Relationships between bubble frequency, departure diameter and rise velocity in nucleate boiling

Many analyses of boiling heat transfer include the terms bubble frequency f, bubble diameter D, and bubble rise velocity u, in their expressions for nucleate boiling heat flux and critical heat flux. In order to simplify these expressions individual relationships between f and D, and the relationship u = fD, are often used over the entire range of bubble diameters. Evidence is presented which indicates that a single relationship only approximately correlates f with D for all nucleate boiling bubble diameters. Three separate regions are suggested by the experimental data, which correlate the data for each region better than a single relationship: (a) hydrodynamic region, in which the major forces acting on the bubble are buoyancy and drag: fD12 = 0·90 g12; (b) transition region, in which buoyancy, drag and surface tension forces are comparable: fD34 = 0·44 g12 (cm14); and (c) thermo-dynamic region, in which conditions during bubble growth predominate: D2 = constant. Theoretical explanations for the variation of f with D are proposed for regions (a) and (c). Experimental observations indicate that the relationship u = fD is only approximately valid over the range of bubble diameters: 0·02 >D > 3 cm. The relationship ufD = 1, therefore, should not be incorporated into accurate theoretical analyses of the boiling phenomenon, in which the proportionality constant relating dimensionless groups is obtained as an exact theoretical value.