CFIPS

CFIPS determines how the reference coefficient for inter-phase transfer of momentum and other quantities, FRICCO, is to be calculated, for two-phase flows (i.e. when ONEPHS=F).

Then the transfer coefficient, Cphi, used for a particular dependent variable, e.g. velocity, or temperature, depends on the value of CINT for that variable

The FRICCO values are always calculated for the centres of those mass-continuity cells which are not filled by solid.

For momentum transfer:

• , FRICCO is then "staggered" in EARTH; i.e. the value used is always the average of the two values pertaining to the cells between which the velocity in question is located.

• The CINT values for velocity are set by default so as to ensure that the inter-fluid force per cell is equal to:
       FRICCO * ( other_phase_velocity - own_phase_velocity)

• CFIPS = 0.0 cuts out interphase transport of momentum, heat and mass entirely.

• CFIPS = 1.0E+10 "fixes" the phases together, i.e. ensures that their velocities are equal

  It should be noted that setting EQUVEL = T has a similar effect.

• CFIPS = positive constant, C, say, sets the interphase-transfer coefficient per cell, FRICCO, as follows:

  FRICCO = C*RHO1*R1*max(R2,RLOLIM)*Vol

  where:

  • R1 and R2 are the 1st and 2nd phase volume fractions;
  • Vol is the free cell volume;
  • FRICCO has units of (Newton seconds) / meter;
  • C has units of (Newton seconds) / (kg meter)

• CFIPS = negative constant, C, which must however be either greater than GRND or smaller than GRND10, sets FRICCO thus:
  FRICCO = |C|*RHO2*R2*max(R1,RLOLIM)*Vol
  i.e., as compared with the previous case, it uses the phase-2 density rather than that of phase 1. Dimensions of FRICCO and C are as before.

• CFIPS = GRND causes EARTH to call the open-source GROUND subroutine of PHOENICS, where it expects to find coding, supplied by the user, for calculating values of FRICCO, cell by cell.

• CFIPS = GRND1, GRND2, ..... GRND10 causes EARTH to call open-source GXIFRIC.FOR GROUND subroutine of PHOENICS, and so to take one of the following options supplied by CHAM, according to which:
  • CFIPS=GRND1 selects:
    FRICCO=CFIPC*M1*R2, where
    M1 is the phase-1 mass in the cell, and
    R2 is the phase 2 volume fraction.
    CFIPC has units of (Newton seconds) / (kg meter)

  • CFIPS=GRND2 selects:
    FRICCO=CFIPC*M1*R2*max (relspeed,CFIPA), where
    relspeed is the relative speed between the phases.
    CFIPC has units of (Newton seconds**2) / (kg meter**2)
    CFIPA has units of (meter/second)

  • CFIPS=GRND3 selects:
    FRICCO=CFIPC*M1*R2*(max(relspeed,CFIPA))**CFIPB
    CFIPC has units of (Newton seconds**2) / (kg meter**2)
    CFIPA has units of (meter/second)
    CFIPB is a dimensionless exponent, often chosen as 2.0.

  • CFIPS=GRND4 selects:
    FRICCO=CFIPC*M1*R2* (( max(relspeed,CFIPA) )**CFIPB) * ( EL1**CFIPD )

  • CFIPS=GRND5 selects:
    FRICCO=CFIPC*M2*R1* (( max(relspeed,CFIPA) )**CFIPB) * ( EL1**CFIPD ), where
    M2 is the phase-2 mass in the cell, and
    R1 is the phase-1 volume fraction.

  • CFIPS=GRND6 selects:
    FRICCO=CFIPC*Vol

  • CFIPS=GRND7 selects:
    the dispersed-flow model:

    FRICCO = 0.75*Cd*RHO1*R2!*R1!*Vol*max[relspeed,CFIPA]/CFIPB

    wherein:-
    phase 1 is the carrier and
    phase 2 is dispersed;
    Cd is a dimensionless drag coefficient;
    CFIPB is the particle diameter;
    CFIPD selects:
    the correlation employed for Cd, as described below.

  • CFIPS=GRND8 selects:
    the same drag models as for CFIPS=GRND7, but with phase 2 as carrier and phase 1 dispersed.

If the shadow volume-fraction method is to be used to represent the burning, evaporation or condensation of particles, then the full-field variable RS should be attached to phase 1 via the TERMS command.

The drag-coefficient formulae

Details of these Cd correlations are given under the Encyclopaedia entry 'INTERPHASE DRAG MODELS'. The PIL-variable settings are:

Notes:

• If CFIPB = -Dp, the minus sign activates the removal of R1! from the FRICCO formula.

• For CFIPD=4. & 6. the surface tension must also be defined via CFIPC.

• For CFIPD = 7., the FRICCO formula of the above form is used only when R1 > 0.8; otherwise the well-known Ergun formula is used.

Storage of variables

STORE(CFIP) causes FRICCO to be stored.
STORE(SIZE) causes the particle diameter to be stored.
STORE(VREL) causes relspeed to be stored.
STORE(REYN) causes the particle Reynolds Number to be stored.
STORE(CD) causes Cd to be stored.
STORE(APRJ) causes storage of the projected area per unit
volume (not for CFIPD = 7.)
STORE(WEB) causes the Weber number to be stored if CFIPD=4.
or 5.
STORE(EOTV) causes the Eotvos number to be stored if CFIPD=6.

Further notes

Interphase mass transfer proceeds at the rate FRICCO * CMDOT, when the latter quantity is a positive constant.

See CINT, CMDOT, INTFRC and INTMDT for further information, and also the Encyclopaedia entry 'INTERPHASE DRAG MODELS'.

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