Modeling the system of electrogasdynamic final-control elements

A system of electrogasdynamic final-control elements (plasma actuators) intended for increasing the stability of the boundary layer on a swept wing is considered. The actuators operate on the basis of dielectric barrier discharge. The physical model of the discharge in the air is formulated in the diffusion-drift approximation with account for three charged ionized-gas components, namely, electrons, positive nitrogen and oxygen ions, and negative oxygen ions. The boundary conditions on the dielectric surface are formulated with account for finite desorption and recombination rates of the charged particles. The numerical modeling for an actuator system of particular geometry shows a slight influence of the negative ions on the bulk force generated by each actuator. The main actuator parameters, such as the total longitudinal force and heat release, are shown to considerably depend on the dielectric permeabilities of insulation layers separating the external and internal electrodes. The expressions are derived that make it possible to estimate the gas velocity induced by the bulk force action of the dielectric barrier discharge on the gas flow.     

Control of cross flow in the three-dimensional boundary layer using space-periodic body force action

The possibility of attenuation of the cross flow in the three-dimensional incompressible laminar boundary layer on a sideslipping wing under the action of body force sources simulating the time-average forces generated by a surface electric discharge is estimated. The effect of the distance between the sources and the sideslip angle of the wing on the cross flow velocity is investigated for the source intensity observed experimentally.     

Numerical simulation of an electric discharge in supersonic flow

The two-dimensional problem of supersonic air flow past a spherical electrode is considered on the basis of a joint solution of the Navier-Stokes equations for a neutral gas and the charged-particle transport equations in the diffusion-drift approximation. The self-sustained discharge is considered in the cathode regime of operation of the test electrode in a formulation analogous to that of the experimental study [1]. The thermal and non-thermal (action of the electrostatic force in the cathode layer of the space charge) mechanisms of action of the discharge on the flow field are investigated. Within the framework of the numerical model considered the effect of the electrostatic force turns out to be negligibly small and the main effect of the action on the flow is the heat release driven by the electric currents. The influence of the discharge on the flow field was manifested itself in a reduction of the aerodynamic drag by up to 25%.     

Wave regimes of ascending flow of a thin layer of a viscous liquid in contact with a gas

The flow of a liquid in thin layers is one of the hydrodynamic problems of chemistry and heat engineering. The large surface area of films and their small thickness make it possible to accelerate thermal, diffusive, and chemical processes at the gas-liquid boundary.Theoretical studies of liquid flow in a vertical descending thin layer are presented in [1–4]. In this paper we study ascending wave flows of a liquid in a thin vertical layer in contact with a gas, i.e., flows in the direction opposite the action of the force due to gravity, with account for the action of the gas on the liquid surface. Such motions are encountered when oil is extracted from strata that are saturated with gas. At some distance from the stratum the oil and gas separate: the gas travels at high velocity inside the pipe, occupying a considerable portion of the pipe, and the liquid is displaced toward the pipe walls, forming a thin film. In certain cases a wave-like interface develops between the oil and gas that travels with a velocity greater than that of the liquid but less than the average gas velocity. Similar phenomena are observed in high velocity mass exchangers.We examine the effect of the gas for both laminar and turbulent flow.Studies that neglect the effect of the gas flow on the liquid show that for waves on the film surface whose lengths are considerably longer than the average thickness of the layer, the liquid motion in the film is described by boundary layer equations in which account is taken of the mass force, i.e., the force due to gravity. With some approximation, we can assume that in accounting for the effect of the gas on the liquid the liquid flow is described by these same equations.     

The distribution of particles in a shock-induced boundary layer of a dusty gas over a solid surface

The laminar boundary layer behind a constant-speed shock wave moving through a dusty gas along a solid surface is studied. The Saffman lift force acting on a spherical particle in a gas boundary layer is taken into account. A method for calculating the density profile of dispersed phase near the wall is proposed and some numerical results are given. It is shown that behind the shock wave, there exists a curved thin layer where the density of particles is many times higher than the original one. This dust collection effect may be of essential importance to the problem of dust explosion in industry.     

Effect of a dielectric barrier discharge on laminar-turbulent transition on a flat plate in a disturbed external flow

Numerical simulation is applied to study the distinctive features of the dielectric barrier discharge (DBD) effect on laminar-turbulent transition on a flat plate in the presence of disturbances in the external flow. The density distributions of the electric force and the discharge power acting on the gas are assumed to be uniform within the given discharge volume. To model the external disturbances the value of the turbulent viscosity in the differential model used is assumed to be nonzero at the boundary layer edge.     

激波诱导含灰气体边界层中的粒子分布

本文研究当激波沿着一个固体表面等速地穿越含灰气体运动时所诱导的层流边界层特性。考虑了作用在气体边界层中球形粒子的 Saffman 升力,建议了一种计算近壁区中弥散相密度剖面的方法,并给出了数值计算结果。本文结果表明:在激波后方存在着一个弯曲的薄层区域,其中的粒子密度可以比其波前原始值增加许多倍。这种粒子聚集效应对于工业中粉尘爆炸等实际问题具有重要意义。     

Problem of Pulse Start-up of a Gas Bearing in a Generalized Formulation

The time-dependent motion in the lubricating layer of a gas bearing is analyzed on the basis of the compressible boundary layer equations with allowance for the inertial effects and the transverse temperature drop. After introducing certain assumptions concerning the order of the main dimensionless parameters, approximate expressions for the velocity and temperature are derived. As a result, the problem reduces to the determination of the pressure as a function of the space coordinate and time.     

Simulation of an electrohydrodynamic DC actuator

A semiempirical model of the electrohydrodynamic actuator operating on the basis of a dc corona discharge is proposed. The model is based on calculations of an electric field and a unipolar ion jet generated by a linear ion source on the surface of a dielectric plate and propagating along the plate in the laminar boundary layer. The ion source intensity and the potential difference on the actuator electrodes are determined experimentally. Estimates of the velocity induced by the electrohydrodynamic action in the flat-plate laminar boundary layer are obtained on the basis of the model. A comparison of the calculation results with the available experimental data confirms the adequacy of the model proposed. The effect of the adsorption properties of the dielectric surface on the distributions of the volume and surface electric discharge in the boundary layer is investigated within the framework of this model.     

Shockwave�Cturbulent boundary layer interaction control using magnetically driven surface discharges

This study demonstrates the potential for shockwave?Cturbulent boundary layer interaction control in air using low current DC constricted surface discharges forced by moderate strength magnetic fields. An analytical model describing the physics of magnetic field forced discharge interaction with boundary layer flow is developed and compared to experiments. Experiments are conducted in a Mach 2.6 indraft air tunnel with discharge currents up to 300?mA and magnetic field strengths up to 5?Tesla. Separation- and non-separation-inducing shocks are generated with diamond-shaped shockwave generators located on the wall opposite to the surface electrodes, and flow properties are measured with schlieren imaging, static wall pressure probes and acetone flow visualization. The effect of plasma control on boundary layer separation depends on the direction of the Lorentz force (j × B). It is observed that by using a Lorentz force that pushes the discharge upstream, separation can be induced or further strengthened even with discharge currents as low as 30?mA in a 3-Tesla magnetic field. If shock-induced separation is present, it is observed that by using Lorentz force that pushes the discharge downstream, separation can be suppressed, but this required higher currents, greater than 80?mA. Acetone planar laser scattering is used to image the flow structure in the test section and the reduction in the size of recirculation bubble and its elimination are observed experimentally as a function of actuation current and magnetic field strength.     

Development of slow disturbances in a hypersonic boundary layer

The mechanisms of development of slow time-dependent disturbances in the wall region of a hypersonic boundary layer are established and a diagram of the disturbed flow patterns is plotted; the corresponding nonlinear boundary value problem is formulated for each of these regimes. It is shown that the main factors that form the disturbed flow are the gas enthalpy near the body surface, the local viscous-inviscid interaction level, and the type, either subsonic or supersonic, of the boundary layer as a whole. Numerical and analytical solutions are obtained in the linear approximation. It is established that enhancement of the local viscous-inviscid interaction or an increased role for the main supersonic region of the boundary layer makes the disturbed flow by and large “supersonic”: the upstream propagation of the disturbances becomes weaker, while their downstream growth is amplified. Contrariwise, local viscous-inviscid interaction attenuation or an increased role for the main subsonic region of the boundary layer has the opposite effect. Surface cooling favors an increased effect of the main region of the boundary layer while heating favors an increased wall region effect. It is also found that in the regimes considered disturbances travel from the turbulent flow region downstream of the disturbed region under consideration counter to the oncoming flow, which may be of considerable significance in constructing the nonlinear stability theory.     

Stability of a disperse-mixture flow in a boundary layer

The hydrodynamic stability of a dilute disperse mixture flow in a quasi-equilibrium region of a boundary layer with a significantly nonuniform particle concentration profile is investigated. The mixture is described by a two-fluid model with an incompressible viscous carrier phase. In addition to the Stokes drag, the Saffman lifting force is taken into account in the interphase momentum exchange. On the basis of a numerical solution of the boundary-value problem for a modified Orr-Sommerfeld equation, neutral stability curves are analyzed and the dependence of the critical Reynolds number on the governing parameters is studied. It is shown that taking into account the particle concentration nonuniformity in the main flow and the Saffman lifting force significantly changes the stability limits of the two-phase laminar boundary layer flow. The effect of these factors on the boundary layer stability is considered for the first time.     

Tollmien-Schlichting Waves in a Hypersonic Boundary Layer Flow in the Neighborhood of a Cooled Surface

A nonlinear time-dependent model of the development of longwave perturbations in a hypersonic boundary layer flow in the neighborhood of a cooled surface is constructed. The pressure in the flow is assumed to be induced the combined variation of the thicknesses of the near-wall and main parts of the boundary layer. Numerical and analytic solutions are obtained in the linear approximation. It is shown that if the main part of the boundary layer is subsonic as a whole, its action reduces the perturbation damping upstream and the perturbation growth downstream, while a supersonic, as a whole, main part of the boundary layer creates the opposite effects. An analysis of the solutions obtained makes it possible to conclude that the asymptotic model proposed can describe the three-dimensional instability of the Tollmien-Schlichting waves.     

Modeling of Sliding of a Smooth Indenter over a Viscoelastic Layer Coupled with a Rigid Base

The article deals with constant-speed sliding of a smooth indenter along the boundary of a viscoelastic layer coupled with a rigid half-space. The problem is investigated in a quasistatic statement by constructing a solution for the case of a load sliding, distributed inside of a rectangular element, which allows using the boundary element method and an iterative procedure. The effect of sliding velocity and layer thickness on the contact pressure distribution and the deformation component of the frictional force is studied.     

One-dimensional nonlinear induced dynamics of acoustic waves in a finite three-dimensional domain

The problem of the time-dependent viscous compressible gas flow excited by a small external time-dependent space-and time-periodic force is considered within the framework of the Navier-Stokes equations on a finite interval with periodic boundary conditions. The investigation is carried out numerically for a periodicity interval L, divided by the viscous length, from 10² to 2 × 10³ and external force amplitudes from 10^?4 to 0.1. The nonlinear dynamics of the wave processes are investigated within the framework of this problem. It is shown that nonlinear steady-state oscillations with sharp variation of the quantities in space and time develop when L is greater than or of the order of 10³. This leads to the onset of a continuous spectrum.     

Dynamics of a liquid film sheared by a co-flowing turbulent gas

Consider the dynamics of a thin laminar liquid film flowing over an inclined wall in the presence of a co-flowing turbulent gas. The solution to the full two-phase flow problem poses substantial technical difficulties. However, by making appropriate assumptions, the solution process can be simplified and can provide valuable insights. The assumptions allow us to solve the gas and liquid problems independently. Solving for the gas flow reduces to finding perturbations to pressure and tangential stresses at the interface, influencing the liquid problem through the boundary conditions. We analyze the effect of gas flow on the liquid problem by developing an integral-boundary-layer model, which is valid up to moderate liquid Reynolds numbers. We seek solitary-wave solutions of this model under the influence of gas flow via a pseudo-arclength continuation method. Our computations demonstrate that as a general trend, the wave speed increases with increasing the gas shear and the liquid flow rate. Further insight into the problem is provided via time-dependent computations of the integral-boundary-layer model.     

Role of the static pressure in experiments on flow control by means of surface capacitor discharges

The effect of the static pressure on the reaction force exerted on a plate above whose surface a gas flow has been induced by exciting a capacitor (barrier) discharge is investigated. In the experiments the discharge was restructured so that the reaction force and the corresponding momentum entrained by the neutral flow increased when the pressure was reduced from atmospheric pressure to 200 Torr, the power supplied to the discharge being fixed. The charge exchange effect is of importance for the formation of the resulting gas flow. It is shown that under the experimental conditions the effect of an increase in the force with decrease in pressure is associated with an increase in the plasma volume ahead of the electrodes and the total number of ions in this volume.     

Measuring the velocity of a gas wake in a shock tube from the induced electromotive force

It is shown that the velocity of the gas wake in a shock tube can be measured from the induced electromotive force for argon and xenon at initial pressures greater than 1 mm Hg and conductivities above 1 mho/cm. In a strongly ionized gas ( > 0. 01) the flow velocities measured directly behind the shock front are close to the flow velocities corresponding to steady-state ionization equilibrium. It is noted that the expenditure of energy to dissociate an admixture of air causes a noticeable increase in the velocity of the flow along the entire plug of hot gas. A 3–6% acceleration of the flow along the plug. in the equilibrium ionization zone is observed; this is probably caused by the action of the boundary layer formed on the walls of the shock tube on the free flow.     

Stochastic stability of a rotating shaft

The stochastic stability problem of an elastic, balanced rotating shaft subjected to action of axial forces at the ends is studied. The shaft is of circular cross-section, it rotates at a constant rate about its longitudinal axis of symmetry. The effect of rotatory inertia of the shaft cross-section is included in the present formulation. Each force consists of a constant part and a time-dependent stochastic function. Closed form analytical solutions are obtained for simply supported boundary conditions. By using the direct Liapunov method almost sure asymptotic stability conditions are obtained as the function of stochastic process variance, damping coefficient, damping ratio, angular velocity, mode number and geometric and physical parameters of the shaft. Numerical calculations are performed for the Gaussian process with a zero mean and as well as an harmonic process with random phase.     

Acceleration of a conducting gas in a strong nonstationary electromagnetic field

The problem of nonstationary acceleration of a conducting gas in a channel is solved, together with the problem of a discharge in an electric-circuit. As distinct from other papers, in which the typical solution assumed a thin cluster subject to acceleration, we examine the case in which the gas flow fills the entire channel. The motion of the gas in the channel is examined in one-dimensional formulation, under the assumption that the particle transit time in the channel is small compared to the discharge time and that the electromagnetic force is large compared to the pressure gradient.For impulsive acceleration of the conducting gas, use is made of a discharge with a certain capacitance. Since the (time-variable) resistance of the channel and, consequently, the behavior of the discharge depend upon the channel flow of the conducting gas, the correct solution of the problem of gas acceleration in the induced electromagnetic field can be obtained only by analyzing simultaneously the magnetogasdynamic channel flow and the discharge process in the entire electric circuit. On the other hand, the acceleration of the gas itself is a function of the instantaneous potential difference at the electrodes. Hitherto, such simultaneous solutions were obtained by many investigators under the assumption, proposed in [1], that a channel gas flow may be treated as the motion of a unique narrow cluster, whose length is negligible as compared to the channel length. Experiments and theoretical estimates show, however, that in many cases the conducting gas fills the entire channel length during the acceleration process, so that the assumption of a narrow cluster is not even approximately fulfilled [4, 5].