旋流静态混合器内流场瞬态特性研究
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摘要
旋流静态混合器作为一种新型化工过程强化设备,广泛适用于石油化工、食品加工、化学工业等精细化工中间体和大宗有机化工原料的单元混合操作。与传统的搅拌槽反应器相比,静态混合器大幅度提高设备的生产能力,降低工业生产成本,提高产品收率和质量,减少废弃物排放,产生显著的经济效益和社会效益。但到目前为止,对其瞬态流动特性的理论探讨以及对工业生产过程的指导远没有达到预期的水平。本文分析了SK型混合器内高粘度流体的运动特性;通过对SK型静态混合器的瞬态流场实验测量,重点研究了混合器内瞬态流场的混沌和分形特性;利用计算流体力学软件考察含有不同混合组件的静态混合器的流动阻力和宏观混合传质特性,用以指导这种混合器的优化和放大。
基于流体动力学、非线性动力学及Ottino理论,建立了高粘度流体在SK型静态混合器内的流体流动模型。分析双极坐标系下二维Navier-Stokes方程流函数的边值问题,并建立了相应的流体微分运动方程。用Poincare映射方法对静态混合器内蠕动流的动力学行为进行了数值仿真研究。给出了系统响应随管壁转动频率变化的最大Lyapunov指数曲线图、典型的Poincare截面图和相图。初步判定:高粘度流体在SK型静态混合器内轴截面的径向二次流动存在混沌特性。
为揭示高雷诺数下SK型静态混合器非稳态流动特性,利用激光多普勒测速仪对SK型静态混合器的瞬时速度场进行测量。采用功率谱、最大李雅谱指数、相平面识别混合器内瞬时速度时间序列的混沌特性。基于傅立叶变换对SK型静态混合器速度波动信号进行时域分解,利用自相关函数和互信息函数研究了各个频率段信号的线性相关和非线性相关性。实验研究表明:SK型静态混合器内速度波动时间序列具有混沌特性;功率谱函数随频率的增加呈幂函数衰减;瞬时速度脉动主要能量集中在3.9Hz以下,62.5Hz以上的信号线性无关,75Hz以上的信号不存在非线性和线性相关性。
利用湍流高阶矩参数平坦因子和偏斜因子分析了静态混合器内脉动速度的概率密度函数分布以及与正态分布的定量差别。实验结果表明:SK型静态混合器湍流主体区的的倾斜因子S在-2.79和3.12之间波动,平坦因子数值主要分布在3~9.5之间并且F>3和F<3的区域呈片状间歇性分布,证明了SK型静态混合器速度分布偏离高斯分布程度大并且存在拟序结构。
为了探讨静态混合内非线性、非均匀性和混沌特性机理,利用高速数据采集系统对SK型静态混合器管壁处脉动压力进行测量。结合小波变换模极大值理论对采集的不同进口流量下壁压波动时间序列用Daubechies二阶小波提取1~7尺度下的特征信号,并分别对提取的信号进行R/S分析。通过对压力波动信号不同尺度下的细节信号与概貌信号研究发现,在不同的尺度下表现出不同的分形结构,且随着进口流量的增大,分形结构的变化趋势基本一致。此外,该系统不仅存在确定性非周期成分,而且不同尺度的旋涡之间的能量交换,导致混沌的产生。各尺度信号的能量分布表明,压力波动信号主要体现了宏观尺度的漩涡级串的相互作用。
为了预测旋流静态混合器内非稳态宏观混合特性,利用脉冲示踪法和计算流体力学相结合,基于正交实验原理研究示踪剂在不同雷诺数下、混合元件长径比及监测位置处的停留时间分布特性。分析操作条件对平均停留时间和径向强化系数的影响顺序,比较了MSM、KSM、SSM、RSM四种旋流静态混合器的强化混合效果。结果表明:SK型静态混合器内的液体单相流动的轴向返混系数较小且数量级为10-2,流动状态接近活塞流;极差计算结果表明对停留时间分布影响顺序为:进口流速>混合元件的长径比>监测位置;而监测位置对混合元件的径向强化能力影响最大,KSM的强化能力最大,SSM的强化能力最小。提出强化因子优化混合器的级数,径向强化系数与螺旋叶片级数的负0.638次幂呈线性关系。利用量纲分析和π定理简化了新型静态混合器流动阻力的影响因素之间的关系式,通过数据整理和回归得到了普遍适用的流动阻力摩擦系数关联式,为其工业化应用提供了理论依据。
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.
基于流体动力学、非线性动力学及Ottino理论,建立了高粘度流体在SK型静态混合器内的流体流动模型。分析双极坐标系下二维Navier-Stokes方程流函数的边值问题,并建立了相应的流体微分运动方程。用Poincare映射方法对静态混合器内蠕动流的动力学行为进行了数值仿真研究。给出了系统响应随管壁转动频率变化的最大Lyapunov指数曲线图、典型的Poincare截面图和相图。初步判定:高粘度流体在SK型静态混合器内轴截面的径向二次流动存在混沌特性。
为揭示高雷诺数下SK型静态混合器非稳态流动特性,利用激光多普勒测速仪对SK型静态混合器的瞬时速度场进行测量。采用功率谱、最大李雅谱指数、相平面识别混合器内瞬时速度时间序列的混沌特性。基于傅立叶变换对SK型静态混合器速度波动信号进行时域分解,利用自相关函数和互信息函数研究了各个频率段信号的线性相关和非线性相关性。实验研究表明:SK型静态混合器内速度波动时间序列具有混沌特性;功率谱函数随频率的增加呈幂函数衰减;瞬时速度脉动主要能量集中在3.9Hz以下,62.5Hz以上的信号线性无关,75Hz以上的信号不存在非线性和线性相关性。
利用湍流高阶矩参数平坦因子和偏斜因子分析了静态混合器内脉动速度的概率密度函数分布以及与正态分布的定量差别。实验结果表明:SK型静态混合器湍流主体区的的倾斜因子S在-2.79和3.12之间波动,平坦因子数值主要分布在3~9.5之间并且F>3和F<3的区域呈片状间歇性分布,证明了SK型静态混合器速度分布偏离高斯分布程度大并且存在拟序结构。
为了探讨静态混合内非线性、非均匀性和混沌特性机理,利用高速数据采集系统对SK型静态混合器管壁处脉动压力进行测量。结合小波变换模极大值理论对采集的不同进口流量下壁压波动时间序列用Daubechies二阶小波提取1~7尺度下的特征信号,并分别对提取的信号进行R/S分析。通过对压力波动信号不同尺度下的细节信号与概貌信号研究发现,在不同的尺度下表现出不同的分形结构,且随着进口流量的增大,分形结构的变化趋势基本一致。此外,该系统不仅存在确定性非周期成分,而且不同尺度的旋涡之间的能量交换,导致混沌的产生。各尺度信号的能量分布表明,压力波动信号主要体现了宏观尺度的漩涡级串的相互作用。
为了预测旋流静态混合器内非稳态宏观混合特性,利用脉冲示踪法和计算流体力学相结合,基于正交实验原理研究示踪剂在不同雷诺数下、混合元件长径比及监测位置处的停留时间分布特性。分析操作条件对平均停留时间和径向强化系数的影响顺序,比较了MSM、KSM、SSM、RSM四种旋流静态混合器的强化混合效果。结果表明:SK型静态混合器内的液体单相流动的轴向返混系数较小且数量级为10-2,流动状态接近活塞流;极差计算结果表明对停留时间分布影响顺序为:进口流速>混合元件的长径比>监测位置;而监测位置对混合元件的径向强化能力影响最大,KSM的强化能力最大,SSM的强化能力最小。提出强化因子优化混合器的级数,径向强化系数与螺旋叶片级数的负0.638次幂呈线性关系。利用量纲分析和π定理简化了新型静态混合器流动阻力的影响因素之间的关系式,通过数据整理和回归得到了普遍适用的流动阻力摩擦系数关联式,为其工业化应用提供了理论依据。
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.
引文
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