Distribution of turbulence energy dissipation rates in a Rushton turbine stirred mixer

An approximate method of measuring the turbulence energy dissipation rate () in mixers by use of laser-Doppler measurements of the velocity autocorrelation and turbulence energy was successful in yielding remarkably consistent values. The necessary corrections for periodic, non-dissipative velocity fluctuations were made by an autocorrelation method. Two modes of periodic fluctuation were found to be significant. Transformation of the corrected autocorrelations yielded completely normal turbulence energy spectra.List of symbols c fluctuating concentration, C–C - D impeller diameter - D molecular diffusivity - f() autocorrelation function - E₁ (n) one-dimensional energy spectrum function - k turbulence energy (=q) - L_s macroscale of segregation - L_x integral velocity scale - N impeller rotation rate - N_Sc Schmidt number (v/D) - q turbulence energy (=k) - r radial distance from impeller shaft - R impeller radius - T tank diameter - U, V, W velocity in x, y, z directions - u, v, w velocity fluctuations - u_r, u, u_z fluctuating velocities in radial, tangential, and axial (shaft) directions - U_r, U, U_z velocities - z axial distance from impeller disk - Z tank height - turbulence energy dissipation rate - viscosity - time delay