Mean flow and turbulence measurements of the impingement wall jet on a semi-circular convex surface

The detailed mean flow and turbulence measurements of a turbulent air slot jet impinging on two different semi-circular convex surfaces were investigated in both free jet and impingement wall jet regions at a jet Reynolds number Re_w=12,000, using a hot-wire X-probe anemometer. The parametric effects of dimensionless circumferential distance, S/W=2.79-7.74, slot jet-to-impingement surface distance Y/W=1-13, and surface curvature D/W=10.7 and 16 on the impingement wall jet flow development along a semi-circular convex surface were examined. The results show that the effect of surface curvature D/W increases with increasing S/W. Compared with transverse Reynolds normal stress, [`(v<sup>2</sup> )] /U<sub>m</sub><sup>2</sup> \overline {v^2 } /U_{\rm m}^2 , the streamwise Reynolds normal stress, [`(u² )] /U_m² \overline {u^2 } /U_{\rm m}^2 , is strongly affected by the examined dimensionless parameters of D/W, Y/W and S/W in the near-wall region. It is also evidenced that the Reynolds shear stress, -[`(uv)] /U_m² - \overline {uv} /U_{\rm m}^2 is much more sensitive to surface curvature, D/W.     

Characteristics of single and multiple bursting events in the inner layer. Part 2. Level-crossing events

The grouping method we developed in earlier work is applied to the ejections identified by level crossings of the u'v' signal in the inner layer of a fully developed turbulent channel flow. The groups of ejections and solitary events are separately investigated. Their frequencies, contributions to the mean [`(u￠v￠)]\overline {u'v'} and related conditional averages are reported. It is argued that the packets and single events result from different regeneration mechanisms. The coherent streamwise alignment of the structures within the groups makes the associated scale significantly large. The groups transport large values of the kinetic energy and of the Reynolds shear stress. The results confirm recent studies and show that the main features of the near-wall turbulence dynamics can be adequately revealed by single-point measurements.     

A plane turbulent wall jet on a fully rough surface

The mean velocity field and skin friction characteristics of a plane turbulent wall jet on a smooth and a fully rough surface were studied using Particle Image Velocimetry. The Reynolds number based on the slot height and the exit velocity of the jet was Re = 13,400 and the nominal size of the roughness was k = 0.44 mm. For this Reynolds number and size of roughness element, the flow was in the fully rough regime. The surface roughness results in a distinct change in the shape of the mean velocity profile when scaled in outer coordinates, i.e. using the maximum velocity and outer half-width as the relevant velocity and length scales, respectively. Using inner coordinates, the mean velocity in the lower region of the inner layer was consistent with a logarithmic profile which characterizes the overlap region of a turbulent boundary layer; for the rough wall case, the velocity profile was shifted downward due to the enhanced wall shear stress. For the fully rough flow, the decay rate of the maximum velocity of the wall jet is increased, and the skin friction coefficient is much larger than for the smooth wall case. The inner layer is also thicker for the rough wall case. The effects of surface roughness were observed to penetrate into the outer layer and slightly enhance the spread rate for the outer half-width, which was not observed in most other studies of transitionally rough wall jet flows.     

Adverse pressure gradient turbulent flows over rough walls

An experimental study of a fully developed turbulent channel flow and an adverse pressure gradient (APG) turbulent channel flow over smooth and rough walls has been performed using a particle image velocimetry (PIV) technique. The rough walls comprised two-dimensional square ribs of nominal height, k = 3 mm and pitch, p = 2k, 4k and 8k. It was observed that rib roughness enhanced the drag characteristics, and the degree of enhancement increased with increasing pitch. Similarly, rib roughness significantly increased the level of turbulence production, Reynolds stresses and wall-normal transport of turbulence kinetic energy and Reynolds shear stress well beyond the roughness sublayer. On the contrary, the distributions of the eddy viscosity, mixing length and streamwise transport of turbulence kinetic energy and Reynolds shear stress were reduced by wall roughness, especially in the outer layer. Adverse pressure gradient produced a further reduction in the mean velocity (in comparison to the results obtained in the parallel section) but increased the wall-normal extent across which the mean flow above the ribs is spatially inhomogeneous in the streamwise direction. APG also reinforced wall roughness in augmenting the equivalent sand grain roughness height. The combination of wall roughness and APG significantly increased turbulence production and Reynolds stresses except in the immediate vicinity of the rough walls. The transport velocities of the turbulence kinetic energy and Reynolds shear stress were also augmented by APG across most part of the rough-wall boundary layer. Further, APG enhanced the distributions of the eddy viscosity across most of the boundary layer but reduced the mixing length outside the roughness sublayer.     

Structure of the turbulent boundary layer over a rod-roughened wall

Turbulent coherent structures near a rod-roughened wall are scrutinized by analyzing instantaneous flow fields obtained from direct numerical simulations (DNSs) of a turbulent boundary layer (TBL). The roughness elements used are periodically arranged two-dimensional spanwise rods, and the roughness height is k/δ = 0.05 where δ is the boundary layer thickness. The Reynolds number based on the momentum thickness is varied in the range Re_θ = 300–1400. The effect of surface roughness is examined by comparing the characteristics of the TBLs over smooth and rough walls. Although introduction of roughness elements onto the smooth wall affects the Reynolds stresses throughout the entire boundary layer when scaled by the friction velocity, the roughness has little effect on the vorticity fluctuations in the outer layer. Pressure-strain tensors of the transport equation for the Reynolds stresses and quadrant analysis disclose that the redistribution of turbulent kinetic energy of the rough wall is similar to that of the smooth wall, and that the roughness has little effect on the relative contributions of ejection and sweep motions in the outer layer. To elucidate the modifications of the near-wall vortical structure induced by surface roughness, we used two-point correlations, joint weighted probability density function, and linear stochastic estimation. Finally, we demonstrate the existence of coherent structures in the instantaneous flow field over the rod-roughened surface.     

Effect of different initial conditions on a turbulent round free jet

Velocity measurements were made in two jet flows, the first exiting from a smooth contraction nozzle and the second from a long pipe with a fully developed pipe flow profile. The Reynolds number, based on nozzle diameter and exit bulk velocity, was the same (䏪,000) in each flow. The smooth contraction jet flow developed much more rapidly and approached self-preservation more rapidly than the pipe jet. These differences were associated with differences in the turbulence structure in both the near and far fields between the two jets. Throughout the shear layer for x<3d, the peak in the v spectrum occurred at a lower frequency in the pipe jet than in the contraction jet. For x́d, the peaks in the two jets appeared to be nearly at the same frequency. In the pipe jet, the near-field distributions of f(r) and g(r), the longitudinal and transverse velocity correlation functions, differed significantly from the contraction jet. The integral length scale L_u was greater in the pipe jet, whereas L_v was smaller. In the far field, the distributions of f(r) and g(r) were nearly similar in the two flows. The larger initial shear layer thickness of the pipe jet produced a dimensionally lower frequency instability, resulting in longer wavelength structures, which developed and paired at larger downstream distances. The regular vortex formation and pairing were disrupted in the shear layer of the pipe jet. The streamwise vortices, which enhance entrainment and turbulent mixing, were absent in the shear layer of the pipe jet. The formation of large-scale structures should occur much farther downstream in the pipe jet than in the contraction jet.     

Development of a turbulent boundary layer after a step from smooth to rough surface

The flow developing downstream of a step change from smooth to rough surface condition is studied in the light of Townsend’s wall similarity hypothesis. Previous studies seem to support the hypothesis for channel and pipe flows, but there are considerable controversies about its application to boundary layers and in particular to surface roughness formed by spanwise bars. It has been suggested that this controversy arises from insufficient separation of scales between the boundary layer thickness and the roughness length scale. An experimental investigation has therefore been undertaken where the flow evolves from a fully developed smooth wall boundary layer at high Reynolds numbers over a step in surface roughness (Re _θ = 13,400 at the step). The flow is mapped through the development of the internal layer until the flow is fully developed over the rough wall. The internal layer is found to grow as δ ∼ X ^0.73, and after about 15 boundary layer thicknesses at the step, the internal layer has reached the outer edge of the incoming layer. At the last rough wall measurement station, the Reynolds number has grown to Re _θ ≈ 32,600 and the ratio of boundary layer to roughness length scales is δ/k ≈ 140. The outer layer differences between the smooth and the rough wall data were found to be sufficiently small to conclude that for this setup the Townsend’s wall similarity hypothesis appears to hold.     

Anisotropy of the Reynolds stresses in a turbulent boundary layer on a rough wall

The measured anisotropy invariants of the Reynolds stress tensor in a self-preserving rough wall turbulent boundary layer indicate that the anisotropy is significantly smaller than in a smooth wall layer.RAA is grateful to Dr. P. Spalart for the DNS data. The support of the Australian Research Council is acknowledged.     

Drag reducing outer-layer devices in rough wall turbulent boundary layers

The ability of outer-layer devices to reduce wall shear stress over a substantial streamwise distance in rough-wall turbulent boundary layers has been studied experimentally. The devices examined are a pair of thin flat ribbons placed in tandem as well as those having symmetric airfoil sections. The wall conditions examined are smooth, d- and k-type transverse-groove and sandgrain roughnesses. The wall drag is found to be reduced from the respective normal levels in all rough walls. All k-type rough walls exhibit a similar level of relative wall drag reduction which is also smaller than that in a smooth-wall. The d-type rough walls exhibit a transitional behaviour — the relative wall drag reduction drops from the smooth wall level to that of the k-type roughness with increasing roughness Reynolds number. However, the absolute reductions in the local wall shear stress are similar in both the rough and smooth walls. On the other hand, the relative reductions are lower in the rough walls because of a higher reference drag which is caused by the unique presence of a pressure component on which the devices are not as effective.     

Transitionally rough zero pressure gradient turbulent boundary layers

Near-wall measurements are performed to study the effects of surface roughness and viscous shear stresses on the transitionally rough regime (5 < k ⁺ < 70) of a zero pressure gradient turbulent boundary layer. The x-dependence is known from the eleven consecutive measurements in the streamwise direction, which allows for the computation of the streamwise gradients in the boundary layer equations. Thus, the skin friction is computed from the integrated boundary layer equation with errors of 3 and 5% for smooth and rough, respectively. It is found that roughness destroys the viscous layer near the wall, thus, reducing the contribution of the viscous stress in the wall region. As a result, the contribution in the wall shear stress due to form drag increases, while the viscous stress decreases. This yields Reynolds number invariance in the skin friction as k ⁺ increases into the fully rough regime. Furthermore, the roughness at the wall reduces the high peak of the streamwise component of the Reynolds stress in the near-wall region. However, for the Reynolds wall-normal and shear stress components, its contribution is not significantly altered for sand grain roughness.     

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     

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.     

Self-preservation of rough-wall turbulent boundary layers

It is proposed that all fully rough-wall boundary layers should satisfy self-preservation more closely than a smooth-wall boundary layer. Previous work has shown that the self-preserving forms of the momentum and turbulent kinetic energy equations for a zero pressure gradient turbulent boundary layer, at sufficiently high Reynolds number, require that the wall shear stress is constant with x, and the layer thickness increases linearly with x. Measurements in two rough wall boundary layers suggest these conditions are met without assuming a form for the mean velocity distribution, and are more likely to exist in a fully rough wall layer than a smooth wall layer.     

Reynolds-number-dependence of the maximum in the streamwise velocity fluctuations in wall turbulence

A survey is made of the standard deviation of the streamwise velocity fluctuations in near-wall turbulence and in particular of the Reynolds-number-dependency of its peak value. The following canonical flow geometries are considered: an incompressible turbulent boundary layer under zero pressure gradient, a fully developed two-dimensional channel and a cylindrical pipe flow. Data were collected from 47 independent experimental and numerical studies, which cover a Reynolds number range of R _θ=U _∞ θ/v=300−20,920 for the boundary layer with θ the momentum thickness and R ⁺=u _*R/v=100-4,300 for the internal flows with R the pipe radius or the channel half-width. It is found that the peak value of the rms-value normalised by the friction velocity, u _*, is within statistical errors independent of the Reynolds number. The most probable value for this parameter was found to be 2.71±0.14 and 2.70±0.09 for the case of a boundary layer and an internal flow, respectively. The present survey also includes some data of the streamwise velocity fluctuations measured over a riblet surface. We find no significant difference in magnitude of the normalised peak value between the riblet and smooth surfaces and this property of the normalised peak value may for instance be exploited to estimate the wall shear stress from the streamwise velocity fluctuations. We also consider the skewness of the streamwise velocity fluctuations and find its value to be close to zero at the position where the variance has its peak value. This is explained with help of the equations of the third-order moment of velocity fluctuations. These results for the peak value of the rms of the streamwise velocity fluctuations and also the coincidence of this peak with the zero value of the third moment can be interpreted as confirmation of local equilibrium in the near-wall layer, which is the basis of inner-layer scaling. Furthermore, these results can be also used as a requirement which turbulence models for the second and triple velocity correlations should satisfy. The authors are indebted to Prof. P. Bradshaw for making available his list of references on this topic and for his remarks on “active” and “inactive” motions. We also gratefully acknowledge discussions with Prof. I. Castro regarding the value of σ _u ⁺ above rough walls.     

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.     

Effects of irregular two-dimensional and three-dimensional surface roughness in turbulent channel flows

Wall-resolved Large Eddy Simulation of fully developed turbulent channel flows over two different rough surfaces is performed to investigate on the effects of irregular 2D and 3D roughness on the turbulence. The two geometries are obtained through the superimposition of sinusoidal functions having random amplitudes and different wave lengths. In the 2D configuration the irregular shape in the longitudinal direction is replicated in the transverse one, while in the 3D case the sinusoidal functions are generated both in streamwise and spanwise directions. Both channel walls are roughened in such a way as to obtain surfaces with statistically equivalent roughness height, but different shapes. In order to compare the turbulence properties over the two rough walls and to analyse the differences with a smooth wall, the simulations are performed at the same Reynolds number Re_τ = 395. The same mean roughness height h = 0.05δ (δ the half channel height) is used for the rough walls.The roughness function obtained with the 3D roughness is larger than in the 2D case, although the two walls share the same mean height. Thus, the considered irregular 3D roughness is more effective in reducing the flow velocity with respect to the 2D roughness, coherently with the literature results that identified a clear dependence of the roughness function on the effective slope (see Napoli et al. (2008)), higher in the generated 3D rough wall. The analysis of higher-order statistics shows that the effects of the roughness, independently on its two- or three-dimensional shape, are mainly confined in the inner region, supporting the Townsend’s wall similarity hypothesis. The tendency towards the isotropization is investigated through the ratio between the resolved Reynolds stress components, putting in light that the 3D irregular rough wall induces an higher reduction of the anisotropy, with respect to the 2D case.     

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.     

Effects of two-dimensional V-shaped grooves on turbulent channel flow

Detailed Laser Doppler velocimeter (LDV) measurements have been carried out in a turbulent rectangular channel flow with one rough wall. The roughness elements of two-dimensional spanwise 120° V-shaped grooves are periodically arranged with different depths and pitches. The Reynolds number based on the centerline velocity, and the channel half height ranges from 2,740 to 20,000. The comparisons of turbulence statistics over smooth and rough walls indicate that the present roughness leads to a significant change in the turbulence both in the inner and in the outer flow. Particularly, the distribution density of the grooves is a key parameter to evaluate the effect of roughness. The low-Reynolds-number dependence of turbulence statistics is also observed. The rough walls with the same pitch-to-depth ratio exhibit the equivalent roughness function under the corresponding Reynolds numbers. The disagreement of velocity defect profiles between smooth and rough walls challenges the defect universal law. The variations of the turbulence stresses and Reynolds shear stress decomposition in the outer layer suggest that the turbulent motions may be modified by the present grooves. The importance of sweep events for the present groove-roughened walls is reflected by the differences in relative contribution to Reynolds shear stress from each quadrant and the higher-order moments over smooth and rough walls.     

Near-Wall Modification of an Explicit Algebraic Reynolds Stress Model Using Elliptic Blending

The elliptic blending approach is used in order to modify an Explicit Algebraic Reynolds Stress Model so as to reproduce the correct near wall behaviour of the turbulent stresses. The anisotropy stress tensor is expressed as a linear combination of tensor bases whose coefficients are sensitised to the non-local wall-blocking effect through the elliptic blending parameter γ. This parameter is obtained from a separate elliptic equation. The model does not use the distance from the wall thus it can be easily applied to complex geometries. It is validated against detailed DNS data for mean and turbulence quantities for the case of flow and heat transfer between parallel flat plates at three Reynolds numbers as well as against experimental data for the flow in a backward facing step at Re _H = 28,000. The comparison with DNS results or experiments is quite satisfactory and shows the validity of the approach.     

On the First Boundary Value Problem for Quasilinear Parabolic Equations with Two Independent Variables

This paper is concerned with the global solvability of the first initial boundary value problem for the quasilinear parabolic equations with two independent variables: a(t,x,u,u_xINF>)u_xxm u_t=f(t,x,u,u_xINF>). We investigate the case when the growth of [(|f(t,x,u,p)|)/(a(t,x,u,p))]{{|f(t,x,u,p)|}\over {a(t,x,u,p)}} with respect to p is faster than p² when |p|M X. Conditions which guarantee the global classical solvability of the problem are formulated.