Fractal identification of instantaneous velocity time series in kenics static mixer

To characterize the instabilities of unsteady flow in Kenics Static Mixer (KSM) with 0.04 m in diameter and 1.25 in aspect ratio, the turbulent time series of instantaneous velocity fluctuation were measured by Laser Doppler Particle Analyzer in the turbulent region under the range of Re between 3972 and 11916. A method based on wavelet threshold de-noised transform and fractal theory was used to extract the large-scale turbulent signal with multip-scales resolution under different compact support Symlet wavelets. Results showed that the hurst exponents fluctuated between 0.845 and 0.896 which indicated that the instantaneous large-scale velocity fluctuation have persistence and self similarity fractal in lower phase space. The hurst exponents decreased firstly then increased as axial position increased, but increased firstly then decreased as radial position increased which have two peak value for the single mixing-element. Decomposition error was the minimum under Sym 8-order wavelet, and the velocity signal in the element-transition had the strongest singularity.