Reynolds Number Effects in Wall-Bounded Turbulent Flows

1994 ◽  
Vol 47 (8) ◽  
pp. 307-365 ◽  
Author(s):  
Mohamed Gad-el-Hak ◽  
Promode R. Bandyopadhyay
Keyword(s):  
Reynolds Number ◽  
Coherent Structures ◽  
High Reynolds Number ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Mean Flow ◽  
Reynolds Number Effects ◽  
The Mean ◽  
Low Reynolds ◽  
High Reynolds

This paper reviews the state of the art of Reynolds number effects in wall-bounded shear-flow turbulence, with particular emphasis on the canonical zero-pressure-gradient boundary layer and two-dimensional channel flow problems. The Reynolds numbers encountered in many practical situations are typically orders of magnitude higher than those studied computationally or even experimentally. High-Reynolds number research facilities are expensive to build and operate and the few existing are heavily scheduled with mostly developmental work. For wind tunnels, additional complications due to compressibility effects are introduced at high speeds. Full computational simulation of high-Reynolds number flows is beyond the reach of current capabilities. Understanding of turbulence and modeling will continue to play vital roles in the computation of high-Reynolds number practical flows using the Reynolds-averaged Navier-Stokes equations. Since the existing knowledge base, accumulated mostly through physical as well as numerical experiments, is skewed towards the low Reynolds numbers, the key question in such high-Reynolds number modeling as well as in devising novel flow control strategies is: what are the Reynolds number effects on the mean and statistical turbulence quantities and on the organized motions? Since the mean flow review of Coles (1962), the coherent structures, in low-Reynolds number wall-bounded flows, have been reviewed several times. However, the Reynolds number effects on the higher-order statistical turbulence quantities and on the coherent structures have not been reviewed thus far, and there are some unresolved aspects of the effects on even the mean flow at very high Reynolds numbers. Furthermore, a considerable volume of experimental and full-simulation data have been accumulated since 1962. The present article aims at further assimilation of those data, pointing to obvious gaps in the present state of knowledge and highlighting the misunderstood as well as the ill-understood aspects of Reynolds number effects.

scholarly journals Model-based scaling of the streamwise energy density in high-Reynolds-number turbulent channels

2013 ◽  
Vol 734 ◽  
pp. 275-316 ◽  
Author(s):  
Rashad Moarref ◽  
Ati S. Sharma ◽  
Joel A. Tropp ◽  
Beverley J. McKeon
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Low Rank ◽  
Navier Stokes ◽  
Mean Velocity ◽  
Navier Stokes Equations ◽  
Self Similar ◽  
The Mean ◽  
High Reynolds

AbstractWe study the Reynolds-number scaling and the geometric self-similarity of a gain-based, low-rank approximation to turbulent channel flows, determined by the resolvent formulation of McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382), in order to obtain a description of the streamwise turbulence intensity from direct consideration of the Navier–Stokes equations. Under this formulation, the velocity field is decomposed into propagating waves (with single streamwise and spanwise wavelengths and wave speed) whose wall-normal shapes are determined from the principal singular function of the corresponding resolvent operator. Using the accepted scalings of the mean velocity in wall-bounded turbulent flows, we establish that the resolvent operator admits three classes of wave parameters that induce universal behaviour with Reynolds number in the low-rank model, and which are consistent with scalings proposed throughout the wall turbulence literature. In addition, it is shown that a necessary condition for geometrically self-similar resolvent modes is the presence of a logarithmic turbulent mean velocity. Under the practical assumption that the mean velocity consists of a logarithmic region, we identify the scalings that constitute hierarchies of self-similar modes that are parameterized by the critical wall-normal location where the speed of the mode equals the local turbulent mean velocity. For the rank-1 model subject to broadband forcing, the integrated streamwise energy density takes a universal form which is consistent with the dominant near-wall turbulent motions. When the shape of the forcing is optimized to enforce matching with results from direct numerical simulations at low turbulent Reynolds numbers, further similarity appears. Representation of these weight functions using similarity laws enables prediction of the Reynolds number and wall-normal variations of the streamwise energy intensity at high Reynolds numbers (${Re}_{\tau } \approx 1{0}^{3} {\unicode{x2013}} 1{0}^{10} $). Results from this low-rank model of the Navier–Stokes equations compare favourably with experimental results in the literature.

scholarly journals The streamwise turbulence intensity in the intermediate layer of turbulent pipe flow

2015 ◽  
Vol 774 ◽  
pp. 324-341 ◽  
Author(s):  
J. C. Vassilicos ◽  
J.-P. Laval ◽  
J.-M. Foucaut ◽  
M. Stanislas
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Intermediate Layer ◽  
High Reynolds Number ◽  
Logarithmic Derivative ◽  
Turbulent Pipe Flow ◽  
Mean Flow ◽  
The Mean ◽  
High Reynolds

The spectral model of Perryet al. (J. Fluid Mech., vol. 165, 1986, pp. 163–199) predicts that the integral length scale varies very slowly with distance to the wall in the intermediate layer. The only way for the integral length scale’s variation to be more realistic while keeping with the Townsend–Perry attached eddy spectrum is to add a new wavenumber range to the model at wavenumbers smaller than that spectrum. This necessary addition can also account for the high-Reynolds-number outer peak of the turbulent kinetic energy in the intermediate layer. An analytic expression is obtained for this outer peak in agreement with extremely high-Reynolds-number data by Hultmarket al. (Phys. Rev. Lett., vol. 108, 2012, 094501;J. Fluid Mech., vol. 728, 2013, pp. 376–395). Townsend’s (The Structure of Turbulent Shear Flows, 1976, Cambridge University Press) production–dissipation balance and the finding of Dallaset al. (Phys. Rev. E, vol. 80, 2009, 046306) that, in the intermediate layer, the eddy turnover time scales with skin friction velocity and distance to the wall implies that the logarithmic derivative of the mean flow has an outer peak at the same location as the turbulent kinetic energy. This is seen in the data of Hultmarket al. (Phys. Rev. Lett., vol. 108, 2012, 094501;J. Fluid Mech., vol. 728, 2013, pp. 376–395). The same approach also predicts that the logarithmic derivative of the mean flow has a logarithmic decay at distances to the wall larger than the position of the outer peak. This qualitative prediction is also supported by the aforementioned data.

Vortex Formation for Different Geometry of Cavities Using High Reynolds Number

2014 ◽  
Vol 699 ◽  
pp. 416-421
Author(s):  
Mohd Noor Asril Saadun ◽  
Muhammad Zulhakim Sharudin ◽  
Nor Azwadi Che Sidik ◽  
Mohd Hafidzal Mohd Hanafi
Keyword(s):  
Reynolds Number ◽  
High Reynolds Number ◽  
Stokes Equations ◽  
Vortex Formation ◽  
Flow Characteristics ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Contaminant Removal ◽  
Navier Stokes Equations ◽  
High Reynolds

A preliminary study of Computational Fluid Dynamics (CFD) on the effect of high Reynolds numbers in the cavity has been carried out. Two dimensional model analysis of the flow characteristics were conducted using the numerical solution of Navier-Stokes equations based on the finite difference method. The flow characteristics in the cavity and the driven flow were modeled via turbulence equation modelling. This paper focuses on the effects of different high Reynolds number on the flow pattern of contaminant removal in the cavity. Different types of geometry and aspect ratio of the geometry were used as the parameters of the cavity in this study. Based on visualization of flows between each model with the different parameters used, the results of a comparison analysis focusing on the behavior of the flow were reported.

Similarity Formulations for Turbulent Boundary Layers at High Reynolds Numbers

2003 ◽  
Author(s):  
Gary J. Kunkel ◽  
Ivan Marusic
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Turbulence Intensity ◽  
High Reynolds Number ◽  
Reynolds Numbers ◽  
Mean Flow ◽  
Mixed Flow ◽  
High Reynolds Numbers ◽  
High Reynolds ◽  
New Formulation

Data obtained from the high Reynolds number atmospheric boundary layer are used to analyze existing mean-flow and turbulence intensity similarity formulations. From the results of this analysis a new streamwise turbulence intensity formulation is proposed that is suggested to be applicable across the entire smooth-wall high Reynolds number turbulent boundary layer. The new formulation is also shown to be consistent with the mixed-flow scaling suggested by other studies.

The sweeping decorrelation hypothesis and energy–inertial scale interaction in high Reynolds number flows

1993 ◽  
Vol 248 ◽  
pp. 493-511 ◽  
Author(s):  
Alexander A. Praskovsky ◽  
Evgeny B. Gledzer ◽  
Mikhail Yu. Karyakin ◽  
And Ye Zhou
Keyword(s):  
Reynolds Number ◽  
Strong Correlation ◽  
High Reynolds Number ◽  
Structure Functions ◽  
Higher Order ◽  
Inertial Subrange ◽  
Small Scale ◽  
Mean Flow ◽  
The Mean ◽  
High Reynolds

The random sweeping decorrelation hypothesis was analysed theoretically and experimentally in terms of the higher-order velocity structure functions $D_{u_i}^{(m)}(r) = \left< [u_i^m(x + r) - u_i^m(x)]^2\right>$. Measurements in two high Reynolds number laboratory shear flows were used: in the return channel (Rλ ≈ 3.2 × 103) and in the mixing layer (Rλ ≈ 2.0 × 103) of a large wind tunnel. Two velocity components (in the direction of the mean flow, u1, and in the direction of the mean shear, u2) were processed for m = 1−4. The effect of using Taylor's hypothesis was estimated by a specially developed method, and found to be insignificant. It was found that all the higher-order structure functions scale, in the inertial subrange, as r2/3. Such a scaling has been argued as supporting evidence for the sweeping hypothesis. However, our experiments also established a strong correlation between energy- and inertial-range excitation. This finding leads to the conclusion that the sweeping decorrelation hypothesis cannot be exactly valid.The hypothesis of statistical independence of large- and small-scale excitation was directly checked with conditionally averaged moments of the velocity difference $\left< [u_i(x + r) - u_i(x)]^l\right>_{u_i^*}, l = 2-4$, at a fixed value of the large-scale parameter u*i. Clear dependence of the conditionally averaged moments on the level of averaging was found. In spite of a strong correlation between the energy-containing and the inertial-scale excitation, universality of the intrinsic structure of the inertial subrange was shown.

Stability of the flow of a fluid through a flexible tube at high Reynolds number

1995 ◽  
Vol 302 ◽  
pp. 117-139 ◽  
Author(s):  
V. Kumaran
Keyword(s):  
Growth Rate ◽  
Reynolds Number ◽  
Viscous Dissipation ◽  
High Reynolds Number ◽  
Wall Layer ◽  
Mean Flow ◽  
The Real ◽  
Flexible Tube ◽  
The Mean ◽  
High Reynolds

The stability of the Hagen-Poiseuille flow of a Newtonian fluid in a tube of radius R surrounded by an incompressible viscoelastic medium of radius R < r < HR is analysed in the high Reynolds number regime. The dimensionless numbers that affect the fluid flow are the Reynolds number Re = (ρVR / η), the ratio of the viscosities of the wall and fluid ηr = (ηs/η), the ratio of radii H and the dimensionless velocity Γ = (ρV2/G)1/2. Here ρ is the density of the fluid, G is the coefficient of elasticity of the wall and Vis the maximum fluid velocity at the centre of the tube. In the high Reynolds number regime, an asymptotic expansion in the small parameter ε = (1/Re) is employed. In the leading approximation, the viscous effects are neglected and there is a balance between the inertial stresses in the fluid and the elastic stresses in the medium. There are multiple solutions for the leading-order growth rate do), all of which are imaginary, indicating that the fluctuations are neutrally stable, since there is no viscous dissipation of energy or transfer of energy from the mean flow to the fluctruations due to the Reynolds strees.There is an O(ε1/2) correction to the growth rate, s(1), due to the presence of a wall layer of thickness ε1/2R where the viscous stresses are O(ε1/2) smaller than the inertial stresses. An energy balance analysis indicates that the transfer of energy from the mean flow to the fluctuations due to the Reynolds stress in the wall layer is exactly cancelled by an opposite transfer of equal magnitude due to the deformation work done at the interface, and there is no net transfer from the mean flow to the fluctuations. Consequently, the fluctuations are stabilized by the viscous dissipation in the wall layer, and the real part of s(1) is negative. However, there are certain values of Γ and wavenumber k where s(l) = 0. At these points, the wail layer amplitude becomes zero because the tangential velocity boundary condition is identically satisfied by the inviscid flow solution. The real part of the O(ε) correction to the growth rate s(2) turns out to be negative at these points, indicating a small stabilizing effect due to the dissipation in the bulk of the fluid and the wall material. It is found that the minimum value of s(2) increases ∝ (H − 1)−2 for (H − 1) [Lt ] 1 (thickness of wall much less than the tube radius), and decreases ∝ (H−4 for H [Gt ] 1. The damping rate for the inviscid modes is smaller than that for the viscous wall and centre modes in a rigid tube, which have been determined previously using a singular perturbation analysis. Therefore, these are the most unstable modes in the flow through a flexible tube.

Effects of Free Stream Turbulence on Low Reynolds Number Boundary Layers

1984 ◽  
Vol 106 (3) ◽  
pp. 298-306 ◽  
Author(s):  
I. P. Castro
Keyword(s):  
Reynolds Number ◽  
Boundary Layers ◽  
Free Stream ◽  
Reynolds Numbers ◽  
Length Scale ◽  
Mean Flow ◽  
Low Reynolds Numbers ◽  
Free Stream Turbulence ◽  
Reynolds Number Effects ◽  
Low Reynolds

This paper documents some of the effects of free stream turbulence on the mean flow properties of turbulent boundary layers in zero pressure gradients. Attention is concentrated on flows for which the momentum thickness Reynolds number is less than about 2000. Direct Reynolds number effects are therefore significant and it is shown that such effects reduce as the level of free stream turbulence rises. A modification to Hancock’s [1] empirical correlation relating the fractional increase in skin friction at constant Reynolds number to a free stream turbulence parameter containing a dependence on both intensity and length scale is proposed. While this modification has the necessary characteristic of being a function of the free stream turbulence parameters as well as the Reynolds number, it is argued that the relative importance of intensity and length scale changes at low Reynolds numbers; the data are not inconsistent with this idea. The experiments cover the range 500 ⪝ Reθ ⪝ 2500, u′/Ue ⪝ 0.07, 0.8 ⪝ Le/δ ⪝ 2.9, where u′/Ue is the free stream turbulence intensity and Le/δ is the ratio of the dissipation length scale of the free stream turbulence to the 99 percent thickness of the boundary layer.

scholarly journals A theory for the streamwise turbulent fluctuations in high Reynolds number pipe flow

2012 ◽  
Vol 707 ◽  
pp. 575-584 ◽  
Author(s):  
Marcus Hultmark
Keyword(s):  
Experimental Data ◽  
Reynolds Number ◽  
Pipe Flow ◽  
High Reynolds Number ◽  
Mean Flow ◽  
Mean Velocity ◽  
Theoretical Derivation ◽  
Turbulent Fluctuations ◽  
The Mean ◽  
High Reynolds

AbstractA new theory for the streamwise turbulent fluctuations in fully developed pipe flow is proposed. The theory extends the similarities between the mean flow and the streamwise turbulence fluctuations, as observed in experimental high Reynolds number data, to also include the theoretical derivation. Connecting the derivation of the fluctuations to that of the mean velocity at finite Reynolds number as introduced by Wosnik, Castillo & George (J. Fluid Mech., vol. 421, 2000, pp. 115–145) can explain the logarithmic behaviour as well as the coefficient of the logarithm. The slope of the logarithm, for the fluctuations, depends on the increase of the fluctuations with Reynolds number, which is shown to agree very well with the experimental data. A mesolayer, similar to that introduced by Wosnik et al., exists for the fluctuations for $300\gt {y}^{+ } \gt 800$, which coincides with the mesolayer for the mean velocities. In the mesolayer, the flow is still affected by viscosity, which shows up as a decrease in the fluctuations.

Sign in / Sign up

Export Citation Format

Share Document