Theoretical analysis of an oscillatory plane Poiseuille flow—A link to the design of vortex flow meter

Abstract

Theoretical analysis on an oscillatory plane Poiseuille flow is conducted in terms of a non-dimensional ratio (η) of the channel half-width to Stokes’ layer thickness. The cyclic velocity profiles, the phase shifts and the magnitudes among the driving pressure gradient, the induced wall shear stress, and the volume flux are investigated. Also, the flow physics at a different ratio η is demonstrated. In this study, the mechanism of the driving pressure gradient and the oscillating volume flux is similar to and can be employed to demonstrate the slit flow in the application of the novel vortex flow meter using a slit cylinder as a shedder. When applied to the novel vortex flow meter, the non-dimensional ratio η can be expressed as the relation of the slit width ratio (S/D), the Strouhal number, and the Reynolds number. Finally, a range of η between 0.97 < η < 20 will be suggested for the vortex flow meter at the design stage. Large values of η are employed at a high Reynolds number, and small η is used for low Reynolds number applications. In the novel vortex flow meters, a cylinder with a normal axial slit of width (S) is employed as the shedder. Due to the primary lock-on, the process of vortex shedding synchronizes with the rhythm of slit flow leading to a stable shedding frequency. The value η is well correlated by the value of ηopt obtained by experiments and shows a one-to-one correspondence to the slit ratio at each Reynolds number. Once the design value of ηopt is determined, the optimal slit ratio can be estimated for a fixed applied Reynolds number at the design stage.