Abstract
Unsteady flows of a Bingham non-Newtonian fluid through a circular pipe have been studied numerically. These flows are impulsively started from rest via imposing a cyclic pressure gradient having a specific waveform. Triangular, sinusoidal, and square waves were considered, each varying around a non-zero mean value corresponding to the steady-state one. The parameters varied in this study are the amplitude of the time varying pressure gradient (8), Strouhal (St), Reynolds (Re), and Yield (Y) numbers within the following range: 1 < ε < 2, 0.1 < St. Re < 100, & 0 < Y < 10. Effects of these parameters on flow transients and asymptotic, i.e. pulsatile, flow field characteristics are demonstrated. Two relevant time scales are introduced, a momentum diffusion time scale, τυ = ρR2/ηp, and a periodic convective time scale, τc = 2π/ω. Time-averaged characteristics of the pulsatile flow field are presented as a function of the ratio τυ/τc. Those characteristics are determined to be quasi-steady-state, and steady-state like within the lowest and highest, respectively, of the studied τυ/τc values. Pulsating the flow of a Bingham fluid, within the low and intermediate τυ/τc ranges leads to substantially higher flow rates than the steady-state ones. This is true for all investigated waveforms with the lowest and highest increases corresponding to the triangular and square waves, respectively.
