3 Breakup Dense

download 3 Breakup Dense

of 53

Transcript of 3 Breakup Dense

  • 8/12/2019 3 Breakup Dense

    1/53

    MCEN 6228

    Multiphase Flow

    Surface Tension &Secondary Breakup

  • 8/12/2019 3 Breakup Dense

    2/53

    MCEN 6228

    Multiphase Flow

    Surface Tension

    Liquid is held together by van der Vaals force

    liquid

    gas

    surface distorted surface

  • 8/12/2019 3 Breakup Dense

    3/53

    MCEN 6228

    Multiphase Flow

    Surface Tension

    Definition force Fper unit length, exerted

    parallel to the liquid surface

    Where is the pressure higher: inside a liquid drop,or inside a soap bubble (or are they equal)?

  • 8/12/2019 3 Breakup Dense

    4/53

    MCEN 6228

    Multiphase Flow

    Surface Tension

    Pressure inside a liquid drop

    Pressure inside a liquid film bubble

  • 8/12/2019 3 Breakup Dense

    5/53

    MCEN 6228

    Multiphase Flow

    Surface Tension

  • 8/12/2019 3 Breakup Dense

    6/53

    MCEN 6228

    Multiphase Flow

    Surface Tension

    Characteristic numbers Weber number

    Ohnesorge number

  • 8/12/2019 3 Breakup Dense

    7/53

    MCEN 6228

    Multiphase Flow

    Drop Breakup: Regimes

  • 8/12/2019 3 Breakup Dense

    8/53

    MCEN 6228

    Multiphase Flow

    Drop Breakup: Regimes

  • 8/12/2019 3 Breakup Dense

    9/53

    MCEN 6228

    Multiphase Flow

    Drop Breakup: Regimes

    We = 20: bag breakup

    We = 272: sheet stripping

    We = 952: chaotic breakup

  • 8/12/2019 3 Breakup Dense

    10/53

    MCEN 6228

    Multiphase Flow

    Drop Breakup: Regimes

    We = 5000: chaotic breakup (Joseph et al. 98)

  • 8/12/2019 3 Breakup Dense

    11/53

    MCEN 6228

    Multiphase Flow

    Drop Breakup: TAB Model

    Treat drop as a mass-spring-damper system

    external force

    spring

  • 8/12/2019 3 Breakup Dense

    12/53

    MCEN 6228

    Multiphase Flow

    Drop Breakup: TAB Model

    damper

    breakup criterion

    with

    consider only fundamental mode (n=2)!

  • 8/12/2019 3 Breakup Dense

    13/53

    MCEN 6228

    Multiphase Flow

    Drop Breakup: TAB Model

    Solution

  • 8/12/2019 3 Breakup Dense

    14/53

    MCEN 6228

    Multiphase Flow

    Drop Breakup: TAB Model

    Need to determine shock tube experiments

    !

    !

  • 8/12/2019 3 Breakup Dense

    15/53

    MCEN 6228

    Multiphase Flow

    Drop Breakup: TAB Model

    oscillation of an inviscid spherical drop, mode n(Lamb 45)

    damped oscillation of viscous spherical drop, mode n(Lamb 45)

    !

    !

  • 8/12/2019 3 Breakup Dense

    16/53

    MCEN 6228

    Multiphase Flow

    Drop Breakup: TAB Model

    postulate breakup occurs if oscillation amplitude is halfthe drop radius

    !

    !

    !

    (for initially non-oscillating sphere)

  • 8/12/2019 3 Breakup Dense

    17/53

    MCEN 6228

    Multiphase Flow

    Drop Breakup: TAB Model

    Timescales large We !stripping mode

    low We ! bag mode

  • 8/12/2019 3 Breakup Dense

    18/53

    MCEN 6228

    Multiphase Flow

    Drop Breakup: TAB Model

    What child drops are produced? energy conservation

    !

  • 8/12/2019 3 Breakup Dense

    19/53

    MCEN 6228

    Multiphase Flow

    Drop Breakup: TAB Model

    from experiments

    large We !stripping mode:

    low We ! bag mode:

    replace parent drop by drops with radius randomlysampled from "2-PDF with R32

  • 8/12/2019 3 Breakup Dense

    20/53

    MCEN 6228

    Multiphase Flow

    Drop Breakup: WAVE model

    linear stability analysis of around liquid jet

    Mayer 93

  • 8/12/2019 3 Breakup Dense

    21/53

    MCEN 6228

    Multiphase Flow

    WAVE Model: Jet Breakup

    growth rate vs wave length, parameter: gas densityMayer 93

  • 8/12/2019 3 Breakup Dense

    22/53

    MCEN 6228

    Multiphase Flow

    WAVE Model: Jet Breakup

    growth rate vs wave length, parameter: surface tensionMayer 93

  • 8/12/2019 3 Breakup Dense

    23/53

    MCEN 6228

    Multiphase Flow

    WAVE model: Jet Breakup

    optimal wavelength #and growth rate $(Reitz 87)

    1: liquid, 2: gas

  • 8/12/2019 3 Breakup Dense

    24/53

    MCEN 6228

    Multiphase Flow

    WAVE model: Jet Breakup

    optimal wavelength #and growth rate $(Reitz 87)

  • 8/12/2019 3 Breakup Dense

    25/53

    MCEN 6228

    Multiphase Flow

    Drop Breakup: WAVE Model

    Treat drop breakup as liquid jet breakup

    low We ! bag mode

    large We !stripping mode

    TAB:

    TAB:

  • 8/12/2019 3 Breakup Dense

    26/53

    MCEN 6228

    Multiphase Flow

    Drop Breakup: WAVE model

    What child drops are produced? at t

    buadd drop of size

    Difference between TAB and WAVE

  • 8/12/2019 3 Breakup Dense

    27/53

    MCEN 6228

    Multiphase Flow

    Drop Breakup: DDB model

    Extension of TAB model to non-linear effects Consider center of mass of half-drop Deformation due to extensional flow Equate work done by pressure and

    viscous dissipation to internal energy

    breakup when

    with

  • 8/12/2019 3 Breakup Dense

    28/53

    MCEN 6228

    Multiphase Flow

    Drop Breakup: Alternatives

    Rayleigh-Taylorbreakup model (Bellman & Pennington 54) high relative velocity: catastrophic breakup regime

    wave length Stochastic model(Apte et al. 03)

    (Hwang & Reitz 95)

    (Reitz)

  • 8/12/2019 3 Breakup Dense

    29/53

    MCEN 6228

    Multiphase Flow

    Collision &Coalescence

  • 8/12/2019 3 Breakup Dense

    30/53

    MCEN 6228

    Multiphase Flow

    Particle/Wall Interaction

    Assumptions (hard sphere model) particles are spheres particle deformation is neglected walls are smooth Coulombs friction law once particle stops sliding, no further sliding

    Split interaction into compression phase (1) recovery phase (2)

  • 8/12/2019 3 Breakup Dense

    31/53

    MCEN 6228

    Multiphase Flow

    Particle/Wall Interaction

    Solution use impulse equations

    (3 translational velocities + 3 angular velocities)

    use boundary conditions + friction law (coefficient f) introduce coefficient of restitution e

    sliding may stop in compression, recovery phase,or not at all

    recovery phase impulse

    compression phase impulse

  • 8/12/2019 3 Breakup Dense

    32/53

    MCEN 6228

    Multiphase Flow

    Particle/Wall Interaction

    Two cases:

  • 8/12/2019 3 Breakup Dense

    33/53

    MCEN 6228

    Multiphase Flow

    Particle/Wall Interaction

    Problem large particles will not stay in suspension (e< 1)

    Solution consider non-spherical particles consider roughness of the wall

  • 8/12/2019 3 Breakup Dense

    34/53

    MCEN 6228

    Multiphase Flow

    Particle/Wall Interaction

    Non-spherical particles rx introduces wall normal velocity particles characterized by r(&)

    on impact choose randomly &!r perform analysis as before

    sphere non-sphere

  • 8/12/2019 3 Breakup Dense

    35/53

    MCEN 6228

    Multiphase Flow

    Particle/Wall Interaction

    Rough wall model rough wall as series of inclined planes

    transform velocities to plane coordinate system &use equations as before

  • 8/12/2019 3 Breakup Dense

    36/53

    MCEN 6228

    Multiphase Flow

    Particle/Wall Interaction

    Example near spherical particle in horizontal channel (Shen et al. 89) D = 1.1mm, e = 0.93, f = 0.28

  • 8/12/2019 3 Breakup Dense

    37/53

    MCEN 6228

    Multiphase Flow

    Drop/Wall Interaction

    Interaction of a drop with a hot wall: Experiment

    (Wachters &

    Westerling 66)

    elastic rebound

    vapor film

    prevents wetting

    spreading, splashing

  • 8/12/2019 3 Breakup Dense

    38/53

    MCEN 6228

    Multiphase Flow

    Drop/Wall Interaction

    Watkins & Wang model (90) use critical Weber number from Wachters & Westerling

    &

  • 8/12/2019 3 Breakup Dense

    39/53

    MCEN 6228

    Multiphase Flow

    Drop/Wall Interaction

    Park model (94) use fitted data from Wachters & Westerling for We

    We(0)

    We

  • 8/12/2019 3 Breakup Dense

    40/53

    MCEN 6228

    Multiphase Flow

    Drop/Wall Interaction

    Park model (94) use fitted data from Wachters & Westerling for We

    = D(0)

    = vn(0)

    at t = "t*with 1 < "< 1.548

    exp.:

    exp.:

  • 8/12/2019 3 Breakup Dense

    41/53

    MCEN 6228

    Multiphase Flow

    Drop/Wall Interaction

    Park model (94) mass spreading tangentially & rebounding from wall aims to mimic splash

    (Rieber & Frohn 99)

    (Yarin & Weiss 95)

  • 8/12/2019 3 Breakup Dense

    42/53

    MCEN 6228

    Multiphase Flow

    Drop/Wall Interaction

    Numerous other models Grover et al. 2001 ORourke & Amsden 2000 Naber & Reitz 1988 etc.

    Mostly using energy conservation, distribution arguments correlations from experiments or DNS like numerical

    simulations

    Advanced description requires wall film model

  • 8/12/2019 3 Breakup Dense

    43/53

    MCEN 6228

    Multiphase Flow

    Drop/Wall Interaction

    5mm glycerin-water drop impacting ethanol layer

  • 8/12/2019 3 Breakup Dense

    44/53

    MCEN 6228

    Multiphase Flow

    Drop/Drop Interaction

    Can often be neglected in engine sprays Dominant for rain formation

    terminal velocity is function of D drops collide & merge

    For coalescence drops must be closer than 100A Statistically hard to model, since joined PDFs of

    two drops must be known

  • 8/12/2019 3 Breakup Dense

    45/53

    MCEN 6228

    Multiphase Flow

    Drop/Drop Interaction

    Regime diagram

    (Qian & Law 97)

    hydrocarbon droplets

    "U/2

    U/2

  • 8/12/2019 3 Breakup Dense

    46/53

    MCEN 6228

    Multiphase Flow

    Drop/Drop Interaction

    (Qian & Law 97)

    coalescence

    bouncing

  • 8/12/2019 3 Breakup Dense

    47/53

    MCEN 6228

    Multiphase Flow

    Drop/Drop Interaction

    (Qian & Law 97)

    coalescence

    coalescence

  • 8/12/2019 3 Breakup Dense

    48/53

    MCEN 6228

    Multiphase Flow

    Drop/Drop Interaction

    (Qian & Law 97)

    near head-on

    separation

    near head-on

    separation

  • 8/12/2019 3 Breakup Dense

    49/53

    MCEN 6228

    Multiphase Flow

    Drop/Drop Interaction

    (Qian & Law 97)

    near head-on

    separation

    near head-on

    separation

  • 8/12/2019 3 Breakup Dense

    50/53

    MCEN 6228

    Multiphase Flow

    Drop/Drop Interaction

    (Qian & Law 97)

    coalescence

    off-center

    separation

  • 8/12/2019 3 Breakup Dense

    51/53

    MCEN 6228

    Multiphase Flow

    Drop/Drop Interaction

    (Qian & Law 97)

    off-center

    separation

    off-centerseparation

  • 8/12/2019 3 Breakup Dense

    52/53

    MCEN 6228

    Multiphase Flow

    Drop/Drop Interaction

    Modeling approximate regime diagram on collision detection, determine B and We!collision result from approximated regime diagram

    Statistical modeling is very challenging sincejoined PDFs of two drops are needed

    Phase interface tracked DNS is challenging,since van der Waals forces must be considered

    for correct time of coalescence

  • 8/12/2019 3 Breakup Dense

    53/53

    MCEN 6228

    Multiphase Flow

    Drop/Pool Interaction

    Dancing drops