Hydrodynamic and thermal development of compressible oscillatory flow inside circular channel

In order to study the hydrodynamic and thermal development of compressible oscillatory flow inside a circular channel, the coefficient of hydrodynamic development (CHD) and the coefficient of thermal development (CTD) are proposed as index parameters, based on the temporal–spatial profile characteristics of the velocity and the temperature field. CHD expresses the variation rate of velocity profile along the axial direction at the phase of centerline velocity reaching its maximum, while CTD denotes the variation rate of temperature profile along the axial direction at the phase of maximum temperature difference between the centerline fluid and the wall. Numerical computations are conducted for a given physical model to validate the effectiveness of these two index parameters. The CHD and CTD as a function of the normalized distance from the entrance into the channel are computed and presented. CHD = 0.1 and CTD = 0.1 are suggested to determine the hydrodynamic and thermal entrance lengths, respectively, which is proved acceptable by comparing the velocity and temperature profiles at various positions along the channel axis.

Research highlights
► The study focuses on the entrance effect of compressible oscillatory pipe flow.
► Index parameter CHD is proposed to study the hydrodynamic development.
► Index parameter CTD is proposed to study the thermal development.
► The normalized hydrodynamic entrance length is asymptotic to 1 with increased Va.
► The normalized thermal entrance length approaches to 2 with increased Va.