Stuy on aero-acoustic structural interactions in fan-ucte system Yan-kei CHIANG 1 ; Yat-sze CHOY ; Li CHENG 3 ; Shiu-keung TANG 4 1,, 3 Department of Mechanical Engineering, The Hong Kong Polytechnic University, HKSAR. 4 Department of Builing Service Engineering, The Hong Kong Polytechnic University, HKSAR. ABSTRACT Mitigation of soun raiation from subsonic axial fan in the fan-ucte system at low frequencies remains a technical challenge. Traitional issipative approach such as absorption material often requires sufficiently long attenuation path for esirable noise reuction performance. More avance passive control technology such as membrane housing which relies on vibro-acoustic coupling mechanism works effectively on the attenuation of the first an secon blae passage frequency in case of steay flow. However, the performance of such evice which is compose of thin membrane may be affecte by unsteay flow fiel. This stuy examine the interaction between vortex unsteay motion, a tensione membrane housing of finite length an axial fan with ipole nature using the matche asymptotic expansion technique an potential theory. A two-imensional numerical moel is establishe to explore the soun raiation of each components an the performance of the membrane housing for controlling soun raiation from axial fan in the present of vortex insie uniform mean flow. The results show that there is higher chance of soun amplification when a vortex stream is closer to the light membrane uner weak mean flow spee. Uner the conition of weak mean flow spee, the soun raiation from the membrane is also amplifie when the cavity height is shallower. The result is beneficial for the esign of the evice of membrane housing. Keywors: Axial fans, Flow-inuce noise generation in ucts an pipes I-INCE Classification of Subjects Number(s): 6.1 1. INTRODUCTION The operation of the air conitioning an ventilation system causes noise problem especially at the low frequency regime although such facilities coul improve the comfort quality of human being. The central air conitioning an ventilation system normally compose of fan an uct which is so calle fan-ucte system. The operation of the fan creates vibration noise ue to rotating unbalance or friction between rotating parts, an also the aeroynamic noise. Traitionally, low frequency noise in the fan-ucte system coul be attenuate by ifferent passive approaches such as uct lining (1, ) an the technology of expansion chamber (3). Duct lining with sufficient length can perform well in the range of meium to high frequencies but for low frequencies, the attenuation of noise is ineffecti ve ue to the inherent high magnitue of characteristics impeance of soun absorption material. An it woul cause environmental an hygiene problems when using fibrous absorber (4, 5). Besies, the evice of expansion chambers is traitionally bulky in orer to provie an acceptable acoustical performance for low frequencies noise. It causes unavoiable pressure rop ue to the change of cross sectional area when there is flow. In orer to eliminate the pressure rop an achieve a broaban noise reuction for the uct system, Huang (6) propose the concept of rum-like silencer which compose of two light membranes uner high tension covere with the sie-branch cavities. It can achieve the low frequencies noise attenuation by the effect of membrane vibration. The performance of the rum-like silencer without an with mean flow is stuie experimentally (7, 8). At low rotating spee of fan, the ominant soun generate is cause by fluctuating forces ue to the interaction of flow turbulence with the blaes or fan casing (9). In aition, an unsteay flow 1 kiencyk@gmail.com mmyschoy@polyu.eu.hk 3 mmlcheng@polyu.eu.hk 4 shiu-keung.tang@polyu.eu.hk Inter-noise 14 Page 1 of 1
Page of 1 Inter-noise 14 woul be generate when the fan is operating. This can be normally foun from the air hanling unit. Baae (1) showe that the fan noise has feature of acoustic ipole an the unsteay flow, which is regare as flow turbulent eies (11), compose of the nature of acoustic ipole an quarupole (1). For the unsteay flow, Lamb (13) showe that the former one is cause by the flui force ue to the fore-an-aft isplacement of flui create by the vibration of cyliner. The latter one, state by Powell (14), is the soun of free aeroynamic flows generate by the momentum fluctuations that accelerate the flui particle in orer to attain the local velocity in the shear layer. It is believe that acoustic ipole woul be ominant at the fan when the Mach number is low. For controlling noise in fan-ucte system, many researchers investigate ifferent approach to reuce the fan noise in the propagation path such as uct lining with uniform or non-uniform alignment (15, 16) an membrane absorber box (17, 18). However, very little attention is pai on controlling the noise irectly at the soun source. Recently, Liu et. al (19) investigate the reactive nose control metho by suppressing the soun raiation from fan with ipole nature irectly. They esigne a evice which compose of two tensione membranes with sie-branch cavities to house the ipole soun source. A theoretical moel with uniform mean flow was also establishe to stuy the performance of such a evice. Due to ealing with the complicate vibro-acoustic coupling problem between the membrane an acoustic waves as well as ipole source, they simplifie the moel by consiering steay flui flow in fan-ucte system. However, the fan inuce flui flow fiel is unsteay. In aition, when turbulent flow interacts with the flexible walls, the loaing on the membrane varies with time that may cause significant change of the membrane motion. Hence, it may also probably affect the performance of such membrane housing evice. Therefore the current stuy focuses on examining the interaction between the membrane, acoustics waves an unsteay flow in the fan-ucte system. The numerical moel in the time omain is to be establishe in orer to have more unerstaning the physics behin. An the result will be beneficial to assess the performance of membrane housing evice to control fan noise with the excitation of turbulence. In what follows, Section focuses on the theoretical moel evelopment of cavity backe silencer installe along the fan-ucte system with unsteay flow. The numerical results an iscussions of the vortex ynamics associate with ifferent ipole strengths at ifferent uniform flow spees, at ifferent initial vortex height, as well as the soun raiations are escribe in Section 3. Finally, main conclusions are mae in Section 4.. THEORETICAL MODEL DEVELOPMENT In this section, the theoretical formulations for the preictions of membrane vibrations, unsteay vortex motions an the far-fiel soun raiations are outline. A two-imensional infinitely long uct moel that shown as Fig. 1 with passive noise control evice which containe two flexible membranes, a point vortex with circulation Γ, mean flow spee U an a ipole source is establishe. It consists of a rectangular uct with height a an a silencer with two flexible bounaries backe by cavities of length L an epth h. A vortex is initially locate at the upstream of the uct (x, y ) an the ipole source is at x=, y=.5a. Figure 1 - D theoretical moel of ipole source control with two flexible panels with unsteay flui flow Page of 1 Inter-noise 14
Inter-noise 14 Page 3 of 1 The flexible panels with two sie-branch backe cavities are assume to be very thin an the bening stiffness is ignore. The motion of the lower an upper tensione membranes are governe by the following equations l l l m T D ( p,, ) l uct pl cavity (1) x' an u u u m T D ( p p ) () u, cavity x' where the suffices u an l are representing the quantities relate to the upper an lower membrane respectively, m is the mass ensity of the membrane, T is the tension of membrane per unit length, D is regare as the amping coefficient, η enotes the membrane isplacement, τ is time, x enotes the x-irection for the membrane section, p l,uct an p u,uct are uct-sie acoustic pressure acting on the lower an upper membrane respectively, p l,cavity an p u,cavity are cavity-sie acoustic pressure acting on the lower an upper membrane respectively. The uct-sie flui pressure, p l,uct an p u,uct, are euce by the linearize Bernoulli relationship an the near fiel incompressible velocity potential (), ϕ which is attribute to the membrane vibrations ϕ m, ipole source ϕ, vortex ϕ v an mean flow ϕ f =Ux. The incompressible velocity potential of the acoustic ipole source insie the uct is euce by moelling it as a hyroynamic oublet as the ipole source an oublet are both escribe as the composition of two sources that one is having an inwar volume flow rate an the other one having the outwar volume flow rate with same magnitue. By the potential theory (1), the flui potential is given as the following expression at any point (x,y) insie the uct x, y, m v f (3) where 1 L/ ' l l x x y l m U log cosh cos x ' L/ x ' a a 1 L/ ' u u x x y u U log cosh cos x ' L/, x ' a a x x x x y y y y a a a a e cos e cos e sin e sin a a a a log 4 x x x x y y a a y y a a e cos e cos e sin e sin a a a a x x x x y y y y a a a a e cos e cos e sin e sin a a a a log, 4 x x x x y y a a y y a a e cos e cos e sin e sin a a a a 1 a yv y x xv v tan tan tanh a a 1 a yv y x xv tan tan tanh a a an the linearize Bernoulli relationships are pl, uct U an pu uct U (4), x x y l u, uct y u Inter-noise 14 Page 3 of 1
Page 4 of 1 Inter-noise 14 where ρ is the flui ensity, µ(τ) is the magnitue of volume flow rate create by the source an sink, γ(τ) is a time function that is foun by the matching proceure, ε enotes the half of istance between the source an sink that form the oublet, (x, y ) is the location of the oublet an (x v, y v ) is the vortex position. For the cavity-sie flui pressure, p l,cavity an p u,cavity, the acoustic pressure istribution insie the cavity an along the flexible bounaries is therefore estimate by Finite Difference Time Domain () (FDTD). The FDTD is evelope base on two governing equations of the motion of air particles, which are the conservation of momentum v p (5) an the continuity equation p c v (6) where p represents the acoustic pressure, c is the spee of soun an v is the vector particle velocity which contains two components, the particle velocity in x-irection v x, an the one in y-irection v y. The soun wave propagating insie the cavity is approximate by applying the secon -orer centere ifference operators to iscretize the first-orer erivatives in Eq. (5) an (6). The formulations of FDTD etermines the acoustical pressure an particle velocity at the gri positions where Δx an Δy are the spatial step size in x-irection an y-irection respectively, Δτ enotes the temporal step size, i an j are inictor of spatial points for x- an y-axis respectively, n is the inicator of time instant. The iscretize two-imensional FDTD basic equations in a Cartesian gri are expresse as follows n.5 1 n.5 1 n n vx i, j vx i, j p i 1, j p i, j (7) x n.5 1 n.5 1 n n v y i, j v y i, j p i, j 1 p i, j (8) y n c n.5 1 n.5 1 c n.5 1 n.5 1 i, j p i, j v i, j v i, j v i, j v i, j n1 p x x y y (9) x y The vortex ynamics is therefore preicte by calculating its velocities for both x- an y-irection, which are enotes as u x an u y respectively. The vortex velocities are euce by the use of the velocity potential of Eq. (3) an the following expressions x, y, x, y, u x an u y. x y Without ipole, ue to the interaction between the membrane an the vortex, the far-fiel acoustic pressure raiations can be euce by applying the matche asymptotic expansion technique between the wave equation an the incompressible flui potential of Eq. (3). The wave equation for far-fiel acoustic raiation in plane wave is (3) 1 1 M M (1) x c x c where M enotes the Mach number, U / c. The soun raiations pressure in far-fiel which was escribe by Tang (4) is therefore expresse as the follows / y L v c p ' 1 L / u l x (11) M a a 3. NUMERICAL RESULTS AND DISCUSSIONS For the sake of convenience, the parameters such as length, velocity an ensity are normalize by the following quantities, which are uct height, a, circulation, Γ/a, an air ensity, ρ, respectively. The length of membrane is set to be, locate from -1 to 1. The circulation of vortex remains constant an the initial position of the vortex is place at x =-1. Page 4 of 1 Inter-noise 14
Inter-noise 14 Page 5 of 1 3.1 Effect of vortex With amping D=1, mass an tension of membrane is set to be m 1, T 1. Fig. shows the comparison of the vortex paths with ifferent oublet strengths at mean flow spee U with h.5. When the vortex gets close to the oublet position at x, there is a rop of vortex path ue to the effects of flui fiel create by the oublet. By introucing a oublet 31(ashe line) or 6(ash-ot line), the position of vortex rops ownwar ue to the effect of flui fiel by the oublet. The level of ropping of the vortex increases with the strength of the oublet. Figure - Effects of oublet strength on vortex motion. ( ) ; ( ) 31; ( ) 6. Fig. 3 shows the results of vortex motion with ifferent initial vortex height at mean flow spee U=1. with µ= an h=.5. When the initial vortex height is far away from the centerline of the uct, the variation of the vortex motion is more significant (soli line). In this case, the motion of the vortex is mainly affecte by the lower membrane vibrations. On the other han, when the vortex is initially locate closer to the centerline of the uct, the variation of the vortex position is less significant (ashe line) ue to equalization of release pressure from the upper an lower flexible membrane. The results are consistent with the finings of Tang (4) that a weaker vortex velocity in y-irection is obtaine with the increase of the initial vortex position. In orer to further stuy the vortex path at ifferent flow spee when the vortex is close to the membrane, it is locate at y =.1. Figure 3 - Effects of initial vortex position on vortex motion. ( ) y. 1; ( ) y. 3. Inter-noise 14 Page 5 of 1
Page 6 of 1 Inter-noise 14 Fig. 4 shows its vortex path at ifferent flow spee when the oublet strength is fixe to be 31. Fig. 4(a) an 4(b) show the results for the cavity height of.5 an 1. respectively. It shows that variation of the vortex paths becomes smaller when the mean flow spee is increase ue to the phases of the membrane vibration when the vortex starts to interact with the membrane. The pattern of the vortex path appears to be similar with ifferent cavity height but its magnitue in variation is increase with increasing cavity height. These results are mainly cause by the ifferent responses of membrane vibrations as shown in Fig. 5 which is escribing the membrane vibrating for mean flow spee equals to 1.. The acoustic pressure istributions insie the backe-cavities are not the same with ifferent cavity epths, thus, the acoustic loaings acting on the flexible bounaries for the cavity-sie is ifferent leaing ifferent membrane vibrations as shown in Fig 6. Therefore, the vortex ynamics are influence by the cavity epth inirectly through the changes of flexible bounaries vibrations. Figure 4 - Effects of mean flow spee on vortex motion. (a) h. 5 ; (b) h 1.. ( ) U ; ( ) U. 5 ; ( ) U 1.. Figure 5 - Variations of lower membrane isplacement at ifferent time for U=1.. (a) h. 5 ; (b) h 1.. Page 6 of 1 Inter-noise 14
Inter-noise 14 Page 7 of 1 Figure 6 - Lower membrane isplacement for U=1.. (a) h=.5; (b) h=1.. 3. Effect of far-fiel soun pressure raiation For the far-fiel soun raiation, Fig. 7(a) an 7(b) show the far-fiel acoustic pressure raiations for the moel with backe-cavities height h. 5 an 1. respectively. When there is no mean flow (soli line) in both Fig. 7(a) an 7(b), the ownstream soun raiation is not significant for the time 13.5 where the vortex is still at the upstream of the uct. After the vortex has engage to the membrane section at 13. 5, there is an increase in the acoustic pressure raiation as the membrane vibrates with a larger amplitue ue to the vortex excitation. For the case with mean flow spee U.5 (ashe line), soun is raiate before the vortex interact with the membranes, ue to the membrane vibrations excite by the mean flow. At the time that the vortex has alreay passe the membrane section, same as the case of U that an increase of raiate acoustic pressure is observe ue to the excitation create by the vortex on the membranes. However, there is less significant increase in soun pressure magnitue with higher spee of mean flow after the vortex has engage to the membranes (ash-ot line). The acoustic pressure is mainly generate by two components, which are the vortex an membranes. Fig. 7 emonstrates that the membranes monopole raiation is always ominant. Although the vortex soun is less ominant, the vortex excites the membranes to oscillate vigorously to cause a larger pressure raiation once it starts engaging to the membrane section for U 1 an h. 5. When the mean flow spee is higher, the effect of vortex excitation is less significant as there is less time for the vortex to interact with the membranes. The spectrum of far-fiel soun raiations for the case with h 1. as shown in Fig. 7(b) is ifferent when comparing with a smaller cavity epth in Fig. 7(a). With ifferent cavity heights, the cavity pressure istributions are ifferent such that the acoustic loaings applie on the membranes are not the same. Thus, the vortex ynamics an membrane vibrations are ifferent, as shown in Fig. 4 an 5, with ifferent cavity height as they both epen on the pressure loaings acting on the membranes. Therefore, the spectrum of soun raiation ue to the membrane oscillations an transverse acceleration of vortex in ownstream is ifferent. Inter-noise 14 Page 7 of 1
Page 8 of 1 Inter-noise 14 Figure 7 - Time variations of ownstream soun pressure raiation with ifferent mean flow. (a) h. 5 ; (b) h 1.. ( ) U ; ( ) U. 5 ; ( ) U 1.. Fig. 8 illustrates that the far-fiel acoustic pressure raiate in the moel with U 1., h. 5 an the initial vortex height is y =.1 an.3 respectively. It is observe that the vortex is initially locate closer to the centreline of the uct at y =.3 (ashe line), the soun raiation ue to vortex excite membrane vibrations is relatively smaller when comparing that with y =.1 (soli line). The reuction of far-fiel soun pressure raiation with the increase of the initial vortex height is obtaine ue to the smaller vortex transverse acceleration cause by the pressure equalization between two membranes. Moreover, when the initial vortex height is closer to the centerline of the uct, the ability for the vortex to excite the lower membrane oscillations is reuce ue to the larger istance between the vortex an lower membrane. The soun raiations ue to vortex excitation are thus reuce. Figure 8 - Time variations of ownstream soun pressure raiation with ifferent initial vortex height. ( ) y. 1; ( ) y. 3. Page 8 of 1 Inter-noise 14
Inter-noise 14 Page 9 of 1 4. CONCLUSIONS Theoretical analyses have been conucte to unerstan the flui-structural interactions uner the unsteay flow. The time-varying vortex ynamics an far-fiel time omain soun pressure raiations has been investigate numerically with the changes of several parameters such as the mean flow spees an height of backe-cavity. Major conclusions can be summarize as follows: (1) A two-imensional theoretical formulation has been establishe to examine the performance of silencing evice with tensione membrane covere with a cavity to suppress the axial flow fan with the unsteay flow in the time omain. () With the existence of oublet which simulates the axial fan, it creates a change of volume flow rate of the flui, an thus, affects the flow fiel of surrouning flui. The results illustrate that the effects on the vortex rop cause by the oublet is obvious when the vortex is propagating at x is aroun -.4 to.4. Out of this range, the variations of the vortex paths with an without oublet are similar. It shows that the vortex ynamics at x. 4 or x. 4 are mainly associate with the vibrations of the flexible structures which has strong interaction with the oublet. (3) Without consiering the oublet soun raiation, the far-fiel soun raiations are mainly generate by two components: the membrane oscillations ue to the vibration create rate change of the volumetric flow an vortex excitation ue the transverse acceleration of vortex. From the observations, the effect on the soun raiations ue to the vortex excitation is less significant for a higher mean flow, U=1., as the oscillations of membranes riven by the uniform flow are larger in amplitue comparing with U= an.5. Moreover, the time that allowing the vortex to excite the membrane is less as the vortex velocity in x-irection increases with the mean flow spee. Therefore, when the vortex passes over the membrane sections, the acoustic pressure raiation in ownstream amplifie ue to vortex excitation is less ominant. ACKNOWLEDGEMENTS The first author thanks the Hong Kong Polytechnic University for the research stuentship an General Research Grant from the Hong Kong SAR government (B-Q33E). REFERENCES 1. Beranek LL, Vér IL. Noise an vibration control engineering : principles an applications. New York: John Wiley & Sons, Inc.; 199.. Ingar KU. Notes on soun absorption technology. Poughkeepsie, NY: Noise Control Founation; 1994. 3. Munjal ML. Acoustics of ucts an mufflers with application to exhaust an ventilation system esign. New York: Wiley; 1987. 4. Fuchs HV. From Avance Acoustic Research to Novel Silencing Proceures an Innovative Soun Treatments. ACUSTICA. 1a;87:47-13. 5. Fuchs HV. Alternative Fibreless Absorbers - New Tools an Materials for Noise Control an Acoustic Comfort. ACUSTICA. 1b;87:414-. 6. Huang L. A theoretical stuy of uct noise control by flexible panels. The Journal of the Acoustical Society of America. 1999;16(4):181-9. 7. Choy YS, Huang L. Experimental stuies of a rumlike silencer. The Journal of the Acoustical Society of America. ;11(5):6-35. 8. Choy YS, Huang L. Effect of flow on the rumlike silencer. The Journal of the Acoustical Society of America. 5;118(5):377-85. 9. Kemp NH, Sears WR. Aeroynamic Interference Between Moving Blae Rows. Journal of the Aeronautical Sciences (Institute of the Aeronautical Sciences). 1953;(9):585-97. 1. Baae PK. Effects of Acoustic Loaing on Axial Flow Fan Noise Generation. Noise Control Eng Noise Control Engineering. 1977;8(1). 11. Crighton DG. Raiation from vortex filament motion near a half plane. Journal of Flui Mechanics. 197;51():357-6. 1. Powell A. Theory of Vortex Soun. The Journal of the Acoustical Society of America. 1964;36(1):177-95. 13. Lamb H. Hyroynamics. New York: Dover publications; 1945. Inter-noise 14 Page 9 of 1
Page 1 of 1 Inter-noise 14 14. Powell A. On Aeroynamic Soun from Dilatation an Momentum Fluctuations. The Journal of the Acoustical Society of America. 1961;33(1):1798-9. 15. Parrott TLWWRUSNA, Space Aministration S, Technical Information B. Comparison of measure an calculate moe reistribution associate with spinning moe transmission through circumferentially segmente line ucts. Washington, D.C.; Springfiel, Va.: National Aeronautics an Space Aministration, Scientific an Technical Information Branch ; For sale by the National Technical Information Service]; 1983. 16. Bi W, Pagneux V, Lafarge D, Aurégan Y. An improve multimoal metho for soun propagation in nonuniform line ucts. The Journal of the Acoustical Society of America. 7;1(1):8-9. 17. Ackermann U, Fuchs HV, Rambausek N. Soun absorbers of a novel membrane construction. Applie Acoustics. 1988;5(3):197-15. 18. Frommhol W, Fuchs HV, Sheng S. Acoustic Performance of Membrane Absorbers. Journal of Soun an Vibration. 1994;17(5):61-36. 19. Liu Y, Choy YS, Huang L, Cheng L. Noise suppression of a ipole source by tensione membrane with sie-branch cavities. The Journal of the Acoustical Society of America. 1;13(3):139-4.. Vallentine HR. Applie hyroynamics. Lonon: Butterworths; 1967. 1. Currie IG. Funamental Mechanics of Fluis, Thir Eition: Taylor & Francis;.. Bottelooren D. Finite ifference time omain simulation of low frequency room acoustic problems. The Journal of the Acoustical Society of America. 1995;98(6):33-8. 3. Mechel FP, Munjal L. Formulas of Acoustics: Springer; 8. 4. Tang SK. Vortex soun in the presence of a low Mach number flow across a rum-like silencer. The Journal of the Acoustical Society of America. 11;19(5):83-4. Page 1 of 1 Inter-noise 14