Streamwise Reynolds Normal Stress Research Articles

Numerical investigations of vortex dynamics and loss generation in the corner separation region of a high subsonic compressor blade

Three-dimensional corner separation seriously deteriorates the aerodynamic performance of a compressor blade. In this study, the complicated vortex dynamics and loss mechanism in the corner region of a high subsonic compressor blade (the inlet Mach number is 0.67) are investigated using large eddy simulations (LESs) at a Reynolds number (Re) of 5.6 × 105. The results show that the predicted total pressure loss and outlet flow angle match well with the experimental data, indicating that the LES method can accurately predict the size and strength of corner separation in the compressor blade. With the passage vortex rolling up and further interacting with the low-momentum fluids originating from the end wall boundary layers and the local blade boundary layers, strong shear strain induces a large-scale concentrated shedding vortex (CSV) near the spanwise location of x/H = 0.3. The formation and rolling-up of the CSV not only cause the strongest flow blockage but also strengthen the turbulence anisotropy. As the CSV moves toward the trailing edge, the strong interaction with a pair of counter-rotating vortices shed in the wake region (wake shedding vortex) further accelerates the local generation of turbulent kinetic energy (TKE). Detailed TKE budget analysis shows that the streamwise Reynolds normal stress (w′w′¯) plays the most decisive role in the TKE production term. Furthermore, we demonstrate that the strength of turbulence anisotropy is positively correlated with the TKE budget. Therefore, turbulence anisotropy should be considered carefully in predicting the loss level in the corner region of a compressor blade.

Large-eddy simulation of a planar offset wall-jet with heat transfer: Characterization, turbulent kinetic energy and Reynolds shear stress budgets

Planar wall-attaching offset jets can be found in a variety of engineering applications. In the present work, a planar turbulent offset wall-jet, at a Reynolds number of 7500 and an offset-ratio of 5, with heat transfer is numerically studied using large-eddy simulation (LES). First, a grid sensitivity study is performed and the quality of the mesh used is assessed using LES index of quality of resolution and an appropriate mesh is selected. Next, the solver is validated for mean streamwise velocity, streamwise Reynolds normal stress, and the evolution of coefficient of pressure on the wall, using reference experimental data from the literature. Thereafter, the unsteady flow features of the jet, maximum velocity decay and jet-spread, statistical features of flow and temperature, and turbulent kinetic energy (TKE) budgets and in-plane component of Reynolds shear stress are studied. The streamwise evolution of Nusselt number on the wall shows three distinct peaks and the location of these peaks correlates with a change-of-sign of the wall skin-friction coefficient. The domain can be categorized into three distinct regions namely, the recirculation, impingement and wall-jet regions. Distinct flow and thermal characteristics are observed depending on the region of interest. The peak magnitudes of Reynolds normal and shear stresses increase as one moves from the recirculation region to the impingement region and decreases thereafter attaining a lowest value in the wall-jet region. The heat transfer from the wall is observed to be most effective in the recirculation region. The production of TKE is dominant in all the three regions of the flow, whereas the Reynolds shear stress budgets indicate that the production and velocity–pressure-gradient terms are dominant and balance each other in all the three regions of the flow.

A Comparative Study between Sand- and Gravel-Bed Open Channel Flows in the Wake Region of a Bed-Mounted Horizontal Cylinder

In nature, environmental and geophysical flows frequently encounter submerged cylindrical bodies on a rough bed. The flows around the cylindrical bodies on the rough bed are very complicated as the flow field in these cases will be a function of bed roughness apart from the diameter of the cylinder and the flow velocity. In addition, the sand-bed roughness has different effects on the flow compared to the gravel-bed roughness due to differences in the roughness heights. Therefore, the main objective of this article is to compare the mean velocities and turbulent flow properties in the wake region of a horizontal bed-mounted cylinder over the sand-bed with that over the gravel-bed. Three experimental runs, two for the sand-bed and one for the gravel-bed with similar physical and hydraulic conditions, were recorded to fulfil this purpose. The Acoustic Doppler Velocimetry (ADV) probe was used for measuring the three-dimensional (3D) instantaneous velocity data. This comparative study shows that the magnitude of mean streamwise flow velocity, streamwise Reynolds normal stress, and Reynolds shear stress are reduced on the gravel-bed compared to the sand-bed. Conversely, the vertical velocities and vertical Reynolds normal stress are higher on the gravel-bed than the sand-bed.

Time-resolved wake dynamics of finite wall-mounted circular cylinders submerged in a turbulent boundary layer

Abstract

Effect of periodic perturbations on the turbulence statistics in a backward-facing step flow

Turbulence budget for natural and periodically perturbed backward-facing step flows was studied using particle image velocimetry data, aiming to provide more evidence for the mechanisms of the turbulence production under perturbation. The flow has a Reynolds number of 9630 based on the step height. A synthetic jet actuator deployed at the step corner was used to perturb the flow with a wide range of parameters including different frequencies and amplitudes. The results show that the sizes of the turbulence production terms are enhanced with efficiency when flow is perturbed at a frequency near the shear layer mode frequency. The enhancement is associated with vortical structures produced by the perturbation. The length scale of the structures is similar to the step height. In contrast, the low-frequency perturbation (with a frequency which is 25% of the shear layer mode frequency) has less impact on the turbulence production despite the large amplitude vertical flapping motion of the whole shear layer and large increases in the streamwise Reynolds normal stress occur.

Direct numerical simulations of temporally decelerating turbulent pipe flows

Direct numerical simulations of temporally decelerating turbulent pipe flows are performed to examine the effects of temporal deceleration on the turbulence characteristics. The temporal decelerations are applied with three different values of the decelerating parameter f = |dUb/dt| based on the bulk mean velocity (Ub) to introduce weak, mild and strong decelerations, and the flow rates for all cases are linearly decreased with time. In order to highlight the variation of the turbulent statistics for an unsteady flow, five independent simulations of steady flows are conducted along with the Reynolds number. An inspection of the mean velocity profiles shows that the log law in the overlap region is established with a slight downward shift for the weakly decelerating flow, whereas this is not the case for the strong decelerating flow. A comparison of the Reynolds stress profiles between the unsteady and steady flows displays that the turbulence is highly intensified with an increase of f due to the enhanced vortical structures and that the radial propagation of the turbulence is delayed. An analysis of the turbulent production term of the Reynolds stress budget equation shows that frozen of the strong second-quadrant Reynolds shear stress event plays an important role in delaying the response of the turbulent energy with a decrease of the Reynolds number, leading to an increase in the Reynolds stress. In addition, spectral decomposition of the streamwise Reynolds normal stress into small- and large-scale components reveals that the enhanced turbulence throughout the entire flow for unsteady flows is a direct consequence of the delay of strong large-scale structures, although small-scale structures throughout the wall layer adjust rapidly to temporal deceleration.

PIV measurement downstream of perforated cylinder in deep water

The flow structure of perforated circular cylinders was thoroughly scrutinized by using the technique of high-image-density Particle Image Velocimetry (PIV). The perforated circular cylinder diameter (D=100 mm), was kept constant during the experimental investigation and corresponding Reynolds number was Re=10000 based on the cylinder diameter. Turbulent statistics e.g., planar turbulent kinetic energy, stream-wise Reynolds normal stress, transverse Reynolds normal stress and Reynolds shear stress were computed in the wake region in order to reveal the differences among various porosities in the range of 0.25≤β≤0.80. It would be noted that by increasing porosity, β the flow fluctuations are substantially reduced in the wake region according to the PIV results. As a result, the prevention of Karman Vortex Street was accomplished by the use of perforated cylinders because of elongated and fragmented shear layers and reduced magnitudes of vortices.

Partially filled pipes: experiments in laminar and turbulent flow

Pressure-driven laminar and turbulent flow in a horizontal partially filled pipe was investigated using stereoscopic particle imaging velocimetry (S-PIV) in the cross-stream plane. Laminar flow velocity measurements are in excellent agreement with a recent theoretical solution in the literature. For turbulent flow, the flow depth was varied independently of a nominally constant Reynolds number (based on hydraulic diameter, $D_{H}$; bulk velocity, $U_{b}$ and kinematic viscosity $\unicode[STIX]{x1D708}$) of $Re_{H}=U_{b}D_{H}/\unicode[STIX]{x1D708}\approx 30\,000\pm 5\,\%$. When running partially full, the inferred friction factor is no longer a simple function of Reynolds number, but also depends on the Froude number $Fr=U_{b}/\sqrt{gD_{m}}$ where $g$ is gravitational acceleration and $D_{m}$ is hydraulic mean depth. S-PIV measurements in turbulent flow reveal the presence of secondary currents which causes the maximum streamwise velocity to occur below the free surface consistent with results reported in the literature for rectangular cross-section open channel flows. Unlike square duct and rectangular open channel flow the mean secondary motion observed here manifests only as a single pair of vortices mirrored about the vertical bisector and these rollers, which fill the half-width of the pipe, remain at a constant distance from the free surface even with decreasing flow depth for the range of depths tested. Spatial distributions of streamwise Reynolds normal stress and turbulent kinetic energy exhibit preferential arrangement rather than having the same profile around the azimuth of the pipe as in a full pipe flow. Instantaneous fields reveal the signatures of elements of canonical wall-bounded turbulent flows near the pipe wall such as large-scale and very-large-scale motions and associated hairpin packets whilst near the free surface, the signatures of free surface turbulence in the absence of imposed mean shear such as ‘upwellings’, ‘downdrafts’ and ‘whirlpools’ are present. Two-point spatio-temporal correlations of streamwise velocity fluctuation suggest that the large-scale coherent motions present in full pipe flow persist in partially filled pipes but are compressed and distorted by the presence of the free surface and mean secondary motion.

Turbulence characteristics in wall-wake flows downstream of wall-mounted and near-wall horizontal cylinders

Turbulent characteristics in wall-wake flows downstream of wall-mounted and near-wall cylinders are investigated. The distributions of the defect of streamwise velocity, Reynolds shear stress and turbulence intensities exhibit a certain degree of self-preserving characteristic when they are scaled by their respective peak defect values. For the velocity defect distributions, the vertical distances are scaled by the half-width of peak defect velocity. However, for the distributions of the defects of the Reynolds shear stress and the turbulence intensities, the vertical distances are scaled by the half-width of Reynolds shear stress defect. The peak defects of all the quantities reduce with longitudinal distance signifying the recovery of the upstream distributions of the individual quantities. The third-order correlations reveal that for the wall-mounted cylinder, a streamwise acceleration associated with a downward flux of streamwise Reynolds normal stress (SRNS) in the inner-layer of wall-wake composes sweeps and a streamwise deceleration associated with an upward flux of SRNS in the outer-layer forms ejections. On the other hand, for the near-wall cylinder, a streamwise deceleration associated with a downward flux of SRNS in the inner-layer of wall-wake flow and the gap flow produces the inward interaction events, while the outer-layer characteristic is similar to that of wall-mounted cylinder. The turbulent kinetic energy (TKE) budget in the wake flow demonstrates strong negative pressure energy diffusion in addition to a strong TKE dissipation and diffusion and that in the gap flow exhibits a minor positive peak of pressure energy diffusion and a minor negative peak of TKE diffusion.

Interaction between plasma synthetic jet and subsonic turbulent boundary layer

This paper experimentally investigates the interaction between a plasma synthetic jet (PSJ) and a subsonic turbulent boundary layer (TBL) using a hotwire anemometer and phase-locked particle imaging velocimetry. The PSJ is interacting with a fully developed turbulent boundary layer developing on the flat wall of a square wind tunnel section of 1.7 m length. The Reynolds number based on the freestream velocity (U∞ = 20 m/s) and the boundary layer thickness (δ99 = 34.5 mm) at the location of interaction is 44 400. A large-volume (1696 mm3) three-electrode plasma synthetic jet actuator (PSJA) with a round exit orifice (D = 2 mm) is adopted to produce high-speed (92 m/s) and short-duration (Tjet = 1 ms) pulsed jets. The exit velocity variation of the adopted PSJA in a crossflow is shown to remain almost identical to that in quiescent conditions. However, the flow structures emanating from the interaction between the PSJ and the TBL are significantly different from what were observed in quiescent conditions. In the midspan xy plane (z = 0 mm), the erupted jet body initially follows a wall-normal trajectory accompanied by the formation of a distinctive front vortex ring. After three convective time scales the jet bends to the crossflow, thus limiting the peak penetration depth to approximately 0.58δ99. Comparison of the normalized jet trajectories indicates that the penetration ability of the PSJ is less than steady jets with the same momentum flow velocity. Prior to the jet diminishing, a recirculation region is observed in the leeward side of the jet body, experiencing first an expansion and then a contraction in the area. In the cross-stream yz plane, the signature structure of jets in a crossflow, the counter-rotating vortex pair (CVP), transports high-momentum flow from the outer layer to the near-wall region, leading to a fuller velocity profile and a drop in the boundary layer shape factor (1.3 to 1.2). In contrast to steady jets, the CVP produced by the PSJ exhibits a prominent spatiotemporal behaviour. The residence time of the CVP is estimated as the jet duration time, while the maximum extent of the affected flow in the three coordinate directions (x, y, and z) is approximately 32D, 8.5D, and 10D, respectively. An extremely high level of turbulent kinetic energy production is shown in the jet shear-layer, front vortex ring, and CVP, of which the contribution of the streamwise Reynolds normal stress is dominant. Finally, a conceptual model of the interaction between the PSJ and the TBL is proposed.

DNS of turbulent drag reduction in a pressure-driven rod-roughened channel flow by microfiber additives

The turbulent drag reduction caused by microfiber additives in a pressure-driven rod-roughened channel flow at a nominal shear Reynolds number 395 is presented. Both channel walls are roughened by spanwise rods of square cross section with a height of k+=13.6 which translates to 1.7% of channel width. A pitch-to-height ratio of 8 is chosen. The effect of suspended fibers is modeled by an algebraic closure model, which allows the direct simulation of such complicated physics by significantly reducing the computational costs. Three simulations have been conducted; the Newtonian flow and the drag-reduced flows with two different fiber concentrations. As a result, 12.71% and 16.78% increase in the mean bulk velocities throughout the channel could be achieved for the two concentrations considered here. Also, the mean streamwise and wall-normal velocity profiles as well as Reynolds stresses at various locations between two consecutive roughness elements are presented and discussed. In the drag-reduced flow, the streamwise Reynolds normal stress is increased whereas the spanwise and wall-normal normal stresses are decreased. Also, the magnitude of the Reynolds shear stress is decreased in the fibrous flow.

Blade number effects in a scaled down wind farm

Two 3 × 4 scaled down wind farms were analyzed to understand differences in wind turbine boundary layers when turbines operating at identical power coefficients have two or three blades. Mean streamwise velocities in two bladed turbine near wakes ranged between 10 and 100% larger than those in the three bladed case with large differences just behind the nacelle. In the rotor swept region of far wakes, mean velocity differences between the two arrays were about 10% (max) and became smaller with increasing streamwise direction. Contrary to these findings, regions above and below rotors become less similar deep in the array. Incoming flow to downstream turbines was shown to have greater Reynolds streamwise normal stress for three bladed rotors. Percentage differences ranged between about 30% for the second turbine down to 10% for the fourth turbine. Additionally, there is qualitative evidence that suggests incoming streamwise Reynolds normal stress becomes similar between the two types of turbines, indicating that asymptotically two and three bladed turbines could have similar fatigue loading properties. These results show that use of two bladed turbines would have the most impact when used in a wind farm's first two rows.

Structure of Turbulent Channel Flow Perturbed by a Wall-Mounted Cylindrical Element

The current study reports structural modifications imposed in fully developed, turbulent channel flow by an isolated wall-mounted circular cylinder. The cylinder extended into the logarithmic layer of the flow, perturbing the larger flow scales that embody a significant fraction of the turbulent kinetic energy and Reynolds shear stress. Hot-wire measurements were made in the wake of the wall-mounted circular cylinder at multiple wall-normal and streamwise positions. Besides observing the expected mean velocity deficit in the wake of the cylinder, a secondary peak in streamwise Reynolds normal stress away from the wall was observed, coupled with suppression of the near-wall peak native to the incoming unperturbed, turbulent flow. These observations are similar to those made by Ryan et al. (“Effects of Simple Wall-Mounted Cylinder Arrangements on a Turbulent Boundary Layer,” AIAA Journal, Vol. 49, No. 10, 2011, pp. 2210–2220) for a wall-mounted cylinder protruding into the logarithmic layer of a turbulent boundary layer. Premultiplied velocity spectra elaborated on these energy modifications, specifically the occurrence of two distinct energy peaks at two-thirds of the cylinder height and an attenuation of energy associated with larger flow scales close to the wall. All of these perturbations were found to decay with streamwise distance downstream as the flow relaxed toward the unperturbed state. A clear persistence of the structures at the aforementioned peak at two-thirds cylinder height, similar in scale to the very large-scale motions in canonical wall turbulence, suggests an environment preferring structures of such scale. The influence of the cylinder aspect ratio on the characteristics of the perturbed flow is evaluated, and a distinction in wake structure is identified.

A study of energetic large-scale structures in turbulent boundary layer

This study established the connection in turbulent boundary layers between the first two dominant proper orthogonal decomposition (POD) modes and the instantaneous large-scale turbulence structures. The velocity fields consistent with the signature velocity fields of the hairpin vortex packets in two-dimensional PIV (particle image velocimetry) measurement planes are observed as the major contributors to the first two POD modes. Another kind of equally important turbulence structure is the large region of Q4 vectors, which may possibly be obtained by slicing the outskirts of the three-dimensional structure of the hairpin vortex packet by PIV planes. The streamwise Reynolds normal stress, Reynolds shear stress, and the length scales of the two-point velocity correlation coefficients ρuu and ρuv are noticeably decreased without those large-scale turbulence structures contributing significantly to the first POD mode. Similarity of these results is observed at a higher Reynolds number.

Reynolds-number scaling of turbulent channel flow

Results of an experimental study of smooth-wall, fully developed, turbulent channel flow are presented. The Reynolds number (Rem) based on the channel height and the bulk mean velocity ranged from 10 000 to 300 000. The present results indicate that the skin-friction coefficient (Cf) closely follows a power law for Rem < 62 000. At higher Reynolds numbers, Cf is best described by a log law. Detailed two-component velocity measurements taken at friction Reynolds numbers of Reτ = 1000–6000 indicate that the mean flow and Reynolds shear stress display little or no Reynolds-number dependence. The streamwise Reynolds normal stress ($\overline {u^{\prime 2} } ^ + $u′2¯+), on the other hand, varies significantly with Reynolds number. The inner peak in $\overline {u^{\prime 2} } ^ + $u′2¯+ is observed to grow with Reynolds number. Growth in $\overline {u^{\prime 2} } ^ + $u′2¯+ farther from the wall is documented over the entire range of Reynolds number giving rise to a plateau in the streamwise Reynolds normal stress in the overlap region of the profile for Reτ = 6000. The wall-normal Reynolds normal stress ($\overline {v^{\prime 2} } ^ + $v′2¯+) displays no Reynolds-number dependence near the wall. Some increase in $\overline {v^{\prime 2} } ^ + $v′2¯+ in the outer layer is noted for Reτ ≤ 4000. The trends in the present Reynolds stress results agree qualitatively with recent experimental results from pipe and boundary layer flows.

Passive control of circular cylinder wake in shallow flow

The control of vortex shedding of a circular cylinder in shallow water using a splitter plate located in the downstream of the circular cylinder was studied by employing particle image velocimetry (PIV) technique. Experiments were carried out in a water channel having a test section of 8000mm×1000mm×750mm dimensions at a Reynolds number of 6250. The length of the splitter plate (L) was varied within the range of 0.5⩽L/D⩽2 with an increment of 0.5. The plate was submerged into water at different height ratios (hp/hw) such as 0.25, 0.5, 0.75 and 1.0. Mean velocity vector field, corresponding vorticity contours, streamline topologies and turbulent quantities were calculated using 300 instantaneous velocity vector field measured by PIV. As the ratio of hp/hw increases, the effect of the splitter plate on the suppression of the vortex shedding increases. Flow characteristics and examination of spectra indicate that Karman vortex shedding is attenuated pronouncedly for the cases of L/D⩾1 and hp/hw⩾0.75. The transverse Reynolds normal stress is more effective on the attenuation of turbulent kinetic energy than the streamwise Reynolds normal stress. The value of peak transverse Reynolds normal stress is reduced to 90% of that of the bare cylinder at most.

Near-Bed Turbulence Characteristics at the Entrainment Threshold of Sediment Beds

This experimental study is devoted to quantification of the near-bed turbulence characteristics at an entrainment threshold of noncohesive sediments. Near the bed, the departure in the distributions of the observed time-averaged streamwise velocity from the logarithmic law is more for immobile beds than for entrainment-threshold beds. In the Reynolds shear stress distributions, a damping that occurs near the bed for sediment entrainment is higher than that for immobile beds. Quadrant analysis reveals that in the near-bed flow zone, ejections and sweeps on immobile beds cancel each other, giving rise to the outward interactions, whereas sweeps are the dominant mechanism toward sediment entrainment. The bursting duration for entrainment-threshold beds is smaller than that for immobile beds. On the other hand, the bursting frequency for entrainment-threshold beds is larger than that for immobile beds. The third-order correlations indicate that during sediment entrainment, a streamwise acceleration associated with a downward flux and advection of streamwise Reynolds normal stress is prevalent. The streamwise and the downward vertical fluxes of turbulent kinetic energy (TKE) increase with sediment entrainment. The TKE budget proves that for sediment entrainment, the pressure energy diffusion changes drastically to a negative magnitude, indicating a gain in turbulence production.

Submerged wall jets subjected to injection and suction from the wall

This paper presents an experimental study on turbulent flow characteristics in submerged plane wall jets subjected to injection (upward seepage) and suction (downward seepage) from the wall. The vertical distributions of time-averaged velocity components, turbulence intensity components and Reynolds shear stress at different horizontal distances are presented. The horizontal distributions of wall shear stress determined from the Reynolds shear stress profiles are also furnished. The flow field exhibits a decay of the jet velocity over a horizontal distance. The wall shear stress and the rate of decay of the jet velocity increase in the presence of injection and decrease with suction. Based on the two-dimensional Reynolds-averaged Navier–Stokes equations of a steady turbulent flow, the velocity and Reynolds shear stress distributions in the fully developed zone subjected to no seepage, injection and suction are theoretically computed. The response of the turbulent flow characteristics to injection and suction is analysed from the point of view of similarity characteristics, growth of the length scale and decay of the velocity and turbulence characteristics scales. The significant observation is that the velocity, Reynolds shear stress and turbulence intensities in the fully developed zone are reasonably similar under both injection and suction on applying the appropriate scaling laws. An analysis of the third-order moments of velocity fluctuations reveals that the inner layer of the jet is associated with the arrival of low-speed fluid streaks causing an effect of retardation. On the other hand, the upper layer of the jet is associated with the arrival of high-speed fluid streaks causing an effect of acceleration. Injection influences the near-wall distributions of the third-order moments by increasing the upward turbulent advection of the streamwise Reynolds normal stress. In contrast, suction influences the near-wall distributions of the third-order moments by increasing the downward turbulent advection of the streamwise Reynolds normal stress. Also, injection and suction change the vertical turbulent flux of the vertical Reynolds normal stress in a similar way. The streamwise turbulent energy flux travels towards the jet origin within the jet layer, while it travels away from the origin within the inner layer of the circulatory flow. The turbulent energy budget suggests that the turbulent and pressure energy diffusions oppose each other, and the turbulent dissipation lags the turbulent production. The quadrant analysis of velocity fluctuations reveals that the inward and outward interactions are the primary contributions to the Reynolds shear stress production in the inner and outer layers of the jet, respectively. However, injection induces feeble ejections in the vicinity of the wall.

Turbulence Characteristics in Flows Subjected to Boundary Injection and Suction

The influence of seepage (lateral flow) on the turbulence characteristics in free-surface flows over an immobile rough boundary is investigated. Steady flows having zero-pressure gradient over an immobile rough boundary created by uniform gravels of 4.1 mm in size were simulated experimentally with injection (upward seepage) and suction (downward seepage) applied through the boundary. A Vectrino (acoustic Doppler velocimeter) was used to measure the instantaneous velocities, which are analyzed to explore second- and third-order correlations, turbulent kinetic energy, turbulent energy budget, and conditional Reynolds shear stresses. It is observed that the second-order correlations decrease in presence of injection and increase in suction. The turbulent diffusivity and mixing length increase in presence of injection and decrease in suction. The third-order correlations suggest that the ejections are prevalent over the entire flow depth. The near-boundary flow is significantly influenced by the existence of upward seepage, which is manifested by a reduction in streamwise flux and the vertical advection of streamwise Reynolds normal stress. In addition, the upward flux and the streamwise advection of vertical Reynolds normal stress are also affected. The streamwise flux of turbulent kinetic is found to migrate upstream, while the vertical flux of turbulent kinetic energy is transported upward. The fluxes increase in presence of injection and decrease in suction. Energy budget evidences a lag between the turbulent dissipation and production and an opposing trend in the turbulent and pressure energy diffusions. A quadrant analysis for the conditional Reynolds shear stresses reveals that the ejection and sweep events are the primary contributions toward the total Reynolds shear stress production, with ejections dominating over the entire flow depth. The effect of seepage is shown to affect the magnitude of such events. However, in case of sweeps, this phenomenon is the opposite. The mean-time of occurrence of ejections and that of sweeps in suction are more persistent than those in no-seepage and injection.

Turbulent flow and organized motions over a two-dimensional rough wall

Particle image velocimetry measurements at relatively low Reynolds number in a turbulent boundary layer over a two-dimensional roughened surface are presented and compared to those for a smooth wall. The main goal of the study was to give a contribution to the understanding of the behavior of the turbulent organized motions, when the influence of the wall roughness on the turbulent structures may be expected to be noticeable, i.e., for relatively high roughness and relatively low Reynolds number. In addition, the flow behavior with respect to the wall similarity hypothesis in the case of moderately large values of the roughness height k and moderately low Reynolds number was tested. The behavior of the turbulent coherent motions appears to be similar for the two flows in the outer layer. Quantitative differences, observed mainly in the roughness sublayer, are enlightened comparing spatial velocity correlations and vortex population density and strength in the wall-normal-streamwise plane and in planes parallel to the wall. Mean flows expressed in velocity defect law, inner scaled streamwise Reynolds normal stress, and Reynolds shear stresses profiles show excellent agreement in the outer layer between the rough wall and the smooth surface. Wall normal Reynolds normal stress profiles, instead, show some small discrepancy, but within the measurement uncertainty.