Ultrasonic flowmeters: temperature gradients and transducer geometry effects.

Ultrasonic flowmeter performance is addressed for the case of cylindrically shaped flowmeters employing two reciprocal ultrasonic transducers A and B so as to measure time-of-flight differences between signals transmitted from transducer A towards B followed by an equivalent signal transmitted from transducer B towards A. In the case where a liquid flows through the flowmeter's measuring section ("spoolpiece"), the arrival times of the two signals differ by an amount related to the flow passing between the two transducers. Firstly, a detailed study of flow measurement errors with mean flow in the laminar flow regime is carried out as a function of the mode index and the transducer diameter/cylinder diameter ratio in the case where no temperature gradients are present in the flowmeter sensor. It is shown that all modes except the fundamental mode overestimate the mean flow by a factor of 33.33% while excitation of the fundamental mode solely give error-free measurements. The immediate consequences are that the flowmeter error decreases as the transducer diameter/cylinder diameter ratio approaches 1 from 0 reflecting the fact that the excitation level of the fundamental mode increases from almost 0 to 1 as this ratio approaches 1 from 0. Secondly, the effect on flowmeter performance due to flow-induced temperature gradients is examined. It is shown that the presence of temperature gradients leads to flowmeter errors at the higher-flow values even in the case where the fundamental mode is the only mode excited. It is also deduced that flowmeter errors in general depend on the distance between transducers A and B whether temperature gradients exist or not. This conclusion is not reflected in the usual definition of flowmeter errors given by the so-called mode-dependent deviation of measurement introduced in earlier works.