An investigation of the numerical treatment of condensation

Abstract

The simulation of complete condensation continues to challenge the numerical methods currently used for multi-phase flow modeling; especially at low pressures, the change of phase process from a two-phase mixture to liquid leads to severe pressure field perturbations and often failure of the calculations. During condensation, the local void fraction and pressure decrease rapidly; at the time of complete condensation, the strong nonlinearities of the equations at the phase-change point lead to convergence difficulties and/or unacceptably large mass or energy errors.

Various ad-hoc "fixes" for this phenomenon - often referred to as "water packing" - have been proposed and/or implemented over the last few years. However, they have failed to clarify the core of the problem and are still unsatisfactory. Indeed these solutions cast doubt on the numerical predictions and occasionally are unable to prevent the breakdown of the calculations.

The present investigations have focused on the roots of these difficulties, particularly on the nonlinear effects involved. A time-step control strategy was developed which removes or at least, greatly mitigates the aforementioned computational problems. Numerical experiments as well as a mathematical analysis have both demonstrated the existence of a critical time-step size beyond which larger time-steps shall accommodate the liquid flow field to any perturbations; smaller time-steps shall cause the pressure to bounce, going out of range as it is indeed witnessed for condensation simulations where the time-steps are drastically reduced when the two phases are still coexisting.

Similar studies have been conduced on variety of numerical methods yielding some unexpected results in terms of time-step limit.