Pressure drop and power dissipation in oscillatory wavy-walled-tube flows

Abstract

Pressure drops occurring in oscillatory viscous flows in wavy-walled tubes have been studied experimentally, for Reynolds numbers up to 1500 and Strouhal numbers in the range 0.005 to 0.02, and by numerical solution of the Navier-Stokes equations, for Reynolds numbers up to 200 and Strouhal numbers between 0.005 and 0.1. Agreement was good for values of the mean modulus of the pressure drop at lower Strouhal numbers and for values of the mean power dissipation at all Strouhal numbers.Numerical solutions have shown that the pressure drop may vary non-sinusoidally, even though the imposed variation in flow rate is sinusoidal. This cannot be explained by the nonlinearity of the steady pressure drop-flow rate relationship, and arises because the velocity field is not quasi-steady. In particular energy may be stored in strong vortices formed during the acceleration phase of the flow cycle, and partially returned to the main flow later. The peak pressure drops in such flows, which are associated with the formation of these vortices, can be almost twice as large as values predicted by adding the appropriate quasi-steady and unsteady inertial contributions. This finding is important in the wider context of unsteady conduit flow.The dependences of the mean modulus of the pressure drop and the mean power dissipation on the Strouhal number and frequency parameter were investigated in detail numerically for two geometries. It was not possible to reduce either dependence to a function of a single parameter. The ‘equivalent’ straight-walled tube for power dissipation was found to have a smaller bore than that for pressure drop, leading to smaller ‘phase angles’ than might have been expected at large values of the frequency parameter. This is because as the pressure drop becomes increasingly dominated by unsteady inertia, there remain relatively large recirculations in which energy is dissipated.