The multi-scale nonlinear hydrodynamics in Kenics Static Mixer (KSM) with 100 mm in diameter and 2 in aspect ratio was investigated in this work. The time series of tube-wall pressure fluctuation signals were measured at different flow rates ranged of 100~600 Lh-1 and at different axial positions in the range of 420~580 mm away from the cross-section of mixer inlet. It is difficult for composite signals to make an effective analysis by Sample Entropy (SampEn) based on a single scale. The complexity of tube-wall pressure fluctuation signals in a Kenics static mixer was investigated using Intrinsic Mode Entropy (IMEn) based on Sample Entropy algorithm and Empirical Mode Decomposition (EMD) method. Data sampling length and tolerance are optimized based on intrinsic mode entropy. Results of multi-scale analysis of pressure fluctuations indicated that the Sample entropy reaches maximum in the first scale and progressively decreases according to increase of the decomposed order. It is clear that the movement of high frequency component of the pressure signal is the most complicated and is rich in randomness. With the decomposition scales increasing, the complexity of signal decreases and approaches periodic motion eventually. The intrinsic mode entropy of the tube wall pressure signals in KSM has similar development tendencies in different flow rates. Besides, as the flow rates increased, the macro-scale vortexes play a more and more important role and guide the system to develop toward the stable state.
Error of large-eddy simulation in the wall pressure fluctuation of a turbulent channel flow
