The 4th International Conference on Design Engineering and Science, ICDES 2017 Aachen, Germany, September 17-19, 2017

Copyright © 2017, The Organizing Committee of the ICDES 2017

Study on Optimum Design Method for Small Axial Fan

Toshiyuki HIRANO*1, Toshio OTAKA*2 and Gaku MINORIKAWA*3

*1, 2 Mechanical Engineering Course, Department of Science and Engineering, Kokushikan University 4-28-1, Setagaya, Setagaya City, Tokyo, 154-8515, JAPAN thirano@kokushikan.ac.jp, otaka@kokushikan.ac.jp

*3 Department of Mechanical Engineering, Faculty of Science and Engineering, Hosei University 3-7-2, Kajinocho, Koganei City, Tokyo, 184-8584, JAPAN minori@hosei.ac.jp

Abstract

In order to establish optimum design methodology of small axial fan, response surface method as optimization technique was applied. Small axial fan with impeller diameter of 36 mm was designed, prototyped and examined performance characteristics by CFD and experiment. In the study, relationship between design parameters such as blade cord length, camber and blade setting angle and performance characteristics was examined by multi regression analysis using obtained data. It was found that the methodology showed optimal trends of design parameters visually and improvement of performance was confirmed by simulation and experiment. Keywords: small axial fan, performance, optimum design, response surface, experiment, CFD

1 Introduction In recent years, IT products such as personal

computer, multi-function printer, audio and visual equipment and so on have been widely used because of the development of information and communication technologies. Since the demand for downsizing and improvement of the processing speed is increasing, the packaging density of the devices is getting higher and the thermal design is getting severer. So, the forced air cooling by small axial fan is commonly used in the thermal design. However, the efficiency of small axial fan is extremely low due to not only the aerodynamic viewpoint but also the restriction such as cost and productivity, compared with industrial fans. Thus, there are few reports about the design and performance prediction on small fan [1-9]. In the present study, the response surface method as an optimization technique was applied to the small axial fan design.

2 Design of axial fan In order to apply for car navigation system and so on,

axial fan with the frame size of 40mm was usually adopted. It has the feature that the inside diameter is relatively large to the outside diameter of the impeller. The small axial fan used in this study is shown in Figure 1. The impeller has the outlet diameter of 36mm, and the inner diameter of 23mm and the height of 6.2mm. Table 1 shows the main specification of the airfoil shape designed by this study and the cross sectional view of the blade, respectively. A cambered

plate with the fixed thickness was used for the blade cross-sectional shape in consideration of productivity. The maximum camber and its location were designed to obtain enough lift. The blade number of the impeller was 5 and the thickness was 0.5mm. In order to optimize the impeller, the orthogonal array table of the factors and levels for the experimental design was made. Table 2 and Table 3 show the factors and the orthogonal array table. Although there are many design parameters in fan design, three parameters of the blade setting angle θ on the Tip side, the camber ratio f/L and the blade chord length L that affect the drawing of the blades and the performance were chosen. The base fan had the blade setting angle θ =16deg, the camber of 3% and the blade chord length L=12mm, respectively. In the experiment, the impeller was installed in a casing with DC blushless motor (NIPPON KEIKI WORKS, LF40A12). The inner diameter of the casing was 38mm and the clearance between the blade tip and the casing was 1mm.

(a) 3D model

(b) Cross sectional view of blade

Fig.1 Tested impeller

Table 1 Specification of base impeller

Imp. No. Symbol Unit Specification

Airfoil section Cambered

Plate Camber ratio f/L [%] 6

Camber location x/L [%] 30 Number of blade Z - 5 Blade thickness t [mm] 0.5

Blade chord length (Tip) L [mm] 12 Blade setting angle (Tip) θ [deg.] 16

333

Table 2 Factor and level of tested impeller

Factor Level Setting angle (Tip) θ [deg.] 16, 18, 20

Camber f/L 5, 7.5, 10 Blade chord length (Tip) C [mm] 15, 17.5, 20

Table 3 Orthogonal layout (Parameter assignment) Imp. No.

Blade Setting angle (Tip) θ [deg.]

Camber f/L

Blade Chord length (Tip) C [mm]

1 16 5 15 2 16 7.5 17.5 3 16 10 20 4 18 5 17.5 5 18 7.5 20 6 18 10 15 7 20 5 20 8 20 7.5 15 9 20 10 17.5

3 CFD analysis

CFD (Computational Fluid Dynamics) analysis for the same flow fields as the experiment was performed by using commercial software (Software Cradle SCRYU/Tetra). The calculation grids were mainly non-structural tetra mesh and partially structural hexagonal mesh around the blade and the wall surface. The calculating region consisted of the inlet, the outlet and the fan as rotational region. The number of grids was about 5,800,000. The dimensions of the outlet region imitated the experimental apparatus. The entire and enlarged view of the calculation models are illustrated in Figure 2.

(a) Overall view

(b) Enlarged view of tested fan region

Fig. 2 Overall view of computational grids

As the boundary conditions, the inlet surface was set by atmospheric pressure and the outlet surface was regulated by given flow rates. The tested fan region was constructed by moving meshes as ALE (Arbitrary Lagrangian and Eularian) method. To obtain the maximum flow rate, static pressure at the outlet surface was set to 0Pa. The calculation was performed by steady

RANS (Reynolds Averaged Navier-Stokes) and the turbulent model was a standard k-ε model. The blade efficiency of the tested fan was calculated using the following equation. The torque of the tested fan was the sum of a pressure moment and a viscous force moment on the blade surface.

100TN

QPs (1)

Ps : Static pressure[Pa], Q : flow rate[m3 /min], T: Torque of fan [Nm]

4 Experimental apparatus and method The experimental apparatus is shown in Figure 3.

This apparatus mainly consisted of a tested fan, a chamber, a flow meter and a suction device. The wall static pressure holes were installed at 40mm upstream and downstream of the orifice. The tested fans were manufactured using a stereo lithography machine (EnvisionTEC, ULTRA). The static pressure Ps, which was the wall pressure on the front chamber, was measured by a small digital differential pressure gauge (NAGANO KEIKI, GC31). The flow rate Q was obtained by measuring the flow meter (KEYENCE, FD-A50).

In order to obtain a performance characteristic curve which is called a PQ curve, firstly, the maximum static pressure Psmax was measured by sealing the chamber and the maximum flow rate Qmax was obtained so as the static pressure at the chamber was set to 0Pa by adjusting the suction device. Then dividing Qmax into several points, values of Ps at given Q were obtained. The rotational speed of the impeller was kept at 6,800rpm by adjusting the input voltage.

Fig. 3 Schematic view of test apparatus

5. Results and Discussions Figure 4 shows the calculated PQ curves of the

tested fans. In this figure, the vertical axis indicates the static pressure in the chamber and the horizontal axis indicates the flow rate. The maximum static pressure and the maximum flow rate varied into 31.1-35.5Pa and 0.11-0.14m3/min by changing each parameter. The tendencies of the characteristic curves were almost same.

Figure 5 shows the calculated PQ and efficiency curves of fans No.1, No.2 and No.3. The vertical axes show the static pressure and the blade efficiency, and the horizontal axis shows the flow rate. The blade setting angle of each impeller is β = 16 °, and as the

impeller No. increases, the camber f/L and the chord length C increase. Comparing the analysis results, it can be seen that both the static pressure and the maximum flow rate increased as the impeller No. increased in the region where the flow rate Q was 0.03 m3 / min or greater. It is considered that the blade with a long chord length was not affected by the stall caused by the separation and the lift increased due to the generation of the pressure difference in the larger area.

Figure 6 shows the calculated PQ and efficiency curves of No. 1, No. 4 and No. 7. The camber of each impeller is the same, and as the impeller No. increases, both the blade setting angle and the chord length increase. Comparing the results, both static pressure and maximum flow rate increased as the impeller No. increased. This is also considered that the performance of both the static pressure and the flow rate improved as a result of the increased amount of air pushed out by the fan due to the reaction of the increased lift force.

Figure 7 shows the comparison of the PQ curves and calculated static pressure efficiency curves of No.3 and No.9, in which the largest difference on the efficiency was shown. As shown in Figure 7, the static pressure efficiency η of No.3 was larger than that of No.9 below Q=0.09m3/min. But the static pressure and maximum flow rate of No.3 were lower than that of No.3 over Q=0.09m3/min.

Fig. 4 Performance curves of tested fan (No.1 – 9)

Fig. 5 Performance and efficiency curves of tested

fan (No.1, No.2 and No. 3)

Fig. 6 Performance and efficiency curves of tested

fan (No.1, No.4 and No.7)

Fig. 7 Performance and efficiency curves of tested

fan (No.3 and No.9)

Significance of the three factors was examined by F test on two cases that the maximum static pressure efficiency was set as the objective function (Optimum η) and the maximum flow rate as the objective function (Optimum Q). As a result, the confidence interval was lower than 95% in case of the Optimum η and it is considered that these three factors had little influence. On the other hand, in case of the Optimum Q, the confidence interval of the chord length was slightly less than 95%, but the confidence interval of the blade setting angle and chamber were more than 95%. It is thought that the influence of three factors existed.

The linear regression equation was obtained by least-squares method from the relationship between the objective function and the factors in Table 4 and Table 5. These equations are indicated by equation (2) and equation (3). The expectancy of each level was estimated by using each equation as shown in Table 4. The values of the multiple correlation coefficients, the multiple contributing ratios and the contributing ratios adjusted for the degrees of freedom of correlation, which calculated the precision of the regression model from predicted value, were shown in Table 5. It is considered that there are no correlations in three factors about the Optimum η condition. On the other hand, it is considered that there are correlations in three factors about the Optimum Q condition.

Optimum η: y=23.3-0.139x1-0.020x2+0.015x3 (2)

Optimum Q:

y=0.0472+0.00289x1-0.00213x2+0.00067x3 (3)

Table 4 Orthogonal layout (expectancy)

Imp. No. Static pressure

efficiency η [%] Maximum flow rate

Q[m3/min] 1 21.2 0.114 2 20.0 0.112 3 21.7 0.128 4 20.2 0.123 5 21.6 0.128 6 21.6 0.129 7 21.1 0.128 8 21.2 0.130 9 19.2 0.138

Table 5 Analysis of multiple correlations

Optimum η Optimum QMultiple correlation

coefficient[-] 0.284 0.978

Contributing ratio[-] 0.081 0.960 Contributing ratio

adjusted for the degrees of freedom[-]

-0.470 0.936

The response surface was made by using the

factors and the objective functions. In the study, the response surface had four dimensions because three factors were used to one function. Therefore, one factor was fixed and the three-dimensional chart with other factors as variables was made. Figure 8 shows the response surface of blade setting angle β=16deg. as an example. In this figure, the x, y and z axis indicate the blade chord length C, static pressure efficiency η and camber f/L, respectively. As the results, the optimum values of C, η and f/L in the Optimum η condition were determined as shown in Table 6. In the same way as above, the optimum values in the Optimum Q condition were also determined in Table 6.

Fig. 8 Response surface (β=16°)

Table 6 Optimum value Factor Optimum η Optimum Q

Blade setting angle (Tip) θ [deg.]

16 20

Camber f/L 10 10 Blade Chord length (Tip) C

[mm] 15 20

Figure 9 shows the performance curves of each

optimum fan and base fan, respectively. The fans of Optimum η and base fan were analyzed and also tested. The performance curves of analysis results and experimental results in these fans were same tendency.

(a)Base fan

(b)Optimum η

(b)Optimum Q

Fig.9 Performance and efficiency curves of tested fan

The maximum static pressure efficiency of Optimum η was increased by around 4% compared with that of base fan. In addition, the value of Optimum η was the largest value in those of fans which were designed by the design of experiments. However, it should be considered that the fan of Optimum η was little correlation between the maximum static pressure coefficient and the three factors. On the other hands, the maximum flow rate of Optimum Q was increased by around 8% compared with that of base fan. The value of Optimum Q was the third largest value in those of fans which were designed by the design of experiments.

The impeller was made on the response surface considered to be correlated, and since the maximum flow rate was improved compared with the reference fan, the significance of the response surface method could be confirmed. However, the shape of the optimized impeller has not yet been reached. In this study, it is considered that it influenced the correlation coefficient and the analysis and test result in consideration of the fact that it is a parameter set in the design of the impeller with restrictions setting the casing.

7 Conclusions

In order to optimize the small axial fan by using the response surface, various types of impeller were designed by the design of experiments and the effects of three parameters on the performance were investigated by calculation and experiment. The present study obtained the following conclusions. (1) As a result of creating the response surface, it was

possible to visually judge the optimal parameter trend under fan design conditions in this study. In addition, the small axial fan designed based on the result was able to obtain high static pressure efficiency and maximum flow rate, and it was possible to confirm the effectiveness of the response surface method.

(2) Numerical analysis results and experimental results of the model using the parameters of the obtained optimum solution show almost the same tendencies, and it was found that application of the response surface method to actual machines is possible.

Acknowledgment

This work was supported by JKA and its promotion funds from KEIRIN RACE.

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Received on April 12, 2017 Accepted on May 29, 2017