analysis of multi-domain wave propagation in ic engine
DESCRIPTION
A project on acoustic analysis of wave propagation in the muffler of a vehicle and how it can affect the vehicle performance.TRANSCRIPT
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).