**Journal of Theoretical**

and Applied Mechanics

and Applied Mechanics

**33**, 3, pp. 591-603, Warsaw 1995

### Mathematical modelling in measurements of unsteady flows with ultrasonic flowmeters

In the paper a mathematical model of unsteady flow through an ultrasonic flowmeter has been presented. This mathematical model is based on the Reynolds equation for the axial component of velocity vector and ke turbulence model equations. Unsteady flow was given by suitable formulation of a function representing the gradient of pressure in equation of motion. The equations of the model were numerically solved with the finite-difference method. The model was used for analysis of the influence of velocity profile, variable time, on the flowmeter indications. Pulsating flows and flows with velocity leap were tested. From the numerical testes it results that variability of the velocity profiles time is connected with important changes in sensitivity coefficient of the ultrasonic flowmeter. Variability of this coefficient is mainly influenced by a pulsation amplitude of the mass flux. Small influence of pulsation on the flowmeter indications can be observed only in the case of slow-changing flows, for which the Strouhal number is Sh<0.1. In the case of flows with velocity leap the maximum changes of the sensitivity coefficient are of 4-6%. For flows where the maximum value of Strouhal number in the range of velocity leap is less than 0.1, the range of sensitivity coefficient changes is not wide and it does not exceed the range resulting from increase of the Re number.