Acoustic Performance of Helmholtz Resonator with Neck as Metallic Bellows

Transcription

1 ISSN Acoustic Performance of Helmholtz Resonator with Neck as Metallic Bellows #1 Mr. N.H. Nandekar, #2 Mr. A.A. Panchwadkar 1 nil.nandekar@gmail.com 2 panchwadkaraa@gmail.com 1 PG Student, Pimpri Chinchwad College of Engineering, Pune, India 2 Associate Professor, MED, Pimpri Chinchwad College of Engineering, Pune, India ABSTRACT Helmholtz resonator can show a strongly resonant response at a well-defined frequency when subjected to external excitation. This resonant characteristic can be used effectively to attenuate the generation of sound, by attaching the resonator with neck as metallic bellow. The Helmholtz resonator with neck as metallic bellow type variable resonance attenuator called as multi-degree of freedom type Helmholtz.It has been designed to attenuate several frequencies. Metallic bellow changes single degree freedom system to multi degree freedom system. The objective of this paper is to investigate the resonance frequency, acoustic attenuation performance (Transmission loss) of resonator with neck as metallic bellow to overcome the drawback of Helmholtz resonator to attenuate only narrow-band low-frequency noise. Analytical expression of resonance frequency and transmission loss based on the Newton s second law of motion for this resonator is developed. The resonance frequency and transmission loss will be calculated analytically by using finite element analysis (FEA). The results will be validated experimentally on a Helmholtz resonator with neck as metallic bellow. This will give understanding of actual and theoretical transmission loss of noise. ARTICLE INFO Article History Received :18 th November 2015 Received in revised form : 19 th November 2015 Accepted : 21 st November, 2015 Published online : 22 nd November 2015 Keywords Helmholtz Resonator, Resonance frequency, Transmission loss, FEA Analysis, Metallic bellow. I. INTRODUCTION Noise is, to a great extent, purely subjective personal phenomena. Perhaps the best definition of it is as an unwanted sound. Noise does, however, have two basic characteristics. The first is the physical phenomenon which can be measured and thus used in technical specification. The second is the psycho acoustical characteristic which attempts to judge the effect of noise on human beings. In industries that use small cooling fans, fan noise simply interferes with the ability of the people working nearby to concentrate on their work. The factors of greatest importance to the system designer are the psychological influences on the person rather than the physical influences of sound on the human ear. For above problem on that human being because of that we need to attenuate the noise. A. Helmholtz Resonator Basic Principle A Helmholtz resonator, as shown in Figure 1, is an acoustic band-stop filter comprised of a rigid cavity with a protruding neck that connects the cavity to the system of interest. The behavior of a Helmholtz resonator is analogous to that of a vibration absorber. The volume of air in the neck of the Helmholtz resonator behaves much like a vibration absorber mass and the volume of air in the cavity acts like compliance. The excitation is provided by tonal pressure fluctuations acting over the opening of the neck. The pressure increase within the cavity provides a reacting force analogous to that of a spring. Damping appears in the form 2015, IERJ All Rights Reserved Page 1

2 of radiation losses at the neck ends, and viscous losses due to friction of the oscillating air in the neck. Resonance takes place when the exciting frequency equal to the resonance frequency of the cavity. In this situation, the viscous loss is the biggest. In this way, Helmholtz resonator attenuates the single resonance frequency noise and the noise with narrow band around the resonance frequency. The objective is to investigate the resonance frequencies, acoustic attenuation performance (transmission loss or noise reduction) of Helmholtz resonator with metallic bellow as neck to overcome the drawback of Helmholtz resonator to attenuate only narrow-band low-frequency noise. Helmholtz resonator with neck as Metallic Bellow 1) To design and developing analytical expression of resonance frequency & transmission loss for Helmholtz resonator with neck as metallic bellow in terms of the lumped-parameter theory. 2) To study the effect of geometry on acoustic performance of Helmholtz resonator with neck as metallic bellow. 3) To Develop Helmholtz resonator with Metallic bellows as the neck. 4) To find acoustic pressure (rms) and sound in db value before and after of Helmholtz resonator by using FFT analyzer 5) To find resonance frequency and transmission loss of Helmholtz resonator with neck as metallic bellow by using Finite Element Method. Fig.1.1 Helmholtz resonator basic structure [3] The resonance frequency of a Helmholtz resonator is approximately given in Equation (1) f = (1) Where d and l are respectively the neck diameter and the neck length V is the resonator volume, and c is the sound speed. It can be seen that the resonance frequency is a function of the cavity volume and neck dimensions, but independent of the cavity dimensions. The character of Helmholtz resonator is that the noise damping is notable near the resonance frequency but descend quickly in other frequency. Helmholtz resonator is widely used to reduce the peak value of noise spectrum. It is feasible to design multi-helmholtz resonator to reduce different peak value of noise. In single Helmholtz resonator only design for single frequency level sound can be attenuate. But when frequency varies with respect time then single Helmholtz resonator is not work effectively.there are present so many techniques for noise attenuation for varying frequency, like dual Helmholtz resonator[2], multi Helmholtz resonator[1](connected may be in series and parallel)but this resonator required space is more as compared to single resonator. Some cases space limitation is present in that we can t attenuate noise. Those cases it is possible with Helmholtz resonator with neck as modification. B. Problem Statement Design Helmholtz resonator with neck as metallic bellow for noise reduction in the blower. As blower produce noise of variable frequency range it is not easy to control. Single frequency noise can be easily reduced by using SHR, but when frequency varies at that time required multi degree of freedom Helmholtz resonator system C. Objectives II. METHODOLOGY Modeling methodology consist of five major component illustrated in figure. They are (1) Developing the analytical expression for the Helmholtz resonator with neck as metallic bellow. (2) Design and manufacturing Helmholtz resonator with neck as metallic bellow. (3) Experimentation carried out with two source method.(4) Numerical analysis of mechanism using FEA in this parts model made in CAD software and mesh of this model in Hypermesh software and Analysis will be done in ANSYS software (5) Result and validation, in this part result obtained from experimentation are compared with Numerical result. Fig.2.1 Flowchart of methods followed 2015, IERJ All Rights Reserved Page 2

3 III. THEORETICAL MODEL A. Lump Parameter Model of Helmholtz resonator with neck as metallic bellows In light of the low frequencies of interest in the present study, the geometrical dimensions considered here are significantly smaller than the relatively long wavelengths. Hence, the spatial resolution is ignored next to develop expressions for both the resonance frequencies and transmission loss for a Helmholtz resonator installed in a side branch orientation as shown Where A is the cross-sectional area of the neck, ( 1) displacement of the neck, and Δp the pressure variable quantity in the cavity when the displacement of neck is Δx. According to the definition of bulk modulus, the expression of Δp can be represented by (2) the (3) Applying Eq. (3), the stiffness of the three springs in the equivalent mechanical system of 3-DOF Helmholtz resonator system can be calculated. For Spring 1, its stiffness to the first mass m1 is given by, (4) Fig.3.1 (a) The structure (b) Equivalent Mechanical System [1] B. Equivalent mechanical system Fig.3.1 (a) shows the structure of 3-DOF Helmholtz resonator. It consists of three cylindrical necks and cavities connected in series (Neck 1-Cavity 1-Neck 2-Cavity 2-Neck 3-Cavity 3). Where L1, L2, L3 and D1,D2, D3 are the lengths and diameters of Cavity 1, Cavity2 and Cavity 3 respectively; l1, l2, l3, and d1, d2, d3 are the lengths and diameters of Neck 1, Neck 2 and Neck 3 respectively; p1 is the air pressure in the main pipe, dp the diameter impedance tube, and A1 the cross section area of Neck 1. Fig.3.1 shows Structure and equivalent mechanical system of 3-DOF Helmholtz resonator with neck as metallic bellow. In view of the low frequencies of interest in this project, the geometrical dimensions considered here are significantly at a particular frequency (200Hz and 300Hz). Thus the model of 3-DOF Helmholtz resonator with neck as metallic bellow can be established by lumped parameter theory. pointed out that the mass significant for oscillation of single Helmholtz resonator in air medium is concentrated in the neck (metallic bellow) of the resonator and the volume of resonator acts as a spring, and it also gave out the mechanical-acoustical analogy for single Helmholtz resonator in air medium which is a mass-spring system. According to the theory proposed and taking the effect of viscous friction loss in necks into consideration,3-dof Helmholtz resonator with neck as metallic bellow can be equivalent to 3-DOF mass-spring damping system as shown in Fig. 1(b). The three necks act as three masses (m1, m2 and m3) due to inertia effect of the fluid in necks. The three cavities act as three springs (Spring 1, Spring 2 and Spring 3) due to capacitive effect of the fluid in cavities. The three necks viscous frictions can be equivalent to three damping (c1, c2 and c3) which act on the three masses (m1, m2 and m3). Applying the Hooke s law to the closed cavity, the stiffness of spring can be given by Similarly, the stiffness of Spring 1 to the second mass m2 and m3 According to Fig. 1(b), applying the Newton s second law of motion to Mass 1 yields Where is the mass of air in Neck 1. Applying the Newton s second law of motion to Mass 2 gives Where is the mass of air in Neck 2. Applying the Newton s second law of motion to Mass 3, there is Where is the mass of air in Neck 3. Above three equation rewrite by putting all values of k,m,c For mass 1 (5) 2015, IERJ All Rights Reserved Page 3

4 Similarly, by deriving equations for mass 2 and mass 3,the following matrix form is obtained. From above matrix we get Resonance frequency of Helmholtz resonator with neck as metallic bellow by putting input value and geometrical value of Helmholtz resonator. (6) V. EXPERIMENTAL APPROACH Figure 5.2 shows the instruments used for sound measurements. Helmholtz resonators are placed between a broad-frequency noise source and an anechoic termination The decomposition method was used for the measurement; then utilized to separate incident and reflected waves for calculation of the transmission loss across the element, with one pair of microphone placed before and another pair after the resonator. Since multidimensional waves are excited in the resonator volume, the selected impedance tube diameter ensures planar propagation at the microphones. Figure 5.1 shows the actual setup of experimental. The frequency was set at 100Hz to 400Hz and take reading at before and after of Resonator. IV. NUMERICAL MODEL A. Modeling of Helmholtz resonator with neck as metallic bellow By using of Catia software we have done modeling of Helmholtz resonator. In this work, firstly we have done modeling of each of Helmholtz resonator as with experimental setup supporting part. The figure given below shows the modeling of Helmholtz resonator with neck as metallic bellow. Fig.5.1 Actual setup of experimental Fig.4.1 Modeling of Helmholtz resonator with neck as metallic bellow B. Meshing of Helmholtz resonator with neck as metallic bellow After completion of modeling these model required to convert from infinite element finite element. This process carried out by using meshing software. Hypermesh software is used to get accurate and specified result. Fig.5.2 Instrumentation used for experimentation VI. RESULT AND DISCUSSION Experimental results for transmission loss corresponding to the geometries of neck. At 300 Hz frequency inlet and Outlet reading with Metallic Bellow db/20.0µ Pa Fig.4.2 Meshing of Helmholtz resonator with neck as metallic bellow Fig.6.1 At 300Hz frequency input reading 2015, IERJ All Rights Reserved Page 4

5 db/20.0µ Pa Fig.6.2 At 300Hz frequency output reading Hz 300Hz Upstream Downstream 7. B.Yousefzadeh, M.Mahjoob, N.Mohammadi,A.Shahsavari An experimental study of sound transmission loss(stl)measurement techniques using an impedance tube Acoustic 2008 Paris 8. Z.Tao,A.F.Seybert A Review of current Techniques For Measuring Muffler Transmission Loss SAE 9. Qibo Mao, Stanislaw Pietrzko, Experimental study for control of sound transmission through double glazed window using optimally tuned Helmholtz resonators, (2010) 10. S.K. Tang, On Helmholtz resonators with tapered necks, Journal of Sound and Vibration 279 (2005) Fig.6.3 Comparison of input and output db value VII. CONCLUSION With the use of metallic bellow it is found that there is transmission loss of about 4 db Pressure(rms) value is found 0.1 Pa at inlet and 0.02 Pa at outlet at frequency level of 200Hz indicates the pressure loss at outlet Down ACKNOWLEDGEMENT Thanks to Mr. A.A. Panchwadkar and Dr. S. S. Lakade for their valuable guidance and contribution for developing this study REFRENCES 1. M.B. Xu, A. Selamet, H. Kim, Dual Helmholtz resonator, Applied Acoustics 71 (2010) GUAN Changbina, JIAO Zongxia, Modeling and Optimal Design of 3 Degrees of Freedom Helmholtz Resonator in Hydraulic System, Chinese Journal of Aeronautics 25 (2012) S. Mekid and M. Farooqui, Design of helmholtz resonators in one & two DOF for noise attenuation Sheldon imaoka, Calculating transmission loss in mufflers using ANSYS Workbench Mechanical 14.0, January Rechard Eberhart, Denis Karczub, Piping noise Transmission loss calculating using FEA Noisecon ] Rongting Zhang, Huanhuan Gu, Yusheng Hu, Sihai Xia Investigation on Multi-Helmholtz in pipelines. Resonator in the Discharge System of Rotary Compressor international compressor Engineering Conference, paper , IERJ All Rights Reserved Page 5