A technique to determine total shear stress and polymer stress profiles in drag reduced boundary layer flows

2006 ◽  
Vol 40 (4) ◽  
pp. 589-600 ◽  
Author(s):  
Yongxi Hou ◽  
Vijay S. R. Somandepalli ◽  
M. G. Mungal
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Boundary Layer Flows ◽  
Total Shear Stress ◽  
Stress Profiles ◽  
Total Shear

Comprehensive shear stress analysis of turbulent boundary layer profiles

2019 ◽  
Vol 879 ◽  
pp. 360-389 ◽  
Author(s):  
Kristofer M. Womack ◽  
Charles Meneveau ◽  
Michael P. Schultz
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Pressure Gradient ◽  
Friction Velocity ◽  
Stress Profile ◽  
Pressure Gradients ◽  
Streamwise Location ◽  
Shear Stress Profile ◽  
Total Shear Stress ◽  
Total Shear

Motivated by the need for accurate determination of wall shear stress from profile measurements in turbulent boundary layer flows, the total shear stress balance is analysed and reformulated using several well-established semi-empirical relations. The analysis highlights the significant effect that small pressure gradients can have on parameters deduced from data even in nominally zero pressure gradient boundary layers. Using the comprehensive shear stress balance together with the log-law equation, it is shown that friction velocity, roughness length and zero-plane displacement can be determined with only velocity and turbulent shear stress profile measurements at a single streamwise location for nominally zero pressure gradient turbulent boundary layers. Application of the proposed analysis to turbulent smooth- and rough-wall experimental data shows that the friction velocity is determined with accuracy comparable to force balances (approximately 1 %–4 %). Additionally, application to boundary layer data from previous studies provides clear evidence that the often cited discrepancy between directly measured friction velocities (e.g. using force balances) and those derived from traditional total shear stress methods is likely due to the small favourable pressure gradient imposed by a fixed cross-section facility. The proposed comprehensive shear stress analysis can account for these small pressure gradients and allows more accurate boundary layer wall shear stress or friction velocity determination using commonly available mean velocity and shear stress profile data from a single streamwise location.

Determination of Total Shear Stress and Polymer Stress Profiles in Drag Reduced Boundary Layer Flows With Polymer Injection

2005 ◽  
Author(s):  
Y. X. Hou ◽  
V. S. R. Somandepalli ◽  
M. G. Mungal
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Stress Profile ◽  
Polymer Injection ◽  
Curve Fit ◽  
Shear Stress Profile ◽  
Total Shear Stress ◽  
Total Shear

Two methods of recovering the entire total shear stress profile from incomplete velocity data in turbulent boundary layers are presented and validated for both DNS simulations and experimental measurements. The first method, an exponential-polynomial curve fit, recovers the whole total shear stress profile well by using the data from the outer part of the boundary layer (y/δ > 0.3). However, this curve fit is sensitive to the quality of the data. The second method, a new (1−y) weighted straight line fit, which is very simple and accurate, has been applied to current experiments of drag reduction in zero pressure gradient turbulent boundary layers with polymer injection. The total shear stress profile obtained from this fit is used to estimate the contribution of the polymer stress to the total shear stress.

Establishing the generality of three phenomena using a boundary layer with free-stream passing wakes

2010 ◽  
Vol 664 ◽  
pp. 193-219 ◽  
Author(s):  
XIAOHUA WU
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Free Stream ◽  
Transitional Region ◽  
Hairpin Vortices ◽  
Turbulent Region ◽  
Total Shear Stress ◽  
Total Shear

Direct numerical simulation was performed on an incompressible, smooth flat-plate boundary layer at unit molecular Prandtl number and constant surface temperature under free-stream periodically passing turbulent planar wakes over the momentum thickness Reynolds number range of 80 ≤ Reθ ≤ 1850. This inhomogeneous free-stream wake perturbation source with mean deficit differs markedly from the isotropic turbulent patch used in the previous studies of Wu & Moin (J. Fluid Mech., vol. 630, 2009, p. 5; Phys. Fluids, vol. 22, 2010, 085105). Preponderance of hairpin vortices is observed in both the transitional and turbulent regions of the boundary layer. In particular, the internal structure of merged turbulent spots is a hairpin forest; the internal structure of infant turbulent spots is a hairpin packet. Although more chaotic in the turbulent region, numerous hairpin vortices are readily detected in both the near-wall and outer regions of the boundary layer up to Reθ = 1850. This suggests that the hairpin vortices in the higher-Reynolds-number region are not simply the aged hairpin forests convected from the upstream transitional region. Temperature iso-surfaces in the companion thermal boundary layer are found to be a useful tracer in identifying boundary-layer hairpin vortex structures. Total shear stress overshoots wall shear stress in the transitional region and the excess relaxes gradually in the downstream turbulent region. This overshoot is shown to be associated with a localized streamwise acceleration of the streamwise velocity component. Breakdown of the wake-perturbed laminar boundary layer is closely related to the formation of hairpin packets out of quasi-streamwise vortices. Mean and second-order statistics are in good agreement with previous data on the standard turbulent boundary layer. Downstream of transition, normalized root-mean-square (r.m.s.) wall-shear-stress intensity shows almost no variation with Reθ, whereas normalized r.m.s. wall-pressure intensity increases slightly. Taken together with the previous results of Wu & Moin, the generality of the following three phenomena in quasi-standard boundary layers can be reasonably established, namely, preponderance of hairpin vortices in the transitional as well as in the turbulent regions up to Reθ = 1850, transitional total shear stress overshoot, and a laminar-layer breakdown process closely tied to the formation of hairpin packets.

A Note on a Generalized Eddy-Viscosity Hypothesis

1992 ◽  
Vol 114 (3) ◽  
pp. 463-466 ◽  
Author(s):  
P. Andreasson ◽  
U. Svensson
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Velocity Gradient ◽  
Eddy Viscosity ◽  
Channel Flows ◽  
Length Scale ◽  
Asymmetric Channel ◽  
Boundary Layer Flows ◽  
Turbulent Length Scale ◽  
Model Predictions

The standard eddy-viscosity concept postulates that zero velocity gradient is accompanied by zero shear stress. This is not true for many boundary layer flows: wall jets, asymmetric channel flows, countercurrent flows, for example. The generalized eddy-viscosity hypothesis presented in this paper, relaxes this limitation by recognizing the influence of gradients in the turbulent length scale and the shear. With this new eddy-viscosity concept, implemented into the standard k–ε model, predictions of some boundary layer flows are made. The modelling results agree well with measurements, where predictions with the standard eddy-viscosity concept are known to fail.

Supplementary Boundary-Layer Approximations for Turbulent Flow

1989 ◽  
Vol 111 (4) ◽  
pp. 420-427 ◽  
Author(s):  
L. C. Thomas ◽  
S. M. F. Hasani
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Pressure Gradient ◽  
Adverse Pressure Gradient ◽  
Boundary Layer Flows ◽  
Mean Velocity ◽  
Wide Range ◽  
The Mean ◽  
Wall Shear

Approximations for total stress τ and mean velocity u are developed in this paper for transpired turbulent boundary layer flows. These supplementary boundary-layer approximations are tested for a wide range of near equilibrium flows and are incorporated into an inner law method for evaluating the mean wall shear stress τ0. The testing of the proposed approximations for τ and u indicates good agreement with well-documented data for moderate rates of blowing and suction and pressure gradient. These evaluations also reveal limitations in the familiar logarithmic law that has traditionally been used in the determination of wall shear stress for non-transpired boundary-layer flows. The calculations for τ0 obtained by the inner law method developed in this paper are found to be consistent with results obtained by the modern Reynolds stress method for a broad range of near equilibrium conditions. However, the use of the proposed inner law method in evaluating the mean wall shear stress for early classic near equilibrium flow brings to question the reliability of the results for τ0 reported for adverse pressure gradient flows in the 1968 Stanford Conference Proceedings.

Large- and very-large-scale motions in channel and boundary-layer flows

2007 ◽  
Vol 365 (1852) ◽  
pp. 665-681 ◽  
Author(s):  
B.J Balakumar ◽  
R.J Adrian
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Pipe Flow ◽  
Large Scale ◽  
Reynolds Shear Stress ◽  
Boundary Layer Flows ◽  
Wall Flows ◽  
Large Structures ◽  
Measurement And Analysis ◽  
Common Behaviour

Large-scale motions (LSMs; having wavelengths up to 2–3 pipe radii) and very-LSMs (having wavelengths more than 3 pipe radii) have been shown to carry more than half of the kinetic energy and Reynolds shear stress in a fully developed pipe flow. Studies using essentially the same methods of measurement and analysis have been extended to channel and zero-pressure-gradient boundary-layer flows to determine whether large structures appear in these canonical wall flows and how their properties compare with that of the pipe flow. The very large scales, especially those of the boundary layer, are shorter than the corresponding scales in the pipe flow, but otherwise share a common behaviour, suggesting that they arise from similar mechanism(s) aside from the modifying influences of the outer geometries. Spectra of the net force due to the Reynolds shear stress in the channel and boundary layer flows are similar to those in the pipe flow. They show that the very-large-scale and main turbulent motions act to decelerate the flow in the region above the maximum of the Reynolds shear stress.

scholarly journals Mechanism for initiating secondary currents in channel flows

2009 ◽  
Vol 36 (9) ◽  
pp. 1506-1516 ◽  
Author(s):  
Shu-Qing Yang
Keyword(s):  
Shear Stress ◽  
Secondary Flow ◽  
Flow Region ◽  
Streamwise Velocity ◽  
Vortex Center ◽  
Duct Flow ◽  
Secondary Currents ◽  
Total Shear Stress ◽  
Underlying Mechanisms ◽  
Total Shear

This study investigates the underlying mechanisms that initiate secondary flow in developing turbulent flow along a corner. This is done by theoretical examination of the total shear stress, which is the time-averaged product of instantaneous streamwise velocity U and the velocity Vn normal to the interface. The study shows that lines of zero total shear stress exist in the flow region, which delineate the region of secondary flow. Therefore, the flow region is dividable and eight vortices occur in a duct flow. The theoretical and experimental results show that the division line, separating the neighboring secondary currents in a corner, is not always identical to the bisector of the corner, but deviates from the corner bisector if the aspect ratio is b/h ≠ 1. By simplifying Reynolds equation in the near-bed region, we find that theoretically a lateral variation of streamwise velocity initiates the wall-tangent flow that drives the vortex in the region bounded by zero total shear stress. A simplified method for estimating the vortex center, near-bed secondary velocity, and shape of secondary currents has been proposed, and a good agreement between the measured and predicted features is achieved.

Eddy Viscosity Transport Equations and Their Relation to the k-ε Model

1997 ◽  
Vol 119 (4) ◽  
pp. 876-884 ◽  
Author(s):  
F. R. Menter
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Eddy Viscosity ◽  
Turbulence Models ◽  
Equation Model ◽  
Turbulent Shear ◽  
Boundary Layer Flows ◽  
Turbulent Layer ◽  
Turbulent Shear Stress ◽  
The One

A formalism will be presented which allows transforming two-equation eddy viscosity turbulence models into one-equation models. The transformation is based on Bradshaw’s assumption that the turbulent shear stress is proportional to the turbulent kinetic energy. This assumption is supported by experimental evidence for a large number of boundary layer flows and has led to improved predictions when incorporated into two-equation models of turbulence. Based on it, a new one-equation turbulence model will be derived from the k-ε model. The model will be tested against the one-equation model of Baldwin and Barth, which is also derived from the k-ε model (plus additional assumptions) and against its parent two-equation model. It will be shown that the assumptions involved in the derivation of the Baldwin-Barth model cause significant problems at the edge of a turbulent layer.

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