An approximate analytical solution for bubble departure diameter in a vertical boiling channel

This simplified analytical solution for bubble departure diameter was derived in the connection to the need of determining bubble inclination angle, which the existing literature lacks. A large number of correlations for the departure diameter are currently in use for large-scale numerical simulation of boiling flows in channels. However, while solving for the bubble departure diameter numerically, we found that the choice of a proper bubble inclination angle was very crucial. The solution is based on the force balance that considers the major contribution of buoyancy force and growth force. Of course, the surface tension plays a little role at the time of bubble departure. The growth kinetics we used are our own asymptotic solution and those from the literature. The analytical solutions for the departure diameter and the growth time have been compared with our numerical solutions, the existing correlations and our experiments for different superheats (Jakob number Ja) and pressures. Our analytical solution is found to be reasonably accurate in high Ja. An appreciable deviation from the numerical simulation and some experiments in low Ja suggests that the contribution of micro-layer evaporation is important.