Modeling boiling in a closed container with a small hole

[Hang11]

I'm trying to build a mathematical model of something like Heron's Aeolipile:
http://en.wikipedia.org/wiki/Aeolipile
I'd like to know, based on a known heat flux, the pressure and temperature attained in the container.
I assume as water boils, the control volume loses mass and energy, the pressure and temperature of the vapors will stabilize.

 

[mfb]

The exit velocity of the gas (and therefore mass flow) will have some relation to the pressure difference. Equilibrium happens where you can boil enough water (transfer enough heat) to maintain that mass flow. Temperature is given by the vapour pressure - I would expect no significant deviations from standard pressure and 100°C.

 

[Hang11]

but what kind of pressure increase in the vessel and what steam mass outflow should I get once it reaches a steady state boil?
How would I calculate that?

 

[mfb]

You'll need the rate of heat flow to the container, everything else will follow from that. That rate will depend on your heating mechanism.

 

[Hang11]

Assuming pool boiling, nucleate regime, the equation of the heat flux contains both the saturation temperature and the surface temperature. However, as more heat is pumped into the system (the exhaust is small), the Tsat changes. So , even knowing the heat flux, I still have two unknowns, the surface temperature and the saturation temperature.

 

[mfb]

If the approximation "all water is at 100°C" is not precise enough for your model then you'll have to model heat and gas flow in the water. Every new detail you add in the model gives the same number of unknown quantities as it gives equations to calculate those, as long as you include all relevant material properties and so on.

 

[anorlunda]

40 years ago, I derived a closed form solution for dP/dt, dm(water)/dt, and dm(steam)/dt in a setup very similar to this. It was great fun deriving it from mass balances of water and steam, and energy balances of water and steam, and the properties of water and steam. I used the result in simulators for nuclear power plants.

Give it a try. You'll succeed if you persevere.