Engineering guide
This module calculates flow patterns and pressure drop in fluidized beds according to Section L3.2 of the VDI-Wärmeatlas (VDI Heat Atlas, 12th edition, 2019). Fluidized beds are used in process engineering wherever intensive contact between solid particles and a gas or liquid is required: fluidized bed dryers, fluidized bed combustion, catalytic fluidized bed reactors, granulation and coating plants. For the design, the minimum fluidization point, the pressure drop of the fluidized bed and the pressure drop of the distributor plate must be calculated.
The starting point is the minimum fluidization point: if the approach velocity through a packed bed is increased, its pressure drop grows – for example according to the Ergun equation – until it supports the area-specific weight of the bed. From this minimum fluidization velocity onward the bed is fluidized and the pressure drop remains nearly constant with further increases in velocity. At the upper end, the terminal settling velocity of the individual particles limits the operating range, because above it particle entrainment sets in.
Besides the minimum fluidization velocity, Reynolds and Archimedes numbers, the module also provides the bed expansion in operation as well as the design parameters of the distributor plate: hole diameter, number of holes, velocity in the hole and distributor pressure drop, which must be chosen high enough to ensure uniform fluidization.
Scope
- Flow patterns and pressure drop in fluidized beds
Typical workflow
Enter solid and fluid properties
Solid density, particle size and specific surface area, porosity of the bed at rest as well as density and viscosity of the fluid form the input data. The Archimedes number characterizes the particle-fluid system in dimensionless form.
Determine the minimum fluidization point
From the condition that the pressure drop of the bed reaches the buoyancy-corrected area weight of the layer, the minimum fluidization velocity, the porosity at the onset of fluidization and the Reynolds number at fluidization are calculated; the Ergun equation, for example, serves as the pressure drop model.
Calculate the pressure drop of the fluidized bed
Above the minimum fluidization point the pressure drop supports the bed weight: it follows from the bed height, the porosity and the density difference between solid and fluid, and remains nearly constant over the velocity.
Check the operating range and expansion
The terminal settling velocity of the single particle (laminar or turbulent, via Reynolds and Archimedes numbers) marks the entrainment limit. Between minimum fluidization and entrainment velocity, the operating porosity and from it the expanded fluidized bed height are determined (expansion exponent n).
Design the distributor plate
From hole diameter, free cross-section and number of holes follow the velocity in the hole, the Reynolds number in the hole and, via the drag coefficient, the distributor pressure drop. It is chosen as a sufficient fraction of the bed pressure drop so that all holes are traversed uniformly.
Frequently asked questions
Why does the pressure drop of a fluidized bed remain constant above the minimum fluidization point?
Because the flow supports exactly the buoyancy-corrected weight of the particles. If the velocity increases further, the bed expands: the porosity increases and the specific resistance decreases just enough for the force balance to be maintained. Only when the particle entrainment velocity is reached does this equilibrium break down.
How high should the pressure drop of the distributor plate be chosen?
As a rule of thumb well above zero, typically on the order of 10 to 30 % of the bed pressure drop (at least a few millibar). Too low a distributor pressure drop leads to non-uniform fluidization: some zones are preferentially traversed while others remain as dead zones. For this the module calculates the hole velocity, the drag coefficient and the characteristic number of the distributor.
What happens when the approach velocity reaches the settling velocity of the particles?
Then particle entrainment begins: individual grains are carried out with the fluid and the bed becomes depleted of fines. The permissible operating range of a classical bubbling fluidized bed lies between the minimum fluidization and the entrainment velocity; for broad particle size distributions the settling velocity of the finest relevant fraction is decisive.
Does the calculation apply equally to gas and liquid fluidized beds?
The force balances apply to both. However, liquid fluidized beds usually expand homogeneously, while gas fluidized beds form bubbles from just above the minimum fluidization point; flow pattern, solids mixing and heat transfer then differ significantly. The classification of the fluidization behavior (e.g. by particle size and density difference) should additionally be checked.
Worked example
A fluidized bed of quartz sand is fluidized with air. This worked example calculates the pressure drop of the fluidized bed at the minimum fluidization point.
Given
| Bed height at minimum fluidization HL | 0.40 m |
|---|---|
| Porosity at minimum fluidization εL | 0.45 |
| Solid density ρs (quartz sand) | 2,600 kg/m³ |
| Gas density ρf (air) | 1.2 kg/m³ |
| Gravitational acceleration g | 9.81 m/s² |
Solution
Force balance of the fluidized bed
At the minimum fluidization point the pressure drop supports the buoyancy-corrected area weight of the bed:
Δp = HL · (1 − εL) · (ρs − ρf) · g
Numerical calculation
Δp = 0.40 m · (1 − 0.45) · (2,600 − 1.2) kg/m³ · 9.81 m/s²
Δp = 0.40 · 0.55 · 2,598.8 · 9.81 Pa ≈ 5,609 Pa ≈ 56 mbar
This value remains nearly constant as the gas velocity is increased further up to the entrainment limit and is at the same time the reference quantity for choosing the distributor plate pressure drop.
Result
| Pressure drop of the fluidized bed Δp | ≈ 5,600 Pa ≈ 56 mbar |
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Technical content source: LV-Solved-Problems-Content 628d313247e7