Theoretical and experimental investigation of acoustic performance of multi-chamber reactive silencers

(1)

Theoretical and experimental investigation of acoustic performance of multi-chamber reactive silencers

Hakan Arslan

^a

, Mostafa Ranjbar

^b,^⇑

, Erkan Secgin

^c

, Veli Celik

^b

aDepartment of Mechanical Engineering, Kirikkale University, Kirikkale, Turkey

bDepartment of Mechanical Engineering, Ankara Yildirim Beyazit University, Ankara, Turkey

cTUBITAK Defense and Security Technology Research Support Group, Ankara, Turkey

a r t i c l e i n f o

Article history:

Received 23 May 2018

Received in revised form 17 July 2019 Accepted 27 July 2019

Available online 16 August 2019

Keywords:

Impulsive sound pressure Acoustical analysis Sound transmission loss Insertion loss Noise reduction Reactive silencer

a b s t r a c t

The acoustic attenuation and performance analysis for blast flow field inside a silencer is investigated. In this regard, a silencer system is designed to reduce the exhaust noise. The effect of position and the number of the baffles for each design on sound transmission loss have been investigated using theoretical, numerical and experimental studies. Three prototypes are manufactured for the experimental studies.

Using the measured results, insertion loss graphics have been obtained. The silencer performances are dependent on the baffle geometry, number and the positions. The experimental results are in a good agreement with the simulation results. It is observed that by considering the same number of baffle numbers but located at various locations, the model which shows the best sound transmission loss performance has also the best insertion loss performance and has the least value of peak sound pressure level.

1. Introduction

When the human hearing is exposed to high-intensity noise, the hearing nerves can be damaged and therefore hearing loss can occur. As the human hearing system is not linear, it is sensitive to logarithmic increases of sound pulse with respect to the minimum level of hearing. The level of sound in logarithmic scale is called as decibel (dB)[1]. For example, in the event of a pulse or momentary noise, such as a gunshot or explosion, the peak sound pressure level should not reach 140 dB which may cause perma- nent hearing loss. The hearing frequency range for a normal person is between 20 and 20,000 Hz. However, the most important frequency for hearing detection is around 1200 Hz[2].

One of the most realistic examples of explosive pressure waves is gun fire. Excessive noise occurs when a gun is fired. This includes ignition sound, orbital flight sound, explosion sound at the target, and weapon mechanisms. The barrel burst is formed by the explosion of gunpowder inside the barrel. This rapid gas expansion within the barrel causes an impulsive pressure wave. Acoustic sound pressure level during shooting is 140–180 dB[3]. The barrel pressure wave differs from the noise of the environment in two major features: short time occurrence and high amplitude. Indeed,

pulse duration is usually in order of milliseconds in such case[4].

This is a gradual noise that can cause hearing disorder. Silencer can be used for impulsive noise level reduction. It can be thought of as a tube consisting of chambers for reducing sound waves[5]. Barrel muzzle pressure suppression is important in the design of both large and small caliber weapons. A variety of tools which are used to reduce the barrel pressure depends on experimental investigations[6].

In general, silencers are classified as reactive, dissipative, and hybrid type. Reactive silencers generate dissipative sound waves caused by geometric discontinuity by means of acoustics impedance difference. Dissipative silencers transform sound energy to heat energy; thus, decreases acoustic pressure fluctuations. The silencers which consist of a combination of reactive and absorptive types are called hybrid[7]. The selection of the silencer type and the internal design depends on the frequency band of the sound and using conditions. Reactive type silencers are commonly used as exhaust mufflers. Maher[8]obtained the character of the gunshot voice which is similar to this work. Hudson et al.[9]designed the silencer for small-caliber weapons. They have made experimental measurements for the design of the silencer.

Transfer matrix method (TMM) or four pole parameter study is known for a long time[10]. Transfer matrices are based on linear one-dimensional wave propagation for the calculation of sound transmission loss curves [11]. Davis et al.[12] considered single

⇑ Corresponding author.

E-mail address:mranjbar@ybu.edu.tr(M. Ranjbar).

Contents lists available atScienceDirect

Applied Acoustics

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / a p a c o u s t

(2)

and multiple expansion chambers and resonator. The sound reduction characteristics of several types of silencers were investigated experimentally by them. Igarashi et al.[13,14]used the electrical equivalent network method of a silencer. Different muffler investigations involving transfer matrices for elements were performed by Mechel[15]. Sullivan[16]obtained transmission loss of perforated muffler elements. Mehdizadeh and Paraschivoiu[17]calculated the transmission loss by finite element method for an exhaust system on a certain frequency range. Sreenath and Munjal [18]worked on an electric analogy for an exhaust muffler. They could estimate the insertion loss (IL) of silencers by using the transfer matrix method. In a study done by Munjal[19], the effect of the incompressible average flow was considered on the transmission loss of silencers. Salamat and Ji [20]studied the STL in the circular asymmetric expansion chamber with straight inlet and outlet channels. They investigated the effect of multi- dimensional wave propagation on acoustic attenuation. Vasile and Enescu[21]used numerical and experimental techniques for the evaluation of acoustic performance of a reactive silencer.

Degirmenci and Dirikolu[22]analyzed internal ballistics of a gun barrel and made thermochemical analysis. Theoretical and experimental studies on mufflers were also performed by Weaver[23].

The effects of reflections on STL measurements was evaluated in another work by Fang et al.[24]. Kim et al. used silencers for ventilation systems[25]. Performance calculations for linear and nonlinear input waves were done. Furthermore, several studies were published by Ranjbar et al.[26–33] on the maximization of the sound transmission loss in mufflers.

After a careful review of the previously available works, it is realized that there is a need to do a comprehensive investigation on the theory, simulation and experimental study of gun silencers.

There are very rare articles which deal with these aspects in the same time. This paper presents studies the numerical and experimental acoustic performance of circular silencers with internal explosive flow. In this work, theoretical and numerical calculations, prototype production, test and measurement stages were realised. In this context, transfer matrix method (TMM) was examined. Then, using a finite element analysis (FEA) program, models was created, acoustic analysis was carried out and the obtained results was verified with the experimental examinations.

2. Method 2.1. General

There are various parameters for determining the acoustic properties of silencers, e.g. insertion loss (IL), noise reduction (NR) and sound transmission loss (STL)[10]. IL is defined as the difference between the emitted sound power with and without silencer. NR is the difference between the sound pressure level in input and output of silencer. STL is the logarithmic representation of sound power value with respect to a reference sound power value.

The IL and NR performance criteria are dependent on the sound source and especially on the exit conditions while the STL is com- pletely a silencer character.

In this study, STL curves were obtained with TMM. Finite element method (FEM) is used for (in) the solution of acoustic wave equations. Silencers were design considering the performance criteria obtained by the theoretical analysis and the FEA method, and prototype productions were made in several types. Two experimental setups were consructed. The first experimental setup was made with some assumptions in the laboratory. The second test was performed with a mounted gun silencer in a real environment.

In the first setup, the acoustic medium inside the silencer was air. A constant white noise was produced at the entrance of the silencer.

Microphones were placed in and out positions of the silencer. Full performance of the silencer was not considered due to restrictions introduced by assumtions. However, it may be useful for compar- ison between the prototypes. The second test setup was used for measuring the shot sound level. This system is based on standards and were equipped with appropriate technical characteristics.

Sound measurements were carried out by shooting tests on the poles of the silencers. Several type prototype silencers were manufactured using the obtained results in this study.

2.2. Modelling and testing

In practice, a real silencer consists of several interconnected elements. The sound pressures in the input and the output position were p1and p2and volume velocities were

v

¹^and

v

², respectively.

Boundary conditions are shown inFig. 1. The pipe diameter (d) and length (L) were known.

For the given boundary condition, the transfer matrix (T) of the rigid-walled straight pipe[10]shown inFig. 1is:

T¼ A B

C D

¼ coskL i^q_S^csinkL i_q^S_csinkL coskL

" #

ð1Þ

While k0 is acoustic wave number, x (rad/s) is angular frequency, f is frequency (1/s) and c is the speed of sound (m/s), then:

k0¼

x

c¼2

p

^f

c ð2Þ

and by considering Mach number M;

kc¼ k0

ð1 M²Þ ð3Þ

also assuming S¼

p

^d²

4 ð4Þ

Y¼

q

^c

S ð5Þ

Then the acoustic transfer matrix is

½ ¼T e^iMk^c^LcoskcL iYe^iMk^c^LsinkcL

i

Ye^iMk^c^LsinkcL e^iMk^c^LcoskcL

" #

ð6Þ

The STL is independent of the acoustic sound source. For the sake of simplicity, the duct exit condition is assumed to be ane- choic (non-reflective). The product of the transfer matrices of each element forming the silencer (T_ij) is denoted by T. If it is assumed that the Mach number is very small, then STL with four pole con- stants[10]is

STL¼ 20log Yn

Y1

₁₌₂ 1

2 T11þT12

Ynþ T21Y1þ T22

Y1

Yn

" #

ð7Þ

Fig. 1. Acoustic plane wave propagation in a straight pipe.

(3)

FE models of the silencers were created. Then, the STL and other analysis were performed. The effect of chamber profile, the chamber diameter, the number of chambers and the distance between the chambers on STL were studied.

The STL analysis of the silencers are made with the ABAQUS solver[34] which is an implicit finite element solver. The analysis model of the silencers is constructed using the ABAQUS/explicit finite element solver. Silencer models are designed in two and three dimensions.Fig. 2shows a solid model of a bafflelless and a baffle silencer.

Fig. 2. (a) Silencer without baffle, (b) Silencer with a baffle.

Table 1

Acoustic media properties.

Material Air

Bulk Modulus [Pa] 142,000

Density [kg/m³] 1.2

Speed of sound [m/s] 340

back cover speaker

Middle section broad section

microphones

Fig. 3. Elements of the experimenthal test setup.

(a) silencer length of 161 mm

(b) scilencer length of 500 mm

Fig. 4. FEA final instantaneous sound pressure distribution for the silencer without baffle.

0 3 6 9 12 15 18

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

STL (dB)

Frequency (Hz)

Fig. 5. STL for the baffleless silencers with different lenghts, 161 mm;

500 mm.

(4)

Axial symmetric two-dimensional modeling is preferred in terms of short solution time and ease of modeling in the analysis of the silencers. Axially non-symmetric models are modeled in three dimensions. It is assumed that the acoustic environment is stationary in the analysis model. The acoustic element type duct without baffle four-node, linear, axially symmetric and four-sided ACAX4 were considered[34]. In the two-dimensional axial symmetrical silencer model, the element size is taken as 0.5 mm. In the later analysis, the element size is taken as 0.3 mm and since the same result is obtained, the assumed 0.5 mm value for the element size was considered as adequate. Material properties of the acoustic environment are given inTable 1.

It is assumed that the silencer output is planar and non- reflecting. On the other hand, continuous sound pressure is applied at 1 Pa amplitude. Considering the shooting sound characteristics, the frequency band is set on 350–3000 Hz. The solution step is performed within this frequency range. In the acoustic analysis using the ABAQUS program, the sound pressure level at each point is calculated for each frequency. Add-on software is used to create an STL account. Conduction loss is calculated according to the three- point principle[35].

The sound attenuation of the silencer differs in the open acoustic analysis performed by introducing different pulse sound pressure data at the same silencer. For this reason, the input data is

Fig. 6. FEA pressure distribution results of (a) length 161 mm, 5 baffles; (b) lenght 500 mm, 5 baffles; (c) length 500 mm, 45 baffles.

(a) (b)

0 50 100 150 200 250

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000 6500 7000 7500 8000 8500 9000

STL (dB)

Frequency (Hz)

0 100 200 300 400 500 600 700 800

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000 6500 7000 7500 8000 8500 9000

STL (dB)

Frequency (Hz)

Fig. 7. FEA results for STL (a) 5 baffles, 161 mm height; 5 baffles, 500 mm height; (b) 5 baffles, 500 mm height, 45 baffles, 500 mm height.

(5)

valuable during the evaluation of the obtained analysis result. In the analysis made, it is ensured that the solution results are independent of the input data by using the same input data. Consider- ing that the high acoustical pressure may damage the microphone, it may be appropriate to use the FEA results to compare the silencer performances just because the input data is not very close to the barrel muzzle or the exit of the silencer.

To investigate the effect of the baffle type and position on the performance of the silencer and to use it in other tests, a prototype production is carried out in which the number of baffles and the position can be changed.

Experimental determination of STL in assessing the acoustic performance of silencers is important in terms of design development. A similar type of test system used for testing automotive exhaust and acoustic damping materials is commonly used for silencers. In this case, the STL value of the silencer can be obtained independently of the input impedance. Since the final test of the gun silencer is a more difficult test method to determine the sound level produced by shooting, it is beneficial in an experimental setup that is carried out in the laboratory environment and is not much affected by the background noise.Fig. 3shows the elements forming the experimental test setup[36].

In the experiment setup, the bandwidth of the speaker is between 70 Hz and 20 kHz. The system was tested using National

Instruments USB 4431 analyzer. Data are acquired with high accu- racy using IEPE type sensors with four 24-bit analog inputs, one 24-bit analog output, anti-aliasing filters and 1 kS/s to 102.4 kS/s (kilosample/second) sampling rate on the analyzer hardware. Four 1/4⁰⁰IEPE type G.R.A.S. brand Type46BD type microphones are used to measure the sound pressure level. For the STL account, the frequency range, ambient temperature, and silencer size can be

Fig. 8. FEA instantaneous acoustic pressure distribution of 5 baffles silencers with 3 different diameters (a) 39 mm; (b) 60 mm; (c) 80 mm.

0 50 100 150 200 250

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

STL (dB)

Frequency (Hz)

Fig. 9. STL (FEA) results of silencers with 5 baffles and 3 different geometries, Diameter 39 mm; Diameter 60 mm; Diameter 80 mm.

(6)

entered in the computer software prepared in the LabVIEW program. In this study, the frequency range is 2 Hz, the ambient temperature is 25°C and the silencer size is 161 mm for the prototype production of the silencer experiments. The dimensions and math- ematical calculations of the experimental set-up used to determine the acoustic performance of the silencers are based on the ASTM-E- 2611 standard. This standard relies on the calculation of a transfer matrix with a tube, four microphones and a signal analysis system to measure other important acoustic properties of the STL and materials. It is checked that the test apparatus is reliable in terms of reproducibility.

Fig. 4 shows the acoustic pressure distribution of a silencer without baffle but with two different length. The sizes of the two silencers are taken as 161 mm and 500 mm. It shows that the local pressure decreases with increasing silencer length.

Fig. 5shows the STL variations with respect to the frequency for the two silencer models of the same diameter but 161 mm and 500 mm in length. It shows that the change in the length of baffleless silencer has no effect on the its acoustic performance.

Fig. 6shows the FEA pressure distribution of three silencers of various sizes and number of baffles but with the same diameter.

Fig. 6shows that the silencer with five chambers and the short- est length has the lowest sound pressure at the outlet.Fig. 7shows the STL changes of the silencer models obtained from the FEA result.

Fig. 7(a) shows that the extension of the silencer length does not have a positive contribution to acoustic performance. In Fig. 7(b), it is seen that an increase in the number of chambers for the silencer with 500 mm length caused the STL to increase after 3200 Hz. Considering that the highest frequency of the gun is around 1000–2000 Hz, therefore, there is no positive contribution to the performance of the silencer.

The outer diameter of the silencer is also an important criterion in terms of weight, ease of handling, aiming and ballistics. The outer diameters of the silencer are 39, 60 and 80 mm. The effect of them on STL are investigated. The 5-baffles silencer models are considered.Fig. 8shows the acoustic pressure distribution in these models.

Fig. 10. The acoustic pressure distribution of the first prototype silencer.

Fig. 11. The acoustic pressure distribution of the second prototype silencer.

Fig. 12. The acoustic pressure distribution of third prototype silencer.

0 20 40 60 80 100 120 140 160 180 200

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000

STL (dB)

Frequency (Hz)

Fig. 13. STL (FEA) graph Prototype-1, Prototype-2, Prototype-3.

Table 2

Material properties for the acoustic environment in the silencer.

Material Burnt Gas Powder

Bulk Modulus [Pa] 2,000,000

Density [kg/m3] 3

(7)

Fig. 8shows that the sound waves are not one-dimensional for cases (b) and (c). Here, case (a) shows a better performance.Fig. 9 depicts the STL curve of silencers of 161 mm in length and 39, 60 and 80 mm in outer diameter.

Fig. 9shows that increase of the diameter of the silencer will be more effective at lower frequencies (1000–2500 Hz).

Experiments were also conducted using silencers which were manufactured according FEA results. Shot tests and sound measurement experiments are performed and IL graphs are obtained.

The dimensions of the silencer models in this section are the same, the expansion chamber length is 165 mm and the diameter is 40 mm. The inlet and outlet pipes have a length of 37 mm and 7 mm respectively and a diameter of 10 mm. The element type, size, acoustic pressure load and boundary conditions of the analysis model are taken as the previous case. Material properties of the acoustic environment are determined according to previous case as well. Prototype models have different types of baffles, and the number and location of the baffles are different.

For the STL analysis of the prototype silencers, the acoustic environment of the FEA model is air. The three-dimensional FEA model is performed because the first prototype of silencer is not axially symmetric. Since the second and the third prototypes are axially symmetrical, then the element type of ACAX4 have been used. The model consists of 13,950 elements and 14,880 nodes.

In the axial symmetrical silencer model, the element size is taken as 0.5 mm. In the finite element analysis model, the silencer output is planar and non-reflecting. On the other hand, continuous sound

pressure is applied at 1 Pa amplitude. The solution frequency band is set up to 3000 Hz.

Figs. 10–12show the instantaneous changes of acoustic pressure resulting from FEA analysis of the first, second and third prototype. Comparing theFigs. 10–12, the second prototype shows a better performance in terms of acoustic pressure distribution as it has eight chambers.

Fig. 13shows the resulting STL graphs. It depicts that the STL values of prototypes range from 30 to 192 dB at frequencies higher than 1500 Hz. These values provide very good performance characteristics. First prototype has better STL values than the other prototypes at frequencies between 1400 and 1800 Hz, and the second prototype has better STL values than the other prototypes at frequencies over 1900 Hz. Third prototype has higher STL values than the other prototypes at frequencies between 0 and 1400 Hz.

As an input, the input pressure in the gun shot without a silencer is recorded by the earpiece microphone. This digital sound data is then analyzed. The sound of mechanism and reflection are also recorded in the relevant time interval. The gunpowder gas and material properties are considered as given inTable 2.

In the STL analysis, the prototype-1 is not axially symmetric. A three dimensional FE model is created. Prototype-2 and 3 are modeled symmetrically. The acoustic element type is four-node, linear, axially symmetrical, four-sided ACAX4R. The FEM model consists of 13,950 elements and 14,880 node points. Two-dimensional axial symmetrical silencer model element size is taken as 0.5 mm. Pla- nar output of the silencer is non-reflective. The critical time step is 1.281 10⁷s. The cross-sectional view of the prototype-1 finite element analysis model and the instantaneous change in acoustic pressure is shown inFig. 14.

Fig. 15shows the sound pressure with respect to the time at the input and output nodes of the prototype 1.

Fig. 15indicates that the input peak sound pressure is 1230 Pa and the peak value of the sound pressure at output of the silencer is 303 Pa. The input pressure reaches to the peak at 6 ms, and the exit pressure reaches the peak at 0.8 ms after the input pressure reaches the peak value.

The instantaneous acoustic pressure change obtained from the analysis of the end elements of the prototype-2 silencer is shown inFig. 16.

The sound pressure level at the inlet and outlet points of the prototype-2 is shown inFig. 17.

Fig. 14. The FEA pressure distribution (distribuation) of the first prototype.

-1250 -1000 -750 -500 -250 0 250 500 750

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007

Pressure(Pa)

Time (s)

Fig. 15. Sound pressure for the first prototype, at input, at output.

Input

Output

Fig. 16. The FEA acoustic pressure distribution for the second prototype.

(8)

Fig. 17shows that at the inlet of the silencer, the peak sound pressure is 1239 Pa. At outlet of the silencer, the peak value of the sound pressure is 285 Pa. The input pressure time is 6 ms and the output pressure is reaching the peak at 0.8 ms. Fig. 18 shows the result of the analysis of the third prototype. It represents the instantaneous acoustic pressure change of the model.

Fig. 19shows the sound pressure level at the inlet and outlet points of the prototype-3.

Fig. 19indicates that the input peak sound pressure is 1200 Pa and the peak value of the sound pressure at output of the silencer is 105 Pa. The input pressure reaches to the peak at 6 ms, and the exit pressure reaches the peak at 0.8 ms after the input pressure reaches the peak value.

Examinations of theFigs. 15, 17 and 19shows that the peak sound pressure occurs at one point in the outlet pipe of the silencers. They show that the latest one has the least sound pressure value.

Experimental studies of prototypes are carried out for the veri- fication. Fig. 20 shows the STL graph obtained from the experiments.

FromFig. 20, the second prototype has a better STL characteris- tic on the frequency range of 1200 to 3000 Hz according to first prototype. The third prototype has a better result in the frequency range of 800–2400 Hz than the prototype 2. The 3rd prototype has an STL value of 30 dB better than the 1200 Hz band according to the 2nd.

The sound pressure and the sound pressure level (SPL) graphs obtained by the gun firing using silencer prototypes 1, 2 and 3 are shown inFigs. 21–23. The sound pressure level (SPL) graphs over frequency range of the 20 Hz to 20 kHz obtained by the fast Fourier transform (FFT) analysis.

FromFig. 21(a), it is observed that the peak pressure value of

270 Pa corresponds to 143 dB peak sound level. In this case, the sound reduction amount of the first prototype is 13 dB.Fig. 21(b) shows that Prototype-1 has a sound pressure level above 110 dB in the range of 4900 to 6400 Hz.

Fig. 22(a) shows that the maximum pressure value of99 Pa corresponds to a peak sound pressure level of 134 dB. In this case, the sound reduction amount of the second prototype is 22 dB.

Fig. 22(b) shows that the prototype-2 has a sound pressure level of less than 105 dB over the frequency range of 20 Hz to 20,000 Hz.

Fig. 23(a) shows that the maximum pressure value of96 Pa corresponds to a peak sound pressure level of 133 dB. In this case, the noise reduction amount of the third prototype is 23 dB.Fig. 23 (b) shows that Prototype-3 has a sound pressure level of less than 100 dB in the range of 20 to 4000 Hz.

Moreover, a 1/3 octave band analysis is performed on the gun with and without a silencer. The obtained 1/3 octave band graph is shown inFig. 24.

Fig. 24 shows that the highest SPL value of prototype-1 is 120 dB, which is in the 5000 Hz. The highest SPL value of prototype-2 is 115 dB and is in the 16,000 Hz. The highest SPL value of prototype-3 is 114 dB, which is in the 16,000 Hz. Accord- ingly, prototype-3 performs better in the range of 125 Hz–8000 Hz.

Fig. 25shows the variation of the IL value of the prototype-1, 2 and 3 with respect to frequency.

-1250 -1000 -750 -500 -250 0 250 500 750

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007

Pressure(Pa)

Time (s)

Fig. 17. Sound pressure level of second prototype, at input, at output.

Input

Output

Fig. 18. FEA acoustic pressure distribution of the third prototype.

-1250 -1000 -750 -500 -250 0 250 500 750

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007

Pressure(Pa)

Time (s)

Fig. 19. Sound pressure of the third prototype, at input, at output.

-20 -10 0 10 20 30 40 50 60 70 80

300 600 900 1200 1500 1800 2100 2400 2700 3000

STL (dB)

Frequency (Hz)

Fig. 20. Experimental STL graph, Prototype-1, Prototype-2, Prototype-3.

(9)

(a) (b)

-300 -200 -100 0 100 200 300

5.075 5.076 5.077 5.078 5.079 5.08 5.081 5.082 5.083 5.084 5.085

Pressure (Pa)

Time (s)

80 90 100 110 120

0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

SPL (dB)

Frequency (Hz)

Fig. 21. Prototype-1 shot results.

(a) (b)

-100 -60 -20 20 60 100

7.251 7.252 7.253 7.254 7.255 7.256 7.257 7.258 7.259

Pressure(Pa)

Time (s)

75 80 85 90 95 100 105 110

0 4000 8000 12000 16000 20000

SPL (dB)

Frequency (Hz)

(a) (b)

-100 -75 -50 -25 0 25 50 75 100

6.354 6.355 6.356 6.357 6.358 6.359 6.36 6.361 6.362 6.363 6.364

Pressure(Pa)

Time (s)

75 80 85 90 95 100 105 110 115

0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

SPL (dB)

Frequency (Hz)

0 20 40 60 80 100 120 140

100 160 250 400 630 1000 1600 2500 4000 6300 10000 16000

SPL (dB)

Frequency (Hz)

Fig. 24. Real experimental 1/3 octave band results, Without silencer, Prototype-1, Prototype-2, Prototype-3.

0 5 10 15 20 25 30 35 40

0 300 600 900 1200 1500 1800 2100 2400 2700 3000

IL (dB)

Frequency (Hz)

Fig. 25. Insertion loss, Prototype-1, Prototype-2, Prototype-3.

(10)

Fig. 25shows that the Prototype-2 and 3 have an IL value of more than 10 dB for each frequency. However, Prototype-1 has an IL value of less than 10 dB, between 2700 Hz and 2800 Hz.

Table 3summarizes the maximum and minimum levels of IL values obtained from real tests of the prototypes. The number of resonances frequencies have also been reported.

Table 3indicates that the maximum and minimum IL values of the Prototype-3 have the highest values of 34 and 10 dB compared to the other models. Prototype-3 have 8 resonances. Prototype-1 appears to have the lowest IL value.Table 4shows the root mean squared (RMS) values of the prototypes. The peak sound pressure level of the silencers is also given.

Table 4shows that Prototype-3 has the best performance. The peak sound pressure level of the prototype-3 is 133 dB and has the lowest sound level compared to other silencers. Likewise, the STL RMS value is 34.6 dB and the IL RMS value is 24.6 dB and has the highest value. When STL values are examined, Prototype-1 appears to have a higher value than Prototype-2.Table 5summa- rizes the peak sound pressure level and the amount of attenuation obtained from the shot test of the silencer prototypes.

Table 5shows that the sound pressure measurement result of the silencer without silencer is 1296 Pa and the sound level is 156 dB. This can lead to nonlinearity in acoustic noise propogations across the silencers. Prototype-3 has the lowest sound level of 133 dB.

3. Results and discussions

In this paper, the theoretical and experimental investigations of the acoustic performances of the gun silencers were presented. The insertion loss, the noise reduction and the sound transmission loss criteria were measured and reported. Based on the calculation, analysis and test results, silencer designs and prototype production were realized and real shot experiments were carried out. Thus, design criteria of silencers were determined and original prototype designs were obtained. The transfer matrix is obtained based on the state variables at the input and output points. These state variables are dependent on the wave number, the length of the silencer

element and the acoustic impedance. The sound transmission loss of the silencer is calculated by using acoustic impedance.

The change in the length of without baffle silencer has no effect on its acoustics performance. The silencer with five baffles and the lowest length has the lowest sound pressure at its outlet. STL graph of the silencer showed a shift towards higher frequencies as the silencer diameter grows. This indicated that the diameter of the silencer will be more effective at higher frequencies.

Three different prototypes were produced in which the effect of baffle type and position on the performance of the silencer could be examined experimentally. The number of baffles and their positions could be changed for use in shot tests.

It was observed that the FEA and the experimental results are compatible with each other. As the number of baffles increases, for certain baffle positions, the number of resonances increases.

For the appropriate baffle position, increase in the number of baffles, can increase the maximum STL value as well. The acoustic impedance measurement system allowed the prototype silencers to obtain STL-frequency curves in the laboratory environment.

The shot tests were based on the polygon environment. This system was equipped with devices that had technical specifications in accordance with military standards. Several types of silencer prototypes were designed and fabricated. Separate shot tests were then carried out using these prototypes. Because of these tests, IL graphs were obtained according to the peak sound pressure level and frequency. At the last stage, the produced prototypes have shown superior performance as well. In the future studies, more actual results should be achieved with the joint solution of the fluid dynamics and the acoustic analysis. Using this method, a silencer modeling for a different caliber gun is suggested. It is also suggested that the structural and acoustic analysis should be solved simultaneously by including the material and structural properties of the silencer into the calculations.

Acknowledgements

The authors want to express their appreciation to Mechanical and Chemical Industry Corporation of Turkey and the Turkish Min- istry of Science, Industry and Technology for their support in this work.

References

[1]Everest FA. The master handbook of acoustics. fourth ed. McGrawHill; 2001.

[2]Möser M. Engineering acoustics: an introduction to noise control. second ed. Springer; 2009.

[3]Freytag JC, Begault DR, Peltier CA. The acoustics of gunfire. Internoise 2006 Honolulu, Hawaii, USA, 2006.

[4]Kang KJ, Ko SH, Lee DS. A study on impulsive sound attenuation for a high- pressure blast flowfield. J Mech Sci Technol 2008;22:190–200.

[5]Ranjbar M, Hardtke H-J, Fritze D, Marburg St. Finding the best design within limited time: a comparative case study on methods for optimization in structural acoustics. J Comput Acoust 2010;18:149–64.

[6]Sullivan JW, Crocker MJ. Analysis of concentric tube resonators having unpartitioned cavities. J Acoust Soc Am 1978;64:207–15.

[7]Randall FB. Industrial noise control and acoustics. Marcel Dekker; 2003.

[8]Maher RC. Acoustical characterization of gunshots. Washington D.C., USA: SAFE; 2007.

[9]Hudson MK, Luchini C, Clutter JK, Shyy W. CFD Approach to firearms sound suppressor design. Arkansas: Department of Applied Science, University of Arkansas; 1996.

Table 3

The resonant frequencies of the silencer prototypes and the maximum/minimum IL values.

Prototype No Resonance numbers Resonance frequencies (Hz) Maximum IL (dB) Minimum IL (dB)

1 6 128, 896, 1408, 1792, 2432, 2816 30 2

2 6 0, 512, 1152, 1536, 2432, 2688 32 10

3 8 0, 384, 896, 1536, 2048, 2304, 2560, 2816 34 10

Table 4

STL, IL and peak SPL values of silencer prototypes.

Prototype No STL RMS (dB) IL RMS (dB) Peak SPL (dB)

1 22.8 20 143

2 22 22.7 134

3 34.6 24.6 133

Table 5

Peak SPL values of the silencers and Peak SPL reduction quantities.

Peak Pressure (Pa)

Peak SPL (dB)

Peak SPL reduction amount (dB)

Without silencer 1296 156 –

Prototype-1 270 143 13

(11)

[10]Munjal ML. Acoustics of ducts and mufflers with application to exhaust and ventilation system design. John Wiley & Sons; 1987.

[11]Munjal ML. Analysis and design of mufflers. J Sound Vib 1998;211:425–33.

[12] Davis DD, Stokes GMD, Stevens GL. Theoretical and Experimental Investigation of Mufflers with Engine-exhaust Muffler Design, NACA-TR-1192 (1954).

[13]Igarashi J, Toyoma M. Fundamentals of acoustical silencers, Aeronautical Research Institute Report No. 339. University of Tokyo; 1958. p. 223–41.

[14]Miwa T, Igarashi J. Fundamentals of acoustical silencers. Tokyo: Aeronautical Research Institute; 1959. p. 67–85.

[15]Mechel FP. Formulas of acoustics. Springer-Verlag; 2008.

[16]Sullivan JW. A Method for modeling perforated tube muffler components. I.

Theory. J Acoust Soc Am 1979;66:772–8.

[17]Mehdizadeh OZ, Paraschivoiu M. A three-dimensional finite element approach for predicting the transmission loss in mufflers and silencers with no mean flow. Appl Acoust 2005;66:902–18.

[18]Sreenath AV, Munjal ML. Evaluation of noise attenuation due to exhaust mufflers. J Sound Vib 1970;12:1–19.

[19]Munjal ML. Velocity ratio cum transfer matrix method for evaluation of a muffler. J Sound Vib 1975;39:105–19.

[20]Selamet A, Ji ZL. Acoustic attenuation performance of circular expansion chambers with offset inlet/outlet: analytical approach. J Sound Vib 1998;213:601–17.

[21]Vasile O, Enescu N. Noise reduction in industrial installations using a silencer, SISOM 2010 and session of the commission of acoustics Bucharest, 2010.

[22]Degirmenci E, Dirikolu MH. A thermochemical approach for the determination of convection heat transfer coefficients in a gun barrel. Appl Therm Eng 2012;37:275–9.

[23]Weaver E. Sound transmission in mufflers with multiple perforated co-axial pipes. J Sound Vib 2001;247:379–87.

[24]Fang JH, Zhou YQ, Hu XD, Wang L. Measurement and analysis of exhaust noise from muffler on an excavator. Int J Precis Eng Manuf 2009;10:59–66.

[25]Cheolung DK, Cheolung C, Jeong CWB. The use of hybrid model to compute the nonlinear acoustic performance of silencers for the finite amplitude acoustic wave. J Sound Vib 2010;329:2158–76.

[26]Arslan H, Ranjbar M, Dalkılıç B, Çalık E, Arslan C. On muffler design for transmitted noise reduction. J New Results Sci 2018;7:13–21.

[27]Ranjbar M, Nahid M, Renawi A, Sadeqi Z. Development of an educational noise reduction measurement test bench. J Robotic Mech Syst 2017;2:27–32.

[28]Ranjbar M, Alinaghi Maryam. Effect of liner layer properties on noise transmission loss in absorptive mufflers. Math Model Appl 2016;1:46–54.

[29]Ranjbar M, Kemani M. A comparative study on design optimization of mufflers by genetic algorithm and random search method. J Robotic Mech Syst 2016;1:7–12.

[30] Ranjbar M, Kermani M. On maximization of noise transmission loss in mufflers by geometry modification concept UAB, Birmingham, Alabama, USA. ASME District F - 2013 Early Career Technical Conference, 2013.

[31]Orak M, Ranjbar M, Arslan H. On sound transmission loss maximization of a multi-chamber exhaust system Bursa, Turkey. 9th Automotive Technologies Congress (OTEKON 2018), 2018.

[32]Ranjbar M, Dalkılıç B, Çalık E, Arslan M, Arslan Hakan. On muffler design for transmitted noise reduction. International symposium on multidisciplinary studies and innovative technologies. Turkey: Gaziosmanpasßa University Tokat;

2017.

[33]Ranjbar M, Kermani M. Muffler design by noise transmission loss maximization on narrow band frequency range Bursa, Turkey. 7th automotive technologies congress (OTEKON 2014), 2014.

[34] ABAQUS/CAE User’s Manual. Dassault Systemes (2008).

[35]Wu TW, Wan GC. Muffler performance studies using a direct mixedbody boundary element method and a three-point method for evaluating transmission loss. ASME Trans-J Vib Acoust 1996;118:479–84.

[36]Secgin E. Acoustic attenuation and performance analyis for blast flowfield Doctoral Thesis. Turkey: Kirikkale University; 2014.