Flow rate determination in a connected system with rotating bed reactors
Short video of a coloured dye front moving in a transparent liquid through a pipe connecting an external rotating bed reactor to a larger vessel. The total convective flow rate was calculated to 440 L/h based on linear progression of the dye and assuming steady state turbulent conditions at Reynolds number 7900.
Conditions: A water filled (2 L) connected system consisting of a tank (1 L) to which an external flower baffled vessel (200 mL) was connected via pipes (24.6 mm ID). A SpinChem® rotating bed reactor (RBR) S221 filled with activated carbon (28 mL, 20-50 mesh) was placed in the external vessel and started rotating at 1000 rpm. Maximum velocity (Umax) in the middle of the bottom horizontal pipe was measured by following the movement of methylene blue (1 mL, 40 mg) by means of counting video frames, yielding a linear flow of 0.32 m/s. From the linear flow rate and the kinematic viscosity of water at 20 °C, Reynolds number in the pipe was calculated to 7900, indicating a predominantly turbulent flow for which the velocity profile is represented by U=Umax(1-r/R)1/7, where R is the pipe radius and r is the position from the centre. Numerical integration of this expression over the cross section of the pipe using the quadrature package in SciPy yielded the determined total flow rate. Note that this is an conservative estimate assuming steady state turbulent conditions which might not yet have established shortly after turning on the overhead stirrer. References: Flud mechanics and transfer processes, J.M. Kay, R.M. Nedderman, Cambridge University Press, Cambridge, 1985.