Characteristics of turbulence in a multigrid mixer

The paper describes an experimental investigation to determine the distribution and controls on the rate of energy dissipation per unit mass (B) in an oscillatory multigrid mixer. The study centred on the evaluation of the parameter gamma which was treated as a spatial invariant in the expression epsilon = gammaU(2)/tau (E) in which U-2 signifies a turbulence intensity and tau (E) the Eulerian time scale. This was achieved by using an energy balance, involving the measured power input and the energy losses. When grids were widely spaced, it was evident that the turbulence field was characterised by two principal zones of behaviour. In an internal zone, corresponding to the domain swept by an individual grid, U-2 attained high values compared with other regions and se was essentially constant. Outside this region, the 'external zone', turbulence was characterised by a constant Reynolds number specified by R-Gamma0 = U(0)(2)tau (E0)/nu in which U-0(2) and tau (E0) were scaling parameters and nu the kinematic viscosity. It was shown that gamma could be defined in terms of the far distance behaviour using: the relationship gamma proportional to R-Gamma0/R-lambda0(2) with R-lambda0 = lambda U-0(0)/nu as a turbulence Reynolds number involving the Taylor microscale lambda (0). From an energy balance it was shown that R-lambda0(2) proportional to sigma (RNRS2 beta +1)-R-proportional to with the Reynolds number R-N = fSd/nu, R-S = fS(2)/nu specifying the grid motion, the terms f, S, d and sigma referring to the grid frequency, stroke length, bar diameter and grid solidarity, respectively. Coefficients alpha and beta were linked to the Reynolds number dependence of the power input and the term U-0(2) respectively. For the conditions examined, it was shown that gamma behaved in accordance with the power dependence gamma proportional to R-lambda(-n) with n approximate to 0.6. General expressions were derived to characterise the properties of turbulence in both the internal and external regions. Overall it was suggested that useful estimates of E could be gained from the expression epsilon/<(<epsilon>)over bar> = [U-2/tau (E)]/[U-2/tau (E)] in which the terms <(<epsilon>)over bar> and [...] refer to spatial average values. (C) 2001 Elsevier Science B.V. All rights reserved.