Determination of correlation functions of turbulent velocity and sound speed fluctuations by means of ultrasonic technique |
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Authors: | Tatiana A Andreeva and William W Durgin |
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Institution: | (1) Department of Mathematical Sciences, Saint-Petersburg State Polytechnic University, Saint-Petersburg, 195251, Russia;(2) Department of Mechanical Engineering, California Polytechnic State University, San Luis Obispo, CA 93407, USA |
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Abstract: | An experimental study of the propagation of high-frequency acoustic waves through grid-generated turbulence by means of an
ultrasound technique is discussed. Experimental data were obtained for ultrasonic wave propagation downstream of heated and
non-heated grids in a wind tunnel. A semi-analytical acoustic propagation model that allows the determination of the spatial
correlation functions of the flow field is developed based on the classical flowmeter equation and the statistics of the travel
time of acoustic waves traveling through the kinematic and thermal turbulence. The basic flowmeter equation is reconsidered
in order to take into account sound speed fluctuations and turbulent velocity fluctuations. It allows deriving an integral
equation that relates the correlation functions of travel time, sound speed fluctuations and turbulent velocity fluctuations.
Experimentally measured travel time statistics of data with and without grid heating are approximated by an exponential function
and used to analytically solve the integral equation. The reconstructed correlation functions of the turbulent velocity and
sound speed fluctuations are presented. The power spectral density of the turbulent velocity and sound speed fluctuations
are calculated. |
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Keywords: | |
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