Multiphase wall-bounded turbulence

In many geophysical situations and in all industrial applications, turbulent flows are wall-bounded. Many of these flows are multi-phase, i.e. flows consisting of one or multiple inclusions. The current understanding of these flows is still limited and this makes it important to study them. In this thesis we study these wall-bounded multi-phase flows in two canonical systems: Taylor-Couette flow (TC) and Rayleigh-Bénard convection (RBC). In this work we used spherical and cylindrical particles to investigate if we have reduced skin friction similar to bubbly drag reduction. The global torque measurements showed that these particles barely alter the drag, even at very large particle volume fractions. Surprisingly, we found a preferential alignment for the cylindrical particles with respect to the inner cylinder wall. Using oil and water we are able to create deformable inclusions. Increasing the oil volume fraction over a critical point results in phase inversion with water droplets in oil. In this regime we found drag reduction due to the large water droplets in the flow. This is confirmed with in-situ microscopic imaging. In the last two chapters of this thesis we study the effect of non-homogeneous boundaries in both TC and RBC. Using bands of sandgrain roughness we were able to control the secondary flows in TC. This means that for example roughness like barnacles on the hull of a ship can induce secondary flows that push air bubbles away and thereby, reducing the drag reducing effect

Mixed insulating and conducting thermal boundary conditions in Rayleigh-B\'enard convection

A series of direct numerical simulations of Rayleigh-B\'enard convection, the flow in a fluid layer heated from below and cooled from above, were conducted to investigate the effect of mixed insulating and conducting boundary conditions on convective flows. Rayleigh numbers between $\text{Ra}=10^7$ and $\text{Ra}=10^9$ were considered, for Prandtl numbers $\text{Pr}=1$ and $\text{Pr}=10$. The bottom plate was divided into patterns of conducting and insulating stripes. The size ratio between these stripes was fixed to unity and the total number of stripes was varied. Global quantities such as the heat transport and average bulk temperature and local quantities such as the temperature just below the insulating boundary wall were investigated. For the case with the top boundary divided into two halves, one conducting and one insulating, the heat transfer was found to be approximately two thirds of the fully conducting case. Increasing the pattern frequency increased the heat transfer which asymptotically approached the fully conducting case, even if only half of the surface is conducting. Fourier analysis of the temperature field revealed that the imprinted pattern of the plates is diffused in the thermal boundary layers, and cannot be detected in the bulk. With conducting-insulating patterns on both plates, the trends previously described were similar, however, the half-and-half division led to a heat transfer of about a half of the fully conducting case instead of two-thirds. The effect of the ratio of conducting and insulating areas was also analyzed, and it was found that even for systems with a top plate with only $25\%$ conducting surface, heat-transport of $60\%$ of the fully conducting case can be seen. Changing the 1D stripe pattern to 2D checkerboard tessellations does not result in a significantly different response of the system.Comment: Submitted to JF

Air cavities at the inner cylinder of turbulent Taylor-Couette flow

Air cavities, i.e. air layers developed behind cavitators, are seen as a promising drag reducing method in the maritime industry. Here we utilize the Taylor-Couette (TC) geometry, i.e. the flow between two concentric, independently rotating cylinders, to study the effect of air cavities in this closed setup, which is well-accessible for drag measurements and optical flow visualizations. We show that stable air cavities can be formed, and that the cavity size increases with Reynolds number and void fraction. The streamwise cavity length strongly depends on the axial position due to buoyancy forces acting on the air. Strong secondary flows, which are introduced by a counter-rotating outer cylinder, clearly decrease the stability of the cavities, as air is captured in the Taylor rolls rather than in the cavity. Surprisingly, we observed that local air injection is not necessary to sustain the air cavities; as long as air is present in the system it is found to be captured in the cavity. We show that the drag is decreased significantly as compared to the case without air, but with the geometric modifications imposed on the TC system by the cavitators. As the void fraction increases, the drag of the system is decreased. However, the cavitators itself significantly increase the drag due to their hydrodynamic resistance (pressure drag): In fact, a net drag increase is found when compared to the standard smooth-wall TC case. Therefore, one must first overcome the added drag created by the cavitators before one obtains a net drag reduction.Comment: 14 pages, 13 figure

The influence of wall roughness on bubble drag reduction in Taylor-Couette turbulence

We experimentally study the influence of wall roughness on bubble drag reduction in turbulent Taylor-Couette flow, i.e.\ the flow between two concentric, independently rotating cylinders. We measure the drag in the system for the cases with and without air, and add roughness by installing transverse ribs on either one or both of the cylinders. For the smooth wall case (no ribs) and the case of ribs on the inner cylinder only, we observe strong drag reduction up to $DR=33\%$ and $DR=23\%$, respectively, for a void fraction of $\alpha=6\%$. However, with ribs mounted on both cylinders or on the outer cylinder only, the drag reduction is weak, less than $DR=11\%$, and thus quite close to the trivial effect of reduced effective density. Flow visualizations show that stable turbulent Taylor vortices --- large scale vortical structures --- are induced in these two cases, i.e. the cases with ribs on the outer cylinder. These strong secondary flows move the bubbles away from the boundary layer, making the bubbles less effective than what had previously been observed for the smooth-wall case. Measurements with counter-rotating smooth cylinders, a regime in which pronounced Taylor rolls are also induced, confirm that it is really the Taylor vortices that weaken the bubble drag reduction mechanism. Our findings show that, although bubble drag reduction can indeed be effective for smooth walls, its effect can be spoiled by e.g.\ biofouling and omnipresent wall roughness, as the roughness can induce strong secondary flows.Comment: 10 pages, 5 figure

Controlling secondary flow in Taylor-Couette turbulence through spanwise-varying roughness

Highly turbulent Taylor-Couette flow with spanwise-varying roughness is investigated experimentally and numerically (direct numerical simulations (DNS) with an immersed boundary method (IBM)) to determine the effects of the spacing and axial width $s$ of the spanwise varying roughness on the total drag and {on} the flow structures. We apply sandgrain roughness, in the form of alternating {rough and smooth} bands to the inner cylinder. Numerically, the Taylor number is $\mathcal{O}(10^9)$ and the roughness width is varied between $0.47\leq \tilde{s}=s/d \leq 1.23$, where $d$ is the gap width. Experimentally, we explore $\text{Ta}=\mathcal{O}(10^{12})$ and $0.61\leq \tilde s \leq 3.74$. For both approaches the radius ratio is fixed at $\eta=r_i/r_o = 0.716$, with $r_i$ and $r_o$ the radius of the inner and outer cylinder respectively. We present how the global transport properties and the local flow structures depend on the boundary conditions set by the roughness spacing $\tilde{s}$. Both numerically and experimentally, we find a maximum in the angular momentum transport as function of $\tilde s$. This can be atributed to the re-arrangement of the large-scale structures triggered by the presence of the rough stripes, leading to correspondingly large-scale turbulent vortices.Comment: 20 pages, 7 figures, draft for JF

Rough wall turbulent Taylor-Couette flow: the effect of the rib height

In this study, we combine experiments and direct numerical simulations to investigate the effects of the height of transverse ribs at the walls on both global and local flow properties in turbulent Taylor-Couette flow. We create rib roughness by attaching up to 6 axial obstacles to the surfaces of the cylinders over an extensive range of rib heights, up to blockages of 25% of the gap width. In the asymptotic ultimate regime, where the transport is independent of viscosity, we emperically find that the prefactor of the $Nu_{\omega} \propto Ta^{1/2}$ scaling (corresponding to the drag coefficient $C_f(Re)$ being constant) scales with the number of ribs $N_r$ and by the rib height $h^{1.71}$. The physical mechanism behind this is that the dominant contribution to the torque originates from the pressure forces acting on the rib which scale with rib height. The measured scaling relation of $N_r h^{1.71}$ is slightly smaller than the expected $N_r h^2$ scaling, presumably because the ribs cannot be regarded as completely isolated but interact. In the counter-rotating regime with smooth walls, the momentum transport is increased by turbulent Taylor vortices. We find that also in the presence of transverse ribs these vortices persist. In the counter-rotating regime, even for large roughness heights, the momentum transport is enhanced by these vortices.Comment: 18 pages, 9 figure

Catastrophic phase inversion in high-Reynolds number turbulent Taylor--Couette flow

Emulsions are omnipresent in the food industry, health care, and chemical synthesis. In this Letter the dynamics of meta-stable oil-water emulsions in highly turbulent ($10^{11}\leq\text{Ta}\leq 3\times 10^{13}$) Taylor--Couette flow, far from equilibrium, is investigated. By varying the oil-in-water void fraction, catastrophic phase inversion between oil-in-water and water-in-oil emulsions can be triggered, changing the morphology, including droplet sizes, and rheological properties of the mixture, dramatically. The manifestation of these different states is exemplified by combining global torque measurements and local in-situ laser induced fluorescence (LIF) microscopy imaging. Despite the turbulent state of the flow and the dynamic equilibrium of the oil-water mixture, the global torque response of the system is found to be as if the fluid were Newtonian, and the effective viscosity of the mixture was found to be several times bigger or smaller than either of its constituents.Comment: 5 pages, 4 figure

Effect of axially varying sandpaper roughness on bubbly drag reduction in Taylor-Couette turbulence

We experimentally investigate the influence of alternating rough and smooth walls on bubbly drag reduction (DR). We apply rough sandpaper bands of width $s$ between $48.4\,mm$ and $148.5\,mm$, and roughness height $k = 695\,{\mu}m$, around the smooth inner cylinder (IC) of the Twente Turbulent Taylor-Couette facility. Between sandpaper bands, the IC is left uncovered over similar width $s$, resulting in alternating rough and smooth bands, a constant pattern in axial direction. We measure the DR in water that originates from introducing air bubbles to the fluid at (shear) Reynolds numbers $\textit{Re}_s$ ranging from $0.5 \times 10^6$ to $1.8 \times 10^6$. Results are compared to bubbly DR measurements with a completely smooth IC and an IC that is completely covered with sandpaper of the same roughness $k$. The outer cylinder is left smooth for all variations. Results are also compared to bubbly DR measurements where a smooth outer cylinder is rotating in opposite direction to the smooth IC. This counter rotation induces secondary flow structures that are very similar to those observed when the IC is composed of alternating rough and smooth bands. For the measurements with roughness, the bubbly DR is found to initially increase more strongly with $\textit{Re}_s$, before levelling off to reach a value that no longer depends on $\textit{Re}_s$. This is attributed to a more even axial distribution of the air bubbles, resulting from the increased turbulence intensity of the flow compared to flow over a completely smooth wall at the same $\textit{Re}_s$. The air bubbles are seen to accumulate at the rough wall sections in the flow. Here, locally, the drag is largest and so the drag reducing effect of the bubbles is felt strongest. Therefore, a larger maximum value of bubbly DR is found for the alternating rough and smooth walls compared to the completely rough wall