Stability of a supersonic boundary layer on a permeable surface with heat transfer

The effect of cooling of a permeable surface on the stability of a supersonic boundary layer on it is investigated. As distinct from the case of an impermeable surface, deep cooling can reduce the critical Reynolds number. Common points of the continuous and discrete spectra are found in the region of the disturbance parameters.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 41–46, January–February, 1977.The work was carried out at the Department of Applied Mathematics of the University of Western Ontario in Canada. I am grateful to the Head of the Department Professor J. Blackwell for suggesting the investigation of this problem.     

Radiative heat transfer near a stagnation point in the presence of mass injection into the boundary layer

It is shown that the presence in the boundary layer of components with absorption cross sections that are nonzero in the visible region of the spectrum leads to an increase in the radiant flux reaching the surface as compared with the flux reaching the outer edge of the boundary layer. Conditions permitting the determination of the wavelength intervals on which this effect occurs at any values of the optical thicknesses of the boundary layer are obtained. A criterion, from which it follows that in many flow regimes the effect of vapor injection on the increase of the radiant flux reaching the wall can be neglected, is presented.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 21–30, September–October, 1971.     

Formulas for the heat and diffusion fluxes to a catalytic surface in a chemically nonequilibrium multicomponent boundary layer

On the basis of an asymptotic expansion of the solution of the equations of a multicomponent chemically nonequilibrium boundary layer for large Schmidt numbers, formulas are obtained for the heat flux and the diffusion fluxes of the reaction products and chemical elements on a surface with arbitrary catalytic activity. The results are compared with well-known analytic and numerical solutions. The comparison reveals the high accuracy of the formulas proposed. The results of calculating the diffusional separation of the mixture due to the selectivity of the catalytic properties of the surface with respect to recombination of oxygen and nitrogen atoms are presented. Values of the reduction of the convective heat fluxes due to the catalytic properties of the surface are obtained over a wide range of conditions in the free stream.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 171–176, March–April, 1996.     

Three-dimensional chemically nonequilibrium viscous shock layer on a catalytic surface with allowance for associated heat transfer

A three-dimensional flow of dissociating air past blunt bodies is investigated in the framework of the thin viscous shock layer theory. Multicomponent diffusion and homogeneous chemical reactions, including dissociation, recombination, and exchange reactions, are taken into account. The generalized Rankine-Kugoniot conditions are specified on the shock wave and the conditions which take into account the heterogeneous catalytic reactions, on the surface of the body. The viscous shock layer equations are solved together with the heat equations inside the coating, which is carbon with a deposited thin film of SiO₂, or quartz. The case of a thermally insulated surface is also considered. The problem for the case of the motion of a body along the re-entry trajectory into Earth's atmosphere is investigated numerically. The temperature of the surface and the heat flux toward it are given as a dependence on the height (tine) of the flight for different cases of the specification of the catalytic reactions. It is shown that the difference between the heat fluxes towards the thermally insulated surface and the fluxes toward the heat-conducting surface in the neighborhood of the stagnation point is of the order of 6–12% for all the cases considered. This makes it possible to decouple the solution of the problem of heat conduction in the body.Translated fron Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 140–146, November–December, 1985.deceased     

Analytical study of heat transfer and boundary layer flow with suction and injection

The Governing Principle of Dissipative Processes (GPDP) formulated by Gyarmati into non-equilibrium thermodynamics is employed to study the effects of heat transfer, two dimensional, laminar and constant property fluid flow in the boundary layer with suction and injection. The flow and temperature fields inside the boundary layer are approximated by simple third degree polynomial functions and the variational principle is formulated over the region of the boundary layer. The Euler–Lagrange equations of the principle are obtained as polynomial equations in terms of momentum and thermal layer thicknesses. These equations are solvable for any given values of Prandtl number Pr, wedge angle parameter m and suction/injection parameter H. The obtained analytical solutions are compared with known numerical solutions and the comparison shows the fact that the accuracy is remarkable.     

Heat transfer in a turbulent boundary layer with stepped injection

The asymptotic theory of a turbulent boundary layer has been applied to derive relationships for the heat and mass transfer when there is injection and consequent nonuniformity in the gas composition. Experimental studies are reported on heat and mass transfer with stepped injection of homogeneous and inhomogeneous gases; the results confirm the equations for the heat and mass transfer at a permeable surface when a foreign gas is blown in.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 124–129, July–August, 1973.     

Calculation of a nonequilibrium viscous shock layer with allowance for coupled heat transfer

An investigation is made into the characteristics of coupled heat and mass transfer using the theory of a nonequilibrium viscous shock layer in the case of an axisymmetric blunt body moving along a given trajectory.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 146–153, March–April, 1984.     

Turbulent boundary layer on a catalytic surface in a nonequilibrium dissociating gas

The majority of the studies which consider the flow of a dissociating gas in a turbulent boundary layer are devoted to the investigation of either frozen or equilibrium flows on a flat plate.The frozen turbulent boundary layer has been studied by Dorrance [1], Kutateladze and Leont'ev [2], and Lapin and Sergeev [3]. A study of the effect of catalytic recombination processes at the plate surface on the heat transfer in a frozen turbulent boundary layer was made by Lapin [4].Kosterin and Koshmarov [5], Ginzburg [6], Dorrance [7], and Lapin [8] have studied the turbulent boundary layer on a plate in equilibrium dissociating gas.The calculation of the heat transfer in a turbulent boundary layer on a catalytic plate surface with nonequilibrium dissociation was made by Kulgein [9]. In this study the nonequilibrium nature of the dissociation process was taken into account only in the laminar sublayer, while the flow in the turbulent core was considered frozen. The solution was found numerically using a computer by means of a laborious iteration process.The present paper reports a method for calculating the turbulent boundary layer on a flat catalytic plate with arbitrary dissociation rate. The method, constructed using the assumptions customary for turbulent boundary layer theory, is a successive approximation method. Good convergence of the method is assured by the fact that the effect of the nonequilibrium nature of the dissociation process on the parameter distribution in the boundary layer and, consequently, on the friction and heat transfer may be allowed for merely by finding corrections, usually relatively small, to the distribution of these parameters in the equilibrium or frozen flows. The basis of the study is the two-layer scheme of the turbulent boundary layer. The Prandtl and Schmidt numbers and also their turbulent analogs are taken equal to unity. As the model of the dissociating gas we use the Lighthill model of the ideal dissociating gas [10], extended by Freeman [11] to nonequilibrium flows.     

Extensions of Merk's method to the calculation of laminar boundary layer heat transfer from a non-isothermal surface

The Merk's method for calculating non-similar boundary layer heat transfer from an isothermal surface is extended to the case with non-isothermal surface and the reliability of the method is checked in detail. It is shown that except for some small ranges of β (pressure gradient parameter) and γ (wall temperature distribution parameter), the present method yields accurate heat transfer results. Examples of application of the present method are given for a flow around a circular cylinder and for that past a flat plate. The calculations are performed in the limits Pr→∞ and Pr→0, and the results are compared with those derived from the exact asymptotic theories for these limits.     

Film cooling by injection into a turbulent boundary layer

Most papers on film cooling concern injection of a homogeneous gas. Stollery et al. [1] examined the case of tangential injection of gas into a boundary layer, the specific heat_63-01 differing little from that of the main flow,_63-02.Here we examine the effectiveness of film cooling of a thermally isolated planar wall by local supply to a turbulent boundary layer.     

Study of a three-dimensional turbulent boundary layer with allowance for coupled heat transfer

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 118–124, May–June, 1989.     

Visco-elastic boundary layer flow past a stretching plate with suction and heat transfer

In this paper the study of visco-elastic (Walters' liquid B model) flow past a stretching plate with suction is considered. Exact solutions of the boundary layer equations of motion and energy are obtained. The expressions for the coefficient of skin friction and of boundary layer thickness are obtained.     

Forced convection heat transfer at the boundary layer of a packed bed

Numerical investigations of the nature of the fluid flow pattern and heat transfer at the boundary layer of a packed bed are reported. A volume averaged Navier-Stokes equation is used to predict the fluid flow and a volume averaged heat balance equation the heat transfer. A variable porosity in the packing is assumed in the region near the wall. Simulations are performed using a modified penalty Galerkin finite element method. The case of fully developed hydrodynamic flow and developing thermal flow is studied. The Nusselt number is found to depend on the Reynolds number, Graetz number and ratio of thermal conductivity of the solid and fluid phases. Comparison is made to some experimental literature values.Nomenclature A constant - [A] Navier-Stokes type matrix - B constant - [B] divergence matrix - C _p constant pressure heat capacity - d characteristic length - D _p particle diameter - D _t tube diameter - {F} solicitation vector - Gz Graetz number, z D _t ^–1 Pr _f Re _p - k permeability term - k _f Thermal conductivity of the fluid phase - k _s Thermal conductivity of the solid phase - [K] coefficient matrix for temperature equation - n normal vector - P pressure - Pr _f Prandtl number for the fluid _f C _p k _f ^-1 - r radial coordinate - R _t tube radius - R residual - R _m residual - Re _p Reynolds number for particle, - t tortuosity factor - T temperature - interstitial velocity - z axial coordinate - effective thermal conductivity - penalty parameter - boundary of solution domain - porosity - viscosity - density - test function - solution domain - test function     

Vectored injection into isobaric laminar boundary layer flows

The results of a systematic study of self-similar solutions of the Blasius equation are presented for a wide range of both normal and tangential surface injection velocities. Only flows with non-vanishing shear are considered; however, an arbitrary orientation of the injection vector is allowed. It is found that a positive tangential component of injection (downstream vectoring) significantly increases the mass transfer rate required to blow off the boundary layer. For upstream vectoring, a new group of solutions is found over a certain range of the tangential wall velocity wherein the wall shear is doublevalued.

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Zusammenfassung Es wird eine systematische Untersuchung ähnlicher Lösungen der Blasius-Gleichung in einem weiten Bereich der normalen und tangentialen Ausblasgeschwindigkeit vorgelegt, wobei nur Strömungen mit nicht-verschwindender Schubspannung, aber beliebiger Ausblasrichtung betrachtet werden. Man findet, daß eine positive tangentiale (stromabwärts gerichtete) Komponente der Ausblasgeschwindigkeit den Stoff-übergangsstrom beträchtlich erhöht, der zum Wegblasen der Grenzschicht erforderlich ist. Für stromaufwärts gerichtetes Ausblasen wird eine neue Gruppe von Lösungen in einem gewissen Bereich der tangentialen Wandgeschwindigkeit gefunden, innerhalb dessen die Wandschubspannung verdoppelt wird.