Effect of local heat supply to a turbulent boundary layer on the friction

The results of calculating a supersonic turbulent boundary layer on a flat plate in the presence of thermal energy supply to the boundary layer are presented. Two methods of energy supply are considered: heating a local interval of the surface, which is otherwise thermally insulated and using a local volume heat source. It is shown that for the same amount of heat supplied to the gas volume heating leads, under certain conditions, to greater friction reduction than the surface heating. Localization of the energy supply zone leads to the intensification of the viscous drag reduction effect and to a greater decrease in the local friction coefficient, which extends a considerable distance downstream. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 48–56, January–February, 1997. The work was carried out with financial support from the Russian Foundation for Fundamental Research (project No. 93-013-17600).     

Heat and mass transfer study of impinging turbulent premixed flames

 Impinging jet combusting flows on granite plates are studied. A mathematical model for calculating heat release in turbulent impinging premixed flames is developed. The combustion including radiative heat transfer and local extinction effects, and flow characteristics are modeled using a finite volume computational approach. Two different eddy viscosity turbulence models, namely the standard k–ɛ and the RNG k–ɛ model with and without radiation (discrete transfer model) are assessed. The heat released predictions are compared with experimental data and the agreement is satisfactory only when both radiative heat transfer and local extinction modeling are taken into account. The results indicate that the main effect of radiation is the decrease of temperature values near the jet stagnation point and along the plate surface. Radiation increases temperature gradients and affects predicted turbulence levels independently of the closure model used. Also, the RNG k–ɛ predicts higher temperatures close the solid plate, with and without radiative heat transfer. Received on 13 November 2000 / Published online: 29 November 2001     

Unsteady radiative-convective heat transfer in a high-temperature gas-particle flow past a semi-transparent plate

Numerical simulations of unsteady radiative-convective heat transfer in a turbulent flow of a mixture of gases and solid particles past a semi-transparent plate are performed. An ablation process is demonstrated to occur on the plate surface in the case of intense radiative heating of the plate by an external source with emission in a limited spectral range. Temperature fields and distributions of heat fluxes in the boundary layer and in the plate are calculated. Calculation results are presented, which allow determining the effect of ablation and reflecting properties of the plate surface on the thermal state of the medium in the system containing the boundary layer and the plate under conditions of plate heating by a high-temperature source of radiation. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 3, pp. 140–146, May–June, 2009.     

Experimental investigation of mixed convection in a rectangular duct with a heated plate in the middle of cross section

The flow and heat transfer in an inclined and horizontal rectangular duct with a heated plate longitudinally mounted in the middle of cross section was experimentally investigated. The heated plate and rectangular duct were both made of highly conductive materials, and the heated plate was subjected to a uniform heat flux. The heat transfer processes through the test section were under various operating conditions: Pr ≈ 0.7, inclination angle ϕ = −60° to +60°, Reynolds number Re = 334–1,911, Grashof number Gr = 5.26 × 10²–5.78 × 10⁶. The experimental results showed that the average Nusselt number in the entrance region was 1.6–2 times as large as that in the fully developed region. The average Nusselt numbers and pressure drops increased with the Reynolds number. The average Nusselt numbers and pressure drops decreased with an increase in the inclination angle from −60° to +60° when the Reynolds number was less than 1,500. But when the Reynolds number increased to over about 1,800, the heat transfer coefficients and pressure drops were independent of inclination angles.     

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.     

Supersonic boundary layer on a plate. Comparison of calculation and experiment

For verifying the method of calculating the boundary layer in liquid rocket engine (LRE) nozzles developed by the authors on the basis of a differential three-parameter turbulence model, the boundary layer on a plate in a zero-gradient flow is calculated. Over a wide range of variation of the free-stream Mach number, the temperature factor, and the Reynolds number, based on the momentum thickness of the boundary layer, the calculation agrees satisfactorily with the known experimental data, with respect to both integral and local flow and heat transfer characteristics. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 64–78, November–December, 1998. The work received financial support from the Russian Foundation for Basic Research (project No.96-012-00260).     

Heat transfer studies of the oblique impingement of round jets upon a curved surface

 The effect of jet inclination of the local heat transfer under an obliquely impinging round air jet striking on isothermal circular cylinder is experimentally investigated. The circumferential heat transfer distribution as well as axial Nusselt number is measured. The considered parameters are jet Reynolds number in range of 3800–40,000, and jet inclination angle, ranging from 90 to 20. The experiments are carried out for nozzle sizes, d=3, 5 and 7 mm, and separation distance from 7 to 30 of the nozzle diameter. The output results indicated that the point of maximum heat transfer along the x-axis is shifted upstream and the local heat transfer distribution changed as a function of jet inclination. The magnitude of the shift was found to be significantly higher than that observe for a flat plate. The increasing inclination caused increasing asymmetry around the point of maximum heat transfer, with the upstream side of heat transfer profile dropping off more rapidly than the downstream side. Correlations of both the magnitude and shift of maximum heat transfer point are presented. The surface average heat transfer rate is calculated and compared with the normal impingement. Received on 5 June 2000 / Published online: 29 November 2001     

Effects of Viscous Dissipation on Unsteady Free Convection in a Fluid Past a Vertical Plate Immersed in a Porous Medium

The effects of viscous dissipation on unsteady free convection from an isothermal vertical flat plate in a fluid saturated porous medium are examined numerically. The Darcy–Brinkman–Forchheimer model is employed to describe the flow field. A new model of viscous dissipation is used for the Darcy–Brinkman–Forchheimer model of porous media. The simultaneous development of the momentum and thermal boundary layers are obtained by using a finite difference method. Boundary layer and Boussinesq approximation have been incorporated. Numerical calculations are carried out for various parameters entering into the problem. Velocity and temperature profiles as well as local friction factor and local Nusselt number are shown graphically. It is found that as time approaches infinity, the values of friction factor and heat transfer coefficient approach steady state.     

Combined heat transfer in a boundary layer of a selectiviely absorbing medium on a permeable plate under the conditions of intense radiation heating

Results of a numerical study of unsteady radiative-convective heat transfer in a boundary layer on a thermally thin permeable plate in the presence of intense radiation heating from outside are reported. The conjugate formulation of the problem takes into account the thermal interaction between the plate and an external gas flow. We consider a turbulent flow of an emitting-absorbing medium with the selective character of absorption. Calculation results are analyzed with a view for clarifying the influence of the governing parameters, namely, the relative temperature of an external radiation source, the Stark number, and the injection parameter. The possibility of inversion of a convective heat flux on the plate under the conditions of high-level external radiation is found. Kutateladze Institute of Thermal Physics, Siberian Division, Russian Academy of Sciences, Novosibirisk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 5, pp. 126–133, September–October, 1998.     

Temperature dependent viscosity and thermal conductivity effects on combined heat and mass transfer in MHD three-dimensional flow over a stretching surface with Ohmic heating

An analysis has been carried out to obtain the flow, heat and mass transfer characteristics of a viscous electrically conducting fluid having temperature dependent viscosity and thermal conductivity past a continuously stretching surface, taking into account the effect of Ohmic heating. The flow is subjected to a uniform transverse magnetic field normal to the plate. The resulting governing three-dimensional equations are transformed using suitable three-dimensional transformations and then solved numerically by using fifth order Runge–Kutta–Fehlberg scheme with a modified version of the Newton–Raphson shooting method. Favorable comparisons with previously published work are obtained. The effects of the various parameters such as magnetic parameter M, the viscosity/temperature parameter θ _r , the thermal conductivity parameter S and the Eckert number Ec on the velocity, temperature, and concentration profiles, as well as the local skin-friction coefficient, local Nusselt number, and the local Sherwood number are presented graphically and in tabulated form.     

Thermoelastic bending of a sandwich plate on a deformable foundation

The thermoelastic bending of a circular light-core sandwich plate on a deformable foundation is examined. To describe the kinematics of the plate with asymmetric thickness, the hypothesis of broken normal is adopted. The reaction of the foundation is described by Winkler’s model. The thermomechanical load is local and symmetric. The system of equilibrium equations is derived and solved exactly. Numerical results for three-layer metal-polymer plate are presented __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 2, pp. 96–103, February 2006.     

Experimental investigation on condensation heat transfer and pressure drop of R134a in a plate heat exchanger

Condensation heat transfer of R134a in a vertical plate heat exchanger was investigated experimentally. The local heat transfer coefficients are determined by means of the measured local wall temperatures. A differential energy balance model is developed for data evaluation. It is found that the correlation proposed by Shah using Ψ and Z factors is suitable for condensation in plate heat exchangers and is adopted to fit the measured data.     

Interaction of a supersonic pulse jet with an obstacle

The nonstationary interaction between a supersonic pulse jet and a flat plate perpendicular to the jet axis is studied experimentally and numerically. The time dependences of the pressure and heat flux at various points on the obstacle and the spatial distribution of the density are obtained experimentally. The nonstationary flow is calculated numerically by the Godunov method. The experiments and calculations reveal the effect of the reflected starting shock wave and the front part of the swirled gas outflow on the distribution of the dynamic and thermal loads acting on the plate, in both time and space. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 45–51, March–April, 1998. This research was carried out with partial financial support from the Russian Foundation for Fundamental Research (project No. 96-02-16170).     

Computational flow and heat transfer of a row of circular jets impinging on a concave surface

A computational investigation is carried out to study the flow and heat transfer from a row of circular jets impinging on a concave surface. The computational domain simulates the impingement cooling zone of a gas turbine nozzle guide vane. The parameters, which are varied in the study include jet Reynolds number (Re _d = 5000–67800), inter-jet distance to jet diameter ratio (c/d = 3.33 and 4.67) and target plate distance to jet diameter ratio (H/d = 1, 3 and 4). The flow field, predicted with K-ω turbulence model and using Fluent 6.2.16, is characterized with the presence of a pair of counter rotating vortices, an upwash fountain flow and entrainment. The local pressure coefficient and Nusselt number variations along the concave plate are presented and these values are found to under predict the available experimental data by about 12%.     

Heat transfer peaks on a blunt-nosed triangular plate in hypersonic flow

An experimental investigation [1] of hypersonic flow over a blunt-nosed triangular plate revealed anomalies — the presence on the windward side of narrow bands of intensified heat transfer. Below, this effect is related to the appearance in the flow near the surface of regions of gas spreading induced, in its turn, by the interference between the bow shock (due to the blunt nose) and the leading edges of the plate. This spreading is called inertial, since it takes place at almost constant pressure. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 131–137, March–April, 1994.     

Interaction of a circular turbulent jet with a flat target

Large eddy simulations are performed for an unsteady flow and heat transfer in the region of interaction of a circular turbulent jet with a normally positioned flat obstacle (target). Space-filtered Navier-Stokes equations are closed by the RNG model of eddy viscosity, which takes into account the curvature of streamlines in the region of flow turning. The computations are performed for different dimensionless distances between the nozzle exit and the target and for different Reynolds numbers. The dependence between the Nusselt number distribution over the target surface and the vortex structure of the jet is analyzed. The local and integral characteristics of the flow are compared with the data of a physical experiment. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 1, pp. 55–67, January–February, 2007.     

Transient conjugate heat transfer from a hemispherical plate during free liquid jet impingement on the convex surface

This paper considers the analysis of transient heating of a hemispherical solid plate of finite thickness during impingement of a free liquid jet. A constant heat flux was imposed at the inner surface of the hemispherical plate at t = 0 and heat transfer was monitored for the entire duration of the transient until a steady state condition was reached. Calculations were done for Reynolds number (Re) ranging from 500 to 1,500 and dimensionless plate thicknesses to nozzle diameter ratio (b/d _n) from 0.083 to 1.5. Results are presented for local and average Nusselt number using water as the coolant and various solid materials such as silicon, constantan, and copper. It was detected that increasing the Reynolds number decreases the time for the plate to achieve the steady-state condition. Also, a higher Reynolds number increases the Nusselt number. Hemispherical plate materials with higher thermal conductivity maintain lower temperature non-uniformity at the solid–fluid interface. Increasing the plate thickness decreases the maximum temperature in the solid and increases the time to reach the steady-state condition.     

Surface action of a heat pulse in a tangential flow

The three-dimensional unsteady problem of the action of a localized radiation pulse on an aluminum plate of finite thickness in a tangential airflow is solved on the basis of the Euler equations in the gas phase and the heat conduction equation in the solid. The process is accompanied by the intense evaporation of plate material and the subsequent (after the action of the radiation pulse ceases) intense condensation of aluminum vapor and condensate particles on the surface. The problem is solved on the assumption that the surface is not screened by its disintegration products and the processes associated with the self-radiation of the gas are disregarded. Heat pulses of intensityq=10⁶−10⁷ W/cm² and durationt _i ≈10⁻⁴ sec are investigated. Various regimes are calculated and the effect of the governing parameters on the impulse transmitted to the surface and ablation of the target material is established. A nontraditional approach, based on the idea of statistical modeling of the motion of an inviscid non-heat-conducting gas at the kinetic level, is used for solving the gas dynamic problem. The application of the approach in question to the solution of problems of this class is justified. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.1, pp. 139–146, January–February, 1994.     

Heat transfer due to harmonic variation in the free stream temperatures in a flat plate exposed on both sides

The heat transfer through an infinite flat plate is studied when the temperatures of the two free streams surrounding it are varying harmonically with time and out of phase, with a delay period τ_d. The configuration is a simplified model for the heat transfer through the separating wall in the isochoric counter-current heat exchanger. The results show that apart from the τ_d effect, the perturbation parameters depend mainly on the cavity passing frequency f. At the thick plate solution, the combined passing frequency–delay time influences are significant only when the dimensionless frequency is smaller than 10. Within this range τ_d affects seriously not only the temperature perturbation amplitudes (which determine the thermal stresses) but also the heat fluxes and the accumulated energy ones. When f ≥ 10, the plate behaves as two separate semi-infinite slabs. Heat penetration delays greater than one cavity passing period may be possible.     

On the thermomechanical behavior of a round flexible orthotropic plate

The critical temeprature of an orthotropic round plate at which it loses stability is determined, and its deflection is studied on the basis of flexible plate thermoelasticity. The plate is under conditions of heat exchange with the environment. The approximate method is based on the representation of stresses and displacements in the form of algebraic polynomials. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 4, pp. 95–100, April, 1999.