Muffler Basics

Muffler Performance Requirements Suitable outer geometry. Low pressure drop. Sufficient sound attenuation.

Reactive (reflective) MUFFLER BASICS Definition: A device for reducing sound in pipe or duct systems…. Classification Reactive (reflective) Dissipative Area change Resonators Active Porous material Flow constriction

Measures of damping A number of measures exist. The most common are: Incident Sound power Transmitted Sound power A number of measures exist. The most common are: - “Transmission Loss (TL)” where a reflection free termination is assumed. The TL only depends on the property of the muffler and is independent of the source.

- “Insertion Loss (IL)” For a given source the transmitted sound power (W) is measured downstream for a reference system (e.g. a straight pipe) and with a muffler system. This measure will in particular for low frequencies (plane waves) depend on the properties of the entire system (source + pipe lengths + muffler). - “Noise Reduction (NR)” Here the sound pressure is measured in a cross-section before and after the muffler. This measure depends on the muffler + the termination.

Insertion Loss Change in Sound Pressure Level at the tail pipe outlet resulting from the insertion of a muffler. IL=SPL1-SPL2

Noise Reduction Difference between sound pressure levels measured upstream and downstream of muffler NR = SPLu - SPLd

Area Discontinuity Increase or Decrease

Reactive mufflers Application: Effective for tones in the low frequency range (plane waves). Area change: Note the position of the maxima depends on the temperature since , where T is the temperature in K.

Expansion Chamber High Frequency Effects

Reactive mufflers... Resonators: A reflection factor close to -1 is created when the input impedance (Zin) is zero (resonance condition). TL[dB] fr Zin f [Hz]

Side Branches Zin f [Hz] TL[dB] fr

The Quarter wave resonator Reactive mufflers... TL[dB] fr Zin The Helmholtz-resonator f [Hz] TL[dB] c/4L f [Hz] 3c/4L 5c/4L L Zin The Quarter wave resonator

Increased length and thickness gives increased damping Dissipative mufflers Application: Effective for broad-band sounds. The standard types are based on porous materials and are mainly efficient at mid- or high frequencies. Based on porous mtrl. TL[dB] f [Hz] Increased length and thickness gives increased damping Plane wave range

Dissipative mufflers… Based on flow constrictions Typically realised via perforated pipes or plates with through flow. Can give damping also at low frequencies… TL[dB] f [Hz] Increasing with flow speed

Example: Combined reactive-dissipative car muffler

Measured and simulated TL in the plane wave range (SIDLAB) Without flow With flow M = 0.15

Flow generated noise Created at flow constrictions i.e. regions which create flow separation (turbulence) The sound power generated will limit the maximum damping that can be obtained by a muffler The sound power scales as W ~ U a, where a = 4-6. For dissipative mufflers (of porous type) it is also proportionell to the muffler length. Wtr

Structural by-pass and break-out break–in effects Sound propagating in ducts and pipes create wall vibrations. These vibrations can propagate as structural waves across a muffler thereby creating an alternative transmission path for the acoustic energy. This is called structural by-pass and will limit the maximum damping. The wall vibrations can also radiate sound to the surrounding air (break-out). This energy can, if reflected from external boundaries, excite pipe wall vibrations after the muffler and induce acoustic waves (break-in). This type of phenomenon is particular important for rectangular pipe and duct sections.

The plane wave range - 2-ports pa qa pb qb T qa pb qb a b pa qa qb pb pa Physical system Equivalent circuits

2-ports – in series and parallell 1 2 M This configuration is best treated using the mobility matrix. Then the T-matrix can be calculated… 1 2

A single expansion chamber 1 2 3 1 2 3

Calculate TL using SIDLAB For a single expansion chamber: f [Hz] c/4L 3c/4L 5c/4L TL(dB) Example: A1=0.0025 m2, A2=0.025 m2, L=1 m TLmax=14.1 dB.

Improved performance by adding a l/4 wave resonator… 2 1 3 4 l= ? m 1 3 4 2

SIDLAB simulation.....