Chaotic characteristics of pseudoplastic fluid induced by 6PBT impeller in a stirred vessel
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摘要
Xanthan gum solutions with different mass concentrations were used to study the chaotic characteristics induced by the impeller of perturbed six-bent-blade turbine(6 PBT) in a stirred vessel. Based on the velocity time series obtained by the experiment of particle image velocimetry(PIV), with the software MATLAB(R2016a), the distributions of the largest Lyapunov exponent(LLE) and Kolmogorov entropy(K entropy) of the system, as two important parameters for characterizing the chaotic degree, were investigated respectively. Results showed that both of the LLE and K entropy increased with the increasing speed at the beginning. As the speed was up to 200 r·min-1, the two parameters reached the maximal values meanwhile, corresponding to 0.535 and 0.834, respectively, which indicated that the chaotic degree of the flow field was up to the highest level. When the speed was increased further, both of the LLE and K entropy decreased on the contrary, which meant that the chaotic degree was decreasing. It was also observed that the chaotic characteristics of flow field were hardly affected by the fluid rheology and the detecting positions. The research results will enhance the understanding of the chaotic mixing mechanism and provide a theoretical reference for optimizing impeller structure.
Xanthan gum solutions with different mass concentrations were used to study the chaotic characteristics induced by the impeller of perturbed six-bent-blade turbine(6 PBT) in a stirred vessel. Based on the velocity time series obtained by the experiment of particle image velocimetry(PIV), with the software MATLAB(R2016a), the distributions of the largest Lyapunov exponent(LLE) and Kolmogorov entropy(K entropy) of the system, as two important parameters for characterizing the chaotic degree, were investigated respectively. Results showed that both of the LLE and K entropy increased with the increasing speed at the beginning. As the speed was up to 200 r·min-1, the two parameters reached the maximal values meanwhile, corresponding to 0.535 and 0.834, respectively, which indicated that the chaotic degree of the flow field was up to the highest level. When the speed was increased further, both of the LLE and K entropy decreased on the contrary, which meant that the chaotic degree was decreasing. It was also observed that the chaotic characteristics of flow field were hardly affected by the fluid rheology and the detecting positions. The research results will enhance the understanding of the chaotic mixing mechanism and provide a theoretical reference for optimizing impeller structure.
Xanthan gum solutions with different mass concentrations were used to study the chaotic characteristics induced by the impeller of perturbed six-bent-blade turbine(6 PBT) in a stirred vessel. Based on the velocity time series obtained by the experiment of particle image velocimetry(PIV), with the software MATLAB(R2016a), the distributions of the largest Lyapunov exponent(LLE) and Kolmogorov entropy(K entropy) of the system, as two important parameters for characterizing the chaotic degree, were investigated respectively. Results showed that both of the LLE and K entropy increased with the increasing speed at the beginning. As the speed was up to 200 r·min-1, the two parameters reached the maximal values meanwhile, corresponding to 0.535 and 0.834, respectively, which indicated that the chaotic degree of the flow field was up to the highest level. When the speed was increased further, both of the LLE and K entropy decreased on the contrary, which meant that the chaotic degree was decreasing. It was also observed that the chaotic characteristics of flow field were hardly affected by the fluid rheology and the detecting positions. The research results will enhance the understanding of the chaotic mixing mechanism and provide a theoretical reference for optimizing impeller structure.
引文
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[4]Deyu Luan,Shenjie Zhou,Songying Chen,Cavern development of pseudoplastic fluids stirred by impeller of perturbed six-bent-bladed turbine,Chin.J.Mech.Eng.48(16)(2012)152-157.
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[9]S.M.Shekhar,S.Jayanti,Mixing of pseudoplastic fluids using helical ribbon impellers,AICHE J.49(11)(2004)2768-2772.
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[14]B.Xu,J.F.Gilchrist,Shear migration and chaotic mixing of particle suspensions in a time-periodic lid-driven cavity,Phys.Fluids 22(5)(2010)1-7.
[15]Deyin Gu,Zuohua Liu,Jun Li,Zhaoming Xie,Changyuan Tao,Yundong Wang,Intensification of chaotic mixing in a stirred tank with a punched rigid-flexible impeller and a chaotic motor,Chem.Eng.Process.:Process Intesif.122(2017)1-9.
[16]M.Cudak,J.Karcz,Local momentum transfer process in a wall region of an agitated vessel equipped with an eccentric impeller,Ind.Eng.Chem.Res.50(7)(2011)4140-4149.
[17]De-yu Luan,Shen-jie Zhou,Song-ying Chen,Mixing characteristics of pseudoplastic fluid in a stirred tank with the stirrer composed of perturbed six-bent-bladed turbine,J.Chem.Eng.Chin.Univ.26(5)(2012)787-792.
[18]M.T.Rosenstein,J.J.Collins,C.J.De Luca,A practical method for calculating largest Lyapunov exponents from small data sets,Physica D 65(1)(1993)117-134.
[19]Lv Jinhu,Lu Junan,Chen Shihua,Nonlinear Time Series Analysis and Application,Wuhan University Press,Wuhan,2002.
[20]Deyu Luan,Shengfeng Zhang,Jianping Lu,et al.,Chaotic characteristics enhanced by impeller of perturbed six-bent-bladed turbine in stirred tank,Results Phys.7(2017)1524-1530.
[21]Zuohua Liu,Chao Chen,Renlong Liu,et al.,Chaotic mixing enhanced by rigid-flexible impeller in stirred vessel,Chem.Ind.Eng.(China)65(1)(2014)61-70.
[22]L.I.U.Zuohua,X.U.Chuanlin,H.E.Muchuan,et al.,Oil-water biphase chaotic mixing enhanced by punched rigid-flexible combination impeller in mixer-settler,Chem.Ind.Eng.(China)68(2)(2017)637-642.
[23]Li Meimei,Chaotic Analysis and Prediction for Electric Power Load,Ph D Thesis Sichuan University Press,Chengdu,2004.
[24]De-yu Luan,Shen-jie Zhou,Song-ying Chen,et al.,Chaotic agitation characteristics of shifted 6-bent-blade impeller in pseudoplastic fluid,Chem.Eng.39(9)(2011)41-46.
[25]Deyu Luan,Qiao Chen,Shenjie Zhou,Numerical simulation and analysis of power consumption and Metzner-Otto constant for impeller of 6PBT,Chin.J.Mech.Eng.27(3)(2014)635-640.
[26]J.C.Schouten,F.Takens,V.D.B.Cm,Maximum-likelihood estimation of the entropy of an attractor,Phys.Rev.E Stat.Phys.Plasmas Fluids Relat.Interdiscip.Topics 49(1)(1994)126-129.
[2]L.W.Adams,M.Barigou,CFD analysis of caverns and pseudo-caverns developed during mixing of non-Newtonian fluids,Chem.Eng.Res.Des.85(5)(2007)598-604.
[3]De-yu Luan,Shen-jie Zhou,Song-ying Chen,et al.,CFD simulation of the flow field and cavern formation of pseudoplastic fluid with a 6-bent-blade impeller,Chin.J.Process.Eng.10(6)(2010)1054-1059.
[4]Deyu Luan,Shenjie Zhou,Songying Chen,Cavern development of pseudoplastic fluids stirred by impeller of perturbed six-bent-bladed turbine,Chin.J.Mech.Eng.48(16)(2012)152-157.
[5]Q.Xiao,N.Yang,J.Zhu,et al.,Modeling of cavern formation in yield stress fluids in stirred tanks,AICHE J.60(8)(2014)3057-3070.
[6]L.Pakzad,F.Ein-Mozaffari,P.Chan,Using electrical resistance tomography and computational fluid dynamics modeling to study the formation of cavern in the mixing of pseudoplastic fluids possessing yield stress,Chem.Eng.Sci.63(9)(2008)2508-2522.
[7]E.Galindot,A.W.Nienow,Mixing of highly viscous simulated xanthan fermentation broths with the Lightnin A-315 impeller,Biotechnol.Prog.8(3)(2010)233-239.
[8]J.Sossa-Echeverria,F.Taghipour,Computational simulation of mixing flow of shear thinning non-Newtonian fluids with various impellers in a stirred tank,Chem.Eng.Process.93(2015)66-78.
[9]S.M.Shekhar,S.Jayanti,Mixing of pseudoplastic fluids using helical ribbon impellers,AICHE J.49(11)(2004)2768-2772.
[10]L.Fradette,G.Thome,P.A.Tanguy,et al.,Power and mixing time study involving a Maxblend impeller with viscous Newtonian and non-Newtonian fluids,Chem.Eng.Res.Des.85(A11)(2007)1514-1523.
[11]S.Foucault,Mixing times in coaxial mixers with Newtonian and non-Newtonian fluids,Ind.Eng.Chem.Res.45(1)(2006)352-359.
[12]Y.Fontaine,F.Guntzburger,L.Bertrand,M-C.Fradette,Heuzey,Experimental investigation of the flow dynamics of rheologically complex fluids in a Maxblend impeller system using PIV,Chem.Eng.Res.Des.91(1)(2013)7-17.
[13]Dineshkumar Patel,Farhad Ein‐Mozaffari,Mehrab Mehrvar,Effect of impeller type on continuous‐flow mixing of non‐Newtonian fluids in stirred vessels through dynamic tests,The Canadian Journal of Chemical Engineering 90(2)(2012)290-298.
[14]B.Xu,J.F.Gilchrist,Shear migration and chaotic mixing of particle suspensions in a time-periodic lid-driven cavity,Phys.Fluids 22(5)(2010)1-7.
[15]Deyin Gu,Zuohua Liu,Jun Li,Zhaoming Xie,Changyuan Tao,Yundong Wang,Intensification of chaotic mixing in a stirred tank with a punched rigid-flexible impeller and a chaotic motor,Chem.Eng.Process.:Process Intesif.122(2017)1-9.
[16]M.Cudak,J.Karcz,Local momentum transfer process in a wall region of an agitated vessel equipped with an eccentric impeller,Ind.Eng.Chem.Res.50(7)(2011)4140-4149.
[17]De-yu Luan,Shen-jie Zhou,Song-ying Chen,Mixing characteristics of pseudoplastic fluid in a stirred tank with the stirrer composed of perturbed six-bent-bladed turbine,J.Chem.Eng.Chin.Univ.26(5)(2012)787-792.
[18]M.T.Rosenstein,J.J.Collins,C.J.De Luca,A practical method for calculating largest Lyapunov exponents from small data sets,Physica D 65(1)(1993)117-134.
[19]Lv Jinhu,Lu Junan,Chen Shihua,Nonlinear Time Series Analysis and Application,Wuhan University Press,Wuhan,2002.
[20]Deyu Luan,Shengfeng Zhang,Jianping Lu,et al.,Chaotic characteristics enhanced by impeller of perturbed six-bent-bladed turbine in stirred tank,Results Phys.7(2017)1524-1530.
[21]Zuohua Liu,Chao Chen,Renlong Liu,et al.,Chaotic mixing enhanced by rigid-flexible impeller in stirred vessel,Chem.Ind.Eng.(China)65(1)(2014)61-70.
[22]L.I.U.Zuohua,X.U.Chuanlin,H.E.Muchuan,et al.,Oil-water biphase chaotic mixing enhanced by punched rigid-flexible combination impeller in mixer-settler,Chem.Ind.Eng.(China)68(2)(2017)637-642.
[23]Li Meimei,Chaotic Analysis and Prediction for Electric Power Load,Ph D Thesis Sichuan University Press,Chengdu,2004.
[24]De-yu Luan,Shen-jie Zhou,Song-ying Chen,et al.,Chaotic agitation characteristics of shifted 6-bent-blade impeller in pseudoplastic fluid,Chem.Eng.39(9)(2011)41-46.
[25]Deyu Luan,Qiao Chen,Shenjie Zhou,Numerical simulation and analysis of power consumption and Metzner-Otto constant for impeller of 6PBT,Chin.J.Mech.Eng.27(3)(2014)635-640.
[26]J.C.Schouten,F.Takens,V.D.B.Cm,Maximum-likelihood estimation of the entropy of an attractor,Phys.Rev.E Stat.Phys.Plasmas Fluids Relat.Interdiscip.Topics 49(1)(1994)126-129.