A numerical Study on the Acoustic Characteristics of a ... · The design parameters of impeller are inlet diameter Di, outlet diameter o, ... In this paper, inlet diameter of the

GESTS Int’l Trans. Computer Science and Engr., Vol.20, No.1 17

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A numerical Study on the Acoustic Characteristics of

a Centrifugal Impeller with a Splitter Wan-Ho Jeon1

1 Technical Research Lab., CEDIC Ltd., #1013, Byuksan Digital Valley II, Kasan-dong, Kumchon-gu, Seoul, Korea [email protected]

Many researches have been focused on the fan noise in the context of reducing the noise generated from the fan. However, only a few researches have been carried out on the noise prediction because of the difficulty in obtaining de-tailed information of flow-field and implementing scattering effects by the cas-ing. Recently, the author has developed a new method to predict the noise from a centrifugal fan. By using this method, the sound characteristics of a splitter impeller are analyzed. The objective of this study is to calculate the effects of splitter vanes that are attached to an original impeller on acoustic signature. A Discrete Vortex Method (DVM) is used to describe the flow-field of the cen-trifugal fan. Lowson's equation is used to predict the acoustic far-field pressure. In this paper, four impeller types were considered: original impeller, an impel-ler that has twice number of blade, a splitter impeller, and a splitter impeller that has twice number of splitter blade. This study reveals that the splitter modi-fies the flow-field near the impeller tip more uniformly. The splitter impeller influences the acoustic characteristics as well as the performance. The splitter impeller, which has the splitter to be placed in a jet region is found to improve the acoustic characteristics, and therefore reducing noise.

1 Introduction

Centrifugal turbomachines are commonly used in many air-moving devices due to their ability to achieve relatively high-pressure ratios in a compact configuration compared with axial fans. They are often found in gas turbine engines, heating venti-lation and air conditioning systems, and hydraulic pumps. Because of their wide-spread use, the noise generated by these machines often causes serious environmental issues. The turbomachinery noise is often dominated by tones at blade passage fre-quency and its higher harmonics. This is mainly due to strong interactions between the flow discharged from the impeller and the cutoff of the casing. In addition to discrete tones, the broadband noise is also generated due to the separation, turbulence mixing, and the vortex interaction process.

The numerical method to predict the flow- and acoustic-fields of an axial fan have been studied by many researchers.[1][2] On the contrary, the numerical prediction method for the centrifugal fan has not been studied widely. This is due to the diffi-culty in obtaining detailed information of flow-fields and implementing scattering

18 A Numerical Study on the Acoustic Characteristics of a Centrifugal

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effects by the casing. A numerical method to analyze the acoustic field of the cen-trifugal fan was developed recently by Jeon and Lee.[3][4][5] This method predicts the acoustic pressure with an accuracy of maximum error of 2dB, when compared with the measured data. The impeller is assumed to rotate with a constant angular velocity. The flow-field in the impeller may be treated as being incompressible and inviscid. Based on previous assumption, a Discrete Vortex Method (DVM) is used to describe the flow-field in the centrifugal fan. The force acting on each element of the blade is calculated by the unsteady Bernoulli equation. In order to obtain acoustic far-field signals from the unsteady force fluctuations on the blades, Lowson’s equation is employed in this study.[6] Lowson derived the formula of predicting the acoustic field generated by the moving point force from the wave equation. By applying this equation to each blade element, we may predict the acoustic far-field pressure. In this work, a hybrid method of a discrete vortex method and the Lowson’s equation was used.

Control methods of the tonal noise components of centrifugal fan are well docu-mented. Neise summarized the efforts on reducing the blade passage tone by chang-ing the geometry of the impeller and the cut-off.[7][8] Neise and Koopmann used a resonator to reduce blade passage tones by canceling the unsteady aerodynamic noise sources at the cut-off.[9] Uneven blade spacing is another candidate to spread the strong tonal acoustic power to wide band energy.[10] Use of the splitter between the regular impeller blades may be a decent approach to modify the acoustic characteris-tics of centrifugal impeller.[11] Among the above-mentioned devices, the splitter impeller is found very often in many types of turbomachinery – pump, compressor and fan. But the characteristics of splitter impeller have not been fully understood. The objective of this paper is to identify the effect of splitter on the flow-field and the acoustics of the centrifugal impeller by the numerical method previously mentioned.

In this work, a simple fan model was used in the numerical calculation. The fan model has a centrifugal impeller and a wedge studied by Weidemann.[12] This model was used in his experimental research, and the numerical results were compared by the authors.[3][4] The reasons to adopt his model are two-fold : The first reason is that the acoustic characteristics is well-established by the authors. The second is that the scattering effect of casing was not included in this model. Therefore, the acoustic characteristics of splitter impeller were studied with this fan model.

It was found that the splitter impeller reduces the peak level at BPF and slightly in-creases peak level at 2nd harmonic. This is attributed to the more uniform discharge flow-field in splitter impeller. Optimal position of splitter was found to be in jet re-gion for improved acoustic characteristics.

2 2-Dimensional model of the Splitter Impeller

The splitter impeller, which has a small blade between the regular impeller blades, is used in this paper. The basic shape of the splitter impeller is shown in Fig. 1. The small vane is known to reduce the slip phenomena and raise the performance.[11] Moreover, this small blade reduces the jet-wake flow pattern at impeller discharge.


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DiDo

Small Blade

Original Bladeβi

βo

The peak level at BPF of the impeller was reduced and the 2nd harmonic was slightly increased compared to the regular impeller.[11]

The design parameters of impeller are inlet diameter Di, outlet diameter Do, inlet angle βi and outlet angle βo. The inlet diameter and inlet angle of the impeller are 0.112 meter and 23.4 degrees, and the outlet diameter and outlet angle are 0.28 meter and 33.5 degrees. In this paper, inlet diameter of the splitter was set as 0.2 meter and inlet angle of the splitter as 28°.

The centrifugal fan used in the numerical analysis was a model having a centrifugal impeller and a wedge used by Weidemann.[12] This shape has an advantage that there is no dominant scattering or resonance effect by casing. Thus the study may focus on the acoustics by the impeller only. This model is shown in Fig. 2. The origi-nal impeller has 6 blades and the clearance, s, was 0.01Do.

Fig. 1. Centrifugal Impeller with added blades (Splitter Impeller)

Fig. 2 Dimensions of the impeller and wedge[12]


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3 Numerical Methods

3.1 The prediction of acoustic pressure of a centrifugal fan

The dipole noise is known to be dominant noise source in fan.[13] Therefore, the

sound field generated by the force on the impeller blade is considered here. The aeroacoustic sources of the fan are the fluctuating unsteady forces on impeller, which are generated by the strong interactions between the impeller and the wedge. The small clearance may amplify the force fluctuations, and eventually generate strong tonal noise at BPF and its higher harmonics. In order to predict the acoustic-field by the fan, Lowson’s equation is used.[6] Lowson derived the formula of predicting the acoustic field generated by moving point forces from the wave equation as shown in Eq. (1).

( ) ⎥⎥⎦

⎤

⎢⎢⎣

⎡

⎭⎬⎫

⎩⎨⎧

−+

−

−=−

tM

MF

tF

Mrayx

PP r

r

ii

ro

iio ∂

∂∂∂

π 114 22

(1) Here,

rrM

M iir =

(2)

Eq. (1) indicates that the acoustic pressure of the moving point force is calculated using the time variation of force and the acceleration. By applying this equation to each blade element, we may predict the acoustic pressure in the free-field. The effects of the scattering and reflection due to the wedge are not considered. Only the pattern of the noise source and its radiation to the free-field can be calculated.

Eq. (1) is developed for the acoustic pressure by a moving point force. In this study, the blade is divided as small mesh elements and the forces on those elements are calculated as acting on the center of the element. Thus, the acoustic pressures from the impeller are calculated by superposing every contributions to the overall acoustic pressure.

3.2. Analysis of flow-field of centrifugal fan.

It is assumed that the impeller rotates with a constant angular velocity and the

flow-field in the impeller is incompressible and inviscid. The flow-fields are com-puted by the DVM (Discrete Vortex Method) described as followings. The impeller has NB number of blades, and each blade has nc number of elements. Bound vortices are located at the 1/4 point of each element and control points are taken at the 3/4 point of the element. Wake vortices are shed at the trailing edge of the impeller at every time step to satisfy Kelvin’s theorem. Shed vortices are convected with the local induced velocity. The inlet flow is modeled by a point source located at the


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center of the fan. The wedge is modeled by constant source panels where the control points are taken at the center of the elements. This method was used in the calculation of unsteady flow-field of blade and was applied to a centrifugal pump by Evangelos et al.[14] The induced velocity at a point of the body( cjxr ) is as shown in Eq. (3).

( ) ( ) ( ) ( ) ( )txUtxUtxUtxUtxU cspcwvcbvcQc ,,,,, rrrrrrrrrr

+++= (3) The first term on the right hand side represents the velocity at cjxr induced

by the point source. The second term represents the velocity induced by bound vor-tices of the impeller. The third term represents the velocity induced by wake vortices and the fourth term represents the velocity induced by source panels. The shed vor-tices are convected with the local velocities. The unknown strengths of the bound, the wake vortices and the source pan-els are calculated with the normal boundary condition that there is no flow across the surface boundary (Equation (4)) and Kelvin's theorem (Equation (5-a)).[3][4][5]

[ ] ( ) ( )( )⎩⎨⎧ ×Ω

=⋅+++wedge

impellertxxnxntxUtxUtxUtxU cjjc

jcjcspjcwvjcbvjcQ ,0,

)();();();();(rrr

rrrrrrrrrr

(4)

0)(=

ΓDt

tD m

(5-a)

0)()(1 1

=⎥⎦

⎤⎢⎣

⎡Γ+Γ∑ ∑

= = m

nc

k

nv

kwkbk tt

(5-b)

Here, mΓ is the total circulation of the m-th blade, composed of the circulations of

bound vortices of the blade ( bΓ ) and shed wake vortices ( wΓ ), where m, nc and nv means the number of blades, the number of elements at each blade, and the number of shed vortex particles. Combining eq. (3) with (4) results :

0),()(),( =−⋅ jcjcjc txgxntxu rrrrr (6)

where jcxn )(rr is the normal vector of j th element.

The force on each element of the blade is calculated by the unsteady Bernoulli

equation.

( ) j

j

kbk

j

bjjcnj s

tsxUF Δ

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

Γ+Δ

Γ⋅= ∑

=1∂∂τρ rrrr (7)


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where, Fr

, τr and jsΔ are the normal force on the element, the tangential vector of

the element, and the length of that element, respectively. ρ is the density of working fluid. The torque of the impeller is calculated by Eq. (8)

( )( )∑=

⋅=NBnc

jjcjnj xFT

1

τrr (8)

The theoretical head of the impeller is calculated from the Eq. (9)

QgTHth ρΩ

= (9)

where, g is the acceleration of gravity and Ω is the rotating velocity of impeller.

4 Numerical Results

4.1 Verification of the prediction method by using Weidemann’s centrifugal fan

The centrifugal impeller with a rectangle wedge placed close to the impeller tip is used in this calculation. Weidemann uses this impeller and wedge for the study of the acoustic similarity law.[12] His impeller has 6 blades and rotates at 1200~4100 rpm. The inlet diameter and inlet angle of the impeller are 0.112 meter and 23.4 degrees, and the outlet diameter and outlet angle are 0.28 meter and 33.5 degrees. Numerical calculations of the flow-field are conducted up to 30 non-dimensional times, where one non-dimensional time means one revolution of impeller. The impeller rotates 6 degrees for each computational time step.

Acoustic signals are predicted far-field point at (1.96, 0, 0) and shown in Fig. 3 for the case of 3000 rpm. Here, the origin of the coordinate is the center of the impeller. In this study, the center of impeller is the origin of xy plane. In the spectrum not only the peak frequency but also the amplitude of the tonal sound are similar to those of the experimental data. The circled symbols represent the measured one[12], and the predicted spectra of acoustic pressure by Lowson’s equation is shown together with the calculated acoustic pressure level using Kirchhoff-Helmholtz BEM in squared symbols.[4] Kirchhoff-Helmholtz BEM is a new method to deal with the rotating aeroacoustic sources in BEM.[4][5] The levels at the blade passage frequency and its harmonics are much higher than the level of the broadband noise because of the small gap distance between the impeller tip and the wedge.

Through the numerical calculation, it may be found that the acoustic pressure is proportional to the 8.2U . This is exactly the same value as the experimental one.[12]


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500 1000 1500 20000

20

40

60

80

100

Lowson's MethodBEMExperiment

Frequency

SP

L(dB

)

Fig. 3 Comparison of the predicted acoustic pressure spectrum with measured one[4]

4.2 Analysis of Flow Patterns in the Splitter Impeller

The model used in this research is similar to Weidemann’s centrifugal impeller and wedge. The impellers were changed in various types – the original impeller (Impeller I), the impeller which has double number of blades (Impeller II), the splitter impeller which has 6 blades and 6 splitters (Impeller III) and the splitter impeller which has 6 blades and 12 splitters (Impeller IV). These impellers were shown in Fig 4. The inlet diameters of all splitters are 0.2 meter and the outlet diameters are the same as that of original blade.

Shed vortex particles with the corresponding impeller are shown in Fig. 5. The splitter blade is found to shed wake vortex, too. The rectangle symbols in Fig. 5 for the clockwise-rotating vortex particle, and the triangle symbols for the counter clock-wise-rotating vortex particle are shed in an alternate fashion. Fig. 6 shows the peri-odic patterns of the shed vortex strength. As the blade comes closer to the wedge, the higher negative vortices are generated at the tip of the blade. In the figure, shed vor-tex strength of the impeller with splitter is also shown.

The predicted sound pressure levels were shown in Fig. 7. In the figure, the BPF and its higher harmonic frequencies have dominant peaks. In the case of Impeller II, the BPF is twice of that of the original impeller. In the splitter impeller, the peak level at BPF is reduced by about 10 dB and the 2nd harmonic frequency is raised about 3dB. But the overall sound pressure level is almost the same as that of the original impeller. This trend was found in Dong’s experimental results.[11] In the case of Impeller IV, the peak level at BPF (300Hz) and 2nd harmonic (600Hz) are reduced by about 10dB. But peak level at 900Hz is raised about 6dB. The frequency spectrum of acoustic pressure was reshaped as the splitters are added.

The overall sound pressure levels of each case are 66.7, 67.3, 66.9 and 66.6dB for Impeller I to IV. The overall sound pressure levels are similar to each one, but the acoustic spectra are quite different from each other. The acoustic spectrum may be controlled by adding the splitter.


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In order to identify the reason of acoustic spectrum change, the flows of impellers are calculated in free-fields without a wedge. The distributions of velocities at the discharge of the impellers are modified significantly for the case of the splitter impel-ler. The flow velocity distributions of the original impeller and the splitter impeller are shown in Fig. 8. It can be found that the distributions of the discharged velocities of the splitter impeller are more uniform than those of original impeller case. For the original impeller, the variation of the absolute velocity is 4.5m/s. But in the case of the splitter impeller, the variation is 2.5m/s. As a consequence, in the case of the splitter impeller the variation of the velocity is small and the frequency of the varia-tion is doubled to that of the original impeller. This is major reason for the change of the acoustic spectrum.

(a) Impeller I (b) Impeller II (c) Impeller III (d) Impeller IV

Fig. 4 Configuration of the various impeller types.

(a) Impeller I (b) Impeller II (c) Impeller III (d) Impeller IV

Fig. 5 Trajectories of shed vortex particles after 9 revolutions of impeller.


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Nondimesional time

She

dvo

rtex

stre

ngth

2 4 6 8 10-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

Original BladeAdded Small Vane

Fig. 6 Variations of the shed vortex strength in Impeller III.

Frequency

SP

L(dB

)

0 1000 2000 3000 40000

10

20

30

40

50

60

70

Frequency

SP

L(dB

)

0 1000 2000 3000 40000

10

20

30

40

50

60

70

(a) Predicted SPL of the Impeller I (b) Predicted SPL of the Impeller II

Frequency

SP

L(dB

)

0 1000 2000 3000 40000

10

20

30

40

50

60

70

Frequency

SP

L(dB

)

0 1000 2000 3000 40000

10

20

30

40

50

60

70

(c) Predicted SPL of the Impeller III (d) Predicted SPL of the Impeller IV

Fig. 7 Predicted sound pressure levels at the far-field for four impeller types.

The ta

Vel

ocity

0 100 200 3000

5

10

15

20

25

30

35

Abs olute Ve locityRe lative Ve locity

(a) Velocity vector plot for the Impeller I (b) Absolute and relative velocity variations


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The ta

Rel

ativ

eve

loci

ty

0 100 200 3000

5

10

15

20

25

30

35

Abs olute Ve locityRe lative Ve locity

(c) Velocity vector plot for the Impeller III (d) Absolute and relative velocity variations

Fig. 8 Velocity vector plots for the Impeller I and III

4.3 The effect of the position of splitter

In order to find the optimal position of the splitter, the position of the splitter blade was changed. In this work, two cases were analyzed: a splitter impeller which has the splitter in the wake region (Fig. 9) and a splitter impeller which has the splitter in the jet region (Fig. 10). By comparing the acoustic spectrums of the two cases, it is con-cluded that the splitter located in the jet region is more effective for uniform flow than the other case. The acoustic spectrum of the first case is similar to the original impeller, but the second case is quite different from those of original impeller and the splitter impeller (Impeller III). The overall sound pressure levels are 67.0 and 65.5dB, respectively. Thus, it may be suggested that the splitter be located in the jet region.

Frequency

SP

L(dB

)

0 1000 2000 3000 40000

10

20

30

40

50

60

70

(a) Distributions of shed vortex particles (b) Predicted sound pressure spectrum

Fig.9. The flow and acoustic characteristics for the centrifugal impeller with splitter blades

near the suction side


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Frequency

SP

L(dB

)

0 1000 2000 3000 40000

10

20

30

40

50

60

70

(a) Distributions of shed vortex particles (b) Predicted sound pressure spectrum

Fig.10. The flow and acoustic characteristics for the centrifugal impeller with splitter blades

near the pressure side

5 Conclusion

The flow-field and acoustic-field of the splitter impeller were computed in this work. The numerical model of centrifugal fan was the same as Weidemann’s model of centrifugal impeller with wedge. Splitter impeller was designed and used in the numerical calculation. It is found that the splitter modifies the acoustic characteristics of the centrifugal impeller. The splitter impeller suggested by the author, which has double splitters, gives better acoustic characteristics than those of original impeller. Though the overall SPL is computed to give similar level to the original impeller, the feelings by the human being may be quite different in the sense of sound quality.

In order to identify the reason for the change of acoustic characteristics, the flow of impellers were analyzed in the free-field without a wedge. From the calculation it is found that the distribution of discharge velocity of impeller is more uniform in the case of the splitter impeller than the regular one. This may explain the change of acoustic characteristics.

The positioning effect of the splitter is summarized such that the splitter located in jet region generates lower noise than the splitter in wake region.

References

[1] D. Lohmann, "Prediction of Ducted Radiator Fan Aeroacoustics With a Lifting Surface Method", DGLR/AIAA 14th Aeroacoustic Conference, pp. 576~606, 1992

[2] Wan-Ho Jeon, Duck-Joo Lee, “Analysis of Flow and Sound field of Ducted Axial Fan,” InterNoise 2000, pp.1531-1534, 2000

[3] Wan-Ho Jeon, Duck-Joo Lee, “An Analysis of the flow and aerodynamic acoustic sources of a centrifugal impeller,” Journal of Sound and Vibration, vol. 222, No. 3, pp.505-511, 1999


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[4] Wan-Ho Jeon, Duck-Joo Lee, An Analysis of the Flow and Sound Fields of a Cen-trifugal Fan Located Near a Wedge, AIAA Aeroacoustic conference, AIAA-99-1830, 1999

[5] Wan-Ho Jeon and Duck-Joo Lee, "An Analysis of Generation and Radiation of Sound for a Centrifugal Fan," Seventh International Congress on Sound and Vibra-tion, Germany, pp. 1235~1242, 2000

[6] M.V. Lowson, “The Sound Field for Singularities in Motion,” Proc. Royal Sociery in London, Ser. A, 286, pp.559-572, 1965

[7] W. Neise, "Noise Reduction in Centrifugal Fans : A Literature Survey," Journal of Sound and Vibration, Vol. 45, pp.375-403, 1976

[8] W. Neise, "Review of Noise Reduction Methods for Centrifugal Fans," J. of Engi-neering for Industry, Vol. 104, pp.151-161, 1982

[9] W. Neise, and G. H. Koopmann, "Reduction of Centrifugal Fan Noise by Using Resonators," Journal of Sound and Vibrartion, Vol. 73, pp.297-308, 1980

[10] M. Boltezer, M. Mesaric and A. Kuhelj, "The Influence of Uneven Blade Spacing on the SPL and Noise Spectra Radiated from Radial Fans," Journal of Sound and Vibration, Vol. 216, pp.697-711, 1998

[11] R. Dong, S. Chu and J. Katz, "Effect of Modification to Tongue and Impeller Ge-ometry on Unsteady Flow, Pressure Fluctuations, and Noise in a Centrifugal Pump," Transactions of ASME, Vol. 119, pp.506-515, 1997

[12] J. Weidemann, “Analysis of the relations between acoustic and aerodynamic pa-rameters for a series of dimensionally similar centrifugal fan rotors”, NASA TT F-13,798, 1971

[13] W. Neise, “Review of Fan Noise Generation Mechanisms and Control Methods,” An International INCE Symposium, pp.45-56 (1992)

[14] Evangelos E. Morfiadakis, Spyros G. Voutsinas and Dimitris E. Papantonis, "Un-steady Flow Calculation in a Radial Flow Centrifugal Pump with Spiral Caing," In-ternational J. for Nummerical Meth. in Fluids, Vol. 12, pp.895-908, 1991

Biography

▲ Name: Wan-Ho Jeon Address: #1013, Byuksan Digital Valley II, 481-10, Gasan-dong, Kumcheon-Gu, Seoul, Korea, 153-803 Education & Work experience:

He received a MSc and PhD degrees in Aerospace Engineer-ing from the Korean Advanced Institute of Science and Tech-nology, in 1994, 1999, respectively. He has worked in LG Electronics for aeroacoustic analysis and low noise fan design. He has published over 50 scientific papers. He currently works at CEDIC Ltd. in the areas of Aeroacoustics and devel-opment of the FlowNoise S/W.

Tel: +82-2-2113-0095 E-mail: [email protected]

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A numerical Study on the Acoustic Characteristics of a ... · The design parameters of impeller are inlet diameter Di, outlet diameter o, ... In this paper, inlet diameter of the