Prediction of Heat Transfer in Turbulent, Transpired Boundary Layers

1999 ◽  
Vol 121 (1) ◽  
pp. 186-190 ◽  
Author(s):  
J. Sucec
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Energy Equation ◽  
Integral Form ◽  
Turbulent Boundary Layers ◽  
Equation Solving ◽  
Turbulent Boundary Layer Flow ◽  
Layer Flow

Considered here is turbulent boundary layer flow with injection or suction and pressure gradient along the surface. The velocity and thermal inner laws for transpired turbulent boundary layers are represented by simple power law forms which are then used to solve the integral form of the thermal energy equation. Solving this equation leads to the variation of Stanton number with position, x, along the surface. Predicted Stanton numbers are compared with experimental data for a number of different cases. These include both blowing and suction with constant blowing fractions, F, in zero and non-zero pressure gradient and more complicated situations in which the blowing fraction, F, varies with position or where F or the surface temperature have step changes in value.

A Simple, Accurate Integral Solution for Accelerating Turbulent Boundary Layers With Transpiration

1995 ◽  
Vol 117 (3) ◽  
pp. 535-538 ◽  
Author(s):  
James Sucec
Keyword(s):  
Differential Equation ◽  
Experimental Data ◽  
Skin Friction ◽  
Boundary Layers ◽  
Integral Form ◽  
Skin Friction Coefficient ◽  
Momentum Equation ◽  
Turbulent Boundary Layers ◽  
Integral Solution ◽  
Good Agreement

The inner law for transpired turbulent boundary layers is used as the velocity profile in the integral form of the x momentum equation. The resulting ordinary differential equation is solved numerically for the skin friction coefficient, as well as boundary layer thicknesses, as a function of position along the surface. Predicted skin friction coefficients are compared to experimental data and exhibit reasonably good agreement with the data for a variety of different cases. These include blowing and suction, with constant blowing fractions F for both mild and severe acceleration. Results are also presented for more complicated cases where F varies with x along the surface.

Approach to an asymptotic state for zero pressure gradient turbulent boundary layers

2007 ◽  
Vol 365 (1852) ◽  
pp. 755-770 ◽  
Author(s):  
Hassan M Nagib ◽  
Kapil A Chauhan ◽  
Peter A Monkewitz
Keyword(s):  
Experimental Data ◽  
Pressure Gradient ◽  
Skin Friction ◽  
Boundary Layers ◽  
Classical Theory ◽  
Reynolds Numbers ◽  
Turbulent Boundary Layers ◽  
Careful Examination ◽  
Mean Velocity ◽  
Logarithmic Law

Flat plate turbulent boundary layers under zero pressure gradient at high Reynolds numbers are studied to reveal appropriate scale relations and asymptotic behaviour. Careful examination of the skin-friction coefficient results confirms the necessity for direct and independent measurement of wall shear stress. We find that many of the previously proposed empirical relations accurately describe the local C f behaviour when modified and underpinned by the same experimental data. The variation of the integral parameter, H , shows consistent agreement between the experimental data and the relation from classical theory. In accordance with the classical theory, the ratio of Δ and δ asymptotes to a constant. Then, the usefulness of the ratio of appropriately defined mean and turbulent time-scales to define and diagnose equilibrium flow is established. Next, the description of mean velocity profiles is revisited, and the validity of the logarithmic law is re-established using both the mean velocity profile and its diagnostic function. The wake parameter, Π , is shown to reach an asymptotic value at the highest available experimental Reynolds numbers if correct values of logarithmic-law constants and an appropriate skin-friction estimate are used. The paper closes with a discussion of the Reynolds number trends of the outer velocity defect which are important to establish a consistent similarity theory and appropriate scaling.

Temperature Scalings and Profiles in Forced Convection Turbulent Boundary Layers

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
Xia Wang ◽  
Luciano Castillo ◽  
Guillermo Araya
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Mass Transfer ◽  
Pressure Gradient ◽  
Temperature Profile ◽  
Forced Convection ◽  
Boundary Layers ◽  
Heat Mass Transfer ◽  
Turbulent Boundary Layers ◽  
Similarity Analysis

Based on the theory of similarity analysis and the analogy between momentum and energy transport equations, the temperature scalings have been derived for forced convection turbulent boundary layers. These scalings are shown to be able to remove the effects of Reynolds number and the pressure gradient on the temperature profile. Furthermore, using the near-asymptotic method and the scalings from the similarity analysis, a power law solution is obtained for the temperature profile in the overlap region. Subsequently, a composite temperature profile is found by further introducing the functions in the wake region and in the near-the-wall region. The proposed composite temperature profile can describe the entire boundary layer from the wall all the way to the outer edge of the turbulent boundary layer at finite Re number. The experimental data and direct numerical simulation (DNS) data with zero pressure gradient and adverse pressure gradient are used to confirm the accuracy of the scalings and the proposed composite temperature profiles. Comparison with the theoretical profiles by Kader (1981, “Temperature and Concentration Profiles in Fully Turbulent Boundary Layers,” Int. J. Heat Mass Transfer, 24, pp. 1541–1544; 1991, “Heat and Mass Transfer in Pressure-Gradient Boundary Layers,” Int. J. Heat Mass Transfer, 34, pp. 2837–2857) shows that the current theory yields a higher accuracy. The error in the mean temperature profile is within 5% when the present theory is compared to the experimental data. Meanwhile, the Stanton number is calculated using the energy and momentum integral equations and the newly proposed composite temperature profile. The calculated Stanton number is consistent with previous experimental results and the DNS data, and the error of the present prediction is less than 5%. In addition, the growth of the thermal boundary layer is obtained from the theory and the average error is less than 5% for the range of Reynolds numbers between 5×105 and 5×106 when compared with the empirical correlation for the experimental data of isothermal boundary layer conditions.

“Rough Surface Turbulent Boundary Layer Heat Transfer Using Generalized Reynolds Analogies”

2020 ◽  
Author(s):  
James Sucec
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Boundary Layer Flow ◽  
External Boundary ◽  
Duct Flow ◽  
Layer Flow ◽  
Predicted Values

Abstract Stanton number, St, calculations as a function of position, x, are made for turbulent, external boundary layer flow over aerodynamically rough surfaces and also for a fully developed duct flow with rough top and bottom surfaces. This is accomplished with three different forms of generalized Reynolds analogies from the literature and also with a new data correlation developed with the aid of the thermal inner and outer layers. Comparison of these predicted values of St with experimental data, from the literature, is made for several favorable equilibrium, one non-equilibrium, and a zero pressure gradient as well as a duct flow over “real” roughness patterns. Predictions compare reasonably well with the data for some of the generalized Reynolds analogies.

Calculation of Turbulent Boundary Layers Using Equilibrium Thermal Wakes

2005 ◽  
Vol 127 (2) ◽  
pp. 159-164 ◽  
Author(s):  
James Sucec
Keyword(s):  
Boundary Layer ◽  
Velocity Profile ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Thermal Energy ◽  
Energy Equation ◽  
Turbulent Boundary Layers ◽  
Stanton Number ◽  
Law Of The Wall ◽  
Number Distribution

The combined thermal law of the wall and wake is used as the approximating sequence for the boundary layer temperature profile to solve an integral thermal energy equation for the local Stanton number distribution. The velocity profile in the turbulent boundary layer was taken to be the combined law of the wall and wake of Coles. This allows the solution of an integral form of the x-momentum equation to give the skin friction coefficient distribution. This, along with the velocity profile, is used to solve the thermal energy equation using inner coordinates. The strength of the thermal wake was found by analysis of earlier research results, in the literature, for equilibrium, constant property, turbulent boundary layers. Solutions for the Stanton number distribution with position are found for some adverse pressure gradient boundary layers as well as for those having zero pressure gradient. The zero pressure gradient results cover both fully heated plates and those with unheated starting lengths, including both isothermal surfaces and constant flux surfaces. Comparison of predictions of the present work is made with experimental data in the literature.

An Inverse Inner-Variable Theory for Separated Turbulent Boundary Layers

1992 ◽  
Vol 114 (4) ◽  
pp. 543-553 ◽  
Author(s):  
D. K. Das
Keyword(s):  
Experimental Data ◽  
Pressure Gradient ◽  
Integral Equations ◽  
Boundary Layers ◽  
Initial Conditions ◽  
Turbulent Boundary Layers ◽  
Variable Theory ◽  
Freestream Velocity ◽  
Variable Approach ◽  
Displacement Thickness

An integral method is presented for computing separated and reattached turbulent boundary layers for incompressible two-dimensional flows. This method is a substantial improvement over the inner-variable approach of Das and White (1986), which was based on a direct boundary layer scheme that had several shortcomings. In this new approach, the integral equations have been completely reformulated so that the theory now proceeds in an inverse mode using displacement thickness as input. This new formulation eliminates the need for the second derivative of velocity distribution, which in the past has always been a source of error in all previous inner-variable approaches. Other significant additions are: (a) a single pressure gradient-wake correlation from a large amount of experimental data; and (b) replacement of the wake parameter from the final equations with a more stable parameter, wake velocity. Derivations of integral equations and their final working expressions, in both dimensional and nondimensional forms, are presented in detail. Predictions by this theory for skin friction, freestream velocity, momentum thickness, velocity profile and separation, and reattachment points agree well with experimental data. Sensitivity studies display that the theory is stable against variations in initial conditions, input distributions, and the pressure gradient-wake correlation.

Calculation of Turbulent Boundary Layers Using Equilibrium Thermal Wakes

2002 ◽  
Author(s):  
James Sucec
Keyword(s):  
Boundary Layer ◽  
Velocity Profile ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Thermal Energy ◽  
Energy Equation ◽  
Turbulent Boundary Layers ◽  
Stanton Number ◽  
Law Of The Wall ◽  
Number Distribution

The combined thermal law of the wall and wake is used as the approximating sequence for the boundary layer temperature profile to solve an integral thermal energy equation for the local Stanton number distribution. The velocity profile in the turbulent boundary layer was taken to be the combined law of the wall and wake of Coles. This allows the solution of an integral form of the x-momentum equation, to give the skin friction coefficient distribution. This, along with the velocity profile is used to solve the thermal energy equation using inner coordinates. The strength of the thermal wake was found by analysis of earlier research results, in the literature, for equilibrium, constant property, turbulent boundary layers. Solutions for the Stanton number distribution with position are found for some adverse pressure gradient boundary layers as well as for zero pressure gradient ones. The zero pressure gradient results cover both fully heated plates and those with unheated starting lengths, including both isothermal surfaces and constant flux surfaces. Comparison of predictions of the present work is made with experimental data in the literature.

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