On the perturbation front structure for transport processes with spatial–temporal nonlocality

The onedimensional problem of the propagation of a perturbation front from a point instantaneous source for transport processes with spatial–temporal nonlocality is considered. A class of nonlocality kernels with a singularity of the form t^–1 for small times is used. The front propagation speed v is calculated and an expression for perturbations in the vicinity of the front is derived in the form of an asymptotic series in powers of the parameter = t – xv^–1.     

Study of heat transfer in the separation zones formed in front of supersonic jets in a subsonic carrier flow

The heat transfer taking place between the gas and the surface of the plate in the zone of three-dimensional separation of the turbulent boundary layer in front of a set of supersonic jets injected perpendicularly to a subsonic carrier flow is considered. The aim of this investigation is to establish the main physical characteristics of heat transfer in the separation zones in front of jet obstacles and to obtain the distributions of the local heat-transfer coefficients and the temperature of the thermally insulating wall as functions of the parameters of the carrier flow and the injected jets. Analysis of the experimental results yields certain approximating relationships for the distribution of the local heat-transfer coefficients as functions of the Mach number of the carrier flow M, the Mach number of the jet M_j, the relative boundary-layer displacement thickness _s= _s ^* /d, and the degree of jet superheating T_ojT_o relative to the separation zones in front of supersonic jet obstacles.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 68–72, July–August, 1975.     

Numerical investigation of laminar separation in the case of supersonic flow of viscous gas past spiked bodies

The complete Navier-Stokes equations for a compressible viscous perfect heat conducting gas have been used in a numerical investigation of laminar separation in the case of supersymmetric axisymmetric flow past cylinders with a conical nose and a spike at the front of finite thickness. The flow structure has been studied in its dependence on the length of the spike and the half-angle of the conical tip. For the considered free-stream parameters (2 M 6, 100 Re 500) and spike lengths, which do not exceed the diameter of the cylinder, the existence of steady flow regimes has been established and it has been shown that the spike in front of the body reduces its total drag and the heat flux to its surface.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 126–131, March–April, 1984.     

Experimental investigation of separation of turbulent boundary layer in vicinity of a step

The results of an experimental investigation of the separation of a turbulent boundary layer in the vicinity of a step on a flat plate at M = 2 and 3, and Re = U/v = (26–66)·10⁶ m^–1 are given. The step height was varied from 3 to 16 mm, which corresponded to the range of relative heights 1.1 h/ 7.6, where is the thickness of the boundary layer at the point at which the pressure starts to increase in front of the step. The obtained data for the pressure distribution in front of the step, and on its face and top surface, and the results of probe measurements in the separation and adjacent regions provide a more accurate scheme of the flow. The obtained data are compared with the results of other investigations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 73–80, September–October, 1977.We express our thanks to A. M. Kharitonov for valuable comments made during the discussion of this work, and also to M. A. Gol'dfel'd for kindly providing the experimental data for axisytnmetric steps.     

Numerical solution of the Navier-Stokes equations for flow of gas around a rectangle

A difference scheme of the Lax-Wendroff type was used to solve the Navier-Stokes equations for the problem of flow of a perfect gas around a rectangle (cylinder of rectangular cross section) with and without a front plate for subsonic, transonic, and small supersonic flow velocities (Mach numbers 0.3M2 and Reynolds numbers 1R250). The occurrence and development of front, lateral, and rear separation of the flow are discussed, and the aerodynamic characteristics of the considered bodies are determined.Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 10–17, July–August, 1972.     

Nonsteady supersonic flow over spiked bodies

In longitudinal supersonic flow over spiked cylinders nonsteady regimes can occur in which a separation zone is periodically generated at the spike, grows vigorously in size, and then vanishes. Several authors [1–6] have investigated the physical pattern of flow with separation zone fluctuations (using shadowgraphs) and have determined the boundaries of existence of the nonsteady regime as a function of the ratio between the spike length and diameter of the cylinder. The authors, however, did not systematically study the dependence of the pulsation frequency on the freestream Mach and Reynolds numbers or on the relative diameter and tip angle of the spike. We have undertaken such an investigation. We are concerned primarily with the influence of the dimensionless parameters on the Strouhal number Sh of the separation zone pulsations at a spike attached to the front of a flat-ended cylinder. Earlier investigations [4–6] have been carried out using motion pictures with film speeds up to 32·10³ frames/sec. In the present study we used high-speed motion pictures with a speed of 6.25· 10⁵ frames/sec. This speed allowed us to determine the precise sequence of phases of the pulsations and their relative durations, as well as the speed at which the boundaries of the separation zone move.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 118–124, September–October, 1976.     

Comparison of Calculated and Experimental Data on Supersonic Flow past a Circular Cylinder

The supersonic perfect-gas flow past a circular cylinder is studied on the basis of a numerical analysis of the time-dependent two-dimensional Reynolds equations using a differential q– turbulence model with reference to the experimental conditions. The calculations are carried out at Reynolds and Mach numbers Re=2× 10⁵ and M=1.1, 1.3, and 1.7 and the experimental investigations at Re=1.62×10⁵–2×10⁵ and Mach numbers on the interval 0.7 M 1.7. The calculated and experimental data on the pressure coefficient distribution over the cylinder surface, the location of the separation point on the surface, and the pressure drag coefficient are compared.     

Partition of plastic work into heat and stored energy in metals

This study investigates heat generation in metals during plastic deformation. Experiments were designed to measure the partition of plastic work into heat and stored energy during dynamic deformations under adiabatic conditions. A servohydraulic load frame was used to measure mechanical properties at lower strain rates, 10^–3 s^–1 to 1 s^–1. A Kolsky pressure bar was used to determine mechanical properties at strain rates between 10³ s^–1 and 10⁴ s^–1. For dynamic loading, in situ temperature changes were measured using a high-speed HgCdTe photoconductive detector. An aluminum 2024-T3 alloy and -titanium were used to determine the dependence of the fraction of plastic work converted to heat on strain and strain rate. The flow stress and for 2024-T3 aluminum alloy were found to be a function of strain but not strain rate, whereas they were found to be strongly dependent on strain rate for -titanium.     

Mixed convection flow over a vertical plate with localized heating (cooling), magnetic field and suction (injection)

An analysis is carried out to study the effects of localized heating (cooling), suction (injection), buoyancy forces and magnetic field for the mixed convection flow on a heated vertical plate. The localized heating or cooling introduces a finite discontinuity in the mathematical formulation of the problem and increases its complexity. In order to overcome this difficulty, a non-uniform distribution of wall temperature is taken at finite sections of the plate. The nonlinear coupled parabolic partial differential equations governing the flow have been solved by using an implicit finite-difference scheme. The effect of the localized heating or cooling is found to be very significant on the heat transfer, but its effect on the skin friction is comparatively small. The buoyancy, magnetic and suction parameters increase the skin friction and heat transfer. The positive buoyancy force (beyond a certain value) causes an overshoot in the velocity profiles.A mass transfer constant - B magnetic field - C_fx skin friction coefficient in the x-direction - C_p specific heat at constant pressure, kJ.kg^–1.K - C_v specific heat at constant volume, kJ.kg^–1.K^–1 - E electric field - g acceleration due to gravity, 9.81 m.s^–2 - Gr Grashof number - h heat transfer coefficient, W.m².K^–1 - Ha Hartmann number - k thermal conductivity, W.m^–1.K - L characteristic length, m - M magnetic parameter - Nu_x local Nusselt number - p pressure, Pa, N.m^–2 - Pr Prandtl number - q heat flux, W.m^–2 - Re Reynolds number - Re_m magnetic Reynolds number - T temperature, K - T_o constant plate temperature, K - u,v velocity components, m.s^–1 - V characteristic velocity, m.s^–1 - x,y Cartesian coordinates - thermal diffusivity, m².s^–1 - coefficient of thermal expansion, K^–1 - , transformed similarity variables - dynamic viscosity, kg.m^–1.s^–1 - ₀ magnetic permeability - kinematic viscosity, m².s^–1 - density, kg.m^–3 - buoyancy parameter - electrical conductivity - stream function, m².s^–1 - dimensionless constant - dimensionless temperature, K - w, conditions at the wall and at infinity     

Behaviors of flow mechanisms and heat transfer of non-Newtonian fluids through a spinneret

This investigation examines non-Newtonian flow mechanisms and heat transfer characteristics for a micro spinneret. The working fluid, Polyethylene terephthalate (PET), is the raw material of micro fiber, and a large-scale experimental test model was designed to visualize the complex viscous flow system in the micro spinneret. To visualize the complex convective flow system, an experimental test model was constructed, using glycerin instead of PET. The related parameters of PET were compared with those of glycerin. The power law correlates the shear strain with PET viscosity at various temperatures. The pressure distribution along the flow direction was measured and the flow pattern was visualized using polyethylene (PE) powder of 20–40 m. Similar configurations were calculated for micro spinneret physical parameters to determine the thermal flow characteristics. The Reynolds number in the test model is not less than 10^–2. In the non-Newtonian PET working fluid of practical micro spinneret, flows with Re = 10⁴ to 10^–2 are in the same low Reynolds number flow regime. Therefore, the working fluid is expected to have the same flow characteristic. A numerical solution covering the range of approximately Re = 10^–4 at PET confirms that the flow characteristics of glycerin are constant for Re = 1.228 × 10^–2. The Peclet number in the test model can be adjusted to a value similar to that in the micro spinneret. The flow visualization was compared with that of the numerical solution, and the friction factor and Nusselt number in the micro spinneret were analyzed. Finally, numerical results and friction factor with various exit angles of micro spinneret in a triangular zone flow system were also summarized.     

Numerical analysis of simulation accuracy for hypersonic heat transfer in subsonic jets of dissociated nitrogen

One-dimensional problems of the flow in a boundary layer of finite thickness on the end face of a model and in a thin viscous shock layer on a sphere are solved numerically for three regimes of subsonic flow past a model with a flat blunt face exposed to subsonic jets of pure dissociated nitrogen in an induction plasmatron [1] (for stagnation pressures of (10⁴–3·10⁴) N/m² and an enthalpy of 2.1·10⁷ m²/sec²) and three regimes of hypersonic flow past spheres with parameters related by the local heat transfer simulation conditions [2, 3]. It is established that given equality of the stagnation pressures, enthalpies and velocity gradients on the outer edges of the boundary layers at the stagnation points on the sphere and the model, for a model of radius R_m=1.5·10^–2 m in a subsonic jet the accuracy of reproduction of the heat transfer to the highly catalytic surface of a sphere in a uniform hypersonic flow is about 3%. For surfaces with a low level of catalytic activity the accuracy of simulation of the nonequilibrium heat transfer is determined by the deviations of the temperatures at the outer edges of the boundary layers on the body and the model. For this case the simulation conditions have the form: dU_e/dx=idem, p₀=idem, T_e=idem. At stagnation pressuresP ₀2·10⁴ N/m² irrespective of the catalycity of the surface the heat flux at the stagnation point and the structure of the boundary layer near the axis of symmetry of models with a flat blunt face of radius R_m1.5·10^–2 m exposed to subsonic nitrogen jets in a plasmatron with a discharge channel radius R_c=3·10^–2 m correspond closely to the case of spheres in hypersonic flows with parameters determined by the simulation conditions [2, 3].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 135–143, March–April, 1990.     

Peessure intensification on the front of a shock wave propagating in a heterogeneous system

An increase in pressure in the wave front as compared to the pulse initiating the wave has been observed experimentally in a study of shock-wave propagation in aqueous suspensions of bentonite [1]. In suspensions in which the solid phase is in the form of colloidal size particles =10^–7–10^–8 m of the mineral montmorillonite with mass content c=6%, with multishock loading an intensification of this effect from experiment to experiment was observed [2]. In order to study the principles involved in this anomalous intensification of pressure on the shock wave front, as well as to clarify the effect of the nature of the material in the dispersed phase, experiments were performed with particles of another broad class of clay-like minerals — kaolinite.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 86–92, September–October, 1986.     

Properties of two- and three-dimensional separation flows at supersonic velocities

The results are given of experimental investigations into three-dimensional separation of a turbulent boundary layer in the neighborhood of oblique shock waves, wedge-shaped obstacles, and sweptback steps at Mach numbers M = 2, 2.25, 2.5, 3, 4 and Reynolds numbers Re = u/v = (30–36)· 10⁶ m^–1. The characteristic regimes of the separated flows are considered. There is a discussion of the results of comparison and generalization of the pressure distribution in the two- and three-dimensional separation regions, and empirical dependences are also given for determining some geometrical parameters of these regions. An analogy is found in the characteristic pressures, and pressure distribution for a number of two- and three-dimensional separation flows, which suggests that one could use some of the known methods of analysis of two-dimensional separation of a turbulent boundary layer to calculate estimates for the three-dimensional case. This is confirmed by a comparison of calculated and experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 42–50, May–June, 1979.I am grateful to A. M. Kharitonov and V. S. Dem'yanenko for helpful comments made during the work and for discussion of this paper, and also to V. M. Filatov for assistance in some of the experiments.     

Experimental investigation of return currents in electrogasdynamic flows

An investigation is made of return electric currents in electrogasdynamic flows for laboratory sources of unipolar charged particles. These currents play an important role in the process of airplane electrification as a result of the work of jet engines. Models have been built, making it possible to study the behavior of return currents outside and inside an axisymmetric electrogasdynamic flow, in the absence (single-contour source) and the presence (double contour source) of an external annular neutral jet. It is shown that a rise in the return current J^– outside an electrogasdynamic jet is accompanied by a decrease in the take-off current J °. A decrease in the relative distance L from the source to an external grounded surface and an increase in the ratiov of the velocity of the external neutral jet to the velocity of the electrogasdynamic flow lowers J^– in both grounded and insulated models; in the latter case, where J ° J°0, there is an appreciable return current outside the jet. With an increase in the potential of the source from =0 to the floating potential, the current J^– rises, attaining a maximum, and then decreases. This effect is observed also when J^–=0 in both grounded and insulated models. For the case L–1,v=1, the theoretical and experimental dependences of J^– on the potential of the source , retarding the charged particles of the flow under transitional conditions, are in satisfactory agreement.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 127–134, January–February, 1978.In conclusion, the authors thank A. B. Vatazhin for his interest in the work, and A. P. Strekal and V. F. Kudryashov for their participation in the experiments.     

Radiative heat transfer in an emitting,absorbing, and scattering compressed layer

The aim of the paper is to investigate the screening of radiation from the high-temperature part of the compressed layer by the two-phase ablation products of a graphite axisymmetric body moving under the following conditions through a hypersonic air flow: V = 12–18 km/sec, p_s = 10⁵ Pa, R = 1–3 m, and /₀ = (2.54–5.73)·10^–4. Steady and unsteady sublimation regimes of graphite ablation with strong blowing are considered.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 94–103, March–April, 1984.     

Detecting coherent patterns in a flume by using PIV and IR imaging techniques

We investigated the flow field in a turbulent boundary layer in a flume, by using Particle Image Velocimetry (PIV) and Hot-Foil Infrared Imaging (HFIRI) techniques. Coherent patterns in the flow were identified and characterized by using instantaneous velocity and temperature fields. The velocity fields in the streamwise–spanwise plane were measured in parallel to the temperature distribution of the flume bottom. The identified patterns are represented by means of their spatial characteristics – a non-dimensional spatial separation between streamwise patterns, ⁺.     

Convective stability of a weakly conducting liquid in an electric field

In an inhomogeneously heated weakly conductive liquid (electrical conductivity 10^–12–1 cm^–1) located in a constant electric field a volume charge is induced because of thermal inhomogeneity of electrical conductivity and dielectric permittivity. The ponderomotive forces which develop set the liquid into intense motion [1–6]. However, under certain conditions equilibrium proves possible, and in that case the question of its stability may be considered. A theoretical analysis of liquid equilibrium stability in a planar horizontal condenser was performed in [2, 4]. Critical problem parameters were found for the case where Archimedean forces are absent [2]. Charge perturbation relaxation was considered instantaneous. It was shown that instability is of an oscillatory character. In [4] only heating from above was considered. Basic results were obtained in the limiting case of disappearingly small thermal diffusivity in the liquid (infinitely high Prandtl numbers). In the present study a more general formulation will be used to examine convective stability of equilibrium of a vertical liquid layer heated from above or below and located in an electric field. For the case of a layer with free thermally insulated boundaries, an exact solution is obtained. Values of critical Rayleigh number and neutral oscillation frequency for heating from above and below are found Neutral curves are constructed. It is demonstrated that with heating from below instability of both the oscillatory and monotonic types is possible, while with heating from above the instability has an oscillatory character. Values are found for the dimensionless field parameter at which the form of instability changes for heating from below and at which instability becomes possible for heating from above.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 16–23, September–October, 1976.In conclusion, the author thanks E. M. Zhukhovitskii for this interest in the study and valuable advice.     

Stabilization of plasma flow in a transverse magnetic field

Results are given of a theoretical and experimental investigation of the intensive interaction between a plasma flow and a transverse magnetic field. The calculation is made for problems formulated so as to approximate the conditions realized experimentally. The experiment is carried out in a magneto-hydrodynamic (MHD) channel with segmented electrodes (altogether, a total of 10 pairs of electrodes). The electrode length in the direction of the flow is 1 cm, and the interelectrode gap is 0.5 cm. The leading edge of the first electrode pair is at x = 0. The region of interaction (the region of flow) for 10 pairs of electrodes is of length 14.5 cm. An intense shock wave S propagates through argon with an initial temperature T_o = 293 °K and pressure p_o = 10 mm Hg. The front S moves with constant velocity in the region x < 0 and at time t = 0 is at x = 0. The flow parameters behind the incident shock wave are determined from conservation laws at its front in terms of the gas parameters preceding the wave and the wave velocity W_S. The parameters of the flow entering the interaction region are as follows: temperature T ₀ ¹ = 10,000 °K, pressure P ₀ ¹ = 1.5 atm, conduction ₀ ¹ = 3000 ^–1·m^–1, velocity of flow u ₀ ¹ = 3000 m·sec^–1, velocity of sounda ₀ ¹ = 1600 m·sec^–1, degree of ionization = 2%, 0.4. The induction of the transverse magnetic field B = [0, B_y(x), 0] is determined only by the external source. Induced magnetic fields are neglected, since the magnetic Reynolds number Re_m 0.1. It is assumed that the current j = (0, 0, jz) induced in the plasma is removed using the segmented-electrode system of resistance R_e. The internal plasma resistance is R_i = h(A)^–1 (h = 7.2 cm is the channel height; A = 7 cm² is the electrode surface area). From the investigation of the intensive interaction between the plasma flow and the transverse magnetic field in [1–6] it is possible to establish the place x* and time t* of formation of the shock discontinuity formed by the action of ponderomotive forces (the retardation wave R_T), its velocity W_T, and also the changes in its shape in the course of its formation. Two methods are used for the calculation. The characteristic method is used when there are no discontinuities in the flow. When a shock wave R_T is formed, a system of nonsteady one-dimensional equations of magnetohydrodynamics describing the interaction between the ionized gas and the magnetic field is solved numerically using an implicit homogeneous conservative difference scheme for the continuous calculation of shock waves with artificial viscosity [2].Translated from Izvestiya Akademiya Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 112–118, September–October, 1977.     

Asymptotic solutions of the problem of heat and mass transfer of particles in a fluid

Some questions related to asymptotic analysis (as P , where P is the Péclet number) of problems involving heat and mass transfer of particles in a fluid are considered. The first part of the paper investigates the stationary convective diffusion of a solute to a particle near its front critical point (incidence point). An explicit expression is obtained for the concentration in the region of the front critical point of a solid or liquid particle around which a Stokes flow occurs. In the second part of the paper, a unified formula is obtained for the concentration distribution behind the particle. Appropriate limits in this formula determine the concentration in the mixing region and the inner and convective boundary-layer regions of the diffusion wake. In the final part of the paper, a study is made of the diffusion to a chain of absorbing solid spheres of equal radius a at distances1, 1 1/a P^1/3, from each other on the axis of an oncoming Stokes flow; an integral equation is obtained for the local diffusion flux when a chemical reaction with arbitrary kinetics takes place on the surfaces of the spheres. A certain heterogeneity of the material in the paper is due to the investigation in it of various questions that arise in the solution of more general problems (see, for example, [1–14]) which have not been considered hitherto.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza., No. 1, pp. 89–96, January–February, 1979.     

Model of Formation of the Electric Current in Aircraft Jet Engine Ducts

A possible mechanism of formation of electric currents (engine currents) in aircraft engine jets (with subsequent charging of the aircraft) is investigated. This mechanism is a result of the presence of electrons and ions at concentrations of 10⁷–10¹⁰cm^-3 in the gas flow in the engine duct. The electrons and ions are formed in the fuel combustion chamber as a result of chemo- ionization reactions. The wall flow zones in which the electrical quasi-neutrality of the medium is violated are considered. In these zones a nonzero normal component of the electric current is formed on the wall surface and a streamwise electric current develops in the duct. A general functional dependence of the engine current on the basic dimensionless parameters is obtained on the basis of similarity theory and dimensional analysis. Within the framework of electrical diffusion boundary layer theory a model problem of formation of the maximum possible engine current is formulated. A universal system of equations and boundary conditions, which contains no dimensionless parameters, is obtained and investigated. The engine current is qualitatively estimated for real engines and the calculation results are compared with the experimental data obtained under airfield conditions.