Void wave dispersion in bubbly flows

A linear dispersion relationship is derived using a one-dimensional two-fluid model to investigate void wave dispersion in bubbly flows. This dispersion relationship includes generalized forms of the kinematic wave speed, the characteristics of the system of equations and the relaxation time. The relaxation time turns out to be a key parameter for the void wave dispersion. By using appropriate constitutive relations for bubbly flow, the kinematic wave speed and the characteristics are found. The Froude number is found to be the crucial parameter for void wave dispersion. That is, for two-phase flows with large slip between the phases (the small Froude number case) the dispersion effect is negligible and thus the kinematic wave approximation is valid. However, as the relative velocity decreases (the large Froude number case), void wave dispersion becomes pronounced. In the limit for zero relative velocity, void waves propagate at the same celerity as the characteristics for homogeneous conditions. The model presented herein also shows the existence of a complementary kinematic wave which is related to the kinematic wave speed and the characteristics. (orig.)