Turbulent Channel Flow Research Articles

High-order thread-safe lattice Boltzmann model for high performance computing turbulent flow simulations

We present a highly optimized thread-safe lattice Boltzmann model in which the non-equilibrium part of the distribution function is locally reconstructed via recursivity of Hermite polynomials. Such a procedure allows the explicit incorporation of non-equilibrium moments of the distribution up to the order supported by the lattice. Thus, the proposed approach increases accuracy and stability at low viscosities without compromising performance and amenability to parallelization with respect to standard lattice Boltzmann models. The high-order thread-safe lattice Boltzmann is tested on two types of turbulent flows, namely, the turbulent channel flow at Reτ=180 and the axisymmetric turbulent jet at Re = 7000; it delivers results in excellent agreement with reference data [direct numerical simulations (DNS), theory, and experiments] and (a) achieves peak performance [∼5×1012 floating point operations (FLOP) per second and an arithmetic intensity of ∼7 FLOP/byte on a single graphic processing unit] by significantly reducing the memory footprint, (b) retains the algorithmic simplicity of standard lattice Boltzmann computing, and (c) allows to perform stable simulations at vanishingly low viscosities. Our findings open attractive prospects for high-performance simulations of realistic turbulent flows on GPU-based architectures. Such expectations are confirmed by excellent agreement among lattice Boltzmann, experimental, and DNS reference data.

Turbulent drag reduction in compressible flows using streamwise traveling waves

Skin-friction drag reduction (DR) in supersonic turbulent channel flows using streamwise traveling waves of spanwise velocity (STWSV) has been studied using direct numerical simulations. In the present study, simulations are carried out for different phase speeds of the upstream and downstream traveling waves for a bulk Mach number Mab=1.5 and bulk Reynolds number Reb = 3000. The efficacy of the control has been investigated for other bulk Reynolds numbers as well. The Stokes layer generated by the control affects the near-wall statistics primarily by modifying the coherent structures, thereby either reducing or aggravating the skin-friction drag. For Reb = 3000 and Mab=1.5, a maximum drag reduction (DRmax) of 49% is achieved, primarily due to suppression of sweeps and ejections on application of control. The efficacy of skin-friction drag reduction varies in a small range when Reb is varied from 3000 to 6000; however, the maximum drag reduction is observed for Reb = 4000, owing to a drastic decrease in sweep events. Quadrant analysis reveals that for drag reduction (DR) cases, STWSV reduce magnitude of streamwise u′ and wall-normal w′ velocity fluctuations magnitude and stacks them around zero. In contrast, w′ is increased for drag increase (DI) cases. Skin-friction decomposition using Fukagata, Iwamoto and Kasagi (FIK) identity suggests that the control alters the turbulent component significantly. The behavior of the control is also studied at Mab = 0.3 and 2.5, and it is observed that the maximum drag reduction obtained decreases for high bulk Mach numbers.

Reynolds-number scaling of wall-pressure–velocity correlations in wall-bounded turbulence

Wall-pressure fluctuations are a practically robust input for real-time control systems aimed at modifying wall-bounded turbulence. The scaling behaviour of the wall-pressure–velocity coupling requires investigation to properly design a controller with such input data so that it can actuate upon the desired turbulent structures. A comprehensive database from direct numerical simulations (DNS) of turbulent channel flow is used for this purpose, spanning a Reynolds-number range$Re_\tau \approx 550\unicode{x2013}5200$. Spectral analysis reveals that the streamwise velocity is most strongly coupled to the linear term of the wall pressure, at a Reynolds-number invariant distance-from-the-wall scaling of$\lambda _x/y \approx 14$(and$\lambda _x/y \approx 8$for the wall-normal velocity). When extending the analysis to both homogeneous directions in$x$and$y$, the peak coherence is centred at$\lambda _x/\lambda _z \approx 2$and$\lambda _x/\lambda _z \approx 1$for$p_w$and$u$, and$p_w$and$v$, respectively. A stronger coherence is retrieved when the quadratic term of the wall pressure is concerned, but there is only little evidence for a wall-attached-eddy type of scaling. An experimental dataset comprising simultaneous measurements of wall pressure and velocity complements the DNS-based findings at one value of$Re_\tau \approx 2$k, with ample evidence that the DNS-inferred correlations can be replicated with experimental pressure data subject to significant levels of (acoustic) facility noise. It is furthermore shown that velocity-state estimations can be achieved with good accuracy by including both the linear and quadratic terms of the wall pressure. An accuracy of up to 72 % in the binary state of the streamwise velocity fluctuations in the logarithmic region is achieved; this corresponds to a correlation coefficient of$\approx$0.6. This thus demonstrates that wall-pressure sensing for velocity-state estimation – e.g. for use in real-time control of wall-bounded turbulence – has merit in terms of its realization at a range of Reynolds numbers.

Purely elastic turbulence in pressure-driven channel flows

Solutions of long, flexible polymer molecules are complex fluids that simultaneously exhibit fluid-like and solid-like behavior. When subjected to an external flow, dilute polymer solutions exhibit elastic turbulence-a unique, chaotic flow state absent in Newtonian fluids, like water. Unlike its Newtonian counterpart, elastic turbulence is caused by polymer molecules stretching and aligning in the flow, and can occur at vanishing inertia. While experimental realizations of elastic turbulence are well-documented, there is currently no understanding of its mechanism. Here, we present large-scale direct numerical simulations of elastic turbulence in pressure-driven flows through straight channels. We demonstrate that the transition to elastic turbulence is sub-critical, giving rise to spot-like flow structures that, further away from the transition, eventually spread throughout the domain. We provide evidence that elastic turbulence is organized around unstable coherent states that are localized close to the channel midplane.

Calibrating sub-grid scale models for high-order wall-modeled large eddy simulation

AbstractHigh-order methods have demonstrated orders of magnitude reduction in computational cost for large eddy simulation (LES) over low-order methods in the past decade. Most such simulations are wall-resolved implicit LES (ILES) without an explicit sub-grid scale (SGS) model. The use of high-order ILES for severely under-resolved LES such as wall-modeled LES (WMLES) often runs into robustness and accuracy issues due to the low dissipation embedded in these methods. In the present study, we investigate the performance of several popular SGS models, the static Smagorinsky model, the wall-adapting local eddy-viscosity (WALE) model and the Vreman model, to improve the robustness and accuracy of under-resolved LES using high-order methods. The models are implemented in the high-order unstructured grid LES solver called hpMusic based on the discontinuous flux reconstruction method. The length scales in these SGS models are calibrated using the direct numerical simulation (DNS) database for the turbulent channel flow problem. The Vreman model has been found to produce the most accurate and consistent results with a proper choice of the length scale for WMLES.

Experimental investigation of yaw-angle effects on drag reduction rate for trapezoidal riblets

Effects of the yaw angle on the drag reduction rate of riblets were investigated experimentally for trapezoidal riblets with ridge angle of 30∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$30^\\circ$$\\end{document} and height-to-spacing ratio of 0.5 in a turbulent wind channel at Reynolds numbers (based on the friction velocity and channel half depth) Reτ=520-2100\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{Re}_\ au = 520 - 2100$$\\end{document}. Drag reduction rates were estimated carefully by comparing the streamwise pressure gradients between turbulent channel flows with and without riblets. The maximum drag reduction rate which was about 7% for the streamwise riblets was maintained without any attenuation for the yaw angle ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi$$\\end{document} below 10∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10^\\circ$$\\end{document}. When ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi$$\\end{document} exceeded 10∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10^\\circ$$\\end{document}, the drag reduction rate was attenuated steeply and the performance of riblets was almost lost at ϕ=15∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi = 15^\\circ$$\\end{document}. The yaw angle at which the drag turned to increase was by 10º smaller than the value reported for the saw-tooth riblets. The yaw angle effect on the riblet performance was further examined by detailed comparisons of mean velocity profiles and turbulent structures near the ribbed surfaces for ϕ=10∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi = 10^\\circ$$\\end{document} and 15∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$15^\\circ$$\\end{document}. Although no appreciable difference in the turbulent intensity and pre-multiplied spectrum of near-wall turbulence was found between these cases (ϕ=10∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi = 10^\\circ$$\\end{document} and 15∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$15^\\circ$$\\end{document}), the mean velocity profile for the case of ϕ=15∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi = 15^\\circ$$\\end{document} indicated an evidence of flow separation at the ridges of riblets, leading to the attenuation of drag-reduction rate due to increase in the pressure drag.

Validation of symmetry-induced high moment velocity and temperature scaling laws in a turbulent channel flow.

The symmetry-based turbulence theory has been used to derive new scaling laws for the streamwise velocity and temperature moments of arbitrary order. For this, it has been applied to an incompressible turbulent channel flow driven by a pressure gradient with a passive scalar equationcoupled in. To derive the scaling laws, symmetries of the classical Navier-Stokes and the thermal energy equationshave been used together with statistical symmetries, i.e., the statistical scaling and translation symmetries of the multipoint moment equations. Specifically, the multipoint moments are built on the instantaneous velocity and temperature fields other than in the classical approach, where moments are based on the fluctuations of these fields. With this instantaneous approach, a linear system of multipoint correlation equationshas been obtained, which greatly simplifies the symmetry analysis. The scaling laws have been derived in the limit of zero viscosity and heat conduction, i.e., Re_{τ}→∞ and Pr>1, and they apply in the center of the channel, i.e., they represent a generalization of the deficit law, thus extending the work of Oberlack etal. [Phys. Rev. Lett. 128, 024502 (2022)0031-900710.1103/PhysRevLett.128.024502]. The scaling laws are all power laws, with the exponent of the high moments all depending exclusively on those of the first and second moments. To validate the new scaling laws, the data from a large number of direct numerical simulations (DNS) for different Reynolds and Prandtl numbers have been used. The results show a very high accuracy of the scaling laws to represent the DNS data. The statistical scaling symmetry of the multipoint moment equations, which characterizes intermittency, has been the key to the new results since it generates a constant in the exponent of the final scaling law. Most important, since this constant is independent of the order of the moments, it clearly indicates anomalous scaling.

Clustering, rotation, and swirl of inertial particles in turbulent channel flow

Clustering dynamics of inertial particles in turbulent channel flow are studied via tessellation-based analysis of high-fidelity simulation data at Reτ≈230 with various values of mass loading (10%−100%) and the Stokes number (St+=[1−60]). We then characterise the solenoidal, rotational, and swirling motions of clusters by computing the probability density functions (PDFs) of the divergence, curl, and helicity of the particle velocity, as well as their dependence on wall-normal distance, using the methods of Oujia et al. (2020); Maurel–Oujia et al. (2023). Particle inertia gives heavier tails to the PDFs of divergence and curl, suggesting enhanced intermittency in the convergence/divergence of clusters, and in their rotational motions. The fluctuations of the divergence and curl are most intense in the buffer layer, due to the stronger fluctuations of fluid velocity there. Similarities are identified between the cluster dynamics in the logarithmic region and those in homogeneous isotropic turbulence, including the dependence of divergence, curl, and helicity on Stokes number. The effect of increasing mass loading on cluster dynamics is relatively small except in the viscous sublayer, where attenuation of clustering, rotation, and swirling motions are observed. The effect of increasing Stokes number on the viscous sublayer is different, resulting in more intense convergence/divergence and rotation of particle clusters, as the particles become more independent of the carrier fluid.

Direct numerical simulations of turbulent channel flow with a rib-roughened porous wall

To describe the effects of porous roughness on turbulence, we have carried out direct numerical simulations using the lattice Boltzmann method. The simulated flows are fully developed turbulent flows in channels consisting of a solid smooth top wall and a porous bottom wall with transverse porous ribs whose heights are 10 % of the channel height. The considered ratios of the rib spacing to the rib height are $w/k\simeq 1$ and 9. The Kelvin-cell structure is applied to construct faithfully the porous media whose porosities are $\varphi \ge 0.79$ . Three kinds of porous media having different permeabilities are considered. The most permeable one has an approximately one order higher permeability than that of the least permeable one. The higher permeability case is designed to have a pore scale that is the same as the rib height so that it is the most permeable case for the rib roughness with the designed porosity. In the simulations, the bulk Reynolds number is set to $Re_b=5500$ , and the corresponding permeability Reynolds numbers are $Re_K=2.2\unicode{x2013}7.5$ . The simulated field data and the drag coefficient, which includes both the pressure drag by the ribs and the frictional drag over the porous wall, are analysed to understand the characteristics of the permeable roughness in terms of permeability. The decomposition of the drag coefficient into the integrated laminar, rib-drag, dispersion and turbulence parts elucidates the transition mechanism between the typical d-type to k-type roughness depending on $Re_K$ . By the double (time and space) averaged budget equations for the dispersion and Reynolds stresses, we explain how the energy generated by the roughness transfers to turbulence through dispersion resulting in the k-type characteristics. The nominal roughness sublayer thickness and the characteristic roughness height are introduced with the parameters obtained by fitting the velocity data to Best's and Nikuradse's logarithmic velocity formulae. Along with data in the literature, it is suggested that the ratio of the characteristic roughness height to the nominal roughness sublayer thickness becomes constant irrespective of the rib spacing in the full permeable-wall turbulence at $Re_K> 7$ .

On the Preferential Concentration of Particles in Turbulent Channel Flow: The Effect of the Added-Mass Factor

Preferential concentration, observed in turbulent flows when particle response times are of the same order of the flow’s characteristic timescales, manifests as non-uniform particle distributions in space. Unraveling its governing mechanisms holds crucial implications for both natural and industrial processes reliant on particle-laden flows. Focusing on particles with small inertia, this study employs Direct Numerical Simulations coupled with Lagrangian particle tracking to investigate the influence of the added-mass factor on the preferential concentration of particles denser than the fluid in the one-way coupling regime. It is shown how the added-mass factor β affects particle distribution within the channel through the statistical correlations between particle concentration and typical descriptors of the flow topology. The results suggest that increasing values of β (corresponding to lighter particles) significantly reduce the effectiveness of turbophoresis in producing particle accumulation in the near-wall region. Resulting in a gradual decorrelation between particle concentration and both the strain-rate and the vorticity tensors, higher values of β lead to a more uniform particle distribution, regardless of the Stokes number.

Preferential accumulation of finite-size particles in near-wall streaks

The preference for particles to accumulate at specific regions in the near-wall part is a widely observed phenomenon in wall-bounded turbulence. Unlike small particles more frequently found in low-speed streaks, finite-size particles can accumulate in either low-speed or high-speed streaks. However, mechanisms and influencing factors leading to the different preferential concentration locations still need to be clarified. The present study conducts particle-resolved direct numerical simulations of particle-laden turbulent channel flows to provide a better understanding of this seemingly puzzling behaviour of preferential accumulation. These simulations cover different particle-to-fluid density ratios, particle volume fractions, particle sizes and degrees of sedimentation intensity. We find that the large particle size is the crucial factor that results in particles accumulating in high-speed streaks. Large particles not only are difficult to be conveyed by the quasi-streamwise vortices to low-speed streaks but also can escape from the near-wall region before moving spanwisely out from high-speed streaks. The sedimentation effect allows particles to gather closer to the channel wall and stay longer in the near-wall regions, reinforcing the sweeping mechanism of quasi-streamwise vortices that transport particles from high- to low-speed streaks. As a result, sedimenting particles tend to accumulate in the low-speed streaks.

A Comprehensive Evaluation of Turbulence Models for Predicting Heat Transfer in Turbulent Channel Flow across Various Prandtl Number Regimes

Turbulent heat transfer in channel flows is an important area of research due to its simple geometry and diverse industrial applications. Reynolds-Averaged Navier–Stokes (RANS) models are the most-affordable simulation methodology and are often the only viable choice for investigating industrial flows. However, accurate modelling of wall-bounded flows is challenging in RANS, and the assessment of the performance of RANS models for heated turbulent channel flow has not been sufficiently investigated for a wide range of Reynolds and Prandtl numbers. In this study, five RANS models are assessed for their ability to predict heat transfer in channel flows across a wide range of Reynolds and Prandtl numbers (Pr) by comparing the RANS results with respect to the corresponding Direct Numerical Simulation data. The models include three Eddy Viscosity Models (EVMs): standard k−ϵ, low Reynolds number k−ϵLS, and k−ωSST, as well as two Reynolds Stress Models (RSMs): Launder–Reece–Rodi and Speziale–Sarkar–Gatski models. The study analyses the Reynolds number effects on turbulent heat transfer in a channel flow at a Pr of 0.71 for friction Reynolds number values of 180,395,640, and 1020. The results show that all models accurately predict velocity across all Reynolds numbers, but the accuracy of mean temperature prediction drops with increasing Reynolds number for all models, except for the k−ωSST model. The study also analyses the Pr effects on turbulent heat transfer in a channel flow with Pr values between 0.025 and 10.0. An error analysis is performed on the results obtained from different turbulence models, and it is shown that the k−ωSST model has the smallest error for the predictions of the mean temperature and Nusselt number for high-Prandtl-number flows, while the low Reynolds number k−ϵLS model shows the smallest errors for low-Prandtl-number flows at different Reynolds numbers. An analytical solution is utilised to identify Pr effects on forced convection in a channel flow into three different regimes: analytical region, transitional region, and turbulent diffusion-dominated region. These regimes are helpful to discuss the validity of the models in relation to the Pr. The findings of this paper provide insights into the performance of different RANS models for heat transfer predictions in a channel flow.

Widest scales in turbulent channels

The widest spanwise scales in turbulent channel flows are studied through the use of three periodic channel-flow simulations at friction Reynolds number Reτ=550. The length and height of the channels are the same in all cases (Lx/h=8π and Ly/h=2, respectively), while the width is progressively doubled: Lz/h={4π,8π,16π}. The effects of increasing the domain width cannot be determined with statistical significance in our simulations, since the difference in the statistics between the simulations is of the same order as the errors of convergence. A channel flow similar to the smaller one [Del Álamo et al., “Scaling of the energy spectra of turbulent channels,” J. Fluid Mech. 500, 135–144 (2004)], which was averaged over a very long time, was used as a reference. The one-dimensional spanwise spectrum of the streamwise velocity is computed with the aim of assessing the domain-size effect on the widest scales. Our results indicate that 90% of the total streamwise energetic fluctuations is recovered without a significant influence of the size of the domain. The remaining 10% of the energy reflects that the widest scales in the outer layer are the ones most significantly affected by the spanwise length of the domain. The power-spectral density for kz = 0 remains constant even if the size of the domain in the spanwise direction is increased up to four times the standard spanwise length, indicating that wide, spanwise coherent structures are not an artifact of domain truncation.

Introducing the Rankine vortex method for drag reduction in wall-bounded turbulent flows at low Reynolds number through streamwise vortex manipulation

It is well known that the near-wall streamwise vortices, together with the streaks, are the most important turbulent structures closely associated with drag reduction. Weakening or modifying the streamwise vortices are, thus, general approaches in near-wall turbulent control studies. In this study, a novel approach to manipulate the flow is introduced and applied to a turbulent channel flow in order to achieve drag reduction. The idea behind the “Rankine vortex method” is to generate a force based on the statistical and geometrical information of streamwise vortices. Direct numerical simulations of a turbulent channel flow at a frictional Reynolds number, Reτ, of 180 (based on the driving pressure gradient and channel half-width) are performed. The force is applied in the vicinity of the lower wall of the channel, and the results are comparatively analyzed for the cases with and without force implemented. A drag reduction of 10% is achieved. The theoretical flow control approach presented, along with the associated analysis, has the potential to enhance our current understanding of flow control mechanisms through the manipulation of near-wall turbulence.

Numerical Investigation of a Developed Turbulent Flow and Heat Transfer in a Rectangular Channel with Single-Sided Internal Ribs

Numerical Investigation of a Developed Turbulent Flow and Heat Transfer in a Rectangular Channel with Single-Sided Internal Ribs

Bayesian-Optimized Riblet Surface Design for Turbulent Drag Reduction via Design-by-Morphing With Large Eddy Simulation

Abstract A computational approach is presented for optimizing new riblet surface designs in turbulent channel flow for drag reduction, utilizing design-by-morphing (DbM), large Eddy simulation (LES), and Bayesian optimization (BO). The design space is generated using DbM to include a variety of novel riblet surface designs, which are then evaluated using LES to determine their drag-reducing capabilities. The riblet surface geometry and configuration are optimized for maximum drag reduction using the mixed-variable Bayesian optimization (MixMOBO) algorithm. A total of 125 optimization epochs are carried out, resulting in the identification of three optimal riblet surface designs that are comparable to or better than the reference drag reduction rate of 8%. The Bayesian-optimized designs commonly suggest riblet sizes of around 15 wall units, relatively large spacing compared to conventional designs, and spiky tips with notches for the riblets. Our overall optimization process is conducted within a reasonable physical time frame with up to 12-core parallel computing and can be practical for fluid engineering optimization problems that require high-fidelity computational design before materialization.

On biomimetic surface texturing and its impact on turbulent flow and hydrodynamic forces acting on an early-stage bio-fouling organism

Recent marine anti-fouling research efforts have sought inspiration from bio-mimetic strategies to develop nontoxic solutions. Surface modifications have shown promising results in their ability to disrupt attachment and growth of early-stage organisms under static immersion conditions but very limited research has attempted to explore the interaction between surface textures and flow under turbulent conditions. The study presented in this article focuses on a simple texture, inspired by the growth rings of the Brill fish Scophthalmus rhombus and developed for applications on the blades of tidal stream turbine. A series of Large Eddy Simulations of fully developed turbulent channel flow were performed to assess the influence of the spacing between the texture elements on turbulent stresses. The aim is to characterize the impact of the texture on turbulent stresses by comparison to a smooth surface and identify whether shelters may form within the gaps between textures. The study clarifies the role of dispersive and Reynolds stresses in terms of their impact on hydrodynamic forces acting on a simplified model of a marine diatom. Reynolds shear stresses predominantly govern the intensity of forces, while dispersive shear stress affects the mean hydrodynamic forces acting on the organism at the early stage of settlement.

Impact of sandpaper grit size on drag reduction and plastron stability of super-hydrophobic surface in turbulent flows

In this work, we experimentally investigated the impact of surface roughness on drag reduction as well as the plastron stability of superhydrophobic surfaces (SHSs) in turbulent flows. A series of SHSs were fabricated by spraying hydrophobic nanoparticles on sandpapers. By changing the grit size of sandpapers from 240 to 1500, the root mean square roughness height (krms) of the SHSs varied from 4 to 14 μm. The experiments were performed in a turbulent channel flow facility, where the mean flow speed (Um) varied from 0.5 to 4.4 m/s, and the Reynolds number (Rem) based on Um and channel height changed from 3400 to 26 400. The drag reduction by SHSs was measured based on pressure drops in the fully developed flow region. The plastron status and gas fraction (φg) were simultaneously monitored by reflected-light microscopy. Our results showed a strong correlation between drag reduction and krms+ = krms/δv, where δv is the viscous length scale. For krms+ < 1, drag reduction was independent of krms+. A maximum 47% drag reduction was observed. For 1 < krms+ < 2, less drag reduction was observed due to the roughness effect. And for krms+ > 2, the SHSs caused an increase in drag. Furthermore, we found that surface roughness influenced the trend of plastron depletion in turbulent flows. As increasing Rem, φg reduced gradually for SHSs with large krms, but reduced rapidly and maintained as a constant for SHSs with small krms. Finally, we found that as increasing Rem, the slip length of SHS reduced, although φg was nearly a constant.

Characterization and evolution of local streamline geometry in an incompressible turbulent channel flow

We investigated the statistical characterization and time evolution of local streamline geometry in typical regions of an incompressible turbulent channel flow at the friction Reynolds number Reτ∼1000. Local streamline structure is completely and uniquely determined by one magnitude factor—the magnitude of velocity gradient tensor (VGT) A—and four shape parameters—the second and third invariants of normalized VGT q and r, the intermediate eigenvalue of normalized strain-rate tensor a2, and the cosine of the angle between vorticity and the intermediate eigendirection of normalized strain-rate tensor | cos β|. As the distance to the wall decreases, the joint probability distribution function of q and r becomes more symmetrical and concentrated, while outside the viscous sublayer, the distribution of A in q–r plane gets dispersed. Interestingly, the inertial conditional mean trajectories (CMTs) exhibit a symmetrical picture only in the buffer layer, and outside the viscous sublayer, the pressure CMTs contributing to slow evolution from unstable focus compression geometry to stable focus stretching geometry tend to dominate the q–r plane as getting closer to the wall. Due to combined effects of inertia and pressure, the origin of the q–r plane (pure-shear geometry) acts as an attractor in the central region, the logarithmic region, and the upper part of the buffer layer while acts as a repeller in the lower part of the buffer layer and the viscous sublayer.

A data-driven quasi-linear approximation for turbulent channel flow

A data-driven implementation of a quasi-linear approximation is presented, extending a minimal quasi-linear approximation (MQLA) (Hwang & Ekchardt, J. Fluid Mech., vol. 894, 2020, p. A23) to incorporate non-zero streamwise Fourier modes. A data-based approach is proposed, matching the two-dimensional wavenumber spectra for a fixed spanwise wavenumber between a direct numerical simulation (DNS) (Lee & Moser, J. Fluid Mech., vol. 774, 2015, pp. 395–415) and that generated by the eddy viscosity enhanced linearised Navier–Stokes equations at $Re_\tau \approx 5200$ , where $Re_\tau$ is the friction Reynolds number. Leveraging the self-similar nature of the energy-containing part in the DNS velocity spectra, a universal self-similar streamwise wavenumber weight is determined for the linearised fluctuation equations at $Re_\tau \simeq ~5200$ . The data-driven quasi-linear approximation (DQLA) provides noteworthy enhancements in the wall-normal and spanwise turbulence intensity profiles. It exhibits a qualitatively similar structure in the spanwise wavenumber velocity spectra compared with the MQLA. Additionally, the DQLA offers extra statistical outputs in the streamwise wavenumber coordinates, enabling a comprehensive global analysis of this modelling approach. By comparing the DQLA results with DNS results, the limitations of the presented framework are discussed, mainly pertaining to the lack of the streak instability (or transient growth) mechanism and energy cascade from the linearised model. The DQLA is subsequently employed over a range of Reynolds numbers up to $Re_\tau = 10^5$ . Overall, the turbulence statistics and spectra produced by the DQLA scale consistently with the available DNS and experimental data, with the Townsend–Perry constants displaying a mild Reynolds dependence (Hwang, Hutchins & Marusic, J. Fluid Mech., vol. 933, 2022, p. A8). The scaling behaviour of the turbulence intensity profiles deviates away from the classic $\ln (Re_\tau )$ scaling, following the inverse centreline velocity scaling for the higher Reynolds numbers.