4. Shape Optimization

Response surface method (RSM) combined with threedimensional numerical simulation is introduced to enhance the performance of a regenerative blower. Detailed explanation of the RSM was described in the previous paper [2]. A response model f is assumed as a secondorder polynomial, which can be written as follows:

(3)

where n is the number of design variables, and x and β indicate the design variables and the coefficients, respectively. The number of coefficients (β₀, β₁, etc.) is .

In the present study, pressure and efficiency are selected as an objective function for the shape optimization in the blower.

To enhance the performance of the blower, the shape

of the blower is optimized by introducing two design variables: extension angle (θ) and number of impeller blade (NOB) as shown in Figure 4.

The range of each variable for selection of the points for response evaluation is determined by preliminary calculations, and is summarized in Table 2" target="_self"> Table 2. In the design space, the middle design values of each design variable are those of reference blower. Even interval is taken for

analyzing the effect of design variables on the object function.

5. Numerical Simulation

To determine the object function and analyze the flow characteristics inside the blower, general analysis code, CFX-13 [7], is employed in the present study. It solves compressible Reynolds-averaged Navier-Stokes equations (RANS) and continuity equation.

SST turbulence model with scalable wall function is employed to estimate the eddy viscosity [8]. In computational grids, unstructured grids are used to represent a composite grid system including the impeller and casing domains.

Figure 5 shows the computational grid system. Tetrahedral element is mainly imposed in the casing and impeller where wedge (prism) element having three layers is introduced near the wall. Hexahedral element is also imposed in the inlet and outlet duct to reduce the grid

nodes. The whole grid system in the present simulation has about 2,600,000 nodes. As boundary conditions, atmospheric pressure is specified at the inlet, and mass flow rate is specified at the exit. No-slip and adiabatic wall conditions are used on impeller blade and casing surfaces. Boundary plane between the impeller and casing regions is imposed frozen rotor interference.

Figure 6 shows a computational domain used in the present calculation, which has inlet and outlet ducts and a test blower. The length of inlet and outlet ducts corresponds to 10 times the inner duct diameter.

6. Results and Discussion

6.1. Validation of Numerical Simulation

For the validation of the numerical solutions, the distributions of pressure for the reference blower are compared to the experimental results according to flow rates.

Figure 7 shows that the distributions of local pressure and efficiency, which is obtained by numerical simulation. At the design flow condition, pressure simulated by numerically is 6.92. From the comparisons of pressure of Figures 3 and 7, the tendency of pressure according to the flow rates has almost same. It is noted that maximum efficiency is located at the design flow condition. The shape optimization of the blower is performed at the design flow condition using the numerical results.

6.2. Shape Optimization of the Blower

To evaluate the shape effects of the blower on the objective function, efficiency and pressure, the optimization has been performed. To measure uncertainty in the set of coefficients in a polynomial, ANOVA and regression analysis provided by t-statistic are used and the results are shown in Table 3. Guinta [9] suggested that the typical values of adjusted R² are in the range, 0.9 ≤ adjusted R² ≤ 1.0, when the observed response values are well predicted by the response surface model. Therefore, the present response surfaces obtained are reliable.

Figure 8 shows the contour plot of predicted response surfaces for the object functions of efficiency and pressure

for the design variables. As shown in Figure 8(a), the optimal values for the efficiency are located inside the boundary of the design space. For the pressure in Figure 8(b), optimal value of the NOB is on the outside of the design space. From the response surfaces for efficiency and pressure, optimal positions for each design variable can be found easily. Results of the shape optimization of the regenerative blower for the two design variables at the design flow rate are shown in Tables 4 and 5.

The estimated pressure rise for the optimal blower is successfully increased from 8.89 kPa to 9.18 kPa compared to that of reference one.

Figure 9 shows the results of sensitivity analysis for efficiency. As shown in the figure, the extension angle (θ) is sensitive on the object function compared to that of the number of impeller blade (NOB). This means that the shape optimization using extension angle is more effective to increase efficiency in the blower.

Figure 10 shows blower performance according to extension angles for three different blade numbers. Pressure and efficiency are tendency to increase as the number of impeller blade increases. Pressure has a maximum value at the extension of 52 degree for all number of impeller blades. However, efficiency has the highest value

at the extension of 57 degree for the blade number of 58. It is noted that the positions having maximum pressure and efficiency for the regenerative blower depend on the conditions of design variables.

6.3. Internal Flow Analysis of the Regenerative Blower

To analyze the performance of the regenerative blower

with the different design conditions, internal flow is compared using the results of numerical simulation.

Figure 11 shows the tangential velocity vectors on the three orthogonal planes to the rotational direction for the reference blower. The positions of each plane represent in Figure 11(a). Non-symmetric recirculation flow is formed in the blade passage at the inlet region (Plane 1).

From the distributions of the tangential velocity vectors, the low velocity region is formed at the center of recirculation flow. Strong radial flow is observed at the middle of blade passage due to centrifugal force, which results in the pressure increase at each pressure passage.

Relatively symmetric recirculation flow at the blade passage is formed at the middle and outlet blower passage (Planes 2 and 3).

Figure 12 shows the distributions of streamlines for the reference blower, which is side and front view from the casing. The streamlines are colored by velocity. From the figure, the flow comes through the inlet duct is separated to the both sides of the impeller. In the passage of a blower impeller, flow is accelerated to the radial direction with the rotation of the impeller.

Figure 13 shows the velocity distributions at the blower outlet according to extension angles. As described above, the reference blower has 54 blades and extension angle of 52 degree. Pressure has a maximum value when the extension angle of the blower is 52 degree. From the figure, it is noted that relatively large velocity distortion is observed at the extension angle of 47 and 57 degrees compared to that of 52 degree. Due to the non-uniform flow at the blower passage, pressure increase can be deteriorated by velocity defects. The velocity defects makes larger low velocity region. Low velocity region disturbs to make strong recirculation flow in the each blade passage, thus increases local pressure loss.

Figure 14 shows the distributions of isosurface having the low velocity of 5 m/s for the blade numbers of 54. In the figure, the low velocity region is formed in the both sides of the impeller.

The low velocity region is induced by horizontal inlet

flow and outlet flow having a radial component as shown in Figure 12. From the figure, relatively larger low velocity region is observed at the extension angle of 57 degree where pressure increase is lower compared to that of 52 degree in Figure 10(b).

Figure 15 shows the distributions of pressure for the blade numbers of 54. The reference blower (Figure 15(a)) has higher outlet pressure compared to larger extension angle of 57 degree.

Figure 16 shows the pressure distributions for the

blade numbers of 54. The measuring position is along the casing wall from inlet to outlet as shown in Figure 16(a). Gradually linear increase of pressure is observed for both cases along the measuring positions. It is noted that the pressure increase is caused by momentum force generated inside blade passage.

7. Conclusions

The optimal design of a Cathode blower used for building fuel cell system has been performed by the response surface method and the three-dimensional Navier-Stokes analysis. Two design variables, extension angle and number of impeller blade, are introduced to enhance the pressure and efficiency at the design flow condition.

Throughout the optimization of the blower shape, the pressure rise for the optimal blower is successfully increased up to 3.17% compared with that of reference at the design flow rate. And efficiency is also increased up to 1.4% compared to reference one. From the sensitivity analysis, an extension angle is more effective to increase efficiency in the blower.

From the internal flow analysis, the low velocity region is formed at the center of recirculation flow in the each blade passage. Low velocity region disturbs to make strong recirculation flow in the each blade passage, thus increases local pressure loss. It is noted that the pressure increase is caused by momentum force generated inside blade passage.

8. Acknowledgements

This work was supported by the New & Renewable Energy of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea Government Ministry of Knowledge Economy (No. 20113010030090).

REFERENCES