Validation of the Experimental Setup for the Determination of Transmission Loss of Known Reactive Muffler Model by Using Finite Element Method

Transcription

1 Validation of the Experimental Setup for the etermination of Transmission Loss of Known Reactive Muffler Model by Using Finite Element Method M.B. Jadhav, A. P. Bhattu Abstract: The expansion chamber is one of the most basic types of silencing elements used in intake and exhaust systems. The acoustic behavior of reactive muffler with central inlet, central outlet is investigated in detail by means of experimental method. In this paper experimental setup is developed to predict the acoustic performance of reactive silencer by using two load method and it is validated by determination of transmission loss (TL of known reactive muffler model by using finite element method (FEM. For the model experimental measured transmission loss was compared with that obtained from the finite element method (FEM. From the result it can be concluded that developed setup is reliable to determine TL by experimental method from low to mid frequency range. Keywords: Finite Element Method, Reactive Mufflers, Transmission Loss, Two Load Method. I. INTROUCTION Accurate prediction of sound radiation characteristics from reactive muffler is of significant importance in automotive exhaust system design. The most commonly used parameter to evaluate the sound radiation characteristics of muffler is transmission loss (TL. Transmission loss is one of the most frequently used criteria of muffler performance because it can be predicted very easily from the known physical parameters of the muffler. The transmission loss (TL could be achieved by three methods analytical, numerical, and experimental. However, practical muffler configurations generally have large cross sectional dimensions as well as complex geometries. Analytical methods are cumbersome in the sense that the associated algebra is very complicated so, many times it is impossible to solve such problems by analytical methods [1]. The numerical methods are completely general and allow the analysis of all types of mufflers. But the results achieved by numerical tool i.e. by FEM may not be correct due to many reasons such as modeling errors, meshing errors, assumptions while solving the partial differential equations (solution errors, specifications of approximate boundary conditions, insufficient constraints, selection of meshing elements, types of meshing. Irrespective of these drawbacks numerical methods can be used for optimization of model of complicated shapes and cost involved is less compared to experimental methods. So general practice is to optimize the model by numerical methods and validate the result by experimental methods. For the experimental validation, experimental set up must be developed with due care and precautions. For the validation of experimental setup it is necessary to test the results of model of which analytical, numerical results are known. The measured transmission losses are compared with FEM method, demonstrating that transmission losses can be determined reliably with the setup which is prepared. In general, experimental results are required for verifying the analytical and numerical predictions and also for evaluating the overall performance of a system configuration so as to check if it satisfies the design requirements [2]. In this research paper two load methods is used for measuring transmission loss by experimental method. II. THEORY Two Load Method [3]: In the two load method, two loads should be different to keep results stable. Generally, two loads can be two different length tubes, a single tube with and without absorbing materials. In this research two loads were achieved by outlet tube with and without absorbing material as shown in Figure 1. The two load method is based on the transfer matrix approach. Using the transfer matrix method, one can readily obtain transmission loss of any muffler by using four pole equations from the four positions of microphones. Fig 1.Two Configurations and Schematic Model of Muffler 96

2 Neglecting flow of air, the four poles for elements 1-2 can be The term H ij represents transfer function between P i and P j expressed as (H ij = P j / P i.the four poles for elements 3-4 can be expressed cos kl12 jρc sin kl12 A12 B12 as = j sin kl 12 C cos kl ρc cos kl34 jρc sin kl34 A The four poles for elements 2-3 can be expressed as 34 B34 = j sin kl 34 A B C34 34 cos kl 34 C Where Δ 34(H32aH34b -H32bH 34a + 34(H32b -H 32a A = Δ (H -H B (H -H 34 32a 32b B = Δ 34 (H 34b -H 34a C = 34 34b 34a (H31a -A12H 32a (Δ34H34b - 34-(H 31b-A12H 32b(Δ34H34a - 34 B12 Δ 34(H34b -H 34a B 34(H31a -H 31b-A 12(H32b -H 32a = B Δ (H -H b 34a By using two microphones with random excitation transmission loss can be calculated experimentally. III. EXPERIMENTAL SETUP A schematic diagram of experimental set up for calculating TL of simple expansion muffler is shown in Figure 2. It consists of a noise generation system, noise propagation system and noise measurement system. The TL is measured by transfer function method. The setup has the following main components. Impedance Tube ata acquisition system Noise source with amplifier Sound pressure measuring microphones ρc 1 B TL = 20log 10( A + +ρcc + 2 ρc Fig 2. Schematic iagram of Experimental Setup with Its Components Impedance tube is a rigid tube through which sound propagates and reflects from test sample which results in creation of standing waves in it. It has measuring locations at specific distances from test sample where the acoustic pressure is measured. A sound source device is connected at the one end of impedance tube and test muffler at other end. As we are interested in incident and transmitted wave, two impedance tubes are used on either side of the muffler. The 97

3 main purpose served by impedance tube is providing guidance to sound wave as required for plane wave propagation. The data acquisition system used is a four channel FFT analyzer with an interface for the control and setting of analyzer. It collects the pressure data from microphones and feed it to data recording storage system. It also has a single output channel which is fed to speaker through analyzer. A random noise signal is generated in same analyzer and directed to the speaker via amplifier. The reason behind using random noise (white noise is that it contains equal power density of noise for each frequency. Sound source used is of high power to produce at least 120 db of noise. Pressure field microphones are used for measurement. The two microphones are sufficient as transfer function method is used. Transfer function is evaluated for each set of reading. The actual test setup with required components is shown in Figure 3. Two configurations of set up are used with respect to boundary conditions. IV. EXPERIMENTAL PROCEURE Experimentation for pressure measurement mainly consists of analyzer setting and data processing for TL calculation. The experiment is performed for frequency range of 50 to 3400 Hz. The measurements are taken in two slots with two locations 1-1 and 4-4 as shown in figure respectively to cover desired frequency range [4]. The locations are used for measuring pressure in frequency range Hz, while the locations are used for measuring pressure in frequency range of Hz. The first set of readings is taken for no load condition with both frequency range and same procedure is repeated for with load condition. Two microphones are used for measurement, which are sufficient for measurement of transfer function between sound pressures measured at two locations. One microphone is placed at location 3 and other placed at location 1, 2 and 4 respectively to get transfer function H 31, H 32 and H 34 with respected locations. All other locations except locations where microphone are inserted are sealed with pins to avoid sound leakage. The sound leakage is tested and wax is used to seal these leaks. The obtained transfer functions are then directly used in four-pole element calculations to get TL.. Fig 3. Photograph of Actual Experimental Setup 98

4 V. FINITE ELEMENT METHO In this research a three dimensional finite element method is implemented to evaluate the transmission loss (TL for central inlet central outlet muffler assuming zero Mach number. The numerical analysis was carried out using Comsol program (COMSOL Multiphysics without fluid structure interaction. This program is capable of applying FEM solution to the muffler problem. Parametric solver and linear solver are used. In these cases a frequency of Hz is considered with a frequency resolution of 5 Hz and the frequency response of the sound pressure (transmission loss is observed. The air density and speed of sound are taken as kgm 1 and 343 msec respectively. Automatic meshing (free meshing was used. Tetrahedral elements were used. The element size for the finite element domain was chosen to provide a minimum resolution of 12 elements per wavelength to ensure that the resolution requirements were met and consequently, accuracy was maintained. Figure 4 shows model used for experimentation. Fig 6.Post processing of time domain signal into frequency domain by FFT Fig 4. Model for Experimentation VI. RESULTS Figure 5 and Fig. 6 show time domain signal and FFT signal from Oros FFT analyzer. Fig 5. Time omain Signal Collected By ata Acquisition System Fig 7. Comparison of performance of muffler Figure 7 shows TL comparison for a single expansion chamber muffler. The measured results by experimental method agreed with the FEM results. VII. CONCLUSION In this research paper results of known model are verified by experimental method. In two load method only loads are changed without changing position of source. The experimental results show good agreement with the numerical results. From the results it can be concluded that from the developed experimental setup it is possible to measure the transmission loss of any muffler. The small deviation of the experimental results from the numerical results may be due to leakage of sound from the surrounding, medium quality surface finish of impedance tube, and problems in generating true random (white noise from the FFT. Analytical results assume plane wave propagation which can not predict real behavior of muffler beyond cut on frequencies. So these results are not compared with analytical results. 99

5 REFERENCES [1] T.S.S. Narayana and M.L. Munjal, Prediction and measurement of the four pole parameters of a muffler including higher order mode effects, Noise Control Eng. J. 53 (6, Nov-dec [2] S.N.Y. Gerges and R. Jordan, F.A. Thieme, J.L. bento Coelho, J.P. Arenas, Muffler modeling by transfer matrix method and experimental verification, J. of the Braz. Soc. Of Mech. Sci & Eng. April-June 2005, Vol. XXVII, No 2. [3] Z. Tao and A.F. Seybert, A review of current techniques for measuring muffler transmission loss, SAE [4] International Standard ( , Acoustics, etermination of sound absorption coefficient and impedance in impedance tubes. 100