How much liquid nitrogen?

Main Question or Discussion Point

How much liquid nitrogen???

Hi All,

A liquid nitrogen evaporation question for you :)

A large metal container is kept at constant temperature of 40 degrees Celsius.

This container has a long 10inch diameter tube opening connected to its top.

Through a second opening liquid nitrogen is poured in at a constant flow.

The question is, how many gallons of liquid nitrogen per hour are needed to keep a constant evaporation (cold steam) of 1000psi to exit the 10inch diameter tube opening connected at the top.

(Please do ignore the mechanics involved the nitrogen gas from going back out through its point of entry and other small variables.)

Let me know if you have any questions

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Q_Goest
Homework Helper
Gold Member

Hi solorider. Couple problems:
1) You've implied a large amount of heat flux into the liquid nitrogen (LIN) by stating the container is large and at 40 C but you haven't provided any information about the magnitude of this heat flux. Do you have the heat flux? Do you have any dimensions for this container? And what kind of insulation, if any, is part of this container? The container alone has to be made of metal that is very thick so even that provides some value of insulation.
2) LIN is supercritical above 492 psia so at 1000 psi the nitrogen is supercritical. It doesn't boil because there is no liquid/gas interface. It is all a single phase. Note also you've implied that the nitrogen coming out of the 10" opening is coming out as saturated gas but obviously that's not going to happen. You'll need to define the state somehow.
3) Regarding the outlet, if this is venting to atmospheric pressure there will be a shock wave at the opening so you need to explain what assumptions you're making around this outlet. Information about this outlet is lacking.
4) Regarding the inlet, you said you're pouring this LIN into the container but that's impossible given the critical pressure and the container at 1000 psi so you need to define how the LIN is being added. One could pump it in for example, in which case you would need to evaluate the pumping process including inlet conditions to the pump, heat flux, assumed isentropic efficiency, etc... There's no information on this inlet state.

Are you trying to learn something here or is this a concept you're trying to evaluate?

Good morning Q Goest and thank you for your interest,

I understand your questions and I will try to clarify the best I can.

First off yes it is a real application and I will learn greatly :)

Some of these I rather keep constant to make things easier.

1- Size of the container: 10k gallons.
2- Type of container : 3" thick metal no insulation
3- Heat: Unlimited and constant
4- Opening out to the atmosphere
5- Ignore shock-wave.
6- Ignore inlet mechanism.

About " LIN is supercritical above 492 psia" are you suggesting that the LIN will not turn into gas and will stay liquid because of the pressure?

Cheers

Q_Goest
Homework Helper
Gold Member

Critical pressure is the pressure above which a liquid/gas interface can't exist (assuming there is ONLY nitrogen in the container). What happens is the surface tension essentially disappears. As pressure rises above the critical pressure, there is no more surface tension, no more liquid/gas boundary, and the two phases will begin to mix. Cryogenic pumps for example commonly go above the critical pressure so the stuff coming out is supercritical and isn't really a gas or a liquid. So the question has to be, what state does the LIN start in (pressure and temperature below critical pressure or a saturation pressure) and how does the LIN get up to 1000 psi? Is it pressurized by another media? Does it just heat up till the pressure reaches 1000 psi (such as by loss of vacuum in the annular space of a vacuum insulated tank)? Those two processes are very different and result in different physical states for the nitrogen.

Once it gets up to 1000 psi, is there a burst disk that ruptures? Or does it just keep coming out as the pressure rises? Regardless, there is a shock wave at the outlet to atmosphere. The pressure ratio is well above that required to create the shock wave. But that's ok since it's a common phenomena and well understood.

Once the pressure is up to 1000 psi, how does more LIN get into the 10k gallon tank?

Try and walk through the entire process that occurs to the tank, it will help in defining the process that needs to be analyzed.

- "above the critical pressure so the stuff coming out is supercritical and isn't really a gas or a liquid"
So what does come out? I imagine that what ever is coming out exerts pressure doesn't it?

- LIN begins at a Liquid state.
- The LIN just heat up till the pressure reaches 1000 psi.
- LIN keep coming out as the pressure rises to 1000 psi

"Once the pressure is up to 1000 psi, how does more LIN get into the 10k gallon tank?"
Lets just say the "fresh" LIN continuously flows in with no interruptions. Remember I'm trying to figure the amount of LIN needed for a continual 1000 psi at the outlet.

Cheers

xts

Non-insulated metal container filled with liquid nitrogen would get covered very quickly by thick layer of ice/frost and can't be kept in constant temp +40C except of dramatic supply of energy and near-explosive evapouration of N2

What is the purpose for it? Every safety inspection in the world would imprison you for keeping non-insulated metal container with 40 m^3 of liquid nitrogen.

relax xts .... all is safe and legal :)

Q_Goest
Homework Helper
Gold Member

Hi solorider, Using the term "liquid" in front of "nitrogen" and saying it is at 1000 psi is confusing at the very least. Nitrogen, like any fluid, has some pressure and temperature that it boils at. For nitrogen at atmospheric pressure (14.7 psia) that temperature is around -320 F. When it's inside a tank such as you're suggesting, the gas that boils off increases the pressure of the tank (assuming it can't get out. So as we add heat, the pressure rises. The temperature also rises. If the gas and vapor are in thermal equilibrium, meaning they are at the same temperature because they're in close, physical contact, the liquid is boiling and the gas is at the same temperature as it bubbles out of the liquid.

As the pressure of this boiling mixture increases, the temperature also increases. So at atmospheric pressure (14.7 psia) the temperature is -320 F. But as the pressure rises to the critical pressure of 492 psia, the temperature rises to -232 F. So the temperature has come up a total of 88 degrees F. The same thing happens in the radiator of your car. If you have the cap on the radiator, the pressure increases and the temperature at which the coolant boils at also increases. All liquids do this AFAIK. They all will need to get hotter in order to boil at a higher temperature.

In addition to an increase in temperature, the density of the boiling liquid decreases and the density of the gas which is boiling off increases as the pressure and temperature increases. For nitrogen at atmospheric pressure, the density of the liquid is 50 lbm/ft3 and the density of the gas is 3.5 lbm/ft3. When the pressure reaches 492 psia, the density of the liquid is 24 lbm/ft3 and the density of the gas is 16 lbm/ft3. Note how close together the density of the gas and liquid is as we approach the critical pressure. Also remember the dramatic rise in temperature.

In fact, all the properties change including surface tension. As pressure and temperature increase, the surface tension decreases until it finally fades away at the critical pressure.

When nitrogen gets up to the critical pressure of just over 492 psia, the density of the liquid and gas are the same and the surface tension between the two disappears. There is no longer a boundary between the liquid and gas and there is no difference in density. At this critical pressure and just above it, you could heat up the nitrogen at constant pressure and the nitrogen (assuming it could expand) would warm up and become less dense, but there wouldn't be any liquid. Similarly, you could remove heat from the nitrogen and make it colder and more dense, but there still wouldn't be any liquid/gas interface because there is no surface tension above the critical pressure.

For a restriction such as a round hole in the tank 10" in diameter, the flow rate out of the hole is a function of the density of the fluid. Assuming a discharge coefficient for the hole of 0.6 (which is fairly typical of a choked orifice, though it could be a bit higher) the flow rate is a function of density which is also a function of temperature. For the sake of argument, we know the LIN has warmed up from -320 F to -230 F at around 500 psi, so let's just use -200 F as an example at 1000 psig. At -200 F, the flow is around 3100 lbm/s. It could be much warmer or even much colder. It depends on how the nitrogen got up to 1000 psi. You talk about wanting to put LIN in to keep the pressure up to 1000 psi, but you don't say how. The only realistic way is to pump it in (with a very large, multi stage centrifugal pump). If it was pumped up to that point for example, you have a roughly isentropic compression of the nitrogen. If we assume 100% isentropic efficiency for our pump and assuming our pump went from atmospheric pressure to 1000 psig, the temperature of this 1000 psi nitrogen would be -317 F which is MUCH denser and colder than the nitrogen that simply warmed up. In this case, the flow could be almost 10,000 lbm/s.

So if you want to know how much nitrogen comes out, it's somewhere between about 1000 lbm/s and 10,000 lbm/s and the actual flow rate will depend on what density the supercritical gas is that's blowing out. There is no way to determine what that density is without knowing 'how it got there' so to speak. If it warms up and blows off, it could be fairly warm. If it is being replenished by a pump, it would be very cold. The actual flow rate depends on density which depends on how it got to that point.

Good evening Q Goest,

In addition to the 3 "Recognition"s you have earned, I believe one more is in order = "The Wise one"

Thank you for your help and a happy new year :)