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M. Kupnik, P. O´Leary, A. Schröder, I. Rungger:
"Numerical simulation of ultrasonic transit-time flowmeter performance in high temperature gas flows";
in: "Proc. IEEE Int. Ultrasonics Symp.", IEEE, Honolulu, Hawaii/USA, 2003, ISBN: 0-7803-7923-3, S. 1354 - 1359.

The use of electrostatic transducers avoids the limitations
associated with piezoelectric transducers in gas flowmeters, such
as their restricted maximum allowable gas temperatures and attainable
measuring repetition rates. The measurement at high temperature (up
to 600.C) has necessitated the development of a new and innovative
electrostatic transducer. In this work a structured thermally oxidized
silicon back plate covered with a bulk conducting 3 µm titanium foil
as membrane is used instead of e.g. a metallized polymer film. This
configuration enables the application of transit-time flowmeters to the
measurement of hot pulsating gas flows (up to 3 kHz). Knowledge
of the influence of the temperature and velocity profiles on the wave
propagation in this high temperature range is essential for design
improvements and operating and accuracy limits of the gas flowmeter.
This paper presents a numerical 3-D procedure based on Ray-tracing
to simulate the sound refraction and drift due to different temperature
and velocity profiles for several transducer arrangements. The limits
and dynamics of the used profiles are taken from measured data
acquired on an exhaust train of an automotive combustion engine,
as an exemplary application under extreme operating conditions. The
wave propagation is modelled for a heatable double path flowmeter
with transducers of finite surface. Due to the high dynamics of
the temperature variations and the thermal inertia of the flowmeter,
negative temperature gradients must be taken into account. Since they
result in focusing the wave front and a reversed refraction direction.
The physical limits of transit-time flowmetering in such hot gases can
be determined. The up and down stream travel times and the bestcase-
normalized transmitter-receiver pressure ratios are presented for
different working conditions and measuring set-ups. These results
have been used to optimize the design of the measurement cell
and to find the temperature-induced correction of the usually used
equation to calculate the gas flow velocity. Additionally, clear 3-D
visualizations of the wave fronts and their temporal propagation
through the gas are generated.

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