Development of an unsteady analytical model for predicting infiltration flow rate through the doorway of refrigerated rooms

Infiltration through the doorway, which accounts for a very large part of total cooling load, has been highlighted in the previous studies on energy consumption of cold stores. Usually, the prediction of the infiltration flow rate is based on steady models and CFD simulations. However, the steady models are not very accurate for predictions of dynamic flow rates and the CFD transient simulations are time consuming. In this paper, the infiltration flow inside the door is described by the time-dependent differential equations of motion and continuity. An unsteady analytical model is developed by using these equations based on two independent infiltration procedures. Meanwhile, an equation to calculate the effective length of the infiltration is introduced to the proposed model to help improving prediction accuracy. The transient variables in this model are velocity, density and time. And these equations yield an ODE system, which can be numerically solved by using the Matlab software to get the dynamic infiltration flow rates. This model is validated by two independent experiments: infiltration with small and large door opening sizes respectively. The prediction errors are between ±10% for infiltration air volume and ±12% for infiltration flow rate. The performance of this model is also compared with the steady models. It is concluded that the proposed model has a better accuracy than the steady models in the strong transient occasions (with large door opening sizes). And this model is simpler than the CFD simulations on the calculations of the dynamic infiltration flow rates.