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Numerical simulation of gas liquid dynamics in cylindrical b.pdf

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*Corresponding author. Chemical Engineering Science 54 (1999) 5071}5083 Numerical simulation of gas}liquid dynamics in cylindrical bubble column reactors Jayanta Sanyal*, Sergio VaH squez, Shantanu Roy, M. P. Dudukovic Fluent Inc., Lebanon, NH 03766-1442, USA Chemical Reaction Engineering Laboratory, Department of Chemical Engineering, Washington University, St. Louis, MO 63130, USA Abstract In this paper, we have attempted to validate a transient, two-dimensional axisymmetric simu
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  * Corresponding author.Chemical Engineering Science 54 (1999) 5071 } 5083 Numerical simulation of gas } liquid dynamics in cylindrical bubblecolumn reactors Jayanta Sanyal   * , Sergio Va  H squez  , Shantanu Roy  , M. P. Dudukovic    Fluent Inc., Lebanon, NH 03766-1442, USA  Chemical Reaction Engineering Laboratory, Department of Chemical Engineering, Washington Uni v ersity, St. Louis, MO 63130, USA Abstract In this paper, we have attempted to validate a transient, two-dimensional axisymmetric simulation of a laboratory-scale cylindricalbubble column, run under bubbly  # ow and churn turbulent conditions. The experimental data was obtained via gamma-radiationbased non-invasive  # ow monitoring methods, viz., computer automated radioactive particle tracking (CARPT) provided the data onliquid velocity and turbulence, and computed tomography (CT) determined the gas holdup pro les. The numerical simulation wasdone using the FLUENT software and compares the results from the algebraic slip mixture model, and the two- # uid Euler } Eulermodel. Reasonably, good quantitative agreement was obtained between the experimental data and simulations for the time-averagedgas holdup and axial liquid velocity pro les, as well as for the kinetic energy pro les. The favorable results suggest that the simpletwo-dimensional axisymmetric simulation can be used for reasonable engineering calculations of the overall  # ow pattern and gasholdup distributions.    1999 Elsevier Science Ltd. All rights reserved.  Keywords:  Bubble columns; Axisymmetric simulation; FLUENT; Euler } Euler model; Algebraic slip mixture model 1. Introduction Bubble columns are contactors in which a discontinu-ous gas phase in the form of bubblesmoves relativeto thecontinuous liquid phase. As reactors, they are used ina variety of chemical processes, such as Fischer } Tropschsynthesis (Kolbel & Ralek, 1980; Srivastava, Rao,Cinquegrane & Stiegel, 1990), manufacture of    ne chem-icals (Smidt, Hafner, Jira, Seiber, Sedimeier & Sabel,1962), oxidation reactions (Hagberg & Krupa, 1976; Sit-tig, 1967), alkylation reactions (Gehlawat & Sharma,1970), e % uent treatment (Takahashi, Miyahara& Nishizaki, 1979), coal liquefaction (Shah, 1981), fer-mentation reactions, and more recently, in cell cultures(Katinger, Scheirer, & Kromer, 1979) and production of single cell proteins (Rosenzweig & Ushio, 1974). Theprincipal advantages of bubble columns are the absenceof moving parts, leading to easier maintenance, highinterfacial areas and transport rates between the gas andliquid phases, good heat transfer characteristics, andlarge liquid holdup which is favorable for slow liquid-phase reactions (Shah, Kelkar, Godbole & Deckwer,1982). Operation of bubble columns as reactors is a !  ec-ted by global operating parameters like gas-phase super- cial velocity (the liquid being processed as a batch inmany commercial applications), operating pressure andtemperature, and the liquid height. The actual variablesthat in # uence bubble column performance as reactorsare gas holdup distribution, extent of liquid-phase back-mixing, gas } liquid interfacial area, gas } liquid mass andheat transfer coe $ cients, bubble-size distributions,bubble coalescence and redispersion rates, and bubblerise velocities. In industrial operation, the complex two-phase  # ow and turbulence determines the transient andtime-averaged values of the above variables. The lack of complete understanding of the  # uid dynamics makes itdi $ cult to improve the performance of a bubble columnreactor by judicious selection and control of the operat-ing parameters.The need to establish a rational basis for the inter-pretationofthe interactionof  # uid dynamic variableshasbeen the primary motivation for active research in thearea of bubble column modeling based on computational # uid dynamics (CFD) tools in the last decade (Kuipers& van Swaaij, 1998). Various approaches have beensuggestedforsolving thesame fundamental # ow problemand modeling may be attempted at various levels 0009-2509/99/$-see front matter    1999 Elsevier Science Ltd. All rights reserved.PII: S0 0 09 -2 5 0 9 (9 9 ) 0 0 2 35 - 3  of sophistication. One may choose to treat both thedispersed and continuous phases as interpenetratingpseudo-continua (viz., the Euler } Euler approach, e.g.Sokolichin & Eigenberger, 1994; Becker, Sokolichin& Eigenberger, 1994; Ranade, 1992, 1995, 1997) or thedispersed phase as discrete entities (viz., the Euler } Lag-range approach: e.g. Lapin & Lubbert, 1994; De-vanathan, Dudukovic, Lapin & Lubbert, 1995; Delnoij,Lammers, Kuipers & van Swaaij, 1997a; Delnoij,Kuipers & van Swaaij, 1997b,c). The simulation may bedone fully transient (e.g. Becker, Sokolichin & Eigenber-ger, 1994) or only for the steady-state time-averagedresults (e.g. Torvik & Svendsen, 1990; Svendsen, Jakob-sen & Torvik, 1992; Jakobsen, Svendsen & Hjarbo, 1993,Ranade, 1997). An appropriate mesh and a robust nu-merical solver are crucial for getting accurate solutions(e.g., Sokolichin, Eigenberger, Lapin & Lubbert, 1997).Fundamental modeling of the   ne-scale phenomenaneeded to predict the  # ow pattern at the global scale isalso an issue that confronts the modeler (e.g. see Ranade,1997; Kumar et al., 1995b).Finally, it is highly imperative to validate the simula-tion results against carefully designed non-invasive ex-periments. Unfortunately, reliable data for the  # owpattern and its dynamics in three-dimensional laborat-ory-scale bubble columns is not common in the openliterature, so that most of the validation of the CFDcodesdone in the past has onlybeen attempted onsimpletwo-dimensional systems operating in the bubbly  # owregime (e.g., Becker et al., 1994; Lin, Reese, Hong & Fan,1996; Delnoij et al., 1997a } c).In the present work, the experiments were performedin a 8 in diameter cylindrical air } water bubble columnusing the computerautomatedradioactiveparticletrack-ing (CARPT) and the gamma-raycomputed tomography(CT) facilities. Both bubbly and churn-turbulent bubblecolumn  # ow was simulated using FLUENT, and predic-tions of the two-dimensional axisymmetric approxima-tion are compared against the experimental results. 2. Experimental At the Chemical Reaction Engineering Laboratory,Washington University in St. Louis, USA the uniqueCARPT-CT facilities allow non-invasive monitoring of the  # ow of two phases in opaque multiphase reactors ona single platform (Devanathan, 1991; Yang, Devanathan& Dudukovic, 1992; Kumar, 1994; Degaleesan, 1997).Computer Automated Radioactive Particle Tracking(CARPT) is the method employed for measuring thetime-averaged velocity and turbulence parameters of theliquid phase in the bubble column. In CARPT, oneresorts to tagging the  ` typical  # uid element a  witha gamma ray source. For instance, in a bubble columnexperimentin which the liquid-phase velocity pro le is of interest, the liquid phase is tagged with a 2.3 mm dia-meter,  ` neutrally-buoyant a , hollow polypropylenesphere   lled with radioactive Sc-46 (of 250 } 300   Cistrength). Subsequently, the motion of this sphere ismonitoredusing an array of strategically positioned scin-tillation detectors over a long time span in which theparticle (like any other typical  # uid element) visits eachlocation in the bubble column a large number of times.Data is acquired over a very long time, typically 18 } 20 h,in order to collect su $ cient statistics (typically, two mil-lion or more occurrences in the column) for the tracerparticle to sample instantaneous velocities at all points inthe column. A record of the gamma-ray photon counts ateach detector, and a pre-established calibration betweenthe detector counts and tracer particle location is used toreconstruct the precise particle position at each timeinstant. Time-di !  erencingyields instantaneous velocities,which when averaged at each spatial location over thewhole time span of the experiment, yield the ensemble-averaged velocity  # ow map. By the ergodic hypothesis,this is alsothe time-averagedvelocity eld. The di !  erencebetween instantaneous and average velocity for each cellyields the  # uctuating component of velocity as a timeseries. This time series is then used to construct thecross-correlation matrix of   # uctuating velocity compo-nents. Trace of this matrix can be interpreted as the total # uctuating kinetic energy of   ` turbulence a  per unit vol-ume, while the o !  -diagonal components are directly re-lated to the  ` turbulent Reynolds '  shear stresses a (Devanathan, 1991; Degaleesan, 1997). Error in recon-struction of position using the CARPT technique hasbeen shown to be less than 0.5 cm, and error in spuriousroot-mean-square velocities is less than 5 cm s   in theworst case (Degaleesan, 1997).Computed tomography (CT) can be used to measuretime-averaged phase holdup pro les in a multiphase re-actor,and is usedhere to determinegasholduppro les inthe bubble column operated in bubbly and churn } turbu-lent  # ow. By placing a strong gamma-ray source in theplane of interest and a planar array of scintillation de-tectors in the same line on the other side of the reactor,one measures attenuation of the beam of gamma radi-ation. The attenuation is a function of the line-averagedholdup distribution along the path of the beam. Manysuch  ` projections a  (e.g., 4851 for an 8 in. column) areobtained at di !  erent angular orientations around thereactor. The complete set of projections is then used toback-calculate the cross-sectional distribution of densit-ies. Since the density at any point in the cross-section isa sum of densities of individual phases weighted by theirvolume fractions, the cross-sectional density distributionof any particular phase can be uniquely recovered (if onlytwo phases are present).The total scanning time in the CREL scanner is about2 h, thus the scanned image provides a  time-a v eraged  cross-sectional distribution of mixture density. The CT 5072  J. Sanyal et al.  /   Chemical Engineering Science 54 (1999) 5071 } 5083  setup at CREL provides a spatial resolution of betterthan 5 mm, and a density resolution of about0.04 g cm   (Kumar, Moslemian & Dudukovic, 1995).The results of the two-dimensional holdup distributioncan be subsequently averaged azimuthally for directcomparison with the results of a suitable axisymmetricsimulation. For cylindrical bubble columns, the axisym-metric pro le of the gas holdup measured via CT istypically parabolic, with the highest gas holdup in thecenterofthe column.At lowersuper cialgasvelocity, thepro le is  # atter across the cross-section and becomessigni cantly steeper with the increase in gas velocity.This fact is used to discriminate between bubbly  # owregime and churn-turbulent regime of operation of a bubble column. The liquid circulation in a bubblecolumnis driven by buoyancy of the gas, thus the circula-tion velocities are signi cantly higher (with steeper meanaxial liquid velocity pro les) in the churn } turbulent  # owregime as compared to the bubbly  # ow regime.Details of the experimental setup and procedurefor the particle tracking and the tomographic techniquesmay be found elsewhere (Devanathan, Moslemian& Dudukovic, 1990; Devanathan, 1991; Moslemian,Devanathan & Dudukovic, 1992; Yang et al.,1992; Kumar, 1994; Kumar et al., 1995; Kumar, Moslem-ian & Dudukovic, 1997; Degaleesan, 1997; Roy,Chen, Degaleesan, Gupta, Al-Dahhan & Dudukovic,1998). 3. Numerical Simulation In the present work, the  # ow in the bubble columnreactor was modeled using two di !  erent approachesincorporated in the FLUENT software  *   the Eulerianmultiphase model and the algebraic slip mixturemodel (ASMM). Although both models are usedto predict multiphase  # ows, there are fundamentaldi !  erences in their respective approaches which areoutlined here. 3.1. The Eulerian multiphase model  In the Eulerian two- # uid approach, the di !  erentphases are treated mathematically as interpenetratingcontinua. The derivation of the conservation equationsfor mass, momentum and energy for each of theindividual phases is done by ensemble averagingthe local instantaneous balances for each of the phases(Anderson & Jackson, 1967). The basic assumptions of this formulation used in the present computations are asfollows:   All phasesare treatedas interpenetratingcontinua andthe probability of occurrence of any one phase inmultiple realizations of the  # ow is given by the instan-taneous volume fraction of that phase at that point.Sum total of all volume fractions at a point is identi-cally unity.   Both  # uids are treated as incompressible, and a singlepressure   eld is shared by all phases.   Continuity and momentum equations are solved foreach phase.   Momentum transfer between the phases is modeledthrough a drag term, which is a function of the localslip velocity between the phases. A characteristic dia-meter is assigned to the dispersed phase gas bubbles,and a drag formulation based on a single sphere sett-ling in an in nite medium is used.   Turbulence in either phase is modeled separately.The conservation equations can be written as follows: Continuity  ( kth phase ):  t  (     ) #    ) (     u  )     m    . (1)  Momentum  ( kth phase ):  t  (     u  ) #    ) (     u   u  ) !      p #    )    # F  #     ( K  ( u  ! u  ) # m    u  ), (2)where     is the  k th phase stress } strain tensor, whosecomponents are given by           u     x  #  u     x    ! 23         u     x  . (3)The fourth term on the right-hand side of Eq. (2) repres-ents the interphase drag term, with  K   being the mo-mentum exchange coe $ cient between the  p th and the  k thphases. The evaluation of the needed drag coe $ cientrequires the bubble Reynolds number which is based onthe local slip velocity for a single sphere of constantdiameter sedimenting in stagnant  # uid. In the presentcomputations, the drag coe $ cient,  K   is based on thegeneralized correlations (Morsi & Alexander, 1972).The turbulence in the continuous phase is modeledthrough a set of modi ed  k }   equations with extra termsthat include interphase turbulent momentum transfer(Launder & Spalding, 1974; Elghobashi & Abou-Arab,1983), supplemented with extra terms that include theinterphase turbulent momentum transfer. This term canbe derivedexactly from the instantaneousequation of thecontinuous phase and involves the continuous-dispersedvelocity covariance. The turbulence quantities for thedispersed phase in FLUENT are based on characteristicparticle relaxation time and Lagrangiantime scales (Sim-onin & Viollet, 1990). For the dispersed gas phase, theturbulence closure is e !  ected through correlations from  J. Sanyal et al.  /   Chemical Engineering Science 54 (1999) 5071 } 5083  5073  the theory of dispersion of discrete particles by homo-geneous turbulence (Tchen, 1947).The equations discussed above are solved using anextension of the SIMPLE algorithm (Patankar, 1980).The momentum equations are decoupled using the fullelimination algorithm (FEA). Using SIMPLE-FEA(Spalding, 1980), the variables for each phase are elimi-natedfrom the momentumequationsfor all other phases.The pressure correction equation is obtained by sum-ming the continuity equations for each of the phases. Theequations are then solved in a segregated, iterativefashion and are advanced in time. At each time step, withan initial guess for the pressure   eld, the primary- andsecondary-phase velocities are computed. These are usedin the pressure correction equation (continuity), andbased on the discrepancy between the guessed pressure eld and the computed   eld, the velocities, holdups and # uxes are suitably modi ed to obtain convergence in aniterative manner. 3.2. The Algebraic Slip Mixture Model  The Algebraic Slip Mixture Model (ASMM) has anunderlying philosophy that is quite distinct from theEuler } Euler  two-  y uid   model (Manninen, Taivassalo& Kallio, 1996). The principal assumptions in this formu-lation are as follows:   It models the phases as two interpenetrating continua,with the probability of existence of each phase ata point in the computational domain given by itsrespective volume fraction (holdup). In general, thetwo phases move at di !  erent velocities.   A  single  equation is solved for continuity of the mix-ture and a single equation is solved for the momentumof the  mixture .   Motion of each phase relative to the center of mass of the mixture in any control volume is viewed as a di !  u-sion of that phase; this introduces the concept of a dif-fusion velocity of each phase (which is analogous anddirectly related to the slip velocity and the drift velo-city, as referred to in the classical drift  # ux model fora mixture, Wallis, 1969).   The Reynolds ' -averaged mixture momentum equationhas a term, called the  di  w  usion stress , which srcinatesbecause of the relative slip between the two phases.This requires closure in terms of the di !  usion velocityof each phase (or, equivalently, the drift or the slipvelocity between the phases). In the ASMM, this issupplied by assuming that the phases are in  local equilibrium  over  short spatial length scales . This meansthat the dispersed phase entity (bubble, particle) al-ways slips with respect to the continuous phase at itsterminal Stokes ' velocity in the local accelaration eld.   The  di  w  usion stress  term is also the only term in whichthe phase volume fractions appear explicitly. In orderto back out the individual phase velocities and volumefraction at the end of the computation at each timestep, it is necessary to solve a di !  erential equation forthe volume fraction of the dispersed phase coupledwith the solution of the mixture equations. This equa-tion is obtained from the equation of continuity for thedispersed phase.   Finally, the turbulent stress term in the mixture equa-tion is closed by solving a  k }   model for the  mixture phase.Based on these assumptions, the   nal equations of theASMM model are formulated as follows.  Equation of continuity for the mixture :  t  (   ) #  x  (   u    ) 0. (4)  Equation for mixture momentum  (  jth component  ):  t  (   u    ) #  x  (   u    u    ) !  p  x  #  x       u     x  #  u     x    #   g  # F  #  x         u      u      . (5) Volume fraction equation for the secondary phase :  t  (     ) #  x  (     u    ) !  x  (     u      ). (6)The above equations are formulated in terms of themixture density,    , mixture viscosity,    , and the mass-averaged mixture velocity,  u  , which are de ned as fol-lows:           ,            ,  u         u    . (7) u     is the drift velocity of the  k th phase with respect tothe mixture center of mass, and is related to the slipvelocity with respect to the continuous phase in thefollowing manner: u    u  ! u  v    ! 1           v    , (8)where  v     is the slip velocity of the  k th phase with respectto the continuous phase. In the ASMM, the slip velocityis calculated based on the assumption of local equilib-rium between the phases over short spatial scales. The 5074  J. Sanyal et al.  /   Chemical Engineering Science 54 (1999) 5071 } 5083

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