Muffler Acoustics – Application to Automotive Exhaust Noise Control

COURSE LAYOUT

Week 1:Introduction and Basic Concepts
Mufflers for controlling noise emission from internal combustion engines: Overview & Motivation, Development of the one-dimensional acoustic equation: Planar wave propagation in a duct with/without uniform mean flow, Sound speed, Boundary conditions, Free-response (transient signals) and forced-response (continuous time signals), Progressive and standing waves, Resonance frequencies of a closed/open-ended uniform duct Week 2:Three-dimensional acoustic field: Solution of the Helmholtz equation
Rectangular and circular waveguides (ducts), Hard-wall ducts - Normal modes and resonance frequencies of transverse modes, Concept of cut-on and cut-off frequency, Evanescent modes, Solutions including the convective effect of uniform mean flow, Waveguides with compliant walls: Soft-wall modes in rectangular and circular dissipative ducts with local/bulk reacting lining Week 3:Terminologies and Theory of Acoustic Filters…1
Units for measurement of sound and intensity, Sound Pressure Level, Intensity Level, Sound Power Level, Impedance: Acoustic impedance, Specific (characteristic) acoustic impedance and Mechanical impedance, Impedance at a section of a 1-D uniform tube, Radiation impedance, Lumped system analysis, Impedance of an Orifice or a Short Narrow Duct, End-correction for an open-ended tube in an un-flanged/flanged baffle, Impedance of a large Volume (Capacitance), Electro-acoustic analogies (Kirchhoff’s laws) and electrical circuit representation of an acoustic filter (exhaust) system: Thevenin and Norton forms, Side-branch resonators such as Helmholtz resonators, Quarter-wave resonators, Extended-tube resonators, Concentric Hole-Cavity Resonators, Acoustical Filter Performance: Transmission Loss, Insertion Loss and Level Difference. Week 4:Theory of Acoustic Filters…2
Simple (sudden) area discontinuity such as inlet and outlet and acoustic power relations, Simple Expansion chambers of uniform cross-section without and with tube extensions, End-inlet and side-outlet, Side-Inlet and Side-Outlet system, Transfer [T] matrix modelling of acoustic filter elements including lumped elements, Cascading of mufflers (filters): Overall transfer-matrix of the system, Evaluation of four-pole or transfer [T] matrix parameters, Expression for Transmission Loss (TL) in terms of the four-pole parameters, TL graphs of simple muffler systems
Week 5:Acoustic propagation in one-dimensional ducts with gradually varying area
Webster’s Horn equation: Conical, hyperbolic, parabolic and exponential ducts. Analytical solution and numerical approaches such as stepped-segmentation and Matrizant method, Transfer matrix modelling and TL performance Week 6:Flow-acoustic analysis of perforated element mufflers
Aeroacoustic state variables, Transfer matrices of tubular elements, Extended-tube elements, simple area discontinuity, Perforated Elements with Two-Interacting ducts: Concentric-tube resonators, cross-flow expansion and contraction elements, conical-concentric tube resonator (Matrizant analysis), Perforated elements with three-interacting ducts, Commercially used perforated duct mufflers, Acoustic impedance of perforates Week 7:Network analysis of multiply-connected mufflers: Non-unique wave propagation paths
Herschel-Quincke tubes, Perforated elements with several interacting ducts: Three-pass double reversal chambers, Muffler with non-overlapping perforated ducts and a baffle, Impedance [Z] matrix: Characterization of multi-port elements, Single-inlet and double-outlet systems, Evaluation of TL performance in [Z] matrix parameters Week 8:Three-dimensional analysis of mufflers: Analytical approach
Sudden-area (expansion and contraction) discontinuities: Continuity of acoustic pressure and velocity fields, Rectangular and Circular Cylindrical Geometries Derivation of a Green’s function solution: Point-source representation of a portAcoustic pressure response or Transfer functions, Uniform piston-drive model: Modelling of ports as rigid oscillating pistons,Characterization of a single-inlet and single-outlet/double-outlet muffler in terms of [Z] or [T] matrix: Simple-expansion chamber, flow-reversal, end-inlet and side-outlet, side-inlet and side-outlet muffler configurations.Comparison of TL performance obtained using the Point-Source and the Uniform piston-driven model, Some parametric studies
Week 9:Three-dimensional analysis of mufflers: Analytical approach (Contd.)
Analytical mode-matching (AMM) approach, Computation of TL performance 7 derivation of the four-pole parameters Circular Cylindrical muffler configuration with an extended-inlet and extended-outlet without/with concentric perforated bridging tube, Large (industrial) muffler configurations, Brief overview of Finite Element (FE) analysis of mufflers: Use of commercial software, Comparison of results obtained from analytical and FE models, Self-study: Analysis of large circular muffler with side port(s) Week 10:Dissipative ducts and Parallel Baffle Mufflers
Acoustically lined Rectangular and Circular Ducts with a Moving medium, Transfer matrix relation for a Dissipative Duct, Transverse Wave numbers (stationary medium), Normal Impedance of the lining, Transmission Loss Performance of Lined Duct Silencers and Bends, Parallel Baffle Mufflers, Plenum Chambers, Flow-generated noiseWeek 11:Experimental techniques based on use of an impedance tube
Terminologies based on the ASTM standard, Detailed construction of the impedance tube and microphone spacing consideration, Microphone calibration Impedance of a passive termination: The Probe-Tube (single microphone) method, Two-Microphone and Transfer Function Methods Four-pole parameters of a muffler system incorporating mean flow effect:Two-source location method, Two-Load method, Comparison of the two methods Discussion on experimental and numerical/analytical resultsWeek 12:Muffler Design: Practical considerations
Requirements & Practical considerations of an Engine Exhaust Muffler, Straight-through reactive perforated mufflers with double-tuned neck extensions at inlet and outlet, Dual chamber and plug-mufflers, Combination or Hybrid mufflers with neck extensions - for high-pressure gas exhaust applications, Mufflers with side-port(s), Design of short elliptical end-chambers, Design for Insertion Loss, Back-pressure considerations, Design for quieting air-conditioning or ventilation systems