Chemistry Reference
In-Depth Information
definition used in this text. The fluid mechanics field partly prefers the
angle between the normal to the flow and the transducer which corre-
sponds to the incident angle
θ
i
in Fig. 3.3.
If the transducer is in direct contact with the fluid in the pipe, there is
mainly the velocity range which is of interest to determine the Doppler
angle. Small angles (e.g. 60
◦
) allow the measurement of low flow ve-
locities, while larger angles are preferred for fast flows. The averaging
decreases with the Doppler angle (McArdle and Newhouse, 1996).
When measuring through the pipe wall or some kind of delay line
or wedge, the corresponding refraction angles and losses have to be
considered (Messer and Aidun, 2009). The angle can be calculated
according to Snell's law:
c
1
sin
θ
=
c
2
sin
θ
t
i
where
c
1
and
c
2
are the sound velocities in the two media and
θ
i
and
θ
t
are the incidence and transmittance angles, respectively. Thus, the
closer the sound velocities of the two materials, the smaller the angle
change. The ratio of the amplitudes of transmitted and incident waves
T
θ
also depends on the material densities
ρ
1
and
ρ
2
and is (Hill
et al.
,
2004) as follows:
T
θ
=
ρ
2
c
2
cos
θ
i
−
ρ
1
c
1
cos
θ
t
(3.1)
ρ
θ
+
ρ
θ
2
c
2
cos
1
c
1
cos
i
t
1
c
1
−
2
ρ
2
c
2
cos
θ
i
c
2
sin
2
=
c
2
cos
θ
+
ρ
θ
i
i
ρ
2
Mounting the transducer either with or against the flow direction
should not influence the measured flow profile seen from the sign of the
velocity.
3.4
ACOUSTIC PROPERTIES
The measurement of the acoustic properties of particulate suspensions
and other food systems has been investigated by many researchers in
the past decades. The acoustic properties comprise mainly of ultrasonic
velocity, attenuation coefficient and acoustic impedance (McClements,
1997).
3.4.1
Propagation
There are different modes of sound propagation, the three most im-
portant being compression, shear and surface waves. The velocity
