12.1.5. Two-Fluid Model

This section contains keywords relating to the Two-Fluid Model.

12.1.5.1. KT_TYPE

Data Type: CHARACTER

Applies to solids model(s): TFM

Solids phase stress model [Algebraic].

Table 12.37 Valid Values

Name

Default?

Description

ALGEBRAIC

Granular energy algebraic formulation.

AHMADI

Cao and Ahmadi (1995). Int. J. Multiphase Flow 21(6), 1203.

GD_99

Garzo and Dufty (1999). Phys. Rev. E 59(5), 5895.

GHD

Garzo, Hrenya and Dufty (2007). Phys. Rev. E 76(3), 31304

GTSH

Garzo, Tenneti, Subramaniam, Hrenya (2012). J.Fluid Mech. 712, 129.

IA_NONEP

Iddir & Arastoopour (2005). AIChE J. 51(6), 1620

LUN_1984

Lun et al (1984). J. Fluid Mech., 140, 223.

SIMONIN

Simonin (1996). VKI Lecture Series, 1996-2

12.1.5.2. FRICTION_MODEL

Data Type: CHARACTER

Applies to solids model(s): TFM

Solids stress friction model selection.

Table 12.38 Valid Values

Name

Default?

Description

NONE

Only solids pressure

SCHAEFFER

Schaeffer friction model. 1987, Journal of Differential Equations 66, 19–50.

SRIVASTAVA

Srivastava and Sundaresan friction model. 2003, Powder Technology 129(1-3):72-85

GUO_BOYCE

Guo-Boyce friction model, 2021. Proceedings of the National Academy of Sciences, 118 (35).

12.1.5.3. BLENDING_FUNCTION

Data Type: CHARACTER

Applies to solids model(s): TFM

Blend the Schaeffer stresses with the stresses resulting from algebraic kinetic theory around the value of EP_STAR. [NONE]

Table 12.39 Valid Values

Name

Default?

Description

NONE

No blending

TANH_BLEND

Hyperbolic tangent function

SIGM_BLEND

Scaled sigmodial function

12.1.5.4. YU_STANDISH

Data Type: LOGICAL

Applies to solids model(s): TFM

Use Yu-Standish correlation to compute maximum packing for polydisperse systems.

A.B. Yu and N. Standish. Powder Tech, 52 (1987) 233-241

Table 12.40 Valid Values

Name

Default?

Description

.TRUE.

Use the Yu-Standish correlation.

.FALSE.

Do not use the Yu-Standish correlation.

12.1.5.5. FEDORS_LANDEL

Data Type: LOGICAL

Applies to solids model(s): TFM

Use Fedors-Landel correlation to compute maximum packing for binary (only) mixtures of powders.

R.F. Fedors and R.F. Landel. Powder Tech, 23 (1979) 225-231

Table 12.41 Valid Values

Name

Default?

Description

.TRUE.

Use the Fedors-Landel correlation.

.FALSE.

Do not use the Fedors-Landel correlation.

12.1.5.6. RDF_TYPE

Data Type: CHARACTER

Applies to solids model(s): TFM

Radial distribution function (RDF) at contact.

Table 12.42 Valid Values

Name

Default?

Description

CARNAHAN_STARLING

Carnahan, N.F. and Starling K.E., (1969). The Journal of Chemical Physics, Vol. 51(2):635-636. Only applies to monodisperse cases.

MA_AHMADI

Ma, D. and Ahmadi, G., (1986). The Journal of Chemical Physics, 84(6):3449. Only applies to monodisperse cases.

LEBOWITZ

Lebowitz, J.L. (1964) The Physical Review, A133, 895-899. Only applies to polydisperse cases.

MODIFIED_LEBOWITZ

Iddir, H. Y., Modeling of the multiphase mixture of particles using the kinetic theory approach. Doctoral Dissertation, Illinois Institute of Technology, Chicago, Illinois, 2004, (chapter 2, equations 2-49 through 2-52.) Only applies to polydisperse cases.

MANSOORI

Mansoori, GA, Carnahan N.F., Starling, K.E. Leland, T.W. (1971). The Journal of Chemical Physics, Vol. 54:1523-1525. Only applies to polydisperse cases.

MODIFIED_MANSOORI

van Wachem, B.G.M., Schouten, J.C., van den Bleek, C.M., Krishna, R. and Sinclair, J. L. (2001) AIChE Journal 47:1035–1051. Only applies to polydisperse cases.

12.1.5.7. ADDED_MASS

Data Type: LOGICAL

Applies to solids model(s): TFM

Flag to include the added (or virtual) mass force. This force acts to increase the inertia of the dispersed phase, which tends to stabilize simulations of bubbly gas-liquid flows.

12.1.5.8. M_AM

Data Type: INTEGER

Applies to solids model(s): TFM

The disperse phase number to which the added mass is applied.

12.1.5.9. C_E

Data Type: DOUBLE PRECISION

Applies to solids model(s): TFM

Coefficient of restitution for particle-particle collisions.

12.1.5.10. R_P(PHASE, PHASE)

Data Type: DOUBLE PRECISION

  • \(1 \le Phase \le 2\)

  • \(1 \le Phase \le 2\)

Coefficient of restitution for particle-particle collisions specific to GHD theory implementation.

12.1.5.11. E_W

Data Type: DOUBLE PRECISION

Coefficient of restitution for particle-wall collisions when using Johnson and Jackson partial slip BC (BC_JJ_PS).

12.1.5.12. PHIP

Data Type: DOUBLE PRECISION

Applies to solids model(s): TFM

Specularity coefficient associated with particle-wall collisions when using Johnson and Jackson partial slip BC (BC_JJ_PS). If Jenkins small frictional BC are invoked (JENKINS) then PHIP is not used.

12.1.5.13. PHIP0

Data Type: DOUBLE PRECISION

Applies to solids model(s): TFM

Specify the value of specularity coefficient when the normalized slip velocity goes to zero when BC_JJ_M is .TRUE.. This variable is calculated internally in MFiX. Do not modify unless an accurate number is known.

12.1.5.14. C_F

Data Type: DOUBLE PRECISION

Applies to solids model(s): TFM

Coefficient of friction between the particles of two solids phases.

12.1.5.15. PHI

Data Type: DOUBLE PRECISION

Applies to solids model(s): TFM

Angle of internal friction (in degrees). Set this value to zero to turn off plastic regime stress calculations.

12.1.5.16. PHI_W

Data Type: DOUBLE PRECISION

Applies to solids model(s): TFM

Angle of internal friction (in degrees) at walls. Set this value to non-zero (PHI_W = 11.31 means TAN_PHI_W = MU = 0.2) when using Johnson and Jackson partial slip BC (BC_JJ_PS) with Friction model or Jenkins small frictional boundary condition.

12.1.5.17. EPS_F_MIN

Data Type: DOUBLE PRECISION

Applies to solids model(s): TFM

Minimum solids fraction above which friction sets in. [0.5]

12.1.5.18. EP_S_MAX(PHASE)

Data Type: DOUBLE PRECISION

  • \(1 \le Phase \le 10\)

Applies to solids model(s): TFM

Maximum solids volume fraction at packing for polydisperse systems (more than one solids phase used). The value of EP_STAR may change during the computation if solids phases with different particle diameters are specified and Yu_Standish or Fedors_Landel correlations are used.

12.1.5.19. SEGREGATION_SLOPE_COEFFICIENT

Data Type: DOUBLE PRECISION

Applies to solids model(s): TFM

Used in calculating the initial slope of segregation: see Gera et al. (2004) - recommended value 0.3. Increasing this coefficient results in decrease in segregation of particles in binary mixtures.

12.1.5.20. V_EX

Data Type: DOUBLE PRECISION

Applies to solids model(s): TFM

Excluded volume in Boyle-Massoudi stress.

Table 12.43 Valid Values

Name

Default?

Description

0.0

Boyle-Massoudi stress is turned off.

12.1.5.21. MU_S0(PHASE)

Data Type: DOUBLE PRECISION

  • \(1 \le Phase \le 10\)

Applies to solids model(s): TFM

Specified constant viscosity. If any value is specified then:

  • kinetic theory calculations (granular_energy) are off, which

    means zero granular pressure contribution (P_S = 0)

  • frictional/plastic calculations are off, which means zero

    frictional viscosity contributions, however, a plastic pressure term is still invoked (P_STAR)

  • LAMBDA_S = -2/3 MU_S0

12.1.5.22. DIF_S0(PHASE)

Data Type: DOUBLE PRECISION

  • \(1 \le Phase \le 10\)

Applies to solids model(s): TFM

Specified constant solids diffusivity [m^2/s in SI].

12.1.5.23. EP_STAR

Data Type: DOUBLE PRECISION

Applies to solids model(s): TFM

Packed bed void fraction. Used to calculate plastic stresses (for contribution to viscosity) and when to implement plastic pressure, P_STAR. Specifically, if EP_G < EP_STAR, then plastic pressure is employed in the momentum equations.

12.1.5.24. CLOSE_PACKED(PHASE)

Data Type: LOGICAL

  • \(1 \le Phase \le 10\)

Applies to solids model(s): TFM

Flag to enable/disable a phase from forming a packed bed. Effectively removes plastic pressure term from the solids phase momentum equation.

Table 12.44 Valid Values

Name

Default?

Description

.TRUE.

The phase forms a packed bed with void fraction EP_STAR.

.FALSE.

The phase can exceed close pack conditions so that it maybe behave like a liquid.

12.1.5.25. JENKINS

Data Type: LOGICAL

This flag affects how the momentum and granular energy boundary conditions are implemented when using BC_JJ_PS BC.

Table 12.45 Valid Values

Name

Default?

Description

.FALSE.

Use standard boundary conditions.

.TRUE.

Use Jenkins small frictional boundary condition.