The behavior of an open system is modeled. Thus, for special cases, the void fraction is predicted as a function of location and time. The open system may be an open vessel or a vessel with an open relief device. A single governing equation is derived based on combining the material and energy balances with the churn-turbulent drift flux relationship and assuming no radial gradients. This partial differential equation is not solved. It is, however, bounded by homogeneous and all vapor venting. These special cases are solved. In homogeneous venting the key variable is time. In all vapor venting under pseudo-steady-state conditions the key variable is location. The solution of the partial differential equation is also discussed.
Under pseudo-steady-state and churn-turbulent conditions, the open system is modeled. The minimum void fractions (corresponding to a maximum liquid inventory) with all vapor venting, for vertical, horizontal, and spherical vessels are predicted and compared. Analytical expressions for the local and average void fractions in a vertical vessel and non-unity distribution parameters are presented. Void fraction profiles are compared for three cases: 1. vertical cylinders with distribution parameters (Co values) of unity and 1.5, 2. horizontal and vertical cylinders with varying L/D ratios, and 3. spheres with inscribed vertical cylinders having constant gas production to bubble rise ratio (Ψ′ value). The vertical cylinder average void fraction for non-unity distribution parameters can now be calculated analytically. The horizontal cylinder average void fraction predicted by turning it upright results in an over prediction of at most 4%. The sphere average void fraction predicted via an inscribed vertical cylinder, with the same Ψ′ value, is consistenly high by at most 8%.