The effect of element size on the solution is examined by varying the maximum and minimum element sizes in the meshed domain. The deviation in transmission loss value at the peak frequency due to change in element size is observed. Table 1 shows the result of grid sensitivity test for the proposed configuration 1.
Table 1. Grid sensitivity test
Table 1 shows that the transmission loss value decreases with decrease in element size. As the effect of element size is less significant, a shorter computational time becomes next interest. So that a medium grid size of 22.2 mm (maximum) and 4 mm (minimum) is chosen for the study.
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9 RESULTS AND ANALYSIS
The dimensions of key elements such as single expansion chamber, Helmholtz chamber and multiple expansion structure are varied and the performance of noise reduction is analysed.
Three design cases as described in table 2 is analysed.
Table 2. Three design cases based on width of cavity
Sl. No Description Configuration
Case1 Multiple expansion chamber for 100% width of cavity 1 Case 2 Single expansion chamber for 50% width of cavity and
multiple expansion chamber for 50% width of cavity.
1
Case 3 Helmholtz chamber concentric with multiple expansion chamber that cover 100% width of cavity.
2
The sound transmission loss resulted in all the three cases is compared in figure 37.
Figure 37.Effect of design changes on sound transmission loss.
Figure 37 shows the sound transmission loss obtained in three different design cases from which the effect of key elements of proposed configurations on noise reduction can be observed. The STL is the maximum for the design case 1 with the peak value of 240 dB and
it is more than 50 dB for the frequency range from 1400 Hz to 3250 Hz. The peak value is reduced in design case-2 due to inclusion of single expansion chamber for half the width of the cavity replacing a portion of multiple expansion structure. It can be observed by comparing case-1 and case-2 that the use of multiple expansion structure gives a larger performance for noise reduction for higher frequencies. This is due to increased area of contact and high viscous dissipation of medium and high frequency sound waves. The performance due to use of single expansion chamber in case-1 is better for low frequency noises from 500 Hz to 1420 Hz because of its larger size. In order to get further higher STL for low frequency sound input, a Helmholtz chamber is included in design case-3. By combining a multiple expansion structure with Helmholtz chamber, a maximum STL of 173 dB is achieved at the frequency of 620 Hz and more than 50 dB transmission loss is obtained for the frequency range from 600 Hz to 1000 Hz. The effect of chamber width in multiple expansion structure on STL is studied for case 3 in presence of Helmholtz chamber. The results are compared in figure 38.
Figure 38.Effect of chamber width in multiple expansion structure for case-3.
Figure 38 shows that the maximum sound transmission loss occurs when the chamber width is kept 1 mm. The performance is reduced when chamber width is increased to 10 mm and to 21 mm. This is due to larger number of expansions at lower chamber width that cause increased area of contact and higher viscous dissipation of sound. Due to the combined effect of Helmholtz chamber and multiple expansion structure, the STL increases for the majority
47
of lower frequencies between 10 Hz to 600 Hz with decrease in chamber width. In order to observe the effect of chamber width in multiple expansion structure in absence of Helmholtz chamber, the case-1 is evaluated as shown in figure 39.
Figure 39.Effect of chamber width in multiple expansion structure for case-1.
Figure 39 shows that the peak value of STL is decreased with increase in chamber width in multiple expansion structure from 1 mm to 20 mm. In the absence of Helmholtz chamber, the STL for low frequency noises increases with increase in chamber width. But the noise reduction performance in the low frequencies is much lesser than that compared to case-3.
It can be inferred that the use of multiple expansion structure alone gives highest noise reduction performance for medium frequency noises ranging from 1000 Hz to 3250 Hz. The use of Helmholtz chamber concentric with multiple expansion structure gives highest noise reduction performance for lower frequency noises ranging from 600 Hz to 1000 Hz. Increase of chamber width in multiple expansion structure widens the frequency bandwidth for noise reduction and decreases the peak transmission loss.
10 CONCLUSIONS AND SUMMARY
The air path from the sound generating end is a crucial spot for passive noise reduction by means of sound energy absorption and multiple reflections. Absorption of sound takes place due to viscous dissipation in the air field caused by velocity differences between air molecules. Use of solid obstacles inside the air path promotes the sound absorption due to viscous dissipation. As the amplitude of sound wave is maximum at a quarter of its wavelength, the length of solid surface contact needs to be greater than quarter of the wavelength. Structures with continuous pores are particularly useful for accomplishing the sound absorption due to increased surface contact.
Helmholtz cavity works with principle of increasing the amplitude of sound waves near the contacting surface by creating resonance vibration. It helps in dissipation of low frequency waves with minimal length of surface contact. Another way of sound cancelling is possible by interfering a sound wave with another sound wave having 180ophase difference. The sound from same source is allowed to travel in two different paths and meet each other when a phase difference of 180o is obtained. This method is called as passive destructive interference. Creating partitions in muffler devices increases the characteristic length of sound travel that causes the increase of sound transmission loss through the muffler. The noise reduction performance of combined partitions is remarkably higher than that of individual partitions.
This study concludes that design complexity of cavity is a potential parameter affecting the performance of passive noise reduction. By creating multiple expansions along the sound carrying air path, the peak of sound transmission loss increases steeply. Increasing the width of each expansions, decreases the peak of sound transmission loss but increases the frequency bandwidth of sound reduction from lower frequency zones. By replacing 50%
width of multiple expansion structure by a single expansion chamber, the peak transmission loss of the structure decreases almost 40%. Use of Helmholtz cavity concentric to multiple expansion structure causes higher sound transmission loss in low frequency regions.
49
Multiple expansion structure introduced in the study provides a peak transmission loss of 240 decibels and completely controls the sound less than 50 decibels for medium frequency range from 1000 Hz to 3250 Hz. Use of combination of Helmholtz cavity with multiple expansion structure in a concentric arrangement, provides a peak transmission loss of 173 decibels for a frequency of 620 Hz and completely controls the sound less than 50 decibels for a frequency range between 600 Hz to 1000 Hz.
The use of additive manufacturing technologies such as FDM and PBF are suitable for manufacturing complex structures with continuous pores that uses two or more sound absorption mechanisms. The design process of noise reduction cavity structure should also account for design for additive manufacturing as discussed in this study. The figure 40 shows the strategy flow for development of additively manufacturable noise reduction cavity structures working on atmospheric conditions.
Figure 40. Strategy for development of AM based noise reduction cavity structures.
As shown in figure 40, the sound absorption elements are first chosen according to frequencies of noise to be reduced. A combination of absorption mechanisms is developed by assembling different absorption elements to design a noise reduction cavity. The design of the cavity is checked with DFAM rules and corrections are to be made. The cavity is numerically modelled by finite elements and the STL value is calculated. Based on peak
Identification of input noise properties Stratagy for selection of sound absorption elements Design of noise reduction cavity based on absorption elements
Correction of cavity design according to rules of DFAM
Acoustic analysis of cavity using FEM to calculate sound transmission loss Optimize the design for higher transmission loss and larger bandwidth of frequency
Modelling wall structure for noise reduction cavity Correction of wall structure design according to rules of DFAM
Additive manufacturing of wall structure of cavity
transmission loss and bandwidth of frequencies of higher transmission loss, the design parameters of the cavity are optimized. Wall structure for the cavity is designed according to rules of DFAM and finally manufactured using FDM or PBF process.
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11 FURTHER STUDY
The noise reduction performance of cavity structures is to be analysed for different temperatures and fluid flow velocity depending on the specific applications. Experimental analysis of sound transmission loss for new cavity structures has to be carried in different working conditions.
Light weight wall structures as shown in figure 41 are manufacturable with wide range of innovative designs using additive manufacturing. The use of air gaps inside the walls increases the noise reduction performance in light weight constructions (Harun et al. 2012, p. 246). The future study has to be carried on structure and air borne noise reduction across different hollow wall structures.
Figure 41. Cross section of sandwich cored light weight walls (Bagsik et al. 2014, p. 697).
As shown in figure 41, the light weight wall structures have a combination of fluid and solid media. A vibro-acoustic analysis has to be carried to investigate the sound transmission loss across the structure that is made of materials with different densities.
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