(1) The body

The cross-sectional area of the outlet wind tunnel should be designed to be more than 16 times the maximum measurable area of the air outlet of the axial flow fan (because the test surface required by the axial flow fan is large, the wind tunnel is designed in this way).

#### (2) Rectifier

There is one set consisting of a front and one back box, with three pieces in each group. The area opening rate should be maintained at 50–60%. It is used to stabilize the fluid flow and ensure the reliability of measurement. Since the measurement of Sections 6 and 7 downstream of the nozzle and the static pressure of the fan are located upstream of the rectifier plate, in order to avoid the design of the rectifier plate affecting the measurement of these two sections, the maximum bounce velocity of the rectifier plate must be maintained at Sections 2 and 6 within 10% of the flow rate. Meanwhile, the measurement section (upstream of the nozzle) is also encountered downstream of the rectifier, so it specifies a local maximum speed of 0.1 M downstream of the rectifier unless the local maximum speed is less than 2 m/s; otherwise, it must not exceed 25% of the average flow rate.

#### (3) Multi-nozzle

This wind tunnel has seven nozzles with throat diameters of 30, 25, 25, 20, 15, 10, and 5. The nozzles with different diameters can measure different air volumes. The test fans with different nozzles can measure different air volumes. As air flows through the nozzle, a speed boundary layer is formed between the solid surface, and the correction factor is needed when calculating the flow rate. When the fluid velocity is slow, the speed boundary layer is relatively large, and the error is also relatively small when estimating the flow rate. It is large, so the Reynolds number will be set above 12,000 during the measurement; in order to avoid excessive changes in the air properties such as density and temperature, the flow rate will be controlled below Mach number 0.1 during the test. In order to prevent the flow fields between the nozzles from interfering with each other, the position of the nozzles is also clearly specified in the AMCA (Air Movement and Control Association, AMCA) specification, as shown in Figure 5.

#### **4. Case Study**

To investigate the influence of various parameters on fan performance, three different fan designs are investigated in this study and their parameters are shown in Table 3.


**Table 3.** Table of fan parameters.

The purpose of this step is to find new fan designs with potential performance gains, and those three representative designs as shown in Table 4 are categorized in order to determine the design direction of this study based on the results obtained from GRA.


#### *4.1. Analysis of the Correlation Degree of Gray Information*

The procedures of building the analysis model in relation to the gray information are explained sequentially as follows.

Step 1: The initial values of the design parameters for evaluation are shown in Table 5. These values are converted by GRA for initialization, and the results are shown in Table 6.


**Table 5.** Initial values of design parameters.

**Table 6.** Initialization of design parameters for gray relational analysis (GRA) *X*<sup>0</sup> = [*x*0(1), *x*0(2), ··· , *xi*(*k*)].


Step 2: Obtain the difference sequence,Δ0,*<sup>i</sup>* = *<sup>X</sup>*0(*k*) <sup>−</sup> *Xi*(*k*) , as shown in Table 7.



Step 3: From Table 7, the maximum and minimum values of the difference sequence can be determined as Δmin = Δ1,1(2) = 0.0000 and Δmax = Δ4,3(1) = 0.2667, respectively.

Step 4: Set the threshold value for gray correlation degrees at 0.5. The gray correlation degrees of various variance factors can be obtained as shown in Table 8.

**Table 8.** Gray correlation degree *ri*(*k*).


Step 5: Calculate each variance factor *Xi* for its average difference in the design parameters *X*<sup>0</sup> of the correlation degree in relation to the gray information *r*(*X*0, *Xi*). The resulting correlation degrees in relation to the gray information are shown in Table 9.


**Table 9.** Correlation degrees in relation to the gray information *r*(*X*0, *Xi*).

#### *4.2. Configuration of the Numerical Model*

As shown in Figure 6, a numerical model of the dual-impeller fan was built for the case study. The dimensions of the inlet and outlet zones were determined based on the recommended values in order to reflect a real scenario of no impedance to the air flow into the ambient.

#### *4.3. Settings of Model Parameters*

#### A. Settings of boundary conditions

The main consideration of the settings of boundary conditions is to reflect the physical phenomena of the surrounding environment and objects around the target model. It is critical to meet the physical phenomena or else the calculation result of the simulation might be affected. A designer might also be misguided into making a wrong decision. In this case study, the boundary conditions include the inlet boundary condition, outlet boundary condition, and wall boundary condition, which are described as follows.

1. Inlet boundary condition: The inlet condition is for the initial calculation. In order to simulate the condition of a fan in an infinite domain, a normal atmospheric pressure of *P0* is set at the inlet.

2. Outlet boundary condition: In order to simulation the air flow that is generated by the rotating impellers into the ambient, a normal atmospheric pressure of *P0* is also set at the outlet.

3. Wall boundary condition: For a fluid flow passing along a wall, it needs to satisfy not only the non-permeable condition but also the no-slip condition.

In addition to the above-mentioned conditions, this case study includes the following assumptions in order to simplify the complexity of the flow field calculation.


#### B. Mesh settings

As shown in Figure 7, the total number of cells is 1,957,013 for the dual impellers and 2,659,498 for the entire system, including the inlet and the outlet. As the mesh for the inlet and the outlet is used for the analysis of the upstream and downstream flow fields and for the boundary conditions, more cells are required at the locations that are closer to the dual impellers in order to simulate the complicated flow field locally. For the domain that is upstream to the dual impellers, the size of a cell is the largest at the inlet. Similarly, the size of a cell is the largest at the outlet for the domain that is downstream to the impellers. This is because no complex geometry exists at either the inlet or the outlet.

#### *4.4. Simulation Results of Fans*

The results of numerical simulation make it easy to understand the aerodynamic characteristics and the flow field of fans, which serve as the foundation for further investigation, analysis, and improvement. The contours of pressure, as shown in Figure 8, allow us to better understand the influence of pressure on the entire system in the flow field being analyzed as well as the velocity distribution of the fluid at the centerline section.

Lastly, the one to be compared is the resulting flow rate by numerical calculations. Based on the predicted flow rates of Table 10 by simulation at the outlet, it is known that the flow rate of 40.4 CFM in No. 2 is the maximum, whereas the change of incidence angle still has the effect of increasing the flow rate, but for the phenomenon of recirculation occurring along the upper edge of the impeller and between the blades, no big improvement is observed.

#### **Table 10.** Predicted flow rates by simulation.


The weighted averages of the correlation degrees x*1*~x*<sup>n</sup>* are determined by the following equation. By applying the weighted averages to the flow rate and the static pressure of each fan design, the resulting values of maximum flow rate and maximum static pressure are shown in Table 11.

**Table 11.** Weighted averages of the maximum flow rate and the maximum static pressure.


In this study, simulation of three kinds of different fan designs designated as No. 1, No. 2, and No. 3 was conducted separately. Verifications of the various results obtained, including flow rates and air pressures, were also conducted by the simulation. With the simulation results obtained, consistency verification was further conducted on these results by the correlation degree of gray information. Observation and comparison were conducted both on the maximum static pressure and the maximum flow rate. It can be found in the simulation results that the maximum flow rate of No. 2 is apparently 9% higher than that of No. 1, whereas the maximum static pressure of No. 2 is also about 8% higher than that of No. 1, as shown in Figure 6.

#### *4.5. Comparison Between the Results of Simulation and Experiment*

Method of measuring the performance curve of a fan

The testing of fan characteristics is accomplished on a wind tunnel, as shown in Figure 9. The performance of a fan is usually determined by several operating points instead of a single point of

#### *Symmetry* **2020**, *12*, 227

static pressure versus air flow rate, because it is typically not considered as a stable system. Moreover, when a fan operates under a constant input power, the resulting flow rate varies inversely proportional to the output air pressure. In this study, the procedure of measuring fan performance is as follows.

	- A. Turn on the thermometer, hygrometer, barometer, fiber-optic tachometer, and inverter one hour before measurement. Make sure the equipment operates at a stable state. A testing workbench with a wind tunnel is shown in Figure 10a. The fan to be tested is mounted on the front plate of the main chamber. Care should be taken to ensure that the fan is sealed adequately to prevent leakage.
	- B. Turn on the test fan and the auxiliary blower for several minutes until both of them run stably. Adjust the blast gate from fully open to fully closed and check the air flow through the chamber. Check the readings of each of the equipment.
	- C. Measure the pressure difference between the free-flow condition (free deliver) and the no-flow condition (shut off). Divide the pressure difference into nine segments for determining the pressure increment and the data acquisition points.

(**a**) Testing workbench with a wind tunnel (**b**) Specimen under wind-tunnel testing

**Figure 10.** Wind-tunnel testing.
