Spray Cooling Simulation
Theory: removing heat by evaporating droplets
Overview
How is spray cooling different from just pouring water on?
Cooling with a water stream carries heat mainly as the water warms (sensible heat). Spray cooling puts fine droplets on the surface and evaporates them there, removing latent heat. Water's heat of vaporisation is over 500 times the heat to warm it by 1 K, so the same water carries far more heat. In exchange there's more to consider: droplet size and speed, whether they spread or splash on impact, and whether the surface is so hot that a vapour film forms (the Leidenfrost effect). Let's calculate the basics.
Water required
Top: the minimum water flux to carry heat flux $q''$ by complete evaporation. Bottom: the ratio of water needed by single-phase cooling with a rise of $\Delta T_{1\phi}$.
Droplet lifetime (d² law)
The squared diameter falls linearly in time. $B$ is the transfer number, larger in hotter gas. Lifetime scales with diameter squared, so a third of the diameter means a ninth of the lifetime.
Does the droplet splash?
On impact a droplet either spreads and sticks or splashes. In Mundo and co-workers' experiments, splashing occurred for $K$ above 57.7.
Leidenfrost's water drops
Drip water on a hot pan: moderately hot, it evaporates at once; much hotter, the drop beads up and skitters about, lasting a long time. The German physician Leidenfrost recorded this in 1756 — a vapour film forms under the drop and hinders heat transfer. In spray cooling and quenching, an overly hot surface enters this state and cooling capacity drops sharply. Once the surface falls below the Leidenfrost point, droplets wet it and cooling suddenly accelerates.
Worked examples
Example 1: water to remove 1 MW/m²
| Method | Water per m² | Per cm² (100 W) |
|---|---|---|
| Full evaporation (from 25 °C) | 0.39 kg/s | 2.3 mL/min |
| Single-phase, 20 K rise | 12.0 kg/s | 72 mL/min |
With full evaporation, 88% of the heat goes as latent heat, and the water needed is 1/31 of single-phase cooling.
Example 2: droplet lifetime in 500 °C gas
| Initial diameter | Time to evaporate |
|---|---|
| 10 µm | 1.6 ms |
| 30 µm | 15 ms |
| 100 µm | 160 ms |
| 300 µm | 1.5 s |
Example 3: droplet impact (water, 25 °C)
| Diameter, speed | We | Re | K | Outcome |
|---|---|---|---|---|
| 30 µm, 10 m/s | 42 | 336 | 28 | Spreads |
| 30 µm, 30 m/s | 374 | 1,008 | 109 | Splashes |
| 100 µm, 10 m/s | 138 | 1,120 | 68 | Splashes |
| 100 µm, 30 m/s | 1,246 | 3,361 | 269 | Splashes |
I thought smaller and faster droplets were always better, but too fast and they splash.
Small droplets evaporate fast and cover the surface finely. Speed helps by stirring the film, releasing vapour and carrying heat. But too fast and droplets shatter and splash, leaving before they evaporate: at 30 µm, 10 m/s spreads but 30 m/s splashes, and at 100 µm even 10 m/s splashes. And droplets that are too small can be pushed back by the vapour flow near the surface and never arrive. Nozzle selection balances droplet size and speed.
How to simulate
- Track droplets as Lagrangian particles exchanging momentum, heat and mass with the gas.
- Specify droplet size distribution (e.g. Sauter mean) and velocity from measurements or nozzle data.
- Switch wall-impact models (stick, spread, splash, rebound) according to surface temperature.
- Above the Leidenfrost point, account for a vapour film instead of a liquid film.
- Couple with conduction in the cooled solid and follow the cooling regime as surface temperature changes.
“The steel strip that wouldn't cool”
On a hot-rolling line, a 900 °C steel strip sprayed with water at first cooled less than expected, then suddenly began cooling fast past a certain temperature. At high temperature the droplets didn't wet the steel but bounced on a vapour film, with low cooling capacity; past the Leidenfrost point they wet the surface and cooling surged. When this switch happens at different places across the strip, uneven temperature causes warping and property scatter. Water flow and nozzle layout are now set with this transition in mind.
Common mistakes
Mistakes and fixes
| Mistake | Effect | Fix |
|---|---|---|
| Constant heat transfer coefficient | Large error with temperature | Vary regime with temperature |
| Ignoring Leidenfrost | Hot-surface cooling overestimated | Include film boiling |
| Single droplet size | Wrong evaporation and reach | Use size distribution |
| Ignoring splash | Cooling overestimated | Use impact models |
| Not solving gas flow | Wrong trajectories | Couple with gas flow |
I'd like to learn related topics.
Related pages include boiling heat transfer, pool boiling CFD, condensation heat transfer, conjugate heat transfer and thermal stress analysis.
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