A numerical Study on the Acoustic Characteristics of a Centrifugal Impeller with a Splitter

Transcription

1 GESTS Int l Trans. Computer Siene and Engr., Vol.2, No.1 17 A numerial Study on the Aousti Charateristis of a Centrifugal Impeller with a Splitter Wan-Ho Jeon 1 1 Tehnial Researh Lab., CEDIC Ltd., #113, Byuksan Digital Valley II, Kasan-dong, Kumhon-gu, Seoul, Korea wheon@edi.biz Many researhes have been foused on the fan noise in the ontext of reduing the noise generated from the fan. However, only a few researhes have been arried out on the noise predition beause of the diffiulty in obtaining detailed information of flow-field and implementing sattering effets by the asing. Reently, the author has developed a new method to predit the noise from a entrifugal fan. By using this method, the sound harateristis of a splitter impeller are analyzed. The obetive of this study is to alulate the effets of splitter vanes that are attahed to an original impeller on aousti signature. A Disrete Vortex Method (DVM) is used to desribe the flow-field of the entrifugal fan. Lowson's equation is used to predit the aousti far-field pressure. In this paper, four impeller types were onsidered: original impeller, an impeller that has twie number of blade, a splitter impeller, and a splitter impeller that has twie number of splitter blade. This study reveals that the splitter modifies the flow-field near the impeller tip more uniformly. The splitter impeller influenes the aousti harateristis as well as the performane. The splitter impeller, whih has the splitter to be plaed in a et region is found to improve the aousti harateristis, and therefore reduing noise. 1 Introdution Centrifugal turbomahines are ommonly used in many air-moving devies due to their ability to ahieve relatively high-pressure ratios in a ompat onfiguration ompared with axial fans. They are often found in gas turbine engines, heating ventilation and air onditioning systems, and hydrauli pumps. Beause of their widespread use, the noise generated by these mahines often auses serious environmental issues. The turbomahinery noise is often dominated by tones at blade passage frequeny and its higher harmonis. This is mainly due to strong interations between the flow disharged from the impeller and the utoff of the asing. In addition to disrete tones, the broadband noise is also generated due to the separation, turbulene mixing, and the vortex interation proess. The numerial method to predit the flow- and aousti-fields of an axial fan have been studied by many researhers.[1][2] On the ontrary, the numerial predition method for the entrifugal fan has not been studied widely. This is due to the diffiulty in obtaining detailed information of flow-fields and implementing sattering

2 18 A Numerial Study on the Aousti Charateristis of a Centrifugal effets by the asing. A numerial method to analyze the aousti field of the entrifugal fan was developed reently by Jeon and Lee.[3][4][5] This method predits the aousti pressure with an auray of maximum error of 2dB, when ompared with the measured data. The impeller is assumed to rotate with a onstant angular veloity. The flow-field in the impeller may be treated as being inompressible and invisid. Based on previous assumption, a Disrete Vortex Method (DVM) is used to desribe the flow-field in the entrifugal fan. The fore ating on eah element of the blade is alulated by the unsteady Bernoulli equation. In order to obtain aousti farfield signals from the unsteady fore flutuations on the blades, Lowson s equation is employed in this study.[6] Lowson derived the formula of prediting the aousti field generated by the moving point fore from the wave equation. By applying this equation to eah blade element, we may predit the aousti far-field pressure. In this work, a hybrid method of a disrete vortex method and the Lowson s equation was used. Control methods of the tonal noise omponents of entrifugal fan are well doumented. Neise summarized the efforts on reduing the blade passage tone by hanging the geometry of the impeller and the ut-off.[7][8] Neise and Koopmann used a resonator to redue blade passage tones by aneling the unsteady aerodynami noise soures at the ut-off.[9] Uneven blade spaing is another andidate to spread the strong tonal aousti power to wide band energy.[1] Use of the splitter between the regular impeller blades may be a deent approah to modify the aousti harateristis of entrifugal impeller.[11] Among the above-mentioned devies, the splitter impeller is found very often in many types of turbomahinery pump, ompressor and fan. But the harateristis of splitter impeller have not been fully understood. The obetive of this paper is to identify the effet of splitter on the flow-field and the aoustis of the entrifugal impeller by the numerial method previously mentioned. In this work, a simple fan model was used in the numerial alulation. The fan model has a entrifugal impeller and a wedge studied by Weidemann.[12] This model was used in his experimental researh, and the numerial results were ompared by the authors.[3][4] The reasons to adopt his model are two-fold : The first reason is that the aousti harateristis is well-established by the authors. The seond is that the sattering effet of asing was not inluded in this model. Therefore, the aousti harateristis of splitter impeller were studied with this fan model. It was found that the splitter impeller redues the peak level at BPF and slightly inreases peak level at 2 nd harmoni. This is attributed to the more uniform disharge flow-field in splitter impeller. Optimal position of splitter was found to be in et region for improved aousti harateristis. 2 2-Dimensional model of the Splitter Impeller The splitter impeller, whih has a small blade between the regular impeller blades, is used in this paper. The basi shape of the splitter impeller is shown in Fig. 1. The small vane is known to redue the slip phenomena and raise the performane.[11] Moreover, this small blade redues the et-wake flow pattern at impeller disharge.

3 GESTS Int l Trans. Computer Siene and Engr., Vol.2, No.1 19 The peak level at BPF of the impeller was redued and the 2 nd harmoni was slightly inreased ompared to the regular impeller.[11] The design parameters of impeller are inlet diameter D i, outlet diameter D o, inlet angle β i and outlet angle β o. The inlet diameter and inlet angle of the impeller are.112 meter and 23.4 degrees, and the outlet diameter and outlet angle are.28 meter and 33.5 degrees. In this paper, inlet diameter of the splitter was set as.2 meter and inlet angle of the splitter as 28. The entrifugal fan used in the numerial analysis was a model having a entrifugal impeller and a wedge used by Weidemann.[12] This shape has an advantage that there is no dominant sattering or resonane effet by asing. Thus the study may fous on the aoustis by the impeller only. This model is shown in Fig. 2. The original impeller has 6 blades and the learane, s, was.1do. βi Small Blade βo Original Blade Do Di Fig. 1. Centrifugal Impeller with added blades (Splitter Impeller) Fig. 2 Dimensions of the impeller and wedge[12]

4 2 A Numerial Study on the Aousti Charateristis of a Centrifugal 3 Numerial Methods 3.1 The predition of aousti pressure of a entrifugal fan The dipole noise is known to be dominant noise soure in fan.[13] Therefore, the sound field generated by the fore on the impeller blade is onsidered here. The aeroaousti soures of the fan are the flutuating unsteady fores on impeller, whih are generated by the strong interations between the impeller and the wedge. The small learane may amplify the fore flutuations, and eventually generate strong tonal noise at BPF and its higher harmonis. In order to predit the aousti-field by the fan, Lowson s equation is used.[6] Lowson derived the formula of prediting the aousti field generated by moving point fores from the wave equation as shown in Eq. (1). xi yi Fi Fi P Po = + 2 4π aor 1 M r ( ) 2 1 M t M r t r (1) Here, M r = M i ri r (2) Eq. (1) indiates that the aousti pressure of the moving point fore is alulated using the time variation of fore and the aeleration. By applying this equation to eah blade element, we may predit the aousti pressure in the free-field. The effets of the sattering and refletion due to the wedge are not onsidered. Only the pattern of the noise soure and its radiation to the free-field an be alulated. Eq. (1) is developed for the aousti pressure by a moving point fore. In this study, the blade is divided as small mesh elements and the fores on those elements are alulated as ating on the enter of the element. Thus, the aousti pressures from the impeller are alulated by superposing every ontributions to the overall aousti pressure Analysis of flow-field of entrifugal fan. It is assumed that the impeller rotates with a onstant angular veloity and the flow-field in the impeller is inompressible and invisid. The flow-fields are omputed by the DVM (Disrete Vortex Method) desribed as followings. The impeller has NB number of blades, and eah blade has n number of elements. Bound vorties are loated at the 1/4 point of eah element and ontrol points are taken at the 3/4 point of the element. Wake vorties are shed at the trailing edge of the impeller at every time step to satisfy Kelvin s theorem. Shed vorties are onveted with the loal indued veloity. The inlet flow is modeled by a point soure loated at the

5 GESTS Int l Trans. Computer Siene and Engr., Vol.2, No.1 21 enter of the fan. The wedge is modeled by onstant soure panels where the ontrol points are taken at the enter of the elements. This method was used in the alulation of unsteady flow-field of blade and was applied to a entrifugal pump by Evangelos et al.[14] The indued veloity at a point of the body( x r ) is as shown in Eq. (3). r r r r r r r r r r U ( x, t) = U Q ( x, t) + U bv ( x, t) + U wv ( x, t) + U sp ( x, t) (3) The first term on the right hand side represents the veloity at x r indued by the point soure. The seond term represents the veloity indued by bound vorties of the impeller. The third term represents the veloity indued by wake vorties and the fourth term represents the veloity indued by soure panels. The shed vorties are onveted with the loal veloities. The unknown strengths of the bound, the wake vorties and the soure panels are alulated with the normal boundary ondition that there is no flow aross the surfae boundary (Equation (4)) and Kelvin's theorem (Equation (5-a)).[3][4][5] r r r r r r r r [ U ( x ; t) + U ( x ; t) + U ( x ; t) + U ( x ; t) ] Q bv wv sp r r n( x ) r r r ( n( x ) x ( t) ), Ω =, wedge impeller (4) D m Γ ( t) = Dt n Γ ( t) + nv bk k = 1 k = 1 Γ wk ( t) m = (5-a) (5-b) Here, Γ m is the total irulation of the m-th blade, omposed of the irulations of bound vorties of the blade ( Γ ) and shed wake vorties ( Γ ), where m, n and nv b means the number of blades, the number of elements at eah blade, and the number of shed vortex partiles. Combining eq. (3) with (4) results : r r r r r u( x, t) n( x ) g( x, t) = where x n r ( r ) is the normal vetor of th element. The fore on eah element of the blade is alulated by the unsteady Bernoulli equation. r r r r Γb Fn U ( x ) (7) ρ τ + Γbk Δs = Δs t k=1 w (6)

6 22 A Numerial Study on the Aousti Charateristis of a Centrifugal where, F r, τ r and Δ s are the normal fore on the element, the tangential vetor of the element, and the length of that element, respetively. ρ is the density of working fluid. The torque of the impeller is alulated by Eq. (8) T = NBn ( F n ( x r τ ) = 1 r (8) The theoretial head of the impeller is alulated from the Eq. (9) H th T Ω = (9) ρ g Q where, g is the aeleration of gravity and Ω is the rotating veloity of impeller. 4 Numerial Results 4.1 Verifiation of the predition method by using Weidemann s entrifugal fan The entrifugal impeller with a retangle wedge plaed lose to the impeller tip is used in this alulation. Weidemann uses this impeller and wedge for the study of the aousti similarity law.[12] His impeller has 6 blades and rotates at 12~41 rpm. The inlet diameter and inlet angle of the impeller are.112 meter and 23.4 degrees, and the outlet diameter and outlet angle are.28 meter and 33.5 degrees. Numerial alulations of the flow-field are onduted up to 3 non-dimensional times, where one non-dimensional time means one revolution of impeller. The impeller rotates 6 degrees for eah omputational time step. Aousti signals are predited far-field point at (1.96,, ) and shown in Fig. 3 for the ase of 3 rpm. Here, the origin of the oordinate is the enter of the impeller. In this study, the enter of impeller is the origin of xy plane. In the spetrum not only the peak frequeny but also the amplitude of the tonal sound are similar to those of the experimental data. The irled symbols represent the measured one[12], and the predited spetra of aousti pressure by Lowson s equation is shown together with the alulated aousti pressure level using Kirhhoff-Helmholtz BEM in squared symbols.[4] Kirhhoff-Helmholtz BEM is a new method to deal with the rotating aeroaousti soures in BEM.[4][5] The levels at the blade passage frequeny and its harmonis are muh higher than the level of the broadband noise beause of the small gap distane between the impeller tip and the wedge. Through the numerial alulation, it may be found that the aousti pressure is 2. 8 proportional to the U. This is exatly the same value as the experimental one.[12]

7 GESTS Int l Trans. Computer Siene and Engr., Vol.2, No Lowson's Method BEM Experiment Frequeny Fig. 3 Comparison of the predited aousti pressure spetrum with measured one[4] 4.2 Analysis of Flow Patterns in the Splitter Impeller The model used in this researh is similar to Weidemann s entrifugal impeller and wedge. The impellers were hanged in various types the original impeller (Impeller I), the impeller whih has double number of blades (Impeller II), the splitter impeller whih has 6 blades and 6 splitters (Impeller III) and the splitter impeller whih has 6 blades and 12 splitters (Impeller IV). These impellers were shown in Fig 4. The inlet diameters of all splitters are.2 meter and the outlet diameters are the same as that of original blade. Shed vortex partiles with the orresponding impeller are shown in Fig. 5. The splitter blade is found to shed wake vortex, too. The retangle symbols in Fig. 5 for the lokwise-rotating vortex partile, and the triangle symbols for the ounter lokwise-rotating vortex partile are shed in an alternate fashion. Fig. 6 shows the periodi patterns of the shed vortex strength. As the blade omes loser to the wedge, the higher negative vorties are generated at the tip of the blade. In the figure, shed vortex strength of the impeller with splitter is also shown. The predited sound pressure levels were shown in Fig. 7. In the figure, the BPF and its higher harmoni frequenies have dominant peaks. In the ase of Impeller II, the BPF is twie of that of the original impeller. In the splitter impeller, the peak level at BPF is redued by about 1 db and the 2 nd harmoni frequeny 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 ase of Impeller IV, the peak level at BPF (3Hz) and 2 nd harmoni (6Hz) are redued by about 1dB. But peak level at 9Hz is raised about 6dB. The frequeny spetrum of aousti pressure was reshaped as the splitters are added. The overall sound pressure levels of eah ase are 66.7, 67.3, 66.9 and 66.6dB for Impeller I to IV. The overall sound pressure levels are similar to eah one, but the aousti spetra are quite different from eah other. The aousti spetrum may be ontrolled by adding the splitter.

8 24 A Numerial Study on the Aousti Charateristis of a Centrifugal In order to identify the reason of aousti spetrum hange, the flows of impellers are alulated in free-fields without a wedge. The distributions of veloities at the disharge of the impellers are modified signifiantly for the ase of the splitter impeller. The flow veloity distributions of the original impeller and the splitter impeller are shown in Fig. 8. It an be found that the distributions of the disharged veloities of the splitter impeller are more uniform than those of original impeller ase. For the original impeller, the variation of the absolute veloity is 4.5m/s. But in the ase of the splitter impeller, the variation is 2.5m/s. As a onsequene, in the ase of the splitter impeller the variation of the veloity is small and the frequeny of the variation is doubled to that of the original impeller. This is maor reason for the hange of the aousti spetrum. (a) Impeller I (b) Impeller II () Impeller III (d) Impeller IV Fig. 4 Configuration of the various impeller types. (a) Impeller I (b) Impeller II () Impeller III (d) Impeller IV Fig. 5 Traetories of shed vortex partiles after 9 revolutions of impeller.

9 GESTS Int l Trans. Computer Siene and Engr., Vol.2, No Shed vortex strength Original Blade Added Small Vane Nondimesional time Fig. 6 Variations of the shed vortex strength in Impeller III Frequeny Frequeny (a) Predited SPL of the Impeller I (b) Predited SPL of the Impeller II Frequeny Frequeny () Predited SPL of the Impeller III (d) Predited SPL of the Impeller IV Fig. 7 Predited sound pressure levels at the far-field for four impeller types Ve loity Absolute Veloity Relative Veloity The ta (a) Veloity vetor plot for the Impeller I (b) Absolute and relative veloity variations

10 26 A Numerial Study on the Aousti Charateristis of a Centrifugal Relative veloity Absolute Veloity Relative Veloity The ta () Veloity vetor plot for the Impeller III (d) Absolute and relative veloity variations Fig. 8 Veloity vetor plots for the Impeller I and III 4.3 The effet of the position of splitter In order to find the optimal position of the splitter, the position of the splitter blade was hanged. In this work, two ases were analyzed: a splitter impeller whih has the splitter in the wake region (Fig. 9) and a splitter impeller whih has the splitter in the et region (Fig. 1). By omparing the aousti spetrums of the two ases, it is onluded that the splitter loated in the et region is more effetive for uniform flow than the other ase. The aousti spetrum of the first ase is similar to the original impeller, but the seond ase is quite different from those of original impeller and the splitter impeller (Impeller III). The overall sound pressure levels are 67. and 65.5dB, respetively. Thus, it may be suggested that the splitter be loated in the et region Frequeny (a) Distributions of shed vortex partiles (b) Predited sound pressure spetrum Fig.9. The flow and aousti harateristis for the entrifugal impeller with splitter blades near the sution side

11 GESTS Int l Trans. Computer Siene and Engr., Vol.2, No Frequeny (a) Distributions of shed vortex partiles (b) Predited sound pressure spetrum Fig.1. The flow and aousti harateristis for the entrifugal impeller with splitter blades near the pressure side 5 Conlusion The flow-field and aousti-field of the splitter impeller were omputed in this work. The numerial model of entrifugal fan was the same as Weidemann s model of entrifugal impeller with wedge. Splitter impeller was designed and used in the numerial alulation. It is found that the splitter modifies the aousti harateristis of the entrifugal impeller. The splitter impeller suggested by the author, whih has double splitters, gives better aousti harateristis than those of original impeller. Though the overall SPL is omputed 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 hange of aousti harateristis, the flow of impellers were analyzed in the free-field without a wedge. From the alulation it is found that the distribution of disharge veloity of impeller is more uniform in the ase of the splitter impeller than the regular one. This may explain the hange of aousti harateristis. The positioning effet of the splitter is summarized suh that the splitter loated in et region generates lower noise than the splitter in wake region. Referenes [1] D. Lohmann, "Predition of Duted Radiator Fan Aeroaoustis With a Lifting Surfae Method", DGLR/AIAA 14th Aeroaousti Conferene, pp. 576~66, 1992 [2] Wan-Ho Jeon, Duk-Joo Lee, Analysis of Flow and Sound field of Duted Axial Fan, InterNoise 2, pp , 2 [3] Wan-Ho Jeon, Duk-Joo Lee, An Analysis of the flow and aerodynami aousti soures of a entrifugal impeller, Journal of Sound and Vibration, vol. 222, No. 3, pp , 1999

12 28 A Numerial Study on the Aousti Charateristis of a Centrifugal [4] Wan-Ho Jeon, Duk-Joo Lee, An Analysis of the Flow and Sound Fields of a Centrifugal Fan Loated Near a Wedge, AIAA Aeroaousti onferene, AIAA , 1999 [5] Wan-Ho Jeon and Duk-Joo Lee, "An Analysis of Generation and Radiation of Sound for a Centrifugal Fan," Seventh International Congress on Sound and Vibration, Germany, pp. 1235~1242, 2 [6] M.V. Lowson, The Sound Field for Singularities in Motion, Pro. Royal Soiery in London, Ser. A, 286, pp , 1965 [7] W. Neise, "Noise Redution in Centrifugal Fans : A Literature Survey," Journal of Sound and Vibration, Vol. 45, pp , 1976 [8] W. Neise, "Review of Noise Redution Methods for Centrifugal Fans," J. of Engineering for Industry, Vol. 14, pp , 1982 [9] W. Neise, and G. H. Koopmann, "Redution of Centrifugal Fan Noise by Using Resonators," Journal of Sound and Vibrartion, Vol. 73, pp , 198 [1] M. Boltezer, M. Mesari and A. Kuhel, "The Influene of Uneven Blade Spaing on the SPL and Noise Spetra Radiated from Radial Fans," Journal of Sound and Vibration, Vol. 216, pp , 1998 [11] R. Dong, S. Chu and J. Katz, "Effet of Modifiation to Tongue and Impeller Geometry on Unsteady Flow, Pressure Flutuations, and Noise in a Centrifugal Pump," Transations of ASME, Vol. 119, pp , 1997 [12] J. Weidemann, Analysis of the relations between aousti and aerodynami parameters for a series of dimensionally similar entrifugal fan rotors, NASA TT F- 13,798, 1971 [13] W. Neise, Review of Fan Noise Generation Mehanisms and Control Methods, An International INCE Symposium, pp (1992) [14] Evangelos E. Morfiadakis, Spyros G. Voutsinas and Dimitris E. Papantonis, "Unsteady Flow Calulation in a Radial Flow Centrifugal Pump with Spiral Caing," International J. for Nummerial Meth. in Fluids, Vol. 12, pp , 1991 Biography Name: Wan-Ho Jeon Address: #113, Byuksan Digital Valley II, 481-1, Gasan-dong, Kumheon-Gu, Seoul, Korea, Eduation & Work experiene: He reeived a MS and PhD degrees in Aerospae Engineering from the Korean Advaned Institute of Siene and Tehnology, in 1994, 1999, respetively. He has worked in LG Eletronis for aeroaousti analysis and low noise fan design. He has published over 5 sientifi papers. He urrently works at CEDIC Ltd. in the areas of Aeroaoustis and development of the FlowNoise S/W. Tel: wheon@edi.biz