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.     

Experimental study on flow control of the turbulent boundary layer with micro-bubbles

The effect of micro-bubbles on the turbulent boundary layer in the channel flow with Reynolds numbers (Re) ranging from \(0.87\times 10 ^{5}\) to \(1.23\times 10^{5}\) is experimentally studied by using particle image velocimetry (PIV) measurements. The micro-bubbles are produced by water electrolysis. The velocity profiles, Reynolds stress and instantaneous structures of the boundary layer, with and without micro-bubbles, are measured and analyzed. The presence of micro-bubbles changes the streamwise mean velocity of the fluid and increases the wall shear stress. The results show that micro-bubbles have two effects, buoyancy and extrusion, which dominate the flow behavior of the mixed fluid in the turbulent boundary layer. The buoyancy effect leads to upward motion that drives the fluid motion in the same direction and, therefore, enhances the turbulence intense of the boundary layer. While for the extrusion effect, the presence of accumulated micro-bubbles pushes the flow structures in the turbulent boundary layer away from the near-wall region. The interaction between these two effects causes the vorticity structures and turbulence activity to be in the region far away from the wall. The buoyancy effect is dominant when the Re is relatively small, while the extrusion effect plays a more important role when Re rises.     

Three-component,time-resolved velocity statistics in the wall region of a turbulent pipe flow

Three-component, coincident, time-resolved velocity measurements were obtained in the near wall region, y ⁺ < 100, of a fully developed turbulent pipe flow. The measurements were conducted in the ARL/PSU glycerin tunnel at a Reynolds number (Re _h), based on pipe radius and centerline velocity, of 6436 and an Re of approximately 730. The reported data include velocity statistics up to fourth order, Reynolds stresses and three component, coincident turbulent velocity spectral estimates. The current data are generally in quite good agreement with the fully developed channel flow direct numerical simulation (DNS) results of Antonia et al. (1992) at Re 700 - 700. The accuracy of the current experimental data and the very good agreement with the DNS results provides evidence for the accuracy of the DNS solutions and thus Antonia's conclusions of very near wall, y ⁺ < 20, Re dependence on turbulent velocity statistics. The very good agreement between the low Re rectangular channel flow DNS results and the low Re flat plate turbulent boundary layer statistics of Karlsson and Johansson (1988) suggests that for y ⁺ < 30 statistics of similar flows of differing geometry may be compared on the basis of equal Re . The current data are available on disk or by anonymous ftp by the first author.     

Creating homogeneous and isotropic turbulence without a mean flow

A novel method of creating homogeneous and isotropic turbulence with small mean flow has been developed. Eight synthetic jet actuators on the corners of a cubic chamber can create energetic turbulence with root-mean-square (rms) velocities as large as 0.87 m/s, corresponding to a Taylor microscale Reynolds number, Re , of 218. Stationary turbulence results show that the turbulence was isotropic, with the rms velocity ratio equal to 1.03, and also homogeneous within the region of interest. Natural decaying turbulence measurements confirmed the power-law decay of the turbulent kinetic energy, with the decay exponent n equal to 1.86 for an initial Re of 224.     

Predicting Turbulent Spectra in Drag-reduced Flows

In the present work we describe how turbulent skin-friction drag reduction obtained through near-wall turbulence manipulation modifies the spectral content of turbulent fluctuations and Reynolds shear stress with focus on the largest scales. Direct Numerical Simulations (DNS) of turbulent channels up to Re _τ = 1000 are performed in which drag reduction is achieved either via artificially removing wall-normal turbulent fluctuations in the vicinity of the wall or via streamwise-travelling waves of spanwise wall velocity. This near-wall turbulence manipulation is shown to modify turbulent spectra in a broad range of scales throughout the whole channel. Above the buffer layer, the observed changes can be predicted, exploiting the vertical shift of the logarithmic portion of the mean streamwise velocity profile, which is a classic performance measure for wall roughness or drag-reducing riblets. A simple model is developed for predicting the large-scale contribution to turbulent fluctuation and Reynolds shear stress spectra in drag-reduced turbulent channels in which a flow control acts at the wall. Any drag-reducing control that successfully interacts with large scales should deviate from the predictions of the present model, making it a useful benchmark for assessing the capability of a control to affect large scales directly.     

Influence of the surface roughness on the third-order moments of velocity fluctuations

Roughness wall effects in a zero pressure gradient turbulent boundary layers were investigated using hot-wire anemometry. The skewness and diffusion factors of u and v, the longitudinal and normal velocity fluctuations, were measured and represented using wall variables. The results indicate that the wall roughness removes the crossover point between sweep and ejection events to the outer region of the layer for a single Reynolds number Re _θ  > 3,000. This behaviour exhibits that the roughness surface favours the maintaining of sweep events obtained by a quadrant analysis. These results show that communication between the wall region and outer region of a turbulent boundary layer exists and the wall similarity hypothesis for a rough wall is questionable. The effect of the wall roughness on the position of the point crossover from sweep to ejection motions with respect to the wall seems to be the same as that obtained when the Reynolds number is higher. Received: 8 March 2000/Accepted: 15 May 2000     

Distribution of turbulent intensity in a gravel-bed flume

Detailed measurements have been taken for the longitudinal turbulent intensities of flow in a gravel-bed flume. The experimental results indicate that the distribution of turbulent intensity greatly depends on the relative roughness. In comparison with the smooth-bed results, the roughness makes the flow turbulence become well-distributed, especially in the region near the bed and in the case of smaller H/K _s values. In addition, the cross sectional average of turbulent intensity is also discussed in this paper, and the results show that the roughness makes flow turbulence much more intense.List of symbols D _u empirical constant - H flow depth - K _s roughness height - N , the mean turbulence intensity over the cross section - Re ^* , roughness Reynolds number - u the RMS of streamwise fluctuating velocity - u _* friction velocity - mean bulk velocity - x coordinate alined with mainstream velocity (x = 0 is channel entrance) - y vertical coordinate to the rough bed (y = 0 is the top of the rough elements) - y ⁺ _u empirical constant - v kinematic viscosity     

Low Reynolds number effects in open-channel turbulent boundary layers

The present study reports measurements of a turbulent boundary layer in an open-channel flow using fiber-optic laser Doppler anemometry. The Reynolds numbers based on momentum thickness and depth of flow are in the range 750≤Re _θ ≤2,400 and 15,300≤Re _h ≤54,200, respectively. It is shown that an accurate estimate of the wall shear stress can be made by fitting a fifth-order polynomial to the near-wall data. The effect of Reynolds number on the mean turbulence intensity and triple correlation is examined using both conventional scaling laws and the recent scaling laws proposed by George and Castillo. The present results show that different scaling laws lead to different conclusions on low Reynolds number effects.     

Flows in the initial sections of channels with permeable walls

Calculations of two types of flows in the initial sections of channels with permeable walls are carried out on the basis of semiempirical turbulence theories during fluid injection only through the walls and during interaction of the external flow with the injected fluid. Experimental studies of the first type [1–3] show that at least within the limits of the lengths L/h<30 and L/a< 50 (2h is the distance between permeable walls of a flat channel anda is the tube radius) the velocity distributions in the laminar and turbulent flow regimes differ little and are nearly self-similar for solutions obtained in [4]. For sufficiently large Reynolds numbers, Re₀>100 (Re₀=v₀h/ or Re₀=v₀ a/, where v₀ is the injection velocity), and small fluid compressibility, the axial velocity component is described by the relations for ideal eddying motion: u=(/2)x× cos (y/2) in a flat channel and u=x cos (y²/2) in atube (the characteristic values for the coordinates are, respectively, h anda). Measurements indicate the existence of a segment of laminar flow; its length depends on the Reynolds number of the injection [3]. In the turbulent regime the maximum generation of turbulent energy occurs significantly farther from the wall than in parallel flow. Flows of the second type in tubes were studied in [5–7]. These studies disclosed that for Reynolds numbers of the flow at the entrance to the porous part of the tube Re=u₀ a/<3.10³ fluid injection with v₀/u₀>0.01 leads to suppression of turbu lence in the initial section of the tube. An analogous phenomenon was observed in the boundary layer with v₀/u₀>0.023 [8, 9]. Laminar-turbulent transition in flows with injection was explained in [10, 11] on the basis of hydrodynamic instability theory, taking into account the non-parallel character of these flows. The mechanisms for the development of turbulence and reverse transition in channels with permeable walls are not theoretically explained. Simple semiempirical turbulence theories apparently are insufficient for this purpose. In the present work results are given of calculations with two-parameter turbulence models proposed in [12, 13] for describing complex flows. Due to the sharp changes of turbulent energy along the channel length, a numerical solution of the complete system of equations of motion was carried out by the finite-difference method [14].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 43–48, September–October, 1976.     

Upstream roughness and Reynolds number effects on turbulent flow structure over forward facing step

This paper presents results of experiments conducted to investigate the effects of Reynolds number and upstream wall roughness on the turbulence structure in the recirculation and recovery regions of a smooth forward facing step. A reference smooth upstream wall and a rough upstream wall made from sand gains were studied. For the smooth upstream wall, experiments were conducted at Reynolds number based on the freestream velocity and step height (h), Re_h = 4940, 8400 and 8650. The rough wall experiments was performed at Re_h = 5100, 8200 and 8600 to closely match the corresponding Re_h experiment over the smooth wall. The reattachment lengths in the smooth wall experiments were L_r/h ≈ 2.2, but upstream roughness significantly reduced these values to L_r/h ≈ 1.3. The integral scales within the recirculation bubbles were independent of upstream roughness and Reynolds number; however, upstream roughness significantly increased the spatial coherence and integral scales outside the recirculation bubbles and in the recovery region. Irrespective of the upstream wall condition, the redeveloping boundary layer recovered at 25h from reattachment.     

Simulations of Turbulent Flow in a Plane Asymmetric Diffuser

Large-eddy simulations (LES) of a planar, asymmetric diffuser flow have been performed. The diverging angle of the inclined wall of the diffuser is chosen as 8.5°, a case for which recent experimental data are available. Reasonable agreement between the LES and the experiments is obtained. The numerical method is further validated for diffuser flow with the diffuser wall inclined at a diverging angle of 10°, which has served as a test case for a number of experimental as well as numerical studies in the literature (LES, RANS). For the present results, the subgrid-scale stresses have been closed using the dynamic Smagorinsky model. A resolution study has been performed, highlighting the disparity of the relevant temporal and spatial scales and thus the sensitivity of the simulation results to the specific numerical grids used. The effect of different Reynolds numbers of the inflowing, fully turbulent channel flow has been studied, in particular, Re _b  = 4,500, Re _b  = 9,000 and Re _b  = 20,000 with Re _b being the Reynolds number based on the bulk velocity and channel half width. The results consistently show that by increasing the Reynolds number a clear trend towards a larger separated region is evident; at least for the studied, comparably low Reynolds-number regime. It is further shown that the small separated region occurring at the diffuser throat shows the opposite behaviour as the main separation region, i.e. the flow is separating less with higher Re _b . Moreover, the influence of the Reynolds number on the internal layer occurring at the non-inclined wall described in a recent study has also been assessed. It can be concluded that this region close to the upper, straight wall, is more distinct for larger Re _b . Additionally, the influence of temporal correlations arising from the commonly used periodic turbulent channel flow as inflow condition (similar to a precursor simulation) for the diffuser is assessed.     

Turbulent channel flow with 2D wedges of random height on one wall

Direct numerical simulations (DNS) of a turbulent channel flow with 2D wedges of random height on the bottom wall have been performed. In addition, two other simulations have been carried out to assess the effect of the geometry on the overlying flow. In the first simulation, the four smallest elements were removed while in the other, a uniform distribution of wedges with the same area was used. Two Reynolds numbers were studied, Re_b=2500 and Re_b=5000 which correspond in case of smooth walls to Re_τ=180 and 300, respectively. Roughness on the wall induces separated regions, the reattachment occurring on the walls of the wedges or on the bottom wall. The pressure gradients on the walls increase the ejections and inrushes towards the wall. As a consequence the flow is more isotropic. The mechanism inducing an improved isotropy has been explained in term of the spectra and budgets of Reynolds stress. The comparison of the 3 surfaces has shown that near the wall, the uniformly distributed roughness represents only a poor approximation of the surface with wedges of random height. The Reynolds stresses, pressure distribution and spectra on the modified wall agree well with those on the random surface. Energy spectra show the pitch to height ratio of the largest elements to be the more appropriate geometrical parameter to describe the geometry.     

Scalar transport from a point source in flows over wavy walls

Simultaneous measurements of the velocity and concentration field in fully developed turbulent flows over a wavy wall are described. The concentration field originates from a low-momentum plume of a passive tracer. PLIF and digital particle image velocimetry are used to make spatially resolved measurements of the structure of the scalar distribution and the velocity. The measurements are performed at three different Reynolds numbers of Re _b = 5,600, Re _b = 11,200 and Re _b = 22,400, respectively, based on the bulk velocity u _b and the total channel height 2h. The velocity field and the scalar field are investigated in a water channel with an aspect ratio of 12:1, where the bottom wall of the test section consists of a train of sinusoidal waves. The wavy wall is characterized by the amplitude to wavelength ratio α = 0.05 and the ratio β between the wave amplitude and the half channel height where β = 0.1. The scalar is released from a point source at the wave crest. For the concentration measurements, Rhodamine B is used as tracer dye. At low to moderate Reynolds number, the flow field is characterized through a recirculation zone which develops after the wave crest. The recirculation zone induces high intensities of the fluctuations of the streamwise velocity and wall-normal velocity. Furthermore, large-scale structures are apparent in the flow field. In previous investigations it has been shown that these large-scale structures meander laterally in flows over wavy bottom walls. The investigations show a strong effect of the wavy bottom wall on the scalar mixing. In the vicinity of the source, the scalar is transported by packets of fluid with a high scalar concentration. As they move downstream, these packets disintegrate into filament-like structures which are subject to strong gradients between the filaments and the surrounding fluid. The lateral scale of the turbulent plume is smaller than the lateral scale of the large-scale structures in the flow field and the plume dispersion is dominated by the structures in the flow field. Due to the lateral meandering of the large-scale structures of the flow field, also the scalar plume meanders laterally. Compared to turbulent plumes in plane channel flows, the wavy bottom wall enhances the mixing effect of the turbulent flow and the spreading rate of the scalar plume is increased.     

Effect of Roughness on Wall-Bounded Turbulence

Direct numerical simulation of turbulent incompressible plane-channel flow between a smooth wall and one covered with regular three-dimensional roughness elements is performed. While the impact of roughness on the mean-velocity profile of turbulent wall layers is well understood, at least qualitatively, the manner in which other features are affected, especially in the outer layer, has been more controversial. We compare results from the smooth- and rough-wall sides of the channel for three different roughness heights of h ⁺= 5.4, 10.8, and 21.6 for Re _τ of 400, to isolate the effects of the roughness on turbulent statistics and the instantaneous turbulence structure at large and small scales. We focus on the interaction between the near-wall and outer-layer regions, in particular the extent to which the near-wall behavior influences the flow further away from the surface. Roughness tends to increase the intensity of the velocity and vorticity fluctuations in the inner layer. In the outer layer, although the roughness alters the velocity fluctuations, the vorticity fluctuations are relatively unaffected. The higher-order moments and the energy budgets demonstrate significant differences between the smooth-wall and rough-wall sides in the processes associated with the wall-normal fluxes of the Reynolds shear stresses and turbulence kinetic energy. The length scales and flow dynamics in the roughness sublayer, the spatially inhomogeneous layer within which the flow is directly influenced by the individual roughness elements, are also examined. Alternative mechanisms involved in producing and maintaining near-wall turbulence in rough-wall boundary layers are also considered. We find that the strength of the inner/outer-layer interactions are greatly affected by the size of the roughness elements.     

Reynolds‐stress modelling of M = 2.25 shock‐wave/turbulent boundary‐layer interaction

M = 2.25 shock‐wave/turbulent‐boundary‐layer interactions over a compression ramp for several angles (8, 13 and 18°) at Reynolds‐number Re=7 × 10³ were simulated with three low‐Reynolds second‐moment closures and a linear low‐Reynolds standard k–ε model. A detailed assessment of the turbulence closures by comparison with both mean‐flow and turbulent experimental quantities is presented. The Reynolds‐stress model which is wall‐topology free and which uses an optimized redistribution closure, is in good agreement with experimental data both for wall‐pressure and mean‐velocity profiles. Detailed analysis of three components of the Reynolds‐stress tensor (comparison with measurements and transport‐equation budgets) provides a critical evaluation of full Reynolds‐stress models for the separated supersonic compression ramp. The discrepancy observed in the shock‐wave foot region, between computations and measurements for the Reynolds‐stresses profiles, could be explained by considering the experimental shock‐wave oscillation and directions for future modelling work are indicated. Copyright © 2007 John Wiley & Sons, Ltd.     

Velocity measurements in a plane turbulent air jet at moderate Reynolds numbers

An experimental investigation of the moderate Reynolds number plane air jets was undertaken and the effect of the jet Reynolds number on the turbulent flow structure was determined. The Reynolds number, which was defined by the jet exit conditions, was varied between 1000 and 7000. Other initial conditions, such as the initial turbulence intensity, were kept constant throughout the experiments. Both hot-wire and laser Doppler anemometry were used for the velocity measurements. In the moderate Reynolds number regime, the turbulent flow structure is in transition. The average size and the number of the large scale of turbulence (per unit length of jet) was unaffected by the Reynolds number. A broadening of the turbulent spectra with increasing Reynolds number was observed. This indicated that there is a decrease in the strength of the large eddies resulting from a reduction of the relative energy available to them. This diminished the jet mixing with the ambient as the Reynolds number increased. Higher Reynolds numbers led to lower jet dilution and spread rates. On the other hand, at higher Reynolds numbers the dependence of jet mixing on Reynolds number became less significant as the turbulent flow structure developed into a self-preserving state.List of symbols b _u velocity half-width of the jet - C _u, C _u,0 constants defining the velocity decay rate - D nozzle width - E _u one dimensional power spectrum of velocity fluctuations - f frequency - K _u, K _u,0 constants defining the jet spread rate - k wavenumber (2f/U) - L longitudinal integral scale - R ₁₁ correlation function - r separation distance - Re jet Reynolds number (U ₀ D/v) - St Strouhal number (fD/U ₀) - t time - U axial component of the mean velocity - U _m mean velocity on the jet axis - U ₀ mean velocity at the jet exit - u the rms of u - u fluctuating component of the axial velocity - V lateral component of the mean velocity - fluctuating component of the lateral velocity - x axial distance from the nozzle exit - y lateral distance from the jet axis - z spanwise distance from the jet axis - v kinematic viscosity - time lag A version of this paper was presented as paper no. 86-0038 at the AIAA 24th Aerospace Sciences Meeting, Reno NV, USA, January 1986     

The effect of a systematic change in surface roughness skewness on turbulence and drag

Previous work by the authors (Flack and Schultz, 2010) has identified the root-mean-square roughness height, k_rms, and the skewness, Sk, of the surface elevation distribution as important parameters in scaling the skin-friction drag on rough surfaces. In this study, three surfaces are tested in turbulent boundary layer flow at a friction Reynolds number, Re_τ = 1600–2200. All the surfaces have similar root-mean-square roughness height, while the skewness is varied. Measurements are presented using both two-component LDV and PIV. The results show the anticipated trend of increasing skin-friction drag with increasing skewness. The largest increase in drag occurs going from negative skewness to zero skewness with a more modest increase going from zero to positive skewness. Some differences in the mean velocity and Reynolds stress profiles are observed for the three surfaces. However, these differences are confined to a region close to the rough surface, and the mean velocity and Reynolds stress profiles collapse away from the wall when scaled in outer variables. The turbulence structure as documented through two-point spatial correlations of velocity is also observed to be very similar over the three surfaces. These results support Townsend’s (1976) concept of outer-layer similarity that the wall boundary condition exerts no direct influence on the turbulence structure away from the wall except in setting the velocity and length scales for the outer layer.     

Investigation of the spatio-temporal flow structure in the buffer region of a turbulent boundary layer by means of multiplane stereo PIV

In order to examine the physical process associated with the production and transport of turbulence in wall bounded flows, a fully developed turbulent boundary layer flow along a flat plate is investigated in stream-wise span-wise planes at y⁺10, 20, and 30, and Re7,800 by using a high-resolution multiplane stereo PIV system. Of particular interest are the structural features of the coherent flow structures, such as their average size and shape, but their intensity, dynamics, and interaction are also examined. The information is deduced from the joint probability density function of the velocity fluctuations and from various correlation, cross-correlation, and conditional-correlation functions. Furthermore, characteristic instantaneous velocity fields are analyzed in order to examine the importance of the individual coherent flow structures for the production of turbulence and the transport of Reynolds stresses.     

Outer layer similarity in fully rough turbulent boundary layers

Turbulent boundary layer measurements were made on a flat plate covered with uniform spheres and also on the same surface with the addition of a finer-scale grit roughness. The measurements were carried out in a closed return water tunnel, over a momentum thickness Reynolds number (Re) range of 3,000–15,000, using a two-component, laser Doppler velocimeter (LDV). The results show that the mean profiles for all the surfaces collapse well in velocity defect form. Using the maximum peak to trough height (R_t) as the roughness length scale (k), the roughness functions (U⁺) for both surfaces collapse, indicating that roughness texture has no effect on U⁺. The Reynolds stresses for the two rough surfaces also show good agreement throughout the entire boundary layer and collapse with smooth wall results outside of the roughness sublayer. Quadrant analysis and the velocity triple products show changes in the rough wall boundary layers that are confined to y<8k_s, where k_s is the equivalent sand roughness height. The present results provide support for Townsends wall similarity hypothesis for uniform three-dimensional roughness. However, departures from wall similarity may be observed for rough surfaces where 5k_s is large compared to the thickness of the inner layer.     

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.