Numerical modeling of the turbulent convection mode in a vertical layer

An approach to the numerical modeling of turbulent natural convection modes on the basis of two-dimensional nonstationary Navier-Stokes equations without the use of additional empirical information is elucidated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkostii Gaza, No. 5, pp. 8–15, September–October, 1977.The authors are grateful to A. G. Kirdyashkin for consultations on the method and results of the experiments to G. S. Glushko for useful remarks, and to K. G. Dubovik for aid in performing the computations.     

Effect of rotation on the convective stability of large-scale disturbances in a turbulent fluid

Linear equations of turbulent convection in the presence of rotation are derived within the framework of a phenomenological approach. It is shown that the amplification of large-scale disturbances is possible only for the essentially inhomogeneous problem when the dimensions of the large-scale disturbance exceed the characteristic scale of density variation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 3–9, July–August, 1989.     

Thermal convection in a nonequilibrium turbulent medium with rotation

The equations of thermal convection in a rotating plane horizontal layer of nonequilibrium turbulent fluid are obtained, the system of equations is linearized and the boundary value problem is formulated. Some general properties of the perturbation spectrum are found and a solution, which includes the classical solution in the absence of turbulence as a limiting case, is obtained.Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 62–70, November–December, 1994.     

Turbulent thermal convection in wide horizontal fluid layers

Turbulence in thermal convection is investigated for flows in which the production of turbulence energy is due solely to buoyancy, and the statistics of the flow are homogeneous in horizontal planes. New experimental results for high Rayleigh number unsteady turbulent convection in a horizontal layer heated from below and insulated from above are presented and compared to turbulent Rayleigh convection, convection in the planetary boundary layer, and laboratory penetrative convection. Mean temperature fields are correlated in terms of wall layer scales and convection scales. Joint statistics of turbulent temperature and horizontal velocity and vertical velocity through fourth order are presented for the core region of the convection layer.This paper was presented at the Ninth Symposium on Turbulence, University of Missouri-Rolla, October 1–3, 1984     

The effect of thermal boundary conditions and density stratification on the appearance of convection in the atmospheres of planets and stellar envelopes

In the present article a study is made of the effect of density stratification and thermal boundary conditions which are a consequence of the parametrization of the small-scale turbulent convection in the spherical layers of a compressible gas on the emergence of large-scale convection.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 149–158, March–April, 1985.     

Variational model of a turbulent rotating flow

A model of effectively viscous turbulent flows satisfying the Navier-Stokes equations and certain slip conditions at the walls is analyzed. The turbulent viscosity is determined on the basis of the principle of minimum energy dissipation rate, whose significance and conditions of applicability are discussed in detail. A new separated turbulent flow model is outlined. The problem of turbulent flow in a porous rotating tube is solved. The existence of two metastable flow regimes is predicted: one with an axial circulation zone, the other straight-through. In the case of a strongly swirled flow the first of these has a greater probability of realization; however, as the rotation weakens, in a certain critical situation the circulation zone collapses, after which the flow can only be straight-through. Despite the absence of empirical content, every aspect of the proposed theory is in good agreement with the experimental research on vortex chamber flows.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 22–32, May–June, 1985.     

Development of a two-dimensional turbulent jet in an infinite space

The second and third terms in the asymptotic expansion of the stream function in the nonsimilar problem of the development of a two-dimensional turbulent jet in an unbounded space are found in final form. Results of experimental investigations of free turbulent jets are cited, and the effect of the initial velocity profile on the aerodynamic characteristics of the jet is considered. The problem of the development of a two-dimensional turbulent jet in an unbounded space has been considered in [1–3]. The existing solution is similar, and is valid only at a sufficiently large distance from the slit. Allowance for the finite dimensions of the slit leads to a nonsimilar problem. The papers [4–6] are devoted to the experimental investigation of the free two-dimensional turbulent jet.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 137–142, July–August, 1971.     

Use of Galerkin's method to investigate transitions in a problem of Rayleigh convection

Galerkin's method is used to study transitions in the problem of convection of a fluid in a horizontal layer with free isothermal boundaries (Rayleigh's model).Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 22–27, March–April. 1984.I thank V. I. Yudovich for constant interest in the work.     

Self-similar reverse flows in the region of separation of a turbulent boundary layer

The Kármán momentum equation and very simple scaling arguments relating to the profiles of the turbulent tangential stresses are used to construct a self-similar reverse flow of an incompressible fluid that, depending on the values of the empirical constants occurring in it, can be realized either behind the separation point of a turbulent boundary layer or in front of its point of reattachment. The empirical constants are determined by means of several independent experimental studies on turbulent separating flows of liquids and gases at subsonic and supersonic velocities.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. A, pp. 173–177, July–August, 1988.     

A physical mechanism of large-scale structure generation in turbulent convection

The generation of large-scale structures during turbulent convection in a rotating layer of incompressible fluid heated by internal heat sources is considered. The results of a theoretical and experimental investigation of a physical mechanism of large-scale structure formation which operates under conditions of high-intensity small-scale turbulent convection and low boundary heat transfer are discussed. The theoretical investigation is based on a system of evolutionary equations obtained for the transverse space moments of the physical fields, which describes the motion in thin layers of rotating fluid. The stability of the solution of the mathematical model is studied using the small perturbation method. As a result, a condition of existence of longwave instability of the system and a criterion determining the threshold of its onset are obtained. The theoretical conclusions are confirmed by a series of experiments carried out on a laboratory model. The design of the laboratory apparatus and the experimental technique are described.Moscow, Perm'. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 20–29, September–October, 1996.     

Investigation of the structure of transition and turbulent convection conditions in a vertical layer

Results are presented of an investigation of the instantaneous and average characteristics of turbulent convection in a vertical layer, starting from the two-dimensional unsteady Navier-Stokes equations. This paper studies the evolution of large-scale and fine structure during transition from laminar flow to turbulent.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 66–75, November–December, 1978.The authors thank V. L. Gryaznov for useful discussions and help in the first stage of the work and V. I. Baranov for his help in taking the movie film.     

Method of generalized similitude in free convection problems with arbitrary distribution of the temperature or heat flux on a vertical wall

The self-similar problem of free convection near a heated vertical plate was solved for the first time in [1] for the simplest case of a constant wall temperature. In [2], Yang proved the existence of a self-similar solution to the problem of free convection for vertical plates and cylinders on the surfaces of which the temperature has a power-law distribution. In [3], Yang's solution was generalized to the case of free convection near a slender figure of revolution, but also only in the self-similar case of a power-law distribution of the temperature on the wall. In [4], this problem was solved in an extended nonsimilar formulation but by an artificial and not general method similar to Gertler's, the convergence of the approximations being slow. The present paper contains the solution to the problem of free convection near a vertical plate with arbitrary distribution of the temperature or heat flux on its surface. Rigorous application of the method of generalized similitude [5] leads in this case to universal equations that present insuperable computational difficulties, which forces one to use a simplified but fairly general method to solve this class of problems.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 167–170, May–June, 1980.I thank L. G. Loitsyanskii and E. M. Smirnov for discussing the results and for valuable comments.     

Hydrodynamic structure of accelerated turbulent boundary layers

The aim of the paper is to determine the velocity profile and friction law in turbulent boundary layers that develop under conditions of a negative longitudinal pressure gradient (dP/dx < 0). In contrast to the numerous studies devoted to this problem and based on semi-empirical closure of the hydrodynamic equations, general expressions (containing, of course, some empirical coefficients) will be obtained on the basis of dimensional and similarity arguments alone. In this sense, the results of the paper are a natural continuation of the analysis of decelerated turbulent wall flows by Kader and Yaglom [1, 2]. It is shown that the general dependences found in this manner agree well with numerous experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 29–37, May–June, 1983.I thank A. M. Yaglom for his interest in the work and valuable advice during it.     

Experimental investigation of flow and heat transfer for the ethanol-water solution and FC-72 in rectangular microchannels

Rapid development of super scale integration circuit (IC) provides unprecedented challenge to thermal control for aviation electronic equipments. To solve the problem of cooling electronic chips and devices for aircraft avionics, this paper experimentally investigated the characteristics of single-phase forced convection heat transfer and flow resistance in rectangular microchannels with two liquid coolants. One was 30% of ethanol–water solution, the most commonly used coolant in aviation. The other was FC-72, the latest coolant for electronic equipments. Based on the experimental data collected and those available in the open literature, comparisons and analyses were carried out to evaluate the influences of liquid velocity, supercooling temperature, microchannel structures and wall temperature etc. on the heat transfer behaviors. And the correlations of flow resistance and heat transfer characteristics were provided for the ethanol–water solution and FC-72 respectively. The results indicate transition from laminar to turbulent flow occurs at the Reynolds number of 750–1,250 for FC-72, and the behaviors of flow and heat transfer in rectangular microchannels strongly depend on the kind of coolant and geometric configuration of microchannels.     

Energy-balance equation for turbulent pulsations in the theory of the free turbulent boundary layer

Semiempirical expressions are proposed for the coefficient of turbulent viscosity and for the scale of turbulence in the equations for the free turbulent boundary layer in an incompressible fluid, these equations consisting of the equation of continuity, the equations of motion, and the equation for the average energy balance in the turbulent pulsations. The advantage of the expressions over the existing ones is that the two empirical constants in the equations have nearly the same values for circular and plane turbulent streams and also for a turbulent boundary layer at the edge of a semiinfinite homogeneous flow with a stationary fluid. The mean-energy distribution and the mean energy of the turbulent pulsations computed in this paper agree well with the experimental values.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 75–79, November–December, 1970.     

Drop evaporation in a turbulent gas jet

Evaporation of a semidispersive drop system in a turbulent gas jet is considered. A method for calculating drop evaporation in a turbulent gas jet is proposed based on a simplified solution of the scattering problem for an evaporating admixture. Evaporation of water as it is atomized in a turbulent air jet is experimentally studied. Approximate agreement is obtained between the results of the calculations and experiments.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 73–79, January–February 1976.     

A turbulent jet with heavy components

The method of integral relationships is used to solve the problem of the initial and fundamental segments of a submerged turbulent jet containing heavy particles. The effect of the particles on turbulent structure of the jet is considered. Results for jet velocity on the axis and dynamic jet boundary agree with experiment.Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 6, pp. 41–49, November–December, 1972.     

The turbulent boundary layer on the moving surface of a cylindrical body

A study is made of the problem of a two-dimensional turbulent boundary layer on the moving surface of a cylindrical body (a Rankine oval with a relative elongation of four) moving at constant velocity in an incompressible fluid. For the numerical simulation of the turbulent flow of the fluid, the boundary layer is divided into exterior and interior regions in accordance with a two-layer model, using different expressions for the coefficients of turbulent transfer for each region. A study was nade of the development of the boundary layer on the body at different speeds of the body surface and different Reynolds numbers. The following integral characteristics were found by numerical calculation: the work of friction as the body is displaced; the work expended on the movement of its surface; and, for a flow regime with separation, the work of the pressure force. In this case the following model of separation flow is assumed: beyond the singular point in the solution of the boundary layer equations that indicates the appearance of a region of reverse flow, the pressure and friction stress on the wall are constant and are determined by their values at the singular point.Translated from Izvestiya Akademii Nauk SSSH, Mekhanika Zhidkosti i Gaza, No. 5, pp. 61–67, September–October, 1984.Finally, the author would like to thank G. G. Chernyi and Yu. D. Shevelev for useful discussions and for their interest in this work.     

Steady-state shapes of bodies melted by aerodynamic heating

The variation of the shape of bodies exposed to aerodynamic ablation has been the subject of a considerable amount of research. One particular aspect of the general problem, namely, the problem of the steady-state shapes, i.e., those that do not vary as a result of ablation, was solved in [1, 2] for convective heat transfer on the assumption that the effective enthalpy of the material is constant. In this case a distinctive feature of the solution is the presence of corner points (breaks) on the steady-state shapes. Here, the problem is solved without assuming a constant effective enthalpy — the ablation rate is determined on the basis of a numerical solution of the equations describing the ablation of glassy materials, the flow of the molten film over the surface being calculated on the basis of the complete system of boundary-layer equations for an incompressible fluid [3]. It is shown that for a uniform heat transfer regime (laminar or turbulent) the steady-state shapes are smooth bodies without corner points. In the mixed heat transfer regime, in the general case the problem has no solution.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 122–127, July–August, 1987.     

Change in the thickness of an incompressible turbulent boundary layer in the presence of a longitudinal pressure gradient

Dimensional analysis is used to find the change in the thickness of a turbulent boundary layer that develops under conditions of a strong positive or negative pressure gradient. Comparison of the expression for the thickness with the available experimental data makes it possible to determine the universal constant in the expression. An interpolation dependence is proposed, this holding for all not too rapidly varying velocity distributions on the outer boundary of the turbulent boundary layer. The results of calculations made with this dependence are compared with numerous experimental data on the change in the thickness of turbulent boundary layers.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2. pp. 150–156, March–April, 1979.