Effects of wall permeability on turbulence

In order to understand the effects of the wall permeability on turbulence near a porous wall, flow field measurements are carried out for turbulent flows in a channel with a porous bottom wall by a two-component particle image velocimetry (PIV) system. The porous media used are three kinds of foamed ceramics which have almost the same porosity (0.8) but different permeability. It is confirmed that the flow becomes more turbulent over the porous wall and tends to be turbulent even at the bulk Reynolds number of Re_b=1300 in the most permeable wall case tested. Corresponding to laminar to turbulent transition, the magnitude of the slip velocity on the porous wall is found to increase drastically in a narrow range of the Reynolds number. To discuss the effects of the wall roughness and the wall permeability, detailed discussions are made of zero-plane displacement and equivalent wall roughness for porous media. The results clearly indicate that the turbulence is induced by not only the wall roughness but the wall permeability. The measurements have also revealed that as Re_b or the wall permeability increases, the wall normal fluctuating velocity near the porous wall is enhanced due to the effects of the wall permeability. This leads to the increase of the turbulent shear stress resulting in higher friction factors of turbulence over porous walls.     

Direct numerical simulation of turbulent heat transfer over fully resolved anisotropic porous structures

Lattice Boltzmann direct numerical simulations of turbulent heat transfer over and inside anisotropic porous media are performed. This study considers turbulent plane channel flows whose bottom walls are made from the porous media at the bulk Reynolds number of 2900 with isothermal and conjugate heat transfer wall conditions. Four different porous walls are considered. They are walls with only the wall-normal permeability, with the wall-normal and spanwise permeabilities, with the wall-normal and streamwise permeabilities, and with the isotropic wall-normal, spanwise and streamwise permeabilities. The porosity of the porous walls ranges from 0.6 to 0.8. Discussions on the effects of the anisotropic permeability on turbulent thermal fields are carried out by the instantaneous flow visualizations and the statistical quantities. In particular, temperature fluctuations, turbulent and dispersion heat fluxes are examined both inside and outside the porous walls. Finally, the heat transfer performance is discussed considering the effects of the anisotropic permeability.     

Turbulence characteristics over k-type rib roughened porous walls

To understand the permeability effects on turbulent rib-roughened porous channel flows, particle image velocimetry measurements are performed at the bulk Reynolds number of 5000–20000. Solid impermeable and porous ribs are considered for the rib-roughness whose geometry is categorised in the k-type roughness whose pitch/rib-height is 10. Three isotropic porous media with nearly the same porosity: 0.8, and different permeabilities (0.004, 0.020, 0.033 mm²) are applied. It is observed that the recirculation between the ribs becomes weak and the recirculation vortex submerges into the porous wall as the wall permeability and Reynolds number increase for both solid and porous rib cases while the recirculation vanishes in high permeable cases. These phenomena result in characteristic difference in turbulence quantities. By fitting the mean velocity profiles to the log-law form, the permeability effects of both rib and bottom wall on the log-law parameters and the equivalent sand-grain roughness are discussed. It is concluded that the zero-plane displacement increases while the von Kármán constant and the equivalent sand-grain roughness decrease as the wall and rib permeability increases.     

Transport Mechanism of Interface Turbulence over Porous and Rough Walls

To understand turbulent transport mechanisms of interface turbulence over porous and rough walls, statistical analyses using direct numerical simulation (DNS) data are carried out at a bulk Reynolds number of 3000. The presently considered porous wall, whose porosity is 0.71, consists of interconnected staggered cube arrays and the rough wall has the same surface structure. Through quadrant and budget term analyses, the transport mechanisms of the plane averaged Reynolds stress are investigated and mutual dependency between turbulence and dispersion is elucidated. Moreover, the influence of the Kelvin-Helmholtz instability on turbulent transport is clarified.     

Lattice Boltzmann simulations of turbulent shear flow between parallel porous walls

The effects of two parallel porous walls are investigated, consisting of the Darcy number and the porosity of a porous medium, on the behavior of turbulent shear flows as well as skin-friction drag. The turbulent channel flow with a porous surface is directly simulated by the lattice Boltzmann method （LBM）. The Darcy-Brinkman- Forcheimer （DBF） acting force term is added in the lattice Boltzmann equation to simu- late the turbulent flow bounded by porous walls. It is found that there are two opposite trends （enhancement or reduction） for the porous medium to modify the intensities of the velocity fluctuations and the Reynolds stresses in the near wall region. The parametric study shows that flow modification depends on the Darcy number and the porosity of the porous medium. The results show that, with respect to the conventional impermeable wall, the degree of turbulence modification does not depend on any simple set of param- eters obviously. Moreover, the drag in porous wall-bounded turbulent flow decreases if the Darcy number is smaller than the order of O（10-4） and the porosity of porous walls is up to 0.4.     

Drag reduction of turbulent channel flows over an anisotropic porous wall with reduced spanwise permeability

The direct numerical simulation(DNS) is carried out for the incompressible viscous turbulent flows over an anisotropic porous wall. Effects of the anisotropic porous wall on turbulence modifications as well as on the turbulent drag reduction are investigated. The simulation is carried out at a friction Reynolds number of 180, which is based on the averaged friction velocity at the interface between the porous medium and the clear fluid domain. The depth of the porous layer ranges from 0.9 to 54 viscous units. The permeability in the spanwise direction is set to be lower than the other directions in the present simulation. The maximum drag reduction obtained is about 15.3% which occurs for a depth of 9 viscous units. The increasing of drag is addressed when the depth of the porous layer is more than 25 wall units. The thinner porous layer restricts the spanwise extension of the streamwise vortices which suppresses the bursting events near the wall. However, for the thicker porous layer, the wall-normal fluctuations are enhanced due to the weakening of the wall-blocking effect which can trigger strong turbulent structures near the wall.     

Turbulence Characteristics in Flows Over Solid and Porous Square Ribs Mounted on Porous Walls

PIV measurements have been performed for turbulent flows in a rib-mounted channel whose bottom wall is made of a porous layer. The ratio of the rib and channel heights is fixed at 0.5. The effects of the wall and rib permeability are investigated focusing on the separating and reattaching flows at the bulk Reynolds number of 10³???10⁴. Three kinds of foamed ceramics are employed as the porous media. They have the same porosity of 0.8 but each permeability is different from the others. Its normalized values by the rib height are 0.89 × 10^???4, 1.47 × 10^???4 and 3.87 × 10^???4. Two kinds of square cylinder ribs: an impermeable smooth solid rib or a permeable porous rib which is made of the same porous medium as that for the bottom wall are used. The obtained turbulent velocity fields of the solid rib flows indicate that the turbulent intensity behind the rib becomes weak and the recirculation bubble in the clear channel tends to vanish as the the wall permeability increases. In the porous rib flow, the recirculation and the reattachment point shift downstream and turbulence becomes weaker due to the bleeding flow through the rib. In the higher permeability cases, the recirculation bubble hardly exists due to the flows through not only the bottom wall but also the porous rib. From the measurements, it is suggested that in the solid rib flows, a reverse flow region exists inside the porous wall whereas in porous rib flows, such reverse flow does not exist at higher permeability.     

Direct numerical simulation of low Reynolds number flows in an open‐channel with sidewalls

A direct numerical simulation of low Reynolds number turbulent flows in an open‐channel with sidewalls is presented. Mean flow and turbulence structures are described and compared with both simulated and measured data available from the literature. The simulation results show that secondary flows are generated near the walls and free surface. In particular, at the upper corner of the channel, a small vortex called inner secondary flows is simulated. The results show that the inner secondary flows, counter‐rotating to outer secondary flows away from the sidewall, increase the shear velocity near the free surface. The secondary flows observed in turbulent open‐channel flows are related to the production of Reynolds shear stress. A quadrant analysis shows that sweeps and ejections are dominant in the regions where secondary flows rush in toward the wall and eject from the wall, respectively. A conditional quadrant analysis also reveals that the production of Reynolds shear stress and the secondary flow patterns are determined by the directional tendency of the dominant coherent structures. Copyright © 2009 John Wiley & Sons, Ltd.     

Vortex reynolds number in turbulent boundary layers

The effects of vortex Reynolds number on the statistics of turbulence in a turbulent boundary layer have been investigated. Vortex Reynolds number is defined as the ratio of circulation around the vortex structure to the fluid viscosity. The vortex structure of the outer region was modeled and a full numerical simulation was then conducted using a high-order spectral method. A unit domain of the outer region of a turbulent boundary layer was assumed to be composed of essentially three elements: a wall, a Blasius mean shear, and an elliptic vortex inclined at 45° to the flow direction. The laminar base-flow Reynolds number is roughly in the same range as that of a turbulent boundary layer based on eddy viscosity, and the vortex-core diameter based on the boundary-layer thickness is nearly the same as the maximum mixing length in a turbulent boundary layer. The computational box size, namely, 500, 150, and 250 wall units in the streamwise, surface-normal, and spanwise directions, respectively, is approximately the same as the measured quasi-periodic spacings of the near-wall turbulence-producing events in a turbulent boundary layer. The effects of vortex Reynolds number and the signs of the circulation on the moments of turbulence were examined. The signs mimic the ejection and sweep types of organized motions of a turbulent boundary layer. A vortex Reynolds number of 200 describes the turbulence moments in the outer layer reasonably well.     

A bypass wake induced laminar/turbulent transition

The process of laminar to turbulent transition induced by a von Karman vortex street wake, was studied for the case of a flat plate boundary layer. The boundary layer developed under zero pressure gradient conditions. The vortex street was generated by a cylinder positioned in the free stream. An X-type hot-wire probe located in the boundary layer, measured the streamwise and normal to the wall velocity components. The measurements covered two areas; the region of transition onset and development and the region where the wake and the boundary layer merged producing a turbulent flow. The evolution of Reynolds stresses and rms-values of velocity fluctuations along the transition region are presented and discussed. From the profiles of the Reynolds stress and the mean velocity profile, a ‘negative' energy production region along the transition region, was identified. A quadrant splitting analysis was applied to the instantaneous Reynolds stress signals. The contributions of the elementary coherent structures to the total Reynolds stress were evaluated, for several x-positions of the near wall region. Distinct regions in the streamwise and normal to the wall directions were identified during the transition.     

Numerical analysis of turbulent flow in a rotating U-bend with roughened walls

A numerical analysis has been performed for a developing turbulent flow in a rotating U-bend of strong curvature with rib-roughened walls using an anisotropic turbulent model. In this calculation, an algebraic Reynolds stress model is used to precisely predict Reynolds stresses, and a boundary-fitted coordinate system is introduced as a method of coordinate transformation to set the exact boundary conditions along the complicated shape of U-bend with rib-roughened walls. Calculated results for mean velocity and Reynolds stresses are compared to the experimental data in order to validate the proposed numerical method and the algebraic Reynolds stress model. Although agreement is certainly not perfect in all details, the present method can predict characteristic velocity profiles and reproduce the separated flow generated near the outer wall, which is located just downstream of the curved duct. The Reynolds stresses predicted by the proposed turbulent model agree well with the experimental data, except in regions of flow separation.     

Temporal development of turbulent boundary layers with embedded streamwise vortices

The interaction of streamwise vortices with turbulent boundary layer has been investigated using large-eddy simulation. The initial conditions are a pair of counterrotating Oseen vortices with flow between them directed toward the wall (common-flow-down), superimposed on various instantaneous realizations of a turbulent boundary layer. The time development of the vortices and their interaction with the boundary layer are studied by integrating the filtered Navier-Stokes equations in time. The most important effects of the vortices on the boundary layer are the thinning of the boundary layer between vortices (downwash region) and the thickening of the boundary layer in the upwash region. The vortices first move toward the wall as a result of the self-induced velocity, and then apart from each other because of the image vortices due to the solid wall. The Reynolds stress profiles highlight the highly three-dimensional structure of the turbulent boundary layer modified by the vortices. The presence of significant turbulent activity near the vortex center and in the upwash region suggests that localized instability mechanisms in addition to the convection of turbulent energy by the secondary flow are responsible for this effect. High levels of turbulent kinetic energy and secondary stresses in the vicinity of the vortex center are also observed. The numerical results show good agreement with experimental results.This work was supported by the Office of Naval Research under Grant N00014-89-J-1638. Computer time was supplied by the San Diego Supercomputing Center.     

Parametric Study on a Sinusoidal Riblet for Drag Reduction by Direct Numerical Simulation

The direct numerical simulation of fully developed turbulent channel flow with a sinusoidal riblet surface has been carried out at the friction Reynolds number of 110. Lateral spacing of adjacent walls in a sinusoidal riblet is varied sinusoidally in the streamwise direction. The average lateral spacing of a sinusoidal riblet is larger than the diameter of a quasi-streamwise vortex and its wetted area is smaller than that of ordinary straight-type riblets. We investigate the effect of sinusoidal riblet design parameters on the drag reduction rate and flow statistics in this paper. The parametric study shows that the maximum total drag reduction rate is approximately 9.8% at a friction Reynolds number of 110. The riblet induces downward and upward flows in the expanded and contracted regions, respectively, which contribute to periodic Reynolds shear stress. However, the random Reynolds shear stress decreases drastically as compared with the flat surface case, resulting in the reduction of total drag owing to the sinusoidal riblet. We also performed vortex tracking to discuss the motion of the vortical structure traveling over the sinusoidal riblet surface. Vortex tracking and probability analysis for the core of the vortical structure show that the vortical structure is attenuated owing to the sinusoidal riblet and follows the characteristic flow. These results show that the high skin-friction region on the channel wall is localized at the expanded region of the riblet walls. In consequence, the wetted area of the riblet decreases, resulting in the drag-reduction effect.     

Flow Regimes in Packed Beds of Spheres from Pre-Darcy to Turbulent

Characteristics of flow regimes in porous media, along the processes of energy dissipation in each regime, are critical for applications of such media. The current work presents new experimental data for water flow in packed steel spheres of 1- and 3-mm diameters. The porosity of the porous media was about 35 % for both cases. The extensive dataset covered a broad range of flow Reynolds number such that several important flow regimes were encountered, including the elusive pre-Darcy regime, which is rarely or never seen in porous-media literature and turbulent regime. When compared to previous information, the results of this study are seen to add to the divergence of available data on pressure drop in packed beds of spheres. The divergence was also present in the coefficients of Ergun equation and in the Kozeny–Carman constant. The porous media of the current work were seen to exhibit different values of permeability and Forchheimer coefficient in each flow regime. The current data correlated well using the friction factor based on the permeability (measured in the Darcy regime) and the Reynolds number based on the same length scale. An attempt was made to apply recent theoretical results regarding the applicability of the quadratic and cubic Forchheimer corrections in the strong and weak inertia regime.     

Passive Scalar in a Turbulent Channel Flow with Wall Velocity Disturbances

Direct Numerical Simulations (DNS) of a passive scalar in a turbulent channel flow with a normal velocity disturbance on the lower wall are presented for high and low Reynolds numbers. The aim is to reproduce the complex physics of turbulent rough flows without dealing with the geometric complexity. In addition, isothermal walls that cannot be easily assigned in an experiment, are considered. The paper explains the increase of heat transfer through the changes of the velocity and thermal structures. As in real rough flows, the transpiration produces an isotropization of the turbulence near the wall.     

Transition from vortex to wall driven turbulence production in the Taylor–Couette system with a rotating inner cylinder

Axisymmetrically stable turbulent Taylor vortices between two concentric cylinders are studied with respect to the transition from vortex to wall driven turbulent production. The outer cylinder is stationary and the inner cylinder rotates. A low Reynolds number turbulence model using the k‐ω formulation, facilitates an analysis of the velocity gradients in the Taylor–Couette flow. For a fixed inner radius, three radius ratios 0.734, 0.941 and 0.985 are employed to identify the Reynolds number range at which this transition occurs. At relatively low Reynolds numbers, turbulent production is shown to be dominated by the outflowing boundary of the Taylor vortex. As the Reynolds number increases, shear driven turbulence (due to the rotating cylinder) becomes the dominating factor. For relatively small gaps turbulent flow is shown to occur at Taylor numbers lower than previously reported. Copyright © 2002 John Wiley & Sons, Ltd.     

Phase-locked analysis of velocity fluctuations in a turbulent free swirling jet after vortex breakdown

Large-scale organized vortical structures were studied experimentally in a free swirling jet of air experiencing vortex precession (PVC) at ambient conditions. Detailed measurements were performed in the region near the nozzle exit using phase-locked LDV and PIV, at a Reynolds number of Re ?? 24,400 and a swirl parameter S ?? 1.0. The investigation allowed reconstruction of the time-averaged flowfield, with the associated distribution of turbulent fluctuations, the phase-locked structure of the jet and the associated precessing vortex structure. An original joint analysis of power spectra and probability density functions of velocity data led to quantification of the PVC effect on turbulent fluctuations. This analysis showed that the PVC contribution can be properly separated from the background random turbulence, reproducing the results of phase-locked measurements. It is found that the background turbulence in the near field is substantially weaker if compared to the coherent fluctuations induced by vortex precession.     

Generalised Couette flow of two immiscible viscous fluids with heat transfer using Brinkman model

The present study deals with generalised Couette flow of two viscous, incompressible, immiscible fluids with heat transfer in presence of heat source through two straight parallel horizontal walls. The lower wall is bounded below, by a naturally permeable material of high porosity and the flow inside the porous medium is assumed to be of moderate permeability, modelled by Brinkman equation. The flow domain is divided into three zones to obtain analytical solutions of the momentum and energy equations. To link various flow regions, appropriate matching conditions have been used. The effects of permeability parameter, Reynolds number and viscous parameter on velocity field and the effects of Reynolds number, viscous parameter, permeability parameter, constant heat source and Brinkman number on temperature distribution in different zones are discussed graphically. The mass flow rate, skin-friction factor and rates of heat transfer at the upper boundary and porous interface are discussed with the help of tables.     

Structure of near wall turbulence downstream of a wall mounted protrusion: an interesting Reynolds stress suppression phenomena

A local suppression in the generation of near wall Reynolds stress is achieved by modifying the buffer region and sublayer (y ⁺ <30) of a turbulent pipe flow with a 16.4 wall unit high wall mounted protrusion. Multi-component, multi-point, time resolved laser Doppler velocimetry measurements are made in the undisturbed and modified ARL/PSU glycerin tunnel pipe flow at a Reynolds number of approximately 10000. A downstream converging flow field is produced by the divergence of the approaching mean flow around the protrusion. A pair of counter-rotating vortices, 15 wall units in diameter with common flow down, are generated by the protrusion and also contribute to the wall directed flow convergence. The convergence region is 15 wall units high and more than 100 wall units long and appears to decouple the near wall region from the outer turbulent wall layer. Locally, turbulent velocity fluctuations in the form of Reynolds stress producing events, sweeps and ejections, are retarded within this region. This results in a reduction in near wall uv Reynolds stress and local wall shear. Interestingly, the counter-rotating vortices act to increase turbulent diffusion in a manner which is uncorrelated with Reynolds stress generation.     

Effect of Flow Structures on Turbulence Statistics of Taylor-Couette Flow in the Torque Transition State

Direct numerical simulations of Taylor-Couette flow from Re= 8000 to 25000 have been conducted to investigate changes of turbulence statistics in the transition of the Reynolds number dependency of the mean torque near Re= 10000. The velocity fluctuations are decomposed into the contributions of the Taylor vortex and remaining turbulent fluctuations. Significant Reynolds number dependencies of these components are observed in the radial profiles of the Reynolds stress and the transmission of the mean torque. The contributions of Taylor vortex and turbulent components in the net amount of mean torque are evaluated. The Taylor vortex component is overtaken by the turbulent counterpart around Re= 15000 when they are defined as the azimuthally averaged component and the remnants. The results show that the torque transition can be explained by the competition between the contributions of azimuthally averaged Taylor vortex and the remaining turbulent components.