Rough-wall Turbulent Boundary Layers Research Articles

Stochastic modelling of the instantaneous velocity profile in rough-wall turbulent boundary layers

The statistical properties of uniform momentum zones (UMZs) are extracted from laboratory and field measurements in rough wall turbulent boundary layers to formulate a set of stochastic models for the simulation of instantaneous velocity profiles. A spatiotemporally resolved velocity dataset, covering a field of view of $8 \times 9\,{\rm m}^2$ , was obtained in the atmospheric surface layer using super-large-scale particle image velocimetry (SLPIV), as part of the Grand-scale Atmospheric Imaging Apparatus (GAIA). Wind tunnel data from a previous study are included for comparison (Heisel et al., J. Fluid Mech., vol. 887, 2020, R1). The probability density function of UMZ attributes such as their thickness, modal velocity and averaged vertical velocity are built at varying elevations and modelled using log-normal and Gaussian distributions. Inverse transform sampling of the distributions is used to generate synthetic step-like velocity profiles that are spatially and temporally uncorrelated. Results show that in the wide range of wall-normal distances and $Re_\tau$ up to $\sim O(10^6)$ investigated here, shear velocity scaling is manifested in the velocity jump across shear interfaces between adjacent UMZs, and attached eddy behaviour is observed in the linear proportionality between UMZ thickness and their wall normal location. These very same characteristics are recovered in the generated instantaneous profiles, using both fully stochastic and data-driven hybrid stochastic (DHS) models, which address, in different ways, the coupling between modal velocities and UMZ thickness. Our method provides a stochastic approach for generating an ensemble of instantaneous velocity profiles, consistent with the structural organisation of UMZs, where the ensemble reproduces the logarithmic mean velocity profile and recovers significant portions of the Reynolds stresses and, thus, of the streamwise and vertical velocity variability.

An integral method to determine mean skin friction in turbulent boundary layers

This study is concerned with accurately determining the mean skin friction in a zero-pressure-gradient turbulent boundary layer. By assuming a linear relation for the weighted total shear stress in the near-wall region, an integral method to evaluate the skin friction is proposed. The method requires the wall-normal profiles of the mean streamwise velocity and Reynolds shear stress within the range of y/δ≤0.4 at only one streamwise location, where δ is the boundary layer thickness. A number of direct numerical simulation and experimental data available in the literature are employed to validate the accuracy of the method over a wide range of Reynolds numbers. The skin friction coefficient obtained using the proposed method is found to be within ±4% in agreement with the published values in both the smooth- and rough-wall turbulent boundary layers. A comparison of the present approach with several existing methods is presented, showing that the proposed skin friction relation is robust and accurate.

Systematic study of the Reynolds number and streamwise spacing effects in two-dimensional square-bar rough-wall turbulent boundary layers

Two-dimensional square-bars roughness significantly influences the drag coefficient and coherent structures of turbulent boundary layer flow. A pitch ratio of 8 can induce the maximum drag effect for the turbulent boundary layer compared to other pitch ratios at a moderate friction Reynolds number. Hot-wire experiment results show that a wide range of pitch ratios has similar energy modulation by transferring energy from the largest scale structures to the smaller ones.

A new equivalent sand grain roughness relation for two-dimensional rough wall turbulent boundary layers

The effects of different geometries of two-dimensional (2-D) roughness elements in a zero pressure gradient (ZPG) turbulent boundary layer (TBL) on turbulence statistics and drag coefficient are assessed using single hot-wire anemometry. Three kinds of 2-D roughness are used: (i) circular rods with two different heights, $k= 1.6$ and 2.4 mm, and five different streamwise spacing of $s_{x}= 6k$ to $24k$ , (ii) three-dimensional (3-D) printed triangular ribs with heights of $k= 1.6$ mm and spacing of $s_{x}= 8k$ and (iii) computerized numerical control (CNC) machined sinewave surfaces with two different heights, $k= 1.6$ and 2.4 mm, and spacing of $s_{x}= 8k$ . These roughnesses cover a wide range of ratios of the boundary layer thickness to the roughness height ( $23 < \delta /k < 41$ ), where $\delta$ is the boundary layer thickness. All roughnesses cause a downward shift on the wall-unit normalised streamwise mean velocity profile when compared with the smooth wall profiles agreeing with the literature, with a maximum downward shift observed for $s_{x}= 8k$ . In the fully rough regime, the drag coefficient becomes independent of the Reynolds number. Changing the roughness height while maintaining the same spacing ratio $s_{x}/k$ exhibits little influence on the drag coefficient in the fully rough regime. On the other hand, the effective slope $(ES)$ and the height skewness $(k_{sk})$ appear to be major surface roughness parameters that affect the drag coefficient. These parameters are used in a new expression for $k_{s}$ , the equivalent sand grain roughness, developed for 2-D uniformly distributed roughness in the fully rough regime.

Study of a rough-wall turbulent boundary layer under pressure gradient

The behaviour of a fully rough-wall turbulent boundary layer subjected to different pressure gradients is investigated for different Reynolds numbers using hot-wire measurements. Mean velocity and velocity root-mean-square measurements indicate that the boundary layer remains in a self-preserving state regardless of the pressure gradient. However, different pressure gradients lead to different self-preservation states, as suggested by the lack of collapse of the velocity profile between the pressure gradient cases. The results also indicate that the roughness effect is more important than the pressure gradient; particularly, the closer the wall, the more dominant the roughness effect over the pressure gradient effect on the boundary layer. Finally, both spectral and proper orthogonal decomposition analyses applied to the hot-wire measurements indicate that the pressure gradient impacts predominantly the large-scale motion.

Empirical Model for Low-Speed Rough-Wall Turbulent Boundary Layer Pressure Spectra

An empirical model for estimating surface pressure spectra in high Reynolds number rough-wall turbulent boundary layers in the low-speed regime is presented. The model is based on the low-frequency mean velocity defect scaling [1] and the high-frequency shear friction velocity scaling [2]. This model satisfactorily predicts surface pressure spectra measured over a wide range of roughness configurations in high Reynolds number flows free of transitional effects. These data also provide insights into the characteristics of the turbulent scales which are on the order of the roughness size and comprise the mid-frequency region. The slope of this region is highly dependent on roughness element density and element-relative measurement location. This contradicts the premise of an overlap region with slope . An evanescent pressure decay model provides evidence that the slope changes are due to a roughness-dependent pressure decay within the interstitial flow and suggests that a traditional mid-frequency similarity law may not be possible.

Modeling of Cube Array Roughness: RANS, Large Eddy Simulation, and Direct Numerical Simulation

AbstractFlow over arrays of cubes is an extensively studied model problem for rough wall turbulent boundary layers. While considerable research has been performed in computationally investigating these topologies using direct numerical simulation (DNS) and large eddy simulation (LES), the ability of sublayer-resolved Reynolds-averaged Navier–Stokes (RANS) to predict the bulk flow phenomena of these systems is relatively unexplored, especially at low and high packing densities. Here, RANS simulations are conducted on six different packing densities of cubes in aligned and staggered configurations. The packing densities investigated span from what would classically be defined as isolated, up to those in the d-type roughness regime, filling in the gap in the present literature. Three different sublayer-resolved turbulence closure models were tested for each case: a low Reynolds number k–ϵ model, the Menter k–ω SST model, and a full Reynolds stress model. Comparisons of the velocity fields, secondary flow features, and drag coefficients are made between the RANS results and existing LES and DNS results. There is a significant degree of variability in the performance of the various RANS models across all comparison metrics. However, the Reynolds stress model demonstrated the best accuracy in terms of the mean velocity profile as well as drag partition across the range of packing densities.

Turbulent boundary layer flow over regularly and irregularly arranged truncated cone surfaces

Aiming to study the rough-wall turbulent boundary layer structure over differently arranged roughness elements, an experimental study was conducted on flows with regular and random roughness. Varying planform densities of truncated cone roughness elements in a square staggered pattern were investigated. The same planform densities were also investigated in random arrangements. Velocity statistics were measured via two-component laser Doppler velocimetry and stereoscopic particle image velocimetry. Friction velocity, thickness, roughness length and zero-plane displacement, determined from spatially averaged flow statistics, showed only minor differences between the regular and random arrangements at the same density. Recent a priori morphometric and statistical drag prediction methods were evaluated against experimentally determined roughness length. Observed differences between regular and random surface flow parameters were due to the presence of secondary flows which manifest as high-momentum pathways and low-momentum pathways in the streamwise velocity. Contrary to expectation, these secondary flows were present over the random surfaces and not discernible over the regular surfaces. Previously identified streamwise-coherent spanwise roughness heterogeneity does not seem to be present, suggesting that such roughness heterogeneity is not necessary to sustain secondary flows. Evidence suggests that the observed secondary flows were initiated at the front edge of the roughness and sustained over irregular roughness. Due to the secondary flows, local turbulent boundary layer profiles do not scale with local wall shear stress but appear to scale with local turbulent shear stress above the roughness canopy. Additionally, quadrant analysis shows distinct changes in the populations of ejection and sweep events.

Spatial resolution effects on measurements in a rough wall turbulent boundary layer

Spatial resolution effects on measurements in a rough wall turbulent boundary layer

The Influence of Element Thermal Conductivity, Shape, and Density on Heat Transfer in a Rough Wall Turbulent Boundary Layer With Strong Pressure Gradients

Abstract Formation mechanisms for turbine roughness are manifold, including erosion, corrosion, deposition, and spallation or more recently additive manufacturing processes. Consequently, the resulting surfaces differ remarkably not only in roughness shape, height, and density but also in element thermal conductivity. Because the roughness elements extend into the boundary layer, their temperature distribution has a direct influence on the thermal boundary layer and thus on the resulting convective heat transfer. In the current study, heat transfer distributions along a flat plate with more than 20 deterministic rough surface topographies that differ in element eccentricity, height and density are measured. For each surface roughness, measurements are conducted using two different element thermal conductivities (0.2 W/(mK) and 30 W/(mK)), two pressure distributions, four Reynolds numbers between 3 × 105 and 7.5 × 105 and various inlet turbulence intensities in the range of 1.5 % to 8 %. The pressure distributions resemble a typical suction and pressure side, respectively. Results show a heat transfer increase of up to 60 % for the high thermal conductivity surfaces and up to 50 % for the low conductivity ones. While heat transfer on the high conductivity surfaces is always higher than on the low conductivity ones, the difference becomes smaller with decreasing element density.

Reynolds number effect on the response of a rough wall turbulent boundary layer to local wall suction

Abstract

Automated terrain generation for precise atmospheric boundary layer simulation in the wind tunnel

This study presents a two-stage framework to characterize boundary layer wind tunnel (BLWT) approach flows naturally developed over grid roughness for partial atmospheric boundary layer (ABL) simulation. The first stage applies curve fitting techniques to a comprehensive series of high-resolution spatially-averaged velocity profile measurements to estimate aerodynamic roughness parameters (ARPs) for a wide range of homogeneous (i.e., equal height) roughness element configurations. For this study, an automated (i.e., computer-controlled) 62 ​× ​18 roughness element array called the Terraformer was used to generate 33 unique roughness element fields. The mean flow structure was captured downwind to the Terraformer, where key ARPs—i.e., the urban canopy attenuation coefficient, zero-plane displacement height, shear (friction) velocity, roughness length, and Coles’ wake strength coefficient—were estimated. In contrast to previous ABL modeling methods that primarily focused on curve fitting of the inertial sublayer (ISL), the proposed approach applies the urban canopy exponential profile within the roughness sublayer (RSL), the log law in the ISL, and the law of the wake in the outer wake layer to model full-depth (i.e., floor to freestream) rough-wall turbulent boundary layers. Further, the method explicitly captures potential variability of Reynolds shear stress in the ISL and the wake strength in the outer layer to generalize characterization of naturally-developed BLs produced by traditional tunnel designs. The second stage applies a morphometric model for each ARP—calibrated with estimates from Stage 1—to predict flow characteristics for a wide range of roughness element configurations, with the goal of producing a deterministic solution for selecting an element configuration to satisfy user-specified aerodynamic objectives for the approach flow. The calibrated models effectively interpolate between estimates, e.g., ARPs estimated for open and suburban terrains can be applied in the second stage model calibration to predict ARPs for a “rough-open” condition without further experimentation. The findings of this study demonstrate that coupling the proposed framework with a mechanized roughness element grid can significantly reduce the trial-and-error required to commission a BLWT, while improving the quality of flow characterization.

Gabor mode enrichment in large eddy simulations of turbulent flow

Abstract

Analysis of the different sources of stress acting in fully rough turbulent flows over geometrical roughness elements

The discrete element roughness method is considered in this article for the prediction of turbulent flows over rough walls. This approach is derived by ensemble- and volume-averaging the Navier–Stokes equations, providing double-averaged Navier–Stokes equations, and yielding three unknown terms in the momentum equation: the Reynolds stress and dispersive stress tensors and the average drag force acting on the roughness elements. This work aims at analyzing these different terms, quantifying their respective contributions to the near-wall momentum budget, and providing guidance for their modeling. For this purpose, relevant data of turbulent flows are required. Roughness-resolved Reynolds-averaged Navier–Stokes simulations of transitionally and fully rough channel flows over academic roughness configurations are performed at high friction Reynolds numbers ranging from 3500 to 8000. Comparisons with existing and new velocity measurements performed in rough-wall turbulent boundary layers provide support to the simulation results, a particular emphasis being given on the validity of the numerical results in the wake of the roughness elements. These numerical results highlight the influence of roughness elements geometry and density on the roughness drag coefficient and the dispersive stress. It is particularly suggested that the standard roughness drag closure model should be revisited for double-averaged flows. Furthermore, the dispersive stress is shown to mainly originate from the wake of the roughness elements, an observation that could be leveraged for its modeling. However, since this stress contributes only marginally to the global stress and to the skin friction coefficient, such a modeling may not be critical at first order.

Roughness effect in an initially laminar channel flow

The possibility of generating and maintaining turbulence in an initially laminar channel flow is investigated for two Reynolds numbers and 2100 (based on bulk velocity, and half-height of the channel, ). The study is carried out through a direct numerical simulation based on the lattice Boltzmann method (LBM). The channel consists of two parallel walls separated by a distance where the roughness elements are mounted on both walls. It was observed that when the transverse square bars span half the width of the channel and are mounted in a ‘staggered’ formation, the flow becomes fully turbulent with strong similarities to fully rough wall turbulent channel flows at much higher Reynolds number, as reported in the literature. For example, the rough wall mean velocity profile exhibits a significant downward shift when compared to the smooth wall one. Also, the turbulent kinetic energy budget is similar to its counterpart in rough wall turbulent channel flows at much higher Reynolds numbers than the present ones. It is further shown that the present velocity spectra compared very well with that obtained in a rough wall turbulent boundary layer. Finally, some elements of the possible physical mechanism allowing the generation, growth and sustainability of turbulence are proposed.

Drag forces on sparsely packed cube arrays

Flow over aligned and staggered cube arrays is a classic model problem for rough-wall turbulent boundary layers. Earlier studies of this model problem mainly looked at rough surfaces with a moderate coverage density, i.e. $\unicode[STIX]{x1D706}_{p}>O(3\,\%)$, where $\unicode[STIX]{x1D706}_{p}$ is the surface coverage density and is defined to be the ratio between the area occupied by the roughness and the total ground area. At lower surface coverage densities, i.e. $\unicode[STIX]{x1D706}_{p}<O(3\,\%)$, it is conventionally thought that cubical roughness acts like isolated roughness elements; and that the single-cube drag coefficient, i.e. $C_{d}\equiv f/(\unicode[STIX]{x1D70C}U_{h}^{2}h^{2})$, equals $C_{R}$. Here, $f$ is the drag force on one cubical roughness element, $\unicode[STIX]{x1D70C}=\text{const.}$ is the fluid density, $h$ is the height of the cube, $U_{h}$ is the spatially and temporally averaged wind speed at the cube height, and $C_{R}$ is the drag coefficient of an isolated cube. In this work, we conduct large-eddy simulations and direct numerical simulations of flow over wall-mounted cubes with very low surface coverage densities, i.e. $0.08\,\%<\unicode[STIX]{x1D706}_{p}<4.4\,\%$. The large-eddy simulations are at nominally infinite Reynolds numbers. The results challenge the conventional thinking, and we show that, at very low surface coverage densities, the single-cube drag coefficient may increase as a function of $\unicode[STIX]{x1D706}_{p}$. Our analysis suggests that this behaviour may be attributed to secondary turbulent flows. Secondary turbulent flows are often found above spanwise-heterogeneous roughness. Although the roughness considered in this work is nominally homogeneous, the secondary flows in our simulations are very similar to those observed above spanwise-heterogeneous surface roughness. These secondary vortices redistribute the fluid momentum in the outer layer, leading to high-momentum pathways above the wall-mounted cubes and low-momentum pathways at the two sides of the wall-mounted cubes. As a result, the spatially and temporally averaged wind speed at the cube height, i.e. $U_{h}$, is an underestimate of the incoming flow to the cubes, which in turn leads to a large drag coefficient $C_{d}$.

Experimental investigation of vertical turbulent transport of a passive scalar in a boundary layer: Statistics and visibility graph analysis

The dynamics of a passive scalar plume in a turbulent boundary layer is experimentally investigated via vertical turbulent transport time-series. Data are acquired in a rough-wall turbulent boundary layer that develops in a recirculating wind tunnel set-up. Two source sizes in an elevated position are considered in order to investigate the influence of the emission conditions on the plume dynamics. The analysis is focused on the effects of the meandering motion and the relative dispersion. First, classical statistics are investigated. We found that (in accordance with previous studies) the meandering motion is the main responsible for differences in the variance and intermittency, as well as the kurtosis and power spectral density, between the two source sizes. On the contrary, the mean and the skewness are slightly affected by the emission conditions. To characterize the temporal structure of the turbulent transport series, the visibility algorithm is exploited to carry out a complex network-based analysis. Two network metrics -- the average peak occurrence and the assortativity coefficient -- are analysed, as they can capture the temporal occurrence of extreme events and their relative intensity in the series. The effects of the meandering motion and the relative dispersion of the plume are discussed in the view of the network metrics, revealing that a stronger meandering motion is associated with higher values of both the average peak occurrence and the assortativity coefficient. The network-based analysis advances the level of information of classical statistics, by characterizing the impact of the emission conditions on the temporal structure of the signals in terms of extreme events and their relative intensity. In this way, complex networks provide -- through the evaluation of network metrics -- an effective tool for time-series analysis of experimental data.

Effects of wall suction on a 2D rough wall turbulent boundary layer

Hot-wire measurements carried out in a 2D rough wall turbulent boundary layer subjected to a wall suction through a porous strip show that the outer part of the boundary layer is deflected inward (toward the wall), thus impacting on the roughness elements close to the suction strip. This leads to an increased drag coefficient associated with an increased energy input, arguably, resulting from an intensified shedding of vortical structures from the roughness elements. Conversely to the smooth wall case, suction does not lead to relaminarization of the boundary layer. It also seems that suction does not alter significantly the turbulence structure of the boundary layer.

LES-DEM simulations of sediment saltation in a rough-wall turbulent boundary layer

Sediment saltation in a rough-wall turbulent boundary layer was simulated with a coupled model with large eddy simulation and a discrete element model. The aim is to quantify the saltation process using eddy-resolving fluid simulations and Lagrangian particle tracking. The four-way coupling approach in this work considered the fluid–particle, particle–particle, and particle–wall interactions. Five simulations were performed. For comparison, one simulation with the flow field replaced by a simple log-law profile was also performed. The simulated saltation trajectory, velocity, and collision angles were analysed and we found: (1) Turbulent fluctuation and random collision with the bed are two controlling factors for particle trajectory. Without turbulent fluctuation, the loss of saltation information is severer in the streamwise direction than in other directions. In the spanwise direction, bed collision plays a comparable role to turbulent fluctuation. (2) Particle velocities in the streamwise and vertical directions follow skew-normal distributions. (3) Turbulent fluctuations make the incidence angle wider and slightly enhance the correlation between the incidence and reflection angles.

The spatial structure of the logarithmic region in very-high-Reynolds-number rough wall turbulent boundary layers

Using super-large-scale particle image velocimetry (SLPIV), we investigate the spatial structure of the near-wall region in the fully rough atmospheric surface layer with Reynolds number$Re_{\unicode[STIX]{x1D70F}}\sim O(10^{6})$. The field site consists of relatively flat, snow-covered farmland, allowing for the development of a fully rough turbulent boundary layer under near-neutral thermal stability conditions. The imaging field of view extends from 3 m to 19 m above the ground and captures the top of the roughness sublayer and the bottom of an extensive logarithmic region. The SLPIV technique uses natural snowfall as seeding particles for the flow imaging. We demonstrate that SLPIV provides reliable measurements of first- and second-order velocity statistics in the streamwise and wall-normal directions. Our results in the logarithmic region show that the structural features identified in laboratory studies are similarly present in the atmosphere. Using instantaneous vector fields and two-point correlation analysis, we identify vortex structures sharing the signature of hairpin vortex packets. We also evaluate the zonal structure of the boundary layer by tracking uniform momentum zones (UMZs) and the shear interfaces between UMZs in space and time. Statistics of the UMZs and shear interfaces reveal the role of the zonal structure in determining the mean and variance profiles. The velocity difference across the shear interfaces scales with the friction velocity, in agreement with previous studies, and the size of the UMZs scales with wall-normal distance, in agreement with the attached eddy framework.