New Mixing-Length Approach for the Mean Velocity Profile of Turbulent Boundary Layers

2005 ◽  
Vol 127 (2) ◽  
pp. 393-396 ◽  
Author(s):  
M. H. Buschmann ◽  
M. Gad-el-Hak
Keyword(s):  
Velocity Profile ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Mixing Length ◽  
Mean Velocity ◽  
The Mean

The mean velocity profile of turbulent boundary layers with system rotation

2000 ◽  
Vol 408 ◽  
pp. 323-345 ◽  
Author(s):  
T. B. NICKELS ◽  
P. N. JOUBERT
Keyword(s):  
Velocity Profile ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Secondary Flows ◽  
Pressure Gradients ◽  
Mean Velocity ◽  
System Rotation ◽  
Linear Correction ◽  
The Mean ◽  
The University

This paper examines changes in the mean velocity profiles of turbulent boundary layers subjected to system rotation. Analysis of the data from several studies conducted in the large rotating wind tunnel at the University of Melbourne shows the existence of a universal linear correction to the velocity profile in the logarithmic region. The appropriate parameters relevant to rotation are derived and correlations are found between the parameters. Flows with adverse pressure gradients, zero pressure gradients and secondary flows are examined and all appear to exhibit the universal linear correction, suggesting that it is robust.

Turbulent Flow Near a Rough Wall

1992 ◽  
Vol 114 (4) ◽  
pp. 537-542 ◽  
Author(s):  
Yang-Moon Koh
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Velocity Profile ◽  
Boundary Layers ◽  
Simple Formula ◽  
Turbulent Boundary Layers ◽  
Mean Velocity ◽  
Friction Factors ◽  
Special Cases ◽  
The Mean

By introducing the equivalent roughness which is defined as the distance from the wall to where the velocity gets a certain value (u/uτ ≈ 8.5) and which can be represented by a simple function of the roughness, a simple formula to represent the mean-velocity distribution across the inner layer of a turbulent boundary layer is suggested. The suggested equation is general enough to be applicable to turbulent boundary layers over surfaces of any roughnesses covering from very smooth to completely rough surfaces. The suggested velocity profile is then used to get expressions for pipe-friction factors and skin friction coefficients. These equations are consistent with existing experimental observations and embrace well-known equations (e.g., Prandtl’s friction law for smooth pipes and Colebrook’s formula etc.) as special cases.

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.

Mean-Velocity Profile of Turbulent Boundary Layers Approaching Separation

AIAA Journal ◽  
2006 ◽  
Vol 44 (11) ◽  
pp. 2465-2474 ◽  
Author(s):  
Thomas Indinger ◽  
Matthias H. Buschmann ◽  
Mohamed Gad-el-Hak
Keyword(s):  
Velocity Profile ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Mean Velocity

scholarly journals High-resolution velocity measurement in the inner part of turbulent boundary layers over super-hydrophobic surfaces

2016 ◽  
Vol 801 ◽  
pp. 670-703 ◽  
Author(s):  
Hangjian Ling ◽  
Siddarth Srinivasan ◽  
Kevin Golovin ◽  
Gareth H. McKinley ◽  
Anish Tuteja ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Velocity Profile ◽  
Drag Reduction ◽  
Slip Velocity ◽  
Reynolds Shear Stress ◽  
Turbulent Boundary Layers ◽  
Mean Velocity ◽  
Roughness Elements ◽  
The Mean

Digital holographic microscopy is used for characterizing the profiles of mean velocity, viscous and Reynolds shear stresses, as well as turbulence level in the inner part of turbulent boundary layers over several super-hydrophobic surfaces (SHSs) with varying roughness/texture characteristics. The friction Reynolds numbers vary from 693 to 4496, and the normalized root mean square values of roughness $(k_{rms}^{+})$ vary from 0.43 to 3.28. The wall shear stress is estimated from the sum of the viscous and Reynolds shear stress at the top of roughness elements and the slip velocity is obtained from the mean profile at the same elevation. For flow over SHSs with $k_{rms}^{+}<1$, drag reduction and an upward shift of the mean velocity profile occur, along with a mild increase in turbulence in the inner part of the boundary layer. As the roughness increases above $k_{rms}^{+}\sim 1$, the flow over the SHSs transitions from drag reduction, where the viscous stress dominates, to drag increase where the Reynolds shear stress becomes the primary contributor. For the present maximum value of $k_{rms}^{+}=3.28$, the inner region exhibits the characteristics of a rough wall boundary layer, including elevated wall friction and turbulence as well as a downward shift in the mean velocity profile. Increasing the pressure in the test facility to a level that compresses the air layer on the SHSs and exposes the protruding roughness elements reduces the extent of drag reduction. Aligning the roughness elements in the streamwise direction increases the drag reduction. For SHSs where the roughness effect is not dominant ($k_{rms}^{+}<1$), the present measurements confirm previous theoretical predictions of the relationships between drag reduction and slip velocity, allowing for both spanwise and streamwise slip contributions.

The Ultimate Asymptote and Mean Flow Structure in Toms’ Phenomenon

1970 ◽  
Vol 37 (2) ◽  
pp. 488-493 ◽  
Author(s):  
P. S. Virk ◽  
H. S. Mickley ◽  
K. A. Smith
Keyword(s):  
Velocity Profile ◽  
Drag Reduction ◽  
Flow Structure ◽  
Viscous Sublayer ◽  
Mixing Length ◽  
Mean Flow ◽  
Mean Velocity ◽  
Law Of The Wall ◽  
Length Constant ◽  
The Mean

The maximum drag reduction in turbulent pipe flow of dilute polymer solutions is ultimately limited by a unique asymptote described by the experimental correlation: f−1/2=19.0log10(NRef1/2)−32.4 The semilogarithmic mean velocity profile corresponding to and inferred from this ultimate asymptote has a mixing-length constant of 0.085 and shares a trisection (at y+ ∼ 12) with the Newtonian viscous sublayer and law of the wall. Experimental mean velocity profiles taken during drag reduction lie in the region bounded by the inferred ultimate profile and the Newtonian law of the wall. At low drag reductions the experimental profiles are well correlated by an “effective slip” model but this fails progressively with increasing drag reduction. Based on the foregoing a three-zone scheme is proposed to model the mean flow structure during drag reduction. In this the mean velocity profile segments are (a) a viscous sublayer, akin to Newtonian, (b) an interactive zone, characteristic of drag reduction, in which the ultimate profile is followed, and (c) a turbulent core in which the Newtonian mixing-length constant applies. The proposed model is consistent with experimental observations and reduces satisfactorily to the Taylor-Prandtl scheme and the ultimate profile, respectively, at the limits of zero and maximum drag reductions.

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.

On the invariant mean velocity profile for compressible turbulent boundary layers

2017 ◽  
Vol 18 (2) ◽  
pp. 186-202 ◽  
Author(s):  
Bin Wu ◽  
Weitao Bi ◽  
Fazle Hussain ◽  
Zhen-Su She
Keyword(s):  
Velocity Profile ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Invariant Mean ◽  
Mean Velocity

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.

Direct numerical simulation of hypersonic turbulent boundary layers. Part 4. Effect of high enthalpy

2011 ◽  
Vol 684 ◽  
pp. 25-59 ◽  
Author(s):  
L. Duan ◽  
M. P. Martín
Keyword(s):  
Boundary Layers ◽  
Transport Model ◽  
Turbulent Boundary Layers ◽  
Turbulence Structure ◽  
Mean Velocity ◽  
Reynolds Analogy ◽  
High Enthalpy ◽  
Turbulent Schmidt Number ◽  
Wide Range ◽  
The Mean

AbstractIn this paper we present direct numerical simulations (DNS) of hypersonic turbulent boundary layers to study high-enthalpy effects. We study high- and low-enthalpy conditions, which are representative of those in hypersonic flight and ground-based facilities, respectively. We find that high-enthalpy boundary layers closely resemble those at low enthalpy. Many of the scaling relations for low-enthalpy flows, such as van-Driest transformation for the mean velocity, Morkovin’s scaling and the modified strong Reynolds analogy hold or can be generalized for high-enthalpy flows by removing the calorically perfect-gas assumption. We propose a generalized form of the modified Crocco relation, which relates the mean temperature and mean velocity across a wide range of conditions, including non-adiabatic cold walls and real gas effects. The DNS data predict Reynolds analogy factors in the range of those found in experimental data at low-enthalpy conditions. The gradient transport model approximately holds with turbulent Prandtl number and turbulent Schmidt number of order unity. Direct compressibility effects remain small and insignificant for all enthalpy cases. High-enthalpy effects have no sizable influence on turbulent kinetic energy (TKE) budgets or on the turbulence structure.

Sign in / Sign up

Export Citation Format

Share Document