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.

Turbulent boundary layer statistics at very high Reynolds number

2015 ◽  
Vol 779 ◽  
pp. 371-389 ◽  
Author(s):  
M. Vallikivi ◽  
M. Hultmark ◽  
A. J. Smits
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
High Reynolds Number ◽  
Reynolds Numbers ◽  
Working Fluid ◽  
Mean Velocity ◽  
High Reynolds Numbers ◽  
Layer Flow ◽  
High Reynolds ◽  
Very High

Measurements are presented in zero-pressure-gradient, flat-plate, turbulent boundary layers for Reynolds numbers ranging from $\mathit{Re}_{{\it\tau}}=2600$ to $\mathit{Re}_{{\it\tau}}=72\,500$ ($\mathit{Re}_{{\it\theta}}=8400{-}235\,000$). The wind tunnel facility uses pressurized air as the working fluid, and in combination with MEMS-based sensors to resolve the small scales of motion allows for a unique investigation of boundary layer flow at very high Reynolds numbers. The data include mean velocities, streamwise turbulence variances, and moments up to 10th order. The results are compared to previously reported high Reynolds number pipe flow data. For $\mathit{Re}_{{\it\tau}}\geqslant 20\,000$, both flows display a logarithmic region in the profiles of the mean velocity and all even moments, suggesting the emergence of a universal behaviour in the statistics at these high Reynolds numbers.

Temperature Control of Blow-Down, Supersonic Tunnels

1956 ◽  
Vol 60 (541) ◽  
pp. 67-70
Author(s):  
T. A. Thomson
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Reynolds Number ◽  
Mach Number ◽  
Reynolds Numbers ◽  
Stagnation Temperature ◽  
Blow Down ◽  
High Reynolds Numbers ◽  
Experimental Errors ◽  
High Reynolds

The blow-down type of intermittent, supersonic tunnel is attractive because of its simplicity and because relatively high Reynolds numbers can be obtained for a given size of test section. An adverse characteristic, however, is the fall of stagnation temperature during runs, which can affect experiments in several ways. The Reynolds number varies and the absolute velocity is not constant, even if the Mach number and pressure are; heat-transfer cannot be studied under controlled conditions and the experimental errors arising from the effect of heat-transfer on the boundary layer vary in time. These effects can become significant in quantitative experiments if the tunnel is large and the variation of temperature very rapid; the expense required to eliminate them might then be justified.

An Intermittent High-Reynolds-Number Wind Tunnel

1977 ◽  
Vol 28 (4) ◽  
pp. 259-264 ◽  
Author(s):  
J L Stollery ◽  
A V Murthy
Keyword(s):  
Reynolds Number ◽  
Wind Tunnel ◽  
High Reynolds Number ◽  
Reynolds Numbers ◽  
Simple Method ◽  
High Reynolds Numbers ◽  
Reservoir Conditions ◽  
High Reynolds ◽  
Cryogenic Wind Tunnel ◽  
Performance Estimates

SummaryThe paper suggests a simple method of generating intermittent reservoir conditions for an intermittent, cryogenic wind tunnel. Approximate performance estimates are given and it is recommended that further studies be made because this type of tunnel could be valuable in increasing the opportunities for research at high Reynolds numbers.

scholarly journals Revisiting Batchelor's theory of two-dimensional turbulence

2007 ◽  
Vol 591 ◽  
pp. 379-391 ◽  
Author(s):  
DAVID G. DRITSCHEL ◽  
CHUONG V. TRAN ◽  
RICHARD K. SCOTT
Keyword(s):  
Reynolds Number ◽  
Mathematical Analysis ◽  
High Reynolds Number ◽  
Reynolds Numbers ◽  
Inertial Range ◽  
Two Dimensional ◽  
Simple Modification ◽  
High Reynolds Numbers ◽  
Decaying Turbulence ◽  
High Reynolds

Recent mathematical results have shown that a central assumption in the theory of two-dimensional turbulence proposed by Batchelor (Phys. Fluids, vol. 12, 1969, p. 233) is false. That theory, which predicts a χ2/3k−1 enstrophy spectrum in the inertial range of freely-decaying turbulence, and which has evidently been successful in describing certain aspects of numerical simulations at high Reynolds numbers Re, assumes that there is a finite, non-zero enstrophy dissipation χ in the limit of infinite Re. This, however, is not true for flows having finite vorticity. The enstrophy dissipation in fact vanishes.We revisit Batchelor's theory and propose a simple modification of it to ensure vanishing χ in the limit Re → ∞. Our proposal is supported by high Reynolds number simulations which confirm that χ decays like 1/ln Re, and which, following the time of peak enstrophy dissipation, exhibit enstrophy spectra containing an increasing proportion of the total enstrophy 〈ω2〉/2 in the inertial range as Re increases. Together with the mathematical analysis of vanishing χ, these observations motivate a straightforward and, indeed, alarmingly simple modification of Batchelor's theory: just replace Batchelor's enstrophy spectrum χ2/3k−1 with 〈ω2〉 k−1 (ln Re)−1).

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.

AN INITIAL STUDY OF THE FLOW AROUND AN AEROFOIL AT HIGH REYNOLDS NUMBERS USING CONTINUATION

2012 ◽  
Vol 22 (10) ◽  
pp. 1250255 ◽  
Author(s):  
C. WALES ◽  
A. GAITONDE ◽  
D. JONES
Keyword(s):  
Reynolds Number ◽  
High Reynolds Number ◽  
Solution Space ◽  
Reynolds Numbers ◽  
Initial Study ◽  
Continuation Methods ◽  
High Reynolds Numbers ◽  
Large Systems ◽  
High Reynolds ◽  
Reynolds Number Flows

Nonlinearities are an important feature of high Reynolds numbers flows about aircraft. Standard time stepping schemes, used in computational fluid dynamics simulations, are unable to capture the whole solution space, breaking down in the region of bifurcations. The extension of continuation techniques to such flows is therefore attractive. CFD schemes yield large systems of equations and the associated difficulties of applying continuation methods to such large systems need to be overcome. Whilst previous studies of fluids using continuation have been published, these are mainly limited to much lower Reynolds numbers. In high Reynolds number flows, inertial forces dominate and turbulence must be modeled. This study has shown that continuation can be used effectively for high Reynolds number flows demonstrated through the presentation of a number of test cases.

Fully resolved measurements of turbulent boundary layer flows up to

2018 ◽  
Vol 851 ◽  
pp. 391-415 ◽  
Author(s):  
M. Samie ◽  
I. Marusic ◽  
N. Hutchins ◽  
M. K. Fu ◽  
Y. Fan ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Turbulence Intensity ◽  
High Reynolds Number ◽  
Reynolds Numbers ◽  
Turbulent Boundary Layers ◽  
Energy Spectra ◽  
Wall Region ◽  
Velocity Measurements ◽  
Number Range ◽  
High Reynolds

Fully resolved measurements of turbulent boundary layers are reported for the Reynolds number range $Re_{\unicode[STIX]{x1D70F}}=6000{-}20\,000$. Despite several decades of research in wall-bounded turbulence there is still controversy over the behaviour of streamwise turbulence intensities near the wall, especially at high Reynolds numbers. Much of it stems from the uncertainty in measurement due to finite spatial resolution. Conventional hot-wire anemometry is limited for high Reynolds number measurements due to limited spatial resolution issues that cause attenuation in the streamwise turbulence intensity profile near the wall. To address this issue we use the nano-scale thermal anemometry probe (NSTAP), developed at Princeton University to conduct velocity measurements in the high Reynolds number boundary layer facility at the University of Melbourne. The NSTAP has a sensing length almost one order of magnitude smaller than conventional hot-wires. This enables us to acquire fully resolved velocity measurements of turbulent boundary layers up to $Re_{\unicode[STIX]{x1D70F}}=20\,000$. Results show that in the near-wall region, the viscous-scaled streamwise turbulence intensity grows with $Re_{\unicode[STIX]{x1D70F}}$ in the Reynolds number range of the experiments. A second outer peak in the streamwise turbulence intensity is also shown to emerge at the highest Reynolds numbers. Moreover, the energy spectra in the near-wall region show excellent inner scaling over the small to moderate wavelength range, followed by a large-scale influence that increases with Reynolds number. Outer scaling in the outer region is found to collapse the energy spectra over high wavelengths across various Reynolds numbers.

Effects of Reynolds Number and Free-Stream Turbulence on Boundary Layer Transition in a Compressor Cascade

2000 ◽  
Author(s):  
Heinz-Adolf Schreiber ◽  
Wolfgang Steinert ◽  
Bernhard Küsters
Keyword(s):  
Boundary Layer ◽  
Free Stream ◽  
Reynolds Numbers ◽  
Boundary Layer Transition ◽  
Bypass Transition ◽  
Layer Transition ◽  
Free Stream Turbulence ◽  
High Reynolds Numbers ◽  
High Turbulence ◽  
High Reynolds

An experimental and analytical study has been performed on the effect of Reynolds number and free-stream turbulence on boundary layer transition location on the suction surface of a controlled diffusion airfoil (CDA). The experiments were conducted in a rectilinear cascade facility at Reynolds numbers between 0.7 and 3.0×106 and turbulence intensities from about 0.7 to 4%. An oil streak technique and liquid crystal coatings were used to visualize the boundary layer state. For small turbulence levels and all Reynolds numbers tested the accelerated front portion of the blade is laminar and transition occurs within a laminar separation bubble shortly after the maximum velocity near 35–40% of chord. For high turbulence levels (Tu > 3%) and high Reynolds numbers transition propagates upstream into the accelerated front portion of the CDA blade. For those conditions, the sensitivity to surface roughness increases considerably and at Tu = 4% bypass transition is observed near 7–10% of chord. Experimental results are compared to theoretical predictions using the transition model which is implemented in the MISES code of Youngren and Drela. Overall the results indicate that early bypass transition at high turbulence levels must alter the profile velocity distribution for compressor blades that are designed and optimized for high Reynolds numbers.

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