A ray tracing model of a V-configuration transit time difference flow meter based on the ray deflection effect

A new ray tracing model of the transit time difference clamp-on flow meter is presented which uses the deflection of the ray by the flow to introduce the transit time difference. It is shown analytically that the deflection, even at low flows, completely accounts for the transit time difference that is predicted by the conventional model where the ray is considered to be fixed in space, assuming that the flow is slow and uniform. This principle is extended to non-uniform analytic flow profiles using a simple stepping algorithm, then it is incorporated into a model including effects of mode conversion at all of the material interfaces, attenuation and beam spread. The new model is used to analyse the different paths that ultrasonic energy takes through a clamp-on meter on two example UPVC pipes. It is found that the ultrasonic behaviour is much more complex than in metal pipes due to the wider range of possible paths through the system.