scholarly journals Analysis of the Contribution of Large Scale Motions to the Skin Friction of a Zero-Pressure-Gradient Turbulent Boundary Layer Using the Renard-Deck Decomposition

2021 ◽  
Vol 1 (1) ◽  
Author(s):  
Bihai Sun ◽  
Muhammad Shehzad ◽  
Daniel Jovic ◽  
Christophe Cuvier ◽  
Christian Willert ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Skin Friction ◽  
Large Scale ◽  
Skin Friction Coefficient ◽  
Turbulent Shear ◽  
The Mean ◽  
Component Particle

Coherent flow structures in turbulent boundary layers have been an active field of research for many decades, as they might be the key to reveal the mechanics of turbulence production and transport in turbulent shear flows. Renard and Deck (2016) proposed a theoretical decomposition for the mean skin-friction coefficient based on the mean kinetic energy budget in the streamwise direction. This decomposition, referred to as the Renard-Deck (RD) decomposition, decomposes the mean skin friction generation into three physical mechanisms in an absolute reference frame, namely, direct viscous dissipation, turbulent kinetic energy production, and spatial growth. In this study, the large scale motions (LSMs) are extracted using a proper orthogonal decomposition (POD) of the velocity field based on high-spatial-resolution two-dimensional – two-component particle image velocimetry (HSR 2C-2D PIV) of a zero-pressure-gradient turbulent boundary layer (ZPG-TBL), and their effect on the skin friction via RD decomposition.

A supersonic turbulent boundary layer in an adverse pressure gradient

1990 ◽  
Vol 211 ◽  
pp. 285-307 ◽  
Author(s):  
Emerick M. Fernando ◽  
Alexander J. Smits
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Pressure Distribution ◽  
Large Scale ◽  
Adverse Pressure Gradient ◽  
Large Scale Structures ◽  
Streamline Curvature ◽  
The Mean ◽  
Scale Structures

This investigation describes the effects of an adverse pressure gradient on a flat plate supersonic turbulent boundary layer (Mf ≈ 2.9, βx ≈ 5.8, Reθ, ref ≈ 75600). Single normal hot wires and crossed wires were used to study the Reynolds stress behaviour, and the features of the large-scale structures in the boundary layer were investigated by measuring space–time correlations in the normal and spanwise directions. Both the mean flow and the turbulence were strongly affected by the pressure gradient. However, the turbulent stress ratios showed much less variation than the stresses, and the essential nature of the large-scale structures was unaffected by the pressure gradient. The wall pressure distribution in the current experiment was designed to match the pressure distribution on a previously studied curved-wall model where streamline curvature acted in combination with bulk compression. The addition of streamline curvature affects the turbulence strongly, although its influence on the mean velocity field is less pronounced and the modifications to the skin-friction distribution seem to follow the empirical correlations developed by Bradshaw (1974) reasonably well.

Experimental Investigation of Turbulent Boundary Layers Under Favorable Pressure Gradient

2010 ◽  
Author(s):  
Pranav Joshi ◽  
Joseph Katz
Keyword(s):  
Boundary Layer ◽  
Friction Coefficient ◽  
Pressure Gradient ◽  
Skin Friction ◽  
Velocity Profiles ◽  
Skin Friction Coefficient ◽  
Mean Velocity ◽  
Freestream Velocity ◽  
Favorable Pressure Gradient ◽  
The Mean

The goal of this research is to study the effect of favorable pressure gradient (FPG) on the near wall structures of a turbulent boundary layer on a smooth wall. 2D-PIV measurements have been performed in a sink flow, initially at a coarse resolution, to characterize the development of the mean flow and (under resolved) Reynolds stresses. Lack of self-similarity of mean velocity profiles shows that the boundary layer does not attain the sink flow equilibrium. In the initial phase of acceleration, the acceleration parameter, K = v/U2dU/dx, increases from zero to 0.575×10−6, skin friction coefficient decreases and mean velocity profiles show a log region, but lack universality. Further downstream, K remains constant, skin friction coefficient increases and the mean velocity profiles show a second log region away from the wall. In the initial part of the FPG region, all the Reynolds stress components decrease over the entire boundary layer. In the latter phase, they continue to decrease in the middle of the boundary layer, and increase significantly close to the wall (below y∼0.15δ), where they collapse when normalized with the local freestream velocity. Turbulence production and wallnormal transport, scaled with outer units, show self-similar profiles close to the wall in the constant K region. Spanwise-streamwise plane data shows evidence of low speed streaks in the log layer, with widths scaling with the boundary layer thickness.

The Effect of Biofilms on Turbulent Boundary Layers

1999 ◽  
Vol 121 (1) ◽  
pp. 44-51 ◽  
Author(s):  
M. P. Schultz ◽  
G. W. Swain
Keyword(s):  
Boundary Layer ◽  
Friction Coefficient ◽  
Turbulent Boundary Layer ◽  
Skin Friction ◽  
Layer Structure ◽  
Reynolds Shear Stress ◽  
Skin Friction Coefficient ◽  
Laser Doppler Velocimeter ◽  
Reynolds Stresses ◽  
The Mean

Materials exposed in the marine environment, including those protected by antifouling paints, may rapidly become colonized by microfouling. This may affect frictional resistance and turbulent boundary layer structure. This study compares the mean and turbulent boundary layer velocity characteristics of surfaces covered with a marine biofilm with those of a smooth surface. Measurements were made in a nominally zero pressure gradient, boundary layer flow with a two-component laser Doppler velocimeter at momentum thickness Reynolds numbers of 5600 to 19,000 in a recirculating water tunnel. Profiles of the mean and turbulence velocity components, including the Reynolds shear stress, were measured. An average increase in the skin friction coefficient of 33 to 187 percent was measured on the fouled specimens. The skin friction coefficient was found to be dependent on both biofilm thickness and morphology. The biofilms tested showed varying effect on the Reynolds stresses when those quantities were normalized with the friction velocity.

The effects of a favourable pressure gradient and of the Reynolds number on an incompressible axisymmetric turbulent boundary layer. Part 1. The turbulent boundary layer

1998 ◽  
Vol 359 ◽  
pp. 329-356 ◽  
Author(s):  
H. H. FERNHOLZ ◽  
D. WARNACK
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Skin Friction ◽  
Boundary Layers ◽  
Reynolds Stresses ◽  
The Mean

The effects of a favourable pressure gradient (K[les ]4×10−6) and of the Reynolds number (862[les ]Reδ2[les ]5800) on the mean and fluctuating quantities of four turbulent boundary layers were studied experimentally and are presented in this paper and a companion paper (Part 2). The measurements consist of extensive hot-wire and skin-friction data. The former comprise mean and fluctuating velocities, their correlations and spectra, the latter wall-shear stress measurements obtained by four different techniques which allow testing of calibrations in both laminar-like and turbulent flows for the first time. The measurements provide complete data sets, obtained in an axisymmetric test section, which can serve as test cases as specified by the 1981 Stanford conference.Two different types of accelerated boundary layers were investigated and are described: in this paper (Part 1) the fully turbulent, accelerated boundary layer (sometimes denoted laminarescent) with approximately local equilibrium between the production and dissipation of the turbulent energy and with relaxation to a zero pressure gradient flow (cases 1 and 3); and in Part 2 the strongly accelerated boundary layer with ‘inactive’ turbulence, laminar-like mean flow behaviour (relaminarized), and reversion to the turbulent state (cases 2 and 4). In all four cases the standard logarithmic law fails but there is no single parametric criterion which denotes the beginning or the end of this breakdown. However, it can be demonstrated that the departure of the mean-velocity profile is accompanied by characteristic changes of turbulent quantities, such as the maxima of the Reynolds stresses or the fluctuating value of the skin friction.The boundary layers described here are maintained in the laminarescent state just up to the beginning of relaminarization and then relaxed to the turbulent state in a zero pressure gradient. The relaxation of the turbulence structure occurs much faster than in an adverse pressure gradient. In the accelerating boundary layer absolute values of the Reynolds stresses remain more or less constant in the outer region of the boundary layer in accordance with the results of Blackwelder & Kovasznay (1972), and rise both in the vincinity of the wall in conjunction with the rising wall shear stress and in the centre region of the boundary layer with the increase of production.

Investigation of the influence of miniature vortex generators on the large-scale motions of a turbulent boundary layer

2021 ◽  
Vol 932 ◽  
Author(s):  
C.I. Chan ◽  
R.C. Chin
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Turbulent Boundary Layer ◽  
Velocity Fluctuation ◽  
High Speed ◽  
Large Scale ◽  
Vortex Generators ◽  
Mean Flow ◽  
Low Speed ◽  
The Mean

Well resolved large-eddy simulation data are used to study the physical modulation effects of miniature vortex generators (MVGs) in a moderate Reynolds number zero pressure gradient turbulent boundary layer. Large-scale counter-rotating primary vortex pairs (PVPs) imposed by the MVG contribute to the formation of streamwise streaks by transporting high momentum fluids from the outer regions of the boundary layer towards the wall, giving rise to high-speed regions centred at the PVP. Consequently, low-speed regions are formed along the outer flank of the PVP, resulting in a pronounced alternating high- and low-speed flow pattern. The PVP also relates to regions with skin friction modification, where a local skin friction reduction of up to 15 % is obtained at the low-speed region, but the opposite situation is observed over the high-speed region. The MVG-induced flow feature is further investigated by spectral analysis of the triple decomposition velocity fluctuation. Pre-multiplied energy spectra of the streamwise MVG-induced velocity fluctuation reveal that the large-scale induced modes scale with the spanwise wavelength and the length of the MVG, but the energy peak is eventually repositioned to the size of the near-wall streaks in the streamwise direction. Analysis of the triple decomposition of the kinetic energy transport equations revealed the significance of the mean flow gradient in generating kinetic energy which sustains the secondary motion. There is also an energy transfer between the turbulent and MVG-induced kinetic energy independent of the mean flow.

Near-wall measurements in a three-dimensional turbulent boundary layer

1997 ◽  
Vol 350 ◽  
pp. 189-208 ◽  
Author(s):  
DEBORA A. COMPTON ◽  
JOHN K. EATON
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Kinetic Energy ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Turbulent Kinetic Energy ◽  
Three Dimensional ◽  
Mean Flow ◽  
The Mean ◽  
Near Wall

An experiment was performed to measure near-wall velocity and Reynolds stress profiles in a pressure-driven three-dimensional turbulent boundary layer. An initially two-dimensional boundary layer (Reθ≈4000) was exposed to a strong spanwise pressure gradient. At the furthest downstream measurement locations there was also a fairly strong favourable streamwise pressure gradient.Measurements were made using a specially designed near-wall laser-Doppler anemometer (LDA), in addition to conventional methods. The LDA used short focal length optics, a mirror probe suspended in the flow, and side-scatter collection to achieve a measuring volume 35 μm in diameter and approximately 65 μm long.The data presented include mean velocity measurements and Reynolds stresses, all extending well below y+=10, at several profile locations. Terms of the turbulent kinetic energy transport equation are presented at two profile locations. The mean flow is nearly collateral (i.e. W is proportional to U) at the wall. Turbulent kinetic energy is mildly suppressed in the near-wall region and the shear stress components are strongly affected by three-dimensionality. As a result, the ratio of shear stress to turbulent kinetic energy is suppressed throughout most of the boundary layer. The angles of stress and strain are misaligned, except very near the wall (around y+=10) where the angles nearly coincide with the mean flow angle. Three-dimensionality appears to mildly reduce the production of turbulent kinetic energy.

A New Integral Method for Analyzing the Turbulent Boundary Layer With Arbitrary Pressure Gradient

1969 ◽  
Vol 91 (3) ◽  
pp. 371-376 ◽  
Author(s):  
F. M. White
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Skin Friction ◽  
Shape Factor ◽  
Single Equation ◽  
Skin Friction Coefficient ◽  
New Method ◽  
Momentum Thickness ◽  
New Approach

For routine calculations of the properties of the incompressible turbulent boundary layer with arbitrary pressure gradient, the presently accepted method is the Karman integral technique, which consists of three simultaneous equations, the three unknowns being the momentum thickness, the skin friction, and the shape factor. Considerable empiricism is contained in the Karman method, so that the reliability is only fair. The present paper derives an entirely new method, based upon a suggestion of R. Brand and L. Persen. The new approach results in a single equation for the skin friction coefficient, with the only parameter being the nominal Reynolds number and the only empiricism being a single assumption about the effect of pressure gradient. No other variables, such as shape factor or momentum thickness, are needed, although they can of course be calculated as byproducts of the analysis. The new method also contains a built-in separation criterion, which was the most glaring omission of the Karman technique. Agreement with experiment is as good or better than the most reliable Karman methods in use today.

The accelerated fully rough turbulent boundary layer

1977 ◽  
Vol 82 (3) ◽  
pp. 507-528 ◽  
Author(s):  
Hugh W. Coleman ◽  
Robert J. Moffat ◽  
William M. Kays
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Stress Tensor ◽  
Skin Friction ◽  
Shape Factor ◽  
Reynolds Shear Stress ◽  
Smooth Wall ◽  
Mean Velocity

The behaviour of a fully rough turbulent boundary layer subjected to favourable pressure gradients both with and without blowing was investigated experimentally using a porous test surface composed of densely packed spheres of uniform size. Measurements of profiles of mean velocity and the components of the Reynolds-stress tensor are reported for both unblown and blown layers. Skin-friction coefficients were determined from measurements of the Reynolds shear stress and mean velocity.An appropriate acceleration parameterKrfor fully rough layers is defined which is dependent on a characteristic roughness dimension but independent of molecular viscosity. For a constant blowing fractionFgreater than or equal to zero, the fully rough turbulent boundary layer reaches an equilibrium state whenKris held constant. Profiles of the mean velocity and the components of the Reynolds-stress tensor are then similar in the flow direction and the skin-friction coefficient, momentum thickness, boundary-layer shape factor and the Clauser shape factor and pressure-gradient parameter all become constant.Acceleration of a fully rough layer decreases the normalized turbulent kinetic energy and makes the turbulence field much less isotropic in the inner region (forFequal to zero) compared with zero-pressure-gradient fully rough layers. The values of the Reynolds-shear-stress correlation coefficients, however, are unaffected by acceleration or blowing and are identical with values previously reported for smooth-wall and zero-pressure-gradient rough-wall flows. Increasing values of the roughness Reynolds number with acceleration indicate that the fully rough layer does not tend towards the transitionally rough or smooth-wall state when accelerated.

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