Dynamics of Flow Through Porous Media with Unsteady Phase Permeabilities

The influence of nonequilibrium effects developing due to the formation of an emulsion of each phase (gas bubbles in the water and water dust in the gas) on the flow dynamics is investigated with reference to the displacement of water by a gas. The nonequilibrium effects manifest themselves in a change in the shape of the phase permeability curves (they become convex) and the threshold phase saturations in the course of flow through the porous medium. A kinetic equation in which the relaxation time is proportional to the seepage rate is used to describe such effects. The case in which the liquid displaced by the gas is itself gassed and the volume concentration of the gas bubbles is constant is considered.     

Effect of freestream nonequilibrium on flow past a wedge

We examine the effect of flow freezing in the nozzle of a hypersonic wind tunnel on the parameters of nonequilibrium flow past a wedge.Zhigulev's solution [1] for vibrational relaxation is extended to the nonequilibrium freestream case.It is shown that in this case the perturbations of the frozen-flow parameters behind the oblique shock wave can change sign if the flow in the working section deviates significantly from equilibrium.A method is proposed for converting experimental results obtained in tunnels with frozen flow to the case of equilibrium freestream flow past the body.The author wishes to thank O. Yu. Polyanskyi and V. P. Agavonov for their interest in this study.     

Three-dimensional numerical simulation of free convection in a plane-parallel flow

The results are given of numerical simulation of convection in Couette and Poiseuille flow for stationary (T*/t = 0) and uniformly increasing (T*/t = = const) mean temperature of the convective layer. Numerical experiments were made for air (Prandtl number Pr = 0.7) in the range of Rayleigh numbers 2 000 Ra 44 000. The results confirm the conclusion drawn in earlier studies that at slightly supercritical Ra the dominant forms in the convection are cylindrical rolls with helical circulation. The rolls are oriented along the direction of the flow and are stationary formations. When a certain value of Ra, which depends on the vertical distribution of the temperature and velocity, is reached, the roll structure is deformed by transverse perturbations. All the considered flow forms have a stabilizing influence on the transverse modes, occurring at larger Rayleigh numbers than is the case for convection in a fluid at rest. The perturbations are displaced at a phase velocity close to the mean velocity of the undisturbed flow. In the considered range of Rayleigh numbers, a shear flow does not have an appreciable influence on the heat transfer, although there is a certain tendency for the Nusselt number to be larger in a shear flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 127–135, May–June, 1979.We thank N. M. Sazanovich and L. I. Derevich for assistance in the calculations.     

On the Quasi‐Steadiness Hypothesis as Applied to Gas Exhaustion from a Receiver

A semiempirical method of determining the stabilization time for a quasisteady mode of gas exhaustion from a receiver after sudden opening of the nozzle and the time evolution of the real flow rate at the stage of the transitional process are considered. The numerical solution of the equations of exhaustion gas dynamics in a twodimensional formulation and the results of model experiments demonstrated that the method can be used to estimate the conditions of applicability of the quasisteadiness hypothesis and to determine the discharge coefficient of the nozzle with controlled accuracy.     

Analysis of turbulent boundary layer interaction with an external supersonic flow behind a step

An integral method of analyzing turbulent flow behind plane and axisymmetric steps is proposed, which will permit calculation of the pressure distribution, the displacement thickness, the momentum-loss thickness, and the friction in the zone of boundary layer interaction with an external ideal flow. The characteristics of an incompressible turbulent equilibrium boundary layer are used to analyze the flow behind the step, and the parameters of the compressible boundary layer flow are connected with the parameters of the incompressible boundary layer flow by using the Cowles-Crocco transformation.A large number of theoretical and experimental papers devoted to this topic can be mentioned. Let us consider just two [1, 2], which are similar to the method proposed herein, wherein the parameter distribution of the flow of a plane nearby turbulent wake is analyzed. The flow behind the body in these papers is separated into a zone of isobaric flow and a zone of boundary layer interaction with an external ideal flow. The jet boundary layer in the interaction zone is analyzed by the method of integral relations.The flow behind plane and axisymmetric steps is analyzed on the basis of a scheme of boundary layer interaction with an external ideal supersonic stream. The results of the analysis by the method proposed are compared with known experimental data.Notation x, y longitudinal and transverse coordinates - X, Y transformed longitudinal and transverse coordinates - , ^*, ^** boundary layer thickness, displacement thickness, momentum-loss thickness of a boundary layer - , ^*, ^** layer thickness, displacement thickness, momentum-loss thickness of an incompressible boundary layer - u, velocity and density of a compressible boundary layer - U, velocity and density of the incompressible boundary layer - , stream function of the compressible and incompressible boundary layers - , dynamic coefficient of viscosity of the compressible and incompressible boundary layers - r₁ radius of the base part of an axisymmetric body - r radius - R transformed radius - M Mach number - friction stress - p pressure - a speed of sound - s enthalpy - v Prandtl-Mayer angle - P Prandtl number - P_t turbulent Prandtl number - r₂ radius of the base sting - b step depth - =0 for plane flow - =1 for axisymmetric flow Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 33–40, May–June, 1971.In conclusion, the authors are grateful to M. Ya. Yudelovich and E. N. Bondarev for useful comments and discussions.     

Optimal Profiling of the Supersonic Part of a Plug Nozzle Contour

The problem of the optimal profiling of the supersonic part of a plug nozzle contour is solved within the framework of the ideal (inviscid and non-heat-conducting) gas model. The contours obtained provide a thrust maximum for given uniform sonic flow in the radial critical section of the nozzle, given constraints on the nozzle dimensions, and a given outer pressure (counterpressure). The initial sonic regions of the optimal contours are profiled on the basis of the condition that there the flow Mach number is unity. Varying the initial sonic region length makes it possible to construct nozzles of different sizes. The possibilities of the computational programs developed are demonstrated with reference to the example of plug nozzles, optimal when operated in a vacuum. It is shown that low thrust losses are obtained even for moderate nozzle dimensions. In the examples calculated, the optimal plug nozzles provide a greater thrust than the optimal axisymmetric and two-dimensional nozzles with an axial sonic flow for the same lengths and gas flow rates.     

Interaction of the vortex structures formed in parallel pulsed jets

The experimental investigation of the lateral interaction of the heads of pulsed jets and primary shock waves at various nozzle spacings and pressure ratio numbers is described. The various stages of formation of a composite pulsed jet issuing from a multinozzle block are classified and the flow development mechanisms are explored. It is shown for both a block and a single nozzle the shock wave travels with almost the same velocity, whereas the jet front formed at the exit from a single nozzle moves much more slowly than the jet front formed beyond a nozzle block. Long-lived lateral bursts of gas, whose dimensions are an order greater than those of the jet bursts, are detected. Their long period of existence considerably increases the stabilization time of the steady-state structure and parameters as compared with a single pulsed jet with the same flow rate.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 153–159, November–December, 1987.     

Supersonic nonequilibrium flow past segmental bodies of a mixture simulating the atmosphere of venus

Calculations of the flow of the mixture 0.94 CO₂+0.05 N₂+0.01 Ar past the forward portion of segmentai bodies are presented. The temperature, pressure, and concentration distributions are given as a function of the pressure ahead of the shock wave and the body velocity. Analysis of the concentration distribution makes it possible to formulate a simplified model for the chemical reaction kinetics in the shock layer that reflects the primary flow characteristics. The density distributions are used to verify the validity of the binary similarity law throughout the shock layer region calculated.The flow of a CO₂+N₂+Ar gas mixture of varying composition past a spherical nose was examined in [1]. The basic flow properties in the shock layer were studied, particularly flow dependence on the free-stream CO₂ and N₂ concentration.New revised data on the properties of the Venusian atmosphere have appeared in the literature [2, 3] One is the dominant CO₂ concentration. This finding permits more rigorous formulation of the problem of blunt body motion in the Venus atmosphere, and attention can be concentrated on revising the CO₂ thermodynamic and kinetic properties that must be used in the calculation.The problem of supersonic nonequilibrium flow past a blunt body is solved within the framework of the problem formulation of [4].Notation V body velocity - shock wave standoff - universal gas constant - ratio of frozen specific heats - hRt/m enthalpy per unit mass undisturbed stream P pressure - density - T temperature - m molecular weight - c_p specific heat at constant pressure - (X) concentration of component X (number of particles in unit mass) - R body radius of curvature at the stagnation point - _j rate of j-th chemical reaction shock layer P V ² pressure - density - TT temperature - mm molecular weight Translated from Izv. AN SSSR. Mekhanika Zhidkosti i Gaza, Vol. 5, No. 2, pp. 67–72, March–April, 1970.The author thanks V. P. Stulov for guidance in this study.     

Investigation of isothermal flow of a mixture of gas and particles in a channel of variable section

Isothermal flow of a gas with particles is investigated analytically, which makes it possible to analyze all possible flow regimes in channels of different shapes. It is shown that in a channel of constant section there are two possibilities: either an equilibrium regime is established with constant flow parameters, or the gas reaches the velocity of sound, and then further flow in the channel is impossible (blocking of the channel). In a contracting nozzle, blocking also occurs if the channel is sufficiently long. In an expanding nozzle when there are particles in the gas with a velocity lower than the gas velocity, it is possible to have flow regimes with transition through the velocity of sound: a subsonic flow goes over into a supersonic flow and, conversely, it is also possible to have a flow in which there is blocking of the channel, which is quite different from the flow of a pure gas in an expanding nozzle and is due to the influence of interphase friction on the flow. The variation of the pressure along the flow can be nonmonotonic with points of local maximum or minimum which do not coincide with the singular point at which the gas velocity reaches the velocity of sound. In the case of nonequilibrium gas flows with particles in a Laval nozzle, the velocity of the gas may become equal to the isothermal velocity of sound not only in the exit section of the nozzle or in its expanding part, as noted in [4–6], but also at the minimal section, since it is possible to have flows for which the velocities of the phases are equalized at this section.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 61–68, October–December, 1981.     

Experimental investigation of a turbulent jet carrying heavy particles of a disperse phase

The results are given of an experimental investigation of an immersed jet carrying heavy spherical particles in the case of uniform velocity fields of the particles and the gas and uniform concentration of the particles at the nozzle exit. The laser-optical method was used to measure the velocity fields of the gas and the particles and the concentration of the latter in the flow-rate concentration range of the additive from 0 to 1.5 and particle diameters from 35 to 67 m. It was found that the flow in the jet is essentially nonequilibrium, the disequilibrium and intensity of the mixing in the jet depending on the concentration of the additive and the diameter of the particles. The investigation of the initial section revealed a somewhat anomalous behavior of the jet at a comparatively small (₀=0.5) flow-rate concentration of the additive, and this indicates a need to take into account the prehistory of the flow in the construction of a method for calculating the initial section of a two-phase jet.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 26–31, September–October, 1981.     

Control of low-speed turbulent separated flow using jet vortex generators

A parametric study has been performed with jet vortex generators to determine their effectiveness in controlling flow separation associated with low-speed turbulent flow over a two-dimensional rearward-facing ramp. Results indicate that flow-separation control can be accomplished, with the level of control achieved being a function of jet speed, jet orientation (with respect to the free-stream direction), and jet location (distance from the separation region in the free-stream direction). Compared to slot blowing, jet vortex generators can provide an equivalent level of flow control over a larger spanwise region (for constant jet flow area and speed).Nomenclature C _p pressure coefficient, 2(P-P_)/V ² - C _Q total flow coefficient, Q/ v - D ₀ jet orifice diameter - Q total volumetric flow rate - R Reynolds number based on momentum thickness - u fluctuating velocity component in the free-stream (x) direction - V free-stream flow speed - VR ratio of jet speed to free-stream flow speed - x coordinate along the wall in the free-stream direction - jet inclination angle (angle between the jet axis and the wall) - jet azimuthal angle (angle between the jet axis and the free-stream direction in a horizontal plane) - boundary-layer thickness - momentum thickness - lateral distance between jet orifices A version of this paper was presented at the 12th Symposium on Turbulence, University of Missouri-Rolla, 24–26 Sept. 1990     

Steady flow of a liquid metal in a rectangular MHD channel

The known experimental studies of steady flows of a liquid metal in magnetohydrodynamic (MHD) channels of rectangular section [1–4] were performed only for a few values of the Reynolds number, which does not permit a clear delineation of the fundamental governing laws of the flow in the zone of transition from laminar to turbulent flow. In addition, the study of turbulent MHD flows has been limited to two-dimensional channels.Below we present some results of experimental studies of the effect of a transverse magnetic field on the resistance coefficient for mercury flow in an MHD channel with side ratio 1 to 2.5. The choice of a channel with this side ratio was dictated by the need for studies of the intermediate case between flows in two-dimensional and square channels, which differ significantly from one another because of the different effect of the walls parallel to the magnetic field. In our studies, for each value of the Hartmann number the investigations were made for 30–50 values of the Reynolds number.Notation B₀ flux density of the applied magnetic field - M Hartmann number - R Reynolds number - _tm resistance factor of turbulent MHD flow - _* critical value of the resistance factor - geometric parameter of channel - the component of resistance factor in ordinary hydrodynamics due to pulsations - normed function - electric conductivity of metal - viscosity of metal - R₀ shydraulic radius - N smagnetic field parameter     

The secondary flow induced around a sphere in an oscillating stream of elastico-viscous liquid

The present paper is devoted to the theoretical study of the secondary flow induced around a sphere in an oscillating stream of an elastico-viscous liquid. The boundary layer equations are derived following Wang's method and solved by the method of successive approximations. The effect of elasticity of the liquid is to produce a reverse flow in the region close to the surface of the sphere and to shift the entire flow pattern towards the main flow. The resistance on the surface of the sphere and the steady secondary inflow increase with the elasticity of the liquid.Nomenclature a radius of the sphere - b ^ik contravariant components of a tensor - e contravariant components of the rate of strain tensor - F() see (47) - G total nondimensional resistance on the surface of the sphere - g _ik covariant components of the metric tensor - f, g, h secondary flow components introduced in (34) - k ₀ measure of relaxation time minus retardation time (elastico-viscous parameter) - K =k ₀ ²/V ₀ ² , nondimensional parameter characterizing the elasticity of the liquid - n measure of the ratio of the boundary layer thickness and the oscillation amplitude - N, T defined in (44) - p arbitrary isotropic pressure - p _ik covariant components of the stress tensor - p ^ik contravariant components of the stress tensor associated with the change of shape of the material - R =V ₀ a/v, the Reynolds number - S =a/V ₀, the Strouhall number - r, , spherical polar coordinates - u, v, w r, , component of velocity - t time - V(, t) potential velocity distribution around the sphere - V ₀ characteristic velocity - u, v, t, y, P nondimensional quantities defined in (15) - reciprocal of s - density - defined in (32) - defined in (42) - ₀ limiting viscosity for very small changes in deformation velocity - complex conjugate of - oscillation frequency - = ₀/, the kinematic coefficient of viscosity - , defined in (52) - (, y) stream function defined in (45) - =(NT/2n)^1/2 y - /t convective time derivative (1) _ik      

On the effects of a periodic, spanwise variation of suction upon asymptotic suction flow

Summary The effects of superposing streamwise vorticity, periodic in the lateral direction, upon two-dimensional asymptotic suction flow are analyzed. Such vorticity, generated by prescribing a spanwise variation in the suction velocity, is known to play an important role in unstable and turbulent boundary layers. The flow induced by the variation has been obtained for a freestream velocity which (i) is steady, (ii) oscillates periodically in time, (iii) changes impulsively from rest. For the oscillatory case it is shown that a frequency can exist which maximizes the induced, unsteady wall shear stress for a given spanwise period. For steady flow the heat transfer to, or from a wall at constant temperature has also been computed.Nomenclature (x, y, z) spatial coordinates - (u, v, w) corresponding components of velocity - (, , ) corresponding components of vorticity - t time - stream function for v and w - v _w mean wall suction velocity - nondimensional amplitude of variation in wall suction velocity - characteristic wavenumber for variation in direction of z - T temperature - P pressure - density - coefficient of kinematic viscosity - coefficient of thermal diffusivity - (/v _w)² - frequency of oscillation of freestream velocity - nondimensional amplitude of freestream oscillation - /v _w ² - z z - y –v _w y/ - v _w ² t/4 - /v _w - U ₀ characteristic freestream velocity - u/U ₀ - coefficient of viscosity - _w wall shear stress - Prandtl number (/) - q heat transfer to wall - T _w wall temperature - T (T _w–T)/(T _w–)     

Numerical modeling of flow with chemical reactions in a strong shock wave with approximate allowance for translational nonequilibrium

The effect of translational nonequilibrium on the course of chemical reactions in a shock wave is studied using the beam–gas model extended to the case of a multicomponent gas. For Arrhenius reactions of general form with collisions between beam and gas molecules, a modified expression of reaction rate is obtained that takes into account the relative motion of the two media. A procedure for numerical solution of the problem is considered, and calculation results for a shock wave in a dissociating air at an oncoming flow velocity of 6000 m/sec are given.     

Effect of Streamwise Streaky Structures on Turbulization of a Circular Jet

Experimental investigations of the influence of streamwise streaky structures on turbulization of a circular laminar jet are described. The qualitative characteristics of jet evolution are studied by smoke visualization of the flow pattern in the jet and by filming the transverse and longitudinal sections of the jet illuminated by the laser sheet with image stroboscopy. It is shown that the streaky structures can be generated directly at the nozzle exit, and their interaction with the Kelvin–Helmholtz ring vortices leads to emergence of azimuthal beams ( structures) by a mechanism similar to threedimensional distortion of the twodimensional Tollmien–Schlichting wave at the nonlinear stage of the classical transition in nearwall flows. The effect of the jetexhaustion velocity and acoustic action on jet turbulization is considered.     

Formation of an eddy current in the thermal acceleration of a completely ionized plasma

The steady-state plane slowly varying flow of a completely ionized nonviscous quasi-neutral plasma in a shaped channel with continuous metal walls is considered. The Hall effect is taken into account. It is shown that for 1, where is the plasma parameter ( = 8p/B², p is the gas-kinetic pressure of the plasma, and B is the magnetic field strength), the acceleration of the plasma is necessarily accompanied by the appearance of natural electromagnetic fields and an electric current, the distribution of which for small discharge voltages has an eddy-current form. The eddy currents disappear when the discharge voltage is increased. The acceleration of a plasma with isothermal electrons is investigated in detail.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 30–34, November–December, 1971.     

Axial flow of gelling materials through a circular pipe

Summary A set of constitutive equations for a group of incompressible materials of technological importance previously proposed by the authors is used to analyze the axial flow of a gelling Binghamlike material. Through five material parameters these constitutive equations account for the phenomena of breakdown in rigidity after deformation has occurred and of recovery in rigidity in the state of continued deformation or in the state of rest. Due to the complexity of predicting the flow of such nonlinear materials only the steady state behaviour in general seems to be tractable.The solution presented here describes the steady state axial flow of this type material through a circular pipe. It is shown that, depending on the choice of material parameters, two separate solutions may occur. As in the case of axial flow of a Bingham material or a retarded Bingham material a concentric core with rigid body motion is found. Analytically the radius of this core enters into the formulation of the requirements that must be fulfilled to establish a continuous flow field.It is further shown that volume flow rate dependence on the current pressure gradient may be a function of the loading history. For a specific case this dependence is shown in graphical form.     

Influence of transport processes on steady regimes of a chemical flow reactor with reaction of the type a → b,a+b→2c

An approximate analytic solution is obtained to the problem of the concentration distribution in a one-dimensional chemical flow reactor for a reaction of the type A B, A + B 2C in the approximation of a weak reaction. The method of small perturbations up to terms of third order is used. A study is made of the influence of the intensity of longitudinal mixing on the degree of transformation, the selectivity, and the yield. It is found that the optimal level of longitudinal mixing in the weak reaction approxmation is determined by a dimensionless parameter that is a combination of the dimensionless rates of the chemical reactions. The dependence of the optimal Péclet number on this parameter is found. Characteristic regions are determined on the plane of the determining parameters in which the interaction of the physical and chemical processes in the reactor leads to different results, which must be taken into account when choosing the type and the parameters of a chemical reactor.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 106–113, November–December, 1982.     

Influence of Variable Permeability on Combined Convection Along a Nonisothermal Wedge in a Saturated Porous Medium

Mixed convection along a vertical nonisothermal wedge embedded in a fluid-saturated porous media incorporating the variation of permeability and thermal conductivity is studied. The surface temperature is assumed to vary as a power of the axial coordinate measured from the leading edge of the plate. A nonsimilar mixed convection parameter and a pseudo-similarity variable are introduced to cast the governing boundary layer equations into a system of dimensionless equations which are solved numerically using finite difference method. The entire mixed convection regime is covered by the single nonsimilarity parameter =[1+(Ra _x /Pe _x )^1/2]^–1 from pure forced convection (=1) to pure free convection (=0). The problem is solved using nonsimilarity solution for the case of variable wall temperature. Velocity and temperature profiles as well as local Nusselt number are presented. The wedge angle geometry parameter is ranged from 0 to 1.