The boundary layers of a fully ionized two-temperature plasma with given component temperatures at an electrode

The flow of a plasma with different component temperatures in the boundary layers at the electrodes of an MHD channel is investigated without any assumptions as to self-similarity. For the calculation of the electron temperature, the full energy equation for an electron gas [1] is solved with allowance for the estimates given in [2]. In contrast to [3, 4], the calculation includes the change in temperature of electrons and ions along the channel caused by the collective transport of energy, the work done by the partial pressure forces, and the Joule heating and the energy exchange between the components. The problem of the boundary layers in the flow of a two-temperature, partially ionized plasma past an electrode is solved in simplified form by the local similarity method in [5–7]. In these papers, either the Kerrebrock equation is used [5, 6] or the collective terms are omitted from the electron energy equation [7].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 3–10, September–October, 1972.The author thanks V. V. Gogosov and A. E. Yakubenko for interest in this work.     

On nonisothermal electroconvection

The flow from the tip of a needle electrode is caused by the Coulomb force acting on the space charge [1–3]. This charge is formed because of the dependence of the conductivity on the temperature, nonuniformity of which is due to Joule heating [1] and the electric field intensity [2] or processes near the electrode [3–5]. The present paper considers the stability of a dielectric liquid between spherical electrodes in order to elucidate the possibility of a thermoelectrohydrodynainic flow due to Joule heating. In the presence of external heating, the possibility of such a flow has been demonstrated both experimentally and theoretically [6–8].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 133–137, March–April, 1980.     

Modeling of the transient processes in the channels of an EHD pump

The nonstationary process of development of weakly conducting electrohydrodynamic flow in the channel of an EHD pump with plane permeable electrodes, between which a potential difference is created from an external source, is considered in the hydraulic approximation within the framework of the model proposed in [1, 2]. It is shown that the efficiency of the EHD device can be improved if in the fluid the spatial process of ion formation is retarded, while the recombination process is intense. The effect of the flow velocity on the formation of a space charge region in the interelectrode gap is investigated. On a certain range of the problem parameters the flow induced in the channel substantially modifies the space charge distribution as a result of the blowoff of narrow diffusion electrode ion layers. This creates a nonmonotonic dependence of the fluid velocity on the applied potential difference.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 30–41, May–June, 1994.     

Flexural Vibrations of a Piezoelectric Bimorph with a Cut Internal Electrode

Stationary vibrations of a bimorph plate composed of two piezoelectric layers of equal thickness are studied. There is an infinitely thin cut electrode between the layers. A model of flexural vibrations of the bimorph that is based on the variational equation generalizing the Hamilton principle in electroelasticity is proposed. For the plane problem, a system of equations of motion is derived and the boundary conditions and the conjugate conditions at the interface of the regions of the cut electrode are formulated. For the TsTS–19 piezoceramics, resonance and antiresonance frequencies are calculated. The values obtained are compared with the calculation results obtained with the use of the Kirchhoff model and the finite–element method. It is shown that the use of a plate with a cut electrode allows one to increase the efficiency of vibration excitation compared to the case of a continuous internal electrode.     

Transmission coefficient of a grid electrode

The behavior of conducting emulsion drops (carrying a constant charge) in the region between electrodes connected to dc sources is studied. Assuming that the concentration of the dispersed phase is reasonably low, the problem may be reduced to one of determining the motion of an isolated drop close to the electrode. The trajectories of the drops in a flow passing around the electrode are then calculated, allowing for charge exchange between the drops and the electrode, and the electrode transmission coefficient is determined in relation to the parameters of the problem. An analogous situation was envisaged in earlier papers [1, 2] for a single cylindrical electrode but without allowing for the recharging of the particles.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 157–158, May–June, 1974.     

Calculation of the main characteristics of a turbulent stream of incompressible fluid in a pipe

The reports [1–5] are devoted to the calculation of the characteristics of the steady turbulent flow of an incompressible fluid in a straight round pipe using the model of A. N. Kolmogorov, Additional assumptions are introduced in these reports, such as not allowing for energy diffusion or molecular viscosity, dividing the region of flow into arbitrary layers, etc. In the present report the problem is solved in a more general formulation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 161–163, September–October, 1977.     

Aerodynamics of end-wall boundary layer in a vortex chamber

The need for the inclusion of end-wall boundary layers in the study of the aerodynamics of vortex chambers has been frequently mentioned in the literature. However, owing to limited experimental data [1–3] with reliable information on the wall layers, the existing computational methods for end-wall boundary layers are not well-founded. The question of which parameters determine the formation of end-wall flow remains debatable. In some studies [4, 5], the vortex chambers are conditionally divided into short and long chambers. However, there is no unique opinion on the role of end-wall flows in vortex chambers of different lengths. It has also not been established for what geometric and flow parameters the chamber could be considered long or short. In the present study, as in [1, 5–8], solution is obtained for the end-wall boundary-layer equations using integral methods, considering the boundary layer in the radial direction in the form of a submerged wall jet. Such an approach made it possible to use the laws for the development of wall jets [9], and obtain fairly simple relations for integral parameters, skin friction, mass flow in the boundary layer, and other characteristics. Results are compared with available experimental data and computations of others authors; turbulent flow is considered; results for laminar boundary layer are given in [10].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 117–126, September–October, 1986.     

Instability and flow of a weakly conducting fluid in the presence of oxidation-reduction reactions at electrodes and recombination

Experiments show that a weakly conducting fluid in a plane-parallel system of electrodes is set into motion if the field intensity is sufficiently great [1–5]. The loss of stability is due to the formation of charges near the electrodes and the influence of the Coulomb forces on these charges. The formation of the space charges is usually attributed to oxidation-reduction electrode reactions and bulk recombination of the ions formed at the electrodes [1–4]. In the present paper, the stability of a weakly conducting fluid in a plane-parallel system of electrodes with symmetric distribution of the space charge is studied. The methods of the theory of solution bifurcation are used to construct the stationary flow which arises after the loss of stability and to investigate the stability of this flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 20–26, July–August, 1981.     

Modeling of natural ionospheric flight conditions

In simulating conditions for flight of spacecraft in the upper layers of the atmosphere one must model the ionization, excitation, and dissociation of the flow [1], in addition to other parameters. Modeling of these parameters is important, in particular, in investigations of sensors intended for measuring flight parameters aborad a spacecraft, tests of structural materials, and determination of the aerodynamic characteristics of spacecraft. The studies described here employ multielectrode probes, a metastable particle detector, and catalytic sensors to investigate the ionized, dissociated, and excited components of high-speed free-molecular flow in a facility [2] which models flight conditions in the upper atmospheric layers. It is shown that the degrees of ionization and dissociation, and also the metastable particle concentration in the flow, correspond to the natural values of these parameters at altitudes H = 120–200 km.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 31–35, November– December, 1977.     

Criteria for the detachment of a three-dimensional boundary layer

On the assumption that the character of the flow in a specified section of the boundary layer depends solely on the behavior of the external flow in the immediate vicinity of the section under consideration, criteria are derived for the detachment of laminar and turbulent boundary layers in the case of three-dimensional flow. The detachment criteria so found are a consequence of the necessary condition for the detachment of a three-dimensional boundary layer deduced earlier [1].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 50–54, July–August, 1970.     

Definition and calculation of effective ambipolar diffusion coefficients for a laminar multicomponent ionized boundary layer

Effective diffusion coefficients substantially facilitate solution of detailed problems for multicomponent boundary layers with frozen-in reactions in the flow and heterogeneous reactions at the wall; they provide physically lucid correlation formulas and final equations for the convective heat flow to the undamaged solid as well as for the mass loss rate or effective erosion enthalpy if the walls are subject to thermochemical attack [1–5].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 60–72, July–August, 1970.     

Stability of transonic two-phase flow

The nature of a singular point in the stability of one-dimensional transonic flow of a vapor-drop mixture in a channel of variable cross section is considered within the framework of a two-lquid hydrodynamical model. It is shown that the singular point in the case of any lags of the drops preserves the nature of a saddle inherent to homogeneous gas flow, shifting only towards the divergent part of the channel if the content of condensed phase is not too high. Here the transition of subsonic two-phase flow into supersonic flow is stable and the predominance of drop agglomeration over fragmentation and the positive curvature of the channel profile are stabilizing factors. The saddle nature of the singularity is possible only if the lag of the drops is not too high in the case of flows with a higher content of condensed phase. In the opposite case, the point at which the speed of sound is attained loses the nature of a saddle point.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 163–171, January–February, 1976.     

Motion of a fluid between rotating cones

A study is made of the steady axisymmetric flow of a viscous fluid between two cones rotating in opposite ways round a common axis. It is shown that as in the case of the flow of fluid swirled by plane disks rotating at different speeds [1], there can be two regimes of motion in the system: a Batchelor regime with quasirigid rotation of the fluid outside the boundary layers [2] and a Stewartson regime in which the azimuthal flow is concentrated only in the boundary layers [3]. In the Stewartson regime, a boundary layer analogous to that in the single disk problem (see, for example, [4–6]) forms in the region of each cone far from the apex. For the flows outside the boundary layers, simple expressions are found which make it possible to obtain a conception of the circulation of the fluid as a whole. With minor alterations, the results can be applied to the case of the rotation of other curved surfaces.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 58–64, March–April, 1985.The author thanks A. M. Obukhov for suggesting the subject and for his interest in the work, and A. V. Danilov and S. V. Nesterov for useful discussions.     

Asymptotic analysis of the equations of a three-dimensional boundary layer

The asymptotic solutions of the self-similar equations of two- and three-dimensional boundary layers have been investigated by many authors (see, for example, [1–3]). In [4, 5], asymptotic solutions were found for non-self-similar equations for two-dimensional flow, and the propagation of perturbations near the external edge of the boundary layer was analyzed. In the present paper, asymptotic solutions are obtained for the non-self-similar equations of a three-dimensional laminar boundary layer of an incompressible fluid. It is shown that the conclusion drawn in [5] — that the boundary conditions can be transferred from infinity to a finite distance from the wall — is also true for three-dimensional flow. The obtained solutions explain the experimentally well-known phenomenon of the conservativeness of the secondary currents. The essence of this phenomenon is that a change in the sign of the transverse (along the normal to a streamline of the external flow) pressure gradient is accompanied by a very rapid change in the direction of the secondary flow near the wall, whereas in the upper layers of the boundary layer the direction remains unchanged for a substantial time.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 155–157, September–October, 1979.     

Boundary layer on a circular sector

The finite difference method is used to investigate laminar and turbulent boundary layers on a flat surface in the case of circular streamlines of the exterior flow. It is shown that when the flow is turned through large angles the behavior of the boundary layer over a finite circular sector differs qualitatively from an infinite sector. A study is made of the influence of the Mach number, the angle through which the flow is turned, and the wall temperature on the secondary flows in the boundary layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 35–41, January–February, 1982.     

Transverse subsonic flow past a cylinder

At around the critical Reynolds number Re = (1.5–4.0)·10⁵ there is an abrupt change in the pattern of transverse subsonic flow past a circular cylinder, and the drag coefficient C_x decreases sharply [1]. A large body of both experimental and computational investigations has now been made into subsonic flow past a cylinder [1–4]. A significant contribution to a deeper understanding of the phenomenon was made by [4], which gives a physical interpretation of a number of theoretical and experimental results obtained in a wide range of Re. Nevertheless, the complicated nonstationary nature of flow past a cylinder with separation and the occurrence of three-dimensional flows when two-dimensional flow is simulated in wind tunnels do not permit one to regard the problem as fully studied. The aim of the present work was to make additional experimental investigations into transverse subsonic flow past a cylinder and, in particular, to study the possible asymmetric stable flow regimes near the critical Reynolds number.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 154–157, March–April, 1980.     

Weakly rarefied gas flows between nonuniformly heated parallel plates

The aim of this research is to establish the validity of the predictions of the theory of slow nonisothermal flows, to study the limits of applicability (with respect to the Knudsen number) of the conclusions reached and to determine the effect of the Knudsen layers on these flows on the basis of a numerical investigation of slow nonisothermal weakly rarefied gas flow in a plane infinite channel with weakly nonequilibrium heating of the walls and a finite wall temperature difference. The gas flow is described by a relaxation transport equation. The results obtained show how quickly, as the Knudsen number decreases, the solutions of the transport equation outside the Knudsen layers tend to the solution of the equations of gas dynamics of slow nonisothermal flows (and not to the solution of the Navier-Stokes equations).Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 115–121, January–February, 1988.     

Free convection in inclined layers of liquid and with a jumpwise change in the temperature of the heat-transfer surfaces

This paper gives the results of investigations of hydrodynamics and heat transfer with the laminar flow of a liquid in inclined layers, closed at the ends, as well as in layers of liquid with a jumpwise change in the temperature of the heat-transfer surface, under conditions of free convection.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 115–121, November–December, 1971.     

Particle suspension in a simple shear flow

A hydrodynamic model describing the particle distribution over the cross-section of a finely dispersed flow is proposed. The model is constructed on the basis of notions concerning the diffusion of particles induced by their random displacements in the process of relative motion of neighboring layers at constant shear velocity. It is shown that the suspension capacity of the flow is large for small particles due to thermal fluctuations and for relatively large particles due to shear-induced particle pulsations. There are critical particle sizes for which the particles are suspended and transported by the flow less effectively than larger or smaller particles.Ekaterinburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 112–121, January–February, 1995.     

Prediction of salt conditions in irrigated soils in the presence of drainage

The equations of convective diffusion are solved for two flat layers, using the method of finite integral transformations. Exact solutions are obtained to the problem in the presence of a descending or ascending filtration flow.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 113–117, November–December, 1972.