PROJECT GUIDE:

Dr. Trinath Kar

Asst. Prof. (Mech. Dept)

ITER(“SOA” UNIVERSITY)

PRESENTED BY :- Himanshu Mohanta Mohit Ku. Mandal Sumanath Sahu Runa Das

Generation of Noise in IC Engine

Combustion takes place in a spontaneous, discrete & localized manner within the cylinder of IC engine.

The reaction being highly exothermic produces a lot of energy .

A major part of this energy contributes to the high pressure

within the cylinder resulting in the formation of high energy

shock wave.

As this shock wave travels in the form of wave front, it

gradually loses energy density due to expansion & ultimately

resulting in audible noise.

Noise Flow Path

Sound Waves:-A wave is a disturbance that propagates through space and time, accompanied by

transference of energy .

Sound is a longitudinal wave whose amplitude is the difference between the

pressure of the undisturbed air and the maximum pressure caused by the wave.

Acoustic Pressure:-Acoustic Pressure:- Acoustic pressure (p) is the local pressure deviation from the ambient (or

equilibrium) pressure caused by a sound wave.

Particle Velocity:-Particle Velocity:-

Particle velocity (u) is the velocity of a particle in a medium as it transmits wave.

Where the particle moves back and forth and is in the direction the sound wave.

MATHEMATICAL MODEL The propagation of sound wave in single

domain can be mathematically represented

using the following differential equations :-

Continuity Equation

ρo ∂u / ∂z = ∂ρ / ∂t ----- (1)

• Equation of Dynamic Equilibrium

∂p / ∂z = ρo ∂u / ∂t ------ (2)

From (1) & (2) , we get,

• Helmholtz Equation

∂2p / ∂z2 = (1/a0)2 (∂2p / ∂t2)

For wave propagation in multiple domain

Helmholtz equation can be found out as long as the domain is non-

interactive.

For interactive domains, we can not form stand alone wave equations.

All practical applications have multiple wave domains. i.e., Automobile

exhaust systems.

Thus, we need different way to solve them.

ANALYSISPeano-Baker Series:-

• Peano-Baker is basically an integral method.

• In this method the whole domain is assumed as a single part.

• An asymptotic solution is derived using the Peano-Baker series of

matrix calculus for different variable area ducts .

(n steps)

Matrizant method:-

Matrix analysis is based on Eigen-value decomposition.

Eigen-value decomposition is the representation of the matrix in

terms of its Eigen-values & Eigen vectors.

{v '} = [γ]{v}

or, {v} = e ∫[γ] dz

or, {v} = e [Ф]

[Ф] = [ψ] [λ] [ψ]-1

e[Ф] = [ψ] [eλ] [ψ]-1

ANALYSISANALYSIS

COMPARISON

Peano-Baker Series

1.Based on cumulative integral

calculus.

2.Entire domain is assumed as a single

segment.

3.Multiple integrations are involved .

4.Convergence is slow as every time

the solution starts from identity

matrix .

Matrizant

1.Based on Eigen-value

decomposition .

2.Entire domain is discretised into a no.

of segments .

3.Single integration can solve the

problem.

4.Convergence is fast .

Hence, considering the various advantages we prefer to use Matrizant method .

DISCRETISED BASIC ACOUSTIC ELEMENTS(DBAE)

1,3,5,7,9 : Tube2: Sudden Expansion4,8 : Sudden Contraction6 : Extended Inlet

Tube

Extended Area Change

Cross Flow CTR

Conc. Tube Resonator

Variable area CTR

Reversal Area Change

Reversal Chamber

Variable area Tubes

Types of Resonators used in Exhaust System

APPLICATION

Exhaust Pipe of RTR-160 :-

APPLICATION

Exhaust Pipe of Honda Bebek :-

Results :-

Results :-

References :-

Sullivan, J. W. and Crocker, M. J. Analysis of concentric tube resonators having unpartitioned cavities, J. Acoust. Soc. Am., 64 (1),207-215, (1978).

Kar, T. and Munjal, M. L. Generalized analysis of a muffler with any number of interacting ducts, J. Acoust. Soc. Am., 285 (3),585-596, (2005).

Dokumaci, E. Sound transmission in mufflers with multiple perforated coaxial pipes, J. Sound Vib., 247 (3), 379-387, (2001).

Alfredson, R. J. The propagation of sound in a circular duct of continuously varying cross-sectional area, J. Sound Vib., 23 (4), 433-442, (1972).

Miles, J. H. Acoustic transmission matrix of a variable area duct or nozzle carrying a compressible subsonic flow, J. Acoust. Soc. Am.,69 (6), 1577-1586, (1981).

Dokumaci, E. On the transmission of sound in a non-uniform duct carrying a subsonic compressible flow, J. Sound Vib., 210 (3),391-401, (1998).

Frazer, R. A., Duncan, W. J., and Collar, A. R. Elementary Matrices and Some Applications to Dynamics and Differential Equations, Cambridge University Press, (1952).

Dokumaci, E. An exact transfer matrix formulation of plane sound wave transmission in inhomogeneous ducts, J. Sound Vib., 217 (5),879-882, (1998).

Melling, T. H. The acoustic impedance of perforates at medium and high sound level, J. Sound Vib., 29 (1), 1-65, (1973).1195, (1986).