An Eddy Viscosity Calculation Method for a Turbulent Duct Flow

1991 ◽  
Vol 113 (4) ◽  
pp. 616-619 ◽  
Author(s):  
R. A. Antonia ◽  
D. K. Bisset ◽  
J. Kim
Keyword(s):  
Eddy Viscosity ◽  
Reynolds Shear Stress ◽  
Outer Region ◽  
Reynolds Numbers ◽  
Duct Flow ◽  
Viscosity Method ◽  
Mean Velocity ◽  
The Mean ◽  
Turbulent Duct Flow ◽  
Good Agreement

The mean velocity profile across a fully developed turbulent duct flow is obtained from an eddy viscosity relation combined with an empirical outer region wake function. Results are in good agreement with experiments and with direct numerical simulations in the same flow at two Reynolds numbers. In particular, the near-wall trend of the Reynolds shear stress and its variation with Reynolds number are similar to those of the simulations. The eddy viscosity method is more accurate than previous mixing length or implicit function methods.

LDV and PIV Velocity Results in a Thermosiphon

2003 ◽  
Author(s):  
J. Kulman ◽  
D. Gray ◽  
S. Sivanagere ◽  
S. Guffey
Keyword(s):  
Large Scale ◽  
Single Phase ◽  
Flow Characteristics ◽  
Reynolds Numbers ◽  
Flow Patterns ◽  
Laser Doppler Velocimeter ◽  
Mean Velocity ◽  
Developed Turbulence ◽  
The Mean ◽  
Good Agreement

Heat transfer and flow characteristics have been determined for a single-phase rectangular loop thermosiphon. The plane of the loop was vertical, and tests were performed with in-plane tilt angles ranging from 3.6° CW to 4.2° CCW. Velocity profiles were measured in one vertical leg of the loop using both a single-component Laser Doppler Velocimeter (LDV), and a commercial Particle Image Velocimeter (PIV) system. The LDV data and PIV data were found to be in good agreement. The measured average velocities were approximately 2–2.5 cm/s at an average heating rate of 70 W, and were independent of tilt angle. Significant RMS fluctuations of 10–20% of the mean velocity were observed in the test section, in spite of the laminar or transitional Reynolds numbers (order of 700, based on the hydraulic diameter). These fluctuations have been attributed to vortex shedding from the upstream temperature probes and mitre bends, rather than to fully developed turbulence. Animations of the PIV data clearly show these large scale unsteady flow patterns. Multiple steady state flow patterns were not observed.

Comparison of turbulent boundary layers over smooth and rough surfaces up to high Reynolds numbers

2016 ◽  
Vol 795 ◽  
pp. 210-240 ◽  
Author(s):  
D. T. Squire ◽  
C. Morrill-Winter ◽  
N. Hutchins ◽  
M. P. Schultz ◽  
J. C. Klewicki ◽  
...  
Keyword(s):  
Outer Region ◽  
Reynolds Numbers ◽  
Streamwise Velocity ◽  
Rough Wall ◽  
Turbulent Shear ◽  
Smooth Wall ◽  
Mean Velocity ◽  
Wide Range ◽  
Velocity Variance ◽  
The Mean

Turbulent boundary layer measurements above a smooth wall and sandpaper roughness are presented across a wide range of friction Reynolds numbers, ${\it\delta}_{99}^{+}$, and equivalent sand grain roughness Reynolds numbers, $k_{s}^{+}$ (smooth wall: $2020\leqslant {\it\delta}_{99}^{+}\leqslant 21\,430$, rough wall: $2890\leqslant {\it\delta}_{99}^{+}\leqslant 29\,900$; $22\leqslant k_{s}^{+}\leqslant 155$; and $28\leqslant {\it\delta}_{99}^{+}/k_{s}^{+}\leqslant 199$). For the rough-wall measurements, the mean wall shear stress is determined using a floating element drag balance. All smooth- and rough-wall data exhibit, over an inertial sublayer, regions of logarithmic dependence in the mean velocity and streamwise velocity variance. These logarithmic slopes are apparently the same between smooth and rough walls, indicating similar dynamics are present in this region. The streamwise mean velocity defect and skewness profiles each show convincing collapse in the outer region of the flow, suggesting that Townsend’s (The Structure of Turbulent Shear Flow, vol. 1, 1956, Cambridge University Press.) wall-similarity hypothesis is a good approximation for these statistics even at these finite friction Reynolds numbers. Outer-layer collapse is also observed in the rough-wall streamwise velocity variance, but only for flows with ${\it\delta}_{99}^{+}\gtrsim 14\,000$. At Reynolds numbers lower than this, profile invariance is only apparent when the flow is fully rough. In transitionally rough flows at low ${\it\delta}_{99}^{+}$, the outer region of the inner-normalised streamwise velocity variance indicates a dependence on $k_{s}^{+}$ for the present rough surface.

Mean-flow scaling of turbulent pipe flow

1998 ◽  
Vol 373 ◽  
pp. 33-79 ◽  
Author(s):  
MARK V. ZAGAROLA ◽  
ALEXANDER J. SMITS
Keyword(s):  
Friction Factor ◽  
Friction Velocity ◽  
Outer Region ◽  
Reynolds Numbers ◽  
Velocity Profiles ◽  
Mean Velocity ◽  
Velocity Scale ◽  
The Mean ◽  
Log Law ◽  
High Reynolds

Measurements of the mean velocity profile and pressure drop were performed in a fully developed, smooth pipe flow for Reynolds numbers from 31×103 to 35×106. Analysis of the mean velocity profiles indicates two overlap regions: a power law for 60<y+<500 or y+<0.15R+, the outer limit depending on whether the Kármán number R+ is greater or less than 9×103; and a log law for 600<y+<0.07R+. The log law is only evident if the Reynolds number is greater than approximately 400×103 (R+>9×103). Von Kármán's constant was shown to be 0.436 which is consistent with the friction factor data and the mean velocity profiles for 600<y+<0.07R+, and the additive constant was shown to be 6.15 when the log law is expressed in inner scaling variables.A new theory is developed to explain the scaling in both overlap regions. This theory requires a velocity scale for the outer region such that the ratio of the outer velocity scale to the inner velocity scale (the friction velocity) is a function of Reynolds number at low Reynolds numbers, and approaches a constant value at high Reynolds numbers. A reasonable candidate for the outer velocity scale is the velocity deficit in the pipe, UCL−Ū, which is a true outer velocity scale, in contrast to the friction velocity which is a velocity scale associated with the near-wall region which is ‘impressed’ on the outer region. The proposed velocity scale was used to normalize the velocity profiles in the outer region and was found to give significantly better agreement between different Reynolds numbers than the friction velocity.The friction factor data at high Reynolds numbers were found to be significantly larger (>5%) than those predicted by Prandtl's relation. A new friction factor relation is proposed which is within ±1.2% of the data for Reynolds numbers between 10×103 and 35×106, and includes a term to account for the near-wall velocity profile.

Axisymmetric internal waves generated by a travelling oscillating body

1969 ◽  
Vol 35 (2) ◽  
pp. 219-224 ◽  
Author(s):  
T. N. Stevenson
Keyword(s):  
Internal Waves ◽  
Salt Solution ◽  
Reynolds Numbers ◽  
Mean Velocity ◽  
Dispersive Waves ◽  
The Mean ◽  
Oscillating Sphere

Experiments are presented in which axisymmetric internal waves are generated by an oscillating sphere moving vertically in a stably stratified salt solution. The Reynolds numbers for the sphere based on the diameter and the mean velocity are between 10 and 200. Lighthill's theory for dispersive waves is used to calculate the phase configuration of the internal waves. The agreement between experiment and theory is reasonably good.

scholarly journals Global energy fluxes in turbulent channels with flow control

2018 ◽  
Vol 857 ◽  
pp. 345-373 ◽  
Author(s):  
Davide Gatti ◽  
Andrea Cimarelli ◽  
Yosuke Hasegawa ◽  
Bettina Frohnapfel ◽  
Maurizio Quadrio
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Energy Dissipation ◽  
Velocity Field ◽  
Flow Control ◽  
Reynolds Shear Stress ◽  
Power Input ◽  
Energy Fluxes ◽  
Mean Velocity ◽  
The Mean

This paper addresses the integral energy fluxes in natural and controlled turbulent channel flows, where active skin-friction drag reduction techniques allow a more efficient use of the available power. We study whether the increased efficiency shows any general trend in how energy is dissipated by the mean velocity field (mean dissipation) and by the fluctuating velocity field (turbulent dissipation). Direct numerical simulations (DNS) of different control strategies are performed at constant power input (CPI), so that at statistical equilibrium, each flow (either uncontrolled or controlled by different means) has the same power input, hence the same global energy flux and, by definition, the same total energy dissipation rate. The simulations reveal that changes in mean and turbulent energy dissipation rates can be of either sign in a successfully controlled flow. A quantitative description of these changes is made possible by a new decomposition of the total dissipation, stemming from an extended Reynolds decomposition, where the mean velocity is split into a laminar component and a deviation from it. Thanks to the analytical expressions of the laminar quantities, exact relationships are derived that link the achieved flow rate increase and all energy fluxes in the flow system with two wall-normal integrals of the Reynolds shear stress and the Reynolds number. The dependence of the energy fluxes on the Reynolds number is elucidated with a simple model in which the control-dependent changes of the Reynolds shear stress are accounted for via a modification of the mean velocity profile. The physical meaning of the energy fluxes stemming from the new decomposition unveils their inter-relations and connection to flow control, so that a clear target for flow control can be identified.

PIV Measurements in Square Backward-Facing Step

2007 ◽  
Vol 129 (8) ◽  
pp. 984-990 ◽  
Author(s):  
Mika Piirto ◽  
Aku Karvinen ◽  
Hannu Ahlstedt ◽  
Pentti Saarenrinne ◽  
Reijo Karvinen
Keyword(s):  
Shear Stress ◽  
Reynolds Stress ◽  
Reynolds Shear Stress ◽  
Experimental Tests ◽  
Expansion Ratio ◽  
Spanwise Direction ◽  
Duct Flow ◽  
Backward Facing Step ◽  
Mean Velocity ◽  
Stress Profiles

Measurements with both two-dimensional (2D) two-component and three-component stereo particle image velocimetry (PIV) and computation in 2D and three-dimensional (3D) using Reynolds stress turbulence model with commercial code are carried out in a square duct backward-facing step (BFS) in a turbulent water flow at three Reynolds numbers of about 12,000, 21,000, and 55,000 based on the step height h and the inlet streamwise maximum mean velocity U0. The reattachment locations measured at a distance of Δy=0.0322h from the wall are 5.3h, 5.6h, and 5.7h, respectively. The inlet flow condition is fully developed duct flow before the step change with the expansion ratio of 1.2. PIV results show that the mean velocity, root mean square (rms) velocity profiles, and Reynolds shear stress profiles in all the experimental flow cases are almost identical in the separated shear-layer region when they are nondimensionalized by U0. The sidewall effect of the square BFS flow is analyzed by comparing the experimental statistics with direct numerical simulation (DNS) and Reynolds stress model (RSM) data. For this purpose, the simulation is carried out for both 2D BFS and for square BFS having the same geometry in the 3D case as the experimental case at the lowest Reynolds number. A clear difference is observed in rms and Reynolds shear stress profiles between square BFS experimental results and DNS results in 2D channel in the spanwise direction. The spanwise rms velocity difference is about 30%, with experimental tests showing higher values than DNS, while in contrast, turbulence intensities in streamwise and vertical directions show slightly lower values than DNS. However, with the modeling, the turbulence statistical differences between 2D and 3D RSM cases are very modest. The square BFS indicates 0.5h–1.5h smaller reattachment distances than the reattachment lengths of 2D flow cases.

scholarly journals Natural logarithms

2013 ◽  
Vol 718 ◽  
pp. 1-4 ◽  
Author(s):  
B. J. McKeon
Keyword(s):  
Turbulent Flows ◽  
Reynolds Numbers ◽  
Streamwise Velocity ◽  
Wall Turbulence ◽  
Significant Advance ◽  
Mean Velocity ◽  
Velocity Fluctuations ◽  
Logarithmic Scaling ◽  
The Mean ◽  
High Reynolds

AbstractMarusic et al. (J. Fluid Mech., vol. 716, 2013, R3) show the first clear evidence of universal logarithmic scaling emerging naturally (and simultaneously) in the mean velocity and the intensity of the streamwise velocity fluctuations about that mean in canonical turbulent flows near walls. These observations represent a significant advance in understanding of the behaviour of wall turbulence at high Reynolds number, but perhaps the most exciting implication of the experimental results lies in the agreement with the predictions of such scaling from a model introduced by Townsend (J. Fluid Mech., vol. 11, 1961, pp. 97–120), commonly termed the attached eddy hypothesis. The elegantly simple, yet powerful, study by Marusic et al. should spark further investigation of the behaviour of all fluctuating velocity components at high Reynolds numbers and the outstanding predictions of the attached eddy hypothesis.

Turbulent Vorticity Diffusion in the Stronger Wall Jet Managed by a Flat Plate Wing in the Outer Layer

2015 ◽  
Author(s):  
Takuma Katayama ◽  
Shinsuke Mochizuki
Keyword(s):  
Shear Stress ◽  
Flat Plate ◽  
Outer Layer ◽  
Large Scale ◽  
Reynolds Shear Stress ◽  
Three Dimensional ◽  
Quantitative Relationship ◽  
Wall Jet ◽  
Mean Velocity ◽  
The Mean

The present experiment focuses on the vorticity diffusion in a stronger wall jet managed by a three-dimensional flat plate wing in the outer layer. Measurement of the fluctuating velocities and vorticity correlation has been carried out with 4-wire vorticity probe. The turbulent vorticity diffusion due to the large scale eddies in the outer layer is quantitatively examined by using the 4-wire vorticity probe. Quantitative relationship between vortex structure and Reynolds shear stress is revealed by means of directly measured experimental evidence which explains vorticity diffusion process and influence of the manipulating wing. It is expected that the three-dimensional outer layer manipulator contributes to keep convex profile of the mean velocity, namely, suppression of the turbulent diffusion and entrainment.

A Continuous Prediction Method for Fully Developed Laminar, Transitional, and Turbulent Flows in Pipes

1975 ◽  
Vol 42 (1) ◽  
pp. 51-54 ◽  
Author(s):  
N. W. Wilson ◽  
R. S. Azad
Keyword(s):  
Turbulent Flows ◽  
Flow Characteristics ◽  
Prediction Method ◽  
Reynolds Numbers ◽  
Mean Flow ◽  
Number Range ◽  
Circular Pipes ◽  
The Mean ◽  
Single Set ◽  
Good Agreement

A single set of equations is developed to predict the mean flow characteristics in long circular pipes operating at laminar, transitional, and turbulent Reynolds numbers. Generally good agreement is obtained with available data in the Reynolds number range 100 < Re < 500,000.

Free Span Vibrations of Submarine Pipelines in Steady Flows—Effect of Free-Stream Turbulence on Mean Drag Coefficients

1985 ◽  
Vol 107 (4) ◽  
pp. 415-420 ◽  
Author(s):  
A. To̸rum ◽  
N. M. Anand
Keyword(s):  
Free Stream ◽  
Fluid Flows ◽  
Reynolds Numbers ◽  
Steady Flows ◽  
Mean Velocity ◽  
Free Stream Turbulence ◽  
The Mean ◽  
Elastically Supported ◽  
Wave Induced ◽  
Rigid Smooth

In this paper part of the results of a laboratory study related to free span vibrations of submarine pipelines in steady and wave-induced fluid flows are summarized. Tests have been carried out using an elastically supported rigid smooth circular cylinder close to a plane smooth boundary in steady flows with turbulence intensities of 3.4, 5.5, and 9.5 percent for four cylinder gap to diameter ratios, G/D equal to 0.5, 0.75, 1.0, and 3.0. The range of Reynolds numbers based on mean velocity of flow and cylinder diameter was 0.65·104 to 0.35·105. Effect of turbulence intensity on the mean drag force and vibration amplitudes are discussed.

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