Analysis of vertical profiles of mean velocity, shear stress and turbulent viscosity in a wave-current environment through RANS numerical simulations

AbstractOver the last two decades, both experiments and simulations have demonstrated that transverse wall oscillations with properly selected amplitude and frequency can reduce turbulent drag by as much as $40\hspace{0.167em} \% $. In this paper, we develop a model-based approach for designing oscillations that suppress turbulence in a channel flow. We utilize eddy-viscosity-enhanced linearization of the turbulent flow with control in conjunction with turbulence modelling to determine skin-friction drag in a simulation-free manner. The Boussinesq eddy viscosity hypothesis is used to quantify the effect of fluctuations on the mean velocity in flow subject to control. In contrast to the traditional approach that relies on numerical simulations, we determine the turbulent viscosity from the second-order statistics of the linearized model driven by white-in-time stochastic forcing. The spatial power spectrum of the forcing is selected to ensure that the linearized model for uncontrolled flow reproduces the turbulent energy spectrum. The resulting correction to the turbulent mean velocity induced by small-amplitude wall movements is then used to identify the optimal frequency of drag-reducing oscillations. In addition, the control net efficiency and the turbulent flow structures that we obtain agree well with the results of numerical simulations and experiments. This demonstrates the predictive power of our model-based approach to controlling turbulent flows and is expected to pave the way for successful flow control at higher Reynolds numbers than currently possible.

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Direct numerical simulations of turbulent flows over superhydrophobic surfaces

Journal of Fluid Mechanics ◽

10.1017/s0022112008004916 ◽

2009 ◽

Vol 620 ◽

pp. 31-41 ◽

Cited By ~ 132

Author(s):

MICHAEL B. MARTELL ◽

J. BLAIR PEROT ◽

JONATHAN P. ROTHSTEIN

Keyword(s):

Shear Stress ◽

Wall Shear Stress ◽

Numerical Simulations ◽

Slip Velocity ◽

Direct Numerical Simulations ◽

Superhydrophobic Surfaces ◽

Shear Stresses ◽

Reynolds Stresses ◽

Mean Velocity ◽

Wall Shear

Direct numerical simulations (DNSs) are used to investigate the drag-reducing performance of superhydrophobic surfaces (SHSs) in turbulent channel flow. SHSs combine surface roughness with hydrophobicity and can, in some cases, support a shear-free air–water interface. Slip velocities, wall shear stresses and Reynolds stresses are considered for a variety of SHS microfeature geometry configurations at a friction Reynolds number of Reτ ≈ 180. For the largest microfeature spacing studied, an average slip velocity over 75% of the bulk velocity is obtained, and the wall shear stress reduction is found to be nearly 40%. The simulation results suggest that the mean velocity profile near the superhydrophobic wall continues to scale with the wall shear stress but is offset by a slip velocity that increases with increasing microfeature spacing.

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On Wind-induced Flows in Closed Channels

Australian Journal of Physics ◽

10.1071/ph670001 ◽

1967 ◽

Vol 20 (1) ◽

pp. 1

Author(s):

CHJ Johnson

Keyword(s):

Shear Stress ◽

Turbulent Viscosity ◽

Surface Slope ◽

Flow Conditions ◽

Closed Channel ◽

Mean Velocity ◽

Induced Flow ◽

The Mean ◽

Stress Profiles ◽

Wind Induced Flow

The mean velocity and shear-stress profiles for a wind-induced flow in a closed channel with constant surface slope are first derived using a turbulent viscosity constructed by dimensional arguments. Using a perturbation analysis based on the fact that the surface slope is small, these results are extended to the case where the surface slope, and hence flow conditions generally, are allowed to vary in a downwind direction. Explicit results are obtained for the velocity and shear-stress profiles and also for the surface slope as a function of distance downwind. The results agree quite well with experiment, although better agreement would probably be obtained by using a more elaborate turbulent iscosity_

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Saturation mechanism and generated viscosity in gravito-turbulent accretion disks

Astronomy and Astrophysics ◽

10.1051/0004-6361/202038023 ◽

2020 ◽

Vol 640 ◽

pp. A53

Author(s):

L. Löhnert ◽

S. Krätschmer ◽

A. G. Peeters

Keyword(s):

Growth Rate ◽

Numerical Simulations ◽

Accretion Disks ◽

Gravitational Instability ◽

Turbulent Viscosity ◽

Radial Distance ◽

Maximum Growth ◽

Wave Number ◽

Radiative Cooling ◽

Mixing Length

Here, we address the turbulent dynamics of the gravitational instability in accretion disks, retaining both radiative cooling and irradiation. Due to radiative cooling, the disk is unstable for all values of the Toomre parameter, and an accurate estimate of the maximum growth rate is derived analytically. A detailed study of the turbulent spectra shows a rapid decay with an azimuthal wave number stronger than ky−3, whereas the spectrum is more broad in the radial direction and shows a scaling in the range kx−3 to kx−2. The radial component of the radial velocity profile consists of a superposition of shocks of different heights, and is similar to that found in Burgers’ turbulence. Assuming saturation occurs through nonlinear wave steepening leading to shock formation, we developed a mixing-length model in which the typical length scale is related to the average radial distance between shocks. Furthermore, since the numerical simulations show that linear drive is necessary in order to sustain turbulence, we used the growth rate of the most unstable mode to estimate the typical timescale. The mixing-length model that was obtained agrees well with numerical simulations. The model gives an analytic expression for the turbulent viscosity as a function of the Toomre parameter and cooling time. It predicts that relevant values of α = 10−3 can be obtained in disks that have a Toomre parameter as high as Q ≈ 10.

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Predicting Sulfidic and Naphthenic Acid Corrosion

CORROSION ◽

10.5006/1.3319109 ◽

2009 ◽

Vol 65 (12) ◽

pp. 831-844 ◽

Cited By ~ 12

Author(s):

J. Hau

Keyword(s):

Shear Stress ◽

Exposure Time ◽

Acid Corrosion ◽

Naphthenic Acid ◽

Naphthenic Acids ◽

Sulfur Compounds ◽

Velocity Shear ◽

Threshold Behavior ◽

Temperature Range ◽

Si Content

Abstract This paper reviews the factors that are hindering the development of models to predict corrosion due to sulfur compounds, naphthenic acids, or both, acting simultaneously on steels within the temperature range typically from 230°C to 400°C. These factors are identified as data scattering that do not distribute normally, variables or factors that do not exert their influence in a gradual manner but as a threshold behavior, and the interactions between the factors of sulfidic and naphthenic acid corrosion; exposure time, temperature, and velocity (shear stress); and the chromium and molybdenum content of the steels (Si content is not discussed). Not dealing with the interactions is probably the largest obstacle, followed by data scattering.

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On turbulent boundary-layer separation

Journal of Fluid Mechanics ◽

10.1017/s0022112068000728 ◽

1968 ◽

Vol 32 (2) ◽

pp. 293-304 ◽

Cited By ~ 36

Author(s):

V. A. Sandborn ◽

C. Y. Liu

Keyword(s):

Boundary Layer ◽

Shear Stress ◽

Turbulent Boundary Layer ◽

Analytical Study ◽

Boundary Layer Separation ◽

Mean Velocity ◽

Laminar Separation ◽

Layer Separation ◽

Turbulent Separation ◽

Separation Model

An experimental and analytical study of the separation of a turbulent boundary layer is reported. The turbulent boundary-layer separation model proposed by Sandborn & Kline (1961) is demonstrated to predict the experimental results. Two distinct turbulent separation regions, an intermittent and a steady separation, with correspondingly different velocity distributions are confirmed. The true zero wall shear stress turbulent separation point is determined by electronic means. The associated mean velocity profile is shown to belong to the same family of profiles as found for laminar separation. The velocity distribution at the point of reattachment of a turbulent boundary layer behind a step is also shown to belong to the laminar separation family.Prediction of the location of steady turbulent boundary-layer separation is made using the technique employed by Stratford (1959) for intermittent separation.

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The accelerated fully rough turbulent boundary layer

Journal of Fluid Mechanics ◽

10.1017/s0022112077000810 ◽

1977 ◽

Vol 82 (3) ◽

pp. 507-528 ◽

Cited By ~ 31

Author(s):

Hugh W. Coleman ◽

Robert J. Moffat ◽

William M. Kays

Keyword(s):

Boundary Layer ◽

Shear Stress ◽

Turbulent Boundary Layer ◽

Pressure Gradient ◽

Stress Tensor ◽

Skin Friction ◽

Shape Factor ◽

Reynolds Shear Stress ◽

Smooth Wall ◽

Mean Velocity

The behaviour of a fully rough turbulent boundary layer subjected to favourable pressure gradients both with and without blowing was investigated experimentally using a porous test surface composed of densely packed spheres of uniform size. Measurements of profiles of mean velocity and the components of the Reynolds-stress tensor are reported for both unblown and blown layers. Skin-friction coefficients were determined from measurements of the Reynolds shear stress and mean velocity.An appropriate acceleration parameterKrfor fully rough layers is defined which is dependent on a characteristic roughness dimension but independent of molecular viscosity. For a constant blowing fractionFgreater than or equal to zero, the fully rough turbulent boundary layer reaches an equilibrium state whenKris held constant. Profiles of the mean velocity and the components of the Reynolds-stress tensor are then similar in the flow direction and the skin-friction coefficient, momentum thickness, boundary-layer shape factor and the Clauser shape factor and pressure-gradient parameter all become constant.Acceleration of a fully rough layer decreases the normalized turbulent kinetic energy and makes the turbulence field much less isotropic in the inner region (forFequal to zero) compared with zero-pressure-gradient fully rough layers. The values of the Reynolds-shear-stress correlation coefficients, however, are unaffected by acceleration or blowing and are identical with values previously reported for smooth-wall and zero-pressure-gradient rough-wall flows. Increasing values of the roughness Reynolds number with acceleration indicate that the fully rough layer does not tend towards the transitionally rough or smooth-wall state when accelerated.

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Processing time series data (velocity, shear stress) from the pulse width modulated-constant temperature anemometer (PWM-CTA)

ICIASF 2001 Record, 19th International Congress on Instrumentation in Aerospace Simulation Facilities (Cat. No.01CH37215) ◽

10.1109/iciasf.2001.960280 ◽

2002 ◽

Cited By ~ 1

Author(s):

J.F. Foss ◽

T.J. Hicks

Keyword(s):

Time Series ◽

Shear Stress ◽

Constant Temperature ◽

Pulse Width ◽

Processing Time ◽

Time Series Data ◽

Velocity Shear ◽

Series Data ◽

Pulse Width Modulated ◽

Constant Temperature Anemometer

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Global energy fluxes in turbulent channels with flow control

Journal of Fluid Mechanics ◽

10.1017/jfm.2018.749 ◽

2018 ◽

Vol 857 ◽

pp. 345-373 ◽

Cited By ~ 7

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.

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A theory of turbulence in stratified fluids

Journal of Fluid Mechanics ◽

10.1017/s0022112070001313 ◽

1970 ◽

Vol 42 (2) ◽

pp. 349-365 ◽

Cited By ~ 25

Author(s):

Robert R. Long

Keyword(s):

Boundary Layer ◽

Turbulent Boundary Layer ◽

Density Profile ◽

Richardson Number ◽

Mixed Volume ◽

Volume Of Fluid ◽

Velocity Shear ◽

Mean Velocity ◽

Large Wave ◽

The Mean

An effort is made to understand turbulence in fluid systems like the oceans and atmosphere in which the Richardson number is generally large. Toward this end, a theory is developed for turbulent flow over a flat plate which is moved and cooled in such a way as to produce constant vertical fluxes of momentum and heat. The theory indicates that in a co-ordinate system fixed in the plate the mean velocity increases linearly with heightzabove a turbulent boundary layer and the mean density decreases asz3, so that the Richardson number is large far from the plate. Near the plate, the results reduce to those of Monin & Obukhov.Thecurvatureof the density profile is essential in the formulation of the theory. When the curvature is negative, a volume of fluid, thoroughly mixed by turbulence, will tend to flatten out at a new level well above the original centre of mass, thereby transporting heat downward. When the curvature is positive a mixed volume of fluid will tend to fall a similar distance, again transporting heat downward. A well-mixed volume of fluid will also tend to rise when the density profile is linear, but this rise is negligible on the basis of the Boussinesq approximation. The interchange of fluid of different, mean horizontal speeds in the formation of the turbulent patch transfers momentum. As the mixing in the patch destroys the mean velocity shear locally, kinetic energy is transferred from mean motion to disturbed motion. The turbulence can arise in spite of the high Richardson number because the precise variations of mean density and mean velocity mentioned above permit wave energy to propagate from the turbulent boundary layer to the whole region above the plate. At the levels of reflexion, where the amplitudes become large, wave-breaking and turbulence will tend to develop.The relationship between the curvature of the density profile and the transfer of heat suggests that the density gradient near the level of a point of inflexion of the density curve (in general cases of stratified, shearing flow) will increase locally as time goes on. There will also be a tendency to increase the shear through the action of local wave stresses. If this results in a progressive reduction in Richardson number, an ultimate outbreak of Kelvin–Helmholtz instability will occur. The resulting sporadic turbulence will transfer heat (and momentum) through the level of the inflexion point. This mechanism for the appearance of regions of low Richardson number is offered as a possible explanation for the formation of the surfaces of strong density and velocity differences observed in the oceans and atmosphere, and for the turbulence that appears on these surfaces.

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