This project was to investigate the changes-over-time of thermodynamic and flow state variables of the refrigerant fluid flow within the sealed system of a household refrigerator. The sealed system consists of the condenser, evaporator, compressor, and capillary tube. These components force the fluid through the refrigeration cycle shown below.
In this work, the convection bond graph concept introduced by Brown to model the evaporator portion. This is a reasonable approach as, once the architecture of the model is proven for any portion of the sealed system, all components can be modeled using the same approach by varying the geometric and heat transfer parameters.
This model uses four state variables for each segment of tubing: mass of refrigerant, temperature of the refrigerant, momentum of the refrigerant, and temperature of the tubing wall. The state dynamics for each segment of tubing are:
While this equation is relatively straightforward, several of the terms in the equations are highly non-linear. For example, the enthalpy and pressure are non-analytic functions of the state variables (temperature and specific volume) and must be evaluated using something like NIST REFPROP. Other terms, such as the pressure drop and heat transfer coefficients can only be calculated by selecting correlations that are appropriate for the regime (one-phase or two-phase) and have been experimentally shown to have some predictive power for the flow rates and regimes that are expected.
Beyond this, the temperature state equation must be replaced when the fluid is two-phase:
By employing certain numerical integrators, these equations were used to simulate an evaporator flooding scenario. In this scenario, the evaporator starts out at high temperature with superheated refrigerant vapor. At time t=0, dense two-phase refrigerant enters the evaporator which begins to absorb heat from the system.
This scenario was simulated as described. When simulating short time scales, it was possible to recreate certain high-speed dynamics, such as pressure waves caused by sudden phase changes (boiling):
While this was interesting, the dynamics were not relevant to the time scales at which household refrigerators operate. Certain numerical techniques were employed to speed the simulation and focus on only the relevant time scales. The result of a one-hour simulation are shown below:
