scholarly journals Characteristics of Low Reynolds Number Shear-Free Turbulence at an Impermeable Base

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
W. H. M. Wan Mohtar ◽  
A. ElShafie
Keyword(s):  
Reynolds Number ◽  
Horizontal Velocity ◽  
Energy Spectra ◽  
Integral Length Scale ◽  
Length Scale ◽  
Turbulence Structure ◽  
Viscous Damping ◽  
Water Tank ◽  
Velocity Data ◽  
Standard Profile

Shear-free turbulence generated from an oscillating grid in a water tank impinging on an impermeable surface at varying Reynolds number74≤Rel≤570was studied experimentally, where the Reynolds number is defined based on the root-mean-square (r.m.s) horizontal velocity and the integral length scale. A particular focus was paid to the turbulence characteristics for lowRel<150to investigate the minimum limit ofRelobeying the profiles of rapid distortion theory. The measurements taken at near base included the r.m.s turbulent velocities, evolution of isotropy, integral length scales, and energy spectra. Statistical analysis of the velocity data showed that the anisotropic turbulence structure follows the theory for flows withRel≥117. At lowRel<117, however, the turbulence profile deviated from the prediction where no amplification of horizontal velocity components was observed and the vertical velocity components were seen to be constant towards the tank base. Both velocity components sharply decreased towards zero at a distance of≈1/3of the integral length scale above the base due to viscous damping. The lower limit whereRelobeys the standard profile was found to be within the range114≤Rel≤116.

Effect of external turbulence on the evolution of a wake in stratified and unstratified environments

2015 ◽  
Vol 772 ◽  
pp. 361-385 ◽  
Author(s):  
Anikesh Pal ◽  
Sutanu Sarkar
Keyword(s):  
Reynolds Number ◽  
Spatial Organization ◽  
Isotropic Turbulence ◽  
Free Stream ◽  
Vertical Direction ◽  
Integral Length Scale ◽  
Moderate Intensity ◽  
Length Scale ◽  
Wake Turbulence ◽  
External Turbulence

Direct numerical simulations are performed to study the evolution of a towed stratified wake subject to external turbulence in the background. A field of isotropic turbulence is combined with an initial turbulent wake field and the combined wake is simulated in a temporally evolving framework similar to that of Rind & Castro (J. Fluid Mech., vol. 710, 2012a, p. 482). Simulations are performed for external turbulence whose initial level varies between zero and a moderate intensity of up to 7 % relative to the free stream and whose initial integral length scale is of the same order as that of the wake turbulence. A series of simulations are carried out at a Reynolds number of 10 000 and Froude number of 3. Background turbulence, especially at a level of 3 % or above, is found to have substantial quantitative effects in the stratified simulations. Turbulence inside the wake increases due to the entrainment of external turbulence, and the energy transfer through turbulent production from mean to fluctuating velocity also increases, leading to reduced mean velocity. The profiles of normalized mean and turbulence quantities in the stratified wake exhibit little change in the vertical direction but the horizontal spread increases in comparison to the case with undisturbed background. The spatial organization of the internal wave field is disrupted even at the 1 % level of external turbulence. However, key characteristics of stratified wakes such as the formation of coherent pancake vortices and the long lifetime of the mean wake are robust to the presence of fluctuations in the background. A corresponding series of simulations for the unstratified situation is carried out at the same Reynolds number of 10 000 and with similar levels of external turbulence. The change of mean and turbulence statistics is found to be weaker in the unstratified cases compared with the corresponding stratified cases and also weaker relative to that found by Rind & Castro (J. Fluid Mech., vol. 710, 2012a, p. 482) at a similar level of external turbulence relative to the free stream and similar integral length scale. Theoretical arguments and additional simulations are provided to show that the level of external turbulence relative to wake turbulence (dissimilar between the present investigation and Rind & Castro (J. Fluid Mech., vol. 710, 2012a, p. 482)) is a key governing parameter in both stratified and unstratified backgrounds.

Reynolds-number dependence of turbulent velocity and pressure increments

2001 ◽  
Vol 444 ◽  
pp. 343-382 ◽  
Author(s):  
B. R. PEARSON ◽  
R. A. ANTONIA
Keyword(s):  
Reynolds Number ◽  
Fourth Order ◽  
Transverse Velocity ◽  
Inertial Range ◽  
Integral Length Scale ◽  
Length Scale ◽  
Scaling Exponents ◽  
Velocity Increments ◽  
The Mean ◽  
Reynolds Number Dependence

The main focus is the Reynolds number dependence of Kolmogorov normalized low-order moments of longitudinal and transverse velocity increments. The velocity increments are obtained in a large number of flows and over a wide range (40–4250) of the Taylor microscale Reynolds number Rλ. The Rλ dependence is examined for values of the separation, r, in the dissipative range, inertial range and in excess of the integral length scale. In each range, the Kolmogorov-normalized moments of longitudinal and transverse velocity increments increase with Rλ. The scaling exponents of both longitudinal and transverse velocity increments increase with Rλ, the increase being more significant for the latter than the former. As Rλ increases, the inequality between scaling exponents of longitudinal and transverse velocity increments diminishes, reflecting a reduced influence from the large-scale anisotropy or the mean shear on inertial range scales. At sufficiently large Rλ, inertial range exponents for the second-order moment of the pressure increment follow more closely those for the fourth-order moments of transverse velocity increments than the fourth-order moments of longitudinal velocity increments. Comparison with DNS data indicates that the magnitude and Rλ dependence of the mean square pressure gradient, based on the joint-Gaussian approximation, is incorrect. The validity of this approximation improves as r increases; when r exceeds the integral length scale, the Rλ dependence of the second-order pressure structure functions is in reasonable agreement with the result originally given by Batchelor (1951).

Normalized dissipation rate in a moderate Taylor Reynolds number flow

2017 ◽  
Vol 818 ◽  
pp. 184-204 ◽  
Author(s):  
Alejandro J. Puga ◽  
John C. LaRue
Keyword(s):  
Reynolds Number ◽  
Dissipation Rate ◽  
Isotropic Turbulence ◽  
Longitudinal Velocity ◽  
Integral Length Scale ◽  
Length Scale ◽  
Velocity Correlation ◽  
Time Resolved ◽  
Reynolds Number Flow ◽  
Active Grid

Time-resolved velocity measurements are obtained using a hot-wire in a nearly homogeneous and isotropic flow downstream of an active grid for a range of Taylor Reynolds numbers from$191$to$659$. It is found that the dimensionless dissipation rate,$C_{\unicode[STIX]{x1D716}}$, is nearly a constant for sufficiently high values of Taylor Reynolds number,$R_{\unicode[STIX]{x1D706},u_{q}}$, and is approximately equal to$0.87$. This value is approximately$5\,\%$less than the value reported by Boset al.(Phys. Fluids, vol. 19 (4), 2007, 045101), which is obtained using DNS/LES (direct numerical simulation combined with large eddy simulation) for decaying homogeneous and isotropic turbulence, and is in excellent agreement with the active grid experiment of Thormann & Meneveau (Phys. Fluids, vol. 26 (2), 2014, 025112.). The results presented herein show that deviation from isotropy may cause inconsistencies in the computation of$C_{\unicode[STIX]{x1D716}}$. As a result, it is suggested that the velocity scale be the square root of the turbulence kinetic energy. The integral length scale measurements obtained from the longitudinal velocity correlation are in close agreement with the integral length scale measured from the peak of the energy spectrum,$\unicode[STIX]{x1D705}E_{11}(\unicode[STIX]{x1D705})$, where$\unicode[STIX]{x1D705}$is the wavenumber and$E_{11}(\unicode[STIX]{x1D705})$is the one-dimensional power spectrum of the downstream velocity.

scholarly journals Waves and vortices in the inverse cascade regime of stratified turbulence with or without rotation

2016 ◽  
Vol 806 ◽  
pp. 165-204 ◽  
Author(s):  
Corentin Herbert ◽  
Raffaele Marino ◽  
Duane Rosenberg ◽  
Annick Pouquet
Keyword(s):  
Reynolds Number ◽  
Numerical Simulations ◽  
Direct Numerical Simulations ◽  
Vertical Shear ◽  
Energy Spectra ◽  
Stratified Turbulence ◽  
Viscous Effects ◽  
Inverse Cascade ◽  
Main Effects ◽  
The Waves

We study the partition of energy between waves and vortices in stratified turbulence, with or without rotation, for a variety of parameters, focusing on the behaviour of the waves and vortices in the inverse cascade of energy towards the large scales. To this end, we use direct numerical simulations in a cubic box at a Reynolds number $Re\approx 1000$, with the ratio between the Brunt–Väisälä frequency $N$ and the inertial frequency $f$ varying from $1/4$ to 20, together with a purely stratified run. The Froude number, measuring the strength of the stratification, varies within the range $0.02\leqslant Fr\leqslant 0.32$. We find that the inverse cascade is dominated by the slow quasi-geostrophic modes. Their energy spectra and fluxes exhibit characteristics of an inverse cascade, even though their energy is not conserved. Surprisingly, the slow vortices still dominate when the ratio $N/f$ increases, also in the stratified case, although less and less so. However, when $N/f$ increases, the inverse cascade of the slow modes becomes weaker and weaker, and it vanishes in the purely stratified case. We discuss how the disappearance of the inverse cascade of energy with increasing $N/f$ can be interpreted in terms of the waves and vortices, and identify the main effects that can explain this transition based on both inviscid invariants arguments and viscous effects due to vertical shear.

Determination of Incompressible Flow Friction in Smooth Circular and Noncircular Passages: A Generalized Approach Including Validation of the Nearly Century Old Hydraulic Diameter Concept

1988 ◽  
Vol 110 (4) ◽  
pp. 431-440 ◽  
Author(s):  
N. T. Obot
Keyword(s):  
Reynolds Number ◽  
Friction Factor ◽  
Critical Reynolds Number ◽  
Pressure Coefficient ◽  
Hydraulic Diameter ◽  
Length Scale ◽  
The Difference ◽  
Friction Method ◽  
Reduced Data

It has been demonstrated conclusively that the widely observed differences in data for frictional pressure coefficient between circular and noncircular passages derive from the inseparably connected effects of transition and the choice of a length scale. A relatively simple approach, the critical friction method (CFM), has been developed and when applied to triangular, rectangular, and concentric annular passages, the reduced data lie with remarkable consistency on the circular tube relations. In accordance with the theory of dynamical similarity, it has also been shown that noncircular duct data can be reduced using the hydraulic diameter or any arbitrarily defined length scale. The proposed method is what is needed to reconcile such data with those for circular tubes. With the hydraulic diameter, the critical friction factor almost converges to a universal value for all passages and the correction is simply that required to account for the difference in critical Reynolds number. By contrast, with any other linear parameter, two corrections are needed to compensate for variations in critical friction factor and Reynolds number. Application of the method to roughened passages is discussed.

The Effects of Freestream Turbulence, Turbulence Length Scale, and Exit Reynolds Number on Turbine Blade Heat Transfer in a Transonic Cascade

2010 ◽  
Vol 133 (1) ◽  
Author(s):  
J. S. Carullo ◽  
S. Nasir ◽  
R. D. Cress ◽  
W. F. Ng ◽  
K. A. Thole ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Turbine Blade ◽  
Surface Heat ◽  
Length Scale ◽  
Freestream Turbulence ◽  
Surface Heat Transfer ◽  
Mach Numbers ◽  
Turbulence Length ◽  
Turbulence Length Scale

This paper experimentally investigates the effect of high freestream turbulence intensity, turbulence length scale, and exit Reynolds number on the surface heat transfer distribution of a turbine blade at realistic engine Mach numbers. Passive turbulence grids were used to generate freestream turbulence levels of 2%, 12%, and 14% at the cascade inlet. The turbulence grids produced length scales normalized by the blade pitches of 0.02, 0.26, and 0.41, respectively. Surface heat transfer measurements were made at the midspan of the blade using thin film gauges. Experiments were performed at the exit Mach numbers of 0.55, 0.78, and 1.03, which represent flow conditions below, near, and above nominal conditions. The exit Mach numbers tested correspond to exit Reynolds numbers of 6×105, 8×105, and 11×105, based on true chord. The experimental results showed that the high freestream turbulence augmented the heat transfer on both the pressure and suction sides of the blade as compared with the low freestream turbulence case. At nominal conditions, exit Mach 0.78, average heat transfer augmentations of 23% and 35% were observed on the pressure side and suction side of the blade, respectively.

Infrared Reynolds number dependency of the two-dimensional inverse energy cascade

2011 ◽  
Vol 667 ◽  
pp. 463-473 ◽  
Author(s):  
ANDREAS VALLGREN
Keyword(s):  
Reynolds Number ◽  
Cascade Range ◽  
Energy Cascade ◽  
Energy Spectra ◽  
Small Scale ◽  
Two Dimensional ◽  
Inverse Energy Cascade ◽  
Linear Friction ◽  
Non Local ◽  
Reynolds Number Dependency

High-resolution simulations of forced two-dimensional turbulence reveal that the inverse cascade range is sensitive to an infrared Reynolds number, Reα = kf/kα, where kf is the forcing wavenumber and kα is a frictional wavenumber based on linear friction. In the limit of high Reα, the classic k−5/3 scaling is lost and we obtain steeper energy spectra. The sensitivity is traced to the formation of vortices in the inverse energy cascade range. Thus, it is hypothesized that the dual limit Reα → ∞ and Reν = kd/kf → ∞, where kd is the small-scale dissipation wavenumber, will lead to a steeper energy spectrum than k−5/3 in the inverse energy cascade range. It is also found that the inverse energy cascade is maintained by non-local triad interactions.

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