Characteristics of turbulence in a multigrid mixer

Abstract

The paper describes an experimental investigation to determine the distribution and controls on the rate of energy dissipation per unit mass ( ε) in an oscillatory multigrid mixer. The study centred on the evaluation of the parameter γ which was treated as a spatial invariant in the expression ε= γU 2/ τ E in which U 2 signifies a turbulence intensity and τ 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 τ E was essentially constant. Outside this region, the ‘external zone’, turbulence was characterised by a constant Reynolds number specified by R Γ0 = U 0 2 τ E0/ ν in which U 0 2 and τ E0 were scaling parameters and ν the kinematic viscosity. It was shown that γ could be defined in terms of the far distance behaviour using the relationship γ∝ R Γ0 / R λ0 2 with R λ0 = λ 0 U 0/ ν as a turbulence Reynolds number involving the Taylor microscale λ 0. From an energy balance it was shown that R λ0 2∝ σR N α R S 2 β+1 with the Reynolds number R N= fSd/ ν, R S= fS 2/ ν specifying the grid motion, the terms f, S, d and σ referring to the grid frequency, stroke length, bar diameter and grid solidarity, respectively. Coefficients α and β 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 γ behaved in accordance with the power dependence γ∝ R λ − n with n≈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 ε could be gained from the expression ε/ ε =(U 2/τ E )/〈U 2/τ E 〉 in which the terms ε ̄ and 〈⋯〉 refer to spatial average values.