Near-wall Turbulent Structures Research Articles

Characteristics of shear stress fluctuations in polymer solutions and their relation to turbulent structures in channel flows

In this study, the wall shear stress in the channel flow of polyacrylamide polymers was investigated through electrochemical experiments, and the effects of the polymer concentration were evaluated at different Reynolds numbers. The objective was to explore the relationship between the changes in the drag reduction and near-wall turbulence structure induced by the polymer. The experiments were conducted using polymer concentrations of 0, 20, 50, 100, and 150 ppm, and a drag reduction of approximately 23% was achieved at a bulk Reynolds number of Reb = 18 750. In the electrochemical method, the working electrode was arranged spanwise, and simultaneous measurements were performed for eight electrodes to discuss the scale of the near-wall low-speed streaks and burst events. A comprehensive analysis of the correlation of the wall shear stress in the streamwise direction and the cross-spectrum of two points in the spanwise direction revealed that large streamwise and spanwise scales of near-wall low-speed streaks were generated at high polymer concentrations. Furthermore, the results obtained using the variable interval time averaging technique indicated that polymer incorporation suppressed the wall shear stress fluctuations and weakened both the intensity and frequency of the bursting events.

The statistical characteristics and auto-regeneration of backflow in non-Newtonian turbulent pipe flow

The backflow phenomenon in shear-thinning and shear-thickening fluids is investigated in pipe flows at friction Reynolds number Reτ=180 via direct numerical simulations. Conditional average results show that the extreme fluctuation of wall shear stress around the backflow regions is more abrupt under the shear-thinning effect. The statistical characteristics of the backflow at different flow indices from 0.5 to 1.5 show remarkable differences. The probability of the backflow events at the wall increases in both the shear-thinning and the shear-thickening fluids under different mechanisms. The backflow occurs more frequently and exists further away from the wall in the shear-thinning fluids owing to the suppressed near-wall turbulent structures and the laminarization at low flow indices. The increase in the probability of the backflow events in the shear-thickening fluids is caused by increased Q2 and Q4 events in the near-wall region. The variation in the size and the lifespan of the backflow regions with the flow index is very prominent which both increase with the shear-thinning effect and decrease as the flow becomes dilatant. In the weakly turbulent flow of shear-thinning fluid, large backflow regions appear near the leading edge of the turbulent spots where the off-axial turbulent fluctuations are significantly lowered. Observations show the linked evolution between the hairpin vortices and the backflow regions induced underneath the strong spanwise rotations. The backflow follows the auto-regeneration process of the hairpin vortices in a packet which results in coherent streamwise-aligned backflow regions under the hairpin packets confined closer to the wall.

Curvature effects on the structure of near-wall turbulence

The interaction between near-wall turbulence and wall curvature is described for the incompressible flow in a plane channel with a small concave–convex–concave bump on the bottom wall, with height comparable to the wall-normal location of the main turbulent structures. The analysis starts from a database generated by a direct numerical simulation and hinges upon the anisotropic generalised Kolmogorov equations, i.e. the exact budget equations for the second-order structure function tensor. The influence of the bump on the wall cycle and on the energy production, redistribution and transfers is described in the physical and scale spaces. Over the upstream side of the bump, the energy drained from the mean flow to sustain the streamwise fluctuations decreases, and the streaks of high and low streamwise velocity weaken and are stretched spanwise. After the bump tip, instead, the production of streamwise fluctuations grows and the streaks intensify, progressively recovering their characteristic spanwise scale. The wall-normal fluctuations, and thus the quasi-streamwise vortices, are sustained by the mean flow over the upstream side of the bump, while energy flows from the vertical fluctuations to the mean field over the downstream side. On the concave portion of the upstream side, the near-wall fluctuations form structures of spanwise velocity which are consistent with Taylor–Görtler vortices at an early stage of development. Their evolution is described by analysing the scale-space pressure–strain term. A schematic description of the bump flow is presented, in which various regions are identified according to the signs of curvature and streamwise pressure gradient.

Turbulent boundary layer over porous media with wall-normal permeability

Porous walls are a widely used passive flow control technique, which shows potential in reducing skin friction and mitigating flow-introduced noise. In the present study, porous media with wall-normal permeability is applied to a flat plate to investigate its interaction with the turbulent boundary layer at the Reynolds number based on friction velocity of Reτ=225. Time-resolved planar and tomographic particle image velocimetry were employed to identify the impact on mean statistics and coherent structures. An overall skin friction reduction of 22% is achieved. The porous wall induces counter-rotating streamwise vortex pairs at the spanwise sides of each pore, leading to momentum transport and the generation of alternative low- and high-speed regions close to the wall. Slip velocity is obtained, associated with the reduction in turbulent fluctuations and Reynolds shear stress. The streamwise velocity streaks and the hairpin vortices are significantly distorted compared with the smooth wall condition due to the downwash and upwash motion, featuring a notable reduction in the number and scale of the coherent structures, in which the skin friction reduction mechanism is related to. The proper orthogonal decomposition analysis returns the most energetic unsteady modes. Although the wall-coherent mode type remains to dominate the production of turbulent fluctuations, the scale and energy content of wall-incoherent modes increase, confirming the modification of the distribution and scale of near-wall turbulent structures.

Near-wall numerical coherent structures and turbulence generation in wall-modelled large-eddy simulation

Near-wall turbulence structures and generation in the wall-modelled large-eddy simulation (WMLES) are revealed. To elucidate the turbulence structures driving a near-wall turbulence generation in the WMLES, flat-plate turbulent boundary-layer flows calculated by the WMLES and direct numerical simulation (DNS) are closely investigated. A conditional-averaging technique is applied to the instantaneous flow fields and the near-wall statistical structures of the ejection and sweep pairs, which produce the turbulence, are revealed to exist even in the WMLES although the structures are non-physically elongated compared with those obtained by the DNS. Since the near-wall turbulence structures in the WMLES are revealed not to be disordered, but to be coherent structures with low- and high-speed fluids alternating in the spanwise direction, it is suggested that the near-wall turbulence generation in the WMLES is explained by the numerically elongated coherent structures. Furthermore, the Reynolds number effects of wall-bounded turbulent flows, i.e. the appearance of the outer peak in the energy spectrum of the streamwise velocity fluctuations at increasing Reynolds numbers, is found not to be reproduced by the WMLES, and the origin of the outer peak is discussed in association with the inner–outer-layer interactions. The near-wall turbulence structures in the WMLES could depend heavily on the computational grids and the numerical methods. Therefore, additional cases varying the grid resolutions and the numerical methods (numerical schemes and sub-grid-scale models) are also conducted to confirm the consistency of the present conclusions.

Structure function tensor equations with triple decomposition

Exact budget equations are derived for the coherent and stochastic contributions to the second-order structure function tensor. They extend the anisotropic generalised Kolmogorov equations (AGKE) by considering the coherent and stochastic parts of the Reynolds stress tensor, and are useful for the statistical description of turbulent flows with periodic or quasi-periodic features, like, for example, the alternate shedding after a bluff body. While the original AGKE describe production, transport, inter-component redistribution and dissipation of the Reynolds stresses in the combined space of scales and positions, the new equations, called $\varphi$ AGKE, contain the phase $\varphi$ as an additional independent variable, and describe the interplay among the mean, coherent and stochastic fields at the various phases. The newly derived $\varphi$ AGKE are then applied to a case where an exactly periodic external forcing drives the flow: a turbulent plane channel flow modified by harmonic spanwise oscillations of the wall to reduce drag. The phase-by-phase action of the oscillating transversal Stokes layer generated by the forcing on the near-wall turbulent structures is observed, and a detailed description of the scale-space interaction among mean, coherent and stochastic fields is provided thanks to the $\varphi$ AGKE.

Modeling the wall shear stress in large-eddy simulation using graph neural networks

AbstractAs the Reynolds number increases, the large-eddy simulation (LES) of complex flows becomes increasingly intractable because near-wall turbulent structures become increasingly small. Wall modeling reduces the computational requirements of LES by enabling the use of coarser cells at the walls. This paper presents a machine-learning methodology to develop data-driven wall-shear-stress models that can directly operate, a posteriori, on the unstructured grid of the simulation. The model architecture is based on graph neural networks. The model is trained on a database which includes fully developed boundary layers, adverse pressure gradients, separated boundary layers, and laminar–turbulent transition. The relevance of the trained model is verified a posteriori for the simulation of a channel flow, a backward-facing step and a linear blade cascade.

Coherent near-wall structures and drag reduction by spanwise forcing

We examine interaction mechanisms between the drag-reducing streamwise-traveling waves of spanwise wall velocity applied at the wall of a turbulent channel flow, and near-wall turbulent coherent structures. In particular, we focus our analysis on the drag-reduction-induced modifications of the quasi-streamwise vortices that populate the near-wall region of turbulent flows through a conditional averaging procedure. We observe that, while the streamwise-traveling waves share most of the drag-reducing mechanisms with the spanwise wall oscillations, some important differences related to the finite phase speed of the wave and the different properties of the generalized Stokes layer exist.

Mitigation of turbulent noise sources by riblets

A feasibility study is presented on the application of riblets to suppress turbulent pressure sources leading to a reduction in the generation of aerofoil self-noise. It is shown that riblets can reduce skin friction as well as the turbulence intensity inside the boundary layer. In addition, near-wall turbulence structures were found to be dissipated quite rapidly when crossing the riblets surface. It is found that riblets (1) slightly reduce the wall fluctuating pressure power spectral density level at the low and high frequency ranges, but cause an increase at the mid frequency range, and (2) reduce the lateral turbulence coherence length scale across a large frequency range. As a result, riblets have the potential to reduce trailing edge noise at the low and high frequency regions. The fundamental mechanism by which riblets reduce the turbulent intensity level inside the boundary layer is investigated by studying the spatio-temporal evolution of turbulent spots, which are commonly regarded as the building blocks of a turbulent boundary layer. In this paper two mechanisms are proposed. First, the enhanced momentum achieved at the becalmed region of each turbulent spot will lead to a reduction in the overall turbulence intensity obtained when turbulent spots merge downstream. Second, the internal turbulence level at the rear part of a turbulent spot can be reduced directly by an enhanced re-laminarisation effect.

Effect of secondary currents on the flow and turbulence in partially filled pipes

Large-eddy simulations of turbulent flow in partially filled pipes are conducted to investigate the effect of secondary currents on the friction factor, first- and second-order statistics and large-scale turbulent motion. The method is validated first and simulated profiles of the mean streamwise velocity, normal stresses and turbulent kinetic energy (TKE) are shown to be in good agreement with experimental data. The secondary flow is stronger in half- and three-quarters full pipes compared with quarter full or fully filled pipe flows, respectively. The origin of the secondary flow is examined by both the TKE budget and the steamwise vorticity equation, providing evidence that secondary currents originate from the corner between the free surface and the pipe walls, which is where turbulence production is larger than the sum of the remaining terms of the TKE budget. An extra source of streamwise vorticity production is found at the free surface near the centreline bisector, due to the two-component asymmetric turbulence there. The occurrence of dispersive stresses (due to secondary currents) reduces the contribution of the turbulent shear stress to the friction factor, which results in a reduction of the total friction factor of flows in half and three-quarters full pipes in comparison to a fully filled pipe flow. Furthermore, the presence of significant secondary currents inhibits very-large-scale motion (VLSM), which in turn reduces the strength and scales of near-wall streaks. Subsequently, near-wall coherent structures generated by streak instability and transient growth are significantly suppressed. The absence of VLSM and less coherent near-wall turbulence structures is supposedly responsible for the drag reduction in partially filled pipe flows relative to a fully filled pipe flow at an equivalent Reynolds number.

Direct numerical simulation of turbulent duct flow with inclined or V-shaped ribs mounted on one wall

In this research, highly disturbed turbulent flow of distinct three-dimensional characteristics in a square duct with inclined or V-shaped ribs mounted on one wall is investigated using direct numerical simulation. The turbulence field is highly sensitive to not only the rib geometry but also the boundary layers developed over the side and top walls. In a cross-stream plane secondary flows appear as large longitudinal vortices in both inclined and V-shaped rib cases due to the confinement of four sidewalls of the square duct. However, owing to the difference in the pattern of cross-stream secondary flow motions, the flow physics is significantly different in these two ribbed duct cases. It is observed that the mean flow structures in the cross-stream directions are asymmetrical in the inclined rib case but symmetrical in the V-shaped rib case, causing substantial differences in the momentum transfer across the spanwise direction. The impacts of rib geometry on near-wall turbulence structures are investigated using vortex identifiers, joint probability density functions between the streamwise and vertical velocity fluctuations, statistical moments of different orders, spatial two-point autocorrelations and velocity spectra. It is found that near the leeward and windward rib faces, the mean inclination angle of turbulence structures in the V-shaped rib case is greater than that of the inclined rib case, which subsequently enhances momentum transport between the ribbed bottom wall and the smooth top wall.

Secondary Flow in Smooth and Rough Turbulent Circular Pipes: Turbulence Kinetic Energy Budgets

Direct Numerical Simulations have been performed for turbulent flow in circular pipes with smooth and corrugated walls. The numerical method, based on second-order finite discretization together with the immersed boundary technique, was validated and applied to various types of flows. The analysis is focused on the turbulence kinetic energy and its budget. Large differences have been found in the near-wall region at low Reynolds number. The change in the near-wall turbulent structures is responsible for increase of drag and turbulence kinetic energy. To investigatselinae the effects of wall corrugations, the velocity fields have been decomposed so as to isolate coherent and incoherent motions. For corrugated walls, we find that coherent motions are strongest for walls covered with square bars aligned with the flow direction. In particular, the coherent contribution is substantial when the bars are spaced apart by a distance larger than their height. Detailed analysis of the turbulence kinetic energy budget shows for this set-up a very different behavior than for the other types of corrugations.

Statistical interpretation of LDA measurements in naturally developing turbulent drag-reducing flow using invariant theory

Turbulent drag reduction by an extremely diluted aqueous solution of polyacrylamide was studied in a fully developed plane channel flow under non-tripped flow conditions allowing the natural development of turbulence presumably from the initially laminar like a flow state. Using laser-Doppler anemometry, all components of the Reynolds stress tensor were measured. This permitted the determination of the turbulence anisotropy and independent invariants of the anisotropy tensor. Introducing a measure for the departure of the Reynolds stress tensor from the statistically axisymmetric state that ensures laminarity, fundamental insights relating the origin of turbulence and turbulent drag reduction were analyzed in light of the measured results and existing databases of direct numerical simulations. The chief mechanism relevant to the onset of turbulence and turbulent drag reduction deduced from analytic considerations involving only kinematic constraints was confirmed by the experimental data. Parametrization of the drag reduction effect in terms of the Deborah number based on turbulence quantities evaluated at the wall supports the deduction of the polymer-turbulence interaction in terms of the elastic properties of the polymer and the near-wall turbulence structure.

Turbulence modulations and drag reduction by inertialess spheroids in turbulent channel flow

Previous studies on nonspherical particle-fluid interaction were mostly confined to tiny fiber-like particles, which were observed to induce turbulence drag reduction. Nevertheless, with the presence of disk-like particles how wall turbulence is modulated and whether drag reduction occurs are still unknown. Motivated by those open questions, we perform two-way coupled direct numerical simulations of inertialess spheroids in a turbulent channel flow with additional particle stresses to account for the feedback from spheroids on the fluid phase. The results demonstrate that tiny disk-like particles can also lead to significant turbulence modulations and drag reduction in wall turbulence. Moreover, the attenuation of turbulent activities and the alteration of turbulence anisotropy are observed in the laden flows. To explain the different performances of drag reduction by fibers and disks in the channel flow, we propose a mechanism by analyzing the modulated near-wall turbulence structures and particle shear stress. We find that the spheroidal particles weaken the quasistreamwise vortices through negative work and, therefore, attenuate the Reynolds shear stress. However, the mean shear stress generated by particles, which is particle shape-dependent, partly compensates for the reduction of Reynolds shear stress and thus affects the efficiency of drag reduction. The present study implies that tiny disk-like particles can be an alternative drag reduction agent applied in wall turbulence.

Differences of turbulence modulation by heavy particles on solid wall and erodible bed surface

In this paper, wall-resolved large-eddy simulation of turbulence, Lagrangian point-force model of particle tracking, and two-way coupling approach are used to simulate the particle-laden flow over a rigid wall. The flow is a turbulent open channel flow with the particle-free friction Reynolds number of Reτ=4200. Together with the simulated results over an erodible bed from Zheng et al. [J. Fluid Mech. 918, 1–27 (2021)], the influence of the lower boundary condition of particle motion with the wall-normal gravity on turbulence modulation is thoroughly compared. It is found that high-inertia (St+=244.5) particles studied in this work moving over a rigid wall increase the mean fluid velocity and the scales of turbulence structures away from the wall, suppress turbulence fluctuations and Reynolds stress, and reduce the scales of turbulence structures near the wall as compared with the particle-free flow. Gravitational settling of particles accounts for most of the changes, and the crossing trajectory caused by particles bouncing near the rigid wall is responsible for the reduction of the scales of the near-wall turbulence structures. On the contrary, the splashing process of particles over the erodible bed leads to the decrease in the mean fluid velocity, the anisotropic variation of turbulent kinetic energy, the shrink of the outer turbulence structure, and the enlargement of the near-wall streaks. The results reveal the significance of the near-wall particle motion (rebound or splashing) on turbulence modulation.

A direct numerical simulation study of flow modulation and turbulent sedimentation in particle-laden downward channel flows

Fully resolved direct numerical simulations of turbulent downward channel flow laden with finite-size spherical particles are performed using the lattice Boltzmann method. Unlike upward particle-laden channel flows, the potential energy of settling particles serves as the driving force in the downward channel flows. Furthermore, the particles have an overall positive slip velocity at the center which causes the lateral hydrodynamic force to drive particles away from the center region. Both changes in the flow driving mechanism and the particle distribution affect the details of turbulence modulation in the downward channel, when compared to the upward channel flow. In this study, we focus on the effect of different particle terminal velocities, i.e., different particle settling Reynolds numbers, on the turbulent modulation of particle-laden downward channel flows. Indeed, the simulation results for downward channel flow show larger local particle concentration in the near-wall region, relative to the upward channel. It is also found that the level of particle near-wall accumulation increases with the particle terminal velocity. Opposite to the upward channel flows, the fluid-phase mean velocity in the downward channel flows is increased by heavy particles in the channel center, but reduced in the buffer layer. The reduction of mean velocity in the buffer layer is caused by the particle accumulation in low-speed streak regions. For the largest particle settling Reynolds number case (ReT = 30) investigated, strong accumulation of particles in the buffer layer interrupts the near-wall turbulence structures and thus leads to the reductions of fluid turbulence intensity and Reynolds stress.

Effects of shear-thinning rheology on near-wall turbulent structures

Turbulent channel flow simulation of a shear-thinning fluid is considered – see Arosemena et al. (J. Fluid Mech., vol. 908, 2021, p. A43) – and compared with a Newtonian base case to reveal the effects of the shear-dependent rheology on the near-wall structures. Analyses of different flow statistics revealed that, for the shear-thinning fluid case, the streamwise vortices appear to grow in size, depart from the wall and present a lessening in their intensity. Information regarding variations in the quasi-longitudinal vortices is also obtained from three-dimensional structures identified through a normalized $Q$-criterion. With shear-thinning rheology, it is shown that the structures are comprised of wall-attached and -detached families which are taller than for a Newtonian fluid. Also, for a given height, the structures appear to be longer, with approximately the same width and overall larger volume for the shear-thinning fluid case; albeit their fractal dimension remains the same when compared to the Newtonian base case. Moreover, it is observed that the number density of vortical structures decreases with shear-thinning fluid behaviour. These observations, in conjunction with the known changes to the longitudinal velocity structures which appear to be less streaky, more spanwise separated and thickened with shear-thinning rheology, strongly suggest that the near-wall self-sustaining process has been disrupted. As we move slightly away from the wall and with shear-thinning behaviour, the local increase in viscosity seems to lead to less energetic vortices whereas the streaks are provided with an additional source of energy due to fluctuations in viscosity.

Composite active drag control in turbulent channel flows

A composite drag control (CDC) combining the opposition (OC) and spanwise opposed wall-jet forcing (SOJF) methods is investigated. A maximum drag reduction of about 33% is obtained for CDC -- much higher than that produced by either individual method (namely, 19% for SOJF and 23% for OC). Flow analysis shows that CDC can take advantage of both OC and SOJF methods to better suppress drag producing near-wall turbulent structures --vortices and streaks. Our results suggest prospects of employing a composite control strategy for effective skin friction drag reduction, particularly at very high Reynolds numbers.

On the scaling of turbulence in a high Reynolds number tidal flow

Abstract

Acoustic pulsation for heat transfer abatement in supersonic channel flow

The impact of periodic pulsation normal to the flow passage on the heat and momentum transport is studied using direct numerical simulations. The selected test case is the fully developed supersonic turbulent flow at Reynolds numbers Reb=ρ¯bU¯bδ/μ¯wall=3000 and 6000 and Mach number Mcl=U¯cl/c¯cl≈1.5, bounded by isothermal walls. The pulsation is introduced by imposing a time-periodic uniform body-force in the spanwise directions, mimicking two acoustic drivers placed on the side-walls that are operating with a 180° phase difference. Results indicate that the spanwise pulsation at a moderate forcing amplitude, with the spanwise velocity oscillation amplitude W̃cl≈12% of bulk streamwise velocity or W̃cl+=W̃cl/uτ≈2, can create about 8% reduction in the Nusselt number (Nu), as well as in the skin friction coefficient (Cf), if applied at the optimal pulsation period T+=Tuτ2/ν¯wall within [173, 346], where T=2π/ωf. The excitation outside this band fails to achieve such high levels of modulations in heat and momentum transport processes near the walls. Visualizing the instantaneous temperature field reveals a periodic tilting of the near-wall turbulent structures that is translated into a decay in the energy of the streamwise vortices and an increase in the mean spanwise distance of such structures. The effect of the excitation on reducing the turbulent heat flux and Reynolds shear stress is studied, and the resulting streaming temperature and velocity profiles are discussed.