Moving Boudary Models for Dynamic Simulations of Two-phase Flows

Two-phase flows are commonly found in components in energy systems such as evaporators and boilers. The performance of these components depends among others on the controller. Transient models describing the evaporation process are important tools for determining control parameters, and fast low order models are needed for this purpose. This article describes a general moving boundary (MB) model for modeling two-phase flows. Furthermore the general MB-model is reduced to model a typical dry-expansion evaporator. The reduced MB-model thus captures the phenomena as the general MB-model does but is less complex. The reduced MB-model is well suited for control purposes both for determining control parameters and for model based control strategies and examples of a controlled refrigeration system are shown. The general MB model divides the flow into three regions (liquid, two-phase and vapor) and consequently the wall also into three regions corresponding to the flow regions. The flow regions are each described by a mass balance and an energy balance, and the wall regions are each described by an energy balance. Some typical model simplifications in MB-models naturally lead to high DAE-index problems. The Dymola Modelica translator can automatically reduce the DAE index and thus makes efficient simulation possible. Usually the flow entering a dry-expansion evaporator in a refrigeration system is two-phase, and there is thus no liquid region. The general MB model has a number of special cases where only some regions are present. The case of an evaporator with only a two-phase region and a vapor region is specifically treated here. The evaporator model is made dimensionless and non-important terms are identified using values for a typical dry-expansion evaporator in a refrigeration system. The evaporator model is thereby further reduced in complexity giving a nice simple model well suited for control purposes. It is shown, that the MB-model is numerically robust to sudden changes in the system as e.g. a pressure change from a compressor start-up, which can be a problem if a discretized homogeneous model is used. The overall robustness and the simplicity of the MB model, makes it well suited for open loop as well as closed loop simulations of two-phase flows. Simulation results for an evaporator in a refrigeration system are shown. The open loop system is simulated both with the reduced MB-model and a discretized homogeneous model and the two responses are compared as well as the simulation time. The closed loop response of the evaporator controlled by a PID controller is shown using the MB model, and the control parameters are found. Finally some discussions are given on limitations and advantages of MB-models.