竖直管内汽（气）液固多相流动沸腾过程的流体动力学研究
|
摘要
管内流动沸腾过程是流动与沸腾两种基本物理过程的有机结合。而将固体颗粒加入到沸腾两相流动过程中形成汽液固三相流动,能够很好地解决换热管内的防除垢问题,且能达到强化传热目的。但其复杂的流动特性使人们采用已有的研究方法很难揭示系统内存在的非线性特征,从而影响对沸腾多相流系统的认识和该技术的推广应用。本文利用非线性研究方法中的混沌理论作为研究工具,通过自己编写有关计算混沌特征量的程序,考察汽(气)液固多相流动沸腾过程的流体动力学特性,为此类系统的应用提供更加坚实的理论依据。
以蒸发器内的竖直换热管为对象,考察了气液固三相、汽液两相及汽液固三相自然循环流动、汽液两相及汽液固三相强制循环流动过程,通过对多相流动沸腾过程的压力波动信号的确定性混沌分析,首次对竖直管内汽(气)液固多相流动沸腾过程的压力波动信号进行了混沌识别,证明此类系统具有混沌特征。另外,对汽液两相自然循环流动过程的温度时间序列进行了较深入分析。
理论和实验研究结果表明:大颗粒的气液固三相循环流化床的压力波动信号具有混沌信号的特征。热流密度的变化对多相沸腾系统的功率谱密度函数有一定的影响,且功率谱密度函数的主峰个数及第一主峰的起始频率能反映出流型的变化规律。汽液两相自然循环流动中,随着介质粘度的增加,加热段循环温度降低,循环过程更加稳定。不同表观液速下,随着热流密度的增加,汽液两相强制循环流压力波动信号的分维数有变大的趋势,说明汽液两相流动的复杂程度在加剧,流动接近随机运动。热流密度对汽液两相流压力波动信号的关联维数、Kolmogorov熵和Lyapunov指数均有较明显影响,且都为有限正值,可用这些非线性特征参数预测流型的变化。汽液固三相自然循环及强制循环流动过程中,颗粒体积分率对压力波动信号的关联维数、K熵及Lyapunov指数均有影响,且可从这些特征参数对流动状态进行粗略划分。在沸腾两相流中加入固体颗粒使流动过程更加稳定,且能较好地将流动状态控制在泡状流阶段,有利于系统的稳定操作。
Solid particles fluidized by the two-phase boiling mixture may accomplish sufficient deposit removal to keep boiling surfaces clean. This results in a self-cleaning fluidized flow boiling heat exchanger. The particles additionally enhance the heat transfer. This hydrodynamics of a vapor liquid solid boiling flow is very complex. This complexity which results mainly from the strong nonlinearity and structural heterogeneity of particle-fluid flow system, makes simple methods not sufficient for elucidating their intrinsic characteristics. In this paper, deterministic chaos theory is applied to study the nonlinear characteristics of this flow boiling system. And a set of software which were verified and can used to describe actual system dynamic behavior qualitatively and quantitatively were developed and modified. Hydrodynamics of boiling multi-phase flow were studied, so as to supply more theory foundation for the vapor (gas) liquid solid flow technique.
Experiments are carried out in the paper to study the feature of pressure fluctuation in vertical tube for boiling multi-phase flow. The gas-liquid-solid, natural circulation of vapor-liquid two phase and vapor-liquid-solid three phase, forced circulation of vapor-liquid two phase and vapor-liquid-solid three phase were studied. On the basis of detailed study on chaos theory of pressure fluctuation in boiling multi-phase flow, such as statistical analysis, quantitative analysis and qualitative analysis, it is evidence that boiling multi-phase flow system is a deterministic system. In addition to, the prime analysis of temperature signal on vapor-liquid two phase natural circulation flow was carried.
The investigation results show that the pressure fluctuation signal in coarse circulation fluidized bed with big particles had chaos characterization. And the effects of heat flux on power spectrum density function of the pressure fluctuations are stressed study, and the flow regime transitions is correlation to number and frequency of the main peak value of power spectrum density function. The temperature of circulation liquid decreases with liquid viscosity increasing, and the circulation process becomes more steady in the vapor-liquid two-phase natural circulation. The effects of solid holdup on correlation dimension, K entropy and Lyapunov exponent of pressure fluctuation signal are studied in vapor-liquid-solid three phase natural circulation and forced circulation. And flow pattern can be identified by chaos characteristic parameter. By comparing vapor-liquid two-phase with vapor-liquid-solid three phase, the advantage of mixed solid particle in vapor-liquid two phase boiling is that flow process become more steady and flow regime can maintain bubble flow. In different velocity of flow, the fractal dimension of the pressure fluctuation time series in vapor-liquid two-phase forced circulation increased with increase of heat flux. The Kolmogorov entropy and correlation dimension have change with difference of heat flux. A positive, nonfinite estimate of correlation dimension and Kolmogorov entropy provides further evidence that pressure fluctuation signals behave chaotically. It can be concluded that the flow pattern transition on basis of characteristic parameters can be predicted.
以蒸发器内的竖直换热管为对象,考察了气液固三相、汽液两相及汽液固三相自然循环流动、汽液两相及汽液固三相强制循环流动过程,通过对多相流动沸腾过程的压力波动信号的确定性混沌分析,首次对竖直管内汽(气)液固多相流动沸腾过程的压力波动信号进行了混沌识别,证明此类系统具有混沌特征。另外,对汽液两相自然循环流动过程的温度时间序列进行了较深入分析。
理论和实验研究结果表明:大颗粒的气液固三相循环流化床的压力波动信号具有混沌信号的特征。热流密度的变化对多相沸腾系统的功率谱密度函数有一定的影响,且功率谱密度函数的主峰个数及第一主峰的起始频率能反映出流型的变化规律。汽液两相自然循环流动中,随着介质粘度的增加,加热段循环温度降低,循环过程更加稳定。不同表观液速下,随着热流密度的增加,汽液两相强制循环流压力波动信号的分维数有变大的趋势,说明汽液两相流动的复杂程度在加剧,流动接近随机运动。热流密度对汽液两相流压力波动信号的关联维数、Kolmogorov熵和Lyapunov指数均有较明显影响,且都为有限正值,可用这些非线性特征参数预测流型的变化。汽液固三相自然循环及强制循环流动过程中,颗粒体积分率对压力波动信号的关联维数、K熵及Lyapunov指数均有影响,且可从这些特征参数对流动状态进行粗略划分。在沸腾两相流中加入固体颗粒使流动过程更加稳定,且能较好地将流动状态控制在泡状流阶段,有利于系统的稳定操作。
Solid particles fluidized by the two-phase boiling mixture may accomplish sufficient deposit removal to keep boiling surfaces clean. This results in a self-cleaning fluidized flow boiling heat exchanger. The particles additionally enhance the heat transfer. This hydrodynamics of a vapor liquid solid boiling flow is very complex. This complexity which results mainly from the strong nonlinearity and structural heterogeneity of particle-fluid flow system, makes simple methods not sufficient for elucidating their intrinsic characteristics. In this paper, deterministic chaos theory is applied to study the nonlinear characteristics of this flow boiling system. And a set of software which were verified and can used to describe actual system dynamic behavior qualitatively and quantitatively were developed and modified. Hydrodynamics of boiling multi-phase flow were studied, so as to supply more theory foundation for the vapor (gas) liquid solid flow technique.
Experiments are carried out in the paper to study the feature of pressure fluctuation in vertical tube for boiling multi-phase flow. The gas-liquid-solid, natural circulation of vapor-liquid two phase and vapor-liquid-solid three phase, forced circulation of vapor-liquid two phase and vapor-liquid-solid three phase were studied. On the basis of detailed study on chaos theory of pressure fluctuation in boiling multi-phase flow, such as statistical analysis, quantitative analysis and qualitative analysis, it is evidence that boiling multi-phase flow system is a deterministic system. In addition to, the prime analysis of temperature signal on vapor-liquid two phase natural circulation flow was carried.
The investigation results show that the pressure fluctuation signal in coarse circulation fluidized bed with big particles had chaos characterization. And the effects of heat flux on power spectrum density function of the pressure fluctuations are stressed study, and the flow regime transitions is correlation to number and frequency of the main peak value of power spectrum density function. The temperature of circulation liquid decreases with liquid viscosity increasing, and the circulation process becomes more steady in the vapor-liquid two-phase natural circulation. The effects of solid holdup on correlation dimension, K entropy and Lyapunov exponent of pressure fluctuation signal are studied in vapor-liquid-solid three phase natural circulation and forced circulation. And flow pattern can be identified by chaos characteristic parameter. By comparing vapor-liquid two-phase with vapor-liquid-solid three phase, the advantage of mixed solid particle in vapor-liquid two phase boiling is that flow process become more steady and flow regime can maintain bubble flow. In different velocity of flow, the fractal dimension of the pressure fluctuation time series in vapor-liquid two-phase forced circulation increased with increase of heat flux. The Kolmogorov entropy and correlation dimension have change with difference of heat flux. A positive, nonfinite estimate of correlation dimension and Kolmogorov entropy provides further evidence that pressure fluctuation signals behave chaotically. It can be concluded that the flow pattern transition on basis of characteristic parameters can be predicted.
引文
[1]黄润生.混沌及其应用.武汉:武汉大学出版社,2000.1
[2]王东生.分形、混沌、分形及其应用.合肥:中国科学技术大学出版社,1995.6
[3]吕金虎,陆君安,陈士华.混沌时间序列分析及其应用.武汉:武汉大学出版社,2002
[4]林瑞泰.沸腾换热.北京:科学出版社,1988
[5]鲁钟琪.两相流与沸腾传热.北京:清华大学出版社,2002.1
[6]李修伦,刘绍丛.汽液固三相流化床沸腾换热的研究.化工学报,1993,44(22),224～229
[7]于志家,慕旭宏.气-液-固三相流载气蒸发传热研究.工程热物理学报,1993,14(3):305～308
[8]于志家,徐维勤,沈自求.垂直套管环隙内气液固三相流动沸腾传热的实验研究.工程热物理学报,1993,18(2):234～237
[9]闻建平.汽液固三相流化床沸腾换热的研究:[硕士学位论文].天津:天津大学,1992
[10]李修伦,闻建平.三相流沸腾传热.高校化学工程学报,1995,23(4):50～54
[11]李修伦,闻建平.垂直管内三相流沸腾传热特性.化学工程,1995,23(4):50～54
[12]张利斌.汽液固三相流化床沸腾换热的研究:[硕士学位论文].天津:天津大学,1996
[13]张利斌,李修伦,张金钟等.三相循环流化床中沸腾传热特性.化工学报,1999,50(2):208～215
[14]吴若琼,湛雪辉,刘金.防止氧化铝厂蒸发器结垢的新方法.中南工业大学学报,1999,30(1):45～48
[15]张少峰.三相循环流化床蒸发器防除垢和强化沸腾传热的研究:[博士学位论文].天津:天津大学,2000
[16] Lee G S, Kim S D.Pressure Fluctuations in Turbulent Fluidized Beds.Chem Eng Jpn, 1988, 21(5): 515～521
[17] Bi H T, Grace J R.Flow Regime Diagrams for Gas-Solid Fluidization and Upward Transport.Int J Multiphase Flow,1995,21(6):1229～1236
[18] Bai D, Shibuya E, Nakagawa N, et al. Characterization of Gas Fluidization Regimes Using Pressure Fluctuations. Powder Technology, 1996, 87: 105～111
[19] Aihua Chen, Hsiaotao T Bi. Pressure Fluctuations and Transition from Bubbling to Turbulent Fluidization. Powder Technology, 2003, 133: 237～246
[20] Ruud van Ommen J, Robert Jan de Korte, Cor M. van den Bleek. Rapid Detection of Defluidization Using the Standard Deviation of Pressure Fluctuations. Chemical Engineering and Processing, 2004, 43: 1329～1335
[21] Svoboda K, Cermak J, Hartman M, et al. Influence of Particle Size on Pressure Fluctuations and Slugging in a Fluidized Bed. AIChE J, 1984, 30(3): 513～517
[22] Xu Jian, Bao Xiaojun, Wei Weisheng. Statistical and Frequency Analysis of Pressure Fluctuations in Spouted Beds. Powder Technology, 2004, 140: 141～154
[23] Svensson A,Johnsson F,Leckner B. Fluidization Regimes in Non-slugging Fluidized Beds the Influence of Pressure Drop across the Air Distributor. Powder Technology, 1996, 86: 299～312
[24] Robert, Brown C, Ethan B. Resolving Dynamical Features of Fluidized Beds from Pressure Fluctuations. Powder Technology, 2001, 119: 68～80
[25] Yerrushalmi J, Cankurt N T.Further Studies of the Regimes of Fluidization. Powder Technology, 1979, 24: 187～205
[26] Schober L, Kantzas A, Hugo R. Pressure Fluctuation Analysis of Laboratory Scale Air/polyethylene Fluidized Beds. Canadian Journal of Chemical Engineering, 2004, 82(2): 227～235
[27]蔡平.鼓泡流态化向湍动过渡的判别.化工学报,1986,4:391～401
[28]陈伯川,张宏建,李海青.流化床内颗粒大小在线检测方法的研究.《第三界全国多相流、非牛顿流、物理化学流学术会议论文集》.杭州:1990.160～161
[29]周章玉,石炎福,余华瑞.由压力波动判断气固流化床中的流化类型.化学反应工程与工艺,1999,15(3):262～267
[30]张健,顾丽莉.气液固三相流中压力波动信号与流型.云南化工,2003,30(1):13～15
[31] Lahey R T. An Application of Fractal and Chaos Theory in the Field of Two-Phase Flow and Heat Transfer. Warme-und Stoffubertragung, 1991, 26
[32] Fan L T,Xu Jian,Wei Weisheng,et al. Proceedings of the Tenth Engineering Foundation Conference on Fluidization. Beijing, 2001, 149～156
[33] Briens C L,Briens L A,Hay J,et al. Hurst’s Analysis to Detect Minimum Fluidization and Gas Distribution in Fluidized Beds. AIChE Journal, 1997, 43(7): 1904～1908
[34] Saether G. ,Bendiksen K. et al. The Fractal Statistics of Liquid Slug Lengths. Int. J. Multiphase Flow, 1990: 16(6)
[35] Ryuji Kikuchi, Atsushi Tsutsumi. Characterization of Nonlinear Nonlinear Dynamics in A CirculatingFluidized Bed by Rescaled Range Analysis and Short-Term Predictability Analysis. Chemical Engineering Science, 2001, 56: 6545～6552
[36]朱兰瑾,林诚.气固喷动床压力波动的Hurst分析.福州大学学报(自然科学版),2003,31(2):247～252
[37]朱兰瑾,林诚.R/S分析法在识别气固喷动床流型中的应用.化工科技,2004,15(5):05～10
[38]吴贤国,黄志尧,冀海峰等.分析技术在气固流态化研究中的应用.石油化工自动化,2000,54(6):54～56
[39]吴贤国,黄志尧,王保良等.分析技术在气固流化床起始流化状态研究中的应用.浙江大学学报,2001,35(3):289～292
[40]孙斌,周云龙.气液两相流压差波动信号的Hurst指数计算与分析.华北电力大学学报,2004,31(5):48～51
[41] Grassberger P, Procaccia I. Estimation of The Kolmogorov Entropy from A Chaotic Signal. Phys Rev, 1983, 28A(4): 25914～2593
[42] W. Liebert. Proper Choice of The Time Delay for the Analysis of Chaotic Time Series. Physics Letters A, 1989, 142(2,3): 107～111
[43] Corana A, Rolando C. An Optimized Direct Algorithm to Estimate the Kolmogorov Entropy from a Time Series. Physics Letter A, 1995, 207: 77～82
[44] Albano A M, Passmante A, Farrell M E. Using Higher-Order Correlations to Define an Embedding Window. Physica, 1991, 54D(1,2): 85～97
[45] Sano M,Sawada Y. Measurement of the Lyapunov Spectrum from a Chaotic Time Series. Phys Rev Lett, 1985, 55(10): 1082～1085
[46] Eckmann J P, Ruelle D. Theory of Chaos and Strange Attractor. Rev Mod Phys, 1985, 57(3): 617～654
[47]孙海云,曹庆杰.相空间重构延迟时间的确定.山东工业大学学报,2000,30(2):107～110
[48]赵贵兵,石炎福.气固流化床压力波动的Lyapunov指数谱研究.高校化学工程学报,2000,14(6):558～562
[49]杨志家,赵光宙.关于关联积分和关联维.浙江大学学报(工学版),2000,34(5):523～526
[50]顾丽莉,石炎福,余华瑞.气-液-固三相流中压力波动信号的分维估算.昆明理工大学学报,27(5):117～120
[51]王安良,杨春信.评价奇怪吸引子分形特征的Grassberger-Procaccia算法.物理学报,2002,51(12):2719～2729
[52]李国辉,周世平,徐得名.时间序列最大Lyapunov指数的计算.应用科学学报,2003,21(20): 127～131
[53] Franca F, Acikgoz M. et al. The Use of Fractal Techniques for Flow Regime Identification. Int. J. Multiphase Flow, 1991, 17(4): 545～552
[54] Schouten J C, Van D B, Cor M. Monitoring the Quality of Fluidization Using the Short-term Predictability of Pressure Fluctuations. AIChE J, 1998, 44(1): 48～60
[55] van den Bleek, Marc-Olivier Coppens, Jaap C. Application of chaos analysis to multiphase reactors. Chemical Engineering Science, 2002, 57: 4763~4778
[56] Hay J M, Nelson B H, Briens C L, et al. The Calculation of the Characteristics of a Chaotic Attractor in a Gas-solid Fluidized flow. Chem Eng Sci, 1995, 50(3): 373～380
[57] Cai Y, Wambsgamss M, Jendrzedjczyk J A. Application of Chaoic Theory in Identification of Two-phase Flow Patterns and Transitions in a Small Horizontal Rectangular Channel. ASME J,1996,118
[58] Langford H M., Beasley D E, Ochterbedk J M. Chaos Analysis of Pressure Signals in Upward Air-water Flows. The 3rd conference on Multiphase Flow, ICMF’98, Lyon, France, 1998
[59] Sadasivan P, Unal C, Nelsen R. Nonlinear Aspects of High Heat Flux Nucleate Boiling Heat Transfer. Journal of Heat Transfer, 1995, 117: 981～989
[60] Shoji M, Kohno T, Negishi N. et al. Chaos of Boiling on a Small-size Heater, ASME-JSME Thermal Joint Conference, Maui, HI
[61] Kozma K, Kok H, Sakurna M. et al. Characterization of Two-phase Flow Using Fractal Analysis of Local Temperature Fluctuations. Int. J. Multiphase Flow, 1996, 22(5)
[62]赵贵兵,石炎福,段文锋等.从混沌时间序列同时计算关联维和Kolmogorov熵.计算物理,16(3):309~315
[63]顾丽莉,杨劲,王力红等.多相反应器中压力波动信号的非线性分析.昆明理工大学学报(理工版),2003,28(2):69~76
[64]顾丽莉.气-液-固三相并流体系的混沌动力学特性研究:[博士学位论文] .成都:四川大学,1999
[65]顾丽莉,石炎福,余华瑞.气-液-固三相并流体系的混沌识别.四川大学学报,2000,32(2): 44～47
[66]顾丽莉,石炎福.混沌理论及其在流态化技术中的应用.云南化工,2002,29(4):24～28
[67]顾丽莉,石炎福,余华瑞.气液两相流中压力波动信号的混沌分析.化学反应工程与工艺,1999, 15(4):428～434
[68]马丽萍,石炎福,黄卫星等.循环流化床压力波动信号的间歇性分析.化工学报,2003,54(5): 619～624
[69]马丽萍,石炎福,余华瑞.含噪声混沌信号的小波去噪方法研究[J].信号处理,2002,18(1):83～87
[70]李晓祥,石炎福,顾丽莉等.气液固三相并流系统流型的混沌识别[J] .高校化学工程学报,2002,16(1):84～88
[71]李晓祥,石炎福,黄卫星等.气固循环流化床颗粒浓度波动信号的预测.过程工程学报,2003,3(1):8～13
[72]陈伯川,黄春燕,甄玲等.气固流化床压力信号时间序列复杂性特征研究.仪器仪表学报,2003,24(3):236～240
[73]黄春燕,陈伯川.复杂性理论在气固流体床流型识别中的运用.仪器仪表学报,2002,23(3):893～896
[74]黄轶伦,陈伯川,郑燕萍等.气固流化床压力脉动信号的混沌特征分析[J].化学反应工程与工艺,16(4)～357～362
[75]郑燕萍,黄轶伦,陈伯川等.利用压力脉动信号特征预测流化床结块故障.高校化学工程学报,2000,14(2):128～133
[76]黄蓓,陈伯川,黄轶伦.算法复杂性在气固流化床动力学中的多尺度分析[J] .化工学报,2002,53(12):1270～1275
[77]陈伯川,黄蓓,黄春燕等.三种复杂性测度在气固流化床压力脉动中的应用.高校化学工程学报,2002,16(8):415～420
[78]刘明言,胡宗定,吴建勇.气-液-固三相磁性流化床混沌特性研究.高校化学工程学报,1999, 13(5):476～479
[79]刘明言,胡宗定.气液固三相流化床流区及其过渡的混沌分析.化学反应工程与工艺,2000,16(4):363～367
[80] Mingyan Liu, Juanping Xue, Aihong Qiang. Chaotic Forecasting of Time Series of Heat-transfer Coefficient for an Evaporator with a Two-phase Flow. Chemical Engineering Science, 2005, 60: 883~895
[81]强爱红,刘明言,孙永利.汽液固三相流动沸腾传热系数的非线性特性分析.化工学报,2005,05:34~40
[82]强爱红.汽液固三相流动沸腾传热系数的非线性特性研究:[硕士学位论文].天津:天津大学,2003
[83]白博峰,郭烈锦,陈学俊等.空气水两相流压力波动现象非线性分析.工程热物理学报,2001,22(3):359～362
[84]白博峰,郭烈锦.油气水多相流压力和压差信号特征分析和流型在线识别.工程热物理学报,2002,23(3):357～360
[85]周云龙,孙斌,陆军.水平管内油气水三相流流型转变的实验研究.热能动力工程,2002,1(1):92～94
[86]李正宇,李青,郭方中.沸腾两相流动中的动力学特征量.热科学与技术,2004,3(1):43~46
[87] Packard N H, Cratchfield J P. et al. Geometry Form a Time Series, Phys. Rev. Lett., 1980, 45: 712~716
[88] Takens F. Detecting Stranger Attractors in Turbulence, Lecture Notes in Math, 1981, 898: 361~381
[89] Ruelle D, Takens F. On the Nature of Turbulence. Commum. Math. Phys. 20(1), 1971
[90] Yong Jun Cho, Sa Jung Kim, Seok Hee Nam, et al. Heat Transfer and Bubble Properties in Three-phase Circulation Fluidized Beds. Chemical Engineering Science, 2001, 56, 6107~6115
[91] Mandelbrot B B, Wallis J R. Robustness of the Rescaled Range R/S in the Measurement of Noncyclic Long Run Statistical Dependence. Water Resources Res, 1969, 595): 967~988
[92] Rosenstein M T, Collins J J and De luca C J. A Practical Method for Calculating Largest Lyapunov Exponents from Small Data Sets, Physica D, 1993, 65: 117~134
[93] Yashima M.Stochastic Modeling of Pressure Fluctuations in a Three-Phase Fluidized Bed.AIChE J,1992,38(4):629～634
[94] Yong Kang, Kwang Jae Woo, Myung Han Ko,et al. Particle Dispersion and Pressure Fluctuations in Three-phase Fluided Beds.Chemical Engineering Science,1997, 52(21) :3723～3732
[95] Corana A, Rolando C. An Optimized Direct Algorithm to Estimate the Kolmogorov Entropy from a Time Series. Physics Letters A, 1995, 207: 77~82
[96] Philippe Faure, Henri Korn. A New Method to Estimate the Kolmogorov Entropy from Recurrence Plots: Its Application to Neuronal Signals. Physica D, 1998, 122: 265~279
[97] Toshiyuki Tanaka, Kazuyuko Aihara, Masao Taki. Analysis of Positive Lyapunov Exponents from Random Time Series. Physica D, 1998, 111:42~50
[98] Schaaf, Filip Johnsson, Jaap C. Schouten. Fourier Analysis of Nonlinear Pressure Fluctuations in Gas-solids Flow in CFB Risers-Observing Solids Structures and Gas/particle Turbulence. Chemical Engineering Science, 1999, 54: 5541~5546
[99] Schaaf, J.R. van Ommen, F. Takens, J. C. Schouten. Similarity between Chaos Analysis and Frequency Analysis of Pressure Fluctuations in Fluidized Beds. Chemical Engineering Science, 2004, 59:1829~1840
[100] Drahos J, Tihon J, Serio C. Deterministic Chaos Analysis of Pressure Fluctuations in a Horizontal Pipe at Intermittent Flow Regime. The Chemical Engineering Journal, 1996, 64: 149~156
[101]马军海.复杂非线性系统的重构技术.天津:天津大学出版社,2005.1
[102]赵贵兵,陈纪忠,阳永荣.流化床压力脉动信号时间延迟相关性.化工学报,2002,53(12):1281～1286
[103]任欧旭.汽液固三相循环流化床中汽泡行为研究:[硕士学位论文] .天津:河北工业大学,2003
[104]刘俊杰.管内液固循环流化床流动特性研究:[硕士学位论文] .天津:河北工业大学,2002
[105]顾丽莉.气-液-固三相并流体系的混沌动力学特性研究:[博士学位论文] .成都:四川大学,1999
[106]谢应齐,曹杰.非线性动力学数学方法.北京:气象出版社,2001.10
[107]徐科军,全书海,王建华.信号出来技术.武汉:武汉理工大学出版社,2001.11
[108]楼顺天,李博菡.基于MATLAB的系统分析与设计.西安:西安电子科技大学出版社,1999
[109]周云龙,孙斌,陈飞.气液两相流型智能识别理论及方法.北京:科学出版社,2007
[110]刘代俊.分形理论在化学工程中的应用.北京:化学工业出版社,2006
[111]王振龙.时间序列分析.北京:中国统计出版社,2000
[112]周云龙,孙斌,李岩等.倾斜下降管内气-液两相流流型PSD特征.热科学与技术,2004,3(2):129～132
[113]关跃波,周云龙,孙斌.垂直上水管内空气-水两相流压差波动信号的Hurst指数分析.东北电力学院学报,2005,25(6):14～17
[114]程景耀,王一平,张金利等.自然循环固相强化沸腾传热的实验研究.化学工业与工程,2002,19(5):369～373
[115]刘晓晶,匡波,陈宏等.两相自然循环非线性特征及实验研究.核动力工程,2006,27(1):91～98
[116]刘明言,胡宗定.气液固三相流化床流区及其过渡的混沌分析.化学反应工程与工艺,2000,
[117]白博峰,郭烈锦,陈学俊.热流密度对汽水两相流压力波动特性的影响.核动力工程,2001,22(1):1～6
[118] DiMarco, P.; Clausse, A.; Lahey Jr. R.T.. Analysis of nonlinear instabilities in boiling systems. Dynamics and Stability of Systems, 1991, 6(3), 191-216
[119] Kozma, R, Kok H, Sakum M.. Characterization of Two-phase Flows Using Fractal Analysis of Local Temperature Fluctuation. International Journal of Multiphase Flow, 1996, 22(5): 953-968
[120] Karve Atul A., Uddin Rizwan, Dorning J J. Stability Analysis of BWR Nuclear-coupled Thermal-hydraulics Using a Simple Model. Nuclear Engineering and Design, 1997, 177(1), 155-177
[121] Lee J D, Pan C, Dynamics of Multiple Parallel Boiling Channel Systems with Forced Flows. Nuclear Engineering Design, 1999, 192(1): 31-44.
[122] Cammarata G, Fichera A, Pagano A. Nonlinear Analysis of a Rectangular Natural Circulation Loop. International Communications in Heat and Mass Transfer, 2000, 27(8), 1077-1089
[123] Robert Z, Wilhemus J M, Investigation the Nonlinear Dynamics of Natural-circulation Boiling Two-phase Flows. Nuclear Technology, 2004, 146(3): 244-256.
[124] Liu Mingyan, Xue Juanping, Qiang Aihong. Chaotic Forecasting of Time Series of Heat-transfer Coefficient for an Evaporator with a Two-phase Flow. Chemical Engineering Science, 2005, 60(3): 883-895.
[125]王海燕,盛昭瀚.混沌时间序列相空间重构参数的选取方法.东南大学学报(自然科学版),2000,30(5):113～117
[126]赵贵兵,李天铎,阳永荣等.气固两相流压力波动信号分析.中国粉体技术,2001,7(3):6～10
[127]赵贵兵,石炎福,官国清等.周期信号对计算流化床动力学重构滞时的影响.化工学报,2000,51(3):331～337
[128]赵贵兵,陈纪忠,阳永荣.流化床压力脉动信号时间延迟相关性.化工学报,2002,53(12):1281～1287
[2]王东生.分形、混沌、分形及其应用.合肥:中国科学技术大学出版社,1995.6
[3]吕金虎,陆君安,陈士华.混沌时间序列分析及其应用.武汉:武汉大学出版社,2002
[4]林瑞泰.沸腾换热.北京:科学出版社,1988
[5]鲁钟琪.两相流与沸腾传热.北京:清华大学出版社,2002.1
[6]李修伦,刘绍丛.汽液固三相流化床沸腾换热的研究.化工学报,1993,44(22),224～229
[7]于志家,慕旭宏.气-液-固三相流载气蒸发传热研究.工程热物理学报,1993,14(3):305～308
[8]于志家,徐维勤,沈自求.垂直套管环隙内气液固三相流动沸腾传热的实验研究.工程热物理学报,1993,18(2):234～237
[9]闻建平.汽液固三相流化床沸腾换热的研究:[硕士学位论文].天津:天津大学,1992
[10]李修伦,闻建平.三相流沸腾传热.高校化学工程学报,1995,23(4):50～54
[11]李修伦,闻建平.垂直管内三相流沸腾传热特性.化学工程,1995,23(4):50～54
[12]张利斌.汽液固三相流化床沸腾换热的研究:[硕士学位论文].天津:天津大学,1996
[13]张利斌,李修伦,张金钟等.三相循环流化床中沸腾传热特性.化工学报,1999,50(2):208～215
[14]吴若琼,湛雪辉,刘金.防止氧化铝厂蒸发器结垢的新方法.中南工业大学学报,1999,30(1):45～48
[15]张少峰.三相循环流化床蒸发器防除垢和强化沸腾传热的研究:[博士学位论文].天津:天津大学,2000
[16] Lee G S, Kim S D.Pressure Fluctuations in Turbulent Fluidized Beds.Chem Eng Jpn, 1988, 21(5): 515～521
[17] Bi H T, Grace J R.Flow Regime Diagrams for Gas-Solid Fluidization and Upward Transport.Int J Multiphase Flow,1995,21(6):1229～1236
[18] Bai D, Shibuya E, Nakagawa N, et al. Characterization of Gas Fluidization Regimes Using Pressure Fluctuations. Powder Technology, 1996, 87: 105～111
[19] Aihua Chen, Hsiaotao T Bi. Pressure Fluctuations and Transition from Bubbling to Turbulent Fluidization. Powder Technology, 2003, 133: 237～246
[20] Ruud van Ommen J, Robert Jan de Korte, Cor M. van den Bleek. Rapid Detection of Defluidization Using the Standard Deviation of Pressure Fluctuations. Chemical Engineering and Processing, 2004, 43: 1329～1335
[21] Svoboda K, Cermak J, Hartman M, et al. Influence of Particle Size on Pressure Fluctuations and Slugging in a Fluidized Bed. AIChE J, 1984, 30(3): 513～517
[22] Xu Jian, Bao Xiaojun, Wei Weisheng. Statistical and Frequency Analysis of Pressure Fluctuations in Spouted Beds. Powder Technology, 2004, 140: 141～154
[23] Svensson A,Johnsson F,Leckner B. Fluidization Regimes in Non-slugging Fluidized Beds the Influence of Pressure Drop across the Air Distributor. Powder Technology, 1996, 86: 299～312
[24] Robert, Brown C, Ethan B. Resolving Dynamical Features of Fluidized Beds from Pressure Fluctuations. Powder Technology, 2001, 119: 68～80
[25] Yerrushalmi J, Cankurt N T.Further Studies of the Regimes of Fluidization. Powder Technology, 1979, 24: 187～205
[26] Schober L, Kantzas A, Hugo R. Pressure Fluctuation Analysis of Laboratory Scale Air/polyethylene Fluidized Beds. Canadian Journal of Chemical Engineering, 2004, 82(2): 227～235
[27]蔡平.鼓泡流态化向湍动过渡的判别.化工学报,1986,4:391～401
[28]陈伯川,张宏建,李海青.流化床内颗粒大小在线检测方法的研究.《第三界全国多相流、非牛顿流、物理化学流学术会议论文集》.杭州:1990.160～161
[29]周章玉,石炎福,余华瑞.由压力波动判断气固流化床中的流化类型.化学反应工程与工艺,1999,15(3):262～267
[30]张健,顾丽莉.气液固三相流中压力波动信号与流型.云南化工,2003,30(1):13～15
[31] Lahey R T. An Application of Fractal and Chaos Theory in the Field of Two-Phase Flow and Heat Transfer. Warme-und Stoffubertragung, 1991, 26
[32] Fan L T,Xu Jian,Wei Weisheng,et al. Proceedings of the Tenth Engineering Foundation Conference on Fluidization. Beijing, 2001, 149～156
[33] Briens C L,Briens L A,Hay J,et al. Hurst’s Analysis to Detect Minimum Fluidization and Gas Distribution in Fluidized Beds. AIChE Journal, 1997, 43(7): 1904～1908
[34] Saether G. ,Bendiksen K. et al. The Fractal Statistics of Liquid Slug Lengths. Int. J. Multiphase Flow, 1990: 16(6)
[35] Ryuji Kikuchi, Atsushi Tsutsumi. Characterization of Nonlinear Nonlinear Dynamics in A CirculatingFluidized Bed by Rescaled Range Analysis and Short-Term Predictability Analysis. Chemical Engineering Science, 2001, 56: 6545～6552
[36]朱兰瑾,林诚.气固喷动床压力波动的Hurst分析.福州大学学报(自然科学版),2003,31(2):247～252
[37]朱兰瑾,林诚.R/S分析法在识别气固喷动床流型中的应用.化工科技,2004,15(5):05～10
[38]吴贤国,黄志尧,冀海峰等.分析技术在气固流态化研究中的应用.石油化工自动化,2000,54(6):54～56
[39]吴贤国,黄志尧,王保良等.分析技术在气固流化床起始流化状态研究中的应用.浙江大学学报,2001,35(3):289～292
[40]孙斌,周云龙.气液两相流压差波动信号的Hurst指数计算与分析.华北电力大学学报,2004,31(5):48～51
[41] Grassberger P, Procaccia I. Estimation of The Kolmogorov Entropy from A Chaotic Signal. Phys Rev, 1983, 28A(4): 25914～2593
[42] W. Liebert. Proper Choice of The Time Delay for the Analysis of Chaotic Time Series. Physics Letters A, 1989, 142(2,3): 107～111
[43] Corana A, Rolando C. An Optimized Direct Algorithm to Estimate the Kolmogorov Entropy from a Time Series. Physics Letter A, 1995, 207: 77～82
[44] Albano A M, Passmante A, Farrell M E. Using Higher-Order Correlations to Define an Embedding Window. Physica, 1991, 54D(1,2): 85～97
[45] Sano M,Sawada Y. Measurement of the Lyapunov Spectrum from a Chaotic Time Series. Phys Rev Lett, 1985, 55(10): 1082～1085
[46] Eckmann J P, Ruelle D. Theory of Chaos and Strange Attractor. Rev Mod Phys, 1985, 57(3): 617～654
[47]孙海云,曹庆杰.相空间重构延迟时间的确定.山东工业大学学报,2000,30(2):107～110
[48]赵贵兵,石炎福.气固流化床压力波动的Lyapunov指数谱研究.高校化学工程学报,2000,14(6):558～562
[49]杨志家,赵光宙.关于关联积分和关联维.浙江大学学报(工学版),2000,34(5):523～526
[50]顾丽莉,石炎福,余华瑞.气-液-固三相流中压力波动信号的分维估算.昆明理工大学学报,27(5):117～120
[51]王安良,杨春信.评价奇怪吸引子分形特征的Grassberger-Procaccia算法.物理学报,2002,51(12):2719～2729
[52]李国辉,周世平,徐得名.时间序列最大Lyapunov指数的计算.应用科学学报,2003,21(20): 127～131
[53] Franca F, Acikgoz M. et al. The Use of Fractal Techniques for Flow Regime Identification. Int. J. Multiphase Flow, 1991, 17(4): 545～552
[54] Schouten J C, Van D B, Cor M. Monitoring the Quality of Fluidization Using the Short-term Predictability of Pressure Fluctuations. AIChE J, 1998, 44(1): 48～60
[55] van den Bleek, Marc-Olivier Coppens, Jaap C. Application of chaos analysis to multiphase reactors. Chemical Engineering Science, 2002, 57: 4763~4778
[56] Hay J M, Nelson B H, Briens C L, et al. The Calculation of the Characteristics of a Chaotic Attractor in a Gas-solid Fluidized flow. Chem Eng Sci, 1995, 50(3): 373～380
[57] Cai Y, Wambsgamss M, Jendrzedjczyk J A. Application of Chaoic Theory in Identification of Two-phase Flow Patterns and Transitions in a Small Horizontal Rectangular Channel. ASME J,1996,118
[58] Langford H M., Beasley D E, Ochterbedk J M. Chaos Analysis of Pressure Signals in Upward Air-water Flows. The 3rd conference on Multiphase Flow, ICMF’98, Lyon, France, 1998
[59] Sadasivan P, Unal C, Nelsen R. Nonlinear Aspects of High Heat Flux Nucleate Boiling Heat Transfer. Journal of Heat Transfer, 1995, 117: 981～989
[60] Shoji M, Kohno T, Negishi N. et al. Chaos of Boiling on a Small-size Heater, ASME-JSME Thermal Joint Conference, Maui, HI
[61] Kozma K, Kok H, Sakurna M. et al. Characterization of Two-phase Flow Using Fractal Analysis of Local Temperature Fluctuations. Int. J. Multiphase Flow, 1996, 22(5)
[62]赵贵兵,石炎福,段文锋等.从混沌时间序列同时计算关联维和Kolmogorov熵.计算物理,16(3):309~315
[63]顾丽莉,杨劲,王力红等.多相反应器中压力波动信号的非线性分析.昆明理工大学学报(理工版),2003,28(2):69~76
[64]顾丽莉.气-液-固三相并流体系的混沌动力学特性研究:[博士学位论文] .成都:四川大学,1999
[65]顾丽莉,石炎福,余华瑞.气-液-固三相并流体系的混沌识别.四川大学学报,2000,32(2): 44～47
[66]顾丽莉,石炎福.混沌理论及其在流态化技术中的应用.云南化工,2002,29(4):24～28
[67]顾丽莉,石炎福,余华瑞.气液两相流中压力波动信号的混沌分析.化学反应工程与工艺,1999, 15(4):428～434
[68]马丽萍,石炎福,黄卫星等.循环流化床压力波动信号的间歇性分析.化工学报,2003,54(5): 619～624
[69]马丽萍,石炎福,余华瑞.含噪声混沌信号的小波去噪方法研究[J].信号处理,2002,18(1):83～87
[70]李晓祥,石炎福,顾丽莉等.气液固三相并流系统流型的混沌识别[J] .高校化学工程学报,2002,16(1):84～88
[71]李晓祥,石炎福,黄卫星等.气固循环流化床颗粒浓度波动信号的预测.过程工程学报,2003,3(1):8～13
[72]陈伯川,黄春燕,甄玲等.气固流化床压力信号时间序列复杂性特征研究.仪器仪表学报,2003,24(3):236～240
[73]黄春燕,陈伯川.复杂性理论在气固流体床流型识别中的运用.仪器仪表学报,2002,23(3):893～896
[74]黄轶伦,陈伯川,郑燕萍等.气固流化床压力脉动信号的混沌特征分析[J].化学反应工程与工艺,16(4)～357～362
[75]郑燕萍,黄轶伦,陈伯川等.利用压力脉动信号特征预测流化床结块故障.高校化学工程学报,2000,14(2):128～133
[76]黄蓓,陈伯川,黄轶伦.算法复杂性在气固流化床动力学中的多尺度分析[J] .化工学报,2002,53(12):1270～1275
[77]陈伯川,黄蓓,黄春燕等.三种复杂性测度在气固流化床压力脉动中的应用.高校化学工程学报,2002,16(8):415～420
[78]刘明言,胡宗定,吴建勇.气-液-固三相磁性流化床混沌特性研究.高校化学工程学报,1999, 13(5):476～479
[79]刘明言,胡宗定.气液固三相流化床流区及其过渡的混沌分析.化学反应工程与工艺,2000,16(4):363～367
[80] Mingyan Liu, Juanping Xue, Aihong Qiang. Chaotic Forecasting of Time Series of Heat-transfer Coefficient for an Evaporator with a Two-phase Flow. Chemical Engineering Science, 2005, 60: 883~895
[81]强爱红,刘明言,孙永利.汽液固三相流动沸腾传热系数的非线性特性分析.化工学报,2005,05:34~40
[82]强爱红.汽液固三相流动沸腾传热系数的非线性特性研究:[硕士学位论文].天津:天津大学,2003
[83]白博峰,郭烈锦,陈学俊等.空气水两相流压力波动现象非线性分析.工程热物理学报,2001,22(3):359～362
[84]白博峰,郭烈锦.油气水多相流压力和压差信号特征分析和流型在线识别.工程热物理学报,2002,23(3):357～360
[85]周云龙,孙斌,陆军.水平管内油气水三相流流型转变的实验研究.热能动力工程,2002,1(1):92～94
[86]李正宇,李青,郭方中.沸腾两相流动中的动力学特征量.热科学与技术,2004,3(1):43~46
[87] Packard N H, Cratchfield J P. et al. Geometry Form a Time Series, Phys. Rev. Lett., 1980, 45: 712~716
[88] Takens F. Detecting Stranger Attractors in Turbulence, Lecture Notes in Math, 1981, 898: 361~381
[89] Ruelle D, Takens F. On the Nature of Turbulence. Commum. Math. Phys. 20(1), 1971
[90] Yong Jun Cho, Sa Jung Kim, Seok Hee Nam, et al. Heat Transfer and Bubble Properties in Three-phase Circulation Fluidized Beds. Chemical Engineering Science, 2001, 56, 6107~6115
[91] Mandelbrot B B, Wallis J R. Robustness of the Rescaled Range R/S in the Measurement of Noncyclic Long Run Statistical Dependence. Water Resources Res, 1969, 595): 967~988
[92] Rosenstein M T, Collins J J and De luca C J. A Practical Method for Calculating Largest Lyapunov Exponents from Small Data Sets, Physica D, 1993, 65: 117~134
[93] Yashima M.Stochastic Modeling of Pressure Fluctuations in a Three-Phase Fluidized Bed.AIChE J,1992,38(4):629～634
[94] Yong Kang, Kwang Jae Woo, Myung Han Ko,et al. Particle Dispersion and Pressure Fluctuations in Three-phase Fluided Beds.Chemical Engineering Science,1997, 52(21) :3723～3732
[95] Corana A, Rolando C. An Optimized Direct Algorithm to Estimate the Kolmogorov Entropy from a Time Series. Physics Letters A, 1995, 207: 77~82
[96] Philippe Faure, Henri Korn. A New Method to Estimate the Kolmogorov Entropy from Recurrence Plots: Its Application to Neuronal Signals. Physica D, 1998, 122: 265~279
[97] Toshiyuki Tanaka, Kazuyuko Aihara, Masao Taki. Analysis of Positive Lyapunov Exponents from Random Time Series. Physica D, 1998, 111:42~50
[98] Schaaf, Filip Johnsson, Jaap C. Schouten. Fourier Analysis of Nonlinear Pressure Fluctuations in Gas-solids Flow in CFB Risers-Observing Solids Structures and Gas/particle Turbulence. Chemical Engineering Science, 1999, 54: 5541~5546
[99] Schaaf, J.R. van Ommen, F. Takens, J. C. Schouten. Similarity between Chaos Analysis and Frequency Analysis of Pressure Fluctuations in Fluidized Beds. Chemical Engineering Science, 2004, 59:1829~1840
[100] Drahos J, Tihon J, Serio C. Deterministic Chaos Analysis of Pressure Fluctuations in a Horizontal Pipe at Intermittent Flow Regime. The Chemical Engineering Journal, 1996, 64: 149~156
[101]马军海.复杂非线性系统的重构技术.天津:天津大学出版社,2005.1
[102]赵贵兵,陈纪忠,阳永荣.流化床压力脉动信号时间延迟相关性.化工学报,2002,53(12):1281～1286
[103]任欧旭.汽液固三相循环流化床中汽泡行为研究:[硕士学位论文] .天津:河北工业大学,2003
[104]刘俊杰.管内液固循环流化床流动特性研究:[硕士学位论文] .天津:河北工业大学,2002
[105]顾丽莉.气-液-固三相并流体系的混沌动力学特性研究:[博士学位论文] .成都:四川大学,1999
[106]谢应齐,曹杰.非线性动力学数学方法.北京:气象出版社,2001.10
[107]徐科军,全书海,王建华.信号出来技术.武汉:武汉理工大学出版社,2001.11
[108]楼顺天,李博菡.基于MATLAB的系统分析与设计.西安:西安电子科技大学出版社,1999
[109]周云龙,孙斌,陈飞.气液两相流型智能识别理论及方法.北京:科学出版社,2007
[110]刘代俊.分形理论在化学工程中的应用.北京:化学工业出版社,2006
[111]王振龙.时间序列分析.北京:中国统计出版社,2000
[112]周云龙,孙斌,李岩等.倾斜下降管内气-液两相流流型PSD特征.热科学与技术,2004,3(2):129～132
[113]关跃波,周云龙,孙斌.垂直上水管内空气-水两相流压差波动信号的Hurst指数分析.东北电力学院学报,2005,25(6):14～17
[114]程景耀,王一平,张金利等.自然循环固相强化沸腾传热的实验研究.化学工业与工程,2002,19(5):369～373
[115]刘晓晶,匡波,陈宏等.两相自然循环非线性特征及实验研究.核动力工程,2006,27(1):91～98
[116]刘明言,胡宗定.气液固三相流化床流区及其过渡的混沌分析.化学反应工程与工艺,2000,
[117]白博峰,郭烈锦,陈学俊.热流密度对汽水两相流压力波动特性的影响.核动力工程,2001,22(1):1～6
[118] DiMarco, P.; Clausse, A.; Lahey Jr. R.T.. Analysis of nonlinear instabilities in boiling systems. Dynamics and Stability of Systems, 1991, 6(3), 191-216
[119] Kozma, R, Kok H, Sakum M.. Characterization of Two-phase Flows Using Fractal Analysis of Local Temperature Fluctuation. International Journal of Multiphase Flow, 1996, 22(5): 953-968
[120] Karve Atul A., Uddin Rizwan, Dorning J J. Stability Analysis of BWR Nuclear-coupled Thermal-hydraulics Using a Simple Model. Nuclear Engineering and Design, 1997, 177(1), 155-177
[121] Lee J D, Pan C, Dynamics of Multiple Parallel Boiling Channel Systems with Forced Flows. Nuclear Engineering Design, 1999, 192(1): 31-44.
[122] Cammarata G, Fichera A, Pagano A. Nonlinear Analysis of a Rectangular Natural Circulation Loop. International Communications in Heat and Mass Transfer, 2000, 27(8), 1077-1089
[123] Robert Z, Wilhemus J M, Investigation the Nonlinear Dynamics of Natural-circulation Boiling Two-phase Flows. Nuclear Technology, 2004, 146(3): 244-256.
[124] Liu Mingyan, Xue Juanping, Qiang Aihong. Chaotic Forecasting of Time Series of Heat-transfer Coefficient for an Evaporator with a Two-phase Flow. Chemical Engineering Science, 2005, 60(3): 883-895.
[125]王海燕,盛昭瀚.混沌时间序列相空间重构参数的选取方法.东南大学学报(自然科学版),2000,30(5):113～117
[126]赵贵兵,李天铎,阳永荣等.气固两相流压力波动信号分析.中国粉体技术,2001,7(3):6～10
[127]赵贵兵,石炎福,官国清等.周期信号对计算流化床动力学重构滞时的影响.化工学报,2000,51(3):331～337
[128]赵贵兵,陈纪忠,阳永荣.流化床压力脉动信号时间延迟相关性.化工学报,2002,53(12):1281～1287