Development length of sinusoidally pulsating laminar pipe flows in moderate and high Reynolds number regimes

Recent studies on laminar, fully-developed, sinusoidally pulsating pipe flows have revealed the existence of a unique signature map that can be used for the measurement of the arbitrary time-varying, instantaneous mass flow rate from the recorded axial pressure gradient data and vice versa. This measuring technique is, however, valid for the hydrodynamically fully-developed flow of an incompressible fluid. The present study, therefore, deals with the numerical evaluation of the required development length as functions of the mean Reynolds number, the amplitude of mass flow rate pulsation and the pulsation frequency in the moderate and high Reynolds number regimes. The investigation shows that in the low-frequency, quasi-steady regime, the instantaneous variations of L/D can be predicted by the steady-state results for corresponding instantaneous Reynolds numbers. On the other hand, at higher pulsation frequencies, considerable deviation from the pure sinusoidal signal occurs for the development length and its amplitude decreases with increase in pulsation frequency. Finally, using the results of the present simulations, a simple correlation is proposed that can be used in order to predict the maximum development during a cycle as functions of Re M , m ˙ A ∗ and F.