| Static mixers, also known as motionless mixers, have been widely used in the PI fields. They are available in petrochemical plants, food and chemical industries for mixing applications of fine chemical intermediates and large bulk organic chemical raw material. Their use in continuous processes create prominent benefits for the economy and society and is an attractive alternative to conventional agitation since increased production capability, reduced manufacturing costs, higher yield and lessened offal exhaust can be achieved at lower cost. The following works have been done because the relevant theory research and directions for engineering application have not got the expected aims until recently. The flow characteristic of high viscous fluids inside a Kenics static mixer (KSM) was analyzed. The chaotic and fractal characteristic of instantaneous flow field in the KSM were experimental investigated. The flow resistance and mass transfer of tracer in the static mixers with different arrangements twisted-leaves were paid more attention employing the computational fluid dynamics software.A modified model for the high viscosity fluids motion inside the KSM was established based on hydrokinetics, nonlinear dynamics and Ottino theory. The stream function formulation of the two-dimensional Navier-Stokes equations was developed with boundary conditions using the bipolar coordinates. Corresponding differential flow equations of stokes flow were derived and analyzed using Poincare mapping method. The bifurcation diagrams were given about the response changes with the frequency ratio, and the largest lyapunov exponent profiles and Poincare maps at some frequencies were given. The simulation results indicate that the secondary flow characteristic of high viscosity fluids has obvious chaos motion feature in its axial cross-sections. In order to evaluate the characteristic of unsteady flow in KSM with 0.04 m in diameter and 1.25 in aspect ratio, the time series of instantaneous velocity were measured with Laser Doppler Anemometry. The power spectrum function, the largest Lyapunov exponent and phase plane were applied to identify the chaotic characteristic of instantaneous velocity time series, respectively. The fluctuation signals of velocity are decomposed into different frequency bands signals based on Fourier transform. The linear and nonlinear correlation characteristics of different frequency bands signals are evaluated with auto-correlation function and mutual information function, respectively. The experimental results indicate that the signals of more than 62.5 Hz in frequency have no linear correlation, and the signals of more than 75 Hz in frequency should be considered as noise for linear or nonlinear correlation. The frequency for main energy of fluctuations is below 3.9 Hz, and the velocity fluctuation has power-law attenuation between power amplitude and frequency.The deviations between the probability density functions of the Cartesian velocity fluctuations in KSM and the corresponding normal distribution described by turbulent higher order items, skewness and flatness factors, were analyzed quantitatively. The experimental results indicate that the value of skewness fluctuates from -2.79 to 3.12, which means that the distribution of velocity field is not a normal distribution, and the existence of coherent structure is indicated by the distribution of flatness of pulsant velocity in a range of 3~9.5, and the zones of F<3 and F>3 are concurrence with intermittence which will alter according to diversification the axial position of cross-sections. Furthermore, the variations of the probability density functions with Reynolds number were examined.In order to understand the intrinsic formalism of heterogeneity, non-linearity and chaotic behavior of fluid system in KSM, the signals of tube-pressure fluctuation dynamics with different flow rates were collected with high speed collector. Tube-pressure signals at different flow rates denoised using the wavelet transform modulus maxima method were firstly decomposed to 1~7 scale detail signals and scale approximation and then evaluated using multi-scale and R/S analysis method based on Daubechies second order wavelet. By analyzing profile of different scale signals, different fractal structure at different scales were found, and there was the similar trend with the flow rate rising. Besides, it showed that there were some non-periodic components in the system, and the similar energy exchange among vortexes caused the diffusion of the turbulence, which was a characteristic of an opening system. The vortex with different scale would cause the chaos. By analyzing energy profile of different scale signals, the pressure fluctuations mainly reflect macro-scale interaction between the vortex and the liquid phase was found.The unsteady mixing processes in the static mixers with different axial arrangements were examined by solving the transport equation of the tracer based on pulse tracer input technique and computational fluid dynamics commerical software-Fluent. The characteristics of residence time distribution (RTD) monitored at different cross-sections with different Reynolds numbers and aspect ratios were evaluated and analyzed based on orthogonal experiment, and the crucial orders of factors were ranked by the range analysis of mean value and square deviation. The results showed that the order of axial back mixing coefficient is 10-2, and the flowing state of the fluid in the KSM approaches plug flows. It is revealed that Reynolds number plays a more important role compared with aspect ratio for back mixing which is reverse for RTD. The mixing-strengthen capability were compared among the MSM, KSM, SSM and RSM mixers based on the concentration response characteristics. By analyzing the CFD results, the ratios Z of pressure drop were found in good agreement with the experimental as well as the results reported in the literature about KSM. Among the different arrangement, KSM has the best strengthen-mixing performance but SSM has the least strengthen capability. Strengthened factor H was proposed to optimize the element number, a linear relationship between radial strengthened factor and negative power of helical element number was concluded. The relationship between all factors influencing flow resistance in the new type static mixers was simplified, and general relationship among them was gained by using the dimensional analysis andπtheorem which offers the theoretical base for the industry application. |
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