Computational Acoustic Attenuation Performance of Helicoidal Resonators Comparable to Experiment

Transcription

1 Comutational Acoustic Attenuation Perormance o Helicoidal Resonators Comarable to Exeriment PhD. Eng. Wojciech LAPKA Poznan University o Technology Institute o Alied Mechanics Division o Vibroacoustics and Systems Biodynamics 3 Piotrowo Street, Poznan POLAND wojciech.laka@ut.oznan.l

2 Outline Introduction Numerical environment Perormance arameters Model or sound attenuation Exerimental set-u Results Conclusions COMSOL Conerence, October 3-5, Boston MA, USA

3 Introduction Helicoidal resonator is a newly develoed acoustic resonator near wellknown Helmholtz resonator s- lead o one helicoidal turn Emty chamber (cavity) Neck Helicoidal roile Circular duct Cylindrical duct Mandrel a) Helmholtz resonator b) helicoidal resonator Figure. Basic comonents o resonators as a art o simle acoustic system - cylindrical duct. As it can be seen in Figure the main dierence between both solutions is that the Helmholtz resonator is located outside the duct, and the helicoidal resonator stands inside the duct. COMSOL Conerence, October 3-5, Boston MA, USA 3

4 Introduction The main urose o this work is to show comutationally obtained the acoustic attenuation erormance o helicoidal resonators which can be comarable to exerimental results. Figure 4. Cylindrical duct with helicoidal resonator inside. Figure 5. Parameters o helicoidal roile. s d,976 d m d,4 g d,4 The most imortant question is: n,67, n,695 How to simulate in comutational enviroment the acoustic systems to obtain results, which can be comarable to exeriment? COMSOL Conerence, October 3-5, Boston MA, USA 4

5 Numerical environment Finite Element Method (FEM) was used to solve three-dimensional (3D) numerical models in the requency domain by the use o time-harmonic Pressure Acoustics alication mode in a COMSOL Multihysics - Acoustics Module comutational alication. The inal solving arameter is the acoustic ressure [Pa], which can be comuted by the use o slightly modiied Helmholtz equation: () cs where ρ is the density o air (ρ =,3 kg/m 3 ), c s is the seed o sound in air (c s =343m/s), and ω gives the angular requency. For investigated models in this work the boundary conditions are o three tyes: For acoustically hard walls at the solid boundaries, which are the walls o the cavity volume, neck, helicoidal roile, mandrel and circular duct, the model uses sound hard (wall) boundary conditions: n () COMSOL Conerence, October 3-5, Boston MA, USA 5

6 Numerical environment The boundary condition at the inlet surace (sound source) o circular duct is a combination o incoming and outgoing lane waves: i i ikkr n ik k n T T ik e k k (3) where Δ T denotes the boundary tangential Lalace oerator, k=ω/c s is the wave number, n is the normal direction vector or investigated circular duct, and wave vector is deined as k=kn k, where n k is the wave-direction vector. In equation (3), reresents the alied outer ressure, and i denotes the imaginary unit. The inlet boundary condition is valid as long as the requency is ket below the cuto requency or the second roagating mode in the cylindrical duct. COMSOL Conerence, October 3-5, Boston MA, USA 6

7 Numerical environment Second tye o the inlet boundary condition (sound source) o cylindrical duct is radiation condition o a sherical wave with an incoming lane wave included, as ollows: (4) which emanates rom inlet circular boundary and allows a radiated wave to leave the modeling domain without relections. At the outlet boundary is set as the radiation boundary condition which allows an outgoing wave to leave the modeling domain with no or minimal relections: k i k i T n (5) 7 r k n k q n i T T e i r ik ikr r ikr r r ik COMSOL Conerence, October 3-5, Boston MA, USA

8 Perormance arameters As an acoustic attenuation erormance arameter is used transmission loss (TL), given by: where: w w o i wi TL log wo,[db] (6) c ds cs is the outgoing ower at the outlet w o, ds c is the incoming ower at the inlet w i. s Insertion Loss (IL), used both in comutations and exeriment, given by: IL= SPL -SPL, [db] (7) SPL the sound ressure level at the outlet o cylindrical duct without ilter, [db] SPL the sound ressure level at the outlet o cylindrical duct with ilter, [db]. COMSOL Conerence, October 3-5, Boston MA, USA 8

9 Sound attenuation model used in NM 9 m rayls or m s Pa d R av a,53 9,, C C s c R ic R C c k C C s c R ic R C c Z Well-known Delany and Bazley model: comlex imedance Z c and wave number k c Bies and Hansen emirical correlation or low resistivity R : C =,978, C =,7, C 3 =,89, C 4 =,595, C 5 =,57, C 6 =,754, C 7 =,87, C 8 =,73. (7) (8) COMSOL Conerence, October 3-5, Boston MA, USA

10 Exerimental set-u Source signal was the white noise. Both helicoidal resonators were made by the use o a three dimensional raid rototying technique SLS. Thus, the shae o resonators is exactly the same as in the simulation. To measure sound ressure levels at the outlet o cylindrical ducts were used Brüel & Kjær s latorm PULSE or noise and vibration analysis equied with Brüel & Kjær s / inch acoustical microhone tye 49-C-. Figure 6. Examle view on the exerimental set u. Figure 7. Schematic view o the exerimental set u in the laboratory exeriment. COMSOL Conerence, October 3-5, Boston MA, USA

11 Results In case o exerimental results that are reresented only by insertion loss (IL), the research made by the use o numerical calculations in COMSOL Multihysics are ocused on achieving the best convergence. Figure 8. Numerical model (NM) -,6m long ie with helicoidal resonator surrounded at the inlet side in the distance o 6cm by an absortive material. Figure 9. Comarison o results or NM or helicoidal resonators with number o turns: a) n=,67, b) n=,695. COMSOL Conerence, October 3-5, Boston MA, USA

12 Results In case o exerimental results that are reresented only by insertion loss (IL), the research made by the use o numerical calculations in COMSOL Multihysics are ocused on achieving the best convergence. Figure. Numerical model (NM) -,6m long ie with helicoidal resonator and m cubic box. Figure. Comarison o results or NM or helicoidal resonators with number o turns: a) n=,67, b) n=,695. COMSOL Conerence, October 3-5, Boston MA, USA

13 Results In case o exerimental results that are reresented only by insertion loss (IL), the research made by the use o numerical calculations in COMSOL Multihysics are ocused on achieving the best convergence. Figure. Numerical model 3 (NM3) - m long ie with helicoidal resonator and m cubic box. Figure 3. Comarison o results or NM3 or helicoidal resonators with number o turns: a) n=,67, b) n=,695. COMSOL Conerence, October 3-5, Boston MA, USA 3

14 Conclusions As it can be observed rom resented results, the best convergence between exerimental and numerical ILs is achieved by modeling just m long ie with helicoidal resonator inside and inlet boundary condition set as sherical wave. This numerical acoustic system geometrically diers a lot rom exerimental set u. It was also observed that in all cases o numerical models (rom NM to NM3) the characteristic or resented helicoidal resonators sound attenuation requency range between about 5Hz to about 34Hz can be simly identiied. But the boundary conditions lay a key role when identiying lower requency range o acoustic characteristics. This study shows that modeling acoustic systems with helicoidal resonators in COMSOL Multihysics don't need to include all o exerimentally used environment to achieve similar results, but the boundary conditions should be roerly used. Also it is a great knowledge to know which exact numerical model should be used to achieve results comarable to exeriment. COMSOL Conerence, October 3-5, Boston MA, USA 4

15 Thank You or Your kind attention Acknowledgements Scientiic work inanced rom the budget or science in the years - 3 as a research roject. Ph. D. Eng. Wojciech LAPKA wojciech.laka@ut.oznan.l COMSOL Conerence, October 3-5, Boston MA, USA