Journal of Mechanical Science and Technology 27 (1) (2013) 33~42

www.springerlink.com/content/1738-494x

DOI 10.1007/s12206-012-1220-y

Response surface method-based optimization of the shroud of an axial cooling fan

for high performance and low noise†

Guangzhi Ren1, Seung Heo1, Tae-Hoon Kim2 and Cheolung Cheong1,*

1School of Mechanical Engineering, Pusan National University, Busan 609-735, Korea 2Engineering Design Department, LG Electronics, Changwon 641-110, Korea

(Manuscript Received June 4, 2012; Revised August 21, 2012; Accepted August 29, 2012)

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Abstract

We optimized the shroud of an axial cooling fan in a mechanical room of a household refrigerator using the response surface method

(RSM) based on numerical predictions in terms of high flow rate and low noise. Computational fluid dynamics (CFD) techniques and an

acoustic analogy were used to predict the volume flow rate (VFR) and noise in the system. The numerical methods were validated by

comparing their VFR and acoustic power level predictions with the measured data. Then, the RSM was used to optimize the design pa-

rameters of the shroud of an axial cooling fan. The numerical prediction using optimum design obtained for maximum VFR from the

RSM showed that the VFR can be increased by 21.8% at the cost of an increase in the acoustic power level by 1 dB. The prediction for

minimum noise reveals that the acoustic power level can be reduced by 3.55 dB at the same flow rate as the original model. The orifice

length of the shroud and the serrated structure are found to contribute significantly to the flow rate and radiated noise, respectively.

Physical reasons for these observations are given based on detailed investigations of the variations of flow fields due to the design pa-

rameters.

Keywords: Shroud; Response surface method; Volume flow rate; Surface acoustic power level

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1. Introduction

A cooling fan system is generally used to cool a condenser

and a compressor in the mechanical room of a refrigerator.

The overall efficiency of the refrigerator depends on the cool-

ing efficiency of the fan system that, in turn, depends on the

volume flow rate (VFR). Thus, the aim of designing a cooling

fan is to maximize its VFR. However, since the fan is also a

dominant contributor to the noise radiated from a refrigerator,

an additional requirement in designing the fan is to minimize

its radiated noise.

Generally, optimization methods can be divided into three

categories: Taguchi methods, genetic algorithms (GAs), and

the response surface method (RSM). Taguchi methods are

statistical methods developed to improve manufactured goods.

Recently, they have been applied to other fields such as engi-

neering [1], biotechnology, marketing, and advertising. GAs

[2] belong to the larger class of evolutionary algorithms (EA)

that generate solutions to optimization problems using tech-

niques inspired by natural evolution.

RSM [3] is a collection of mathematical and statistical tech-

niques for empirical model building. Using design of experi-

ments, the objective is to optimize a response or several re-

sponses that are influenced by several independent parameters

with limited ranges. RSM is capable of solving multiple re-

sponses over the entire area of interest, and producing more

accurate solutions than other methods.

Many studies, recent works among them [4-7], have been

performed to develop fans with high performance and low

noise. To the authors’ best knowledge, the effect of the fan

shroud on fan performance has not been systematically inves-

tigated. In this study, the shroud of an axial cooling fan in a

mechanical room of a household refrigerator is optimized

using the RSM, combined with computational fluid dynamics

(CFD) techniques, and an acoustic analogy for high flow rate

and low noise. Three shroud parameters that influence the

performance of the axial fan cooling system were selected and

optimized using the RSM with respect to the maximum VFR

and lowest noise. Further study was carried out to investigate

the detailed mechanism by which the parameters of the shroud

lead to the optimum results in terms of flow rate and radiated

noise. *Corresponding author. Tel.: +82 51 510 2311, Fax.: +82 51 514 7640

E-mail address: ccheong@pusan.ac.kr † Recommended by Editor Yeon June Kang

© KSME & Springer 2013

34 G. Ren et al. / Journal of Mechanical Science and Technology 27 (1) (2013) 33~42

2. Design of experiment and preliminary study

Generally, the RSM consists of three steps [8]. First, de-

signs of experiments (DOE) are conducted under adequate

and reliable measurements of the responses of interest. Then, a

mathematical model representing the best fit of the data col-

lected from the execution of DOE is determined. Finally, the

values that produce the optimal response are found. In this

section, a design of experiment is made, and a preliminary

study is carried out to validate the computational methods for

the target responses.

2.1 Selection of responses

The RSM was applied in combination with CFD techniques

and an acoustic analogy to obtain the optimum design of the

fan shroud. To achieve the optimal result, two output variables

were selected as the responses for the RSM: the VFR of the

outlets, and the acoustic power of the fan and shroud.

To predict the VFR and flow pattern of the axial fan system,

rotating reference frames [9] were defined. When a moving

reference frame is activated, the equations of motion are modi-

fied to incorporate the additional acceleration terms that occur

due to the transformation from the stationary to the moving

reference frame. The flow around the moving parts can be

modeled by solving these equations for the steady state. For

the velocity formulation with respect to a stationary coordinate

system, the governing equations of fluid flow for a steadily

rotating frame can be written as follows:

Conservation of mass:

0rvt

ρρ

∂+ ∇ ⋅ =

∂

r. (1)

Conservation of momentum:

( ) ( )rv v v v p Ftρ ρ ρ ω τ

∂+ ∇ ⋅ + × = −∇ +∇ ⋅ +

∂

r r r ur r ur. (2)

However, as the Mach number of flow velocity in the cur-

rent problem is less than 0.3, the flow is assumed to be in-

compressible and thus Eqs. (1) and (2) are closed. The VFR

through a surface is computed by summing the value of the

facet area vector multiplied by the facet velocity vector as

follows:

1

n

iiv

i

Q v d A v A=

= ⋅ = ⋅∑∫r ur r ur

. (3)

To predict the noise response of the cooling fan system, we

used the surface acoustic power level [10]. Curle’s integral

based on an acoustic analogy can be used to approximate the

local contribution from a body surface to the total acoustic

power. To that end, we start with Curle’s integral,

( ) ( ) ( ) ( )2

0

1, ,

4

i i i

s

x y n pp x t y dS y

a r tτ

π

− ∂′ =

∂∫r ur ur

(4)

where τ denotes the emission time 0( / )t r aτ = − and S is

the integration surface.

From Eq. (4), the sound intensity in the far field can be ap-

proximated by

( ) ( ) ( )22

2

2 2 2

0

1 cos,

16c

s

pp y A y dS y

a r t

θτ

π∂ ′ ≈ ∂

∫ur ur ur

(5)

where cA is the correlation area, r x y≡ −

r ur, and cosθ is

the angle between x y−r ur

and the wall-normal direction nr.

The total acoustic power emitted from the entire body sur-

face can be computed by

( ) ( )22 2

0 00 0

1sinA

sP p r d d I y dS y

a

π πθ θ ψ

ρ′= =∫ ∫ ∫

ur ur (6)

where

( ) ( ) 2

3

0 012

cA y p

I ya tρ π

∂ ≡ ∂

ur

ur. (7)

Eq. (7) can be interpreted as the local contribution per unit

surface area of the body surface to the total acoustic power.

The surface acoustic power in dB is

10log Aw

ref

PL

P

=

(8)

where Pref is the reference surface acoustic power (Pref = 10-

12W by default).

2.2 Factors and level selection for the RSM

Generally, a mechanical room of a refrigerator consists of

five parts: an axial fan, a shroud, a compressor, a condenser,

and an outer case. The case consists of two inlets and two

outlets. The mechanical room is separated into two parts, up-

stream and downstream, by the axial fan and shroud. The con-

denser is positioned upstream of the fan and the compressor is

located downstream of the fan.

To increase computational efficiency, we simplified the

mechanical room by removing the condenser, which is be-

lieved to have a negligible effect on the variation of VFR and

noise due to the change in shroud shape because the condenser

is located upstream. This assumption is confirmed in Section 4,

where we describe detailed investigations of the variations of

flow fields due to the selected design parameters. The entire

computational domain and computational mesh are shown in

Fig. 1. A steady state model with respect to the rotating refer-

G. Ren et al. / Journal of Mechanical Science and Technology 27 (1) (2013) 33~42 35

ence frame and an RNG k-epsilon viscous model were used in

the computations using the commercial CFD program

ANSYS FLUENTTM (12.1.2, ANSYS Inc.).

To consider grid refinement, numerical computations were

carried out with four different meshes used to model the me-

chanical room. The relationships between the number of mesh

elements and the response values of the VFR and sound

power levels are shown in Figs. 2 and 3, respectively. The

predicted values of the VFR and surface acoustic power level

converge when the element number is above 2 million. There-

fore, 2 million elements were used in all of the subsequent

computations.

Fig. 4 illustrates the definitions of three key design factors

involved in the optimization using the RSM for the cooling

fan system. Factor L represents the distance by which the fan

moved from its original position in the axial-direction (down-

stream direction). As L increases, the distance between the

motor and the fan also increases, which may reduce the inter-

actions between the wake shedding from the motor box and

the fan. In this respect, an increase in L may increase the VFR

and decrease the noise. Factor D represents the orifice length

of the shroud in the axial-direction. As D increases, the flow

pattern increasingly resembles ducted fan flow, which may

increase the flow rate. The factor h represents the height of the

serrated shape as λ is fixed. Some studies have reported that a

saw tooth-shaped trailing edge reduces the fan noise [11, 12].

On the basis of similarity between the flows around the trail-

ing edge and the orifice of a shroud, this factor was selected

for possible noise reduction. Because of the geometrical limi-

tations in the mechanical room and the limitations of saw-

tooth manufacturing capability, parameter L must be greater

than 0 mm and h must be less than 12 mm. The levels of the

factors are summarized in Table 1.

2.3 Experimental validation for numerical method

The accuracy of the numerical methods used for the RSM

must be validated for reliable optimum design. Our numerical

predictions were compared to the measured data to validate

the numerical techniques before the RSM was applied. Four

cases (D = 0 mm; 7 mm; 14 mm; and D = 0 mm with h = 7

mm) were computed with the developed computational do-

main and mesh, as shown in Fig. 1.

For comparison, the VFR was measured using a fan tester

as shown in Fig. 5. The VFR can be calculated with the meas-

ured pressure drop using the following expression:

( )2

1d n

pQ C A Y

ρ β∆

=−

(9)

where Q denotes the VFR, Cd is a nozzle discharge coefficient,

An is the area of the nozzle throat, Y is an expansion factor

accounting for compressibility, ∆p is the measured pressure

Fig. 1. Mesh of the entire mechanical room.

Fig. 2. Variation of predicted VFR versus the number of elements.

Fig. 3. Variation of surface acoustic power level versus the number of

elements.

Table 1. Factors and levels.

Level Factor

-1 0 +1

D (mm) 24.5 31.5 38.5

h (mm) 3 7.5 12

L (mm) 0 10 20

Fig. 4. Three factors of the RSM.

36 G. Ren et al. / Journal of Mechanical Science and Technology 27 (1) (2013) 33~42

drop across the nozzle, ρ is the fluid density upstream of the

nozzle, and β is the contraction ratio. The numerical and ex-

perimental results are compared in Fig. 6.

The experiment was carried out by adding the duct system

that was connected to the outlet of the mechanical room, i.e.,

there was additional loss due to the friction between the flow

and the duct surface. Therefore, the measured values are less

than the predicted values, and the comparison was made using

the relative values from the original case instead of the abso-

lute values in Table 2. As shown in Fig. 6 and Table 2, there is

good agreement between the two results in terms of the rate of

their variations according to the variations of D and h. As

factor D increases, the predicted and measured VFRs increase

in a similar manner. The introduction of a saw tooth shape

(h = 7 mm) also led to a slight increase in the VFR.

The surface acoustic power level was measured using the

international standard ISO-3745 in a hemi-anechoic room, as

shown in Fig. 7. A hypothetical hemisphere was used as the

measurement surface. Ten microphones were located on the

hemisphere for acoustic measurements, and the noise source

was located in a hypothetical reference box. The hypothetical

hemisphere and reference box are shown in Fig. 8. For the A-

weighted sound pressure level or the level in each frequency

band of interest, ISO-3745 requires that an average sound

pressure level over the measurement surface be calculated in

the following form:

0.1

10

1

110log 10

ipi

NLi

p

i

L dBN =

=

∑ (10)

where i

pL denotes the sound pressure level over the measure-

ment surface, i

piL is the sound pressure level at the ith micro-

phone position, and N is the number of microphones. The

surface sound pressure level can be defined as

(a)

(b)

Fig. 5. Fan tester: (a) Schematic of the fan tester layout; (b) Main

structure of the fan tester.

Fig. 6. Comparison of the predicted and measured VFRs.

Table 2. Volume flow fate (VFR) comparison of the numerical and

experimental results (Unit: m3/s).

D = 0 D = 7 D = 14 Serrated

Numerical 0.0375 +8.6% +3.1% +0.6%

Experimental 0.0215 + 3.5% + 2.1% + 1.1%

Fig. 7. Experimental layout in a hemi-anechoic room.

Fig. 8. Plot of measurement surface, reference box, and key micro-

phone positions.

G. Ren et al. / Journal of Mechanical Science and Technology 27 (1) (2013) 33~42 37

1 2

i i

pf pL L K K= − − (11)

where K1 and K2 denote a correction for background noise and

the test environment, respectively.

The sound power level can be given as

10

0

10logi

w pf

SL L dB

S

= +

(12)

where S is the area of the measurement surface and S0 = 1 m2.

Fig. 9 shows a comparison between the predicted and

measured values. There is good agreement between the nu-

merical and experimental results in terms of the rate of varia-

tions due to changes in the design factors. As the variables

change, the predicted surface acoustic power values closely

follow the measure values. However, there is a slight differ-

ence in the absolute values between the two results. This dif-

ference seems to arise because inlet_1 and outlet_1 face the

free space in the numerical simulations as shown in Fig. 1,

while inlet_1 and outlet_1 face the floor in the experiment as

shown in Fig. 7. However, since the other conditions (except

for the relevant design factors) are the same in the experiments,

variations in the measured sound power should be due to

variations of D and h. Our goal is to develop the optimum

design of the fan shroud in terms of VFR and noise. The close

agreement in the rate of variation due the change in design

factors between the predicted and measured values validates

the proposed numerical methods. On the basis of these results,

the numerical methods for predicting the VFR and surface

acoustic power were used in subsequent sections for optimiza-

tion studies.

3. Optimizations using RSMs

In the RSM, it is infeasible to perform a full factorial ex-

periment in which every possible value of each parameter is

tested. Instead, the fractional factorial method, known as face-

centered central composite design (FCCD) [13], was used. In

this design, parameter values corresponding to the corners,

center, and face are shown in Fig. 10. Face-centered central

composite design was used in the implementation of the RSM

method because it requires fewer runs.

To simplify the RSM calculations, the independent vari-

ables were coded to the typical interval (-1, 1). The final RSM

results were obtained using the prescribed numerical tech-

niques summarized in Table 3.

A second-order model is usually used in the RSM, as it is

easy to estimate the parameters of the model. Generally, a

second-order model can be written in the form

0

1 1,

k k

i i ij i j

i i j i

x x xη β β β= = ≤

= + +∑ ∑ . (13)

We introduce four strategies to analyze the RSM results and

to obtain optimum designs. The strategies are described in the

following subsections.

3.1 Maximum volume flow rate

First, the VFR rate was targeted. The following numerical

fitting function was obtained from the RSM calculation of the

VFR in terms of the three coded variables:

Fig. 9. Comparison of the predicted and measured surface acoustic

power levels.

Table 3. RSM results.

x1 x2 x3 VFR

(m3/s)

Sound Power

(10-8 W)

-1 -1 -1 0.0422 0.97

+1 -1 -1 0.0422 0.977

-1 +1 -1 0.0423 0.975

+1 +1 -1 0.0425 0.979

-1 -1 +1 0.0437 1.143

+1 -1 +1 0.0456 1.245

-1 +1 +1 0.0441 1.192

+1 +1 +1 0.0450 1.239

-1 0 0 0.0446 1.016

+1 0 0 0.0451 1.02

0 -1 0 0.0448 1.02

0 +1 0 0.0447 1.025

0 0 -1 0.0423 0.975

0 0 +1 0.0455 1.227

0 0 0 0.0448 1.019

Fig. 10. Face-centered central composite design (FCCD).

38 G. Ren et al. / Journal of Mechanical Science and Technology 27 (1) (2013) 33~42

1 2 3

2 2 2

1 2 3 1 2

1 3 2 3

(2.696 0.021 0.0003 0.074

0.009 0.014 0.066 0.005

0.018 0.005 ) / 60

vQ x x x

x x x x x

x x x x

= + + +

− − − −

+ −

. (14)

The fitting function was obtained using Minitab® software

(14, Minitab Inc.), which is useful for RSM analysis. The

resulting function is in good agreement with the predicted data.

The significant terms for VFR were found to be the variables

D, L, L2, and DL. Fig. 11 shows the variations of the VFR

according to parameter D. The figure demonstrates that pa-

rameter D contributes dominantly to the VFR, and that there is

an optimum value in the considered range. Fig. 12 shows the

iso-contours of the VFR versus L and h. There must be a

maximum point of VFR in the available range of parameters L

and h because parameter D = 0.

Eq. (14) reveals that the VFR is maximized at the values of

the uncoded parameters (D, h, L) = (38.5, 6.15, 17). Under this

condition, the VFR can be increased by 21.8%, and the sur-

face acoustic power level increases 1dB at the same time. To

confirm this optimal design, additional numerical computation

was performed. The predictions showed that the VFR can be

increased by 21.4%, and the surface acoustic power level in-

creases 0.5dB at the same time. There is good agreement be-

tween the RSM optimal results and its corresponding numeri-

cal predictions.

3.2 Minimum sound power

Only the surface acoustic power was minimized. The re-

sponse can be approximated as a fitting function of the three

variables in the following form:

1 2 3

2 2 2

1 2 3 1 2

1 3 2 3

1.024 0.016 0.006 0.117

0.007 0.003 0.076 0.007

0.017 0.005

AP x x x

x x x x x

x x x x

= + + +

− − + −

+ +

. (15)

In Eq. (15) the significant terms for the surface acoustic

power are D, h, L, L2 and DL. The iso-contours versus D and L

are shown in Fig. 13. As factor L increases, the surface acous-

tic power also increases. By the same procedure used in VFR

analysis, the surface acoustic power was minimized with re-

spect to parameter values (D, h, L) = (24.5, 3, 3.5). Under this

condition, the surface acoustic power level increases by 0.1dB,

and the VFR increases by 14.6% at the same time (compared

to the original model). Note that the original model (D, h,

L) = (0, 0, 0) is not included in the computational range. The

minimum surface acoustic power is only in the selected range.

Additional numerical computation to validate this optimal

result predicted that the VFR can be increased by 15.5%, and

the surface acoustic power level increases 0.1dB at the same

time.

3.3 Conversion of VFR into noise

The increased VFR can be converted to noise reduction. To

maintain the cooling capability of the cooling system, the

VFR must be equal to or higher than that of the original model,

0.0375 m3/s. So if the VFR is increased, the rotational speed

of the fan can be reduced to adjust the VFR to the original

level. Therefore, the noise of the system can be reduced due to

the reduction of rotational speed. To confirm the relationships

between the rotational speed and VFR, two models were se-

lected to carry out the computations. The results are shown in

Table 4.

For the fan with D = 24.5 mm, as the RPM decreased by

15.9%, the VFR decreased by 15.8%. For D = 35 mm, as the

RPM decreased by 15.7%, the VFR decreased by 16%. There-

fore, the VFR is linearly proportional to RPM. Note that theo-

retically, the VFR is linearly proportional to RPM.

The relationship of VFR and RPM can be defined as fol-

Fig. 11. Variation in VFR according to parameter D.

Fig. 12. Iso-contours of VFR over variables L and h.

Fig. 13. Iso-contours of acoustic power over variables L and D.

G. Ren et al. / Journal of Mechanical Science and Technology 27 (1) (2013) 33~42 39

lows:

22 1

1

v v

rpmQ Q

rpm= ⋅ (16)

where Qv2 and Qv1 denote the VFR of the operation at rpm2

and rpm1, respectively.

According to the acoustic analogy [14], the relationship be-

tween RPM and acoustic power level can be approximated as

5

22 1

1

10logw w

rpmL L

rpm

= +

(17)

where Lw2 and Lw1 are the sound power level under operation

at rpm2 and rpm1, respectively.

Using the relationship between Eqs. (16) and (17), the

original two-response problem can be converted to a one-

response problem, i.e., the minimum surface acoustic power

level in the allowed range when only low noise is being con-

sidered. The surface acoustic power level after RPM adjust-

ment can be defined as follows:

0

10log( ) 50logA vadjust

ref

P QL

P Q= − (18)

where Ladjust and Q0 denote the surface acoustic power level

after RPM adjustment and the VFR of the original model

(0.0375 m3/s), respectively. By substituting Eqs. (14) and (15)

into Eq. (18), the function of the surface acoustic power level

was confirmed. The design parameters were chosen to mini-

mize Eq. (18). The parameter combination of (38.5, 6.6, 11)

was found for minimizing the surface acoustic power level.

The surface acoustic power level can be reduced by 3.55 dB

compared to that of the original model. Therefore, this method

leads to lower acoustic power levels compared to the results

given in Section 3.2. However, we note that the validity of Eq.

(17) may be arguable. The acoustic power level is in propor-

tion from the fifth to the sixth power of the rotational speed.

This dependence varies according to the operating range of the

fan. A more accurate model representing the relation between

the RPM and acoustic power level may be needed. This illus-

trative computation shows one of strategies available if the

goal is to achieve minimum fan noise at the same flow rate.

3.4 Multiple responses

A useful approach to the optimization of multiple responses

is to use the simultaneous optimization technique popularized

by Derringer and Suich [15]. This procedure uses desirability

functions. The general approach is to first convert each re-

sponse yi into an individual desirability function di over the

range 0 ≤ di ≤ 1. Here, if the response iy is at its goal or

target, di = 1, and if the response is outside an acceptable re-

gion, di = 0. Then, the design variables are chosen to maxi-

mize the overall desirability given by

1/

1 2( ) m

f mD d d d= × × ⋅ ⋅ ⋅× , (19)

where there are m responses.

The individual desirability function is structured as shown

in Fig. 14. If the objective or target T for the response y is a

minimum value such as the surface acoustic power level de-

scribed in this paper, then the desirability function is ex-

pressed as follows:

1 1

1 11 1 1 1

1 1

1 1

1,

,

0,

r

y T

U yd T y U

U T

y U

< −

= ≤ ≤ −

>

. (20)

When weight r = 1, the desirability function is linear.

Choosing r > 1 places more emphasis on being close to the

target value, and choosing 0 < r < 1 makes this less important.

If the target for the response is a maximum value (such as

the VFR maximum used in this study), the desirability func-

tion can be defined as

2 2

2 22 2 2

2 2

2 2

0,

,

1,

t

y L

y Ld L y T

T L

y T

< −

= ≤ ≤ −

>

. (21)

The selections of the target, the acceptable region, and the

weight index for responses are determined by customer re-

quirements. For example, some customers need higher cooling

capability, while others need low noise. In this study, due to

the high sensitivity of the volume flow rate, the parameters of

desirability were selected as (T1 = 0.97, U1 = 0.98, r = 0.1) and

(T2 = 0.045, L2 = 0.043, t = 1) for the surface acoustic power

Table 4. Relationship between RPM and VFR.

RPM 1150 967 15.9%↓ D = 24.5

VFR (m3/s) 0.0433 0.0365 15.8%↓

RPM 1150 970 15.7%↓ D = 35

VFR (m3/s) 0.0433 0.0197 16%↓

Fig. 14. Desirability function plot for minimum value.

40 G. Ren et al. / Journal of Mechanical Science and Technology 27 (1) (2013) 33~42

and flow rate, respectively. Minitab software was used to de-

termine the parameter combination that maximizes the overall

desirability Df = (d1·d2)0.5. The results are shown in Fig. 15.

The figure shows that the maximum VFR is 2.65 CMM and

the minimum surface acoustic power level is 39.9 dB (surface

acoustic power = 0.97 × 10-8 W) under the uncoded parameter

combination (D, h, L) = (25.6, 10.74, 8.1).

4. Analysis of vital parameters

In Section 3, we showed that parameters D and h make sig-

nificant contributions to the VFR and surface acoustic power

level, respectively. Therefore, additional numerical studies

were carried out with various values of D and h to investigate

the physical reasons for these observations.

4.1 Effect of parameter D

Fig. 16 shows the relationship between parameter D and the

predicted VFR.

The figure shows that the VFR increases sharply up to the

value of D = 21 mm and saturates after D > 21 mm. To inves-

tigate this observation further, the variation of vorticity magni-

tudes according to the value of D is shown in Fig. 17. We note

that the vorticity magnitude around the edge of the shroud on

the outlet_2 side (inside the red dotted circle) decreases with

increasing D until D = 21 mm. After D > 21 mm, the vorticity

magnitude (in the red dotted circle) shows little increase. This

trend coincides with the total VFR trend of the outlets as

shown in Fig. 16.

Generally, the existence of a vortex leads to loss of energy.

As the vorticity magnitude increases, the energy loss of the air

flow increases, which causes the VFR to decrease. In addition,

since the vortex also influences the direction of air flow, as

parameter D increases, the air flow direction becomes more

directional toward the outlets, as shown in Fig. 18. With pa-

rameter D increasing, the red arrow and the black arrow are

more directional toward outlet_2 and outlet_1, respectively.

Over D = 21 mm, however, the direction of the red arrow no

longer changes, and the black arrow continues to change and

diverge from the centre of outlet_1. This coincides with the

trend shown in Fig. 16.

4.2 Effect of parameter h

It has been recognized that airfoil trailing edge noise can be

reduced by using a serrated trailing edge to reduce the effi-

ciency of vorticity scattering into the noise [16]. We showed

in Section 3 that the serration structure defined by parameter h

plays an important role in the noise reduction of an axial fan

system. We consider the physical reason behind this observa-

tion.

Fig. 19 shows a contour plot of surface acoustic power lev-

els before and after adding the serration structure to the shroud.

The serrations generate tangential vortices that disrupt the

periodic character of the vortex system in the wake, and can

thereby reduce the tonal radiation.

Experiments were performed to confirm the effect of the

serration structure on noise reduction. The experiment setup is

shown in Fig. 20. Fig. 21 shows a comparison of the spectra of

the noise radiated from the original and serrated models. It is

confirmed that the harmonics of blade passing frequency (BPF)

Fig. 15. Optimization results of surface acoustic power using a

desirability function.

Fig. 16. Total VFR versus parameter D (h = 0, L = 0).

Fig. 17. Contour plots of the vorticity magnitude around the shroud

(z = 0).

G. Ren et al. / Journal of Mechanical Science and Technology 27 (1) (2013) 33~42 41

noise were reduced due to the serrations on the shroud. How-

ever, note that, since there is no significant difference in the

broadband noise components between two results, the noise

reduction in overall level by the serration structure is only 0.5

dB.

5. Conclusion

We applied a response surface methodology based on nu-

merical methods to optimize the shroud of an axial cooling fan

for high performance and low noise. The accuracy of the nu-

merical methods used in the optimization was validated

through comparisons of their predictions of VFRs and acous-

tic power levels with measured values. The final designs of

the shroud obtained from the RSM were shown to increase the

VFR by 21.8% and reduce the surface acoustic power level by

3.55 dB. Further studies to determine the physical reasons for

the observed increase in VFR with increasing D showed that

the strength of vortex shedding from the shroud is inversely

proportional to the VFR of the fan. A detailed investigation of

the flow fields was made to find the reason for the observed

decrease in the acoustic power of the fan with respect to the

serration shape of the shroud. We determined that the serra-

tions generate tangential vortices to break the periodic pattern

of the vortex in the wake, thereby reducing the tonal radiation.

This reasoning was validated using the measured noise spectra.

Acknowledgment

This work was supported by the Human Resource Devel-

opment of the Korea Institute of Energy Technology Evalua-

tion and Planning (KETEP) grant funded by the Korea

government Ministry of Knowledge Economy (No.

20114010203080). This research was financially supported by

the Ministry of Education, Science Technology (MEST) and

National Research Foundation of Korea (NRF) through the

Human Resource Training Project for Regional Innovation.

Fig. 18. Contour plots of velocity magnitude (z = 0).

Fig. 19. Contour plots of surface acoustic power level.

Fig. 20. Experimental layout for serration structure.

Fig. 21. Comparison of original and serrated model spectra.

42 G. Ren et al. / Journal of Mechanical Science and Technology 27 (1) (2013) 33~42

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Cheolung Cheong received his B.S. in

Aerospace Engineering from Seoul Na-

tional University in 1997. He received

his M.S. and Ph.D degrees in Mechani-

cal and Aerospace Engineering from

Seoul National University, Korea, in

1999 and 2003. He is now an associate

professor at the School of Mechanical

Engineering, Pusan National University in Busan, Korea. Dr.

Cheong’s current research interests include fan broadband

noise, wind turbine noise, and computational aeroacoustics.