2. Measurement procedure


The performance improvement that is predicted by the numerical simulation is further compared to the result that is obtained from the wind-tunnel testing, as shown in Table 12. Both the difference in the pressure drop and that in the air-flow rate are within 5%, which indicates a small difference between the simulation and the experiment results.


**Table 12.** Comparison between results from the simulation and the experiment.

### **5. Results and Discussion**

In this study, the gray design GRA was used to determine the important design parameters for improving the design performance of the fan with the best solution for symmetry or asymmetry. Based on the results obtained by GRA, the priority of design parameters for improving performance was determined, and GRA stated that the second design can provide better performance than the other two designs. The effects of these design parameters are further studied through numerical simulations and experiments. The simulation results also showed that the static pressure of the No. 2 design was 1.92 mm-Aq, and its flow rate was 40.4 CFM. Compared to the other two designs, it was obvious that performance-wise, No. 2 was the best of the three fan designs. By taking the weighted averages of the correlation degrees for the design parameters, the resulting maximum static pressures were No. 1: 0.3182, No. 2: 0.3491, and No. 3: 0.3327. Moreover, the maximum flow rates were No. 1: 0.3218, No. 2: 0.3486, and No. 3: 0.3296. It is clear that the maximum flow rate of No. 2 was the largest among these three designs. The most important design parameters can be determined by GRA at an earlier stage of fan design.

The results of the case study indicated that among fan parameters, the one with the greatest influence was the leading-edge radius. The outside diameter is another design parameter that shows a higher correlation degree. However, it is already known that an oversized fan could cause a stall, which leads to the phenomenon of rapidly deteriorating fan performance. Moreover, in space-constrained applications, the outside diameter is typically not selected as one of the design variables, because increasing the outside diameter leads to a bigger fan, which might fail to fit into the available space.

**Author Contributions:** The author contributed to the paper. H.-H.L. collected and organized the data and acts as the corresponding author, J.-H.C. and C.-H.C. proposed the methods. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the Ministry of Science and Technology of the Republic of China under grant MOST-108-2221-E-468-003.

**Conflicts of Interest:** The author declares no conflict of interest.

#### **References**


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