Drying Process Simulation
Theory: drying proceeds in two stages
Overview
In our food drying line, water comes off quickly at first, then it barely dries at all. Would raising the temperature speed it up?
Drying has two stages with different character. At first the surface is wet and water simply evaporates from it, so raising air temperature or speed speeds it up directly (the constant-rate period). Once the surface starts to dry, water from inside can no longer reach the surface fast enough (the falling-rate period). Then thickness and internal diffusion matter more than air conditions, so raising the temperature alone helps less than expected and makes scorching or cracking at the surface more likely.
Constant-rate period
While the surface is wet, all heat from the air goes into evaporation and the surface stays at the wet-bulb temperature $T_{wb}$. $h$ is the heat-transfer coefficient and $h_{fg}$ the latent heat. However hot the air, the surface remains at the wet-bulb temperature throughout, which protects heat-sensitive materials.
Falling-rate period
Treating internal moisture movement as diffusion, the mean moisture ratio $MR$ of a slab of thickness $2L$ drying from both faces follows the series above. $D$ is moisture diffusivity, $X$ moisture content, and $X_0$, $X_e$ the initial and equilibrium contents. Time scales with $L^2/D$, so doubling thickness quadruples drying time.
What dried persimmons and lumber drying share
When making dried persimmons, if the surface dries first into a hard skin, moisture inside struggles to escape. The same happens in lumber drying: if only the surface dries fast, it shrinks and splits — surface checking. Traditionally persimmons are kneaded now and then, and lumber is started under humid conditions and dried gradually. Holding back surface drying so it stays in step with internal diffusion is exactly the idea behind the temperature–humidity schedules of modern dryers.
Worked examples
Example 1: air conditions and constant drying rate
With a heat-transfer coefficient of $h = 25$ W/(m²·K), the wet-bulb temperature was found from psychrometric relations and the constant drying rate computed:
| Air | Wet-bulb temperature | Constant drying rate |
|---|---|---|
| 40 °C, 30% RH | 25.0 ℃ | 0.55 kg/(m²·h) |
| 60 °C, 10% RH | 28.8 ℃ | 1.15 kg/(m²·h) |
| 80 °C, 5% RH | 33.8 ℃ | 1.72 kg/(m²·h) |
Even with 80 °C air, the material surface only reaches about 34 °C while it's wet. The rate depends on the difference between air and wet-bulb temperatures, so drying the air (lowering humidity) or raising air speed to increase the heat-transfer coefficient is as effective as raising the temperature.
Example 2: thickness and falling-rate drying time
With moisture diffusivity $D = 10^{-9}$ m²/s, the time for a slab drying from both faces to reach moisture ratios of 0.5 and 0.1 was computed for several half-thicknesses $L$:
| Half-thickness L | To MR 0.5 | To MR 0.1 |
|---|---|---|
| 2 mm | 0.2 h | 0.9 h |
| 5 mm | 1.4 h | 5.9 h |
| 10 mm | 5.5 h | 23.6 h |
Double the thickness, four times the time. So slicing thinner is the most effective lever.
For materials with long falling-rate periods, yes. Also, going from MR 0.5 to 0.1 takes more than three times as long as reaching 0.5 in the first place. The last bit of moisture is the slowest to remove, so not setting the target moisture lower than necessary is another key to shorter process times.
Simulating a dryer
Key points for CFD
- Airflow distribution: uneven air speed over trays or conveyors causes uneven drying. First solve the airflow with product in place and evaluate the local heat-transfer coefficient.
- Air humidification: downstream air carries more moisture, the gap to wet-bulb shrinks and drying slows. Solve humidity (vapour concentration) as a transported scalar with evaporation from the product as a source.
- Inside the product: when the falling-rate period matters, solve coupled heat and moisture diffusion in the material. Diffusivity varies strongly with moisture and temperature, so take it from test data.
- Empirical models: instead of resolving the interior, fit test drying curves with empirical models such as the Page model and apply them as product surface conditions to lighten the computation.
Dryer efficiency is set by exhaust humidity
Much of a hot-air dryer's energy is lost by exhausting air that hasn't picked up much moisture — throwing away heated air before its capacity is used. Recirculating part of the exhaust, or reducing airflow so air leaves well humidified, can cut fuel substantially for the same drying duty. Push humidity too high, though, and the wet-bulb temperature rises and drying slows, so it is effective to set conditions while watching both drying uniformity and exhaust humidity in CFD.
Common mistakes
Mistakes and fixes
| Mistake | Effect | Fix |
|---|---|---|
| Estimating the whole process at the constant rate | Drying time badly underestimated | Evaluate the falling-rate period by diffusion |
| Raising temperature only | Surface scorching or cracking | Adjust humidity and air speed too |
| Ignoring air humidification | Downstream drying overestimated | Solve humidity as a transported scalar |
| Constant diffusivity | Late-stage rate wrong | Determine moisture and temperature dependence from tests |
I'd like to try other conditions and see the drying curve.
Use the psychrometric calculator for wet-bulb temperature, the convective drying simulator for constant drying rate and the drying kinetics (Page model) simulator for fitting test data. Vacuum drying is covered by the freeze-drying simulator. High-temperature thermal equipment is covered in furnace simulation and kiln analysis.
Related Topics
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