## 4 Numerical Methods and Validation
### Validation of Numerical Model  
To investigate the detailed characteristics of the flow field driven by the axial fan in the outdoor unit more accurately, the virtual fan-performance tester (VFT) is designed. To determine the dimensions of the virtual fan tester and the number of grids for the given outdoor unit, a grid-refinement study was carried out. Figure 4 shows the three types of VFTs made on a basis of D, which is the diameter of the fan. The static pressure on the inflow and outflow planes which are located upstream and downstream, respectively, of the axial-flow fan in the outdoor unit is specified as the inflow and outflow boundary conditions. To reproduce the experimental conditions of the actual fan-performance tester and to predict the P-Q curve of the outdoor unit, the pressure difference between inlet and outlet boundaries is varied. The wall boundary conditions are applied on the four side-planes parallel to the fan rotation axis and on the middle plane separating the upstream and downstream flows. The rotation speed is set to be 1000 RPM.  
The numerical results predicted using the VFTs are compared with the measured one using the actual fan performance tester of which the specifications are described in Section 3.1. The validity of VFT is confirmed by comparing the numerical results with the experimental results. Figure 5 compares the P-Q curves predicted by using the VFTs with the measured data. The agreement is generally good  
Figure 4: Various virtual fan testers used for grid-refinement study.  
between the predicted and measured results in the lower pressure region, but the discrepancy increases as the pressure increases. The difference seems to depend on the size of the virtual fan tester: as the size of the virtual fan tester increases, the agreement between the numerical and experimental results becomes closer. The final dimensions of the VFT and the number of grids are determined using these results, which show that Simulation #3 presents the reasonable agreement up to the operation point. The maximum relative error in the volume flow rate at the fixed static pressure is 4.0%. These results confirm the validity of the current numerical method. Note that the subsequent detailed flow analysis and the optimization were carried out for the operating point where the P-Q curve and the resistance curve, which is mainly due to the heat changer, meet together.  
Aerodynamic noise due to fan-driven flow in the out-door unit is also predicted using the FW-H integral equation in Equation (3). The half-spherical shape of the FW-H integral surface was formed in the downstream direction. Figure 6 compares the predicted sound pressure spectrum with the measured one. There are good agreements at the blade-passing-frequencies between two results, though some differences are noticed in the broadband noise. The difference in the broadband high-frequency range is due to the intrinsic limitation of RANS equations in resolving the random components because the RANS equations are derived by averaging the Navier-Stokes equations. However, the difference between the numerical and experimental results is 2.1 dBA in terms of the overall sound pressure level because the tonal components dominantly contribute to the overall sound pressure level.  
Figure 5: Comparison of predicted P–Q curves with experimental ones.  
Figure 6: Comparison of predicted noise spectrum with experimental ones.