Analytical model of an ultrasonic cross-correlation flow meter, part 1: Stochastic modeling of turbulence

An analytical model of an ultrasonic cross-correlation flow meter has been developed to relate the time delay measured by the meter to the mean velocity profile and statistical properties of turbulent pipe flow. The model expresses the cross-correlation and cross-spectrum of the demodulated ultrasonic signal in terms of the space-time correlations of the turbulence. In Part 1 of this two-part paper, a stochastic model of the turbulent velocity fluctuations is developed. The model provides closed-form analytical formulas for the turbulence correlation and spectrum functions in terms of parameters which can be obtained from empirical data or computational fluid dynamics.