Simulations of Plano-Taylor-Couette Flow

The flow between moving, parallel plates (plane-Couette) and the flow between concentric, rotating cylinders (Taylor-Couette) represent two canonical fluid flow configurations that have been studied in great detail. Here we use numerical simulations to study the flow between conveyor belts composed of a linear region resembling the plane-Couette geometry, and a curved, corner region resembling the Taylor-Couette geometry. The linear region, of length L, smoothly merges into the circular corners with inner and outer belt curvatures, L / r_i and L / r_o, respectively. This system presents a single geometry that includes zones of two classically studied wall-bounded flows, and allows for a continuous topology transformation between the two limits. For L / r_i  << 1, the system tends to a pure Taylor-Couette flow, while in the other limit of L / r_i  >> 1 the geometry is dominated by the plane-Couette flow. We explore the case of pure inner-belt motion, for which the control parameters are the inner-belt Reynolds Number, Re = r_iω_id / ν and the dimensionless curvature of the corner, κ ≡ L / r_i, where d = r_o - r_i  is the gap between the belts, and ω_i  is the angular speed of the inner belt at the corner. We decompose the total dissipation in the system into contributions from the dimensionless torque and the dimensionless drag for varying L / r_i, for a range of Reynolds numbers at a fixed curvature ratio (or radius ratio). The flow structures in both the linear and the curved regions are evaluated, as well as those in the merging zone.