Modeling boiling in a closed container with a small hole

In summary: in summary, you can use mass balances to calculate pressure, temperature, and velocity in a system boiling water.
  • #1
Hang11
3
0
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.
 
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  • #2
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.
 
  • #3
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?
 
  • #4
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.
 
  • #5
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.
 
  • #6
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.
 
  • #7
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.
 

Related to Modeling boiling in a closed container with a small hole

1. How does the size of the hole affect the boiling process?

The size of the hole in a closed container can have a significant impact on the boiling process. A larger hole will allow for more steam to escape, resulting in a faster boiling rate. On the other hand, a smaller hole will restrict the steam flow and result in a slower boiling rate.

2. Is the boiling temperature affected by the size of the hole?

The size of the hole does not directly affect the boiling temperature. However, it can indirectly impact the temperature by influencing the rate at which steam escapes. If more steam is able to escape through a larger hole, the temperature may drop slightly as the energy is released. Conversely, a smaller hole may result in a slight increase in temperature as less energy is released through steam.

3. How do atmospheric pressure and altitude affect boiling in a closed container?

The atmospheric pressure and altitude can both have a significant impact on the boiling process in a closed container. At higher altitudes, the atmospheric pressure is lower, which means that the boiling temperature is also lower. This can result in a slower boiling rate and a longer time to reach the boiling point. Additionally, a change in atmospheric pressure can affect the rate at which steam escapes through the hole, further impacting the boiling process.

4. Can the shape of the container affect the boiling process?

The shape of the container can affect the boiling process in a couple of ways. The shape can influence the distribution of heat within the container, which can impact the boiling rate. Additionally, the shape can also affect the pressure and steam flow within the container, which can affect the boiling temperature and rate.

5. How does the material of the container impact the boiling process?

The material of the container can have a significant impact on the boiling process. Some materials may conduct heat more efficiently, resulting in a faster and more uniform boiling process. Others may be more prone to heat loss, resulting in a slower and less efficient boiling process. Additionally, the material can also affect the pressure and steam flow within the container, which can influence the boiling temperature and rate.

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