform vorticity. The flow velocity may be discontinuous at the boundary of the closed-streamline region. The analysis below is restricted to the specific case of continuous velocity distribution, so that the Bernoulli constant jump at the eddy boundary is zero. Unbounded nonstratified flows of this kind were studied in [1, 2]. Calculations of the corresponding channel flow were restricted to relatively wide channels. Closely related problems were also considered in [3, 4].Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.4, pp. 118–123, May–June, 1993.