Natural Convection, Two-Phase Flow, and Crystallization in a Vacuum Pan Sugar Crystallizer.

A mathematical model of a Vacuum Pan Sugar Crystallizer is developed. This mathematical model is based on the fundamentals of the physics of two-phase flow. Because of the complexity of the model, the time dependent solution is accomplished using numerical methods designed to be executed by a digital computer. The model generates velocity, pressure, temperature, and supesaturation profiles for the Pan, in response to the operating conditions and the design of the Pan. The motivation for the development of this model is to give an analytical tool to study the effects of Pan design, control systems, and operating conditions on the product crystal size distribution. The emphasis of this research is on the development of the numerical methods that are consistent with conservative and transportive principles reflected in the equations of motion. Important features of the numerical code are that it employs a dynamic grid system designed for free surface flows, and is compatible with viscous two-phase flows exhibited in the Pan. The modeling equations are two-dimensional for the volume above the Calandria, but in other areas where two-dimensional equations are an extravagance, one-dimensional and lumped equations are used. The velocity and growth rate profiles provides the information needed for a distributed population balance equation needed to analyze the effect of these profiles on the crystal size distribution. The development of such a population balance is discussed but is not part of the present numerical code. Nonetheless, the model provides valuable information concerning the effects of Pan design, control systems, and operating conditions in a qualitative sense, as demonstrated in the results. Sensitivity studies varying Pan design and operating conditions demonstrate that of the cases studied, the volumn fraction crystals, pan level, heat load, pan pressure, and whether or not the pan major diameter is flared, had the most significant effects on the pan performance. These variations of Pan design and operating conditions were judged significant based on their effect on the velocity and growth profiles, maximum and minimum supersaturation, and average supersaturation. A summary of the results is presented in Chapter 7 and discussions concerning particular cases along with raw data are presented in Chapter 5