Roughness induced boundary slip in microchannel flows

Surface roughness becomes relevant if typical length scales of the system are comparable to the scale of the variations as it is the case in microfluidic setups. Here, an apparent boundary slip is often detected which can have its origin in the assumption of perfectly smooth boundaries. We investigate the problem by means of lattice Boltzmann (LB) simulations and introduce an ``effective no-slip plane'' at an intermediate position between peaks and valleys of the surface. Our simulations show good agreement with analytical results for sinusoidal boundaries, but can be extended to arbitrary geometries and experimentally obtained surface data. We find that the detected apparent slip is independent of the detailed boundary shape, but only given by the distribution of surface heights. Further, we show that the slip diverges as the amplitude of the roughness increases.Comment: 4 pages, 6 figure

Controlling heat transport and flow structures in thermal turbulence using ratchet surfaces

In this combined experimental and numerical study on thermally driven turbulence in a rectangular cell, the global heat transport and the coherent flow structures are controlled with an asymmetric ratchet-like roughness on the top and bottom plates. We show that, by means of symmetry breaking due to the presence of the ratchet structures on the conducting plates, the orientation of the Large Scale Circulation Roll (LSCR) can be locked to a preferred direction even when the cell is perfectly leveled out. By introducing a small tilt to the system, we show that the LSCR orientation can be tuned and controlled. The two different orientations of LSCR give two quite different heat transport efficiencies, indicating that heat transport is sensitive to the LSCR direction over the asymmetric roughness structure. Through a quantitative analysis of the dynamics of thermal plume emissions and the orientation of the LSCR over the asymmetric structure, we provide a physical explanation for these findings. The current work has important implications for passive and active flow control in engineering, bio-fluid dynamics, and geophysical flows.Comment: 5 pages, 5 figures, Physical Review Letters (in Press

The Wall-Jet Region of a Turbulent Jet Impinging on Smooth and Rough Plates

The study reports direct numerical simulations of a turbulent jet impinging onto smooth and rough surfaces at Reynolds number Re = 10,000 (based on the jet mean bulk velocity and diameter). Surface roughness is included in the simulations using an immersed boundary method. The deflection of the flow after jet impingement generates a radial wall-jet that develops parallel to the mean plate surface. The wall-jet is structured into an inner and an outer layer that, in the limit of infinite local Reynolds number, resemble a turbulent boundary layer and a free-shear flow. The investigation assesses the self-similar character of the mean radial velocity and Reynolds stresses profiles scaled by inner and outer layer units for varying size of the roughness topography. Namely the usual viscous units $u_{\tau}$ and $\delta_{\upsilon}$ are used as inner layer scales, while the maximum radial velocity $u_{m}$ and its wall-normal location $z_{m}$ are used as outer layer scales. It is shown that the self-similarity of the mean radial velocity profiles scaled by outer layer units is marginally affected by the span of roughness topographies investigated, as outer layer velocity and length reference scales do not show a significantly modified behavior when surface roughness is considered. On the other hand, the mean radial velocity profiles scaled by inner layer units show a considerable scatter, as the roughness sub-layer determined by the considered roughness topographies extends up to the outer layer of the wall-jet. Nevertheless, the similar character of the velocity profiles appears to be conserved despite the profound impact of surface roughness

Turbulent impinging jets on rough surfaces

This work presents direct numerical simulations (DNS) of a circular turbulent jet impinging on rough plates. The roughness is once resolved through an immersed boundary method (IBM) and once modeled through a parametric forcing approach (PFA) which accounts for surface roughness effects by applying a forcing term into the Navier–Stokes equations within a thin layer in the near-wall region. The DNS with the IBM setup is validated using optical flow field measurements over a smooth and a rough plate with similar statistical surface properties. In the study, IBM-resolved cases are used to show that the PFA is capable of reproducing mean flow features well at large wall-normal distances, while less accurate predictions are observed in the near-wall region. The demarcation between these two regions is approximately identified with the mean wall height of the surface roughness distribution. Based on the observed differences in the results between IBM- and PFA-resolved cases, plausible future improvements of the PFA are suggested

From Rayleigh-B\'enard convection to porous-media convection: how porosity affects heat transfer and flow structure

We perform a numerical study of the heat transfer and flow structure of Rayleigh-B\'enard (RB) convection in (in most cases regular) porous media, which are comprised of circular, solid obstacles located on a square lattice. This study is focused on the role of porosity $\phi$ in the flow properties during the transition process from the traditional RB convection with $\phi=1$ (so no obstacles included) to Darcy-type porous-media convection with $\phi$ approaching 0. Simulations are carried out in a cell with unity aspect ratio, for the Rayleigh number $Ra$ from $10^5$ to $10^{10}$ and varying porosities $\phi$, at a fixed Prandtl number $Pr=4.3$, and we restrict ourselves to the two dimensional case. For fixed $Ra$, the Nusselt number $Nu$ is found to vary non-monotonously as a function of $\phi$; namely, with decreasing $\phi$, it first increases, before it decreases for $\phi$ approaching 0. The non-monotonous behaviour of $Nu(\phi)$ originates from two competing effects of the porous structure on the heat transfer. On the one hand, the flow coherence is enhanced in the porous media, which is beneficial for the heat transfer. On the other hand, the convection is slowed down by the enhanced resistance due to the porous structure, leading to heat transfer reduction. For fixed $\phi$, depending on $Ra$, two different heat transfer regimes are identified, with different effective power-law behaviours of $Nu$ vs $Ra$, namely, a steep one for low $Ra$ when viscosity dominates, and the standard classical one for large $Ra$. The scaling crossover occurs when the thermal boundary layer thickness and the pore scale are comparable. The influences of the porous structure on the temperature and velocity fluctuations, convective heat flux, and energy dissipation rates are analysed, further demonstrating the competing effects of the porous structure to enhance or reduce the heat transfer

Rheological measurements of large particles in high shear rate flows

This paper presents experimental measurements of the rheological behavior of liquid-solid mixtures at moderate Stokes and Reynolds numbers. The experiments were performed in a coaxial rheometer that was designed to minimize the effects of secondary flows. By changing the shear rate, particle size, and liquid viscosity, the Reynolds numbers based on shear rate and particle diameter ranged from 20 to 800 (Stokes numbers from 3 to 90), which is higher than examined in earlier rheometric studies. Prior studies have suggested that as the shear rate is increased, particle-particle collisions also increase resulting in a shear stress that depends non-linearly on the shear rate. However, over the range of conditions that were examined in this study, the shear stress showed a linear dependence on the shear rate. Hence, the effective relative viscosity is independent of the Reynolds and Stokes numbers and a non-linear function of the solid fraction. The present work also includes a series of rough-wall experiments that show the relative effective viscosity is also independent of the shear rate and larger than in the smooth wall experiments. In addition, measurements were made of the near-wall particle velocities, which demonstrate the presence of slip at the wall for the smooth-walled experiments. The depletion layer thickness, a region next to the walls where the solid fraction decreases, was calculated based on these measurements. The relative effective viscosities in the current work are larger than found in low-Reynolds number suspension studies but are comparable with a few granular suspension studies from which the relative effective viscosities can be inferred

High-fidelity simulations of fully submerged, rigid canopy flows

A detailed analysis of turbulent flows in an open channel over rigid submerged canopies, at a moderate bulk Reynolds number (i.e. Reb = UbH=v = 6000, H being the open channel depth and Ub the bulk velocity) has been carried out. Untangling the physical behaviour of these flows can become an impossible task if all the parameters that govern their physics are kept into account, e.g. the density of the layer, the level of submersion of the canopy and the flexibility of the stems, just to mention few of them. Nepf (2012a), after reviewing a number of relevant previous research works on canopy flows in her annual review, suggests to classify the behaviour of the flow by considering the geometrical features of the filamentous layer only. In the case of submerged canopies, based on the solidity of the canopy, three particular regimes are identified: sparse, dense and transitional. While sparse canopies are treated as rough walls, the form drag yielded by the filaments in a dense canopy induces the onset of two inflection points in the mean velocity profile. These two inflection points divide the intra-canopy flow into separate regions: an inner region, very close to the bed, populated by stems generated wakes, an outer region that mainly extends above the canopy and is usually modelled as a flow over a porous/rough wall, and an overlap region (Poggi et al., 2004). The latter can be assumed to behave as a peculiar Couette flow (in the literature it has been also described as a mixing-layer region, see Finnigan, 2000) characterised by large fluctuations produced by the meandering of the flow in between the canopy elements. Finally, the transitional regime can be thought of as a dense regime with a higher penetration of the upper layer flow structures into the canopy, where they concentrate (Nepf, 2012a). Although some phenomenological models for dense canopy regimes are proposed in the literature, they are either based on two dimensional or even local one-dimensional measurements (Ghisalberti and Nepf, 2004, Nepf, 2012a, Poggi et al., 2004, Raupach et al., 1996) or on numerical simulations that adopt simpli- fied canopy models (Bailey and Stoll, 2013, 2016, Finnigan et al., 2009, Watanabe, 2004). In this context, the present thesis provides an accurate and detailed characterisation of canopy flows through a fully resolved, numerical approach tackling rigid, filamentous canopies made of cylindrical stems mounted normally to an impermeable wall. Firstly, a transitional-dense regime has been considered. Specifically, the first part of the thesis provides a novel and detailed insight that includes a new phenomenological model that also covers the character of the flow within the canopy. Moreover, an original scaling for the mean flow quantities is also proposed. The new approach allows highlighting important similarities and simplify the analysis. In the second part of the thesis, a parametric study aimed to investigate the relation between the height of the canopy (i.e. its solidity) and the flow regimes is performed. Specifically, four canopy configurations have been considered. All of them share the same in-plane solid fraction while the canopy to open channel height ratio, h=H, has been selected within the range h=H = [0:05; 0:4]. The lowest and the highest values are representative of a quasi- sparse and a dense canopy regime, respectively. The other two h=H ratios nominally belong to the transitional regime values. The systematic variation of the height of the filamentous layer allowed us to unravel the main features characterising the different regimes. Particular attention has been paid to the relative locations of the two inflection points of the mean velocity profile and the virtual wall origin (origin seen from the outer flow located in the canopy layer). In view of the relative variations of their distance from the wall and the canopy tip, we propose to adopt the crossing between the internal inflection point and the virtual origin as a condition to infer the transition between canopy flow regimes when the solidity is varied. The structures of the different regimes have been also compared, highlighting the role played by the increasing solidity of the canopy as a natural splitter between the logarithmic structures of the outer flow and the coherent structures located inside the canopy. The wall-normal permeability of the canopy is identified as the main vehicle to transfer momentum through the different canopy layers, playing an important role in shaping the structures of the flow within the filamentous layer. Finally, a new scaling that adapts the flow conditions to the sparsity of the canopy is proposed. All the results presented in the thesis have been obtained through fully resolved simulations. To the best of our knowledge, this is the first time that a simulation directly tackles the region occupied by the canopy imposing the zero-velocity condition on every single stem by means of an immersed boundary method, thus overcoming the problem of the canopy modelling. Conversely, the outer flow is dealt with a large-eddy formulation that adopts a state-of-the-art grid independent closure for the unresolved scales of motion (Piomelli et al., 2015, Rouhi et al., 2016). Keywords: canopy flow, scaling, large coherent structures, large-eddy simulation, immersed boundary method