Measurement of parameters of a gas suspension behind a shock wave in foam

A study has been made of the propagation of a shock wave in dry polyhedral foam with cell diameter 1 cm. The experiments were made in a shock tube in the range of Mach numbers M < 1.4 of the shock wave. The interaction of the shock wave with the foam was photographed. This established that the destruction of the foam by the shock wave leads to the formation of a gas-droplet flow behind the shock front. To determine the parameters of the suspension, the flow was probed by He-Ne lasers with different radiation wavelengths. The spectral-transparency method was used to find the modal diameter of the droplets of the gas suspension and the volume concentration of the droplets in the flow. The modal diameter of the droplets was 2m, and the volume concentration of the droplets decreased downstream.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 134–141, May–June, 1993.     

Time studies of ionization processes

Summary Measurements of the temporal growth of ionization between parallel plane electrodes in hydrogen have been made. The results show that for low values ( 40 V/cm mm Hg) of the ratio of electric fieldE to gas pressurep the growth times can be short ( 1s for over-voltages V 1 %) while at values ofE/p 300 V/cm mm Hg the times are of the order of milli seconds withV 5%. Comparison of the experimental data with Davidson's mathematical analysis of current growth based upon the action of primary and secondary ionization processes shows that the relative significance of the possible secondary processes changes asE/p is altered. For the low values ofE/p, the predominant secondary process contributing to the growth was found to be photoelectric emission from the cathode, but with increasing values ofE/p the role of positive ion interaction with the cathode becomes increasingly important. No single secondary process was exclusively operating in any of the conditions examined.     

Calculation of transverse flow of a stream of rarefied gas past a plate

We give the results of a calculation by the Monte Carlo method of the coefficient of resistance and the field of flow past a plate placed perpendicular to a stream of rarefied gas at Mach numbers M = 2–20 and Reynolds numbers Re₀27. The calculations were carried out for two forms of the law governing the variation of the coefficient of viscosity as a function of temperature (T, T). The results are compared with available calculated and experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 106–112, July–August, 1976.     

Experimental investigation of the recovery of the total pressure in a hypersonic wind tunnel with conical and profiled nozzles

Measurements have been made of the coefficient of recovery of the total pressure of a gas flow exhausting from axisymmetric and conical profiled hypersonic nozzles into a cylindrical channel of diameter equal to or greater than the nozzle exit and also in the presence of an Eiffel chamber. The experiments were made at Mach numbers M = 4.83–12.4 in the isentropic core. It is shown that the values of differ slightly (by 5%) from the corresponding value for a normal shock wave at the number M determined for a onedimensional flow by the ratio of the area of the cylindrical channel to the area of the critical section of the nozzle.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 170–173, January–February, 1984.     

A Numerical Study of the Critical Gas Saturation in a Porous Medium

We use porenetwork simulations to study the dependence of the critical gas saturation in solutiongas drive processes on the geometric parameters of the porous medium. We show that for a variety of growth regimes (including global and local percolation, instantaneous and sequential nucleation, and masstransfer driven processes), the critical gas saturation, Sgc, follows a powerlaw scaling with the final nucleation fraction (fraction of sites activated), fq. For 3D processes, this relation reads Sgcfq0.16, indicating a sensitive dependence of Sgc to fq at very small values of fq.     

Propagation of small disturbances in a relaxing and radiating diatomic gas in vibrational nonequilibrium

In radiation gasdynamical problems, where the primary object of investigation is a moving gas, the influence of radiation on the parameters of the gas flow is usually neglected to avoid overcomplication of the problem. The growth and behavior of initial disturbances in a scattering, radiating, absorbing, viscous, heat-conducting gas characterized by local thermodynamic equilibrium has been investigated previously [1]. However, for low pressures (p10^–4 to 10^–3 technical atm) and fairly high temperatures of the active molecular degrees of freedom (T10³ to 3·10³K) the distribution of the molecules among the vibrational levels can differ markedly from the equilibrium distribution due to the or der-of-magnitude closeness of the vibrational relaxation time _c associated with collisions and the radiative deactivation time * of excited molecules [2, 3]. We now analyze normal modes in a vibrationally nonequilibrium medium with allowance for radiation scattering in the vibrational-rotational band. We formulate a dispersion relation and discuss some limiting cases.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 168–171, September–October, 1976.The author is grateful to V. I. Kruglov, Yu. V. Khodyko, and M. A. El'yashevich for their interest and discussions.     

Slow flow of gas past a strongly heated sphere in the presence of blowing and evaporation from its surface

A solution is obtained to the problem of the simultaneous influence of blowing (evaporation) and large temperature differences on the flow past a sphere and on the force acting on it with allowance for the Burnett thermal stresses in the momentum equation. It is assumed that the Reynolds numbers calculated using the blowing velocity and the velocity of the oncoming flow, respectively, have the order Re_w 1 and Re 1. The temperature difference is determined by the boundary conditions, namely, a constant temperature T_w T on the surface of the sphere (VT/T 1). The problem is solved by the method of matched asymptotic expansions with respect to the small parameter Re. The equations reduce to a system of ordinary differential equations, which are solved numerically by the orthogonal sweep method [1]. It is found that under certain conditions the drag of the sphere can become negative.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 128–134, July–August, 1982.I thank O. G. Fridlender for valuable advice and interest in the work.     

Plastic deformation of metals subjected to intensive sources

The elastoplastic strain of metals being formed when they melt under the effect of a point heat source with a pulse duration greater than 10^–6 sec is considered in this paper. The time development of the plastic strain and pressure domains in the melt is investigated. It is shown that two plastic strain domains occur during the interaction under consideration: a relatively broad domain of mechanical influence and a narrow domain of thermal influence. The stress-strain distributions as well as the hydrostatic pressure in the fluid are determined by a quasistationary temperature distribution starting with times corresponding to half (of the quasistationary) the value of the melt radius X 0.5. It is shown that the dimensions of the weak and strong plastic strain domains formed by heat and acoustic waves grow continuously to the quasistationary values, while the hydrostatic pressure in the fluid reaches the maximum value for X 0.3...0.4. The ratio between the radii of the plastic strain zones and of the liquid bath for a quasistationary temperature distribution in the first domain lies within the range 10–50, and does not exceed 1.7 for Cu, Ni, and Fe in the second. The anomalous nature of the development of the strong plastic strain domain in Al, because of migration of the metal grain boundaries to result in collapse of the domain for the values X 0.5 accompanied by a jumplike diminution in the hydrostatic pressure in the fluid, is noted.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 129–140, May–June, 1976.     

Non-Markovian diffusion process in polymers and stretched exponential relaxation

In this contribution, we model the long-time behaviour of the desorption from an LDPE sheet, using non-Markovian random walks. It is shown that the mass of penetrant in the final stage of desorption decays as t ^–m , where m is proportional to the exponent of the probability distribution (t) t ^–(1+u), 0 < v < 1. Furthermore, it is shown that this model may lead to the so-called mechanical stretched exponential relaxation, and that Wagner's memory function can be obtained as a special case.Presented at the second conference Recent Developments in Structured Continua, May 23–25, 1990, in Sherbrooke, Québec, Canada     

“Thermal layer” effect in MHD: Interaction of a parallel shock with a layer of decreased density

Interaction of a parallel fast MHD shock with a layer of decreased density is discussed using ideal MHD approach. This is an extrapolation of gas dynamic thermal layer effect on ideal MHD. Computer simulations show that a magnetic field of a moderate intensity ( 1) may change the character of the flow for intermediate Mach numbers (M 5) and a new raking regime may occur which is not observed in the absence of a magnetic field. Self similar precursor analogous to that in gas dynamics may develop in the case of highM and low density in the layer but magnetic forces essentially decrease its growth rate. This problem appears in connection with cosmical shock propagation where planetary magnetic tails play the role of the thermal layer, and it may also be observed in the laboratory when the shock is strong enough to heat the walls ahead of it.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Gas flow in cylindrical capillaries under intermediate conditions

At present, there are sufficient solutions of the problem of free-molecular gas flow through a short cylindrical channel, for example, [1–3]. In intermediate flow conditions, for Knudsen number Kn 1, solutions have been obtained for the limiting cases: an infinitely long channel [4] and a channel of zero length (an aperture) [5]. However, no solution is known for short channels for Kn 1. The present work reports a calculation by the Monte Carlo method of the macroscopic characteristics of the gas flow through a short cylindrical channel (for various length—radius ratios), taking into account intermolecular collisions.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 187–190, January–February, 1977.     

Entropy effects in hypersonic flow over blunt delta wings

The problem of hypersonic flow over blunt delta wings is considered. It is shown that in the case of large wing lengths x -100, where x is the longitudinal coordinate measured in blunt nose radii, extremal flow regimes characterized by an essentially nonuniform distribution of the gas dynamic parameters (density, entropy, Mach number) may be realized in the shock layer near the windward surface of the wing. The location of the zones of flow convergence or divergence on the surface of a delta wing with sweep angle x=75° is established. For the same wing the ranges of Mach numbers M and angles of attack leading to extremal flow regimes are indicated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, 178–181, March–April, 1991.     

Development of dynamic perturbations in initial stage of a point explosion in a thermally conducting gas

The one-dimensional perturbations originating in a cold homogeneous gas (T₁ = 0, ₁ = const) by the instantaneous release of finite energy at the origin of the coordinates are considered. The starting equations are compiled for a gas in which the heat-transfer mechanism is simulated by a nonlinear thermal conductivity with coefficient Tⁿ. Transformation of the equations to the dimensionless form by the introduction of natural variable allows the simplest path for investigating the process as a whole to be shown by means of the method of perturbations. The initial approximation corresponds to the well-known solution for a thermal wave [1], while subsequent approximations describe the joint development of both, thermal and dynamic perturbations. An investigation of the properties of the solutions and an example of the calculation of the first two approximations (without taking account of the starting approximation) for the case of a point spherical explosion with n = 5 gives a representation of the formation of the shock wave.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 55–62, January–February, 1978.     

Unsteady effects in a thin viscous shock layer near a three-dimensional stagnation point of a body moving with given acceleration and deceleration

An unsteady viscous shock layer near a stagnation point is studied. The Navier-Stokes equations are analyzed in the limit 1, Re₀ , df/dt = ^n-mF(t/^m). The Reynolds number Re₀ is defined in the paper by Eq. (1.3) (df/dt is the velocity of the body with respect to an inertial frame of reference moving with the original steady velocity –V'_t8, ₂ = ( – 1)/( + 1)). Various flow regimes in the case 1, l, n max(2m, m + 1), m 0, where ² = 1/Re₀ are analyzed. Equations are derived that generalize the asymptotic analysis to the case of a viscous unsteady flow of gas in a thin three-dimensional shock layer. The problem of a thin unsteady viscous shock layer near the stagnation point of a body with two curvatures is formulated. Examples of numerical solution are given for different ratios of the principal curvatures of the body, the wall temperature, the parameters of the original steady flow, and the acceleration and deceleration regimes.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 100–111, March–April, 1981.I thank Yu. D. Shevelev for a fruitful discussion of the work.     

Boundary conditions for the equations of two-temperature gas dynamics of a binary mixture with strongly differing masses of the components

A study is made of the problem of the boundary conditions for the equations of two-temperature gas dynamics for a binary mixture with strongly differing masses when (m/M)^1/2 Kn 1 (Kn is the Knudsen number, m is the mass of the light molecules, and M the mass of the heavy molecules). The flow structure is established at velocities of the light and heavy components of the order of the velocity of sound of the heavy component. The formulation of the boundary conditions for the gas-dynamic equations is investigated. It is shown that the only closed boundary layer theory is Prandtl's theory taking into account terms of order Kn^1/2.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 93–98, September–October, 1982.I thank M. N. Kogan, N. K. Makashev, and E. S. Asmolov for assistance in the work and valuable discussions.     

Asymptotic solution of the thin viscous shock layer equations at low Reynolds numbers for a cold surface

Hypersonic three-dimensional viscous rarefied gas flow past blunt bodies in the neighborhood of the stagnation line is considered. The question of the applicability of the gasdynamic thin viscous shock layer model [1] is investigated for the transition flow regime from continuum to free-molecular flow. It is shown that for a power-law temperature dependence of the viscosity coefficient T the quantity (Re)^1/(1+), where = ( – 1)/2 and is the specific heat ratio, is an important determining parameter of the hypersonic flow at low Reynolds numbers. In the case of a cold surface approximate asymptotic solutions of the thin viscous shock layer equations are obtained for noslip conditions on the surface and generalized Rankine-Hugoniot relations on the shock wave at low Reynolds numbers. These solutions give simple analytic expressions for the thermal conductivity and friction coefficients as functions of the determining flow parameters. As the Reynolds number tends to zero, the values of the thermal conductivity and friction coefficients determined by this solution tend to their values in free-molecular flow for an accommodation coefficient equal to unity. This tending of the thermal conductivity and friction coefficients to the free-molecular limit takes place for both two-and three-dimensional flows. The asymptotic solutions are compared with numerical calculations and experimental data.Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, 2004, pp. 159–170. Original Russian Text Copyright © 2004 by Brykina.     

Investigation of the flow past wings of infinite span with a blunt leading edge in the vorticity interaction regime

An asymptotic analysis of the Navier-Stokes equations is carried out for the case of hypersonic flow past wings of infinite span with a blunt leading edge when 0, Re , and M . Analytic solutions are obtained for an inviscid shock layer and inviscid boundary layer. The results of a numerical solution of the problems of vorticity interaction at the blunt edge and on the lateral surface of the wing are presented. These solutions are compared with the solution of the equations of a thin viscous shock layer and on the basis of this comparison the boundaries of the asymptotic regions are estimated.deceasedTranslated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 120–127, November–December, 1987.     

MHD-Effects Due to the Hypersonic Motion of a Cylindrical Body in the Magnetosphere of a Planet for Mutually Perpendicular Orientations of the Generatrix and Magnetic Field

MHD-effects associated with the movement of a weakly conducting cylindrical body in a planetary atmosphere are analyzed numerically. The longitudinal axis of the body is perpendicular to the direction of motion and the field lines of the planetary magnetic field. In the calculations we used data similar to those for the collision of the Shoemaker-Levy 9 comet with Jupiter. The simulation is developed for two atmospheric levels: H100 km (magnetic pressure number R _H1) and H280 km (R _H1). It is shown that the maximum strength of the induced magnetic field is 2–3 orders of magnitude greater than the planetary magnetic field. For small R _H, analytical expressions giving a fairly reliable estimate for the field strength in the shock-compressed space ahead of the body are obtained.     

Boundary kinetic effects in the problem of slow flow over an evaporating heat-conducting spherical particle

It is shown that for sufficiently large values of the thermal conductivity of the condensed phase' as compared with the thermal conductivity of the vapor (/' Kn) the effects associated with the presence of a Knudsen layer on the evaporating surface must be taken into account in order to obtain a solution of the problem of a spherical particle in a slow (Re, 1) continuum (Knudsen number Kn 1) flow of its own vapor. The drag is calculated for various types of boundary conditions on the particle surface.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 134–139, March–April, 1987.In conclusion the authors wish to thank V. S. Galkin and M. N. Kogan for useful discussions.     

Interaction of moderately strong shock waves with a cylinder

The load and force acting on an infinite circular cylinder diffracting a moderately strong shock wave (pressure ratio across the front 1.01–5) are found. The process is simulated mathematically by means of a finite-difference scheme of second order of accuracy. For = 1.4, systematic calculations have been made in a narrow range of shock strengths, which has made it possible to obtain detailed characteristics of not only the transient stage of the process but also the steady state.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 113–119, March–April, 1979.