Unsteady unidirectional flow of a Voigt fluid in the circular duct with different prescribed volume flow rate conditions

Abstract

In the present study, the velocity profile and pressure gradient of the unsteady state unidirectional flow of a Voigt fluid in a circular duct with different prescribed volume flow rate are investigated. The flow motion in the duct is induced by a prescribed inlet volume flow rate which varies with time. Based on the flow conditions prescribed, two basic flow situations are solved; these are a suddenly started, and a constant accelerated, flow respectively. These two results are then applied to a practical case that is a trapezoidal motion which contains three phases of piston motion, the constant acceleration from the rest to a fixed velocity, then maintaining at this velocity, following with the constant deceleration to a stop. In addition, oscillatory flow is also considered.