Velocity and Temperature Profiles in Turbulent Boundary Layers With Tangential Injection

1962 ◽  
Vol 84 (1) ◽  
pp. 45-54 ◽  
Author(s):  
R. A. Seban ◽  
L. H. Back
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Thermal Behavior ◽  
Boundary Layers ◽  
Film Cooling ◽  
Mass Velocity ◽  
Free Stream ◽  
Turbulent Boundary Layers ◽  
Temperature Profiles ◽  
Adiabatic Wall

Velocity and temperature profiles are presented for the turbulent boundary layer downstream of a tangential injection slot for the further clarification of the film-cooling problem. The profiles refer primarily to an injection mass velocity of 0.36 times that of the free stream; these and other auxiliary results demonstrate a complex hydrodynamic and relatively simple thermal behavior in which the temperature profiles appear to be similar in all cases. By using this correspondence together with the approximation of a fully developed hydrodynamic layer in most of the downstream region, it is possible to rationalize the adiabatic wall temperatures that have been presented previously.

scholarly journals Interactions of large-scale free-stream turbulence with turbulent boundary layers

2016 ◽  
Vol 802 ◽  
pp. 79-107 ◽  
Author(s):  
Eda Dogan ◽  
Ronald E. Hanson ◽  
Bharathram Ganapathisubramani
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Boundary Layers ◽  
Large Scale ◽  
Free Stream ◽  
Turbulent Boundary Layers ◽  
Scale Interactions ◽  
Free Stream Turbulence ◽  
Small Scales ◽  
Near Wall

The scale interactions occurring within a turbulent boundary layer are investigated in the presence of free-stream turbulence. The free-stream turbulence is generated by an active grid. The free stream is monitored by a single-component hot-wire probe, while a second probe is roved across the height of the boundary layer at the same streamwise location. Large-scale structures occurring in the free stream are shown to penetrate the boundary layer and increase the streamwise velocity fluctuations throughout. It is speculated that, depending on the extent of the penetration, i.e. based on the level of free-stream turbulence, the near-wall turbulence production peaks at different wall-normal locations than the expected location of $y^{+}\approx 15$ for a canonical turbulent boundary layer. It is shown that the large scales dominating the log region have a modulating effect on the small scales in the near-wall region; this effect becomes more significant with increasing turbulence in the free stream, i.e. similarly increasing $Re_{\unicode[STIX]{x1D706}_{0}}$. This modulating interaction and its Reynolds-number trend have similarities with canonical turbulent boundary layers at high Reynolds numbers where the interaction between the large scales and the envelope of the small scales exhibits a pure amplitude modulation (Hutchins & Marusic, Phil. Trans. R. Soc. Lond. A, vol. 365 (1852), 2007, pp. 647–664; Mathis et al., J. Fluid Mech., vol. 628, 2009, pp. 311–337). This similarity has encouraging implications towards generalising scale interactions in turbulent boundary layers.

Effects of Embedded Vortices on Film-Cooled Turbulent Boundary Layers

1989 ◽  
Vol 111 (1) ◽  
pp. 71-77 ◽  
Author(s):  
P. M. Ligrani ◽  
A. Ortiz ◽  
S. L. Joseph ◽  
D. L. Evans
Keyword(s):  
Heat Transfer ◽  
Boundary Layers ◽  
Film Cooling ◽  
Free Stream ◽  
Flow Behavior ◽  
Local Heat Transfer ◽  
Local Heat ◽  
Turbulent Boundary Layers ◽  
Stream Velocity ◽  
Longitudinal Vortices

Heat transfer effects of longitudinal vortices embedded within film-cooled turbulent boundary layers on a flat plate were examined for free-stream velocities of 10 m/s and 15 m/s. A single row of film-cooling holes was employed with blowing ratios ranging from 0.47 to 0.98. Moderate-strength vortices were used with circulating-to-free stream velocity ratios of −0.95 to −1.10 cm. Spatially resolved heat transfer measurements from a constant heat flux surface show that film coolant is greatly disturbed and that local Stanton numbers are altered significantly by embedded longitudinal vortices. Near the downwash side of the vortex, heat transfer is augmented, vortex effects dominate flow behavior, and the protection from film cooling is minimized. Near the upwash side of the vortex, coolant is pushed to the side of the vortex, locally increasing the protection provided by film cooling. In addition, local heat transfer distributions change significantly as the spanwise location of the vortex is changed relative to film-cooling hole locations.

Prediction of Turbulent Boundary Layer Development in Conical Diffusers

1966 ◽  
Vol 8 (4) ◽  
pp. 426-436 ◽  
Author(s):  
A. D. Carmichael ◽  
G. N. Pustintsev
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Turbulent Boundary Layer ◽  
Boundary Layers ◽  
Shape Factor ◽  
Turbulent Boundary Layers ◽  
Energy Deficit ◽  
Momentum Thickness ◽  
Boundary Layer Development ◽  
Layer Development

Methods of predicting the growth of turbulent boundary layers in conical diffusers using the kinetic-energy deficit equation were developed. Three different forms of auxiliary equations were used. Comparison between the measured and predicted results showed that there was fair agreement although there was a tendency to underestimate the predicted momentum thickness and over-estimate the predicted shape factor.

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.

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.

Compressibility and Variable Density Effects in Turbulent Boundary layers

2006 ◽  
Vol 129 (4) ◽  
pp. 441-448 ◽  
Author(s):  
Kunlun Liu ◽  
Richard H. Pletcher
Keyword(s):  
Boundary Layer ◽  
Mach Number ◽  
Turbulent Boundary Layer ◽  
Boundary Layers ◽  
Wall Temperature ◽  
Stokes Equations ◽  
Variable Density ◽  
Turbulent Boundary Layers ◽  
Reynolds Analogy ◽  
Density Effects

Two compressible turbulent boundary layers have been calculated by using direct numerical simulation. One case is a subsonic turbulent boundary layer with constant wall temperature for which the wall temperature is 1.58 times the freestream temperature and the other is a supersonic adiabatic turbulent boundary layer subjected to a supersonic freestream with a Mach number 1.8. The purpose of this study is to test the strong Reynolds analogy (SRA), the Van Driest transformation, and the applicability of Morkovin’s hypothesis. For the first case, the influence of the variable density effects will be addressed. For the second case, the role of the density fluctuations, the turbulent Mach number, and dilatation on the compressibility will be investigated. The results show that the Van Driest transformation and the SRA are satisfied for both of the flows. Use of local properties enable the statistical curves to collapse toward the corresponding incompressible curves. These facts reveal that both the compressibility and variable density effects satisfy the similarity laws. A study about the differences between the compressibility effects and the variable density effects associated with heat transfer is performed. In addition, the difference between the Favre average and Reynolds average is measured, and the SGS terms of the Favre-filtered Navier-Stokes equations are calculated and analyzed.

Effect of Streamline Curvature on Film Cooling

1977 ◽  
Vol 99 (1) ◽  
pp. 77-82 ◽  
Author(s):  
R. E. Mayle ◽  
F. C. Kopper ◽  
M. F. Blair ◽  
D. A. Bailey
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Film Cooling ◽  
Flat Surface ◽  
Temperature Measurements ◽  
Adiabatic Wall ◽  
Cooling Effectiveness ◽  
Film Cooling Effectiveness ◽  
Streamline Curvature ◽  
Layer Velocity

The effects of streamline curvature on film cooling effectiveness are discussed. Experiments for air discharged through a slot and into a turbulent boundary layer along a flat, convex, and concave surface are described. Adiabatic wall effectiveness measurements on each surface for several blowing rates are presented. Boundary-layer velocity and temperature measurements are also presented for one of the blowing rates. Compared to the results for the flat surface, convex curvature is found to increase the adiabatic wall effectiveness whereas concave curvature is found to be detrimental.

A Simplified Form of the Auxiliary Equation for Use in the Calculation of Turbulent Boundary Layers

1958 ◽  
Vol 62 (567) ◽  
pp. 215-219
Author(s):  
T. J. Black
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Auxiliary Equation ◽  
Pressure Gradients ◽  
Momentum Thickness ◽  
Form Parameter ◽  
New Type ◽  
Simple Quadrature

A New type of auxiliary equation is given for calculating the development of the form-parameter H in turbulent boundary layers with adverse pressure gradients. The chief advantage of this new method lies in the rapidity and ease of calculation which has been achieved, without apparent sacrifice of accuracy.Whereas the growth of momentum thickness in the turbulent boundary layer can now be rapidly calculated by methods involving only simple quadrature, the prediction of the form parameter development remains a laborious task, while the results obtained do not always appear to justify the complexity of the calculations.

On the scaling in sink-flow turbulent boundary layers

2013 ◽  
Vol 737 ◽  
pp. 329-348 ◽  
Author(s):  
Shivsai Ajit Dixit ◽  
O. N. Ramesh
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Physical Space ◽  
Streamwise Velocity ◽  
Turbulent Boundary Layers ◽  
Velocity Spectrum ◽  
Scaling Exponent ◽  
Order Of Magnitude

AbstractScaling of the streamwise velocity spectrum ${\phi }_{11} ({k}_{1} )$ in the so-called sink-flow turbulent boundary layer is investigated in this work. The present experiments show strong evidence for the ${ k}_{1}^{- 1} $ scaling i.e. ${\phi }_{11} ({k}_{1} )= {A}_{1} { U}_{\tau }^{2} { k}_{1}^{- 1} $, where ${k}_{1} $ is the streamwise wavenumber and ${U}_{\tau } $ is the friction velocity. Interestingly, this ${ k}_{1}^{- 1} $ scaling is observed much farther from the wall and at much lower flow Reynolds number (both differing by almost an order of magnitude) than what the expectations from experiments on a zero-pressure-gradient turbulent boundary layer flow would suggest. Furthermore, the coefficient ${A}_{1} $ in the present sink-flow data is seen to be non-universal, i.e. ${A}_{1} $ varies with height from the wall; the scaling exponent −1 remains universal. Logarithmic variation of the so-called longitudinal structure function, which is the physical-space counterpart of spectral ${ k}_{1}^{- 1} $ scaling, is also seen to be non-universal, consistent with the non-universality of ${A}_{1} $. These observations are to be contrasted with the universal value of ${A}_{1} $ (along with the universal scaling exponent of −1) reported in the literature on zero-pressure-gradient turbulent boundary layers. Theoretical arguments based on dimensional analysis indicate that the presence of a streamwise pressure gradient in sink-flow turbulent boundary layers makes the coefficient ${A}_{1} $ non-universal while leaving the scaling exponent −1 unaffected. This effect of the pressure gradient on the streamwise spectra, as discussed in the present study (experiments as well as theory), is consistent with other recent studies in the literature that are focused on the structural aspects of turbulent boundary layer flows in pressure gradients (Harun et al., J. Fluid Mech., vol. 715, 2013, pp. 477–498); the present paper establishes the link between these two. The variability of ${A}_{1} $ accommodated in the present framework serves to clarify the ideas of universality of the ${ k}_{1}^{- 1} $ scaling.

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