Calculation of laminar flow of a viscous fluid between rotating disks

The results are given of a numerical investigation of the laminar flow of a viscous incompressible fluid with heat transfer from the periphery to the center between two rotating disks. The system is a simplified model of one of the elements of the cooling circuit of a gas turbine. The complete Navier—Stokes equations in the vortlcity—flow function variables were solved by an explicit conservative scheme with appoximation of the convective terms of divergence type by directed differences. The calculations were made in a wide range of variation of the dimensionless determining parameters of the problem. The results agree well with the known experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 76–81, January–February, 1982.We thank V. M. Kapinos for discussion and helpful comments.     

Effect of fluid microstructure on stability of plane two-layer flows

The stability of plane two-layer Couette and Poiseuille flows, where the lower layer consists of a Grad-model fluid and the upper layer is a viscous Newtonian fluid, is investigated. The disturbances are assumed to be of the long-wave type, and the analysis involves expansion in wave numbers and is limited by two approximations. Numerical calculations are made for some values of the parameters. The calculations indicate that the rotational energy of the fluid in the lower layer has a destabilizing effect on the flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 125–127, July–August, 1978.     

Simulation of the Onset of Nonstationarity and Chaos in a Hydrodynamic System Governed by a Small Number of Degrees of Freedom

The hypothesis of the onset of nonstationarity and chaos in a hydrodynamic system as a result of the nonlinear interaction of a small number of degrees of freedom is verified experimentally with reference to fluid convection in a toroidal channel. Regimes of motion of a fluid medium which correspond qualitatively to the Lorenz model are obtained experimentally. These include steady-state regimes, their bifurcations, nonuniqueness and instability, unsteady periodic and stochastic regimes. The spectral and statistical characteristics of the and unsteady processes are investigated, the nature of the onset of chaos is analyzed, and the results are compared with calculations. The mathematical model of the problem is refined.     

Quasi-three-dimensional calculation of flow in blade passages of turbines

The flow in turbomachines is currently calculated either on the basis of a single successive solution of an axisymmetric problem (see, for example, [1-A]) and the problem of flow past cascades of blades in a layer of variable thickness [1, 5], or by solution of a quasi-three-dimensional problem [6–8], or on the basis of three-dimensional models of the motion [9–11]. In this paper, we derive equations of a three-dimensional model of the flow of an ideal incompressible fluid for an arbitrary curvilinear system of coordinates based on averaging the equations of motion in the Gromek–Lamb form in the azimuthal direction; the pulsation terms are taken into account in the equations of the quasi-three-dimensional motion. An algorithm for numerical solution of the problem is described. The results of calculations are given and compared with experimental data for flows in the blade passages of an axial pump and a rotating-blade turbine. The obtained results are analyzed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 69–76, March–April, 1991.I thank A. I. Kuzin and A. V. Gol'din for supplying the results of the experimental investigations.     

Impact of a figure of revolution in a stream of incompressible fluid with separation of a jet

The impact interaction of bodies with a fluid in a flow with jet separation has been considered in [1–3], for example. This investigation was in the two-dimensional formulation. The present paper considers the three-dimensional problem of impact of a figure of revolution in a stream of an ideal incompressible fluid with separation of a jet in accordance with Kirchhoff's scheme. A boundary-value problem is formulated for the impact flow potential and solved by the Green's function method. A method for constructing the Green's function is described. Expressions are given for the coefficients of the apparent masses. The results are given of computer calculations of these coefficients in the case of a cone using the flow geometry of the corresponding two-dimensional problem.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 176–180, November–December, 1980.     

Interaction between an acoustic wave and a disc

A numerical solution is obtained to the problem concerning a pressure measurement at the boundary between an ideal compressible fluid and a solid wall. It is assumedthat the fluid occupies a semiinfinite cylinder with a rigid bottom into which an elastic disc is inserted and heldfirmly around its edges. Motion is produced by a pressure wave originating at infinity. A finite-difference grid for this application is described and the results of actual calculations are shown.Deceased.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 84–91, January–February, 1972.The authors thank L. M. Flitman for reviewing the work.     

A scheme of developed cavitation flow past a wedge

A scheme is proposed for studying the symmetric steady flow with developed cavitation of an ideal incompressible and weightless fluid past a wedge in a channel. This scheme generalizes the existing schemes of cavitation flow past bodies and describes flow that is intermediate between the flow past obstacles in the Riabouchinsky and Efros schemes. Detailed calculations have been made for the drag coefficient and the cavity size in the case of a plate in an unbounded flow. The results of the calculations are tabulated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 165–170, January–February, 1983.I thank P. M. Ivanov, Kh. Kh. Kalazhokov, and T. Sokhov for assistance in the computer calculations.     

The maximum flow rate principle and vortex chamber aerodynamics

It is shown that for fixed kinetic energy density the maximum flow rate principle previously used for determining the radius of the free surface of an incompressible fluid flowing from a centrifugal nozzle admits an equivalent formulation within the context of the Lagrangian formalism, which means that the principle can easily be extended to the case of a compressible gas. The results of the calculations are compared with experiment.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 49–55, May–June, 1989.     

Percolation model of two-phase flow through porous media

A physical model of the process of two-phase flow of immiscible fluids through a porous medium is developed and used to make an analytical calculation of the dependence of the relative phase permeabilities on the saturation of the medium by one of the phases. The theory is compared qualitatively with experiment for a model capillary radius frequency function and quantitatively with numerical calculations made on a computer. In both cases good agreement is obtained. The pressure dependences of the phase permeabilities are analyzed. The question of residual saturation with the wetting fluid after completion of the displacement process is investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 88–95, January–February, 1987.     

Principles of Integrated Flow Modeling

Integrated flow modeling is the combination of a traditional flow simulator with a petrophysical model. By combining a petrophysical model with a traditional flow model, it is possible to perform calculations that improve our ability to monitor fluid movement in porous media. This paper outlines the formulation of an integrated flow model IFLO and its multi-variable, Newton–Raphson IMPES solution procedure. The benefits of integrated flow modeling and the underlying principles involved in the integration of a flow model with a petrophysical model are presented. Results from the IFLO model are used to illustrate the principles.     

Calculation of a Heat Flow from a Spherical Particle in a Diatomic Gas

The problem of heat flow from a uniformly heated spherical particle in a diatomic gas is considered. The paper reports results of numerical calculations for an analog of the Bhatnagar–Gross–Krook model of the collision integral under for purely diffuse reflection of the gas molecules from the surface.     

Unsteady gravity-elastic and gravity-capillary ship waves

The development of three-dimensional waves generated by a region of pressures moving uniformly and rectilinearly over the surface of a thin elastic isotropic plate covering an ideal fluid layer of finite depth is investigated. The pressures act starting at a certain instant. A qualitative similarity between the waves occurring and gravity-capillary waves is noted. The calculations are made for an ice cover. This model problem permits examining a number of properties of the oscillations of the ice cover occurring when hauling freight over ice roads, landing and takeoff of aircraft from ice fields, etc. [1]. The development of ship waves in a fluid of finite depth in the absence of a floating plate was investigated in [2, 3] and gravity-capillary waves were studied in [4–6]. Certain properties of steady three-dimensional waves occurring during movement of a load over the surface of a floating elastic plate were established in [1].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 26–32, September–October, 1978.     

Flexural perturbations of free jets of maxwell and Doi-Edwards liquids

Flexural perturbations of high-velocity free jets of drop liquids moving in air are reinforced by the fact that the air pressure on the concave sections of the jet surface is greater than on the convex sections. The linear and nonlinear stages of development of flexural perturbations were studied in [1–5] for viscous Newtonian fluids. The effect of elastic stresses in the fluid on the growth of flexural perturbations of jets was first examined in [6], where it was assumed in an analysis of the growth of small disturbances that surface tension was constant along the jet, i.e., the investigators actually studied a tensed string. The studies [7, 8] examined the linear stage of growth of flexural perturbations of jets of Maxwell liquids. Our goal here is to analyze the dynamics of long-wave flexural perturbations of jets of viscoelastic fluids in both the linear and nonlinear stages of development. The rheological behavior of the fluid is described by two models — the phenomenological (Maxwell) model and the physical-molecular (Doi-Edwards) model. It is shown that the disturbances are oscillatory in character in the nonlinear stage of development. Meanwhile, the results of calculations performed with the Maxwell (M) and Doi-Edwards (DE) rheological models in the given problem agree with each other quantitatively as well as qualitatively.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 43–53, November–December, 1986.     

Ventilated entry of a slender profile into a compressible liquid at subsonic velocity

The problem of vertical entry at subsonic velocity into an ideal compressible fluid is solved in the linear formulation for a slender profile with open attached cavity. An integral equation is obtained for the potential of the accelerations. Expressions are given for the calculation of the drag of a thin wedge and also some results of calculations which show that in the limiting case of infinite depth of penetration, which corresponds to stationary flow past the thin wedge with separation of a jet, an analog of the Prandtl—Glauert theorem holds.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 9–17, July–August, 1980.     

Effect of the percolation heat transfer component on the temperature field and thawing dynamics of soils

The effect of the convective heat transfer component on the temperature field and thawing front dynamics of soils is investigated for high fluid percolation velocities in the thawed zone. The steady state interchange and approximate self-similarity methods are used to obtain upper and lower bounds of the solution of the Stefan problem with a convective heat transfer component in a porous medium. From the results of the calculations conclusions are drawn concerning the accuracy and limits of applicability of the solutions obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 166–171, March–April, 1987.     

Shock Thickness in Monatomic Gases

The entropy balance of a Navier–Stokes–Fourier fluid is used to predict the thickness of a shock wave as a function of the Mach number. The results are in good agreement with experimental observations. Indeed the agreement of our thermodynamic calculations with experiments is better than that of the actual solution of the Navier–Stokes–Fourier equations by Gilbarg and Paolucci [1].     

Effect of the wettability of the reservoir rock on the flow into a well

The effect of the wettability of the reservoir rock on the productivity of a well in a flooded reservoir is analyzed for immiscible fluid systems of the oil-water type by means of a computational experiment. The calculations take into account the presence of a drilling mud filtrate penetration zone in the neighborhood of the well.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 172–175, September–October, 1990.     

Boundary value problems for a model Boltzmann equation with frequency proportional to the molecule velocity

Exact solutions of a model Boltzmann equation with a collision frequency that depends on the molecule velocity and with a BGK (Bhatnagar-Gross-Krook) collision operator are constructed for the problems of weak evaporation and temperature jump in a rarefied vapor above a plane surface. The numerical calculations and a comparison with previous results are given.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 140–153, May–June, 1996.     

Internal pulsations in flows of finely dispersed suspensions

The results are given of calculations for the flow of a finely dispersed suspension when momentum and energy are exchanged between individual particles exclusively through the ambient fluid, i.e., the role of direct collisions between particles is negligible. Using the results, one can not only calculate the rms characteristics of the pseudoturbulence and, in particular, find the stresses in the dispersed phase but also to give a natural explanation of the phenomena observed in experiments on sedimentation and hydrodynamic self-diffusion of particles in monodisperse suspensions.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 91–100, May–June, 1993.