Verification and validation of simulation models were conducted

Verification and validation of simulation models were conducted by comparing numerical results with experimental data reported by Hermes et al. 16. First, the Eulerian multiphase model was applied to simulate the frost formation on a cold flat plate with the temperatures ranging from  to with the same conditions listed in Table 1).

As Figure 1) shows, predictions of the numerical model are in agreement with experimental data. Figure 1) reveals that the average frost thickness increases as the temperature of the cold plate decreases, which is consistent with a number of previous reports.Furthermore, the numerical model was validated by simulating the experiments conducted by Sommers et al. 17. They analysed the frost formation on surfaces with the same size (99.5 mm× 80.2 mm × 3.4 mm) and different wettability.

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As indicated in table (2), the inlet air velocity was set to , relative humidity (RH) was kept at , and the surface temperature was .  As figures (2 and 3) show, numerical predictions agree well with experimental data for the average frost thickness and density, considering the uncertainties in the experimental data.  4.2.

Frosting on a Plate-Fin Evaporator Frost growth on an evaporator surface or a micro-channel heat exchanger, when used in outdoor heat pump or air conditioning systems, can be analysed using the current model. As illustrated in figure (4) one section of a plate-fin evaporator was modelled in a 3D computational domain and conditions were set as listed in table (2) to analyse the local frost thickness and distribution of the frost density.  As shown in figure (4), there is a cooling block with the size of  and a non-cooling block exists before humid air faces the channel cold surfaces. At the inlet  and at the outlet . Furthermore, the fins, upper, and bottom surfaces of the channel, in the cooling block, are walls with the no-sleep velocity boundary condition and  where  is the surface normal vector.

In this work, a parametric analysis was carried out in order to gain insights into the influence of geometrical parameters on the frost features. Three different cases were studied with the geometrical parameters listed in Table 2). The first case was considered the reference geometry, as illustrated in Figure 4), while the other cases varied in the height (H) or bottom width (X2) of the channel and the top width (X1) was fixed. As figure (4) shows, at the beginning frost starts forming on the surface due to the deposition of water vapour and as time goes on, the thickness of the layer increases, leading to the flow blockage. On the other hand, due to the diffusion of water vapour molecules, the density of frost layer increases continuously. From a qualitative point of view there is a good agreement between the numerical results and the experimental observation 18; however, there is no quantitative comparison.In the second case, the FPI (Fins Per Inch) increased from 10.

6 to12.7 while the face area of the section was constant. In fact, in this case the initial mass flow rate of the humid air was equal to the reference value.

In the third case, the face area decreased by reducing X2 and increasing the fin density per length. In this situation, the total number density of fins ( ) increased and the airflow velocity at the inlet was fixed at the reference value, leading to a lower airflow rate through the channel. In order to compare the numerical results of different cases, following non-dimensional parameters and variables are introduced: