Numerical simulation of ultrasonic transit-time flowmeter performance in high temperature gas flows

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 backplate covered with a bulk conducting 3μm 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 3kHz). 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 flow metering in such hot gases can be determined. The up and down stream travel times and the best-case-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.