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.

The Asymptotic Temperature Profile for Forced Convection Turbulent Boundary Layers With and Without Pressure Gradient

2003 ◽  
Author(s):  
Xia Wang ◽  
Luciano Castillo
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Temperature Profile ◽  
Forced Convection ◽  
Boundary Layers ◽  
Power Law ◽  
Equations Of Motion ◽  
Turbulent Boundary Layers ◽  
Similarity Analysis ◽  
Temperature Profiles

Similarity analysis of the equations of motion is used in order to study forced convection turbulent boundary layers with and without pressure gradient. New scalings are found for both the inner and the outer temperature profiles, respectively. It is shown that by normalizing the temperature profiles using the new scalings, the effects from the Pe´clet number and pressure gradient can be removed completely from the profiles. Therefore, the asymptotic solutions can be obtained even at the finite Pe´clet number. Moreover, using the Near-Asymptotic principle, a power law solution is derived for the temperature profile in the overlap region. This power law solution is a consequence of the fact that the boundary layer depends on two different temperature scalings.

An Interferometric Study of Mass Transfer From a Vertical Plate at Low Reynolds Numbers

1966 ◽  
Vol 88 (4) ◽  
pp. 399-406 ◽  
Author(s):  
M. M. El-Wakil ◽  
G. E. Myers ◽  
R. J. Schilling
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Boundary Layer ◽  
Mass Transfer ◽  
Natural Convection ◽  
Free Convection ◽  
Forced Convection ◽  
Boundary Layers ◽  
Reynolds Numbers ◽  
Perturbation Solutions

Experimental concentration profiles in steady-state, two-component boundary layers formed by the evaporation of a volatile liquid from a porous vertical flat plate into a heated airstream were obtained by an interferometric technique. Tests were conducted with benzene and n-heptane as the evaporating fluids with airstream temperatures ranging from 70 to 94 F and airstream velocities ranging from 90 to 120 fpm. The Reynolds number range, based on the distance from the leading edge of the plate, was from 75 to 1800. It was experimentally observed that transition from laminar flow occurred at Reynolds numbers between 300 and 600. These values, much lower than generally reported in the literature for heat transfer alone, are believed to be related to the relatively thick boundary layers induced by mass transfer of the heavier-than-air fluid from the plate and the associated free-convection effects. While the flow was primarily forced convection, the experimental data indicated a strong natural-convection effect when compared with analytical predictions based on forced convection alone. This was due primarily to the mass transfer into the boundary layer. An attempt was made to analytically account for the effects of mass transfer and natural convection on the Sherwood-Reynolds numbers relationship by utilizing perturbation solutions for the analogous heat transfer problem. The trends shown by this analysis agreed with the experimental data in the laminar portion of the boundary layer. The absolute magnitudes, however, still differed significantly, showing that first-order perturbation solutions of the mass transfer and free-convection effects are inadequate and pointing to the need for more theoretical work.

Pressure gradient effects on the large-scale structure of turbulent boundary layers

2013 ◽  
Vol 715 ◽  
pp. 477-498 ◽  
Author(s):  
Zambri Harun ◽  
Jason P. Monty ◽  
Romain Mathis ◽  
Ivan Marusic
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Amplitude Modulation ◽  
Large Scale ◽  
Outer Region ◽  
Adverse Pressure Gradient ◽  
Turbulent Boundary Layers ◽  
Small Scale

AbstractResearch into high-Reynolds-number turbulent boundary layers in recent years has brought about a renewed interest in the larger-scale structures. It is now known that these structures emerge more prominently in the outer region not only due to increased Reynolds number (Metzger & Klewicki, Phys. Fluids, vol. 13(3), 2001, pp. 692–701; Hutchins & Marusic, J. Fluid Mech., vol. 579, 2007, pp. 1–28), but also when a boundary layer is exposed to an adverse pressure gradient (Bradshaw, J. Fluid Mech., vol. 29, 1967, pp. 625–645; Lee & Sung, J. Fluid Mech., vol. 639, 2009, pp. 101–131). The latter case has not received as much attention in the literature. As such, this work investigates the modification of the large-scale features of boundary layers subjected to zero, adverse and favourable pressure gradients. It is first shown that the mean velocities, turbulence intensities and turbulence production are significantly different in the outer region across the three cases. Spectral and scale decomposition analyses confirm that the large scales are more energized throughout the entire adverse pressure gradient boundary layer, especially in the outer region. Although more energetic, there is a similar spectral distribution of energy in the wake region, implying the geometrical structure of the outer layer remains universal in all cases. Comparisons are also made of the amplitude modulation of small scales by the large-scale motions for the three pressure gradient cases. The wall-normal location of the zero-crossing of small-scale amplitude modulation is found to increase with increasing pressure gradient, yet this location continues to coincide with the large-scale energetic peak wall-normal location (as has been observed in zero pressure gradient boundary layers). The amplitude modulation effect is found to increase as pressure gradient is increased from favourable to adverse.

Velocity Profiles of Turbulent Boundary Layers

1969 ◽  
Vol 73 (698) ◽  
pp. 143-147 ◽  
Author(s):  
M. K. Bull
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Velocity Profile ◽  
Boundary Layers ◽  
Experimental Work ◽  
Constant Pressure ◽  
Velocity Profiles ◽  
Turbulent Boundary Layers ◽  
Boundary Layer Equations

Although a numerical solution of the turbulent boundary-layer equations has been achieved by Mellor and Gibson for equilibrium layers, there are many occasions on which it is desirable to have closed-form expressions representing the velocity profile. Probably the best known and most widely used representation of both equilibrium and non-equilibrium layers is that of Coles. However, when velocity profiles are examined in detail it becomes apparent that considerable care is necessary in applying Coles's formulation, and it seems to be worthwhile to draw attention to some of the errors and inconsistencies which may arise if care is not exercised. This will be done mainly by the consideration of experimental data. In the work on constant pressure layers, emphasis tends to fall heavily on the author's own data previously reported in ref. 1, because the details of the measurements are readily available; other experimental work is introduced where the required values can be obtained easily from the published papers.

Governing Parameters of Adverse Pressure Gradient Turbulent Boundary Layers

2018 ◽  
Author(s):  
Yvan Maciel ◽  
Tie Wei ◽  
Ayse G. Gungor ◽  
Mark P. Simens
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Outer Region ◽  
Adverse Pressure Gradient ◽  
Turbulent Boundary Layers ◽  
Inertial Parameter ◽  
Velocity Scale ◽  
Gradient Parameter

We perform a careful nondimensional analysis of the turbulent boundary layer equations in order to bring out, without assuming any self-similar behaviour, a consistent set of nondimensional parameters characterizing the outer region of turbulent boundary layers with arbitrary pressure gradients. These nondimensional parameters are a pressure gradient parameter, a Reynolds number (different from commonly used ones) and an inertial parameter. They are obtained without assuming a priori the outer length and velocity scales. They represent the ratio of the magnitudes of two types of forces in the outer region, using the Reynolds shear stress gradient (apparent turbulent force) as the reference force: inertia to apparent turbulent forces for the inertial parameter, pressure to apparent turbulent forces for the pressure gradient parameter and apparent turbulent to viscous forces for the Reynolds number. We determine under what conditions they retain their meaning, depending on the outer velocity scale that is considered, with the help of seven boundary layer databases. We find the impressive result that if the Zagarola-Smits velocity is used as the outer velocity scale, the streamwise evolution of the three ratios of forces in the outer region can be accurately followed with these non-dimensional parameters in all these flows — not just the order of magnitude of these ratios. This cannot be achieved with three other outer velocity scales commonly used for pressure gradient turbulent boundary layers. Consequently, the three new nondimensional parameters, when expressed with the Zagarola-Smits velocity, can be used to follow — in a global sense — the streamwise evolution of the stream-wise mean momentum balance in the outer region. This study provides a clear and consistent framework for the analysis of the outer region of adverse-pressure-gradient turbulent boundary layers.

Use of k−ε−γ Model to Predict Intermittency in Turbulent Boundary-Layers

2000 ◽  
Vol 122 (3) ◽  
pp. 542-546 ◽  
Author(s):  
Anupam Dewan ◽  
Jaywant H. Arakeri
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Pressure Gradient ◽  
Flat Plate ◽  
Turbulent Kinetic Energy ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Rate Of Dissipation ◽  
Dissipation Equation ◽  
Averaged Model

The intermittency profile in the turbulent flat-plate zero pressure-gradient boundary-layer and a thick axisymmetric boundary-layer has been computed using the Reynolds-averaged k−ε−γ model, where k denotes turbulent kinetic energy, ε its rate of dissipation, and γ intermittency. The Reynolds-averaged model is simpler compared to the conditional model used in the literature. The dissipation equation of the Reynolds-averaged model is modified to account for the effect of entrainment. It has been shown that the model correctly predicts the observed intermittency of the flows. [S0098-2202(00)02403-2]

Equilibrium-Turbulent Boundary Layer Prediction for a Proposed Prandtl Mixing Length Distribution

1968 ◽  
Vol 10 (5) ◽  
pp. 426-433 ◽  
Author(s):  
F. C. Lockwood
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Boundary Layers ◽  
Length Distribution ◽  
Momentum Equation ◽  
Turbulent Boundary Layers ◽  
Mixing Length ◽  
Good Agreement

The momentum equation is solved numerically for a suggested ramp variation of the Prandtl mixing length across an equilibrium-turbulent boundary layer. The predictions of several important boundary-layer functions are compared with the equilibrium experimental data. Comparisons are also made with some recent universal recommendations for turbulent boundary layers since the equilibrium experimental data are limited. Good agreement is found between the predictions, the experimental data, and the recommendations.

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