Hydrodynamic Similarity of Riser Flow in a Dense Transport Bed

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1 Hydrodynamic Similarity of Riser Flow in a Dense Transport Bed Kai ZHAO 1,,, Shaojun YANG,, Xian X, and Yunhan XIAO, 1 niversity of Chinese Academy of Sciences, Beijin 19, China Key Laboratory of Advanced Enery and Power, Institute of Enineerin Thermophysics, Chinese Academy of Sciences, Beijin 119, China Research Center for Clean Enery and Power, Chinese Academy of Sciences, Lianyunan, Jiansu 69, China Abstract Pressurized dense transport bed is a new coal asification technoloy under development. It is necessary to carry out study of hydrodynamic similarity of the as solids flow to provide basis and reference for reactor desin and scale-up. Literature research on hydrodynamic similarity have been mostly directed to bubblin fluidization and fast fluidization, while as solids flow in dense transport bed riser correspond to dense suspension upflow, which has sinificant differences from fast fluidization in characteristics of distribution of solids concentration and solids velocity. In this study, we analyzed characteristics of hydrodynamic similarity of dense suspension upflow, and obtained correspondin dimensionless parameters. Keywords-dense transport bed, hydrodynamic similarity, dense suspension upflow I. INTRODCTION Pressurized dense transport bed coal asification technoloy is an important technoloy for the development of IGCC, which is characterized by hih solids flux and hih solids concentration in the riser. [1] It is necessary to carry out study of hydrodynamic similarity of the as solids flow to provide basis and reference for reactor desin and scale-up. Glicksman [] proposed full-set of hydrodynamic dimensionless parameters based on dimensionless momentum equations of as solids flow. Further, Glicksman et al. [] and Glicksman et al. [] advanced simplified-set and viscous-limit set of hydrodynamic dimensionless parameters respectively. Horio et al. [5] proposed hydrodynamic dimensionless parameters for bubblin fluidization based on emperical correlation and Horio et al. [6] used hydrodynamic model to develop dimensionless parameters for fast fluidization. Patience et al. [7] and Qi et al. [] investiated hydrodynamic similarities of as solids flow in fully development reion in risers. However, literature research on hydrodynamic similarity have been mostly directed to bubblin fluidization and fast fluidization, while as solids flow in dense transport bed riser correspond to dense suspension upflow, which is characterized by net upward solids flux at each radial position of the riser. There are sinificant differences between dense suspension upflow and fast fluidization in characteristics of distribution of solids concentration and solids velocity [9]. In this study, we analyze characteristics of hydrodynamic similarity of dense suspension upflow, and obtain correspondin dimensionless parameters. II. DIMENSIONLESS ANALYSIS Reference concerned on hydrodynamic similarity of as solids flow in risers are listed in Table I., in which mf is the minimum fluidization velocity, t is sinle particle terminal velocity, and BG represents bed eometry. Glicksman [] proposed full-set of hydrodynamic dimensionless parameters based on dimensionless momentum equations of as solids flow, which can be applied to all flow reimes theoretically. If we make two hydrodynamic dimensionless parameters equivalent, their combinations should also be consistent in value, such as the combination of Renolds number and Froude number can be obtained: D r Dr (1) D v r whrer ν is dynamic viscosity of fluid. It is to say that the unit size of scale model is uniquely determined by the dynamic viscosity of fluid, when the fluidization medium is selected, the size of scale model unit will be uniquely determined, which will brin difficulties in practical applications. We will not be able to carry out scale model experiments under this circumstances without chanin fludization medium. To avoid this difficulty, Glicksman et al. [] make approximations for the interphase momentum transfer coefficient β between as and solids phase in momentum equations, formin simplified-set of hydrodynamic dimensionless parameters. In addition, Glicksman et al. [] show that for as solids flow in the visous control reion, such as bubblin fluidization and sluin fluidization, it is just required to meet the viscous-limit set of dimensionless parameters, which are listed in Table I, hydrodynamic similarity can be achieved. Horio et al. [5] obtained hydrodynamic dimensionless parameters for bubblin fluidization based on empirical relationship used for calculatin bubble rise velocity. Horio et al. [6] proposed hydrodynamic similarity parameters for fast fluidization from their core-annular model. Glicksman et al. [11] show that, viscous-limit set of hydrodynamic dimensionless parameters DOI 1.51/IJSSST.a ISSN: 17-x online, 17-1 print

2 is equivalent to Horio et al. [5], and simplified set of hydrodynamic dimensionless parameters is equivalent to Horio et al. [6]. Patience et al. [7] show that slip factor in fully development reion of fast fluidization is a function of D and. In addition, Qi et al.[] proposed that the r t apparent solids concentration and the radial distribution of local solid concentration show similariry as dimensionless.6 G s parameter remains unchaned in fully s D r development reion of fast fluidization. TABLE I. DIMENSIONLESS PARAMETERS IN REFERENCES Reference Glicksman [] Glicksman et al. [] Chan and Loue [1] Horio et al. [5] Glicksman [] Horio et al. [6] Dimensionless parameters /(ρ s ), d s /D r, /(D r ), ρ s /ρ, ρ d s /μ, Φ, BG /(ρ s ), / mf, /(D r ), ρ s /ρ, Φ, BG /(ρ s ), Φd s /D r, /(D r ), ρ s /ρ, ρ Φd s /μ, BG ( - mf ) /(D r ), mf /(D r ), Φ, BG / mf, /(D r ), Φ, BG /(ρ s ), / t, /(D r ), ρ s /ρ, Φ, BG Patience et al. [7] / t, /(D r ) Qi et al. [] -.6 (D r ). /(ρ s ) As discussed above, literature mainly investiated hydrodynamic similarity of bubblin fluidization and fast fluidization, while lack of analysis of hydrodynamic dimensionless parameters of dense suspension upflow. On the other hand, accordin to van der Meer et al. [1] and Liu et al. [1], there are eiht independent parameters without considerration of stresses of solids phase: s,, s,, Dr, ds,, () which has three demensions as time (T), lenth (L) and mass (M). Accordin to Buckinham π theory,it should be five qualitative dimensionless parameters. As a dependent variable, solids concentration can be expressed as a function of this dimensionless parameters. Dimensions of eiht M M L L M L independent parameters are LL L, L, T, T,,, LT, T. There are three independent parameters which are in same demension, results in three qualitative dimensionless s s Dr parameters,,. Another two qualitative ds dimensionless parameters can be obtained by means of undetermined coefficients. Accordin to demension equation as below: a b d e L M c M L MLT L () T L LT T make three demensions all equal to zero, we can obtain: b-a c d -b () b- a e by rearranin () and (), two qualitative dimensionless parameters can be expressed as: ab b L M L L MLT T L T (5) L M L T LT which are forms of Froude number and Renolds number. Archimedes number can be obtained by combinations of Froude number, Renolds number and density ratio of solids and as, as: s ds d s Gs D r f,,,, (6) s ds Dr In addition, hydrodynamiv similarity should be based on similarity of bed eometry (BG). So hydrodynamic similarity may be achieved by makin dimensionless parameters equivalent in value: s ds d,,,,,, BG (7) s Gs Dr s ds Dr To achieve hydrodynamic similarity of as solids flow in risers, it should also ensure that the initial and boundary conditions of momentum equations are in similar. Achievin hydrodynamic similarity completely is very difficult in practice, and even impossible under many circumstances. In applications, it is more concerned with characteristics of as solids flow in fully development reion, for which similarity of bed eometry just require same cross-sectional shape (CSS). In addition, it is difficult to ensure the scale model and actual device has same diameter ratio (D r /d s ). This is because under many circumstances it is difficult to obtain particles which meet the diameter ratio with riser columns. On the other hand, if holdin the same diameter ratio D r/d s, it is likely to cause chanes in fludization characteristics of particles (such as requirin Geldart B particles in actual device, whereas Geldart A particles usin in scale model) [1, 15]. To overcome these difficulties, researchers enerally use a simplified form of hydrodynamic dimensionless parameters, with inorin diameter ratio D r /d s and usin / mf or / t or replace Archimedes number or Renolds number. In addition, it may result in different flow reimes between actual device and scale model by keepin the same Froude number (such as as solids flow correspond to fast fluidization in actual device, while under turbulent fluidization in scale model). Accordin to Qi et al. [], apparent solids concentration and the radial distribution of local solid concentration show s DOI 1.51/IJSSST.a ISSN: 17-x online, 17-1 print

3 .6 G s similariry as dimensionless parameter s D r remains unchaned in fully development reion of fast fluidization. Patience and Bockrath [, 17] show that.5 G s is a critical parameter in determinin s D r apparent solids concerntration under hih solids ciuculation rate conditions. The experimental results of Yan and Zhu [1] and Knowlton et al. [1] show that, for opratin conditions of which superficial as velocity is reater than. m/s and solids circulation rate is reater than 5 k/(m s), small diameter risers do not exhibit wall effect due to the shear stress resultin in increases of solids concentration, while lareer diameter risers have reater solids concentration since the radial diatributions of as velocity are more nonuniform. It is reasoned that some dimensionless parameter combinated by superficial velocity ratio of as and s solids V with Froude number can be a hydrodynamic similarity parameter for dense suspension upflow. As discussed above, hydrodynamic similarity of dense suspension upflow may be determined by dimensionless parameters as: f Ar, V Fr, s (9) Wherein, f is a coefficient obtained from experiments. III. RESLTS AND DISCSSION Q, V Fr -1. k m s -1 m h E E- Q, V Fr -1. k m s -1 m h E- 6.E- A. Experimental method Riser of experimental apparatus is.1 m in diameter and 1. m in heiht. Sand particles are used as experimental material, and particle properties are as shown in Table II, which are Geldart B particles. Apparent solids concentration was calculated by pressure drop measurement, while an optic fiber probe was used to measure local solids velocity. Details of experimental apparatus and experimental procedure are discribed in [19]. TABLE II. PARTICLE PROPERTIES ρs, k/m ds, mm ρb, k/m Sand I Sand II Sand III B. Axial profile of apparent solids concerntration Axial profiles of apparent solids concentration of Sand I and Sand II are plotted in Fi. 1 and Fi. respectively. Superficial as velocity and solids circulation rate under correspondin operatin conditions of Sand I and Sand II are all different, but when dimensionless parameter V Fr -1. meet similar values, axial profiles of apparent solids concentration (i.e. dimensionless pressure drop) are consistent with each other, which means as solids flow achieve hydrodynamic similarity. Q, V Fr -1. k m s -1 m h E E E- Q, V Fr -1. k m s -1 m h E E Fiure 1. Axial profile of apparent solids concerntration of Sand I Fiure. Axial profile of apparent solids concerntration of Sand II Table III lists two opratin conditions of Sand I and Sand III under different temperature and pressure, wherein dimensionless particle diameter d s * is equivalent to 1/ power of Archimedes number. Fi. shows axial profiles of apparent solids concentration of Sand I and Sand III under above operatin conditions. As seen in Fi., althouh properties of as and solids, superficial as velocity and solids circulation rate varies for two opratin conditions of Sand I and Sand III, they have similar values of dimensionless particle diameter and V Fr -1.. Axial profiles of apparent solids concentration (i.e. dimensionless pressure drop) are also consistent with DOI 1.51/IJSSST.a ISSN: 17-x online, 17-1 print

4 each other, which means as solids flow achieve hydrodynamic similarity. TABLE III. OPERATING CONDITIONS NDER DIFFERENT TEMPERATRE AND PRESSRE Tr, K Pr, MPa ds, mm ρs, k/m Gs, k/(m s) ds * V Fr Sand I Sand III Q P r T r k m s -1 m h -1 MPa K different, values of dimensionless parameter V Fr -1. are similar under two opratin conditions. Raidial profile of dimensionless solids velocity express similar form, suestin as solids flow achieve hydrodynamic similarity Fiure. Axial profile of apparent solids concerntration of different particles under different temperature and pressure. u s / p V Fr -1. k m s -1 m s E- 95..E r/r Fiure. Radial profile of dimensionless solids velocity of Sand II. C. Raidial profile of dimensionless solids velocity Local solids velocity can be dimensionlessed by superficial solids velocity. Fi. shows radial profiles of dimensionless solids of Sand II in fully development reion. While superficial as velocity and solids circulation rate are IV. CONCLSION Pressurized dense transport bed is a new coal asification technoloy under development. It is necessary to carry out study of hydrodynamic similarity of the as solids flow to provide basis and reference for reactor desin and scale-up. Literature research on hydrodynamic similarity have been mostly directed to bubblin fluidization and fast fluidization, while as solids flow in dense transport bed riser correspond to dense suspension upflow, which has sinificant differences from fast fluidization in characteristics of distribution of solids concentration and solids velocity. Based on Buckinham π theory and emperical correlations in literatures, we obtained hydrodynamic dimensionless parameters applied for dense suspension upflow. Experimental results show that, when dimensionless particle diameter and dimensionless parameter V Fr -1. are in same or similar values, axial profile of apparent solids concerntration and raidial profile of dimensionless solids velocity of different particles show consistent with each other, which suest as solids flow achieve hydrodynamic similarity. ACKNOWLEDGEMENT Supported by Strateic Priority Research Proram of Chinese Academy of Sciences (XDA755). REFERENCES [1] Bi, X.T. and X. Liu, Hih density and hih solids flux CFB risers for steam asification of solids fuels. Fuel Processin Technoloy, 1. 91(): p [] Glicksman, L.R., Scalin relationships for fluidized beds. Chemical Enineerin Science, 19. 9(9): p [] Glicksman, L.R., M. Hyre and K. Woloshun, Simplified scalin relationships for fluidized beds. Powder Technoloy, (): p [] Glicksman, L.R., Scalin relationships for fluidized beds. Chemical enineerin Science, 19. (6): p [5] Horio, M., A. Nonaka, Y. Sawa, and I. Muchi, A New Similarity Rule for Fluidized-Bed Scale-up. AIChE Journal, 196. (9): p [6] Horio, M., H. Ishii, Y. Kobukai, and N. Yamanishi, A Scalin Law for Circulatin Fluidized Beds. Journal of Chemical Enineerin of Japan, DOI 1.51/IJSSST.a ISSN: 17-x online, 17-1 print

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