🌪️ Fluidized Bed Hydrodynamics & Minimum Fluidization

Calculate gas-solid fluidized bed hydrodynamics: minimum fluidization velocity (Umf), terminal free-fall velocity (Ut), Archimedes number, Geldart particle classification, and bed pressure drop.

⚡ Fortran 90 Engine Double Precision (IEEE 754) ✓ ISO / ASME Validated

📊 Solver Telemetry ● ACTIVE

👁️ Consultations 38

⚡ Calculs faits 32

💾 Téléchargements 384 📦 Code Fortran 4.5 KB

📅 Mise en service Jun 2026

⏱️ Latence < 1 ms

🌪️ Gas-Solid Fluidized Bed Hydrodynamics & Bubble Eruption

Real-time visual simulation: Gas distributor grid, particle bed expansion, and rising void bubbles

📝 Configuration & Presets

🔥 Sand Combustor (Geldart B) ⚡ FCC Regenerator (Geldart A) 🪵 Biomass Gasifier (Geldart D) 💊 Pharma Batch Dryer

🔬 Solid Particle Properties

Particle Diameter d_p [μm]:

Solid Density ρ_p [kg/m³]:

Particle Sphericity ϕ_s: 1.0 for spherical beads, ~0.85 for sand

💨 Fluidizing Gas State & Velocity

Gas Temperature [°C]:

Operating Pressure [bar abs]:

Superficial Gas Velocity U₀ [m/s]:

📐 Bed Column Dimensions

Static Bed Height H₀ [m]:

Column Diameter D [m]:

Wen & Yu / Ergun Fluidization Formulation:
• Archimedes Number: Ar = d_p³ · ρ_g · (ρ_p − ρ_g) · g / μ_g²
• Minimum Fluidization Reynolds: Re_mf = √(33.7² + 0.0408 Ar) − 33.7
• Minimum Fluidization Velocity: U_mf = Re_mf · μ_g / (ρ_g · d_p) [m/s]
• Bed Pressure Drop: ΔP_bed = (1 − ε_mf) · (ρ_p − ρ_g) · g · H₀ [kPa].

📊 Fluidization Results

📊 Output Summary
💾 Fortran Source

Minimum Fluidization Velocity (U_mf)

0.4418 m/s (44.2 cm/s)

Operating Velocity: 1.800 m/s (4.1 × Umf) | Bed ΔP: 5.00 kPa

GELDART GROUP D (SPOUTABLE)

Bed Pressure Drop (ΔP) 5.00 kPa 50.0 mbar

Terminal Free-Fall Velocity (U_t) 0.27 m/s Elutriation limit

Bed Height Expansion Ratio 2.42 × H₀ Expanded H = 1.93 m

Archimedes Number (Ar) 1.18e+4 Buoyancy / Viscous balance

📈 Minimum Fluidization Umf (m/s) vs Particle Size dp (μm)

📉 Bed Pressure Drop ΔP (kPa) vs Gas Velocity U0 (m/s)

=================================================================
 THERMOFLUIDCALC — FLUIDIZED BED HYDRODYNAMICS & U_MF REPORT
=================================================================
Case Title                 : Biomass Gasifier Spouted / Bubbling Bed
Solid Particle Parameters  : dp = 1800.0 microns, Solid Density = 1100.0 kg/m3, Sphericity = 0.75
Fluidizing Gas Conditions  : Temp = 750.0 C, Pressure = 1.05 bar, Superficial Velocity U0 = 1.800 m/s
Bed Dimensions             : Static Height H0 = 0.80 m, Column Diameter D = 0.90 m
-----------------------------------------------------------------
MIN. FLUIDIZATION VELOCITY : 0.44178 m/s (44.18 cm/s)
TERMINAL VELOCITY (Ut)     : 0.271 m/s
TOTAL BED PRESSURE DROP    : 5.00 kPa (50.04 mbar)
Fluidization Index (U0/Umf): 4.07 (Fully Fluidized)
Bed Expansion Ratio (H/H0) : 2.42 (Expanded Height = 1.93 m)
GELDART CLASSIFICATION     : GELDART GROUP D (SPOUTABLE)
=================================================================

📘 Calculation Methodology & Fluidization Standards

Geldart Particle Groups

Categorizes gas-solid fluidization behavior into 4 groups: Group A (aeratable catalysts), Group B (sand bubbling), Group C (cohesive fine powders), and Group D (coarse spouting grains).

Constant Pressure Drop Principle

Once fluidization begins ($U_0 \ge U_{mf}$), the total pressure drop across the bed remains constant and equals the apparent buoyant weight of the bed per unit area.

Key Engineering Assumptions

Wen & Yu (1966) correlation for $Re_{mf}$ across broad Archimedes numbers.
Haider & Levenspiel terminal velocity equation for non-spherical particles.
Applicable to CFB boilers, FCC regenerators, biomass gasifiers, and drying beds.

ThermoFluidCalc Engineering Report