Fluid particle dynamics and the non-local origin of the Reynolds shear stress

2018 ◽  
Vol 847 ◽  
pp. 520-551 ◽  
Author(s):  
Peter S. Bernard ◽  
Martin A. Erinin
Keyword(s):  
Shear Stress ◽  
Channel Flow ◽  
Reynolds Shear Stress ◽  
Mixing Time ◽  
Turbulent Channel Flow ◽  
Structural Features ◽  
Fluid Particle ◽  
Normal Velocity ◽  
Mean Velocity ◽  
Non Local

The causative factors leading to the Reynolds shear stress distribution in turbulent channel flow are analysed via a backward particle path analysis. It is found that the classical displacement transport mechanism, by which changes in the mean velocity field over a mixing time correlate with the wall-normal velocity, is the dominant source of Reynolds shear stress. Approximately 20 % of channel flow at any given time contains fluid motions that contribute to displacement transport. Much rarer events provide a small but non-negligible contribution to the Reynolds shear stress due to fluid particle accelerations and long-lived correlations deriving from structural features of the near-wall flow. The Reynolds shear stress in channel flow is shown to be a non-local phenomenon that is not conducive to description via a local model and particularly one depending directly on the local mean velocity gradient.

Turbulence Measurements in Channel Flows With Rough and Hydrophobic Walls

2007 ◽  
Author(s):  
N. Ahmad ◽  
R. N. Parthasarathy
Keyword(s):  
Shear Stress ◽  
Rough Surface ◽  
Test Section ◽  
Reynolds Shear Stress ◽  
Turbulent Channel Flow ◽  
Surface Flow ◽  
Wall Region ◽  
Mean Velocity ◽  
Image Velocimetry ◽  
Coated Surface

Particle Image Velocimetry (PIV) measurements were made in a fully-developed turbulent channel flow. The channel test section was 1 ft wide and 1 inch in height and was constructed out of plexiglass. One wall of the test section was made removable. Four walls were used: a plexiglass smooth wall, and three hydrophobic walls: (i) a lotus paint coated plexiglass wall, (ii) a treated aluminum sheet attached to the plexiglass wall and (iii) a treated rough surface attached to the plexiglass wall. The bulk velocity was held constant to yield a Reynolds number (based on the channel half-height) of 5,500. Several images were averaged to obtain mean velocity and Reynolds shear stress and turbulence kinetic energy measurements. It was found that the mean velocities in the near-wall region were higher for the lotus-paint coated surface flow and the treated rough surface flow than the flows with the other two surfaces. The friction velocity estimated from the Reynolds shear stress measurements was significantly lower for these two flows as well. The reduction in the wall shear stress in these flows is attributed to the finite slip that occurs at the hydrophobic surfaces.

Logarithmic Expansions for Reynolds Shear Stress and Reynolds Heat Flux in a Turbulent Channel Flow

2008 ◽  
Vol 130 (9) ◽  
Author(s):  
Abu Seena ◽  
A. Bushra ◽  
Noor Afzal
Keyword(s):  
Heat Flux ◽  
Shear Stress ◽  
Channel Flow ◽  
Intermediate Layer ◽  
Reynolds Shear Stress ◽  
Turbulent Channel Flow ◽  
Closure Models ◽  
Fully Developed Turbulent Flow ◽  
Logarithmic Functions ◽  
Heat And Fluid Flow

The heat and fluid flow in a fully developed turbulent channel flow have been investigated. The closure model of Reynolds shear stress and Reynolds heat flux as a function of a series of logarithmic functions in the mesolayer variable have been adopted. The interaction between inner and outer layers in the mesolayer (intermediate layer) arising from the balance of viscous effect, pressure gradient and Reynolds shear stress (containing the maxima of Reynolds shear stress) was first proposed by Afzal (1982, “Fully Developed Turbulent Flow in a Pipe: An Intermediate Layer,” Arch. Appl. Mech., 53, 355–377). The unknown constants in the closure models for Reynolds shear stress and Reynolds heat flux have been estimated from the prescribed boundary conditions near the axis and surface of channel. The predictions are compared with the DNS data Iwamoto et al. and Abe et al. for Reynolds shear stress and velocity profile and Abe et al. data of Reynolds heat flux and temperature profile. The limitations of the closure models are presented.

scholarly journals Numerical simulation of turbulent channel flow over a viscous hyper-elastic wall

2017 ◽  
Vol 830 ◽  
pp. 708-735 ◽  
Author(s):  
Marco E. Rosti ◽  
Luca Brandt
Keyword(s):  
Channel Flow ◽  
Solid Phase ◽  
Turbulent Channel Flow ◽  
Inertial Range ◽  
Spanwise Direction ◽  
Logarithmic Scale ◽  
Normal Velocity ◽  
Mean Velocity ◽  
Elastic Wall ◽  
Hyper Elastic

We perform numerical simulations of a turbulent channel flow over an hyper-elastic wall. In the fluid region the flow is governed by the incompressible Navier–Stokes (NS) equations, while the solid is a neo-Hookean material satisfying the incompressible Mooney–Rivlin law. The multiphase flow is solved with a one-continuum formulation, using a monolithic velocity field for both the fluid and solid phase, which allows the use of a fully Eulerian formulation. The simulations are carried out at Reynolds bulk $Re=2800$ and examine the effect of different elasticity and viscosity of the deformable wall. We show that the skin friction increases monotonically with the material elastic modulus. The turbulent flow in the channel is affected by the moving wall even at low values of elasticity since non-zero fluctuations of vertical velocity at the interface influence the flow dynamics. The near-wall streaks and the associated quasi-streamwise vortices are strongly reduced near a highly elastic wall while the flow becomes more correlated in the spanwise direction, similarly to what happens for flows over rough and porous walls. As a consequence, the mean velocity profile in wall units is shifted downwards when shown in logarithmic scale, and the slope of the inertial range increases in comparison to that for the flow over a rigid wall. We propose a correlation between the downward shift of the inertial range, its slope and the wall-normal velocity fluctuations at the wall, extending results for the flow over rough walls. We finally show that the interface deformation is determined by the fluid fluctuations when the viscosity of the elastic layer is low, while when this is high the deformation is limited by the solid properties.

The structure of the viscous sublayer and the adjacent wall region in a turbulent channel flow

1974 ◽  
Vol 65 (3) ◽  
pp. 439-459 ◽  
Author(s):  
Helmut Eckelmann
Keyword(s):  
Channel Flow ◽  
Turbulent Channel Flow ◽  
Streamwise Velocity ◽  
Viscous Sublayer ◽  
Wall Region ◽  
Normal Velocity ◽  
Mean Velocity ◽  
Velocity Fluctuations ◽  
Mean Values ◽  
The Mean

Hot-film anemometer measurements have been carried out in a fully developed turbulent channel flow. An oil channel with a thick viscous sublayer was used, which permitted measurements very close to the wall. In the viscous sublayer between y+ ≃ 0·1 and y+ = 5, the streamwise velocity fluctuations decreased at a higher rate than the mean velocity; in the region y+ [lsim ] 0·1, these fluctuations vanished at the same rate as the mean velocity.The streamwise velocity fluctuations u observed in the viscous sublayer and the fluctuations (∂u/∂y)0 of the gradient at the wall were almost identical in form, but the fluctuations of the gradient at the wall were found to lag behind the velocity fluctuations with a lag time proportional to the distance from the wall. Probability density distributions of the streamwise velocity fluctuations were measured. Furthermore, measurements of the skewness and flatness factors made by Kreplin (1973) in the same flow channel are discussed. Measurements of the normal velocity fluctuations v at the wall and of the instantaneous Reynolds stress −ρuv were also made. Periods of quiescence in the − ρuv signal were observed in the viscous sublayer as well as very active periods where ratios of peak to mean values as high as 30:1 occurred.

Direct numerical simulation of turbulent channel flow with spanwise rotation

2015 ◽  
Vol 788 ◽  
pp. 42-56 ◽  
Author(s):  
Zhenhua Xia ◽  
Yipeng Shi ◽  
Shiyi Chen
Keyword(s):  
Shear Stress ◽  
Friction Velocity ◽  
Reynolds Shear Stress ◽  
Turbulent Channel Flow ◽  
Streamwise Velocity ◽  
Mean Velocity ◽  
Linear Profile ◽  
Unit Slope ◽  
The Mean ◽  
Spanwise Rotation

A series of direct numerical simulations of turbulent channel flow with spanwise rotation at fixed global friction Reynolds number is performed to investigate the rotation effects on the mean velocity, streamwise velocity fluctuations, Reynolds shear stress and turbulent kinetic energy. The global friction Reynolds number is chosen to be $Re_{{\it\tau}}=u_{{\it\tau}}^{\ast }h^{\ast }/{\it\nu}^{\ast }=180$ ($u_{{\it\tau}}^{\ast }$ is the global friction velocity, $h^{\ast }$ is the channel half-width and ${\it\nu}^{\ast }$ is the kinematic viscosity), while the global-friction-velocity-based rotation number $Ro_{{\it\tau}}=2{\it\Omega}^{\ast }h^{\ast }/u_{{\it\tau}}^{\ast }$ (${\it\Omega}^{\ast }$ is the dimensional angular velocity) varies from 0 to 130. In the previously reported $2{\it\Omega}^{\ast }$-slope region for the mean velocity, a linear behaviour for the streamwise velocity fluctuations, a unit-slope linear profile for the Reynolds shear stress and a $-2Ro_{{\it\tau}}$-slope linear profile for the production term of $\langle u^{\prime }u^{\prime }\rangle$ have been identified for the first time. The critical rotation number, which corresponds to the laminar limit, is predicted to be equal to $Re_{{\it\tau}}$ according to the unit-slope linear profile of the Reynolds shear stress. Our results also show that a parabolic profile of the mean velocity can be identified around the ‘second plateau’ region of the Reynolds shear stress for $Ro_{{\it\tau}}\geqslant 22$. The parabolas at different rotation numbers have the same shape of $1/Re_{{\it\tau}}$, the radius of curvature at the vertex. Furthermore, the system rotation increases the volume-averaged turbulent kinetic energy at lower rotation rates, and then decreases it when $Ro_{{\it\tau}}\gtrsim 16$.

scholarly journals Large-eddy simulation and wall modelling of turbulent channel flow

2009 ◽  
Vol 631 ◽  
pp. 281-309 ◽  
Author(s):  
D. CHUNG ◽  
D. I. PULLIN
Keyword(s):  
Shear Stress ◽  
Large Eddy Simulation ◽  
Channel Flow ◽  
Reynolds Shear Stress ◽  
Turbulent Channel Flow ◽  
Streamwise Velocity ◽  
Wall Region ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Near Wall

We report large-eddy simulation (LES) of turbulent channel flow. This LES neither resolves nor partially resolves the near-wall region. Instead, we develop a special near-wall subgrid-scale (SGS) model based on wall-parallel filtering and wall-normal averaging of the streamwise momentum equation, with an assumption of local inner scaling used to reduce the unsteady term. This gives an ordinary differential equation (ODE) for the wall shear stress at every wall location that is coupled with the LES. An extended form of the stretched-vortex SGS model, which incorporates the production of near-wall Reynolds shear stress due to the winding of streamwise momentum by near-wall attached SGS vortices, then provides a log relation for the streamwise velocity at the top boundary of the near-wall averaged domain. This allows calculation of an instantaneous slip velocity that is then used as a ‘virtual-wall’ boundary condition for the LES. A Kármán-like constant is calculated dynamically as part of the LES. With this closure we perform LES of turbulent channel flow for Reynolds numbers Reτ based on the friction velocity uτ and the channel half-width δ in the range 2 × 103 to 2 × 107. Results, including SGS-extended longitudinal spectra, compare favourably with the direct numerical simulation (DNS) data of Hoyas & Jiménez (2006) at Reτ = 2003 and maintain an O(1) grid dependence on Reτ.

The accelerated fully rough turbulent boundary layer

1977 ◽  
Vol 82 (3) ◽  
pp. 507-528 ◽  
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.

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.

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