Why do two TFM solid phases preserve their initial 1:3 volume-fraction ratio and show nearly identical spatial distributions?

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Hello MFiX developers and users,

I am simulating a cold bubbling fluidized bed containing two particle-size classes using MFiX 25.2.1 and the TFM approach. The case file is `
20_d06d08p13q27.mfx (13.6 KB)

The main problem is that the spatial distributions of the two solid phases are almost identical. Although the absolute volume fractions differ, the second phase remains approximately three times the first phase throughout most of the bed:

[ \varepsilon_{s,2}\approx3\varepsilon_{s,1} ]

Consequently, the local composition remains close to its initial value:

[ X_1=\frac{\varepsilon_{s,1}} {\varepsilon_{s,1}+\varepsilon_{s,2}}\approx0.25, \qquad X_2\approx0.75. ]

The instantaneous contours and time-averaged axial profiles therefore appear to reproduce the initial 1:3 volume-fraction ratio, with very little size segregation or differential transport.

Experimental configuration represented by the simulation

  • Cold air fluidization
  • Column internal diameter: 0.060 m
  • Column height: 1.40 m
  • Initial bed height: 0.1634 m
  • Total bed inventory: approximately 800 g
  • Fine-particle sieve range: 0.355–0.50 mm
  • Coarse-particle sieve range: 0.50–0.71 mm
  • Fine/coarse composition: 25%/75%
  • Gas flow rate: 27 m³/h
  • Superficial gas velocity: 2.654 m/s
  • Estimated mixture minimum fluidization velocity: approximately 0.322 m/s
  • Fluidization number: (U/U_{mf}\approx8.23)

Particle and initial-condition settings

Parameter Solid phase 1 Solid phase 2
Representative diameter 0.4275 mm 0.6050 mm
Density 3817 kg/m³ 3899 kg/m³
Initial volume fraction 0.11 0.33
Initial velocity 0 m/s 0 m/s
Initial granular temperature 0 0

The initial gas volume fraction in the bed is 0.56. A third TFM phase with a diameter of 0.855 mm is still defined in the project, but its initial volume fraction is zero. Thus, MMAX=3, although only phases 1 and 2 are present in this case.

Numerical and model settings

  • Solver: MFiX 25.2.1
  • Model: 2-D TFM
  • Domain: 0.060 m × 1.40 m
  • Grid: 30 × 700 cells
  • Cell size: approximately 2 mm × 2 mm
  • Simulation time: 12 s
  • Initial time step: (1.0\times10^{-4}) s
  • Minimum/maximum time steps: (10^{-7})–(10^{-2}) s
  • Gas–solid drag model: Syamlal–O’Brien
  • Solids viscous-stress model: Lun et al. (1984)
  • Frictional-stress model: Schaeffer
  • Radial distribution function: Lebowitz
  • Particle–particle restitution coefficient: 0.9
  • Interphase friction coefficient, C_F: 0.1
  • Packed-bed void fraction, EP_STAR: 0.3688
  • Internal friction angle: 30°
  • Stress blending: none
  • Energy and species equations: disabled

Boundary conditions

  • Bottom: gas mass inlet, (U_g=2.654) m/s
  • Top: pressure outlet, 101325 Pa
  • Side walls: no-slip for the gas
  • Solids wall condition: Johnson–Jackson partial slip
  • BC_JJ_PS=1
  • Specularity coefficient: PHIP=0.2
  • Particle–wall restitution coefficient: 0.9
  • Wall friction angle: 11.3°

I would appreciate advice on the following questions:
I am simulating a binary bubbling fluidized bed using MFiX 25.2.1. The particle diameters are 0.4275 and 0.6050 mm, with densities of 3817 and 3899 kg/m³. Their initial solid volume fractions are 0.11 and 0.33, corresponding to a 1:3 ratio. The gas velocity is 2.654 m/s, the grid is 30 × 700, and the simulation time is 12 s. I use the Syamlal–O’Brien drag model, Lun et al. (1984) solids-stress model, Schaeffer friction model, C_F=0.1, and Johnson–Jackson partial-slip walls.

During the simulation, the two phases satisfy approximately

[ \varepsilon_{s,2}(x,y,t)\approx3\varepsilon_{s,1}(x,y,t), ]

so their normalized instantaneous contours and axial profiles remain almost identical to the initial 1:3 distribution.

Why do the two solid phases with different particle diameters retain almost identical normalized spatial distributions instead of developing relative motion or size segregation?

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2

First, the attached file doesn’t completely match your description. In 20_d06d08p13q27.mfx:

  • ic_ep_s(2,1) = 0.0 — phase 1 (0.4275 mm) is the empty one. The active pair is phase 2 (0.605 mm, ε_s = 0.11) and phase 3 (0.855 mm, ε_s = 0.328), densities 3899/3862 kg/m³.
  • drag_type = 'GIDASPOW', not Syamlal–O’Brien. (drag_c1/drag_d1 are set but unused with Gidaspow.)
  • Bed height is 0.1675 m in the file.

Please double-check which case your contours came from. That said, both pairs have a ~1.4:1 size ratio at nearly equal density, so the answer is the same either way - what you’re seeing is mostly expected:

  1. Operating point. For the 0.605/0.855 mm pair, mixture U_mf is roughly 0.5 m/s, so U/U_mf ≈ 5 - vigorous bubbling. Bubble-driven convective mixing overwhelms the weak segregation driving force of a 1.4:1 size ratio with matched densities; such mixtures stay well mixed in experiments too. Size segregation is mainly observed close to minimum fluidization (roughly U/U_mf < 2-3). To study it, reduce the gas velocity toward U_mf or run a defluidization test.
  2. Geometry / slugging. In a 0.06 m ID column at 2.65 m/s, bubbles reach the column diameter almost immediately and the bed slugs - the emulsion moves in plugs with little relative phase motion. A 2-D Cartesian domain is also a rough approximation of a 6 cm cylinder.
  3. Solids–solids drag. With KT_TYPE = 'LUN_1984' (per-phase granular temperature), the Syamlal (1987) solids–solids momentum exchange is very stiff in dense regions - it scales with g0, which diverges near packing - so the phase velocities relax toward each other on a short time scale. This is a known limitation: standard TFM under-predicts segregation rates. Sensitivity to C_F is worth checking but won’t change the qualitative behavior. If segregation is the quantity of interest, consider a polydisperse kinetic theory (KT_TYPE = 'IA_NONEP', or 'GHD' - GHD has restrictions on drag model and number of solids phases; see the documentation).

Smaller points:

  • Delete the empty phase and set MMAX = 2 - it only adds cost, and MMAX = 2 is required for GHD anyway.
  • Both phases are initialized perfectly premixed, so the preserved 1:3 ratio is the initial condition persisting - segregation has to develop against the mixing above.
  • 12 s is short for segregation dynamics even under favorable conditions; run longer and time-average only after the startup transient.