Experimental Tests of Mean Velocity Distribution Laws Derived by Lie Group Symmetry Methods in Turbulent Boundary Layers

The response of turbulent boundary layers to sudden changes in surface roughness under adverse-pressure-gradient conditions has been studied experimentally. The roughness used was in the ‘d’ type array of Perry, Schofield & Joubert (1969). Two cases of a rough-to-smooth change in surface roughness were considered in the same arbitrary adverse pressure gradient. The two cases differed in the distance of the surface discontinuity from the leading edge and gave two sets of flow conditions for the establishment and growth of the internal layer which develops downstream from a change in surface roughness. These conditions were in turn different from those in the zero-pressure-gradient experiments of Antonia & Luxton. The results suggest that the growth of the new internal layer depends solely on the new conditions at the wall and scales with the local roughness length of that wall. Mean velocity profiles in the region after the step change in roughness were accurately described by Coles’ law of the wall-law of the wake combination, which contrasts with the zero-pressure-gradient results of Antonia & Luxton. The skin-friction coefficient after the step change in roughness did not overshoot the equilibrium distribution but made a slow adjustment downstream of the step. Comparisons of mean profiles indicate that similar defect profile shapes are produced in layers with arbitrary adverse pressure gradients at positions where the values of Clauser's equilibrium parameter β (= δ*τ−10dp/dx) are similar, provided that the pressure-gradient history and local values of the pressure gradient are also similar.

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Correction: Çakmak, A. New Type Direction Curves in 3-Dimensional Compact Lie Group Symmetry 2019, 11, 387

Symmetry ◽

10.3390/sym12020284 ◽

2020 ◽

Vol 12 (2) ◽

pp. 284

Author(s):

Ali Çakmak

Keyword(s):

Lie Group ◽

Group Symmetry ◽

Compact Lie Group ◽

3 Dimensional ◽

New Type ◽

Lie Group Symmetry

The authors wish to make the following corrections to their paper [...]

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On the streamwise evolution of turbulent boundary layers in arbitrary pressure gradients

Journal of Fluid Mechanics ◽

10.1017/s002211200200825x ◽

2002 ◽

Vol 461 ◽

pp. 61-91 ◽

Cited By ~ 58

Author(s):

A. E. PERRY ◽

IVAN MARUSIC ◽

M. B. JONES

Keyword(s):

Boundary Layers ◽

Scaling Laws ◽

Power Spectra ◽

Adverse Pressure Gradient ◽

Turbulent Boundary Layers ◽

Stream Velocity ◽

Mean Flow ◽

Mean Velocity ◽

Law Of The Wall ◽

The Mean

A new approach to the classic closure problem for turbulent boundary layers is presented. This involves, first, using the well-known mean-flow scaling laws such as the log law of the wall and the law of the wake of Coles (1956) together with the mean continuity and the mean momentum differential and integral equations. The important parameters governing the flow in the general non-equilibrium case are identified and are used for establishing a framework for closure. Initially closure is achieved here empirically and the potential for achieving closure in the future using the wall-wake attached eddy model of Perry & Marusic (1995) is outlined. Comparisons are made with experiments covering adverse-pressure-gradient flows in relaxing and developing states and flows approaching equilibrium sink flow. Mean velocity profiles, total shear stress and Reynolds stress profiles can be computed for different streamwise stations, given an initial upstream mean velocity profile and the streamwise variation of free-stream velocity. The attached eddy model of Perry & Marusic (1995) can then be utilized, with some refinement, to compute the remaining unknown quantities such as Reynolds normal stresses and associated spectra and cross-power spectra in the fully turbulent part of the flow.

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Mean-Velocity Profile of Turbulent Boundary Layers Approaching Separation

AIAA Journal ◽

10.2514/1.18905 ◽

2006 ◽

Vol 44 (11) ◽

pp. 2465-2474 ◽

Cited By ~ 16

Author(s):

Thomas Indinger ◽

Matthias H. Buschmann ◽

Mohamed Gad-el-Hak

Keyword(s):

Velocity Profile ◽

Boundary Layers ◽

Turbulent Boundary Layers ◽

Mean Velocity

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Mean Velocity Scaling and Friction Coefficient Estimation for Rough Surface Turbulent Boundary Layers in Turbomachines

Volume 2B: Turbomachinery ◽

10.1115/gt2014-26776 ◽

2014 ◽

Author(s):

Ju Hyun Shin ◽

Seung Jin Song

Keyword(s):

Flat Plate ◽

Rough Surface ◽

Boundary Layers ◽

Turbine Blades ◽

Axial Compressor ◽

Turbulent Boundary Layers ◽

Flat Plates ◽

Mean Velocity ◽

Coefficient Estimation ◽

Compressor And Turbine Blades

Based on flat plate results, mean velocity and friction coefficient estimation methods are proposed for rough surface turbulent boundary layers on axial compressor and turbine blades. The ratio of the displacement thickness to boundary layer thickness (δ*/δ) was first suggested by Zagarola and Smits (1998) for smooth pipe flows. The same parameter is proposed in this paper to scale the normalized mean velocity defect of smooth and rough surface flat plate turbulent boundary layers with zero, favorable, and adverse pressure gradients. The available mean velocity defect profiles of smooth and rough surface boundary layers from axial compressor and turbine blades are also scaled and compared to the flat plate results. Irrespective of the Reynolds number (Reθ), pressure gradient (K), and roughness (k), δ*/δ provides appropriate scaling for collapsing the flat plate and turbomachinery data. From the results, a new one-variable power law based on δ*/δ is proposed to estimate the mean velocity profile. The proposed power law can accurately estimate boundary layers on flat plates, compressor blades, and turbine blades. Finally, a new empirical Cf correlation is proposed for rough surface turbulent boundary layers under pressure gradients. The proposed Cf correlation is based on that of Bergstrom et al. (2005) and newly incorporates the acceleration parameter K. It can accurately estimate Cf in turbulent boundary layers of rough surface flat plates as well as those of smooth turbine blades.

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A Study on Turbulent Boundary Layers on a Smooth Flat Plate in an Open Channel

Journal of Fluids Engineering ◽

10.1115/1.1366321 ◽

2001 ◽

Vol 123 (2) ◽

pp. 394-400 ◽

Cited By ~ 11

Author(s):

Ram Balachandar ◽

D. Blakely ◽

M. Tachie ◽

G. Putz

Keyword(s):

Flat Plate ◽

Froude Number ◽

Boundary Layers ◽

Open Channel ◽

Reynolds Numbers ◽

Turbulent Boundary Layers ◽

Wall Region ◽

Mean Velocity ◽

Number Range ◽

High Reynolds

An experimental study was undertaken to investigate the characteristics of turbulent boundary layers developing on smooth flat plate in an open channel flow at moderately high Froude numbers (0.25<Fr<1.1) and low momentum thickness Reynolds numbers 800<Reθ<2900. The low range of Reynolds numbers and the high Froude number range make the study important, as most other studies of this type have been conducted at high Reynolds numbers and lower Froude numbers (∼0.1). Velocity measurements were carried out using a laser-Doppler anemometer equipped with a beam expansion device to enable measurements close to the wall region. The shear velocities were computed using the near-wall measurements in the viscous subregion. The variables of interest include the longitudinal mean velocity, the turbulence intensity, and the velocity skewness and flatness distributions across the boundary layer. The applicability of a constant Coles’ wake parameter (Π=0.55) to open channel flows has been discounted. The effect of the Froude number on the above parameters was also examined.

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