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Register a new userDirect numerical simulations of Taylor--Couette turbulence: the effect of sand grain roughness
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Progress in roughness research, mapping any given roughness geometry to its fluid dynamic behaviour, has been hampered by the lack of accurate and direct measurements of skin-friction drag, especially in open systems. The Taylor--Couette (TC) system has the benefit of being a closed system, but its potential for characterizing irregular, realistic, 3-D roughness has not been previously considered in depth. Here, we present direct numerical simulations (DNSs) of TC turbulence with sand grain roughness mounted on the inner cylinder. The model proposed by Scotti (textit{Phys. Fluids}, vol. 18, 031701, 2006) has been improved to simulate a random rough surface of monodisperse sand grains, which is characterized by the equivalent sand grain height $k_s$. Taylor numbers range from $Ta = 1.0times 10^7$(corresponding to $Re_tau = 82$) to $Ta = 1.0times 10^9$($Re_tau = 635$). We focus on the influence of the roughness height $k_s^+$ in the transitionally rough regime, through simulations of TC with rough surfaces, ranging from $k_s^+=5$ up to $k_s^+ = 92$, where the superscript `$+$ indicates non-dimensionalization in viscous units. We find that the downwards shift of the logarithmic layer, due to transitionally rough sand grains exhibits remarkably similar behavior to that of the Nikuradse (textit{VDI-Forschungsheft} 361, 1933) data of sand grain roughness in pipe flow, regardless of the Taylor number dependent constants of the logarithmic layer.
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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.
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.
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 $0.47leq tilde{s}=s/d leq 1.23$, where $d$ is the gap width. Experimentally, we explore $text{Ta}=mathcal{O}(10^{12})$ and $0.61leq tilde s leq 3.74$. 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.
We study periodically driven Taylor-Couette turbulence, i.e. the flow confined between two concentric, independently rotating cylinders. Here, the inner cylinder is driven sinusoidally while the outer cylinder is kept at rest (time-averaged Reynolds number is $Re_i = 5 times 10^5$). Using particle image velocimetry (PIV), we measure the velocity over a wide range of modulation periods, corresponding to a change in Womersley number in the range $15 leq Wo leq 114$. To understand how the flow responds to a given modulation, we calculate the phase delay and amplitude response of the azimuthal velocity. In agreement with earlier theoretical and numerical work, we find that for large modulation periods the system follows the given modulation of the driving, i.e. the system behaves quasi-stationary. For smaller modulation periods, the flow cannot follow the modulation, and the flow velocity responds with a phase delay and a smaller amplitude response to the given modulation. If we compare our results with numerical and theoretical results for the laminar case, we find that the scalings of the phase delay and the amplitude response are similar. However, the local response in the bulk of the flow is independent of the distance to the modulated boundary. Apparently, the turbulent mixing is strong enough to prevent the flow from having radius-dependent responses to the given modulation.
Recent studies have brought into question the view that at sufficiently high Reynolds number turbulence is an asymptotic state. We present the first direct observation of the decay of turbulent states in Taylor-Couette flow with lifetimes spanning five orders of magnitude. We also show that there is a regime where Taylor-Couette flow shares many of the decay characteristics observed in other shear flows, including Poisson statistics and the coexistence of laminar and turbulent patches. Our data suggest that characteristic decay times increase super-exponentially with increasing Reynolds number but remain bounded in agreement with the most recent data from pipe flow and with a recent theoretical model. This suggests that, contrary to the prevailing view, turbulence in linearly stable shear flows may be generically transient.
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