New analytical solutions to the two-phase water faucet problem

The one-dimensional water faucet problem is one of the classical benchmark problems originally proposed by Ransom to study the two-fluid two-phase flow model. With simplifications, such as massless gas phase and no wall and interfacial frictions, analytical solutions had been previously obtained for the transient liquid velocity and void fraction distribution. The water faucet problem and its analytical solutions have been widely used for code assessment, benchmark, and numerical verification. In this work, we present a new set of analytical solutions to the water faucet problem at the steady-state condition, with the gas-phase density's effect on pressure distribution considered. This new set of analytical solutions is used in a rigorous numerical verification process from which the anticipated second-order spatial accuracy is achieved for a second-order spatial discretization scheme. On the contrary, the same anticipated order of accuracy could not be obtained using the Ransom solutions as the reference. In addition, extended Ransom transient solutions for the gas-phase velocity and pressure are derived with the assumption of decoupled liquid and gas pressures. Numerical benchmark on the extended Ransom solutions is also presented.