A Study on the Continuous Spill with Limited Period of Release

In this study, the spread of cryogenic liquid due to a limited period of release is investigated for the first time to clarify the unclear conventional concept regarding two release types, continuous and instantaneous release. In describing instantaneous release, a discharge time has been assumed to be infinitesimally small; however, such an assumption is unreal because there exists a finite period of release no matter how rapid it is. If the discharge time is less than the entire time domain, the instantaneous release model should be added to the continuous model from the end of the time. This combined release that consists of the initial continuous model and subsequent instantaneous model is more realistic than the instantaneous release. The physical phenomenon is governed by three parameters: the evaporation rate per unit area, release time, and spill quantity. Third-order perturbation solutions are obtained and compared with a numerical solution to verify the perturbation solution. For the same spill quantity, the combined model that consists of continuous and subsequent instantaneous model is necessary for small release times, whereas the continuous model is only required for large release times. Additionally, the combined release model is necessary for a small spill quantity at a fixed release time. These two release models are clearly distinguished using the perturbation solution.