Abstract
When the turbulence is detected at two points along the flow direction, the fluid transit time may be equal to the delay time which makes the cross-correlation function of the turbulence maximum. Therefore the flow velocity is determined by this transit time and distance between two detecting points. An analytical expression of the cross-correlation function of the turbulence is derived under the following assumptions.
The behaviour of the fluid particles is the same as that of a random walk. The displacements of the fluid particles due to diffusion corresponding to the longitudinal and transverse velocity fluctuations are not correlated. The auto-correlation function of turbulence is expressed approximately e-ατ2, where α is a constant and τ is delay time.
In a series of experiment the turbulence of air flow is detected by hot-wire anemometers at two points on the center axis of a circular pipe. Comparing with experimental results and theoretical expression, decay and half-width of the cross-correlation functions are discussed.
Transit times which are determined by this correlation method and those by Pitot-tube velocity meter are compared, and those values are coincidented with each other under the ordinary conditions.
