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Indian Institute of Technology Kanpur

Muffler Acoustics – Application to Automotive Exhaust Noise Control

Indian Institute of Technology Kanpur and NPTEL via Swayam


Engine exhaust noise being one of the major contributors towards environmental noise pollution, the design and analysis of exhaust mufflers has been a crucial area of research in the field of engineering noise control. Additionally, there exists significant literature towards designing silencers for reducing fan noise in ventilation and air-conditioning systems. This NPTEL course presents for the first time, a set of dedicated lectures on the theory of exhaust mufflers used for reciprocating internal combustion engines as well as ventilation ducts, and so on. While a basic background in Acoustics is desirable, the course begins with fundamentals including the detailed derivation of the 1-D wave equation before moving to the more involved case of 3-D propagation in waveguides and associated concepts. This is followed by an introduction to the terminologies common in mufflers as well as the basic elements constituting acoustic filters including elctro-acoustic circuit analogies and 1-D or plane-wave analysis. Next, considering planar wave propagation, the flow-acoustic analysis of perforated duct mufflers, and network analysis of multiply-connected complex muffler systems is explained. Advanced analytical/semi-analytical methods as well as finite-element (numerical) models for 3-D analysis of important muffler configurations is presented. Next, the theory of Dissipative and Parallel Baffle Mufflers are taken up. Important experimental methods to evaluate muffler performance are briefly touched upon. The course ends with presentation of, and emphasizing important design concepts. To conclude, this course is likely to evolve into an important advanced undergraduate/postgraduate course for students as well as professionals working in the field of Noise, Vibration and Harshness (NVH).
NonePREREQUISITES : Background in Mechanical Vibrations and Engineering Mathematics Fundamental course in Acoustics (Desirable) INDUSTRIES SUPPORT :Tata Motors, Maruti Udyog, Hyundai, Mahindra & Mahindra - automobile and heavy-duty vehicle manufacturing companies, and possibly defense equipment manufacturing companies.



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

Taught by

Prof. Akhilesh Mimani


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