*2.2. CFD Simulation Points*

The work was based on the microchannel profile in Figure 2. This meant that the tube height/width and longitudinal pitch were fixed in the current work. With these parameters fixed, it was only the transverse tube pitch (*Xt*), the longitudinal length (*Ll*) (or the number of tube rows) and the fin pitch *Fp* that influenced the air-side heat transfer and pressure drop. A 3D model of the microchannel heat exchanger is shown in Figure 3. The fin angle (ϕ) was further dictated by the transverse tube pitch and fin pitch, respectively.

**Figure 3.** 3D model of the microchannel heat exchanger (seven channels, four rows).

For large fin pitches, considered in the current investigation to accommodate long frosting periods, the entrance region was found to be significant and therefore it was ensured to simulate enough longitudinal tubes (or tube rows) to establish fully developed hydraulic and thermal flow. Following this approach and to reduce the number of CFD simulations, the tube local friction and heat transfer coefficients were extracted in order to extent the global friction and heat transfer coefficients to even larger longitudinal lengths (see Section 2.4 (data reduction)). The parameterized geometry and frontal air velocity may be observed in Table 1. Some combinations of geometrical parameters were omitted (*Xt* = 9 mm, *Fp* = 7.5 mm) and (*Xt* = 9 mm, *Fp* = 10 mm) to avoid fin bending in the assembling and soldering process. The criteria used was fin angles less than 45◦. In total, 42 simulations were carried out.


**Table 1.** Heat exchanger parameterization.

The hydraulic diameter (*dh*) and the compactness (β = 4σ/*Atot*) of the microchannel geometries were compared with a baseline plain finned-tube industrial refrigeration evaporator in Figure 4a,b. The baseline is outlined in Kristófersson et al. [24,25]. The tube diameter was 15.6 mm, the tube layout was inline 50 × 50 mm, the fin thickness was 0.35 mm and the fin pitch was 12 mm, and varied from 12 to 2.5 mm to represent a comparison at a similar fin pitch.

**Figure 4.** Hydraulic diameter (**a**) and compactness (**b**) vs. fin pitch of the microchannel evaporator geometries (Table 1) compared with the baseline finned-tube industrial refrigeration evaporator.

The hydraulic diameter of the microchannel geometries is nearly the same as the baseline finned-tube evaporator, while having more decreasing inclination as function of the fin pitch. Smaller fin pitch and transverse tube pitch result in smaller hydraulic diameters. The compactness is greater for the microchannel geometries, especially at higher fin pitch and lower transverse tube pitch compared with the baseline finned-tube evaporator. The greater differences between the hydraulic diameter and the compactness are due to the area contraction ratio (σ), which is smaller for the baseline finned-tube evaporator.

#### *2.3. CFD Modeling Setup*

CFD simulation brings an extensive knowledge of the flow behavior inside the microchannel evaporator and provides local data, which is challenging, and possibly subject to high uncertainties with an experimental setup. The CFD simulations were carried out using the commercial software ANSYS 19.1 with the CFX solver.

#### 2.3.1. Modeling

In order to keep a reasonable simulation time, only a small part of the microchannel was modelled in the CFD simulations. Symmetries were used where the geometry allowed for it. The 3D CFD model is shown in the Figure 5. Moreover, only a single fin was included in the computational domain.

**Figure 5.** 3D model of the simulated geometry (*Xt* = 9.00 mm, *Fp* = 5.00 mm, *Nl* = 35).

The tube and fin walls were assumed to have a constant wall temperature (6 ◦C) consistent with the use of the effectiveness-NTU method for single stream heat exchangers, which was used to calculate the tube local and global heat transfer coefficients. Moreover, the temperature values of the wall and air inlet are independent on the heat exchanger effectiveness, which is valid as long as the air properties can be assumed constant. The derived heat transfer coefficients were, therefore, tube and fin surface averaged. The constant wall temperature means that the heat conduction through the metal (tubes and fins) was disregarded in the CFD calculations, and that it must be included when using the heat transfer correlations. In Appendix A.1, it is demonstrated that the fin efficiency for rectangular fins can be used to model the heat conduction with good accuracy, even though a heat flux concentration (2D effect) occurs near the base of the fin at the microchannel walls. Furthermore, the no-slip condition was employed at the walls, and symmetry condition at the four lateral surfaces. The air was assumed an incompressible ideal gas due to the small temperature changes.

#### 2.3.2. Mesh Analysis

For flow around obstacles, the laminar boundary layer restarts at the tip of each tube, with a transitional flow in their wakes due to vortex formation. For inline rectangular tube configuration, the heat transfer rate is expected to be highest at the leading corner edge of each tube while decreasing along the tube longitudinally. In the wake region, recirculation zones typically appear with lower velocities and heat transfer rate. However, turbulent vortices improve the mixing and increase the heat transfer in the neighborhood regions too [26].

The restart of the boundary layer principle is similar for offset fins, which generally provide a very good heat transfer rate compared to other fin designs [23]. The transition from laminar to turbulent flow may appear for low Reynolds number, *Re* < 500, such as described by Sahiti et al. [27]. The range of Reynolds numbers in the current simulations is from 500 to 4000, therefore the k-ω SST turbulence model, based on the work of Menter [28], was selected. Kim et al. [29] showed that the k-ω SST turbulence model gives better performances, compared to the k-ε and realizable k-ε turbulence models, in terms of predicted *j* and *f* factors for offset fins at *Re* > 1000. Finally, Chimres et al. [30] showed that the k-ω SST turbulence model results in good agreement with experimental heat transfer and pressure drop data for flow around tubes.

A mesh sensitivity analysis was performed. The *y*<sup>+</sup> was kept below one to ensure accurate resolution of the viscous boundary layer, advised by the ANSYS user guide [31] when using the k-ω SST turbulence model. The size of the computational grid was analyzed in order to ensure the grid independence. The values of the global Colburn j-factor and the Fanning f-factor are shown in Figure 6 as function of the mesh size.

**Figure 6.** Colburn j-factor (**left**) and friction f-factor (**right**) as function of the mesh size (*Xt* = 9.00 mm, *Fp* <sup>=</sup> 5.00 mm, *Uf r* <sup>=</sup> 4.40 m·s<sup>−</sup>1).

The difference between two consecutive values of the Colburn j-factor and the Fanning f-factor is lower than 0.5% from 1.3 to 2.2 M elements. Therefore, the mesh of 1.3 M elements was selected to have a good balance between accuracy and calculation speed. The 1.3 M mesh is shown in Figure 7.

**Figure 7.** Computational grid. Frontal view (**left**) and side view (**right**), (*Xt* = 9.00 mm; *Fp* = 5.00 mm).

The mesh was fully structured (only hexahedral elements) to minimize numerical diffusion. Furthermore, the mesh was refined close to the wall to keep the *y*<sup>+</sup> < 1.
