Measurement of the rate of energy dissipation around an oscillating grid by an energy balance approach

An experimental study was carried out to evaluate ϵ around an oscillating grid producing zero-mean shear flow. The spatial average $\text{ϵ}$ throughout the mixing vessel was determined by the mesurement of the net power input of the grid, this complying with a relationship of the form $\text{ϵ}$αf³_DS³ Re^{−$\text{1}\text{2}$} h⁻¹, in which f_D is the driving frequency, S is the stroke length, Re the grid Reynolds number and h the depth of the mixing column. From mesurements of the power spectrum using laser Doppler anemometry, spectral collapse of the power spectra in the domain of the energy containing eddies at different distances from the grid was demonstrated using u² (u as the turbulence r.m.s. velocity) and τ_E (Eulerian time integral scale) as the scaling parameters. From a balance of the power input and the energy losses, together with the feature of spectral collapse, it was shown that ϵ could be estimated by ϵ = γ₁u²/τ_E in this domain of the power spectrum with γ₁ as a multiplying coefficient independent of distance from the grid.

From the spatial dependence of the turbulence parameters it was evident that within about 1.5 mesh lengths of the grid there was a transition region beyond which it was found that spatial variations were consistent with the dependences uαz⁻¹, τ_Eαz², and ϵαz⁻⁴, where z is the distance from the grid.