Inhomogeneous Theory Based on Sound Speed Measurement for Mixture of Water and Many Microbubbles in a Converging-Diverging Tube

In various experimental and theoretical studies on gas-liquid two-phase bubbly flows, many investigators have long focused on a small void fraction case (i.e., volume fraction of gas phase). In this case, a classical formulation of sound speed, i.e., the homogeneous equilibrium sound speed derived by van Wijngaarden (1968), has long been accepted, and the theory for dilute bubbly flows has comprehensively been established. However, the pressure waves in non-dilute (i.e., large void fraction) bubbly flows have not been clarified. This paper clarifies propagation properties of pressure waves generated by the bubble collapse in bubbly flows with a large void fraction (e.g., from 5 % to 20 %) in a converging and diverging tube (i.e., Venturi tube). Firstly, we calculated of the bubble diameter by the results of visualization for bubbly flows via a high-speed video camera. Secondly, we measured the distributions of void fraction, pressure, and sound speed: (i) The void fraction was measured by the constant current method (Uesawa et al., 2012); (ii) The sound speed was evaluated by the TOF (Time Of Flight) method from the measurement result of pressure distributions. Then, we compared sound speed measured with the aforementioned classical sound speed by van Wijngaarden (1968). As a result, the difference between measured and theoretical values becomes large for the case of exceeding the void fraction of the order of 0.05. This implies the existence of an applicable limit of the homogeneous model. Finally, toward an extension of the applicability of homogeneous theory, we propose an heterogeneous theory for sound speed for the case of large void fraction, which will be compared with the experimental data.