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**Design of Mufflers and Silencers**

Lesson 11 Design of Mufflers and Silencers D. W. Herrin, Ph.D., P.E. University of Kentucky Department of Mechanical Engineering Slides © 2006 by A. F. Seybert

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**Types of Mufflers 1. Dissipative (absorptive) silencer: Duct or pipe**

Sound absorbing material (e.g., duct liner) Sound is attenuated due to absorption (conversion to heat) Dept. of Mech. Engineering University of Kentucky 2

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**Types of Mufflers 2. Reactive muffler:**

Sound is attenuated by reflection and “cancellation” of sound waves Compressor discharge details 40 mm Dept. of Mech. Engineering University of Kentucky 3

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**Types of Mufflers 3. Combination reactive and dissipative muffler:**

Sound absorbing material Perforated tubes Sound is attenuated by reflection and “cancellation” of sound waves + absorption of sound Dept. of Mech. Engineering University of Kentucky 4

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**Performance Measures Transmission Loss**

Wi Wt Anechoic Termination Muffler Wr Transmission loss (TL) of the muffler: Dept. of Mech. Engineering University of Kentucky 5

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**Performance Measures Insertion Loss**

SPL1 SPL2 Muffler IL (dB) = SPL1 – SPL2 Insertion loss depends on : TL of muffler Lengths of pipes Termination (baffled vs. unbaffled) Source impedance Note: TL is a property of the muffler; IL is a “system” performance measure. Dept. of Mech. Engineering University of Kentucky 6

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**Example TL and IL Source 2” 6” 24” 12” 12” Expansion Chamber Muffler**

Inlet Pipe Source Outlet Pipe 2” 6” 24” 12” 12” Pipe resonances Dept. of Mech. Engineering University of Kentucky 7

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**The Concept of Impedance**

Flow variable Generalized impedance of a system Z and power supplied W : + SYSTEM Effort variable _ System Type Effort Variable Flow Variable Impedance Z Power supplied W Electrical Voltage (E) Current (I) E/I EI = E2/Z Mechanical Force (F) Velocity (V) F/V FV = F2/Z Acoustic Pressure (P) P/V PVS = P2 S /Z Fluid Volume Flow Rate (Q) P/Q PQ = P2/Z Thermal Temperature (T) Heat Flow Rate/Deg (Q’) T/Q’ TQ’ = T2/Z * For acoustic systems we must multiply by the area S Dept. of Mech. Engineering University of Kentucky 8

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**Network Interpretation Electrical and Acoustic**

Z V Z source load source load Electrical System Acoustical System Dept. of Mech. Engineering University of Kentucky 9

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**Acoustic System Components**

Source V V Any acoustic system P Zt (sound pressure reaction) Input or load impedance Termination impedance Dept. of Mech. Engineering University of Kentucky 10

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Summary 1 Dissipative mufflers attenuate sound by converting sound energy to heat via viscosity and flow resistance – this process is called sound absorption. Common sound absorbing mechanisms used in dissipative mufflers are porous or fibrous materials or perforated tubes. 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. Impedance concepts may be used to interpret reactive muffler behavior. Dept. of Mech. Engineering University of Kentucky 11

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**The Helmholtz Resonator**

Named for: Hermann von Helmholtz, , German physicist, physician, anatomist, and physiologist. Major work: Book, On the Sensations of Tone as a Physiological Basis for the Theory of Music, 1862. von Helmholtz, 1848 Dept. of Mech. Engineering University of Kentucky 12

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**Helmholtz Resonator Model**

V x L L’ is the equivalent length of the neck (some air on either end also moves). SB F = PSB Damping due to viscosity in the neck are neglected (resonance frequency of the Helmholtz resonator) Dept. of Mech. Engineering University of Kentucky 13

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**Helmholtz Resonator Example**

A 12-oz (355 ml) bottle has a 2 cm diameter neck that is 8 cm long. What is the resonance frequency? Dept. of Mech. Engineering University of Kentucky 14

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**Helmholtz Resonator as a Side Branch**

Anechoic termination 35 Hz V = m3 L = 25 mm SB = 2 x 10-4 m2 S = 8 x 10-4 m2 fn = 154 Hz Dept. of Mech. Engineering University of Kentucky 15

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**Network Interpretation**

(any system) zB V zB zA z zA Can we make ZB zero? z (Produces a short circuit and P is theoretically zero.) Dept. of Mech. Engineering University of Kentucky 16

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**The Quarter Wave Resonator**

The Quarter-Wave Resonator has an effect similar to the Helmholtz Resonator: L Sb zB S Dept. of Mech. Engineering University of Kentucky 17

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Summary 2 The side-branch resonator is analogous to the tuned dynamic absorber. Resonators used as side branches attenuate sound in the main duct or pipe. The transmission loss is confined over a relatively narrow band of frequencies centered at the natural frequency of the resonator. Dept. of Mech. Engineering University of Kentucky 18

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**The Simple Expansion Chamber**

18” 2” 6” 2” where m is the expansion ratio (chamber area/pipe area) = 9 in this example and L is the length of the chamber. Dept. of Mech. Engineering University of Kentucky 19

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**Quarter Wave Tube + Helmholtz Resonator**

2” 9” 18” 6” Dept. of Mech. Engineering University of Kentucky 20

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**Extended Inlet Muffler**

18” 2” 6” 9” ( same for extended outlet ) Dept. of Mech. Engineering University of Kentucky 21

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**Two-Chamber Muffler 9” 4” 6” Dept. of Mech. Engineering**

University of Kentucky 22

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**Complex System Modeling**

We would like to predict the sound pressure level at the termination. Source Engine Pump Compressor (intake or exhaust) Area change Expansion chamber Helmholtz Resonator Quarter-wave resonator termination Dept. of Mech. Engineering University of Kentucky 23

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The Basic Idea The sound pressure p and the particle velocity v are the acoustic state variables 2 For any passive, linear component: any acoustic component 1 or p2, v2 p1, v1 Transfer, transmission, or four-pole matrix (A, B, C, and D depend on the component) Dept. of Mech. Engineering University of Kentucky 24

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**Combining Component Transfer Matrices**

Transfer matrix of ith component Dept. of Mech. Engineering University of Kentucky 25

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**Performance Measures Transmission Loss**

Wi Wt Anechoic Termination Wr 2 1 Transmission loss (TL) of the muffler: Dept. of Mech. Engineering University of Kentucky 26

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**The Straight Tube L A S B p2, v2 p1, v1 (x = L) (x = 0)**

must have plane waves B p2, v2 p1, v1 (x = L) (x = 0) Solve for A, B in terms of p1, v1 then put into equations for p2, v2. (note that the determinant A1D1-B1C1 = 1) Dept. of Mech. Engineering University of Kentucky 27

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**Straight Tube with Absorptive Material**

k’,zc (complex wave number and complex characteristic impedance) Dept. of Mech. Engineering University of Kentucky 28

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**Area Change S2 S1 2 1 Dept. of Mech. Engineering 29**

University of Kentucky 29

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**Expansion Chamber Muffler**

straight tube S S’ S area changes (m = S’/S is called the expansion ratio of the muffler) Dept. of Mech. Engineering University of Kentucky 30

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**Expansion Chamber Muffler**

18” 2” 6” (m = 9) Dept. of Mech. Engineering University of Kentucky 31

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**Transfer Matrix of a Side Branch**

SB S 2 1 Dept. of Mech. Engineering University of Kentucky 32

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**Helmholtz Resonator Model**

V x L L’ is the equivalent length of the neck (some air on either end also moves). SB F = PSB Damping due to viscosity in the neck are neglected (resonance frequency of the Helmholtz resonator) Dept. of Mech. Engineering University of Kentucky 33

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Summary 3 The transfer matrix method is based on plane wave (1-D) acoustic behavior (at component junctions). The transfer matrix method can be used to determine the system behavior from component “transfer matrices.” Applicability is limited to cascaded (series) components and simple branch components (not applicable to successive branching and parallel systems). Dept. of Mech. Engineering University of Kentucky 34

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