Steam Pressure Calculation 1

[morninglori]

I have a "simple" problem that I am having trouble with. I have simplified the problem so I can do a bounding calculation.

I have a large, insulated vessel at initially empty (of water) at ambient temperature and pressure. inside the vessel is a small, initially very hot(almost melting point) piece of metal (nickel). Water (ambient temperature)with a fixed flow rate streams into the vessel. The water hits the hot metal and generates steam. The water continues to flow over the hot metal until the metal is cooled enough to not keep generating steam.

I need to determine the maximum pressure of steam in the vessel. I am not sure if it is a thermo problem or a heat transfer problem. any tips on how to solve would be greatly appreciated.


Thank you!

 

[mrpi]

Is it a sealed vessel into which pressurized water is pumped?

I guess you'd have to start with how fast steam is being generated and how fast it heats the air while at the same time looking at how fast the volume and pressure is changing from whats left of the water pouring in. This might be pretty complex.

Depending on the scale and how fast things are happening, some of these may be negligible. I.E a pea sized energy source in an Olympic swimming pool VS red-hot railroad spike in a beer can...

Beat to fit, paint to match.

 

[morninglori]

I am assuming that the vessel is sealed. The water is pumped, and I know that there is a point where the pressure of the steam will be greater than that of water coming in, but I would like to neglect that for now.

The scale of things are more on the order of a hockey puck in a 55gal drum - but the vessel is not a 55gal drum, just the size/volume.

there is a lot "out there" about hot things going into pools of water (nuke power rods, etc) but I am starting with now water.

The more I look at this problem, the more complex it gets.

 

[djack77494]

I don't think your problem is that complex at all. If I got it right, you are starting with a known mass of hot stuff at a given temperature and you want to add a fixed quantity of water and determine the resulting pressure. If the vessel ends being filled with saturated water, then, by heat balance you can calculate the equilibrium temperature (metal + water). From that you turn to your steam tables or their electronic equivalent and find the pressure. Am I missing anything?

 

[morninglori]

Won't there be a steam flash when the water first hits the metal? That will last a certain period of time, right? I picture dropping water onto a hot/dry pan on your stove.

djack - I get what you are saying about when the vessel fills with saturated water, but what about the time before?

I am thinking about in from the perspective of...
time 1: hot stuff in closed vessel.
time 2: small mass of water into vessel, hits hot metal, makes steam, temp of metal lowers, temp and press in vessel increases...
repeat until temp of metal cool enough or metal is submerged in water.

 

[mrpi]

But maybe to be conservative the problem could be looked at without considering heat transfer to the metal, and finding the situation that would result in the most steam... like when the hot mass has boiled all the water it can. djack may have been saying the same thing.

Also consider what degree of accuracy you need. There are other factors such as the boiling heat transfer at the water-heat-source interface, effect of back pressure on the feed pump, etc.


Beat to fit, paint to match.

 

[zdas04]

You'll have to solve it iteratively, I really don't think there is a closed-form solution.

First, figure out how many BTU's are liberated for the known mass cooling from the initial temp to (say) 220F. Then figure out what mass of water would vaporize from that many BTU's. Next find what pressure you would get in a fixed volume by vaporizing that much water. Then go to the saturated steam table and find the temp that goes with that pressure. Repeat the whole process with this temperature as the starting point.

I don't think it will take more than 3-4 iterations to get an answer you can live with.

One thing to keep in mind is that this proceedure is assuming that the water is added at a rate that it all turns to steam until the heat source is used up. If you add water to the process faster than the heat can transfer then you will heat the water but not get past the latent heat of vaporization and may not get any steam (i.e., if you dump 50 gallons of ice water on a hot hockey puck you will get slightly less cool water and any steam that is created in contact with the puck will condense very rapidly in contact with the bulk of the water).

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[rmw]

Is this a homework problem?

rmw

 

[morninglori]

No. this is an actual real life problem. I have just tried to simplify as best as I can to be able to do a "hand calc"

I have looked in my old texts to see if there was a homework problem of this nature, but no luck.

 

[rmw]

Well it looks simple enough to me. You have a known with a known temperature and specific heat BTU/lbm for those of us still stuck in the english system. How much, if any of the water that is converted to steam is a function of the water flow into the vessel and into contact with the mass of the molten metal. If the water flow is high enough, very little steam might be produced. If too low, well, don't be in there with it. It is a thermo flow problem because you have heat in motion and it is a heat transfer problem because you have all the variables that affect heat transfer.

rmw

 

[carnage1]

it sounds like you have a fixed volume. you have water entering at some temperature so you know its entropy, enthalpy, etc you have a fixed mass of molton metal at some temperature, you have a fixed volume of air (you may be able to ignore its partial pressure depending on how exact you need to be).
you should be able find how much water you need to add to be somewhere under the vapor dome (I'd aim for a quality of .5 to have the largest margin of error)
This will give you your final pressure and total water.
for max pressure you could set up a second or third order differintial equation, but it probably isn't worth it. id check pressures at 1/4 total water 1/2 total water and 3/4 total water. look at the graph and decide if it peaks in the middle or if your final pressure is your highest pressure. I'd expect your final pressure to be the highest as there is the most mass and the most energy.
also don't forget the PV work required to pump the water in as it may be enough to matter.

 

[morninglori]

Thank you all so much for your suggestions.

zdas04, I believe your recommendation will bound the problem in a "quick" way. That is what I am going for first.

Thanks!

 

[Compositepro]

There is no way you can calculate peak pressure. It is not an equilibrium problem but a dynamic heat transfer problem. Surface area of the disc exposed to water is a big factor and the presence of air which would interfere with the condensation of steam on cold surfaces.
If you have a lot more water mass than hot metal the final presuure would be almost zero. If the vessel has no vapor volume you could generate hundreds of psi. Your answer will be somewhere in between. I would sugest that you have plenty of vent area on your vessel or a high pressure rating.