Semianalytical solutions of laminar fully developed pulsating flows through ducts of arbitrary cross sections

A semianalytical analysis of fully developed pulsating flows in pipes of noncircular cross section is presented. The flow is assumed to be pressure gradient driven. Details of the analytical treatment of the flow are presented and it is shown that the analysis can be employed for any arbitrary cross-sectional shape. Special considerations are given to laminar pipe flows with circular cross sections and results of the present analysis are compared with those of conventional analytical treatments of the flow. Comparison of the velocity distribution, mass flow-rate pulsation, ratio of amplitudes of the mass flow rate and the pressure gradient, and the corresponding phase lag obtained by the present treatment show excellent agreement with data in the literature. Similar comparisons are also performed for oscillating flow through ducts of square and rectangular cross sections. Numerical data are introduced to confirm the resultant analysis. Finally, a few test cases are presented for sinusoidally pulsating flows through ducts of rectangular and elliptical cross sections with varying aspect ratios. (C) American Institute of Physics.