Approximate calculation of the compressible turbulent boundary layer with heat transfer and arbitrary pressure gradient (original) (raw)
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International Journal of Heat and Mass Transfer, 1995
In the present work, asymptotic methods are used to derive new expressions for the law of the wall, for tiae law of the wake and for the skin-friction and the Stanton number equations, for compressible turbulent boundary layers with heat and mass transfer. The results are compared with previous theories and experiments showing good agreement. The two parameters in the law of the wall, the angular coefficient and the linear coefficient of the straight part of the velocity and the temperature profiles plotted in appropriate logarithmic coordinates, are shown to vary with Math number. Only the second of these parameters, the linear coefficient of the straight line, is shown to vary with the injection rate. No dependence of these parameters on Eckert number, E could be assessed. Also, it emerges from the present analysis that the dissil:ation effects become important only when E = 0(u~-~), u~ = non-dimensional friction velocity.
1965
An experimental investigation was carried out to determine the effects Sof surface roughness on the turbulent boundary lay,r skin friction and heat transfer rates in air at a Mach number of h.93. Four flat plate model configurations were tested, one with a smooth surface and three with rough ourfaceG consisting of 900 V-grooves oriented perpendicular to the flow direction. Simultaneous measurements of the local skin friction and heat transfer were made uoing a floating-elcment skin friction bulance and an insulated-mass calorimeter for Reynolds numbers near 10 million and wallto-free stream temperature ratios from 2.9 to 5.2. The results of these measurements and of boundary layer pressure surveys are presented in both graphical and tabular form and are compared with theoretical predictions.
Fluid Dynamics, 2017
A rational asymptotic theory is proposed, which describes the turbulent dynamic and thermal boundary layer on a flat plate under zero pressure gradient. The fact that the flow depends on a finite number of governing parameters makes it possible to formulate algebraic closure conditions relating the turbulent shear stress and heat flux with the gradients of the averaged velocity and temperature. As a result of constructing an exact asymptotic solution of the boundary layer equations, the known laws of the wall for velocity and temperature, the velocity and temperature defect laws, and the expressions for the skin friction coefficient, Stanton number, and Reynolds analogy factor are obtained. The latter makes it possible to give two new formulations of the temperature defect law, one of which is identical to the velocity defect law and contains neither the Stanton number nor the turbulent Prandtl number, and the second formulation does not contain the skin friction coefficient. The heat transfer law is first obtained in the form of a universal functional relationship between three parameters: the Stanton number, the Reynolds number, and the molecular Prandtl number. The conclusions of the theory agree well with the known experimental data.
Transient Thermal Response of Turbulent Compressible Boundary Layers
Journal of Heat Transfer, 2011
A numerical method is developed with the capability to predict transient thermal boundary layer response under various flow and thermal conditions. The transient thermal boundary layer variation due to a moving compressible turbulent fluid of varying temperature was ...
NUMERICAL STUDY OF TURBULENT BOUNDARY LAYER FLOWS OVER ROUGH SURFACES–PART II: TEMPERATURE PROFILES
Turbulent transfer of momentum and heat over rough surfaces are numerically simulated. The effects of sudden changes are predicted in the cases of turbulent flow around surface-mounted two-dimensional ribs when subjected to a sudden change in surface roughness and temperature. A particular interest of this study is to investigate the sudden changes in the surface roughness for developing thermal boundary layer flow. A two-equation k-eps turbulence model is employed to simulate the turbulent transport. Equations of boundary-layer type were used and a forward marching method was employed for sweeping the computational domain. Wall functions that take into account surface roughness are used to specify the boundary conditions at the surface. The effects of the sudden changes of roughness accounted for the wall functions in the k-eps turbulence model are compared with available experimental data. Four configurations are simulated here, namely one extensive uniformly smooth surface, one extensively uniform rough case, and two cases where the surface roughness varies suddenly from a smooth to a rough and from a rough to a smooth surface. Results are presented for velocity and skin friction coefficient, in addition to comparisons with experimental data. The use of a parabolic solver showed good agreement with experimental values for the mean and local quantities.
Numerical study of turbulent boundary layers with heat transfer and tangential transpiration
International Journal of Numerical Methods for Heat & Fluid Flow, 2004
The hydrodynamic and thermal characteristics of the turbulent boundary layer developed on a porous wall with heat transfer and various angles of transpiration are analyzed numerically with the proper boundary conditions. The wall functions of the viscous and turbulent sub-layers for velocity and temperature are modified to allow for the effect of the angle of injection and suction through the porous wall. The finite difference method based on a control volume approach is used for solving the time averaged Navier-Stokes equations for incompressible flow in conjunction with the standard k-1 turbulence model equations. A non-uniform staggered grid arrangement is used. The parameters studied include the suction and injection velocity (V w) and the angle (a) of the injection and suction. The present numerical results of the normal injection and suction are compared with a known experimental data and a good agreement is obtained. The numerical results also indicate that the characteristics of the turbulent boundary layer such as local friction coefficient and thermal boundary layer thickness are substantially influenced by the velocity and the angle of transpiration.
Turbulent thermal boundary layers with temperature-dependent viscosity
International Journal of Heat and Fluid Flow, 2014
Direct numerical simulations (DNS) of turbulent boundary layers (TBLs) over isothermally heated walls were performed, and the influence of the wall-heating on the thermal boundary layers was investigated. The DNS adopt an empirical relation for the temperature-dependent viscosity of water. The Prandtl number therefore changes with temperature, while the Péclet number is constant. Two wall temperatures (T w = 70°C and 99°C) were considered relative to T 1 = 30°C, and a reference simulation of TBL with constant viscosity was also performed for comparison. In the variable viscosity flow, the mean and variance of the scalar, when normalized by the friction temperature deficit, decrease relative to the constant viscosity flow. A relation for the mean scalar which takes into account the variable viscosity is proposed. Appropriate scalings for the scalar fluctuations and the scalar flux are also introduced, and are shown to be applicable for both variable and constant viscosity flows. Due to the modification of the near-wall turbulence, the Stanton number and the Reynolds analogy factor are augmented by 10% and 44%, respectively, in the variable viscosity flow. An identity for the Stanton number is derived and shows that the mean wall-normal velocity and wall-normal scalar flux cause the increase in the heat transfer coefficient. Finally, the augmented near-wall velocity fluctuations lead to an increase of the wall-normal scalar flux, which contributes favorably to the enhanced heat transfer at the wall.
International Journal of Heat and Mass Transfer, 1994
The effects of pressure gradient on turbulent heat transfer to or from planar surfaces are examined. Only incompressible. equilibrium thermal boundary layers are investigated. The equilibrium condition is characterised by the Clauser parameter p. Temperature profiles which are parametric in fl and the turbulent Prandtl number, Pr,, have been calculated for the range-0.54 < fi d co ; corresponding in one end to a favorable pressure gradient flow beyond which no equilibrium boundary layer is possible and in the other end to turbulent Row at incipient separation, respectively. It is found that an overlap exists between the temperature law of the wall region and the outer defect law region for all values of /I and Pr,, except when /I-+ ;x. The existence of this overlap region gives rise to an expression for the Stanton number which is shown to be a function of fi and Pr,. At incipient separation, the skin friction coe%cient goes to zero while the wall heat flux remains finite. However. the wall heat flux and the Stanton number in this limit cannot be determined because oF the neglect of viscous effects in the present analysis. A modified Reynolds analogy that accounts for the effects of /I and Pr, is deduced and the classical Reynolds analogy is shown to be valid only in the limit of/j goes to zero, Pr, goes to I and the Reynolds number based on the displacement thickness approaches infinity.