Godunov-type solutions for gas-liquid two-phase transient flows with gas release effects

The gas-liquid two-phase homogenous flow has been extensively investigated without the effect of gas release.However,the dissolved gas will release when internal water pressure drops below saturation pressure during hydraulic transients.This results in inaccuracy or even invalidity of the existing model for homogenous flows,especially for the reproduction of two-phase mass transfer processes.To address this problem,this paper couples the gas release model with conservation equations of homogenous flows,which are numerically solved by the second-order Godunov-type scheme(GTS).Specifically,a virtual-cell method is adopted at system boundaries to achieve the same second-order accuracy as interior cells,which is realized by the monotonic upwind scheme for conservation laws(MUSCL-Hancock scheme).Simulated pressure curves by the proposed model are compared with a series of analytical,numerical and experimental results.It indicates that the proposed model with gas release effects reproduces actual pressure responses most accurately,with minimum relative error and root mean squared error compared with experimental data.Moreover,the gas release leads to dynamic synchronous fluctuations of void fraction,wave speed and pressure head,including the opposite trends of void fraction and pressure,and higher void fraction leading to greater wave speed depression.Furthermore,sensitivity analysis is concluded with recommended Courant number,and different gas release effects in different initial void fractions.Present research increases the basic understanding of two-phase mass transfer processes and their implications for hydraulic transients.