ON THE NON-ISENTROPIC SOUND WAVES PROPAGATION OF A STATIONAY OR FLOWING FLUID IN A CYLINDERICAL TUBE FILLED WITH POROUS MEDIA

Abstract

ABSTRACTIt is shown that the five parameters governing the propagation of sound waves in a fluidcontained in rigid cylindrical tubes filled with a saturated porous media are the shearwave number s = R ρω / μ , ratio of specific heats γ , the Prandtl number σ , porosityeand the Darcy number Da = R2 K . A variational solution of the problem with nonisentropicwave’s propagation in a cylindrical tube in the presence and absence of aconvective steady flow is presented. The manner in which the flow influences theattenuation and the phase velocity of the forward and backward propagating acousticwaves is deduced. It is found that the inclusion of the solid matrix or the increasing ofDarcy number increases the attenuation and decreases the phase velocities of theforward, backward and hydrodynamic sound wave’s; this is due to favorable retardingeffect of the solid matrix. The increasing of porosity is found to decrease attenuationand increases phase velocities of the forward, backward and hydrodynamic soundwaves; this is due to absent role of solid matrix in damping sound waves. The effect ofincreasing Mach numbers is found to increase attenuation and decrease phasevelocities for the backward sound waves; this is due favorable retarding steady flowvelocities and decrease attenuation and increase phase velocities of the forward andhydrodynamic sound waves; this is due to favorable steady flow velocities in drivingthese two sound waves.