Discrete gas model to represent distributed free gas in liquids

Transients in fluids containing free air which lumps the free gas at computational sections along, e.g., a pipeline, and treats the liquid between sections as if it were a liquid without free gas are modelled. In order to illustrate the influence of the procedure used to integrate the continuity equation at the discrete gas pockets, two examples, involving a single horizontal frictionless pipeline are given. In one, a transient is introduced by instantaneously lowering the upstream head from 60 m to 10.3 m (pipe level). In the other, upstream head is lowered to 30 m. Results for trapezoidal rule integration show high frequency oscillation after passage of sharp positive and negative pressure pulses. Forward integration results show numerical damping of the physical oscillation. Use of a small time increment reduces this effect.