Roughness Crests Research Articles

Secondary flows in turbulent boundary layers developing over truncated cone surfaces

The evolution of a turbulent boundary layer over truncated cones in staggered and random configurations is investigated using direct numerical simulations. Three random planform densities and one staggered, which closely match the configuration in the recent experiment by Womack et al. (J. Fluid Mech., vol. 933, 2022, A38), are considered. The experiment is also used to validate the present computations which are found to reproduce the flow measurements very accurately. Spanwise heterogeneity in the mean streamwise velocity in the form of high and low momentum pathways was detected in both the staggered and random arrangements, indicating the presence of secondary flows in the cross-stream plane. The momentum pathways found in the staggered arrangements are much weaker and confined near the roughness crest, while in the random arrangements they approach the edge of the boundary layer. We found a clear correlation of the momentum pathways with the leading edge of the roughness, while the correlation to the local topography was very weak for all the cases studied. Vorticity transport analysis is also employed to explore the nature of the secondary flows formed, highlighting the strong presence of vortex stretching near the leading edge of the roughness. The impact of the momentum pathways on the flow statistics, especially in the random arrangements, is demonstrated by the breakdown of outer-layer similarity.

An experimental and numerical study of turbulent oscillatory flow over an irregular rough wall

The hydrodynamics of turbulent oscillatory flow over a gravel-based irregular rough wall is investigated using laser-Doppler anemometry measurements of velocities in a large oscillatory flow tunnel and direct numerical simulation (DNS) of the Navier–Stokes equations. The same periodic irregular roughness was used for both experiments and DNS. Four flow shapes are investigated: sinusoidal, skewed, asymmetric and combined skewed–asymmetric. The experiments were conducted for target Reynolds numbers (based on the Stokes length and standard deviation of free-stream velocity) of$R_{\delta,\sigma }=800$and$R_{\delta,\sigma }=1549$; DNS was conducted for flows with target$R_{\delta,\sigma }=800$. Boundary layer thickness, bottom phase lead and friction factor are in good agreement with previous studies. For the first time, evidence of Prandtl's secondary flows of the second kind in oscillatory flow is presented. Turbulence structure is visualised using isosurfaces of$\lambda _{2}$(Jeong & HussainJ. Fluid Mech., vol. 285, 1995, pp. 69–94), revealing densely packed structures that grow stronger and weaker in correspondence with the free-stream velocity. Reynolds and dispersive stresses peak just below the highest roughness crest, with dispersive stress vanishing a short distance above the roughness. Bursts of turbulence kinetic energy and wake kinetic energy are generated each flow half-cycle, with variable behaviour depending on flow shape. Non-Gaussian turbulence statistics are observed that originate near the wall, becoming increasingly non-Gaussian far from the wall. Probability density functions of turbulence statistics can be closely approximated by a fourth-order Gram–Charlier distribution at most phases and elevations, though when statistics deviate more strongly from Gaussian, streamwise and wall-normal (spanwise) statistics are better described by a Pearson type IV (VII) distribution.

Direct numerical simulation of supersonic turbulent flows over rough surfaces

We perform direct numerical simulation of supersonic turbulent channel flow over cubical roughness elements, spanning bulk Mach numbers $M_b=0.3$ – $4$ , both in the transitional and fully rough regime. We propose a novel definition of roughness Reynolds number which is able to account for the viscosity variations at the roughness crest and should be used to compare rough-wall flows across different Mach numbers. As in the incompressible flow regime, the mean velocity profile shows a downward shift with respect to the baseline smooth wall cases, however, the magnitude of this velocity deficit is largely affected by the Mach number. Compressibility transformations are able to account for this effect, and data show a very good agreement with the incompressible fully rough asymptote, when the relevant roughness Reynolds number is used. Velocity statistics present outer layer similarity with the equivalent smooth wall cases, however, this does not hold for the thermal field, which is substantially affected by the roughness, even in the channel core. We show that this is a direct consequence of the quadratic temperature–velocity relation which is also valid for rough walls. Analysis of the heat transfer shows that the relative drag increase is always larger than the relative heat transfer enhancement, however, increasing the Mach number brings data closer to the Reynolds analogy line due to the rising relevance of the aerodynamic heating.

Direct numerical simulation of turbulent channel flow over random rough surfaces

Abstract

English

Influence of bed roughness on near-bed flow characteristics is of considerable importance, especially in turbulent flows over rough beds. This experimental study is devoted to insight various turbulent flow characteristics such as velocity distributions, Reynolds shear stresses (RSS) and velocity power spectra at the groove, lee and crest level of carrier fluid in an immobile gravel bed stream. Uniform round shape gravels were used in five layers in a laboratory flume. Nortek’s Vectrino four-receiver Acoustic Doppler velocimeter (ADV) probe was used to capture the instantaneous three-dimensional velocity components at groove. The interference between incident and reflected pulses in the ADV data measured in the near-bed flow zone produced spikes. Spikes were detected and filtered with a spike removal algorithm based on the acceleration threshold method. The velocity power spectra provides a satisfactory fit with the Kolmogorov “–5/3 scaling-law” in the inertial subrange. Velocity distributions below the roughness crest level fairly follows a third-degree polynomial series. Key words: Bed roughness, gravel-bed stream, turbulence, Reynolds shear stresses, inertial sub-range.  

A direct comparison of pulsatile and non-pulsatile rough-wall turbulent pipe flow

Pulsatile rough-wall turbulent pipe flow is compared against its non-pulsatile counterpart using data obtained from direct numerical simulation. Results are presented at a mean friction Reynolds number of 540 for a set of three geometrically scaled roughness topographies at a single forcing condition, which, based on existing classifications, falls into the current-dominated very-high-frequency regime. By comparing the pulsatile data against an equivalent non-pulsatile dataset (Chan et al. , J. Fluid Mech. , vol. 854, 2018, pp. 5–33), the key differences (and similarities) between the forced and unforced configurations are identified. A major finding of this study is that the flow in the outer region retains its self-similar functional form under pulsatile rough-wall conditions, and, as a result, Townsend’s outer-layer similarity hypothesis holds for the roughness-forcing combinations considered here. On the other hand, the unsteady cases exhibit a rich array of flow physics in the region beneath the roughness crests not observed in the steady case. These differences are examined using a Moody chart, which encapsulates how the hydraulic properties of pulsatile rough-wall pipe flow differ from their non-pulsatile counterpart.

Large eddy simulations on the effect of the irregular roughness shape on turbulent channel flows

Large Eddy Simulations (LES) are carried out to investigate on the mean flow in turbulent channel flows over irregular rough surfaces. Here the attention is focused to selectively investigate on the effect induced by crests or cavities of the roughness. The irregular shape is generated through the super-imposition of sinusoidal functions having random amplitude and four different wave-lengths. The irregular roughness profile is reproduced along the spanwise direction in order to obtain a 2D rough shape. The analysis of the mean velocity profiles shows that roughness crests induce higher effect in the outer-region whereas roughness cavities cause the highest effects in the inner-region with a reduced effect in the external region. The numerical simulations have been carried out at friction Reynolds number Reτ=395. Similar results have been found for the higher order statistics: turbulence intensities or shear stresses. The analysis of the Reynolds stress anisotropy tensor confirms the existence of specific roles of cavities and crests in the turbulence modulation.

Modulation of near-wall turbulence in the transitionally rough regime

Direct numerical simulations of turbulent channels with rough walls are conducted in the transitionally rough regime. The effect that roughness produces on the overlying turbulence is studied using a modified triple decomposition of the flow. This decomposition separates the roughness-induced contribution from the background turbulence, with the latter essentially free of any texture footprint. For small roughness, the background turbulence is not significantly altered, but merely displaced closer to the roughness crests, with the change in drag being proportional to this displacement. As the roughness size increases, the background turbulence begins to be modified, notably by the increase of energy for short, wide wavelengths, which is consistent with the appearance of a shear-flow instability of the mean flow. A laminar model is presented to estimate the roughness-coherent contribution, as well as the displacement height and the velocity at the roughness crests. Based on the effects observed in the background turbulence, the roughness function is decomposed into different terms to analyse different contributions to the change in drag, laying the foundations for a predictive model.

On the virtual origin determined from momentum equation analysis using experimental data within the roughness sublayer

The centroid of distributed drag acting on a roughness element, which is interpreted as the origin of the distance from the wall, is discussed for a wall-bounded turbulent flow over a rough surface with square ribs arranged with a roughness pitch ratio, PR, of 4. The first and second moments of fluctuating velocity components were measured by one-dimensional laser Doppler velocimetry to estimate spatially averaged quantities in the roughness sublayer. The spatially averaged profiles of the streamwise mean velocity and Reynolds shear stress can be scaled with the representative scales of the mixing layer observed behind a roughness element; these are $${u_{\text{p}}}=\sqrt {{D_{\text{p}}}/\left( {\rho b} \right)}$$ and b, where up is the velocity scale of the driven force for the flow in a cavity, Dp is the form drag acting on a roughness element, $$\rho$$ is the fluid density, and b is the cavity width. The analytical solutions of the spatially averaged profiles can be formulated in exponential form, and are in good agreement with available experimental data. The displacement height, which is the distance from the centroid of the distributed drag to the roughness crest, can be approximately estimated by the spatially averaged Reynolds shear stress profile. The prediction of the displacement height well represents that of the experimental and direct numerical simulation data for 4 ≤ PR ≤ 8. The spatially averaged Reynolds shear stress profiles in the cavity of turbulent boundary layers over square-ribbed rough surfaces can be scaled with the representative scales of the mixing layer behind a roughness element for 4 ≤ PR ≤ 8, where PR is the roughness pitch ratio. The displacement height, which corresponds to the origin of the law of the wall, can be predicted using the scaled spatially averaged Reynolds shear stress profile and increases with the PR as the mixing layer develops over the cavity.

Turbulent Flow Characterization over the Gravel Bed

The double-averaged momentum equations are used as a natural basis for the hydraulics of rough-bed open channel flows, especially with small relative submergence. To study the double-averaged turbulence characteristics in flows over a gravel-bed, a uniform flow over a gravel-bed was run in a laboratory flume and the velocities were measured at different verticals by a vectrino probe. The result reveals that the local time-averaged velocity profiles can be split into three typical classes, namely log, S-shaped and accelerated. In the log class velocity profile fits a logarithmic curve over almost the entire measured profile. S Shaped refers to profiles that can be encountered in wake of macro-roughness bed elements due to flow separation on the lee side. The accelerated profile located in the vicinity of top of the macro-roughness elements and the velocities are slightly higher than log classes but rapidly drop to zero below crest. It never extends to zero bed level above the crest they are not influenced by the bed heterogeneity. The logarithmic law of velocity profile is preserved above the roughness crest and velocity below the crest follows a polynomial. The field of gravel-bed appears to be near Gaussian matches with the work of previous researchers. The Reynolds shear stress is the main governing stress across the flow depth with a damping in the vicinity of gravel bed due to decrease in turbulence level. The form induced stress is prominent below the roughness crest.

Direct numerical simulation of flow over dissimilar, randomly distributed roughness elements: A systematic study on the effect of surface morphology on turbulence

Direct numerical simulations of flow over fourteen dense rough walls with varying geometry are conducted. The effect of a departure from same-size element roughness on turbulence statistics is studied, and the correlation of the roughness function with wall-normal fluctuations at the roughness crest is examined.

Effects of surface roughness on a separating turbulent boundary layer

Separating turbulent boundary layers over smooth and rough flat plates are studied by large-eddy simulations. A suction–blowing velocity distribution imposed at the top boundary of the computation domain produces an adverse-to-favourable pressure gradient and creates a closed separation bubble. The Reynolds number based on the momentum thickness and the free-stream velocity before the pressure gradient begins is 2500. Virtual sand grain roughness in the fully rough regime is modelled by an immersed boundary method. Compared with a smooth-wall case, streamline detachment occurs earlier and the separation region is substantially larger for the rough-wall case, due to the momentum deficit caused by the roughness. The adverse pressure gradient decreases the form drag, so that the point where the wall stress vanishes does not coincide with the detachment of the flow from the surface. A thin reversed-flow region is formed below the roughness crest; the presence of recirculation regions behind each roughness element also affects the intermittency of the near-wall flow, so that upstream of the detachment point the flow can be reversed half of the time, but its average velocity can still be positive. The separated shear layer exhibits higher turbulent kinetic energy (TKE) in the rough-wall case, the growth of the TKE there begins earlier relative to the separation point, and the peak TKE occurs close to the separation point. The momentum deficit caused by the roughness, again, plays a critical role in these changes.

Turbulence over cube-mounted rough bed using spatiotemporal averaging approach

The paper describes an experimental study carried out in a laboratory flume to investigate the turbulent characteristics of cube mounted rough bed (3D flow). The three-dimensional (3D) velocity data are analyzed within the framework of double time-space averaging approach. The study particularly focuses on the changes induced in the mean velocities, turbulent intensities, Reynolds shear stresses, and form-induced normal and shear stress profiles both in time and space domains. The mean velocity profile shows two distinct distributions: linear distribution below the roughness crest and logarithmic distribution above the roughness crest. Within the roughness layer near the bottom, the form-induced stress changes significantly with roughness spacing. To highlight the stress terms and associated turbulent events, the quadrant analysis is performed using form-induced velocity fluctuations. Further, the turbulent kinetic energy budget is also analyzed to examine the bursting events comprehensively.

Hydraulic Performance of an Embankment Weir with Rough Crest

AbstractAn experimental study was conducted on a large embankment weir with smooth and rough crests for a range of flow conditions 0.011≤Q≤0.226 m3/s. Close agreement between the rough and smooth crest experiments was observed in terms of flow patterns, free-surface profiles, and pressure distributions. The crest roughness had effects on the velocity distributions, the boundary layer properties, and the shear stress. On the rough crest, the velocity distributions were shifted upwards, increasing the growth rate of the boundary layer. The calculation of the shear stresses with the law of the wall, outer flow region, and momentum integral methods showed consistent results of about τ/(ρ g H)≈0.0015–0.0018 for the smooth crest and of τ/(ρ g H)≈0.0024 for the rough crest. The crest roughness reduced the discharge performance, while upstream and downstream ramps did not have any effects. The present observations highlighted the relevance of roughness and scaling on the hydraulic performances of weirs.

Turbulence laws in natural bed flows

Characterization of turbulence in natural bed streams is one of the most fascinating problems of fluid dynamics. In this study, a statistical description of turbulence in a natural pebble bed flow is presented applying the laws of turbulence. A laboratory experiment was conducted to measure the three-dimensional instantaneous velocity components in a flow over heterogeneous coarse sediments that simulated a natural bed. The analysis reveals that the spectra (in Fourier space) show a power-law scaling,$E(k)\sim k^{{\it\alpha}}$, suggesting the presence of inertial range turbulence. The exponent${\it\alpha}$is slightly shallower than the Kolmogorov$5/3$scaling law, with this deviation possibly due to the bed roughness heterogeneity and to fluctuation anisotropy. The Taylor frozen-in approximation is broken at smaller scales towards the roughness crest level; therefore, a new statistical tool for the validation of this approximation is proposed. The Kolmogorov$4/5$-law for the longitudinal increments and simultaneously the Monin–Yaglom$4/3$-law for the nonlinear normal fluxes (both in physical space) are preserved, providing an accurate estimation of the turbulent kinetic energy dissipation rate. The heterogeneity of the bed acts to induce the transport of finite kinetic helicity to the outer layer through persistently prolonged vortices. An associated$2/15$-law for the cascade of helicity has been locally found. These findings open a new direction in turbulence research for flows over highly rough beds.

Spatially-averaged turbulent flow over cubical roughness in wave-current co-existing environment

The paper describes an experimental study carried out in a laboratory flume to investigate the interaction of surface-wave with unidirectional current over cube mounted rough-bed (3D flow). The cubes were made of wood and were positioned at the channel-bed with different spacing. The spacing was chosen to represent different roughness types under different spacing conditions as: isolated roughness flow, wake interference flow and skimming flow. The three-dimensional velocity field was measured by an acoustic Doppler velocimetre (ADV). The study particularly focused on the changes induced in the spatially-averaged velocity profiles, turbulence intensities and Reynolds shear stress due to the superposition of waves of different frequencies on current-induced flow. Spatially-averaged velocity profiles show two distinct distributions: linear or exponential distribution below the roughness crest and logarithmic distribution above the roughness crest. It is found that the shift of the velocity profile depends strongly on the spacing of roughness elements. The profile of stream-wise turbulence intensity changes significantly below the roughness crest due to presence of surface wave, whereas bottom-normal spatially-averaged turbulence intensity does not change much with increase in wave frequency. Within the roughness crest near the bottom, the form-induced shear stress changes significantly from negative to positive value with change in roughness spacing, but is not affected much due to the presence of surface-wave.

Turbulence in a transient channel flow with a wall of pyramid roughness

A direct numerical simulation investigation of a transient flow in a channel with a smooth top wall and a roughened bottom wall made of close-packed pyramids is presented. An initially stationary turbulent flow is accelerated rapidly to a new flow rate and the transient flow behaviour after the acceleration is studied. The equivalent roughness heights of the initial and final flows are $k_{s}^{+}=14.5$ and 41.5, respectively. Immediately after the acceleration ends, the induced change behaves in a ‘plug-flow’ manner. Above the roughness crests, the additional velocity due to the perturbation flow is uniform; below the crest, it reduces approximately linearly to zero at the bottom of the roughness elements. The interaction of the perturbation flow with the rough wall is characterised by a series of events that resemble those observed in roughness-induced laminar–turbulent transitions. The process has two broad stages. In the first of these, large-scale vortices, comparable in extent to the roughness wavelength, develop around each roughness element and high-speed streaks form along the ridge lines of the elements. After a short time, each vortex splits into two, namely (i) a standing vortex in front of the element and (ii) a counter-rotating hairpin vortex behind it. The former is largely inactive, but the latter advects downstream with increasing strength, and later lifts away from the wall. These hairpin vortices wrap around strong low-speed streaks. The second stage of the overall process is the breakdown of the hairpin vortices into many smaller multi-scale vortices distributed randomly in space, leading eventually to a state of conventional turbulence. Shortly after the beginning of the first stage, the three components of the r.m.s of the velocity fluctuation all increase significantly in the near-wall region as a result of the vortical structures, and their spectra bear strong signatures of the surface topology. During the second stage, the overall turbulence energy in this region varies only slightly, but the spectrum evolves significantly, eventually approaching that of conventional turbulence. The direct effect of roughness on the flow is confined to a region up to approximately three element heights above the roughness crests. Turbulence in the core region does not begin to increase until after the transition near the wall is largely complete. The processes of transition over the smooth and rough walls of the channel are practically independent of each other. The flow over the smooth wall follows a laminar–turbulent transition and, as known from previous work, resembles a free-stream turbulence-induced boundary layer bypass transition.

First Evidence of Pathology in the Forelimb of the Late Miocene Saber‐Toothed Felid Promegantereon ogygia (Machairodontinae, Smilodontini)

We examined the first evidence of pathology in the forelimb of the primitive saber-toothed felid Promegantereon ogygia, observed in a radius from the late Miocene (Vallesian, MN 10) site of La Roma 2 (Teruel, Spain). This fossil is the first evidence of a member of the Machairodontinae in this locality, and the first fossil of this species found in the Miocene basin of Teruel. The radius shows an exostosis shaped as a rough and wide bony crest probably caused by the lesion and posterior ossification of part of the tendon of the muscle abductor pollicis longus, an important extensor and abductor of the thumb. The lesion was probably due to a tearing or to high levels of exertion experienced by this muscle over a relatively long time, a general type of lesion also observed in other vertebrate fossils. With saber-toothed felids using their thumbs to immobilize prey during the hunt, the studied lesion probably affected in a significant manner the predatory abilities of the animal, causing at least a decrease in its hunting success rate.

Mean force structure and its scaling in rough-wall turbulent boundary layers

AbstractThe combined roughness/Reynolds number problem is explored. Existing and newly acquired data from zero pressure gradient rough-wall turbulent boundary layers are used to clarify the leading order balances of terms in the mean dynamical equation. For the variety of roughnesses examined, it is revealed that the mean viscous force retains dominant order above (and often well above) the roughness crests. Mean force balance data are shown to be usefully organized relative to the characteristic length scale, which is equal or proportional to the width of the region from the wall to where the leading order mean dynamics become described by a balance between the mean and turbulent inertia. This is equivalently the width of the region from the wall to where the mean viscous force loses leading order. For both smooth-wall and rough-wall flows, the wall-normal extent of this region consistently ends just beyond the zero-crossing of the turbulent inertia term. In smooth-wall flow this characteristic length is a known function of Reynolds number. The present analyses indicate that for rough-wall flows the wall-normal position where the mean dynamics become inertial is an irreducible function of roughness and Reynolds number, as it is an inherent function of the relative scale separations between the inner, roughness, and outer lengths. These findings indicate that, for any given roughness, new dynamical regimes will typically emerge as the Reynolds number increases. For the present range of parameters, there appear to be three identifiable regimes. These correspond to the ratio of the equivalent sand grain roughness to the characteristic length being less than, equal to, or greater than$O(1)$. The relative influences of the inner, outer, and roughness length scales on the characteristic length are explored empirically. A prediction for the decay rate of the mean vorticity is developed via extension of the smooth-wall theory. Existing data are shown to exhibit good agreement with this extension. Overall, the present results appear to expose unifying connections between the structure of smooth- and rough-wall flows. Among other findings, the present analyses show promise toward providing a self-consistent and dynamically meaningful way of identifying the domain where the wall similarity hypothesis, if operative, should hold.

Statistics of the turbulent boundary layers over 3D cube-roughened walls

Direct numerical simulations (DNSs) of turbulent boundary layers (TBLs) over three-dimensional (3D) cube-roughened walls were performed and the turbulent characteristics in the inner and outer layers were statistically analyzed. The spanwise spacing was varied over pz/k=2, 3, 4, and 6 (pz is the spanwise spacing between cubes and k is the height of the roughness) to examine the effects of the roughness spacing on the TBLs. The form drag (Cp) reached a maximum at pz/k=3, whereas the skin-friction drag (Cf) reached a minimum at the same extent. The Reynolds stresses in the outer region were shown to increase with increasing pz/k, and similar behavior was observed in the wall-normal velocity fluctuations at the roughness crest (vw+). The properties of the turbulence in the inner and outer layers were found to be well represented by the roughness density (λp).