Ghidersa, B.

Onea, A.

Wörner, Martin

English

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Forschungszentrum Karlsruhein der Helmholtz-GemeinschaftInstitut für ReaktorsicherheitEvaluation of residence time distribution for bubble train flow in a square mini-channel by direct numerical simulation Martin Wörner, Bradut Ghidersa, A. OneaForschungszentrum Karlsruhe, Institut für ReaktorsicherheitECI International Conference on Heat Transfer and Fluid Flow in MicroscaleCastelvecchio Pascoli, 25 – 30 September 20052• Introduction and motivation• Bubble train flow (BTF)– Computational setup– Simulation results and validation• Residence time distribution (RTD)– Procedure to evaluate RTD– Results for RTD of bubble train flow– Model for the RTD• Conclusions and outlook Outline3Gas-liquid flow in narrow channels with rectangular cross section• Examples for devices– Monolithic reactors withcatalytic walls– Micro-channel network (MIT)– Micro bubble column (IMM)• Advantages– Enhanced mixing in liquid slug– Reduced axial dispersion– Efficient mass transfer across interface4Motivation• Experimental investigation of these two-phase flows is difficult because of small dimensions and often yield integral data only• Goal:– Perform direct numerical simulation (DNS) of bubble train flow in a single channel to resolve local flow phenomena – Use DNS results to evaluate residence time distribution for liquid phase5uc = "unit cell"• Elongated bubble which fill almost the entire channel cross section (Taylor bubbles)• Bubbles have identical shape and move with same axial velocity • The flow is fully described by a  unit cell of length Luc consisting of one bubble and one liquid slugFlow characterizationLuc6* Thulasidas, Abraham, Cerro, Chem. Eng. Science 50 (1995) 183-199Numerical set up • In-house code TURBIT-VOF– Navier-Stokes eq. with surface tension term for two incompressible fluids– Volume-of-fluid method (interface is locally approximated as plane)• Consider one flow unit cell only (one bubble, one slug)• Account for influence of trailing/leading unit cells by periodic boundary conditions in axial direction• Co-current upward vertical flow driven by specified pressure gradient• Length of flow unit cell, Luc, is input parameter– simulations for different values of Luc and fixed void fraction  = 33%• Comparison with experiments of Thulasidas et al.*– Air bubbles in silicon oil– Square channel with 2mm  2mm cross section ( W = 2mm)7Computational parameters Case Luc / W Domain Grid Time stepsA1 1 1  1  1 48  48  48 24,000A2 1 1  1  1 64  64  64 60,000B 1.25 1  1.25  1 48  60  48 24,000C 1.5 1  1.5  1 48  72  48 26,000D 1.75 1  1.75  1 48  84  48 26,000E 2 1  2  1 48  96  48 28,000Results on both grids show only slight differences 8Case A29Computed bubble shape and velocity field for different values of LucVelocity field in vertical mid-planeRight half: frame of reference moving with bubble Left half: fixed frame of reference10* Thulasidas, Abraham, Cerro, Chem. Eng. Science 50 (1995) 183-199Comparison with experimentCase Luc / W CaB DB / W (UB–Jtotal)/UB UB/JtotalA 1 0.204 0.81 1.80 0.445B 1.25 0.207 0.84 1.75 0.430C 1.5 0.215 0.85 1.75 0.430D 1.75 0.238 0.85 1.78 0.438E 2 0.253 0.85 1.8 0.445Experimental data* correlated in terms of capillary number CaB ≡ lUB/0.2  0.25 0.82  0.86 1.68  1.84 0.435  0.475  Non-dimensional bubble diameter Relative velocity Non-dimensional UB11* Figures are taken from book "Chemical Reaction Engineering" by O. LevenspielResidence time distribution• The residence time distribution (RTD) is an important measure for characterization of any chemical reactor– The RTD influences yield and selectivity• Common experimental method to determine RTD*– Add tracer at reactor inlet as a pulse and measure the tracer concentration at the outlet12Examples for RTD• Problems for micro reactors– Reaction volume is usually much smaller than the volume of inlet and the volume necessary to measure tracer at outlet• Alternative: Determine RTD from DNS data13Procedure to evaluate RTD from DNS data• Use fully developed DNS results for a certain instant in time• Introduce virtual particles in mesh cells entirely filled with liquid– particle distance = 1 / nppul   (number of particles per unit length)• Track particles in fixed frame of reference– Problem: Velocity field in fixed frame of reference is unsteady– But: steady velocity field in frame of reference moving with bubble– Determine fluid velocity at instant particle position from its relative position to the bubble, which is virtually moved with velocity UB• Store time the particle needs to travel an axial distance of Luc• Normalize histogram for all particles to obtain two RTD curves– E*: no special weighting of particle residence times – E: weighting of particle residence time by axial velocity at release14RTD for single phase planar Poiseuille flow1 2 3 4 51E-30.010.1110E, E*,E** [-] [-] E    (analytical) E*   (analytical) E**  (analytical) E    (numerical) E*   (numerical)12112** **32* *21 2( ) 121 2( )For 2 3:1 23( )1132 33tE t EE tEEtE t                   [ ]t t  150 1 2 3 4 50.00.51.01.52.02.5tB = Luc / UB0 1 2 3 4 50.010.11log10 E [-]t [-]E [-]t [-] nppul = 48   nppul = 64   nppul = 96Case A: grid 48 x 48 x 48Influence of nppul for BTF case AExponentialdecayBubble breakthrough time tB16Compartment modeluc BL L Luc Buc uc B0 for /for /expt L UE Ut L ULU UtL U      uc BL L Luc Buc uc B0 for /for /expt L UE Jt L ULJ JtL U      Plug flow reactor and stirred vessel in series(single phase flow)17Compartment model for case A0 2 4 6 8 100.00.51.01.52.00 5 101E-41E-30.010.11log10 E [-]t [-]Case A:  nppul = 96 ;  Eq. (16) ;  Eq. (17)E [-]t [-]uc BL L Luc Buc uc BVRTD0 for /for /expt L UE Ut L ULU UtL U      uc BL L Luc Buc uc BVRTD0 for /for /expt L UE Jt L ULJ JtL U      18Compartment model for case C0 2 4 6 8 100.00.51.01.52.00 5 101E-41E-30.010.11log10 E [-]t [-]Case C:  nppul = 64 ;  Eq. (16) ;  Eq. (17)E [-]t [-]19Compartment model for case E0 2 4 6 8 100.00.51.01.50 5 101E-30.010.11 t [-]log10 E [-]E [-]t [-]Case E:  nppul = 48 ;  Eq. (16) ;  Eq. (17)20Conclusions • Direct numerical simulation of bubble train flow (BTF)– Square vertical mini-channel of width W = 2 mm– Co-current vertical flow of air bubbles in silicon oil– Good agreement with experimental data from literature• Original procedure to evaluate the liquid phase RTD– Introduction of mass-less particles into volume of liquid phase– Tracking of particles and detecting time to travel distance Luc– Evaluated RTD can be approximated by compartment model with plug flow reactor and stirred vessel in series• Outlook– Identifying better model for liquid RTD of unit cell (?)– Determine RTD for traveling distance nuc · Luc (nuc = 2, 3, ...)– Obtain RTD for arbitrary nuc by convolution of RTD for nuc = 1 (?)

Evaluation of residence time distribution for bubble train flow in a square mini-channel by direct numerical simulation

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Evaluation of residence time distribution for bubble train flow in a square mini-channel by direct numerical simulation

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