Reflections on the acoustic wave propagation speed in homogeneous two-phase flow

Any change in the hydraulic attributes of a pressurized flow system triggered at a specific point is communicated to other parts of the system with a finite velocity, a value variously called the acoustic wave speed, wave celerity, or acoustic velocity. A reasonable estimate of the magnitude of the acoustic velocity plays a key role in modeling single phase flow but also has importance for modeling homogenous liquid-gas two-phase flow as the intensity and path of the resulting transient pressure waves directly depends upon the magnitude of the acoustic velocity. In order to both explore and more accurately estimate the magnitude of the acoustic velocity, a novel energy based approach is presented here. In the new approach, the conversion of the kinetic energy of the flow is partitioned between the strain energy stored in the liquid, gas and pipe wall. The resulting equation differs in interesting ways from the classical form of the equation conventionally presented in standard literature. The results show that the acoustic velocity calculated by the proposed approach is in close agreement with that calculated through conventional approaches when the associated pressure changes are small. However, when significant pressure changes occur, a larger discrepancy occurs that can cause an overestimation of the wave velocity in the classical approach. It is shown that the error has its root in an approximation of the average bulk modulus of elasticity of the mixture. The conventional approach underestimates the energy storing capability of the gas component leading to the overestimation of the acoustic velocity.