10 Design of Mufflers Silencers

1 D. W. Herrin, , University of Kentucky Department of Mechanical Engineering Design of Mufflers and Silencers Design of Mufflers and Silencers Noise and Vibration Short Course 2 Dept. of Mech. Engineering University of Kentucky 1. Dissipative (absorptive) silencer: Sound is attenuated due to absorption (conversion to heat) Sound absorbing material ( , duct liner) Duct or pipe Types of Mufflers Design of Mufflers and Silencers Noise and Vibration Short Course 3 Dept. of Mech. Engineering University of Kentucky 2. Reactive muffler: Sound is attenuated by reflection and cancellation of sound waves Compressor discharge details 40 mm Types of Mufflers Design of Mufflers and Silencers Noise and Vibration Short Course 4 Dept. of Mech. Engineering University of Kentucky 3. Combination reactive and dissipative muffler: Sound is attenuated by reflection and cancellation of sound waves + absorption of sound Sound absorbing material Perforated tubes Types of Mufflers Design of Mufflers and Silencers Noise and Vibration Short Course 5 Dept.

2 Of Mech. Engineering University of Kentucky Transmission loss (TL) of the muffler: Wi Wr Wt Anechoic Termination Muffler Performance Measures Transmission Loss ()tiWWTL10log10dB= Design of Mufflers and Silencers Noise and Vibration Short Course 6 Dept. of Mech. Engineering University of Kentucky IL (dB) = SPL1 SPL2 Insertion loss depends on : G TL of muffler G Lengths of pipes G Termination (baffled vs. unbaffled) G Source impedance Muffler SPL1 SPL2 Note: TL is a property of the muffler; IL is a system performance measure. Performance Measures Insertion Loss Design of Mufflers and Silencers Noise and Vibration Short Course 7 Dept. of Mech. Engineering University of Kentucky 24 12 12 2 6 Source -50-40-30-20-100102002004006008001000 Frequency (Hz)TL and IL (dB)Insertion LossTransmission LossPipe resonances Inlet Pipe Outlet Pipe Expansion Chamber Muffler Example TL and IL Design of Mufflers and Silencers Noise and Vibration Short Course 8 Dept.

3 Of Mech. Engineering University of Kentucky Source Su Any acoustic system Su P (sound pressure reaction) Zt Input or load impedance Termination impedance z=PSu=r+jxzt=PtSut=rt+jxtAcoustic System Components Design of Mufflers and Silencers Noise and Vibration Short Course 9 Dept. of Mech. Engineering University of Kentucky G Dissipative Mufflers attenuate sound by converting sound energy to heat via viscosity and flow resistance this process is called sound absorption. G Common sound absorbing mechanisms used in dissipative Mufflers are porous or fibrous materials or perforated tubes. G Reactive Mufflers attenuate sound by reflecting a portion of the incident sound waves back toward the source. This process is frequency selective and may result in unwanted resonances. G Impedance concepts may be used to interpret reactive muffler behavior. Summary 1 Design of Mufflers and Silencers Noise and Vibration Short Course 10 Dept. of Mech. Engineering University of Kentucky Named for: Hermann von Helmholtz, 1821-1894, German physicist, physician, anatomist, and physiologist.

4 Major work: Book, On the Sensations of Tone as a Physiological Basis for the Theory of Music, 1862. von Helmholtz, 1848 The Helmholtz Resonator Design of Mufflers and Silencers Noise and Vibration Short Course 11 Dept. of Mech. Engineering University of Kentucky F = PSB x V SB L L is the equivalent length of the neck (some air on either end also moves). Damping due to viscosity in the neck are neglected (resonance frequency of the Helmholtz resonator) Helmholtz Resonator Model M x+Kx=PSB x=j uBx=uBj j M K "#$%&'uB=PSBzB=PSBuB=j1SB2"#$%&' M K "#$%&'VScKBo22 =LSMBo = VLScMKzBB == when0 Design of Mufflers and Silencers Noise and Vibration Short Course 12 Dept. of Mech. Engineering University of Kentucky A 12-oz (355 ml) bottle has a 2 cm diameter neck that is 8 cm long. What is the resonance frequency? Helmholtz Resonator Example ()()() = = nBnfVLScf Design of Mufflers and Silencers Noise and Vibration Short Course 13 Dept. of Mech.

5 Engineering University of Kentucky V = m3 L = 25 mm SB = 2 x 10-4 m2 S = 8 x 10-4 m2 fn = 154 Hz Anechoic termination 05101520050100150200250300 Frequency (Hz)TL (dB)35 Hz Helmholtz Resonator as a Side Branch () +=221021log10dBVcSLScTLB Design of Mufflers and Silencers Noise and Vibration Short Course 14 Dept. of Mech. Engineering University of Kentucky Can we make ZB zero? zA V P zB z z zA zB (any system) (Produces a short circuit and P is theoretically zero.) Network Interpretation ABAB zzzzz+=zB=PSBuB=j1SB2!"#$%& M K !"#$%&VLScMKzBB == when0 Design of Mufflers and Silencers Noise and Vibration Short Course A Tuned Dynamic Absorber K1 M1 x F K1 M1 x F K2 M2 Original System / 1 |x/F| Original system Tuned dynamic absorber M2/M1= K2M2=K1M1tune Tuned Dynamic Absorber 15 Dept. of Mech. Engineering University of Kentucky Design of Mufflers and Silencers Noise and Vibration Short Course Resonances in an Open Pipe P = 1 Pa Lp= 1 m source First mode Second Mode etc.

6 1=2Lp=cf1 f1=3432 1()= 2=Lp=cf2 f2=3431 1()=343 Hz16 Dept. of Mech. Engineering University of Kentucky Design of Mufflers and Silencers Noise and Vibration Short Course SPL at Pipe Opening No Resonator 17 Dept. of Mech. Engineering University of Kentucky Design of Mufflers and Silencers Noise and Vibration Short Course Example HR Used as a Side Branch* V = 750 cm3 L = cm (L = cm) DB = 5 cm (SB= cm2) D = 10 cm (S = cm2) fn = 340 Hz Anechoic termination _____ * , engine intake systems () +=221021log10dBVcSLScTLB 18 Dept. of Mech. Engineering University of Kentucky Design of Mufflers and Silencers Noise and Vibration Short Course SPL at Pipe Opening with Resonator 19 Dept. of Mech. Engineering University of Kentucky Design of Mufflers and Silencers Noise and Vibration Short Course 20 Dept. of Mech. Engineering University of Kentucky The Quarter-Wave Resonator has an effect similar to the Helmholtz Resonator: zB L S SB The Quarter Wave Resonator ()()() +=2221044tanlog10 BBSSSSklTLzB= j ocSBcot Lc()=0 whe n Lc=n 2n=1,3, n=n c2 Lfn=nc4 LorL=nc4f=n 4"#$%&' Design of Mufflers and Silencers Noise and Vibration Short Course 21 Dept.

7 Of Mech. Engineering University of Kentucky G The side-branch resonator is analogous to the tuned dynamic absorber. G Resonators used as side branches attenuate sound in the main duct or pipe. G The transmission loss is confined over a relatively narrow band of frequencies centered at the natural frequency of the resonator. Summary 2 Design of Mufflers and Silencers Noise and Vibration Short Course 22 Dept. of Mech. Engineering University of Kentucky 18 2 2 6 where m is the expansion ratio (chamber area/pipe area) = 9 in this example and L is the length of the chamber. The Simple Expansion Chamber ()() ++=klmmklTL22210sin1cos441log10051015202 5300100200300400500600700800 Frequency (Hz)TL (dB) Design of Mufflers and Silencers Noise and Vibration Short Course 23 Dept. of Mech. Engineering University of Kentucky 2 9 18 2 2 6 Quarter Wave Tube + Expansion Chamber 0510152025300100200300400500600700800 Frequency (Hz)TL (dB) Design of Mufflers and Silencers Noise and Vibration Short Course 24 Dept.

8 Of Mech. Engineering University of Kentucky 18 2 2 6 9 (same for extended outlet) Extended Inlet Muffler 0510152025300100200300400500600700800 Frequency (Hz)TL (dB) Design of Mufflers and Silencers Noise and Vibration Short Course 25 Dept. of Mech. Engineering University of Kentucky 9 9 4 6 Two-Chamber Muffler 010203040500100200300400500600700800 Frequency (Hz)TL (dB) Design of Mufflers and Silencers Noise and Vibration Short Course 26 Dept. of Mech. Engineering University of Kentucky Source engine Pump Compressor (intake or exhaust ) Area change Expansion chamber Helmholtz Resonator Quarter-wave resonator termination We would like to predict the sound pressure level at the termination. Complex System Modeling Design of Mufflers and Silencers Noise and Vibration Short Course The sound pressure p and the particle velocity v are the acoustic state variables any acoustic component 1 2 p1, u1 p2, u2 For any passive, linear component: Transfer, transmission, or four-pole matrix (A, B, C, and D depend on the component) The Basic Idea p1=Ap2+BS2u2S1u1=Cp2+DS2u2p1S1u1!

9 "#$#%&#'#=ABCD()*+,-p2S2u2!"#$#%&#'#or 27 Dept. of Mech. Engineering University of Kentucky Design of Mufflers and Silencers Noise and Vibration Short Course p1, u1 p2 ,u2 S L A B (x = 0) (x = L) Solve for A, B in terms of p1, u1 then put into equations for p2, u2. (note that the determinant A1D1-B1C1 = 1) must have plane waves The Straight Tube px()=Ae jkx+Be+jkxux()= 1jk ocdpdxp0()=p1=A+Bu0()=u1=A B ocpL()=p2=Ae jkL+Be+jkLuL()=u2=Ae jkL Be+jkL ocp1=p2coskL()+u2j oc()sinkL()u1=p2j oc()sinkL()+u2coskL()p1S1u1"#$%$&'$($=co skL()j ocS2sinkL()jS1 ocsinkL()S1S2coskL())*+++++, "#$%$&'$($28 Dept. of Mech. Engineering University of Kentucky Design of Mufflers and Silencers Noise and Vibration Short Course 29 Dept. of Mech. Engineering University of Kentucky Combining Component Transfer Matrices []22 =iiiiiDCBATT ransfer matrix of ith component p1S1u1!"#$#%&#'#=T1[]T2[]T3[] Tn[]p2S2u2!"#$#%&#'#=Tsys tem()*+p2S2u2!"#$#%&#'#[]22systemsystems ystemsystemsystem =DCBATD esign of Mufflers and Silencers Noise and Vibration Short Course L k ,zc (complex wave number and complex characteristic impedance) Straight Tube with Absorptive Material p1S1u1!)

10 "#$#%&#'#=cosk'L()jzcS2sink'L()jS1zcsink 'L()S1S2cosk'L()()**+,-----p2S2u2!"#$#%& #'#30 Dept. of Mech. Engineering University of Kentucky Design of Mufflers and Silencers Noise and Vibration Short Course 31 Dept. of Mech. Engineering University of Kentucky S1 S2 1 2 Area Change p1=p2S1u1=S2u2p1S1u1!"#$#%&#'#=1 00 1()*+,-p2S2u2!"#$#%&#'# Design of Mufflers and Silencers Noise and Vibration Short Course 32 Dept. of Mech. Engineering University of Kentucky L S S S straight tube area changes Expansion Chamber Muffler T[]=1 00 1!"#$%&coskL()j ocS'sinkL()jS' ocsinkL()coskL()!"#####$%&&&&&1 00 1!"#$%&T[]=coskL()j ocS'sinkL()jS' ocsinkL()coskL()!"#####$%&&&&& Design of Mufflers and Silencers Noise and Vibration Short Course 33 Dept. of Mech. Engineering University of Kentucky 18 2 2 6 Expansion Chamber Muffler S'S=9 Design of Mufflers and Silencers Noise and Vibration Short Course 34 Dept. of Mech. Engineering University of Kentucky SB S 1 2 Transfer Matrix of a Side Branch p1Su1!