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The direct numerical simulation of an accelerating boundary layer over a rough wall has been carried out to investigate the coupling between the effects of roughness and strong freestream acceleration. While the favourable pressure gradient is sufficient to achieve quasi-laminarization on the smooth wall, on the rough wall the flow reversion is prevented, and higher friction coefficient, faster increase of turbulence intensity compared to the freestream velocity, and more isotropic turbulence near the wall are observed. The logarithmic region of the mean-velocity profile presents an initial decrease in slope as in the smooth case, but soon recovers, as the fully rough regime is reached and a new overlap region is established. A strong coupling between the roughness and acceleration effects develops as roughness leads to more responsive turbulence and prevents the strong acceleration from stabilizing the turbulence, and the acceleration intensifies the velocity scale of the wake field (i.e., the near-wall spatial heterogeneity of the time-averaged velocity distribution). The combined effect is a “rougher” surface as the flow accelerates. In addition, the link between the local values of the freestream and the near-wall velocity depends on the flow history; this explains the different flow responses observed in previous studies, in terms of friction coefficient, turbulent kinetic energy, and Reynolds stress anisotropy. This study elucidates the near-wall flow dynamics, which may be used to explain other non-canonical flows over rough walls.

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... On the suction side, the tripping is always located at x = 0.1c regardless of the angle of attack, while on the pressure side it is at x = 0.1c for the 0 • , 2 • and 5 • angles of attack and at x = 0.25c for α = 10 • . This change in the tripping location on the pressure side of the periodic wing at α = 10 • was necessary since the acceleration parameter K = (ν/U 2 e ) dU e /dx (where U e is the velocity at the boundary layer edge) far exceeded the rule-of-thumb value of (2.5-3) × 10 −6 for relaminarisation (Spalart 1986;Yuan & Piomelli 2015) and the added energy in the tripping region was dissipated before generating turbulence. While this relaminarisation was only present in the periodic case, an early decision was made to match the location of the trip for finite-and infinite-span wings at the same geometric angle of attack α. ...

High-fidelity simulations are conducted to investigate the turbulent boundary layers around a finite-span NACA0012 wing with a rounded wing-tip geometry at a chord-based Reynolds number of $Re_c=200\,000$ and at various angles of attack up to $10^\circ$ . The study aims to discern the differences between the boundary layers on the finite-span wing and those on infinite-span wings at equivalent angles of attack. The finite-span boundary layers exhibit: (i) an altered streamwise and a non-zero spanwise pressure gradient as a result of the variable downwash induced by the wing-tip vortices (an inviscid effect typical of finite-span wings); (ii) differences in the flow history at different wall-normal distances, caused by the variable flow angle in the wall-normal direction (due to constant pressure gradients and variable momentum normal to the wall); (iii) laminar flow entrainment into the turbulent boundary layers near the wing tip (due to a laminar–turbulent interface); and (iv) variations in boundary layer thickness across the span, attributed to the variable wall-normal velocity in that direction (a primarily inviscid effect). These physical effects are then used to explain the differences in the Reynolds stress profiles and other boundary layer quantities, including the reduced near-wall peak of the streamwise Reynolds stress and the elevated Reynolds stress levels near the boundary layer edge, both observed in the finite-span wings. Other aspects of the flow, such as the downstream development of wing-tip vortices and their interactions with the surrounding flow, are reserved for future investigations.

... The Poisson equation is solved directly via Fourier expansions in the spanwise direction (in which the spacing is uniform) followed by a fast cosine-transform in the streamwise direction, and a direct solver for the resulting tridiagonal matrix in the wall-normal direction. The code is parallelised using the message-passing interface (MPI) and has been thoroughly validated and previously applied to similar cases (Keating et al. 2004;Yuan & Piomelli 2015;Wu & Piomelli 2018). Figure 1 shows the computational domain, of dimensions L ...

The large-eddy simulation technique was used to investigate the dynamics of unsteady flow separation on a flat-plate turbulent boundary layer. The unsteadiness was generated by imposing an oscillating, wall-normal velocity profile at the top of the computational domain, and a range of reduced frequencies (k), from a very rapid flutter-like motion to a slow quasi-steady oscillation, was studied. Ambrogi et al. (J. Fluid Mech., vol. 945, 2022, A10) showed that the reduced frequency greatly affects the transient separation process, and at a frequency k = 1, the separation region became unstable and was advected periodically out of the domain. In this paper, we discuss the causes of the observed advection process and the effects of the unsteadiness on the second moments. The time evolution of turbulent kinetic energy, for instance, reveals that an advection-like phenomenon is also present at a very low reduced frequency, but its dynamic behaviour is completely different from that of the intermediate frequency (k = 1). At the intermediate frequency the entire recirculation region is advected downstream, keeping its shape. The advected structure is rotational in nature, and moves at constant speed. In contrast, in the low-frequency case the advected fluid originates at the reattachment point, and the structure is shear-dominated. Particle pathlines reflect the fact that the flow at the low frequency is quasi-steady-state, but show peculiar differences at the intermediate frequency, in which the flow response to the freestream forcing depends on the particle positions in the wall-normal direction.

... rough surface and the overlying boundary layer flow is still under investigation, but rough wall flows show certain simplifications that aid in their understanding and modeling, most notably Townsend's Outer Layer Reynolds Number Similarity Hypothesis, which states that the effect of the roughness is confined to the very-near-wall region (beneath the canopy, within a few roughness heights of the wall), and the boundary layer above will otherwise show Reynolds number similarity [9], for which there is a great deal of evidence [10,8,11]. The effects of pressure gradient on rough wall flows differ only slightly from those on smooth walls; adverse (increasing) pressure gradient (APG) thickens and intensifies the boundary layer, pushing it towards separation [12,13,14] while favorable (decreasing) pressure gradient (FPG) compresses the boundary layer and pushes the turbulence towards re-laminarization; however, in a rough wall flow full re-laminarization is not possible as the acceleration of the flow at the roughness canopy intensifies the near-wall turbulence and effectively makes the flow "rougher" [15,16,17,18]. ...

Models for surface pressure spectra beneath rough wall boundary layers are assessed, with particular emphasis on prediction from steady, Reynolds-Averaged-Navier-Stokes (RANS) data. RANS roughness boundary conditions are shown to have qualitatively good trends between roughness function and roughness Reynolds number, but model-to-model discrepancies remain and the universality of an equivalent sandgrain roughness height for turbulence models is doubtful. Existing empirical models for the surface pressure spectrum show good agreement in some spectral regions and a newly proposed model shows good matching across the spectrum in a variety of pressure gradient conditions. Adjustments are made to existing TNO analytical models to incorporate rough wall effects, including changes to the velocity spectrum model and the inclusion of a wall-shift, shown to be independent of local Reynolds number, pressure gradient, or turbulence model. The mathematical character of the rough wall spectrum has been revealed, but challenges remain to implement both flow and spectral modeling without a priori knowledge of the flow.

... Bourassa and Thomas (2009) related such reverse transition processes to the stabilizing effects of acceleration on near-wall streaky structures caused by the decrease of the wall-normal and spanwise fluctuations, which have been shown to be responsible for the instability of streaks and near-wall vortices (Jiménez and Pinelli, 1999). Piomelli and Yuan (2013) and Yuan and Piomelli (2015a) explained that such a process is the result of diminished redistribution of turbulence kinetic energy (TKE) into wall-normal and spanwise fluctuations, as the pressure fluctuations rapidly decrease with the mean-flow acceleration. On the other hand, prevention of quasi-laminarization has been observed in flow over a rough wall, as the roughness augments the wall-normal and spanwise fluctuations, acting to oppose the stabilizing effect of acceleration. ...

Non-equilibrium wall bounded turbulence and associated noise generation.

Direct numerical simulations of oscillatory flow over a bed made of ripples have been performed. Two oscillatory flow forcing mechanisms have been compared: (i) a sinusoidal external pressure gradient (pressure-driven flow); and (ii) a sinusoidal velocity boundary conditions on the rippled bed (shear-driven flow). In the second case, the oscillations of the bed are such that when observed from a reference frame fixed with the bed, the free stream follows the same harmonic oscillation as in the pressure-driven case. While the outer layers have the same dynamics in the two cases, close to the bed differences are observed during the cycle, mostly because the large form drag across the ripples cannot be reproduced in the shear-driven case. A comparison against experimental data from an oscillating tray apparatus provides a relatively good agreement for the phase-averaged flow when the same forcing is considered (i.e. a shear-driven flow). The pressure-driven case has a comparable error to the shear-driven numerical results over the crest of the ripples, whereas the discrepancy is larger at the troughs. The discrepancies between the two cases are more limited for time-averaged flow quantities, such as the mean flow pattern and the time-averaged Reynolds stress distribution. This suggests that numerical or experimental shear-driven configurations may capture well the net effects of coastal transport processes (which occur in pressure-driven oscillatory flow), but care should be exercised in interpreting phase-dependent dynamics near the troughs. More work is needed to fully assess the sensitivity to the forcing mechanisms in different flow regimes.

Unsteady flow separation of a turbulent boundary layer under dynamic pressure gradients is investigated using the Large-Eddy Simulation technique. The unsteadiness is introduced by prescribing an oscillating freestream vertical-velocity profile at the top boundary of the domain. Although previous studies, including Ambrogi et al. (Journal of Fluid Mechanics, Vol. 945, Aug. 2022, p. A10) and Ambrogi et al. (Journal of Fluid Mechanics, Vol. 972, Oct. 2023, p. A36), focused on the kinematics of the flow and the effects of the oscillation frequency on flow separation, the goal of this paper is to analyze the effects of three time-varying freestream-forcing profiles while the oscillation frequency is kept the same for all Cases. Whereas in Case A the freestream-velocity profile changes from suction–blowing to blowing–suction in a complete cycle, Cases B and C are both suction–blowing only and the strength of the adverse pressure gradient is modulated in time. Moreover, the boundary layer in Case B never approaches a zero-pressure gradient condition. A closed separation bubble is formed for all Cases; however, its dimensions change depending on the far-field forcing. The time evolution of turbulent kinetic energy (TKE) reveals an advection mechanism of turbulent structures out of the domain for all Cases. Whereas in Case A and C the high-TKE region, generated in the separated shear layer, is washed out of the domain as a rigid body, in Case B the separation bubble remains present and the advection mechanism of TKE is characterized by a breathing pattern.

Pressure-induced flow separation, which occurs in the presence of a strong adverse pressure gradient, is very common in many physical systems, ranging from the medical field, to engineering applications, to the natural sciences. In most of the practical applications the pressure gradient varies both spatially and temporally giving rise to a transient separation process often associated with a drop in performance of many systems (e.g. wings, turbomachinery).

Trans-critical CO 2 Rankine cycle has great potential in converting low-grade heat into electricity, because of its good temperature glide matching between working medium and heat source. However, the drastic variation in thermo-physical properties of CO 2 around the pseudo-critical region causes the abnormal flow and heat transfer behaviors. In this paper, the heat transfer deterioration and thermal oscillation in the heat addition of trans-critical CO 2 cycle are investigated by experiments. The test section is heated uniformly by a DC power (0~6 kW) and the minimum Reynolds number in the test section inlet is about 8000 (it is much larger than 2300) for the all cases. A shear stress reconstruction model is corrected by introducing the velocity profile of turbulence in the boundary layer to attempt to provide a quantitative criterion for deterioration and oscillation. The role of buoyancy and thermal acceleration in heat transfer deterioration and thermal oscillation is elucidated by connecting the shearing-stress reconstruction model and experimental results. It is found that, the thermal acceleration in the near-wall zone provides the key motivation to drive the heat transfer deterioration. The thermal oscillation is driven by the transition between partial and full re-laminarization flows in the local zone of heat transfer deterioration. When (Δτ a /τ w) < 1&(Δτ/τ w) tot > 1 or 0.1 < (Δτ/τ w) tot < 1, the turbulence is partially re-laminarized. When(Δτ a /τ w) > 1&(Δτ a /τ w) >> (Δτ bo /τ w), the intense thermal acceleration causes the turbulence to be fully re-laminarized in the near-wall zone and it maintains the new laminar boundary. The turbulence is partially re-laminarized in the lower boundary and it is almost full re-laminarization in the upper boundary of the oscillation wall temperatures. The results confirm that the emergence of heat transfer deterioration and oscillation instability in mixed turbulent convective relate with the change of flow states caused by acceleration and buoyancy effects.

Unsteady separation is a phenomenon that occurs in many flows and results in increased drag, decreased lift, noise emission, and loss of efficiency or failure in flow devices. Turbulence models for the steady or unsteady Reynolds-averaged Navier-Stokes equations (RANS and URANS, respectively) are commonly used in industry; however, their performance is often unsatisfactory. The comparison of RANS results with experimental data does not clearly isolate the modeling errors, since differences with the data may be due to a combination of modeling and numerical errors, and also to possible differences in the boundary conditions. In the present study, we use high-fidelity large-eddy simulation (LES) results to carry out a consistent evaluation of the turbulence models. By using the same numerical scheme and boundary conditions as the LES, and a grid on which grid convergence was achieved, we can isolate modeling errors. The calculations (both LES and RANS) are carried out using a well-validated, second-order-accurate code. Separation is generated by imposing a freestream velocity distribution, that is modulated in time. We examined three frequencies (a rapid, flutter-like oscillation, an intermediate one in which the forcing and the flow have the same timescales, and a quasi-steady one). We also considered three different pressure distributions, one with alternating favorable and adverse pressure gradients (FPGs and APGs, respectively), one oscillating between an APG and a zero-pressure gradient (ZPG), and one with an oscillating APG. All turbulence models capture the general features of this complex unsteady flow as well or better than in similar steady cases. The presence, during the cycle, of times in which the freestream pressure-gradient is close to zero affects significantly the model performance. Comparing our results with those in the literature indicates that numerical errors due to the type of discretization and the grid resolution are as significant as those due to the turbulence model.

The physics of the roughness sublayer are studied by direct numerical simulations (DNS) of an open-channel flow with sandgrain roughness. A double-averaging (DA) approach is used to separate the spatial variations of the time-averaged quantities and the turbulent fluctuations. The spatial inhomogeneity of velocity and Reynolds stresses results in an additional production term for the turbulent kinetic energy (TKE) – the ‘wake production’; it is the excess wake kinetic energy (WKE), generated from the work of mean flow against the form drag, that is not directly dissipated into heat, but instead converted into turbulence. The wake production promotes wall-normal turbulent fluctuations and increases the pressure work, which ultimately leads to more homogeneous turbulence in the roughness sublayer, and to the increase of Reynolds shear stress and the drag on the rough wall. In the fully rough regime, roughness directly affects the generation of the wall-normal fluctuations, while in the transitionally rough regime, the region affected by roughness is separated from the region of intense generation of these fluctuations. The budget of the WKE and the connection between the wake and the turbulence suggest strong interactions between the roughness sublayer and the outer layer that are insensitive to the variation of the outer-layer conditions. Furthermore, the present results may have implications for the relationship between the roughness geometry and the flow dynamics in the region directly affected by roughness.

Large-eddy simulations are carried out in turbulent open-channel flows to determine the roughness function and the equivalent sand-grain roughness height, ks, over sand-grain roughness and different types of realistic roughness replicated from hydraulic turbine blades. A range of Reynolds numbers and mean roughness heights is chosen, leading to both transitionally and fully rough regimes. The start of the fully rough regime is shown to depend on the roughness type, and ks depends strongly on the surface topography. We then examine several existing correlations that predict ks based on the information of the surface geometry. In the cases where the surface slope is an important parameter, the moments of surface height statistics do not predict the roughness function, while the existing forms of slope-based correlations perform well. The range of applicability of various correlations is shown to vary with the roughness topography, as the critical value of the effective slope, separating the waviness and roughness regimes, is shown to be higher for a realistic surface, compared to the value for the more regular types of roughness that were previously studied.

This study investigates the effects of fluctuating pressure gradients on boundary layer turbulence. Two-dimensional (2D) time resolved particle image velocimetry (PIV) measurements have been performed in a zero pressure gradient (ZPG) boundary layer. The streamwise and wall-normal (x, y) components of the fluid material acceleration (Du/Dt and Dv/Dt, respectively) are integrated spatially to obtain the pressure distributions. Large scale pressure fluctuation gradients are found to involve three dimensional flow structures. Ejections, high wall-normal enstrophy flux, and viscous vorticity production occur mostly during periods of ∂p′/∂x < 0 as the fluid accelerates by moving away from the wall. Conversely, fluctuating adverse pressure gradients (∂p′/∂x > 0) are preferentially associated with sweeps, as fluid approaching the wall is decelerating. Consequently, the outward transport of small-scale turbulence is suppressed, and the near-wall enstrophy increases. The instability of the flow associated with the adverse pressure gradients might also contribute to the increased production of near-wall turbulence. Results also indicate that the regions of fluctuating adverse and favorable pressure gradients are likely to be associated with the downwash and upwash sides, respectively, of very large scale roller structures, several boundary layer thicknesses in length.

Turbulent sink flows over smooth or rough walls with sand-grain roughness are studied using large-eddy and direct numerical simulations. Mild and strong levels of acceleration are applied, yielding a wide range of Reynolds number (Reθ = 372 - 2748) and cases close to the reverse-transitional state. Flow acceleration and roughness are shown to exert opposite effects on boundary-layer integral parameters, on the Reynolds stresses, budgets of turbulent kinetic energy, and properties of turbulent structures in the vicinity of the rough surface; statistics exhibit similarity when plotted using inner scaling for cases with the same roughness Reynolds number, k+. Acceleration leads to a decrease of k+, while roughness increases it. For cases with higher k+, the low-speed streaks become destabilized, and turbulent structures near the wall are distributed more uniformly in the wall-parallel plane; they are less extended in the streamwise direction, but more densely packed. Higher k+ also causes decorrelation of the outer-layer hairpin packets with the near-wall structures, probably due to the direct impact of random roughness elements on the hairpin legs. Wall-similarity applies for the fully turbulent cases, in which the outer-layer turbulent statistics are affected by acceleration only. It is shown that being in the hydraulically smooth regime is a necessary condition for reverse-transition, supporting the idea that relaminarization starts from the inner region, where roughness effects dominate.

This paper reports an experimental study of favorable pressure gradient turbulent flow over transverse square ribs in an open channel. The first half of the channel test section has straight parallel side walls, and each of the side walls of the second half of the test section converges linearly to produce the favorable pressure gradient. Two different values of half-angle (a = 1° and 2°) of the converging side walls were used to vary the pressure gradient. For each value of a, transverse square ribs were glued onto the bottom wall both upstream of and within the converging sections. The pitch-to-height ratio of the ribs was varied to produce d-type, intermediate and k-type rib roughness. A particle image velocimetry was used to conduct detailed measurements over the ribs at several planes upstream of and within the converging sections. From these measurements, mean velocities and turbulent quantities were extracted at selected streamwise locations. The distributions of the mean velocities, turbulent intensities, and the mean and turbulent momentum fluxes at the interface between the rib cavities and the overlying boundary layer were used to provide insight into the interaction between the shear layers. The profiles of mean velocity, turbulent intensities, Reynolds shear stress and triple products were obtained to document the characteristics of favorable pressure gradient turbulent flow over square ribs in an open channel.

In this study we focus on the effect of mean and fluctuating pressure gradients on the structure of boundary layer turbulence. Two dimensional, time-resolved PIV measurements have been performed upstream of and inside an accelerating sink flow for inlet Reynolds number of Reθ = 3071, and acceleration parameter of Display FormulaK=1.1×10−6. The time-resolved data enables us to calculate the planer projection of pressure gradient by integrating the in-plane components of the material acceleration of the fluid (neglecting out-of-plane contribution). We use it to study the effect of boundary layer scale fluctuating pressure gradients Display Formula∂p′~/∂x, which are expected to be mostly two-dimensional, on the flow structure. Due to the imposed mean favorable pressure gradient (FPG) within the sink flow, the Reynolds stresses normalized by the local freestream velocity decrease over the entire boundary layer. However, when scaled by the inlet freestream velocity, the stresses increase close to the wall and decrease in the outer part of the boundary layer. This trend is caused by the confinement of the newly generated vortical structures in the near-wall region of the accelerating flow due to combined effects of downward mean flow, and stretching by velocity gradients.Within both the zero pressure gradient (ZPG) and FPG boundary layers, sweeping motions mostly occur during positive fluctuating pressure gradients Display Formula∂p′~/∂x>0 as the fluid moving towards the wall is decelerated by the presence of the wall. Vorticity is depleted in the near-wall region, as the wall absorbs Display Formula−ω′ from the flow by viscous diffusion. On the other hand, ejections occur mostly during periods of favorable fluctuating pressure gradients Display Formula∂p′~/∂x