Correlations

Dimensionless bubble diameter

One correlation for bubble history of direct contact condensation of vapor bubbles in a subcooled liquid such considers a stagnant bubble in liquid dominated by heat transfer, which can be represented as Eq. 2, where \(\beta\) is the dimensionless bubble diameter \({D}/{{D}_{0}}\) with \({D}_{0}\) being the initial bubble diameter, \({Ja}\) is the Jakob number \({\rho}_{l} {c}_{pl} {\Delta {T}_{sub}} / {\rho}_{v} {h}_{fg}\) , and \({Fo}_{0}\) is the Fourier number \({\alpha} {t}/{{D}_{b0}^{2}}\) [1, 2]. This correlation was derived from analysis of the physical phenomena, and does not incorporate a fit to experimental data.

A later correlation, one which does incoprorate a fit to experimental data, is Eq. 29, where \({Re}_{b0}\) and \({Pr}\) are the bubble Reynolds and liquid Prandtl numbers, respectively [2, 3]. Experimental bubble data is nondimensionalized by initial bubble diameter, and correlations are plotted against experimental data in Figure 5. Correlations are plotted for the average initial bubble diameter and velocity of the population of bubbles studied.

Bubble histories seem to correspond roughly with the analytical model by Florschuetz and Chao initially, with later times corresponding to the Yuan et al. model. The present bubble data shows about 0.5 K subcooling. Since correlations are sensitive to subcool temperature, this motivates the collection of bubble data over a wider range of subcooling.