Scattering and velocity dispersion of ultrasonic waves in polycrystals of orthorhombic symmetry

The scattering coefficients and the velocity of propagation of longitudinal and transverse ultrasonic waves in polycrystals of orthorhombic and higher symmetry are computed by the method of renormalization of the equations of motion. The formulas thus obtained are compared with the known asymptotic expressions for long and short waves. A numerical computation carried out for aluminum shows that for qa 1 (q is the wave number;a is the correlation scale) the power index determining the frequency dependence of the scattering coefficient decreases monotonically from 4 to 2 for the transverse waves, while for the longitudinal waves this dependence is nonmonotonic, i.e., the power index decreases from 4 to 1, after which it increases again to 2. In the Rayleigh region (q _l a < 1.) the scattering coefficient of the longitudinal waves increases with a power index smaller than 4.Translated from Zhurnal Prikladnoi Mekhanikii Tekhnicheskoi Fiziki, No. 3, pp. 180–190, May–June, 1976.     

The Effect of Wettability on Three-Phase Relative Permeability

We study three-phase flow in water-wet, oil-wet, and fractionally-wet sandpacks. We use CT scanning to measure directly the oil and water relative permeabilites for three-phase gravity drainage. In an analogue experiment, we measure pressure gradients in the gas phase to determine the gas relative permeability. Thus we find all three relative permeabilities as a function of saturation. We find that the gas relative permeability is approximately half as much in a oil-wet medium than in an water-wet medium at the same gas saturation. The water relative permeability in the water-wet medium and the oil relative permeability in the oil-wet medium are similar. In the water-wet medium the oil relative permeability scales as k _roS _o ⁴ for S _o>S _or, where S _or is the waterflood residual oil saturation. With octane as the oil phase, k _roS _o ² for S _o<S _or, while with decane as the oil phase, k _ro falls sharply for S _o<S _or. The water relative permeability in the oil-wet medium resembles the oil relative permeability in the water-wet medium for a non-spreading oil such as decane. These observations can be explained in terms of wetting, spreading, and the pore scale configurations of fluid.     

Investigation of a compressible turbulent boundary layer and a region of separation at M=5 by a laser Doppler anemometer

Results are cited of an experimental investigation of the structure of a compressible turbulent boundary layer on a thermally insulated cylinder placed longitudinally in the flow. The experiments were conducted at M=5 and Re_x10⁷. In order to establish a longitudinal positive pressure gradient and a region of separation at the end of the cylinder, a tailpiece in the shape of an axisymmetric isentropic compression surface, or conical flaps with various half angles, were mounted. Profiles of the longitudinal velocity component were measured using p_o' and t_o probes, and also using a laser Doppler anemometer (LDA) with a Fabry-Perot interferometer. In the absence of a longitudinal pressure gradient the velocity profiles measured by the different methods were in satisfactory agreement among themselves and with the results of calculations. In the presence of a longitudinal positive pressure gradient, the velocity profiles become less filled and the static pressure, calculated according to the results of measurements of the velocity with the aid of the LDA and the pressure p_o', varied across the thickness of the boundary layer. In the separated region, the recirculating velocity of the flow was measured with the aid of the LDA.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 175–178, March–April, 1976.     

Hypersonic flow over a narrow delta plate at large angles of attack

The problem of hypersonic flow over a flat delta plate with a high sweepback anglex at angles of attack close to /2 is solved using a numerical algorithm based on transition to the conical solution. The existence of conical flow at /2 with the velocity vector directed towards the apex of the plate is established. Values ofC _p/sin² and the thickness of the shock layer in the plane of symmetry of the plate are given as functions of the hypersonic similarity parameterk=tan tanx. A comparison of the calculated and experimental data shows that they are in good agreement.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.5, pp. 183–185, September–October, 1992.     

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.     

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.     

Approximate solution to nonself-similar problem of motion of a piston after an impact

An approximate solution is obtained to the problem of the motion of a piston after an impact and under the influence of gas pressure under the assumption that the parameter = u_o/a _o, where u_o is the initial velocity of the piston anda _o is the velocity of sound in the gas at rest, is small. Functions that determine the law of motion of the piston and the shock wave, and also the gas flow in the disturbed region are found explicitly to terms of order ³ Translated from Izvestiya Akadeinii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 167–171, November–December, 1982.     

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.     

Self-similar solution for deep-penetrating hydraulic fracture propagation

The propagation of a vertical hydraulic fracture of a constant height driven by a viscous fluid injected into a crack under constant pressure, is considered. The fracture is assumed to be rectangular, symmetric with respect to the well, and highly elongated in the horizontal direction (the Perkins and Kern model). The fracturing fluid viscosity is assumed to be different from the stratum saturating fluid viscosity, and the stratum fluid displacement by a fracturing fluid in a porous medium is assumed to be piston-like. The compressibility of the fracturing fluid is neglected. The stratum fluid motion is governed by the equation of transient seepage flow through a porous medium.A self-similar solution to the problem is constructed under the assumption of the quasi-steady character of the fracturing fluid flow in a crack and in a stratum and of a locally one-dimensional character of fluid-loss through the crack surfaces. Crack propagation under a constant injection pressure is characterized by a variation of the crack sizel in timet according to the lawl(t)=l _o (1+At)^1/4, where the constantA is the eigenvalue of the problem. In this case, the crack volume isVl, the seepage volume of fracturing fluidV _f l ³, and the flow rate of a fluid injected into a crack isQ ₀l ^–1.     

A numerical study of supersonic turbulence

We report on simulations of nonstationary supersonic isotropic turbulent flow using the Piecewise-Parabolic Method on uniform grids of 2048² in two dimensions and 256³ in three dimensions. Intersecting shock waves initiate the transfer of energy from long to short wavelengths. Weak shocks survive for many acoustic times _ac. In two dimensions eddies merge over many _ac. In three dimensions vortex sheets break-up into short vortex filaments within two _ac. Entropy fluctuations, produced by strong shocks, are stretched into filaments over several _ac. These filaments persist and are mirrored in the density. We observe three temporal phases: onset, with the initial formation of shocks; quasi-supersonic, with strong density contrasts; and post-supersonic, with a slowly decaying root mean square Mach number. Compressive modes quickly establish a k ^–2 velocity power spectrum. In three dimensions solenoidal modes build-up during the supersonic phase delineating through time a Kolmogorov k ^–5/3 envelope and leaving a self-similarly decaying k ^–0.9 spectrum at lower wave numbers.This work was supported at the University of Minnesota by grants DE-FG02-87ER25035 from the Office of Energy Research of the Department of Energy, AST-8611404 from the National Science Foundation, and by equipment grants from Sun Microsystems, Gould Electronics, Seagate Technology, and the Air Force Office of Scientific Research (AFOSR-86-0239). Partial support for this work has also come from the Army Research Office Contract Number DAAL03-89-C-0038 funding the Army High Performance Computing Research Center (AHPCRC) at the University of Minnesota. At Nice this work was supported under DRET Contract 500-276, under the GdR CNRS-SPI Mécanique des Fluides, and under two special grants from the Observatoire de la Côte d'Azur.     

Influence of boundary conditions on the convective stability of a rotating horizontal layer of liquid

A theoretical study is made of the critical curves for the onset of convection in a plane horizontal layer of liquid rotating with constant angular velocity for different conditions on the boundary of the layer. It is shown that, in contrast to Chandresekhar's curves [1] obtained under the condition of constancy of the temperature on the boundaries, the curves for a constant heat flux lie significantly lower, so that convection occurs earlier for all Taylor numbers. At large Taylor numbers all the stability curves, as in [1], tend to the asymptotes R_C Ta^2/3, where Ta is the Taylor number and R_C is the critical Rayleigh number. A similar investigation for a nonrotating liquid was made in [2].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 124–129, May–June, 1988.We thank G. S. Golitsyn for the proposed subject and constant interest in the work.     

Laminar boundary layer on blunt bodies with account for vorticity of the external flow

This paper presents the technique for and results from numerical calculations of the hypersonic laminar boundary layer on blunted cones with account for the vorticity of the external flow caused by the curved bow shock wave. It is assumed that the air in the boundary layer is in the equilibrium dissociated state, but the Prandtl number is assumed constant, =0.72. The calculations were made in the range of velocities 3–8 km/sec, cone half-angles _k=0°–20°. With account for the vortical interaction of the boundary layer with the external flow, the distribution of the thermal flux and friction will depend on the freestream Reynolds number (other conditions being the same). In the calculations the Reynolds number R, calculated from the freestream parameters and the radius of the spherical blunting, varies from 2.5·10³ to 5.10⁴. For the smaller Reynolds numbers the boundary layer thickness on the blunting becomes comparable with the shock standoff, and for R<2.5·10³ it is apparent that we must reconsider the calculation scheme. With R>5·10⁴ for cones which are not very long the vortical interaction becomes relatively unimportant. The results of the calculations are processed in accordance with the similarity criteria for hypersonic viscous gas flow past slender blunted cones [1, 2].     

Thermal stability of composite superconducting tape under the effect of a two-dimensional dual-phase-lag heat conduction model

Thermal stability of composite superconducting tape subjected to a thermal disturbance is numerically investigated under the effect of a two-dimensional dual-phase-lag heat conduction model. It is found that the dual-phase-lag model predicts a wider stable region as compared to the predictions of the parabolic and the hyperbolic heat conduction models. The effects of different design, geometrical and operating conditions on superconducting tape thermal stability were also studied.a conductor width, (m) - A conductor cross sectional area of, (m²) - As conductor aspect ratio, (a/b) - b conductor thickness, (m) - Bi Biot number - B dimensionless disturbance Intensity - C heat capacity, (J m^–3 K^–1) - D disturbance energy density, (W m^–3) - f volume fraction of the stabilizer in the conductor - g(T) steady capacity of the Ohmic heat source, (W m^–3) - g_max Ohmic heat generation with the whole current in the stabilizer, (W m^–3) - G_max dimensionless maximum Joule heating - h convective heat transfer coefficient, (W m^–2 K^–1) - J current density, (A m^–2) - k thermal conductivity of conductor, (W m^–1 K^–1) - q conduction heat flux vector, (W m^–2) - Q dimensionless Joule heating - R relaxation times ratio (_T/2_q) - t rime, (s) - T temperature, (K) - T_c critical temperature, (K) - T_c1 current sharing temperature, (K) - T_i initial temperature, (K) - T_o ambient temperature, (K) - x, y co-ordinate defined in Fig. 1, (m) - thermal diffusivity (m² s^–1) - dimensionless time - _i dimensionless duration time - dimensionless y-variable - _o superconductor dimensionless thickness - dimensionless temperature - _c1 dimensionless current sharing temperature - 1 dimensionless maximum temperature - dimensionless disturbance energy - numerical tolerance - x width of conductor subjected to heat disturbances, (m) - y thickness of conductor subjected to heat disturbances, (m) - dimensionless x-variable - _o superconductor dimensionless width - stabilizer electrical resistivity, () - _q relaxation time of heat flux, (s) - _T relaxation time of temperature gradient, (s) - i initial - sc current sharing - max maximum - o ambient     

Numerical investigation and self-similar solutions of the glacier-ocean interaction problem

The mathematical modeling of the heat and mass transfer processes in glaciers is an effective means of investigating and predicting their development. A full explanation of the problem of constructing appropriate mathematical models is given in [1–5]. By analyzing the equations involved [3, 6] it is possible to establish the principal factors and dimensionless numbers determining glacier dynamics and provide justification for neglecting the secondary terms. In particular, a simplified closed system of differential equations for the detailed calculation of all the hydrodynamic characteristics of the glacier can be obtained for K_hj « 1 up to O(K _h ² ), where K_h is the ratio of the vertical and horizontal scales of the ice mass investigated (K_h 10^–4–10^–6). In this case many of the qualitative characteristics of glacier dynamics are preserved even in one-dimensional models within the subisothermal approximation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 3–7, September–October, 1986.     

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.     

Fourier transform mechanical spectroscopy of the sol-gel transition in zirconium alkoxide ceramic gels

The gelation of a ceramic precursor, zirconium alkoxide, has been studied using dynamic oscillatory measurements. The gelation time is controlled by varying the concentrations of zirconium propoxide, hydrolysis with water, and acetylacetone concentration which acts as a chelating ligand. Gelation times were varied from minutes to months. The gelation time varied with zirconium concentration to the –10 power, hydrolysis to the –7 power, and ligand concentration of the –17 power. The sol-gel transition was monitored using the criteria of Winter in which GG ⁿ and tan () = tan . It is shown that the use of multiple superimposed sinusoidal waves to simultaneously measure the moduli at several frequencies is faster than using individual frequency sweep experiments. The selection of rate and strain criteria for brittle network gels is discussed in detail.     

Influence of the atomic weight of the target on the magnitude of the energy accommodation coefficient of ions of a partially ionized gas flow

One of the most essential parameters in the investigation of singularities in molecule interaction with the surface of a solid is the energy accommodation coefficient. Data on the positive ion accommodation coefficients in the energy range 1–100 eV are scarce [1], hence the value of _i is often taken close to one, although this condition is not satisfied in practice for the majority of working gases. In this paper we discuss the resultant measurements of the value of _i in a high-speed flow of rarified plasma.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 83–87, May–June, 1979.     

Pressure pulsations on the surface of a sphere in a subsonic stream

Many data are available on the drag C_x and the distribution of the static pressure over the surface of a sphere [1, 2]. However, there are virtually no data on pulsations of the pressure over the surface of a sphere. In the present paper, the results are given of an investigation of the total and spectral levels of the pressure pulsations at different points of the surface of a sphere at M 0.5–1.0 and Re (1.7–2.7)·.10⁶. It was found that the strongest pressure pulsations occur on the side in the region of the angle 90°. In this region at M 0.6–0.8 the relative total level o/q where q is the velocity head in the oncoming stream, reaches values 0.18–0.22. It was established that at M = 0.7–0.9 narrow-band maxima occur in the spectra of the pressure pulsations at frequencies Sh fD/V = 0.2–0.3. Data are also presented on the pulsations of the base pressure behind a spherical segment with short cylindrical and conical trailing edges.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 164–168, September–October, 1981.     

Stability of stationary traveling waves on the surface of a vertical film of viscous fluid

The stability of stationary traveling waves of the first and second families with respect to infinitesimal perturbations of arbitrary wavelength is subjected to a detailed numerical investigation. The existence of a unique region of stability of the first family is established for wave numbers (₁, ₁) corresponding to the optimal wave regime. There are several regions of stability of the second family ( _k , _k),k=2,3,..., lying close to the local flow rate maxima. In the regions of instability the growth rates of perturbations of the first family are several times greater than for the second family. This difference increases with increase in the Reynolds number. The calculations make it possible to explain a number of experimental observations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 33–41, May–June, 1989.The authors are grateful to V. Ya. Shkadov for his constant interest, and to A. G. Kulikovskii, A. A. Barmin and their seminar participants for useful discussions and suggestions.     

Reduction of gas breakdown voltage with pulsed ionizing radiation

An algorithm is described for computer calculation of the dynamic breakdown voltage of a gas gap affected by a spatially uniform pulse of ionizing radiation. The algorithm is based on numerical integration of a system of nonlinear equations with integral boundary conditions. The program is used to calculate the breakdown voltage of an air gap affected by a bell-shaped ionizing pulse. It is shown that the relative reduction in breakdown voltage can amount to tens of percent for a radiation exposure dose rate P₀ 10⁸ R/sec.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 52–60, November–December, 1973.