Inertial flow transitions of a suspension in Taylor–Couette geometry

Abstract

Experiments on the inertial flow transitions of a particle–fluid suspension in the concentric cylinder (Taylor–Couette) flow with rotating inner cylinder and stationary outer cylinder are reported. The radius ratio of the apparatus was $\unicode[STIX]{x1D702}=d_{i}/d_{o}=0.877$, where $d_{i}$ and $d_{o}$ are the diameters of inner and outer cylinders. The ratio of the axial length to the radial gap of the annulus $\unicode[STIX]{x1D6E4}=L/\unicode[STIX]{x1D6FF}=20.5$, where $\unicode[STIX]{x1D6FF}=(d_{o}-d_{i})/2$. The suspensions are formed of non-Brownian particles of equal density to the suspending fluid, of two sizes such that the ratio of annular gap to the mean particle diameter $d_{p}$ was either $\unicode[STIX]{x1D6FC}=\unicode[STIX]{x1D6FF}/d_{p}=30$ or $100$. For the experiments with $\unicode[STIX]{x1D6FC}=100$, the particle volume fraction was $\unicode[STIX]{x1D719}=0.10$ and for the experiments with $\unicode[STIX]{x1D6FC}=30$, $\unicode[STIX]{x1D719}$ was varied over $0\leqslant \unicode[STIX]{x1D719}\leqslant 0.30$. The focus of the work is on determining the influence of particle loading and size on inertial flow transitions. The primary effects of the particles were a reduction of the maximum Reynolds number for the circular Couette flow (CCF) and several non-axisymmetric flow states not seen for a pure fluid with only inner cylinder rotation; here the Reynolds number is $Re=\unicode[STIX]{x1D6FF}d_{i}\unicode[STIX]{x1D6FA}\unicode[STIX]{x1D70C}/2\unicode[STIX]{x1D707}_{s}$, where $\unicode[STIX]{x1D6FA}$ is the rotation rate of the inner cylinder and $\unicode[STIX]{x1D70C}$ and $\unicode[STIX]{x1D707}_{s}$ are the density and effective viscosity of the suspension. For purposes of maintaining uniform particle distribution, the rotation rate of the inner cylinder (or $Re$) was decreased slowly from a state other than CCF to probe the transitions. When $Re$ was decreased, pure fluid transitions from wavy Taylor vortex flow (WTV) to Taylor vortex flow (TVF) to CCF occurred. The suspension transitions differed. For $\unicode[STIX]{x1D6FC}=30$ and $0.05\leqslant \unicode[STIX]{x1D719}\leqslant 0.15$, with reduction of $Re$, additional non-axisymmetric flow states, namely spiral vortex flow (SVF) and ribbons (RIB), were observed between TVF and CCF. At $\unicode[STIX]{x1D719}=0.30$, the flow transitions observed were only non-axisymmetric: from wavy spiral vortices (WSV) to SVF to CCF. The values of $Re$ corresponding to each flow transition were observed to reduce with increase in particle loading for $0\leqslant \unicode[STIX]{x1D719}\leqslant 0.30$, with the initial transition away from CCF, for example, occurring at $Re\approx 120$ for the pure fluid and $Re\approx 75$ for the $\unicode[STIX]{x1D719}=0.30$ suspension. When the particle size was reduced to yield $\unicode[STIX]{x1D6FC}=100$, at $\unicode[STIX]{x1D719}=0.10$, only the RIB (and no SVF) was observed between TVF and CCF.