In this paper, the response surface method using a three-dimensional Navier-Stokes analysis to optimize the shape of a forward-curved-blade centrifugal fan is described. For the numerical analysis, Reynolds-averaged Navier-Stokes equations with the standard $k-ε$ turbulence model are discretized with finite volume approximations. The SIMPLEC algorithm is used as a velocity–pressure correction procedure. In order to reduce the huge computing time due to a large number of blades in forward-curved-blade centrifugal fan, the flow inside of the fan is regarded as steady flow by introducing the impeller force models. Four design variables, i.e., location of cutoff, radius of cutoff, expansion angle of scroll, and width of impeller, were selected to optimize the shapes of scroll and blades. Data points for response evaluations were selected by D-optimal design, and a linear programming method was used for the optimization on the response surface. As a main result of the optimization, the efficiency was successfully improved. Effects of the relative size of the inactive zone at the exit of impeller and momentum fluxes of the flow in scroll on efficiency were further discussed. It was found that the optimization process provides a reliable design of this kind of fan with reasonable computing time.

1.
Kind
,
R. J.
, and
Tobin
,
M. G.
,
1990
, “
Flow in a Centrifugal Fan of the Squirrel-Cage Type
,”
ASME J. Turbomach.
,
112
, pp.
84
90
.
2.
Kim, J. K., and Kang, S. H., 1997, “Effects of the Scroll on the Flow Field of a Sirocco Fan,” ISROMAC-7, Hawaii, pp. 1318–1327.
3.
,
S.
,
Kawaguchi
,
K.
,
Suzuki
,
M.
,
Matsui
,
K.
, and
Kikuyama
,
K.
,
1994
, “
Experimental Study on Low-Noise Multiblade Fan” (First Report, Visualization of Three-Dinensional Flow Between Blades
),
JSME Int. J., Ser. B
,
60
, pp.
102
113
.
4.
Guo
,
E. M.
, and
Kim
,
K. Y.
,
2004
, “
Three-Dimensional Flow Analysis and Improvement of Slip Factor Model for Forward-Curved Blades Centrifugal Fan
,”
KSME Int. J.
,
18
, pp.
302
312
.
5.
Seo
,
S. J.
,
Kim
,
K. Y.
, and
Kang
,
S. H.
,
2003
, “
Calculations of Three-Dimensional Viscous Flow in a Multi-Blade Centrifugal Fan by Modeling Blade Forces
,”
Proc. Inst. Mech. Eng., Part A: Journal of Power and Energy
,
217
, pp.
287
297
.
6.
Lee
,
S. Y.
, and
Kim
,
K. Y.
,
2000
, “
Design Optimization of Axial Flow Compressor Blades With Three-Dimensional Navier-Stokes Solver
,”
KSME Int. J.
,
14
, pp.
1005
1012
.
7.
Jameson, A., Schmidt, W., and Turkel, E., 1981, “Numerical Solutions of the Euler Equation by Finite Volume Methods Using Runge-Kutta Time Stepping Schemes,” AIAA 81-1259.
8.
Shyy
,
W.
,
Papila
,
N.
,
Vaidyanathan
,
R.
, and
Tucker
,
K.
,
2001
, “
Global Design Optimization Aerodynamics and Roket Propulsion Components
,”
Prog. Aerosp. Sci.
,
37
, pp.
59
118
.
9.
Kim
,
K. Y.
, and
Kim
,
S. S.
,
2002
, “
Shape Optimization of Rib-Roughened Surface to Enhance Turbulent Heat Transfer
,”
Int. J. Heat Mass Transfer
,
45
, pp.
2719
2727
.
10.
Sevant
,
N. E.
,
Bloor
,
M. I. G.
, and
Wilson
,
M. J.
,
2000
, “
Areodynamic Design of a Flying Wing Using Response Surface Methodology
,”
J. Aircr.
,
37
, pp.
562
569
.
11.
Ahn
,
C. S.
, and
Kim
,
K. Y.
,
2003
, “
Aerodynamic Design Optimization of an Axial Flow Compressor Rotor
,”
Proc. Inst. Mech. Eng., Part A: Journal of Power and Energy
,
217
, pp.
179
184
.
12.
Han
,
S. Y.
,
Maeng
,
J. S.
, and
Yoo
,
D. H.
,
2002
Shape Optimization of Cutoff in A Multiblade Fan/Scroll System Using Response Surface Methodology
,”
Numer. Heat Transfer, Part B
,
42
, pp.
1
12
.
13.
Launder
,
B. E.
, and
Spalding
,
D. B.
,
1974
, “
The Numerical Computational of Turbulent Flows
,”
Comput. Methods Appl. Mech. Eng.
,
3
, pp.
269
289
.
14.
Fletcher, C. A., 1991, Computational Techniques for Fluid Dynamics I, Springer, Berlin.
15.
Myers
,
R. H.
,
1999
, “
Response Surface Methodology-Current Status and Future Direction
,”
J. Quality Technol.
,
31
, pp.
30
44
.
16.
Box
,
M. J.
, and
Draper
,
N. R.
,
1971
, “
Fractional Designs, the |XTX| Criterion, and Some Related Matters
,”
Technometrics
,
13
, pp.
731
742
.
17.
Venter, G., Haftka, R. T., and Starnes, J. H. Jr., 1996, “Construction of Response Surfaces for Design Optimization Applications,” AIAA 96-4040-CP.
18.
Guinta, A. A., 1997, “Aircraft Multidisciplinary Design Optimization Using Design of Experimental Theory and Response Surface Modeling Methods,” Ph.D. thesis, Department of Aerospace Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA.
19.
Myers, R. H., and Montgomery, D. C., 1995, Response Surface Methodology: Process and Product Optimization Using Designed Experiments, Wiley, New York.
20.
Roth
,
H. W.
,
1981
, “
Optimierung von Trommella¨ufer,-Ventilatoren
,”
Stro¨mungsmechanik und Stro¨mungsmaschinen
,
29
, pp.
1
45
.