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.

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.

Streamwise development of turbulent boundary-layer drag reduction with polymer injection

2008 ◽  
Vol 597 ◽  
pp. 31-66 ◽  
Author(s):  
Y. X. HOU ◽  
V. S. R. SOMANDEPALLI ◽  
M. G. MUNGAL
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Turbulent Boundary Layer ◽  
Drag Reduction ◽  
Reynolds Shear Stress ◽  
Depletion Region ◽  
Stress Profile ◽  
Total Stress ◽  
Polymer Injection ◽  
Shear Stress Profile

Zero-pressure-gradient turbulent boundary-layer drag reduction by polymer injection has been studied with particle image velocimetry. Flow fields ranging from low to maximum drag reduction have been investigated. A previously developed technique – the (1 − y/δ) fit to the total shear stress profile – has been used to evaluate the skin friction, drag reduction and polymer stress. Current results agree well with the semi-log plot of drag reduction vs. normalized polymer flux which has been used by previous workers and can be used as a guide to optimize the use of polymer from a single injector. Detailed flow-field statistics show many special features that pertain to polymer flow. It is shown that the mean velocity responds quickly to the suddenly reduced wall shear stress associated with polymer injection. However, it takes a much longer time for the entire Reynolds shear stress profile to adjust to the same change. The Reynolds shear stress profiles in wall units can be higher than unity and this unique feature can be used to further judge whether the flow is in equilibrium. The streamwise evolution of drag reduction magnitude is used to divide the flow into three regions: development region; steady-state region; and depletion region. The polymer stress is estimated and found to be proportional to drag reduction in the depletion region, but not necessarily so in the other regions. The interaction between injected polymer and turbulent activity in a developing boundary-layer flow is dependent upon the flow history and it produces an equally complex relationship between polymer stress and drag reduction. The stress balance in the boundary layer and the dynamical contribution of the various stresses to the total stress are evaluated and it is seen that the polymer stresses can account for up to 25% of the total stress. This finding is in contrast to channel flows with homogeneous polymer injection where the polymer stress is found to account for up to 60% of the total stress.

The Departure from Equilibrium of Turbulent Boundary Layers

1968 ◽  
Vol 19 (1) ◽  
pp. 1-19 ◽  
Author(s):  
H. McDonald
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Kinetic Energy ◽  
Stress Distribution ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Two Dimensional ◽  
Pressure Distributions ◽  
Momentum Integral ◽  
State Examination

SummaryRecently two authors, Nash and Goldberg, have suggested, intuitively, that the rate at which the shear stress distribution in an incompressible, two-dimensional, turbulent boundary layer would return to its equilibrium value is directly proportional to the extent of the departure from the equilibrium state. Examination of the behaviour of the integral properties of the boundary layer supports this hypothesis. In the present paper a relationship similar to the suggestion of Nash and Goldberg is derived from the local balance of the kinetic energy of the turbulence. Coupling this simple derived relationship to the boundary layer momentum and moment-of-momentum integral equations results in quite accurate predictions of the behaviour of non-equilibrium turbulent boundary layers in arbitrary adverse (given) pressure distributions.

High Freestream Turbulence Effects on Turbulent Boundary Layers

1996 ◽  
Vol 118 (2) ◽  
pp. 276-284 ◽  
Author(s):  
K. A. Thole ◽  
D. G. Bogard
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Boundary Layers ◽  
Outer Region ◽  
Power Spectra ◽  
Turbulent Boundary Layers ◽  
Freestream Turbulence ◽  
Length Scales ◽  
Turbulent Eddies ◽  
Viscous Shear

High freestream turbulence levels significantly alter the characteristics of turbulent boundary layers. Numerous studies have been conducted with freestreams having turbulence levels of 7 percent or less, but studies using turbulence levels greater than 10 percent have been essentially limited to the effects on wall shear stress and heat transfer. This paper presents measurements of the boundary layer statistics for the interaction between a turbulent boundary layer and a freestream with turbulence levels ranging from 10 to 20 percent. The boundary layer statistics reported in this paper include mean and rms velocities, velocity correlation coefficients, length scales, and power spectra. Although the freestream turbulent eddies penetrate into the boundary layer at high freestream turbulence levels, as shown through spectra and length scale measurements, the mean velocity profile still exhibits a log-linear region. Direct measurements of total shear stress (turbulent shear stress and viscous shear stress) confirm the validity of the log-law at high freestream turbulence levels. Velocity defects in the outer region of the boundary layer were significantly decreased resulting in negative wake parameters. Fluctuating rms velocities were only affected when the freestream turbulence levels exceeded the levels of the boundary layer generated rms velocities. Length scales and power spectra measurements showed large scale turbulent eddies penetrate to within y+ = 15 of the wall.

An Approximate Method for the Calculation of Turbulent Boundary Layers in Diffusers

1957 ◽  
Vol 8 (1) ◽  
pp. 58-77 ◽  
Author(s):  
J. F. Norbury
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Pressure Gradient ◽  
Approximate Method ◽  
Boundary Layers ◽  
Stress Gradient ◽  
Adverse Pressure Gradient ◽  
Turbulent Boundary Layers ◽  
Form Parameter ◽  
Parameter Equation

SummaryAn approximate method is described for the calculation of turbulent boundary layers in which the turbulence is developed before the commencement of the adverse pressure gradient, as in most diffuser layers. It is based on a method due to Spence which has been modified and also extended to the calculation of three-dimensional diverging layers such as occur in ducts whose breadth is increasing. The velocity profiles occurring in a diverging layer are examined and it is shown that the inner part obeys the universal logarithmic law, as in two-dimensional layers. This result is used to obtain an equation for the form parameter in diverging layers, by substitution in the equation of motion and incorporation of the equations of momentum and continuity for diverging flow. The form parameter equation contains a term involving the gradient of shear stress at y = θ and values of this term are obtained by the analysis of experimental data and the substitution of known values for all the other terms in the form parameter equation. Values of the term involving shear stress gradient are then correlated in terms of known boundary layer quantities, and the resulting correlation allows the formulation of a step-by-step method for the solution of the form parameter equation. This may be used in conjunction with the momentum equation to predict the boundary layer growth. It was not found possible to effect a satisfactory correlation for boundary layers on lifting aerofoils, in which the turbulence develops within the adverse pressure gradient, and the method cannot be used for the prediction of such layers. The results of a number of calculations are given.

Conditional statistics and flow structures in turbulent boundary layers buffeted by free-stream disturbances

2019 ◽  
Vol 866 ◽  
pp. 526-566 ◽  
Author(s):  
Jiho You ◽  
Tamer A. Zaki
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Kinetic Energy ◽  
Boundary Layers ◽  
Large Scale ◽  
Free Stream ◽  
Turbulent Boundary Layers ◽  
Direct Numerical Simulations ◽  
Free Stream Turbulence ◽  
Conditional Statistics

Direct numerical simulations are performed to study zero-pressure-gradient turbulent boundary layers beneath quiescent and vortical free streams. The inflow boundary layer is computed in a precursor simulation of laminar-to-turbulence transition, and the free-stream vortical forcing is obtained from direct numerical simulations of homogeneous isotropic turbulence. A level-set approach is employed in order to objectively distinguish the boundary-layer and free-stream fluids, and to accurately evaluate their respective contributions to flow statistics. When free-stream turbulence is present, the skin friction coefficient is elevated relative to its value in the canonical boundary-layer configuration. An explanation is provided in terms of an increase in the power input into production of boundary-layer turbulence kinetic energy. This increase takes place deeper than the extent of penetration of the external perturbations towards the wall, and also despite the free-stream perturbations being void of any Reynolds shear stress. Conditional statistics demonstrate that the free-stream turbulence has two effects on the boundary layer: one direct and the other indirect. The low-frequency components of the free-stream turbulence penetrate the logarithmic layer. The associated wall-normal Reynolds stress acts against the mean shear to enhance the shear stress, which in turn enhances turbulence production. This effect directly enlarges the scale and enhances the energy of outer large-scale motions in the boundary layer. The second, indirect effect is the influence of these newly formed large-scale structures. They modulate the near-wall shear stress and, as a result, increase the turbulence kinetic energy production in the buffer layer, which is deeper than the extent of penetration of free-stream turbulence towards the wall.

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.

Calculation of unsteady two-dimensional laminar and turbulent boundary layers with fluctuations in external velocity

1977 ◽  
Vol 355 (1681) ◽  
pp. 225-238 ◽  
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Boundary Layers ◽  
Turbulent Flows ◽  
Reynolds Shear Stress ◽  
Low Frequency ◽  
Analytic Solutions ◽  
Turbulent Boundary Layers ◽  
Two Dimensional ◽  
Boundary Layer Equations

A numerical method is presented for calculating unsteady two-dimensional laminar and turbulent boundary layers with fluctuations in external velocity. The method used an eddy-viscosity formulation to model the Reynolds shear stress term appropriate to turbulent flow and an efficient two-point finite-difference method to solve the governing boundary-layer equations. The method is used to calculate phase angles between the wall shear stress and an oscillating external laminar boundary layer over a flat plate. The results are in excellent agreement with the analytic solutions of Lighthill for the high- and low-frequency limits and provide information in the region between. Similar calculations for turbulent flows are compared with experimental data and the method shown to be more precise than previously described attempts to represent flows of this type. The agreement between calculations and measurements is imperfect but probably within the resolution of the experiments and adequate for engineering purposes.

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