Pool Boiling CFD Analysis
Theory: the lengths and times that govern boiling
Overview
I want to simulate boiling in CFD, but can't decide whether to resolve each bubble or use a model.
First estimate bubble size and bubble spacing. Both are set by the capillary length — the ratio of surface tension to buoyancy — a few millimetres for water. Resolving a bubble directly needs about 20 cells across it, while boiling patterns repeat on wavelengths of a few centimetres, so the domain must span several of those. The ratio fixes the cell count. Counting makes it clear why direct resolution suits research and wall-boiling models suit whole equipment.
Capillary length and instability wavelength
$L_c$ is the length at which surface tension and gravity balance. $\lambda_d$ is the fastest-growing Rayleigh–Taylor wavelength when heavy liquid sits on light vapour; it sets the spacing of vapour columns in film boiling and near CHF.
Bubble departure and nucleation
Left: Fritz's departure diameter (contact angle $\theta$ in degrees). Middle: Zuber's departure frequency. Right: the Lemmert–Chawla nucleation site density often used in RPI wall-boiling models, as a function of wall superheat $\Delta T_{sup}$. All are empirical and scatter widely with surface condition.
The birth of the RPI model
The RPI model, the best-known wall-boiling model, was formulated in the early 1990s by Kurul and co-workers at Rensselaer Polytechnic Institute, whose initials give it its name. It partitions wall heat into liquid convection, evaporation, and 'quenching' as cold liquid refills the site after a bubble departs. It was devised for equipment such as reactor fuel assemblies, where tens of thousands of bubbles can't be resolved individually, and is now built into many commercial CFD codes.
Worked example: scales for saturated water
1 atm versus 7 MPa
| Quantity | 1 atm (100 °C) | 7 MPa (286 °C) |
|---|---|---|
| Capillary length | 2.50 mm | 1.60 mm |
| Critical wavelength λc | 15.7 mm | 10.0 mm |
| Most dangerous wavelength λd | 27.3 mm | 17.4 mm |
| Departure diameter (45°) | 2.34 mm | 1.49 mm |
| Departure frequency (45°) | 39 Hz | 48 Hz |
Effect of contact angle (1 atm)
| Contact angle | Departure diameter | Departure frequency |
|---|---|---|
| 20° | 1.04 mm | 89 Hz |
| 45° | 2.34 mm | 39 Hz |
| 80° | 4.17 mm | 22 Hz |
Grid count for direct bubble resolution
Resolving the 45° departure diameter with 20 cells in a domain two most-dangerous wavelengths square and three high gives, at 1 atm, 0.117 mm cells and 465×465×698 ≈ 150 million cells. At 7 MPa cells shrink to 0.075 mm but so does the domain, leaving the same 150 million. Bubble cycles last tens of milliseconds and interface tracking needs time steps about a thousandth of that, so even a few seconds of physics is a large computation.
Nucleation site density in wall-boiling models
| Wall superheat | Site density | Mean spacing |
|---|---|---|
| 5 K | 28 per cm² | 1.9 mm |
| 10 K | 99 per cm² | 1.0 mm |
| 20 K | 347 per cm² | 0.54 mm |
At 20 K superheat the site spacing is 0.54 mm — much smaller than the 2.3 mm departure diameter.
Then neighbouring bubbles merge before departing, and large vapour patches begin forming on the surface — the picture near critical heat flux, where the wall-boiling model's assumption of individual bubbles breaks down. RPI loses accuracy there, so CHF prediction combines other correlations or models. At 5 K, by contrast, spacing is 1.9 mm, about one bubble size: bubbles form and leave independently, the regime the model handles well. Whichever method you use, compare these scales first to know which regime your calculation is in.
How to proceed
- Compute capillary length, departure diameter and wavelength first to size cells and domain.
- For direct resolution use VOF or level set, and watch interface phase-change model coefficients (e.g. Lee model).
- For whole equipment use Eulerian two-fluid with a wall-boiling model, choosing site density, diameter and frequency correlations for the conditions.
- Couple conduction in the heater solid; wall temperature variations change the boiling distribution.
- Validate against boiling-curve correlations or experiments.
“Polishing the surface made boiling harder”
In one experiment, polishing the heater to a mirror finish raised wall temperature at the same heat flux and delayed boiling onset. Polishing removed the tiny scratches and cavities that seed bubbles, reducing nucleation sites. Wall-boiling site-density correlations don't directly include surface condition, so a different finish can make them far off. Conversely, deliberately micro-structured surfaces that add nucleation sites are used to enhance boiling heat transfer.
Common mistakes
Mistakes and fixes
| Mistake | Effect | Fix |
|---|---|---|
| Domain smaller than wavelength | Unphysical bubble pattern | At least 2 λd |
| Too few cells per bubble | Interface and evaporation error | About 20 cells |
| Unchecked site density | Heat flux off by 2× | Calibrate with data |
| Trusting RPI near CHF | CHF misjudged | Combine with CHF correlations |
| Ignoring wall conduction | Local hot spots missed | Couple with solid |
I'd like to learn related topics.
Related pages include boiling heat transfer, spray cooling, condensation heat transfer, two-phase heat exchangers and conjugate heat transfer.
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