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Register a new userPolymer and surface roughness effects on the drag crisis for falling spheres
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Added by
Jean-Francois Pinton
Publication date
2007
fields
Physics
and research's language is
English
Authors
Nicolas Lyotard
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We make time resolved velocity measurements of steel spheres in free fall through liquid using a continuous ultrasound technique. We explore two different ways to induce large changes in drag on the spheres: 1) a small quantity of viscoelastic polymer added to water and 2) altering the surface of the sphere. Low concentration polymer solutions and/or a pattern of grooves in the sphere surface induce an early drag crisis, which may reduce drag by more than 50 percent compared to smooth spheres in pure water. On the other hand, random surface roughness and/or high concentration polymer solutions reduce drag progressively and suppress the drag crisis. We also present a qualititative argument which ties the drag reduction observed in low concentration polymer solutions to the Weissenberg number and normal stress difference.
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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.
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.
The upper bound of polymer drag reduction is identified as a unique transitional state between laminar and turbulent flow corresponding to the onset of the nonlinear breakdown of flow instabilities.
The impact of wall roughness on fully developed laminar pipe flow is investigated numerically. The roughness is comprised of square bars of varying size and pitch. Results show that the inverse relation between the friction factor and the Reynolds number in smooth pipes still persists in rough pipes, regardless of the rib height and pitch. At a given Reynolds number, the friction factor varies quadratically with roughness height and linearly with roughness pitch. We propose a single correlation for the friction factor that successfully collapses the data.
A new method of accurate calculation of the coefficient of viscosity of a test liquid from experimentally measured terminal velocity of a ball falling in the test liquid contained in a narrow tube is described. The calculation requires the value of a multiplicative correction factor to the apparent coefficient of viscosity calculated by substitution of terminal velocity of the falling ball in Stokes formula. This correction factor, the so-called viscosity ratio, a measure of deviation from Stokes limit, arises from non-vanishing values of the Reynolds number and the ball/tube radius ratio. The method, valid over a very wide range of Reynolds number, is based on the recognition of a relationship between two measures of wall effect, the more widely investigated velocity ratio, defined as the ratio of terminal velocity in a confined medium to that in a boundless medium and viscosity ratio. The calculation uses two recently published correlation formulae based on extensive experimental results on terminal velocity of a falling ball. The first formula relates velocity ratio to Reynolds number and ball-tube radius ratio. The second formula gives an expression of the ratio of the drag force actually sensed by the ball falling in an infinite medium to that in the Stokes limit as a function of Reynolds number alone. It is shown that appropriate use of this correction factor extends the utility of the technique of falling ball viscometry beyond the very low Reynolds number creepy flow regime, to which its application is presently restricted. Issues related to accuracy are examined by use of our own measurements of the terminal velocity of a falling ball in a narrow tube and that of published literature reports, on liquids of known viscosity coefficient.
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