Modelling of Bubble Formation with 
Phase Change at a Submerged Nozzle

In order to enhance the rate of transport between the phases in many direct contact heat and/ or mass exchange processes, a condensable gas is often injected into a liquid through a submerged nozzle. The objective of the present work is to study theoretical steam bubble formation at a single submerged nozzle in subcooled parallel flowing water. 

The system under investigation consists of saturated steam that is injected vertically upwards at temperature through a nozzle (radius ) submerged in subcooled water (bulk temperature ) of depth . The water flows upward at a velocity parallel to the nozzle axis. A non-spherical bubble formation model was modified to calculate the movement of the interfacial elements in parallel flowing water. A force balance at each element generates a set of differential equations of motion in cylindrical coordinates, which can be numerically solved. The total mass balance for the vapour inside the bubble can also be written. 

Assuming that a quadratic temperature profile exists in the boundary layer and that the thickness of the boundary layer is much smaller than the bubble radius, the energy balance equation appropriate for the liquid phase can be simplified to yield a simple integral. The thickness of the boundary layer and the mass flux are related by heat flux continuity at the bubble wall. The effect of a parallel flowing liquid is modelled theoretically by pressure analysis of surrounding liquid. Liquid pressure distribution on the surface of bubble can also be calculated. An explicit finite difference method was extended to solve the equations of bubble formation.

Simulations of steam bubble formation in water were performed for experimental conditions. Figure 1 shows the simulated bubble growth sequences based on the experimental conditions of runs 3 and 4. The bubbles are approximately spherical only in the early stages of formation, eventually becoming noticeably non-spherical and detaching naturally when the neck closes. Six experimental runs were simulated and the results are summarized in Table 1. The present model shows a significant improvement over other models.

Table 1: Comparison of computed results with experimental data of Denekamp et al. (1972).

Figure 1: Computed sequential shapes of steam bubble based on the experimental conditions of runs 3 and 4 from Denekamp et al. (1972): (a) run 3 , (b) run 4. 

Figure 2: Computed detachment time and bubble radius at detachment for different liquid flow velocities. Other conditions correspond to runs 1, 2 and 3.

Figure 2 shows the effect of liquid velocity on the instantaneous bubble size. The symbols represent the equivalent radius and time at detachment for different liquid flow velocities. The main effect of liquid velocity is to affect the detachment time, and thereby the bubble radius at detachment. With increasing of the liquid velocity, the bubble is predicted to detach earlier and the radius at detachment is consequently smaller. 

An improved model for single steam bubble formation at a submerged nozzle in subcooled flowing water has been developed. The simulated results show significant improvement over other theoretical models.