A thermodynamic basis for predicting falling-film mode transitions

• Provides a theoretical framework for understanding and predicting falling-film transitions.
• Places flow regime transitions into a thermodynamic context.
• Contrasts the roles of dynamics and entropy generation minimization in two-phase flows.
• Demonstrates that tube spacing influences transitional Reynolds.
• Suggests functional form for interpreting existing correlations.

Horizontal-tube, falling-film heat exchangers are used in many air-conditioning and refrigeration systems. Depending on the tube diameter and spacing, the flow rate, and fluid properties, when a liquid film falls over a series of horizontal tubes three distinct flow patterns can be manifested. These flow patterns are the droplet mode, the jet mode, and the sheet mode. A thermodynamic analysis is undertaken to predict the transitions between these modes. By seeking the condition corresponding to thermodynamic equilibrium between two neighboring modes, a scaling relation is developed for the transitional Reynolds number. This theoretical framework is used to provide the first explanation for the relationship between the transitional Reynolds number and modified Galileo number which has been previously based solely on experimental observations. This approach offers insight into the prevailing physics, and it suggests a tube-spacing effect on the mode transitions which has not previously been anticipated. Using limited data and prior results from the literature it is found that this effect is likely to exist. The implications of this thermodynamic approach to predicting two-phase flow patterns are discussed in terms of entropy generation minimization and transition hysteresis, as is its incompleteness.