Pulsatile flow in a rotating straight pipe: I. Analysis of the fluid motion inside a nutation fluid damper

Abstract

Rigorous analysis shows that the spin synchronous mode fluid motion inside a nutation fluid damper on board of a spinning satellite can be modeled as an incompressible, laminar pulsatile flow in a circular straight pipe. The pipe rotates with constant angular velocity ω_ about an axis perpendicular to its own axis. The distance between the rotation axis and the pipe axis is much greater than a, the pipe’s radius. The flow is driven by a three-dimensional harmonic oscillation of the pipe wall with frequency Ω and amplitude w′0, and is governed by three-dimensionless parameters: RΩ(=Ωa2/ν), Δ(=ω/Ω), and A( = w′0/Ωa), where ν is the kinematic viscosity of the fluid. Both the asymptotic analysis and the numerical calculation have been carried out for RΩ=0.1–1000 and Δ=0–2 under A≪1. It is found that the rotating effect increases the energy dissipation significantly in comparison with the result of the pulsatile straight pipe flow in an inertia frame (the previous theory for the nutation damper). For Δ=1.5, the energy dissipation in a rotating pipe flow is 5.43 times that in a ‘‘stationary’’ pipe flow for large RΩ, which agrees with the previous experiment. A steady stream is induced by the convective effect for finite values of A. Such steady motion is consisted of axial counter flows together with pairs of counter-rotating vortices in the cross-sectional plane.