Page 756 - Automotive Engineering Powertrain Chassis System and Vehicle Body

Exterior noise: Assessment and control C HAPTER 22.1

+ +
p Silencer p
Z 0 p 0 – 0 Type A p 1 1 – Z 1

p 2 is different to p 1

p + 0 Silencer p + 2 Silencer p +
Z 0 p – 0 Type A p – 2 Z 2 Type B p 1 – 1 Z 1

Fig. 22.1-27 The interacting sound fields in a twin-silencer exhaust system.
fraction of a wavelength; that is, for the limiting case where v is the local kinematic viscocity and P r is the
when the Helmholtz number ka approaches zero (the Prandtl number for the gas in the pipe P r ¼ mc P where m
k
plane wave cut-off occurs at ka ¼ 1.84). is the shear viscosity and k is the thermal conductivity
For zero outflow, the modulus of the reflection co- (Davies, 1988).
efficient is unity at low Helmholtz number and reduces The speed of sound varies with the relation
with increasing Helmholtz number (the higher-frequency p ffiffiffiffiffiffiffiffiffiffi
sound transmitted is reflected less than the low- c ¼ gRT (22.1.65)
frequency sound – i.e. the high-frequency sound is radi-
ated more than the low-frequency sound). where
The effect of mean outflow is to increase R throughout R ¼ specific gas constant,
the frequency range. The effect of mean inflow is to T ¼ absolute temperature (K)
decrease R throughout the frequency range. As an added complication the values of g and R also
vary with gas composition and temperature, but for air in
22.1.3.12.11 The general effects of temperature an intake, values of g ¼ 1.4 and R ¼ 290 are reasonable,
and flow speed whilst for exhaust gas g ¼ 1.35 and R ¼ 285 might be
In addition to its effect on the reflection coefficient at an chosen.
unflanged pipe termination, the effect of a steady mean For intake systems, it is reasonable to assume a sound
1
flow on isentropic acoustic plane wave propagation in speed in the order of 343 m s . The final effect of flow
a duct of constant area is to modify the appropriate on the acoustic performance of silencers is complex, and
wavenumber k. With flow, the distance between the defies simple calculations.
2
nodes of a standing wave is reduced by a factor (1 M )
where M is the Mach number of the flow. In other words, 22.1.3.12.12 Calculating mach numbers
the effective duct lengths are reduced. Regrettably, the car fitted with an IC engine is a rather
The presence of a mean flow alters the values of the inefficient means of turning chemical energy into tractive
wavenumber by a factor 1/1 M (Davies, 1988). The effort.
Mach number in the duct varies with the mass flow rate In fact, as will be demonstrated here, under urban
of gas (or the engine speed and load) and the gas density driving conditions, only 20% (or less) of the chemical
(or the gas composition and temperature). energy in gasoline is made available for tractive effort at
The wavenumbers are also affected by changes in the wheels. For the case of the engine in isolation,
temperature through variations in the speed of sound Heywood calls this the thermal conversion efficiency
(see also the effect of sound-absorbing materials – Sec- (Heywood, 1988)
tion 21.1.9) as:
W c
u h ¼ (22.1.66)
b ¼ complex wavenumber ¼ ia (22.1.63) tc h m Q HV
c c f
where
where a is a visco-thermal attenuation coefficient which
for plane wave propagation in a circular pipe of radius a is W c ¼ work output from the cycle
h c ¼ combustion efficiency
given by:
m f ¼ mass of fuel
1=2
1 vu 1=2 1 Q HV ¼ heating value of fuel
a ¼ 1 þðg 1Þ
ac 2 P r
To obtain the thermal conversion efficiency for
(22.1.64) a complete vehicle, the chain of efficiencies has to be

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