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

ABSTRACT
It is shown that the five parameters governing the propagation of sound waves in a fluid
contained in rigid cylindrical tubes filled with a saturated porous media are the shear
wave number s = R ρω / μ , ratio of specific heats γ , the Prandtl number σ , porosityε
and the Darcy number Da = R2 K . A variational solution of the problem with nonisentropic
wave’s propagation in a cylindrical tube in the presence and absence of a
convective steady flow is presented. The manner in which the flow influences the
attenuation and the phase velocity of the forward and backward propagating acoustic
waves is deduced. It is found that the inclusion of the solid matrix or the increasing of
Darcy number increases the attenuation and decreases the phase velocities of the
forward, backward and hydrodynamic sound wave’s; this is due to favorable retarding
effect of the solid matrix. The increasing of porosity is found to decrease attenuation
and increases phase velocities of the forward, backward and hydrodynamic sound
waves; this is due to absent role of solid matrix in damping sound waves. The effect of
increasing Mach numbers is found to increase attenuation and decrease phase
velocities for the backward sound waves; this is due favorable retarding steady flow
velocities and decrease attenuation and increase phase velocities of the forward and
hydrodynamic sound waves; this is due to favorable steady flow velocities in driving
these two sound waves.