The flow field produced by a pitched blade turbine: Characterization of the turbulence and estimation of the dissipation rate

This paper compares various methods which have been used for the estimation of turbulent length scales, and/or the rate of dissipation of turbulence kinetic energy (ε) in stirred tanks. The system examined was a four-blade, 45° pitched blade turbine rotating in a cylindrical, fully baffled tank with velocity measurement by laser Doppler anemometry. Four methods were chosen for experimental application. The methods used, and the principles upon which they rest, can be summarized as follows: the gradient hypothesis method uses the constitutive equation from the k-ε model; Taylor's hypothesis is used to convert time derivatives to spatial derivatives; dimensional arguments lead to the estimation of ε from k using a constant length scale; finally, the autocorrelation coefficient function is used to calculate the Eulerian integral time scale, which is then combined with k to estimate ε. Various corrections have been suggested for each of these methods, many of which were tested and compared in this work. Although all these methods have previously been applied in stirred tanks, the underlying assumptions and approximations have often been implicit. The impact of these assumptions on the final result, in particular, the importance of the trailing vortices, has been evaluated in a quantitative sense in this paper.