This book presents a three-dimensional analysis of acoustic wave propagation in an elliptical waveguide, and applies the equations and concepts to design axially short elliptical end-chamber muffler configurations which are an important component of a complex multi-pass muffler used in a modern-day automotive exhaust system. A general solution of the Helmholtz equation in elliptical cylindrical co-ordinates is presented in terms of the Mathieu and modified Mathieu modal functions. This is followed by the tabulation and analysis, for the first time, of the non-dimensional resonance frequencies of the transverse modes of a rigid-wall elliptical waveguide for a complete range of aspect ratio. The modal shape patterns of the first few circumferential, radial and cross-modes are examined with particular attention to the pressure nodal ellipses and hyperbolae. An analytical formulation is then outlined for characterizing a single-inlet and single-outlet elliptical muffler with the inlet located on the end face and the outlet located either on the end face or side-surface. The ensuing chapter is devoted toward analyzing the Transmission Loss (TL) performance of different short end-chamber mufflers, namely (a) the straight-flow configuration having ports located on the opposite face, (b) the flow-reversal configuration with ports located on the same end face and (c) configuration with inlet port on the end face and outlet on the side surface. Design guidelines are formulated in terms of the optimal location of inlet and outlet ports which suppresses the deteriorating influence of certain higher-order modes, thereby delivering a broadband TL performance. Directions for future work are discussed toward the end.

In summary, this book is a one-stop solution for a practicing automotive engineer designing mufflers, for an applied mathematician studying wave propagation in elliptical geometries, and also as a niche area within noise control engineering.

Autorentext

AKHILESH MIMANI is an Assistant Professor at Department of Mechanical Engineering, Indian Institute of Technology Kanpur (IITK), Uttar Pradesh India. Akhilesh received his PhD (2012) in Mechanical Engineering from the prestigious Indian Institute of Science, Bangalore specializing in muffler and duct acoustics. He has completed research associate positions at The University of Adelaide (2016), University of New South Wales Sydney (2017) and University of Technology Sydney (2018) before joining IITK in 2018. Akhilesh has 10 years of experience in the analysis and design of mufflers for automotive and industrial applications which includes consultancy. His other research interests include computational and experimental aeroacoustics, array processing techniques such as time-reversal and beamforming for source localization, and application of the finite element method to acoustic wave propagation problems. Akhilesh's work has been published in reputed international journals and conference proceedings, and he has received funding from both government and industry, in addition to travel grants.

Inhalt
1 Introduction
1.1 Motivation and Historical Developments
1.2 Wave Propagation in Elliptical Domain: Occurrence of Mathieu functions
1.3 Necessary use of Elliptical Mufflers in Automotive Applications
1.4 Objectives (to present a coherent account on the different aspects of
analysis and design of elliptical chamber mufflers for automotive applications)
1.5 Organization of the Brief

2 General Solution of the Helmholtz equation in Elliptical Cylindrical Co-ordinates
2.1 Computation of the Mathieu and the Modified Mathieu Functions
2.2 Resonance Frequencies of Hard-Wall Elliptical Cylindrical Waveguides
2.2.1 Numerical Computation of q-Parameters and the Corresponding Cut-on Frequencies
2.3 Tabulation of q-Parameters and the Non-Dimensional Resonance Frequency 2.4 First Few Hard-Wall Transverse Modes
2.4.1 Radial Modes
2.4.2 Circumferential Modes
2.4.2.1 Even Modes
2.4.2.2 Odd Modes
2.4.3 Cross-modes
2.5 Polynomial Interpolation Expressions

3 Characterization of a Single-Inlet and Single-Outlet Elliptical Cylindrical Muffler
3.1 Derivation of the Green's Function
3.2 End-Inlet and End-outlet Elliptical Configuration
3.2.1 Straight-Flow Configuration
3.2.2 Flow-Reversal Configuration
3.3 End-Inlet and Side-Outlet Configuration
3.4 Side-Inlet and Side-Outlet Configuration
3.5 Evaluating the Impedance [Z] Matrix Parameters
3.6 Transmission Loss Performance in terms of Scattering [S] Matrix Parameters
4 Analysis and Design of Short End-Chamber Mufflers
4.1 Straight-flow and Flow-Reversal Configurations
4.1.1 Optimal Port Location for Broadband Attenuation Performance
4.1.1.1 Parametric Investigation of Variation in Aspect Ratio
4.2 End-inlet and Side-Outlet Configuration
4.3 Formulation of General Design Guidelines

5 Analysis and Design of Long Chamber Mufflers
5.1 End-Inlet and Side-Outlet Configuration
5.1.1 Optimal Port Location for Broadband Attenuation Performance
5.2 End-Inlet and Side-Outlet Configuration
5.2.1 Optimal Port Location for Broadband Attenuation Performance
5.3 Formulation of General Design Guidelines

6 Justification of the 1-D Transverse Plane Wave Theory for Short Chambers

7 Analysis of Semi-Elliptical/Semi-Circular Cylindrical Chambers
7.1 Solution of Wave Equation
7.1.1 Semi-Elliptical Geometry
7.1.2 Semi-Circular Geometry
7.2 Characterization of Mufflers with Different Inlet/Outlet Port Configurations
7.3 Optimal Port Location for Broadband Attenuation Performance
7.4 Formulation of General Design Guidelines

8 Concluding Remarks