Effect of pressure gradient of friction and heat transfer in a dusty boundary layer

Approximate analytic expressions for the local friction and heat transfer coefficients in a dusty laminar boundary layer are obtained and tested in the case of an incompressible carrier phase, power-law variation of the external gas flow velocity and small velocity and temperature phase disequilibrium. These expressions supplement the numerical analysis of the dusty boundary layer on a blunt body [1, 2] and the asymptotic calculation of the friction and heat transfer in a quasiequilibrium dusty gas boundary layer on a plate [3]. The combined effect of dustiness and pressure gradient on the friction and heat transfer coefficients is discussed. The results obtained can be used for the practical calculation of the friction and heat transfer in a quasiequilibrium dusty laminar boundary layer and for interpreting the corresponding experimental data. Tomsk. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 105–108, September–October, 1988.     

Reynolds analogy in a dusty laminar boundary layer

The nonisothermal Blasius problem for a gas suspension is considered on the basis of the equations of a quasiequilibrium two-phase laminar boundary layer [1–3]. Approximate analytical expressions are obtained for the friction and heat transfer coefficients and their region of applicability is estimated; the Reynolds analogy between friction and convective heat transfer processes [4] is extended to the case of a dusty quasiequilibrium laminar boundary layer. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 160–162, November–December, 1986.     

Two-phase mass injection from the stagnation zone of a blunt body in a hypersonic flow

A mathematical model of the hypersonic steady gas flow over the stagnation zone of an axisymmetric blunt body with given two-phase injection from the surface is proposed. The two-continuum model of a dusty gas [3] is used for describing the flow in the region of the wall. The problem is solved in the boundary layer and thin viscous shock layer approximations. On the basis of the numerical calculations the distribution of the parameters of the carrier and dispersed phases near the axis of symmetry is obtained. The similarity parameters determining the convective heat transfer are found. The stagnation point heat fluxes with and without particles are compared. The range of parameters on which particles can significantly reduce the heat transfer is determined.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.4, pp. 60–66, July–August, 1992.     

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.     

Boundary layer on a blunt body in a flow of dusty gas

The problem of interaction of gas-dust flows with solid surfaces arose in connection with the study of the motion of aircraft in a dusty atmosphere [1–2], the motion of a gas suspension in power generators, and in a number of other applications [3]. The presence of a disperse admixture may lead to a significant increase in the heat fluxes [4] and to erosion of the surface [5]. These phenomena are due to the joint influence of several factors — the change in the structure of the carrier-phase boundary layer due to the presence of the particles, collisions of the particles with the surface, roughness of the ablating surface, and so forth. This paper continues an investigation begun earlier [6–7] into the influence of particles on the structure of the dynamical and thermal two-phase boundary layer formed around a blunt body in a flow. The model of the dusty gas [8] has an incompressible carrier phase. The method of matched asymptotic expansions [9] is used to obtain the equations of the two-phase boundary layer. In the frame-work of the refined classification made by Stulov [6], it is shown that the form of the boundary layer equations is different in the presence and absence of inertial precipitation of the particles. The equations are solved numerically in the neighborhood of the stagnation point of the blunt body. The temperature and phase velocity distributions in the boundary layer, and also the friction coefficients and the heat transfer of the carrier phase are found for a wide range of the determining parameters. In the case of an admixture of low-inertia particles that are not precipitated on the body, it is shown that even when the mass concentration of the particles in the undisturbed flow is small their accumulation in the boundary layer can lead to a sharp increase in the thermal fluxes at the stagnation point.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 99–107, September–October, 1985.I thank V. P. Strulov for a discussion.     

Unsteady Boundary Layer on a Blunt Body in a Hypersonic Flow of Non-Uniform Dusty Gas

The unsteady heat transfer at the stagnation point on a blunt body traveling at hypersonic velocity through a layer of nonuniform dusty gas with low-inertia particles (not deposited on the body surface) is investigated. Using the matched asymptotic expansion method, the equations of the two-phase unsteady boundary layer near the symmetry axis of the body are derived with account for the polydispersity of the particles. The structure of the unsteady boundary layer and the variation of the friction and heat transfer coefficients at the stagnation point are studied numerically. Layered nonuniformities of the particle concentration and size are considered, the limits of variation of the thermal and mechanicals loads are found, and the effect of the dust polydispersity on the heat transfer is investigated.     

Approximate calculation of the interaction of supersonic flow with a laminar layer in the flow separation region

The distributions of the pressure, friction, and heat transfer coefficients in the separation zone of a laminar boundary layer ahead of a wedge on a plate are calculated approximately. The integral method of Cohen and Reshotko is used to calculate the flow in the boundary layer.     

Boundary layer in the vicinity of the stagnation point of a body of axial symmetry in a turbulent stream

The flow in the boundary layer in the vicinity of the stagnation point of a flat plate is examined. The outer stream consists of turbulent flow of the jet type, directed normally to the plate. Assumptions concerning the connection between the pulsations in velocity and temperature in the boundary layer and the average parameters chosen on the basis of experimental data made it possible to obtain an isomorphic solution of the boundary layer equations. Equations are obtained for the friction and heat transfer at the wall in the region of gradient flow taking into account the effect of the turbulence of the impinging stream. It is shown that the friction at the wall is insensitive to the turbulence of the impinging stream, while the heat transfer is significantly increased with an increase in the pulsations of the outer flow. These properties are confirmed by the results of experimental studies [1–4].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 83–87, September–October, 1973.     

Mixed convection boundary layer flow on a continuous flat plate with variable viscosity

The influences of variable viscosity and buoyancy force on laminar boundary layer flow and heat transfer due to a continuous flat plate are examined. The deviation of the velocity and temperature fields as well as of the skin friction and heat transfer results from their constant values are determined by means of similarity solutions.     

Calculation of the viscosity effect on the aerodynamic characteristics of slender bodies at hypersonic flow velocities

Approximating dependences of the local coefficients of friction, heat transfer, and pressure induced by a boundary layer on the generalized similarity parameters, including the inviscid flow characteristics, are obtained on the basis of the results of a numerical calculation of hypersonic flow past a number of plane and axisymmetric bodies. If the inviscid flow characteristics are known, these relations can be used to take the viscosity approximately into account under conditions of interaction between the laminar boundary layer and the hypersonic inviscid stream [1].Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 142–150, July–August, 1995.     

Laminar-turbulent flow over wedges mounted on sharp and blunt plates

The flow pattern and the heat transfer on sharp and blunt flat plates near a wedge in a Mach 6 stream are experimentally investigated for two Reynolds numbers corresponding to the laminar and transitional states of the undisturbed boundary layer ahead of the wedge. It is shown that, as in a two-dimensional flow, plate bluntness leads to the attenuation of the heat transfer in the boundary layer/shock wave interference zone. However, when a certain threshold value of the bluntness is exceeded, a further increase in the bluntness has almost no effect on the heat transfer. For the first time, an experiment conducted in an intermittent (blow-down) wind tunnel has been based on the comprehensive use of panoramic (global) techniques for measuring the heat transfer and pressure coefficients and a method for visualizing the surface friction employing the luminescence effect after UV irradiation.     

Method of mean-mass parameters for a three-dimensional boundary layer in a flow with vorticity

When a gas flows with hypersonic velocity over a slender blunt body, the bow shock induces large entropy gradients and vorticity near the wall in the disturbed flow region (in the high-entropy layer) [1]. The boundary layer on the body develops in an essentially inhomogeneous inviscid flow, so that it is necessary to take into account the difference between the values of the gas parameters on the outer edge of the boundary layer and their values on the wall in the inviscid flow. This vortex interaction is usually accompanied by a growth in the frictional stress and heat flux at the wall [2, 3]. In three-dimensional flows in which the spreading of the gas on the windward sections of the body causes the high-entropy layer to become narrower, the vortex interaction can be expected to be particularly important. The first investigations in this direction [4–6] studied the attachment lines of a three-dimensional boundary layer. The method proposed in the present paper for calculating the heat transfer generalizes the approach realized in [5] for the attachment lines and makes it possible to take into account this effect on the complete surface of a blunt body for three-dimensional laminar, transition, or turbulent flow regime in the boundary layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 80–87, January–February, 1981.     

A spatial laminar boundary layer on a streamline in conical external flow of a uniform gas in the absence of sources and sinks

Theoretical study of a three-dimensional laminar boundary layer is a complex problem, but it can be substantially simplified in certain particular cases and even reduced to the solution of ordinary differential equations.One such particular case is the flow of a compressible gas on a streamline in conical external flow. The case is of considerable practical importance because the local heat fluxes may take extremal values on such lines.Such flow, except for the conical case, has been examined [1–4], and an approximate method has been given [1] on the basis of integral relationships and a special form for the approximating functions. A numerical solution has been given [2, 3] for such flow around an infinite cylinder. It was assumed in [1–3] that the Prandtl number and the specific heats were constant, and that the dynamic viscosity was proportional to temperature. Heat transfer has been examined [4] near a cylinder exposed to a flow of dissociated air.Here we give results from numerical solution of a system of ordinary differential equations for the flow of a compressible gas in a laminar boundary layer on streamlines in conical external flow, with or without influx or withdrawal of a homogeneous gas. It is assumed that the gas is perfect and that the dynamic viscosity has a power-law temperature dependence.     

Calculation of the boundary layer of a transparent gas on a radiating surface

Heat transfer in the laminar boundary layer of a transparent gas flowing aroud a plane radiating surface is studied. Radiative heat-transfer processes in gases may be divided into two main groups. The first involves heat transfer in absorbing and radiating media. In this case, the effect of radiation lies in the introduction of new terms into the energy equation, representing internal heat sources and sinks. The second group embraces heat-transfer processes in a transparent gas when the effect of radiation on convection expresses itself solely by way of the boundary conditions. Here we study a case of practical importance belonging to the second group: heat transfer in the laminary boundary layer of a transparent gas flowing around a flat plate with the thermal flux q_w specified on its surface.Novosibirsk. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 107–110, January–February, 1972.     

Numerical Modeling of Unsteady Radiative–Convective Heat Transfer on a Flat–Plate Boundary Layer in a Selectively Emitting and Scattering Medium

A conjugation problem for radiative–convective heat transfer in a turbulent flow of a high–temperature gas—particle medium around a thermally thin plate is considered. The plate experiences intense heating from an outside source that emits radiation in a restricted spectral range. Unsteady temperature fields and heat–flux distributions along the plate are calculated. The results permit prediction of the effect of the type and concentration of particles on the dynamics of the thermal state of both the medium in the boundary layer and the plate itself under conditions of its outside heating by a high–temperature source of radiation.     

Second-order effects in unsteady laminar compressible three-dimensional stagnation-point boundary layers

The flow, heat and mass transfer at the stagnation point of a three-dimensional body in unsteady laminar compressible fluid with variable properties have been studied using a second-order boundary-layer theory when the basic potential flow admits selfsimilarity. Both nodal and saddle point regions have been considered. The equations governing the flow have been solved numerically using an implicit finite-difference scheme. It is observed that the enhancement or reduction in the skin friction and heat transfer due to the second-order boundary layers depends upon the values of the parameter characterizing the unsteadiness in the free-stream velocity, the nature of the stagnation point, the variation of the density-viscosity product across the boundary layer, mass transfer and the wall temperature. The suction increases the skin friction and heat transfer whereas injection does the opposite.     

Boundary layer and heat transfer in a two-phase gas-evaporating droplet medium

An asymptotic model of the flow in the laminar boundary layer of a gas-evaporating droplet mixture is constructed within the framework of the two-continuum approximation. The case of evaporation of the droplets into an atmosphere of their own vapor is examined in detail with reference to the example of longitudinal flow over a hot flat plate. Numerical and asymptotic solutions of the boundary layer equations constructed are found for a number of limiting situations (low droplet concentration, no droplet deposition, significant droplet deposition). The development of the flow with respect to the longitudinal coordinate is studied and it is shown that in the absence of droplet deposition a region of pure vapor may be formed near the surface. Similarity criteria are established and the mechanism of surface heat transfer enhancement is studied for a low evaporating droplet concentration in the boundary layer. In the inertial deposition regime the results of calculating the integral heat transfer coefficient are found to correspond with the experimental data [1].Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 42–50, May–June, 1992.     

Heat transfer enhancement for laminar natural convection along a vertical plate due to sub-millimeter-bubble injection

Sub-millimeter-bubble injection is one of the most promising techniques for enhancing heat transfer for the laminar natural convection of liquids. However, flow and heat transfer characteristics for laminar natural convection of water with sub-millimeter bubbles have not yet been fully understood. The purpose of this study is to experimentally clarify the effects of sub-millimeter-bubble injection on the laminar natural convection of water along a heated vertical plate. The use of thermocouples and a particle tracking velocimetry (PTV) technique are applied to temperature and velocity measurements, respectively. The temperature measurement shows that the ratio of the heat transfer coefficient with sub-millimeter-bubble injection to that without injection increases with an increase in the bubble flow rate or a decrease in the wall heat flux and that the ratio ranges from 1.35 to 1.85. Moreover, it is concluded from simultaneous measurement of temperature and velocity that the heat transfer enhancement is directly affected by flow modification due to bubbles rising near the heated vertical plate.     

Investigation of laminar sublayer on permeable surfaces with injection

The thin-wall region — the laminar (or viscous) sublayer, in which the molecular mechanism of transfer predominates — plays an important role in friction and heat-transfer processes in a turbulent boundary layer. In particular, the relation between the sublayer thickness and the height of the surface roughness determines the nature of the flow — hydrodynamically smooth or rough — over the surface. This is of great practical importance and, hence, the roughness criterion has become the subject of numerous and systematic investigations. There are exhaustive data for the majority of the commonest cases encountered in practice [1]. The velocity on the boundary of the laminar sublayer appears as an important parameter in two-layer calculation schemes (e.g., [2–4], etc.). Although the theoretical analysis of a turbulent boundary layer with injection started several decades ago, there are at present hardly any reliable experimental data which can be used to determine the variation of the parameters within and at the boundary of the sublayer in relation to the injection rate. In this work we used interferometric diagnostics for precision experimental investigations of the parameters of the laminar sublayer on permeable surfaces with injection.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 66–72, September–October, 1977.