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    Available online at www.sciencedirect.com

    Computers and Chemical Engineering 32 (2008) 19431955

    Two-phase mass transfer coefficient prediction in stirredvessel with a CFD model

    F. Kerdouss, A. Bannari, P. Proulx , R. Bannari, M. Skrga, Y. LabrecqueDepartment of Chemical Engineering, Universite de Sherbrooke, Sherbrooke, QC J1K 2R1, Canada

    Received 23 February 2006; received in revised form 2 October 2007; accepted 17 October 2007

    Available online 26 October 2007

    Abstract

    In the present paper, gas dispersion in a laboratory scale (5 L) stirred bioreactor is modelled using a commercial computational fluid dynamics(CFD) code FLUENT 6.2 (Fluent Inc., USA). A population balance model (PBE) is implemented in order to account for the combined effect of

    bubble breakup and coalescence in the tank. The impeller is explicitly described in three dimensions using the two-phase and Multiple Reference

    Frame (MRF) Model. Dispersed gas and bubbles dynamics in the turbulent flow are modelled using an EulerianEulerian approach with dispersed

    k turbulent model and modified standard drag coefficient for the momentum exchange. Parallel computing is used to make efficient use of the

    computational power in order to predict spatial distribution of gas hold-up, Sauter mean bubble diameter, gasliquid mass transfer coefficient and

    flow structure. The numerical results from different distribution of classes are compared with experimental data and good agreement is achieved.

    2007 Elsevier Ltd. All rights reserved.

    Keywords: Bioreactor; Bubble size; Computational fluid dynamics (CFD); Gas dispersion; Mass transfer; Mixing; Multiphase flow; Parallel computing; Population

    balances; Stirred tank

    1. Introduction

    Modellingof thecomplexflow in a chemical or bioprocessing

    reactor, in the presence of a rotating impeller, is a computa-

    tional challenge. Although computational fluid dynamics (CFD)

    commercial codes have made impressive steps towards the solu-

    tion of such engineering problems over the last decade, it still

    remains a difficult task to use such codes to help the design

    and the analysis of bioreactors. The scientific and technical lit-

    erature on the subject has rapidly evolved from single-phase,

    rotating impeller systems (Jenne & Reuss, 1997; Luo, Issa, &

    Gosman, 1994; Micale, Brucato, & Grisafi, 1999; Rutherford,

    Lee, Mahmoudi, & Yianneskis, 1996; Tabor, Gosman, & Issa,1996) to population balance methods aiming at the prediction

    of the disperse phase bubble sizes using different approaches

    (Bakker & Van Den Akker, 1994; Kerdouss, Bannari, & Proulx,

    2006; Kerdouss, Kiss, Proulx, Bilodeau, & Dupuis, 2005; Lane,

    Schwarz, & Evans, 2005, 2002; Venneker, Derksen, & Van Den

    Corresponding author.E-mail address: pierre.proulx@usherbrooke.ca(P. Proulx).

    Akker, 2002). As a function of the type of results expected,

    modelling of bioreactors can be made simpler to target over-

    all parametric study or more complex to try to describe finely

    the bubble size distribution. Single bubble size models can be

    used to decrease the computational effort while maintaining a

    local description of the two-phase flow details (Deen, Solberg,

    & Hjertager, 2002; Friberg, 1998; Hjertager, 1998; Khopkar,

    Rammohan, Ranade, & Dudukovic, 2005; Morud & Hjertager,

    1996; Ranade, 1997; Ranade & Deshpande, 1999). Detailed

    models using multiple bubble sizes typically more than 10 size

    bins, give more information on the secondary phase behavior

    (Alopaeus, Koskinen, & Keskinen, 1999; Alopaeus, Koskinen,

    Keskinen, & Majander, 2002; Dhanasekharan, Sanyal, Jain &

    Haidari, 2005; Venneker et al., 2002). The formulation of the

    bubble size bins equations involves transport by convection

    and source/sink terms for the coalescence or breakup (Chen,

    Dudukovic, & Sanyal, 2005a, 2005b; Sanyal, Marchisio, Fox,

    & Dhanasekharan, 2005). Modern numerical techniques making

    efficient use of the computational efficiency of modern comput-

    ers have to be used in order to address this problem. Sliding

    meshes (SM) or Multiple Reference Frames (MRF) are tech-

    niques available to model the rotation of the impeller in the

    0098-1354/$ see front matter 2007 Elsevier Ltd. All rights reserved.

    doi:10.1016/j.compchemeng.2007.10.010

    mailto:pierre.proulx@usherbrooke.cahttp://dx.doi.org/10.1016/j.compchemeng.2007.10.010http://dx.doi.org/10.1016/j.compchemeng.2007.10.010mailto:pierre.proulx@usherbrooke.ca
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    1944 F. Kerdouss et al. / Computers and Chemical Engineering 32 (2008) 19431955

    Nomenclature

    a interfacial area (m1)a(v, v

    ) break frequency (s1)

    B birth (m3 s1)b(v) breakup frequency (s1)C death (m3 s1)C liquid phase dissolved oxygen saturation concen-

    tartion (kg m3)CL dissolved oxygen concentration in liquid phase

    (kgm3)CD drag coefficient

    c constant (1.0)

    cf increase coefficient of surface area

    D impeller diameter (m)

    DO2 oxygen diffusion coefficient (m2 s1)

    d bubble diameter (m)

    do sparger orifice (m)

    d32

    Sauter mean diameter (m)F volumetric force (N m3)

    f fraction

    g acceleration due to gravity (9.81 m s2)H liquid height (m)I unit tensor

    H Henrys constant (Pa kg1 m3)K exchange coefficient (kg m3 s1)k1 constant (0.923)

    kL mass transfer coefficient (m s1)

    m(v) mean number of daughter produced by breakup

    (2)N angular velocity (rad s1)

    n number density of bubble class (m3)PC coalescence efficiency

    PO2 partial pressure of oxygen (Pa)

    p pressure (Nm2)p(v, v

    ) probability

    Re Reynolds numberR interphase force (N m3)r position vector (m)T tank diameter (m)

    t time (s)U average velocity (m s1)uij bubble approaching turbulent velocity (ms

    1)

    u bubble turbulent velocity (m s1

    )v bubble volume (m3)We Weber number

    x abscissa or pivot of the i th parent class (m3)

    Greek symbols

    volume fraction

    1 constant (2.05)

    constant (2.046)

    (a, x) incompelte gamma function

    fraction reassigned to nearby classes pivot

    ij Kroneckers symbol

    turbulent dissipation energy (m2 s3) eddy size (m)

    viscosity (kgm1 s1) defined in Eq. (32)

    test function

    ij collision frequency (m3 s1) density (kg m3) surface tension (N m1) characteristic time (s) stress tensor (kg m1 s2)B breakup rate (m

    3 s1) size ratio (/di)

    ij size ratio (di/dj)

    Subscripts

    B breakup

    C coalescence

    eff effective

    G gas phase

    i phase number; axis indices of space coordinates,

    class index

    j axis indices of space coordinates, class index

    lam laminar

    L liquid phase

    t turbulent

    reactor (Luo et al., 1994). Parallel computing, adaptive unstruc-

    tured meshes are some of the tools used to make efficient useof the computational power. In the present study we compare

    overall two-phase mass transfer coefficients measured in a lab-

    oratory scale (3 L) New Brunswick BioFlo 110 bioreactor to

    computational results obtained with the CFD software FLU-

    ENT.

    2. Experimental setup

    A 3 L New Brunswick BioFlo 110 bioreactor (T = 12.5cm)with 2 L working volume is used in this study. This reactor is

    equipped with automatic feedback controllers for temperature,

    mixing and dissolved oxygen. The mixing is driven by a 45pitched blade impeller with 3 blades (D = 0.075 cm) mountedon a 10 mm diameter shaft placed at the centerline of the biore-

    actor and located at 76 mm from the headplate of the vessel.

    The gas is supplied through a 0.04 m diameter ring sparger with

    6 holes of 1 mm in diameter located 50 mm under the center

    of the impeller (see Fig. 2). The dissolved oxygen concen-

    tration is measured with a polarographic-membrane dissolved

    oxygen probe (InPro 6800 series O2 sensors from METTLER

    TOLEDO) and monitored with a computer interface. The biore-

    actor is de-aerated by sparging with N2 until only minimum

    levels of dissolved oxygen remained. At this point, air is dif-

    fused into the reactor until saturation is achieved. In the present

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    F. Kerdouss et al. / Computers and Chemical Engineering 32 (2008) 19431955 1945

    paper, numerical simulations are compared to the experimen-

    tal data (conducted at 20 C) of a stirred tank filled with tapwater with a total height of H= 4/3T, gas flow rate of 1.0 105 m3 s1 and an impeller rotation speed of 600 rpm corre-sponding to a turbulent Reynolds number, Re = LND2/L 3.75 104. The water properties are set as L = 998.2 k g m3,L

    =0.001kgm1 s1. The surface tension, , is assumed as

    0.073Nm1 (CRC Handbook, 2002). The properties of air areset as G = 1.225kgm3, G = 1.789 105 kg m1 s1. Theassumption of constant density is taken here as the pressure

    change from the bottom to the surface of the vessel is low

    (Psurfae/Pbottom 0.98).

    3. Numerical model

    3.1. Governing flow equations

    The gas and liquid are described as interpenetrating con-

    tinua and equations for conservation of mass and momentum

    are solved for each phase. The flow model is based onsolving NavierStokes equations for the EulerianEulerian

    multiphase model along with dispersed multiphase k tur-

    bulent model. FLUENT uses phase-weighted averaging for

    turbulent multiphase flow, and then no additional turb