Evaluation of entrainment formulations for liquid/gas plumes from underwater blowouts

A numerical model using the Lagrangian approach developed to simulate the fate of liquid/gas blowouts in deepwater is presented, and three entrainment formulations are tested: HOULT, JETLAG and CORJET parameterizations, given by Hoult et al. (1969), Lee and Cheung (1990) and Jirka (2004), respectively. The results are discussed and compared with field and laboratory observations. These formulations differ both in shear and forced contributions to the entrainment. As expected, the qualitative analysis of the dynamics of a liquid plume shows that the entrainment of ambient water decreases the acceleration due to buoyancy, and the plume and ambient momentums become increasingly similar over time. However, simulations of field and laboratory cases, where different plumes (gas, liquid and gas/liquid) were discharged into environments with different ambient stratifications and cross-flows, show that the JETLAG parameterization provides the best results, while HOULT (CORJET) overestimates (underestimates) the entrainment. Additional numerical experiments applying only the JETLAG formulation are performed, considering different plume composition, ambient condition, nozzle diameter and initial discharge. For all the studied cases, the simulated results are in good agreement with the observations. Especially noteworthy were field experiments with gas released at depth of 50-60 m. The vertical plume velocity decreased during the ascending motion, but after a certain level, the velocity increased. This feature was simulated by the JETLAG parameterization, and a closer analysis reveals the increase of buoyancy due to gas expansion exceeding the decrease caused by the entrainment. These results encourage the use of this model in realistic and complex situations. This article is protected by copyright. All rights reserved.