12.1.19. Two-fluid model (TFM)

This section contains keywords relating to the Two-fluid model (TFM).

12.1.19.1. 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.

12.1.19.2. 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 12.88 Valid Values

Name

Default?

Description

NONE

◉

No blending

TANH_BLEND

Hyperbolic tangent function

SIGM_BLEND

Scaled sigmodial function

12.1.19.3. C_E

Data Type: DOUBLE PRECISION

Applies to solids model(s): TFM

Coefficient of restitution for particle-particle collisions.

12.1.19.4. C_F

Data Type: DOUBLE PRECISION

Applies to solids model(s): TFM

Coefficient of friction between the particles of two solids phases.

12.1.19.5. 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 12.89 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.

12.1.19.6. 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].

12.1.19.7. E_W

Data Type: DOUBLE PRECISION

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

12.1.19.8. 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.

12.1.19.9. 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.

12.1.19.10. EPS_F_MIN

Data Type: DOUBLE PRECISION

Applies to solids model(s): TFM

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

12.1.19.11. 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 12.90 Valid Values

Name

Default?

Description

.TRUE.

Use the Fedors-Landel correlation.

.FALSE.

◉

Do not use the Fedors-Landel correlation.

12.1.19.12. FRICTION_MODEL

Data Type: CHARACTER

Applies to solids model(s): TFM

Solids stress friction model selection.

Table 12.91 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).

12.1.19.13. JENKINS

Data Type: LOGICAL

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

Table 12.92 Valid Values

Name

Default?

Description

.FALSE.

◉

Use standard boundary conditions.

.TRUE.

Use Jenkins small frictional boundary condition.

12.1.19.14. KT_TYPE

Data Type: CHARACTER

Applies to solids model(s): TFM

Solids phase viscous stress model [Algebraic].

Table 12.93 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

12.1.19.15. M_AM

Data Type: INTEGER

Applies to solids model(s): TFM

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

12.1.19.16. 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

12.1.19.17. 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.

12.1.19.18. 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.

12.1.19.19. 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.

12.1.19.20. 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.

12.1.19.21. 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.

12.1.19.22. RDF_TYPE

Data Type: CHARACTER

Applies to solids model(s): TFM

Radial distribution function (RDF) at contact.

Table 12.94 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.

12.1.19.23. 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.

12.1.19.24. V_EX

Data Type: DOUBLE PRECISION

Applies to solids model(s): TFM

Excluded volume in Boyle-Massoudi stress.

Table 12.95 Valid Values

Name

Default?

Description

0.0

Boyle-Massoudi stress is turned off.

12.1.19.25. 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 12.96 Valid Values

Name

Default?

Description

.TRUE.

Use the Yu-Standish correlation.

.FALSE.

◉

Do not use the Yu-Standish correlation.