Faculty Advisor

Durgin W.W.

Faculty Advisor

Dimentberg M.F.

Faculty Advisor

Olinger D.J.

Faculty Advisor

Hou Z.

Faculty Advisor

Weekes S


"The present study utilizes the ultrasonic travel-time technique to diagnose grid-generated turbulence. The statistics of the travel-time variations of ultrasonic wave propagation along a path are used to determine some metrics of the turbulence. The motivation for this work stems from the observation of substantial delta-t variation in ultrasonic measuring devices like flow meters and circulation meters. Typically, averaging can be used to extract mean values from such time series. The corollary is that the fluctuations contain information about the turbulence. Experimental data were obtained for ultrasonic wave propagation downstream of a heated grid in a wind tunnel. Such grid-generated turbulence is well characterized and features a mean flow with superimposed velocity and temperature fluctuations. The ultrasonic path could be perpendicular or oblique to the mean flow direction. Path lengths were of the order of 0.3 m and the transducers were of 100 kHz working frequency. The data acquisition and control system featured a very high-speed analog to digital conversion card that enabled excellent resolution of ultrasonic signals. Experimental data for the travel-time variance were validated using ray acoustic theory along with the Kolmogorov “2/3” law. It is demonstrated that the ultrasonic technique, together with theoretical models, provides a basis for turbulent flow diagnostics. As a result, the structure constant appearing in the Kolmogorov “2/3” law is determined based on the experimental data. The effect of turbulence on acoustic waves, in terms of the travel time, was studied for various mean velocities and for different angular orientations of the acoustic waves with respect to the mean flow. Average travel time in the presence of turbulence was shorter then in the undisturbed media. The effect of the time shift between the travel times in turbulent and undisturbed media is associated with Fermat’s principle. The travel time and log-amplitude variance of acoustic waves were investigated as functions of travel distance and mean velocity over a range of Reynolds number varying from 4000 to 20000. Experimental data are interpreted using classical ray acoustic approach and the parabolic acoustic equation approach together with the perturbation method. It was experimentally demonstrated that there is a strong dependence of the travel time on the mean velocity even in the case where the propagation of acoustic waves is perpendicular to the mean velocity. The effect of thermal fluctuations, which result in fluctuations of sound speed, was studied for two temperatures of the grid: (no grid heating) and . A semi analytical acoustic propagation model that allows determination of the spacial correlation functions of flow field is developed based on the classical flow meter equation and statistics of the travel time of acoustic waves traveling through the velocity and the thermal turbulence. The basic flow meter equation is reconsidered in order to take into account sound speed fluctuations and turbulent velocity. The resulting equation is written in terms of correlation functions of travel time, sound speed fluctuation and turbulent velocity fluctuations. Experimentally measured travel time statistics data with and without grid heating are approximated by Gaussian function and used to solve the integral flow meter equation in terms of correlation functions analytically."


Worcester Polytechnic Institute

Degree Name



Mechanical Engineering

Project Type


Date Accepted





grid generated turbulence, wave propagation, acoustics, Ultrasonic flowmetering, Turbulence, Waves, Sound, Ultrasonic equipment, Numerical grid generation (Numerical analysis)