Evolution of length scales and turbulence spectra in the extrapolation of exchanger size

摘要

Attempts to determine the energy spectrum (or spectral energy distribution) for all values of its wave number argument are a fundamental objective of turbulence theory. Detailed predictions of the energy spectrum are not yet possible for more than a very few classes of idealized flows. Nevertheless, to make practical headway, it is necessary to evolve a heuristic physical picture of turbulent flow.Of particular interest in partic1e-fluid interaction is the comparison of scale lengths in each region of the spectrum. When partic1e inertia can be neglected, the diffusion, energy-containing, and inertial subranges of the spectrum are of most interest.While the Kolmogorov theory on the energy cascade is useful for describing the energy processes in an idealized turbulent flow, its applicability to the prediction of turbulence is restricted to isotropic or homogeneous flows (or the isotropic portion of turbulent flows, namely the smaller-scale characteristics of the flow). Most practical flows of interest involve at least violation of isotropy through the introduction of shear and, in most situations, non-homogeneities as a result of shear flow variation. Turbulent energy spectra for such flows are significantly more complicated and must inc1ude the features representative of the coherent structures.We have performed LDA measurements in various locations of the flow field in two static mixers (of diameters 20 mm and 54 mm) of HEV type (High Efficiency Vortex): the same geometry is at the base of the two mixers obtained by a simple homothety. The flow in this geometry is highly non uniform, and the turbulence is produced by small fins fixed at the walls of an empty duct, so that the longitudinal vortices and the wake effects predominate over the wall turbulence.The work consists to study the shape modification of the turbulent spectra in the size extrapolation and to test the traditional extrapolation laws, while comparing, in the two mixers, spectra and scales of turbulence at constant velocity or constant Reynolds number.