Developing turbulent boundary layers with system rotation

1985 ◽  
Vol 157 ◽  
pp. 405-448 ◽  
Author(s):  
J. H. Watmuff ◽  
H. T. Witt ◽  
P. N. Joubert
Keyword(s):  
Skin Friction ◽  
Boundary Layers ◽  
Large Scale ◽  
Turbulent Boundary Layers ◽  
Momentum Balance ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Mean Velocity ◽  
Secondary Circulations ◽  
Spatially Periodic

Measurements are presented for low-Reynolds-number turbulent boundary layers developing in a zero pressure gradient on the sidewall of a duct. The effect of rotation on these layers is examined. The mean-velocity profiles affected by rotation are described in terms of a common universal sublayer and modified logarithmic and wake regions.The turbulence quantities follow an inner and outer scaling independent of rotation. The effect appears to be similar to that, of increased or decreased layer development. Streamwise-energy spectra indicate that, for a given non-dimensional wall distance, it is the low-wavenumber spectral components alone that are affected by rotation.Large spatially periodic spanwise variations of skin friction are observed in the destabilized layers. Mean-velocity vectors in the cross-stream plane clearly show an array of vortex-like structures which correlate strongly with the skin-friction pattern. Interesting properties of these mean-flow structures are shown and their effect on Reynolds stresses is revealed. Near the duct centreline, where we have measured detailed profiles, the variations are small and there is a reasonable momentum balance.Large-scale secondary circulations are also observed but the strength of the pattern is weak and it appears to be confined to the top and bottom regions of the duct. The evidence suggests that it has minimally affected the flow near the duct centreline where detailed profiles were measured.

scholarly journals Evolution and structure of sink-flow turbulent boundary layers

2001 ◽  
Vol 428 ◽  
pp. 1-27 ◽  
Author(s):  
M. B. JONES ◽  
IVAN MARUSIC ◽  
A. E. PERRY
Keyword(s):  
Boundary Layers ◽  
Velocity Profiles ◽  
Turbulent Boundary Layers ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Mean Velocity ◽  
Flow Measurements ◽  
Law Of The Wall ◽  
The Mean ◽  
Logarithmic Law

An experimental and theoretical investigation of turbulent boundary layers developing in a sink-flow pressure gradient was undertaken. Three flow cases were studied, corresponding to different acceleration strengths. Mean-flow measurements were taken for all three cases, while Reynolds stresses and spectra measurements were made for two of the flow cases. In this study attention was focused on the evolution of the layers to an equilibrium turbulent state. All the layers were found to attain a state very close to precise equilibrium. This gave equilibrium sink flow data at higher Reynolds numbers than in previous experiments. The mean velocity profiles were found to collapse onto the conventional logarithmic law of the wall. However, for profiles measured with the Pitot tube, a slight ‘kick-up’ from the logarithmic law was observed near the buffer region, whereas the mean velocity profiles measured with a normal hot wire did not exhibit this deviation from the logarithmic law. As the layers approached equilibrium, the mean velocity profiles were found to approach the pure wall profile and for the highest level of acceleration Π was very close to zero, where Π is the Coles wake factor. This supports the proposition of Coles (1957), that the equilibrium sink flow corresponds to pure wall flow. Particular interest was also given to the evolutionary stages of the boundary layers, in order to test and further develop the closure hypothesis of Perry, Marusic & Li (1994). Improved quantitative agreement with the experimental results was found after slight modification of their original closure equation.

Laboratory Study on the Turbulent Boundary Layers Over Wind-Waves Roughness

2018 ◽  
Author(s):  
Tunggul Bhirawa ◽  
Kevin ◽  
Jung H. Lee ◽  
Jason P. Monty
Keyword(s):  
Boundary Layers ◽  
Laboratory Study ◽  
Large Scale ◽  
Wind Waves ◽  
Turbulent Boundary Layers ◽  
Large Field ◽  
Reynolds Stresses ◽  
Surface Drag ◽  
Mean Velocity ◽  
Stationary Surface

A laboratory study of turbulent boundary layers over wind-generated waves using Particle Image Velocimetry (PIV) in a wind-wave flume at the University of Melbourne is presented. The experiments are taken at two different wind speeds of 5.5 and 8.5 m/s at a fetch length of 3.5 m. Two types of multi-camera measurement are specifically tailored to capture the flow behaviours. The first is a measurement with high spatial resolution, with aims of characterizing the mean velocity, surface drag and Reynolds stresses over the non-stationary surface. The second type is a large field-of-view measurement, designed to capture the large-scale turbulent motions which are directly associated with the surface-wave topography. Although the turbulent flow is developed over a non-stationary surface (i.e. wind-generated waves), it embodies similarities in both integral parameters and Reynolds stress behaviours to the turbulent flows over stationary rough surfaces. This observation could open a possibility to develop an important turbulence model as well as drag prediction over wind-generated waves, which could be closely related to stationary rough-wall boundary layers.

Low-Reynolds-Number Turbulent Boundary Layers in Zero and Favorable Pressure Gradients

1983 ◽  
Vol 27 (03) ◽  
pp. 147-157 ◽  
Author(s):  
A. J. Smits ◽  
N. Matheson ◽  
P. N. Joubert
Keyword(s):  
Friction Coefficient ◽  
Skin Friction ◽  
Boundary Layers ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Skin Friction Coefficient ◽  
Turbulent Boundary Layers ◽  
Pressure Gradients ◽  
Mean Flow ◽  
Low Reynolds

This paper reports the results of an extensive experimental investigation into the mean flow properties of turbulent boundary layers with momentum-thickness Reynolds numbers less than 3000. Zero pressure gradient and favorable pressure gradients were studied. The velocity profiles displayed a logarithmic region even at very low Reynolds numbers (as low as Rθ = 261). The results were independent of the leading-edge shape, and the pin-type turbulent stimulators performed well. It was found that the shape and Clauser parameters were a little higher than the correlation proposed by Coles [10], and the skin friction coefficient was a little lower. The skin friction coefficient behavior could be fitted well by a simple power-law relationship in both zero and favorable pressure gradients.

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

2002 ◽  
Vol 461 ◽  
pp. 61-91 ◽  
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.

Lateral straining of turbulent boundary layers. Part 2. Streamline convergence

1997 ◽  
Vol 349 ◽  
pp. 1-30 ◽  
Author(s):  
N. R. PANCHAPAKESAN ◽  
T. B. NICKELS ◽  
P. N. JOUBERT ◽  
A. J. SMITS
Keyword(s):  
Pressure Gradient ◽  
Boundary Layers ◽  
Turbulent Transport ◽  
Turbulent Boundary Layers ◽  
Local Effect ◽  
Wall Region ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Dimensional Parameter ◽  
Outer Flow

Experimental measurements are presented showing the effects of streamline convergence on developing turbulent boundary layers. The longitudinal pressure-gradient in these experiments is nominally zero so the only extra rate-of-strain is the lateral convergence. Measurements have been made of mean flow and turbulence quantities at two different Reynolds numbers. The results show that convergence leads to a significant reduction in the skin-friction and an increase in the boundary layer thickness. There are also large changes in the Reynolds stresses with reductions occurring in the inner region and some increase in the outer flow. This is in contrast to the results of Saddoughi & Joubert (1991) for a diverging flow of the same included angle and zero pressure-gradient which show much smaller changes in the stresses and an approach to equilibrium. A new non-dimensional parameter, βD, is proposed to characterize the local effect of the convergence and it is shown how this parameter is related to Clauser's pressure-gradient parameter, βx. It is suggested that this is an equilibrium parameter for turbulent boundary layers with lateral straining. In the present flow case βD increases rapidly with streamwise distance leading to a significant departure from equilibrium. Measurement of terms in the transport equations suggest that streamline convergence leads to a reduction in production and generation and large increases in mean advection. The recovery of the flow after the removal of convergence has been shown to be characterized by a significant increase in the turbulent transport of shear-stress and turbulent kinetic energy from the very near-wall region to the flow further out where the stresses have been depleted by convergence.

Scaling of Favorable Pressure Gradient Turbulent Boundary Layers With Eventual Relaminarization

2005 ◽  
Author(s):  
Rau´l Bayoa´n Cal ◽  
Xia Wang ◽  
Luciano Castillo
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Reynolds Shear Stress ◽  
Velocity Profiles ◽  
Turbulent Boundary Layers ◽  
Reynolds Stresses ◽  
Mean Velocity ◽  
Favorable Pressure Gradient ◽  
The Mean

Applying similarity analysis to the RANS equations of motion for a pressure gradient turbulent boundary layer, Castillo and George [1] obtained the scalings for the mean deficit velocity and the Reynolds stresses. Following this analysis, Castillo and George studied favorable pressure gradient (FPG) turbulent boundary layers. They were able to obtain a single curve for FPG flows when scaling the mean deficit velocity profiles. In this study, FPG turbulent boundary layers are analyzed as well as relaminarized boundary layers subjected to an even stronger FPG. It is found that the mean deficit velocity profiles diminish when scaled using the Castillo and George [1] scaling, U∞, and the Zagarola and Smits [2] scaling, U∞δ*/δ. In addition, Reynolds stress data has been analyzed and it is found that the relaminarized boundary layer data decreases drastically in all components of the Reynolds stresses. Furthermore, it will be shown that the shape of the profile for the wall-normal and Reynolds shear stress components change drastically given the relaminarized state. Therefore, the mean velocity deficit profiles as well as Reynolds stresses are found to be necessary in order to understand not only FPG flows, but also relaminarized boundary layers.

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.

Experiment on Turbulent Boundary Layers on a Concave Wall

1975 ◽  
Vol 26 (1) ◽  
pp. 25-40 ◽  
Author(s):  
Ronald M C So ◽  
George L Mellor
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Boundary Layers ◽  
Present Experiment ◽  
Large Scale ◽  
Turbulent Boundary Layers ◽  
Turbulence Level ◽  
Mean Velocity ◽  
Concave Wall ◽  
Transverse Profile

SummaryThe present experiment describes the behaviour of a turbulent boundary layer on a concave wall. At the onset of curvature there appears a fairly coherent wavelike transverse profile of mean velocity. This disturbance might be interpreted as a kind of large scale Taylor-Görtler type instability superimposed on a conventional turbulent boundary layer; further downstream the coherence degenerates as the turbulence level increases. Boundary-layer profile measurements were made at positions of maxima and minima of transverse profiles of (U-component) mean velocity. The boundary layer at the minima positions is found to be twice as thick as that at the maxima positions. Also, turbulent intensities inside the boundary layer are substantially increased as a result of the concave curvature of the surface.

Reynolds Number Dependence of Zero Pressure Gradient Turbulent Boundary Layers Including Third-Order Moments and Spatial Correlations

2020 ◽  
Vol 142 (5) ◽  
Author(s):  
Ralph J. Volino
Keyword(s):  
Reynolds Number ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Field Measurements ◽  
Turbulent Boundary Layers ◽  
Quadrant Analysis ◽  
Shear Stresses ◽  
Reynolds Stresses ◽  
Spatial Correlations ◽  
Mean Velocity

Abstract Measurements were made in zero pressure gradient turbulent boundary layers on a smooth wall, at momentum thickness Reynolds numbers, ranging from 800 to 6340. The experiments were conducted in a recirculating water tunnel. Two-component velocity profiles were acquired using laser Doppler velocimetry at five streamwise stations and three different freestream velocities. Velocity field measurements were acquired using particle image velocimetry in streamwise-wall normal and streamwise–spanwise planes. Profiles of mean velocity and turbulence statistics including the Reynolds normal and shear stresses, and triple products of the velocity fluctuations are presented in both inner and outer coordinates. Variations in the profiles at representative distances from the wall are presented and quantified as functions of Reynolds number. The triple products are explained in terms of transport of Reynolds stresses though motions associated with quadrant analysis, and variation with Reynolds number is consistent with that of Reynolds stresses. The structure of turbulence was considered through two-point correlations of the fluctuations in velocity fields. In general, the shape and inclination angles of the structures did not change with Reynolds number, but some streamwise and spanwise growth was observed as Reynolds number increased.

Optimal disturbances and large-scale energetic motions in turbulent boundary layers

2018 ◽  
Vol 860 ◽  
pp. 40-80
Author(s):  
Timothy B. Davis ◽  
Ali Uzun ◽  
Farrukh S. Alvi
Keyword(s):  
Boundary Layers ◽  
Large Scale ◽  
Homogeneous Solution ◽  
Turbulent Boundary Layers ◽  
Wall Turbulence ◽  
Energy Spectra ◽  
Mean Flow ◽  
Slow Development ◽  
Wake Modes ◽  
Optimal Disturbances

We examine disturbances leading to optimal energy growth in a spatially developing, zero-pressure-gradient turbulent boundary layer. The slow development of the turbulent mean flow in the streamwise direction is modelled through a parabolized formulation to enable a spatial marching procedure. In the present framework, conventional spatial optimal disturbances arise naturally as the homogeneous solution to the linearized equations subject to a turbulent forcing at particular wavenumber combinations. A wave-like decomposition for the disturbance is considered to incorporate both conventional stationary modes as well as propagating modes formed by non-zero frequency/streamwise wavenumber and representative of convective structures naturally observed in wall turbulence. The optimal streamwise wavenumber, which varies with the spatial development of the turbulent mean flow, is computed locally via an auxiliary optimization constraint. The present approach can then be considered, in part, as an extension of the resolvent-based analyses for slowly developing flows. Optimization results reveal highly amplified disturbances for both stationary and propagating modes. Stationary modes identify peak amplification of structures residing near the centre of the logarithmic layer of the turbulent mean flow. Inner-scaled disturbances reminiscent of near wall streaks, and amplified over short streamwise distances, are identified in the computed streamwise energy spectra. In all cases, however, propagating modes surpass their stationary counterpart in both energy amplification and relative contribution to total fluctuation energy. We identify two classes of large-scale energetic modes associated with the logarithmic and wake layers of the turbulent mean flow. The outer-scaled wake modes agree well with the large-scale motions that populate the wake layer. For high Reynolds numbers, the log modes increasingly dominate the energy spectra with the predicted streamwise and wall-normal scales in agreement with superstructures observed in turbulent boundary layers.

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