Sadhana

, Volume 9, Issue 4, pp 255–269

Noise reduction with perforated three-duct muffler components

Authors

  • K Narayana Rao
    • Department of Mechanical EngineeringIndian Institute of Science
  • M L Munjal
    • Department of Mechanical EngineeringIndian Institute of Science
Article

DOI: 10.1007/BF02811968

Cite this article as:
Narayana Rao, K. & Munjal, M.L. Sadhana (1986) 9: 255. doi:10.1007/BF02811968

Abstract

This paper describes the authors’ distributed parameter approach for derivation of closed-form expressions for the four-pole parameters of the perforated three-duct muffler components. In this method, three simultaneous second-order partial differential equations are first reduced to a set of six first-order ordinary differential equations. These equations are then uncoupled by means of a modal matrix. The resulting 6 × 6 matrix is reduced to the 2 × 2 transfer matrix using the relevant boundary conditions. This is combined with transfer matrices of other elements (upstream and downstream of this perforated element) to predict muffler performance like noise reduction, which is also measured. The correlation between experimental and theoretical values of noise reduction is shown to be satisfactory.

Keywords

Mufflersnoise controltransfer matrix method

Appendix D. Notation

A1,A0

internal areas of inlet and exit pipes, respectively

c0

velocity of wave propagation

d

internal diameter of pipe

f

frequency

i

iota, √−1

k

wave number, (θ/c0)

l

length of pipe

M

Mach number, (W0/c0)

Mi

inlet Mach number

M0

exit Mach number

p0

pressure of the undisturbed fluid

p

fluctuating pressure

t

time co-ordinate

temp

temperature

u1,2,u2,3

radial fluctuating velocities at 1, 2 and 2, 3 interfaces of the control volume, respectively

W0

velocity of the undisturbed fluid

w

fluctuating velocity

Y

characteristic impedance,c0/A

z

axial co-ordinate

ρ0

density of undisturbed fluid

ρ

fluctuation in density

θ

circular frequency

ζ1, ζ2

acoustical impedances at 1, 2 and 2, 3 interfaces, respectively

Copyright information

© the Indian Academy of Sciences 1986