An Experimental and Theoretical £ Investigation of Annular Steam ...

- 36 -
very sensitive to the choice of the trigger level V. (cf. fig.
3.8). Thus a variation of V on 10% could give up to 50% difference
in the estimated value of 6. As a result of this relationship,
the uncertainty of the present measuring method is believed
to be up to 50%.
3.3.5. Wave Frequencies and Velocities
In sect. 3.2.5 it was mentioned that the frequency and the
velocity of the roll waves are estimated from auto- and crosscorrelations
of the needle signals. The auto-correlation was
Fourier-transformed by the spectrum display to obtain the power
spectrum S (f) . Examples of power spectra are shown in fig. 3.35.
It was shown by Webb (1970) that the peak in a power spectrum
corresponds to the wave frequency measured by manual counting
of peaks on a trace of the time-varying film thickness. This
wave frequency f , together with the frequency range Af over
which the power density is more than half of the maximum value,
is entered in tables A15 and A16. It is seen that f.. increases
w
and Af
w
becomes broader when the film thickness decreases. At
the smallest values o' : 6 it was impossible to determine values
of f and Af because the intensity of the auto-correlation was
w w •*
too small.
Examples of the cross-correlation C (t) of signals from two
needles 0.5 m apart are shown in fig. 3.26. Webb (1970) also
showed that the position of the largest peak in a cross-correlation
corresponds to the time taken for a wave to pass between
two probes. Thus the wave velocity v (m/s) can be found from
L n
v
w = f~ (3.34)
w
where L
n
(m) is the distance between the needles and T,.
w
(s) is
estin.^ted from the cross-correlations.
The wavelength A (m) and the wavenumber k (m~ ) can now be
yf
w
calculated:
X = v /f (3.35)
W W W
K - 2 "/*w
(3.36)