Stationary flow driven by non-sinusoidal time-periodic pressure gradients in wavy-walled channels Articles uri icon

publication date

  • October 2023

start page

  • 693

end page

  • 705

volume

  • 122

International Standard Serial Number (ISSN)

  • 0307-904X

Electronic International Standard Serial Number (EISSN)

  • 1872-8480

abstract

  • The classical problem of secondary flow driven by a sinusoidally varying pressure gradient is extended here to address periodic pressure gradients of complex waveform, which are present in many oscillatory physiological flows. A slender two-dimensional wavy-walled channel is selected as a canonical model problem. Following standard steady-streaming analyses, valid for small values of the ratio ..of the stroke length of the pulsatile motion to the channel wavelength, the spatially periodic flow is described in terms of power-law expansions of ... , with the Womersley number assumed to be of order unity. The solution found at leading order involves a time-periodic velocity with a zero time-averaged value at any given point. As in the case of a sinusoidal pressure gradient, effects of inertia enter at the following order to induce a steady flow in the form of recirculating vortices with zero net flow rate. An improved two-term asymptotic description of this secondary flow is sought by carrying the analysis to the following order. It is found that, when the pressure gradient has a waveform with multiple harmonics, the resulting velocity corrections display a nonzero flow rate, not present in the single-frequency case, which enables stationary convective transport along the channel. Direct numerical simulations for values of ... of order unity are used to investigate effects of inertia and delineate the range of validity of the asymptotic limit .... The comparisons of the time-averaged velocity obtained numerically with the two-term asymptotic description reveals that the latter remains remarkably accurate for values of ... exceeding 0.5. As an illustrative example, the results of the model problem are used to investigate the cerebrospinal-fluid flow driven along the spinal canal by the cardiac and respiratory cycles, characterized by markedly non-sinusoidal waveforms.

subjects

  • Industrial Engineering

keywords

  • steady streaming; oscillatory flow; non-sinusoidal pressure