Lagrangian Autocorrelations of Fluctuating Velocities

The chaotic motion of the solids in gas fluidized beds necessitates the measurement of the fluctuating and mean velocities of the solids for thorough understanding of their dynamic behavior. The statistical information of the fluctuating velocity may be obtained from the Lagrangian autocorrelations. 

The Lagrangian autocorrelation coefficient R,a(x,t) at a given position x is defined by Tennekes and Lumley (1972) as 

The Lagrangian velocity autocorrelations can be used to evaluate several important quantities that characterize the fluctuating motion of solids, 

FIGURE 9.12 Typical distribution of Lagrangian autocorrelation coefficients in axial direction for 500- im glass particles at u0 = 54.8 cm/s 

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