Application of the method of integral diffusion to investigation of turbulent transfer

A number of authors have critically examined semiempirical mixing length theories [1]. A defect of these theories is connected with the fact that the magnitude of the mixing length, which is assumed to be small in constructing the theory, turns out in experiments to be comparable with the characteristic dimensions of the flow region. Thus, the concept of volume convection [2–4] or integral diffusion [5], which is understood to be a transfer mechanism in which the friction stress is not expressed in terms of the velocity gradient, is introduced along with the concept of gradient diffusion. In addition, there are a number of experimental papers [6] in which it is shown that the turbulent friction stress cannot be equal to zero at the place in the flow where the derivative of the velocity is equal to zero. Mixing length theory does not describe this effect.It is possible to generalize mixing length theory [7–9] in a way which eliminates these defects. Flow of an incompressible fluid is considered.     

Structure of the front of oil displacement by a solution of an active additive under nonisothermal conditions when the water saturation of the stratum is high

The structure of the front of oil displacement by a solution of an active additive under nonisothermal conditions in the large-scale approximation without allowance for heat losses has been studied in detail by Braginskaya and Entov [1, 2]. In the present paper, this study is augmented by an analysis of displacement problems when the initial water saturation of the stratum is high. These problems simulate the use of active additives and the pumping of hot water in the lat stage of extraction when an appreciable fraction of the oil has already been displaced from the stratum by ordinary flooding and the initial water saturation of the stratum is high. The exposition is based on the earlier studies [1, 2], whose content is assumed known.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 176–180, January–February, 1982.I thank V. M. Entov for suggesting the problem and helpful discussions.     

On the shape of a slender axisymmetric nonstationary cavity

Very few studies have been made of three-dimensional nonstationary cavitation flows. In [1, 2], differential equations were obtained for the shape of a nonstationary cavity by means of a method of sources and sinks distributed along the axis of thin axisymmetric body and the cavity. In the integro-differential equation obtained in the present paper, allowance is made for a number of additional terms, and this makes it possible to dispense with the requirement ¦ In ¦ 1 adopted in [1, 2]. The obtained equation is valid under the weaker restriction 1. In [3], the problem of determining the cavity shape is reduced to a system of integral equations. Examples of calculation of the cavity shape in accordance with the non-stationary equations of [1–3] are unknown. In [4], an equation is obtained for the shape of a thin axisymmetric nonstationary cavity on the basis of a semiempirical approach. In the present paper, an integro-differential equation for the shape of a thin axisymmetric nonstationary cavity is obtained to order ² ( is a small constant parameter which has the order of the transverse-to-longitudinal dimension ratio of the system consisting of the cavity-forming body, the cavity, and the closing body). A boundary-value problem is formulated and an analytic solution to the corresponding differential equation is obtained in the first approximation (to terms of order ² In ), A number of concrete examples is considered.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 38–47, July–August, 1980.I thank V. P. Karlikov and Yu. L. Yakimov for interesting discussions of the work.     

Unsteady supersonic flow around blunt bodies with detached shock wave

The numerical method of calculating the supersonic three-dimensional flow about blunt bodies with detached shock wave presented in [1–3] is applied to the case of unsteady flow. The formulation of the unsteady problem is analogous to that of [4], which assumes smallness of the unsteady disturbances.The paper presents some results of a study of the unsteady flow about blunt bodies over a wide range of variation of the Mach number M=1.50– and dimensionless oscillation frequency l/V=0–1.0. A comparison is made with the results obtained from the Newton theory.     

Calculation of the discharge of underground explosion gases into the atmosphere

Nonstationary gas filtration from the cavity of a camouflaged underground explosion through a disaggregated porous medium is calculated. The computations were carried out for a spherically symmetric gas experiencing two-dimensional motion. A two-term law of filtration was used. The space-time pressure distribution of the gas within the medium was obtained. Motion hodographs of the front of filtration and the interface between the explosion products and air were constructed. The influence of the soil filtration characteristics and pressure in the cavity was investigated. The time at which gas is discharged into the atmosphere is determined based on well-known data on the permeability of certain types of rocks that have undergone the effects of an explosion. The variation of gas flow with time as a function of explosion depth is established.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 111–120, January–February, 1976.     

Transition of nonone-dimensional flows produced by explosions into one-dimensional flows

A particular class of flows resulting from explosions is considered and two processes are analyzed, both independently and as coupled processes: the transition of the solution to the problem of nonpoint explosion to the corresponding point regime and the transition of the solution to the problem of an explosion with nonone-dimensional initial conditions to a corresponding one-dimensional solution (not necessarily a point solution).Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 93–99, July–August, 1983.     

Selection of an initial approximation in an asymptotic representation of the solution of the problem of a point-source thermal explosion in a nonlinearly heat-conducting gas

Qualitative analysis shows [1] that the initial stage of a point-source thermal explosion in a homogeneous stationary gas is characterized by the predominance of radiative heat transfer. This finding is related to the nonlinear dependence of the coefficient of radiative heat transfer on the temperature of the gas T. The function (T) can be assigned in power form =/n T^n–1, where is a dimensional constant and n>1 is the nonlinearity exponent. In complete agreement with the qualitative conclusions in [1], the author of [2] found by the asymptotic method that for short periods of time after the explosion, radiative heat transfer occurs independently of the motion of the gas and completely determines it. Here, the occurrence of the shock wave in [2] is connected with the convergence of the asymptotic solution on the well-known self-similar solution for a thermal explosion in a non-heat-conducting gas [3]. Conversely, the experimental findings and qualitative analysis of the problem in [1, 4] indicate that an isothermal shock wave can occur within a finite period of time after a thermal explosion. The shock then separated from the region heated by radiation [1], while radiative heat transfer turns out to have a diminishing effect on its motion. The role of heat transfer is negligible far from the site of the explosion, and the motion of the shock becomes self-similar [3]. Using the example of a plane thermal explosion in a nonlinearly heat-conducting ideal gas for the case n1, here we propose an asymptotic representation of the solution of the above problem which will make it possible to analyze the generation of an isothermal shock wave.Translated from Zhurnal Prikladnoi Mekhanikii Tekhnicheskoi Fiziki, No. 3, pp. 84–90, May–June, 1986.We thank K. B. Pavlov for his constant attention to the work and his critical observations.     

On physical criteria for the selection of wood for soundboards of musical instruments

In order to develop criteria for the physical evaluation of wood for soundboards of musical instruments, measurements were made of dynamic Young's modulusE, static Young's modulusE, internal frictionQ ^–1 in longitudinal direction, and specific gravity for numerous species of broad-leaved wood. From the results obtained, including those of our previous paper on coniferous wood [1], it was found that the suitability of wood for soundboards could be evaluated by the quantity ofQ ^–1/(E/), and that there were very high correlations betweenQ ^–1/(E/) andE/, and betweenE andE, regardless of wood species. Consequently, it becomes possible to select practically any wood suitable for soundboards by using the value ofE/, which can be measured easily, and it was derived that the relation betweenE/ andQ ^–1 of wood could be expressed by an exponential equation regardless of wood species.     

Instability of a plane axisymmetric flow with a shear discontinuity in the velocity profile

It is proposed to investigate the stability of a plane axisymmetric flow with an angular velocity profile (r) such that the angular velocity is constant when r < r_O – L and r > r_O + L but varies monotonically from ₁ to ₂ near the point r_O, the thickness of the transition zone being small L r_O, whereas the change in velocity is not small ¦₂ – ₁¦ ₂, ₁. Obviously, as L O short-wave disturbances with respect to the azimuthal coordinate (k=m/r_O 1/r_O) will be unstable with a growth rate-close to the Kelvin—Helmholtz growth rate. In the case L=O (i.e., for a profile with a shear-discontinuity) we find the instability growth rate _O and show that where the thickness of the discontinuity L is finite (but small) the growth rate does not differ from _O up to terms proportional to kL 1 and 1/m 1. Using this example it is possible to investigate the effect of rotation on the flow stability. It is important to note that stabilization (or destabilization) of the flow in question by rotation occurs only for three-dimensional or axisymmetric perturbations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 111–114, January–February, 1985.     

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.     

Flow around stepped bodies with strong compression in a shock layer

This article discusses plane and axisymmetric flows of a nonviscous ideal gas around bodies of stepped form, forming with a Mach number M= and an adiabatic indexN1. The greatest amount of attention is paid to the case where there is no Newtonian free layer, but the shock layer is detached at great distances from the nose of the body.Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 4, pp. 104–112, July–August, 1973.     

Some problems of nonisothermal steady flow of a viscous fluid

The paper presents solutions to the problems of plane Couette flow, axial flow in an annulus between two infinite cylinders, and flow between two rotating cylinders. Taking into account energy dissipation and the temperature dependence of viscosity, as given by Reynolds's relation =₀ exp (–T) (₀, =const). Two types of boundary conditions are considered: a) the two surfaces are held at constant (but in general not equal) temperatures; b) one surface is held at a constant temperature, the other surface is insulated.Nonisothermal steady flow in simple conduits with dissipation of energy and temperature-dependent viscosity has been studied by several authors [1–11]. In most of these papers [1–6] viscosity was assumed to be a hyperbolic function of temperature, viz. =_m 1/1+²(T–T_m.Under this assumption the energy equation is linear in temperature and can he easily integrated. Couette flow with an exponential viscosity-temperature relation. =₀ e ^–T (₀, =const), (0.1) was studied in [7, 8]. Couette flow with a general (T) relation was studied in (9).Forced flow in a plane conduit and in a circular tube with a general (T) relation was studied in [10]. In particular, it has been shown in [10] that in the case of sufficiently strong dependence of viscosity on temperature there can exist a critical value of the pressure gradient, such that a steady flow is possible only for pressure gradients below this critical value.In a previous work [11] the authors studied Polseuille flow in a circular tube with an exponential (T) relation. This thermohydrodynamic problem was reduced to the problem of a thermal explosion in a cylindrical domain, which led to the existence of a critical regime. The critical conditions for the hydrodynamic thermal explosion and the temperature and velocity profiles were calculated.In this paper we treat the problems of Couette flow, pressureless axial flow in an annulus, and flow between two rotating cylinders taking into account dissipation and the variation of viscosity with temperature according to Reynolds's law (0.1). The treatment of the Couette flow problem differs from that given in [8] in that the constants of integration are found by elementary methods, whereas in [8] this step involved considerable difficulties. The solution to the two other problems is then based on the Couette problem.     

Formation of a large radiation-induced fire

In connection with ecological and climatic problems and, in particular, the nuclear winter theory much attention has recently been paid to the study of the possible consequences of large fires and explosions [1–5]. Below, on the basis of the model proposed in [6, 7] we investigate the initial stage of development of a fire induced by the light emitted by a powerful explosion in the atmosphere. The situation above the seat of combustion (the aerodynamics of the layer of air adjacent to the ground, the configuration and characteristics of the smoke cloud formed) is analyzed.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 17–25, January–February, 1992.     

Oscillographic study of electrical explosion in copper and gold

An oscilloscope is used to measure electrical resistance as a function of enthalpy in copper and gold during the process of electrical explosion of wire samples. The enthalpy at the initial point of the explosion process was greater in value than at the melting point of the metal. The electrical explosion phenomenon is considered from the viewpoint of the kinetics of the liquid-metalvapor transition under impulse-heating conditions. The degeneration of the initial point of the electrical explosion for liquid-phase heating over periods less than 10^–7 sec is explained by disruption of the stability of homogeneous-vapor-nucleus formation.Translated from Zhurnal Prikladnoi Mekhaniki Tekhnicheskoi Fiziki, No. 3, pp. 54–58, May–June, 1974.     

Hypersonic multicycle gas jet with a high degree of underexpansion at the nozzle exit

Experimental research on highly underexpanded gas jets flowing from supersonic nozzles into an ambient medium has shown that for fairly large Mach and Reynolds numbers at the nozzle exit the jet consists of several cycles or barrels [1–3]. The authors have made a theoretical study of these jets, using the nonstationary analogy method (law of plane sections). An approximate model of the flow is constructed and an analytic solution is obtained for the location of the boundary of the multicycle jet. The corresponding equivalent nonstationary problem of the expansion of a cylindrical slug of gas is solved numerically. The results are found to be consistent with the experimental data and make it possible to explain a number of observations. It is shown, for example, that the experimentally observed decrease in the amplitude of the cycles (maximum radius of the barrels) as they progress downstream is due to the dissipation of energy in shock waves. It appears that the length of the cycles is more or less independent of the dissipation and almost constant. The effect of the removal (supply) of heat, for example, due to radiation, the relaxation of internal degrees of freedom, etc., on the geometry of the jet is examined. It is shown that the removal of heat leads to a decrease in the amplitude of the cycles and the supply of heat to an increase, but, like dissipation, neither affects the length of the cycles. The problem of a jet in a weakly inhomogeneous atmosphere is solved. It has shown that the jet geometry possesses an adiabatic invariant linking the length and amplitude of the cycles.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 27–35, November–December, 1984.     

Shear Instability at the “Explosion Product–Metal” Interface for Sliding Detonation of an Explosive Charge

Periodic perturbations at the explosion product–metal interface were studied experimentally. Experiments were performed for both spherical and plane geometry. Critical conditions of wave formation (detonation velocity of an explosive charge D 6.9 mm/sec) are determined, and an explanation of this effect is given. It is found experimentally that a dynamic pulse causes intense plastic strains at the explosion products–metal interface, leading to thermal softening of the steel boundary layer. In this layer, Kelvin–Helmholtz instability occurs. Calculationanalytical estimates of the critical boundary unstable wavelength agree satisfactorily with experimental results.     

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     

Area rule for integral quantities

In hydrodynamics and aerodynamics there is an area rule for nearly axisymmetric bodies. It states that the drag [1–3], the coefficient of heat transfer and the ablation [4], and also the wake parameters [5] of a three-dimensional body are equal to the analogous quantities for an axisymmetric body which has the same distribution of the cross sectional area along the axis. In some cases, the area rule holds for bodies which depart strongly from axial symmetry [6]. It is shown in the present paper that equality also holds for other integral quantities and not only in hydrodynamic problems.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 157–159, July–August, 1981.We thank Yu. B. Lifshits for helpful comments.     

Two-Phase Models of Formation of Cavitating Spalls in a Liquid

The dynamics of the structure of a liquid layer structure (with microbubbles of a free gas) behind a rarefaction wave front is studied numerically using the two-phase Iordansky–Kogarko–van Wijngaarden model and the frozen mass-velocity field model. An analysis of the initial stage of cavitation by the Iordansky–Kogarko–van Wijngaarden model showed that tensile stresses behind the rarefaction wave front relax quickly and the mass-velocity field in the cavitation zone turns out to be frozen. This effect is used to describe the late stage of the development of the cavitation zone. These models were combined to study the formation of cavitating spalls in a free-surface liquid under shock-wave loading.     

Electric and thermal conductivity anisotropy of an articulated medium

It is well known that articulation may cause the electric and thermal conducting properties of a medium to become anisotropic. Extensive experimental data relating to the conductivity of rock were presented in [1], and according to these data the ambient resistance in the case of an orderly arrangement of cracks noticeably depends on the direction along which it is measured; an ellipsoid of resistance anisotropy can be constructed from the measurement results. A pronounced correlation between the orientations of the resistivity extrema and the orientation of the crack system is observed here. A comparison betwen the direction rose of the fractures and the direction rose of the articulation carried out for different regions has shown that they are identical. A crack density tensor T describing the average (with respect to a given volume) geometry of the articulation has been introduced [2, 3]. In the current work, it is proved that T can be effectively used in problems involving anisotropic electrical and thermal conductivity. The resistivity tensor and thermal-conductivity coefficient tensor K, which characterize the anisotropy of the electrical and thermal conducting properties, are expressed in terms of t. The structure of this relation is established; the equations presented allow us to find the form of and K if the articulation parameters are known.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 141–144, January–February, 1976.