Turbulent Pulsating Flow through Circular Ducts

In the present paper, a numerical method has been demonstrated which works on an overall NewtonRaphson type algorithm and is capable of solving the “inverse” problem for turbulent, fullydeveloped, pulsating pipe flows, where the mass flow rate, rather than the pressure gradient is prescribed as a periodic function of time. The momentum equation, governing the transient, fullydeveloped pulsating flow of an incompressible fluid through a circular duct has been considered. Turbulence has been addressed by employing the low Reynolds number ! " k model. From the numerical solutions, the ratio of amplitudes of the mass flow rate and the pressure gradient signals along with their phase difference have been presented as functions of dimensionless pulsating frequency in the form of a signature map. The results of preliminary experiments have also been presented for comparison. Further, the results for low frequency pulsations have also been obtained using the Blasius equation for friction factor and are found to compare well both with the experiments and the numerical results.