Two Tanks Connected by Gas Valve - Temperature Rise? Adiabatic Compression?

[markdblissmn]

I have a two part question: No, this is not homework. Reference my other threads (

http://www.eng-tips.com/viewthread.cfm?qid=354606).

1. Why is nitrogen used in autoclaves?
2. What is the temperature rise and fill time for a two tank connected system. Is adiabatic compression valid?

Suppose I have an air receiver and vessel connected together by a short (negligible) section of pipe and a ball valve. The air receiver is 200gallon in size, and charged to 100psig. The vessel is 74.6gallon, and at 0psig. The ball valve Cv is 10.0. All gas is initially at 72degF. When the ball valve is opened, compressed air flows from the receiver to the vessel. I am not sure how to calculate the final gas temperature once the gas pressure settles. See attached Excel file.

I know the final pressure is Pfinal = (P1V1 +P2V2)/Ptot. In this scenario, the Pfinal is 72.83psig. Pfinal = (200*100 + 74.6*0)/(200+74.6) See attached.

I have setup a spreadsheet with an iterative deltaTime calculation. Based on the deltaPressure, I know if the flow is choked or not. If choked or not, I know the flow formulas (

http://www.forberg.com/pdf/techSup/Home_Tech Support_Valve Flow_calc_and_sizing.pdf).

I then can calculate the amount of gas transferred during the small deltaTime period. For the above scenario, it gets there 6.8seconds. Again, see attached.

How do I find the temperature rise? Is there a temperature rise? I am not sure and wonder if the following is true: The gas in the high pressure cylinder flows across the valve and turns into velocity, and drops in temperature. It then increases in pressure in the vessel and increases in temperature. Does the gas go from room temp to cold back to room temp? There is not temperature rise? Is this correct?

The application I have needs to minimize the fill time of the vessel. I want to get to the vessel's final pressure as fast as possible. I don't want to use an inert gas. I want to use compressed air - the facility has a large central compressor which I could use to charge my receiver.

Thanks! - Mark

Mark Bliss

 

[25362]

I wonder if, after the quick (probably adiabatic) expansion, knowing the final volumen, V[sub]f[/sub], and the final pressure, P[sub]f[/sub], one can estimate the final temperature, T[sub]f[/sub], by applying: P[sub]f[/sub]V[sub]f[/sub] = RT[sub]f[/sub], as if the air were an ideal gas.

For a non adiabatic process, other more experienced contributors may clarify what is happening in both containers as time passes.

 

[Compositepro]

Nitrogen is used in autoclaves to lower the risk of fires. Your other question may have some intellectual interest but I don't see much practical value.

 

[racookpe1978]

This problem has been asked several times before in both heat exchange and mechanical engineering, once in the pipe forum: though never with a practical application - though often as in a "textbook" or homework problem.

 

[markdblissmn]

There is a huge heat treating opportunity I am working on currently, where I want to pressurize a vessel to a certain value in as little time as possible. We would like to use air instead of nitrogen, as the facility has a large central compressed air supply available. I am worried about the effects on heat/explosion within the vessel and the hot component.

If it were a homework problem, I would care about the timing of responses. But I don't care. I don't care if I get a response in a week or two. I'm looking for an expert on pressure vessel flow, concerns, and the thermodynamics of flow across the valve and then re-pressurizing.

Mark

Mark Bliss

 

[iainuts]

Hi Mark. I think what you want to do is to model this system using basic principals. To do that, you need:
[ul]
[li]Thermodynamics[/li]
[li]Heat transfer[/li]
[li]Fluid flow through pipes/valves[/li]
[/ul]
Your system can be broken up into 3 sections. The first is the supply vessel, the second is the piping and the third is the receiving vessel.

Draw a control volume around the first vessel and apply the first law which is reduces to: dU = U2 - U1 = Qin - Hout
or U2 = U1 + Qin - Hout
One problem is, you need a fluid properties database to do this type of work. We have a proprietary one where I work but you can purchase a very similar database from NIST called REFPROP.

http://www.nist.gov/srd/nist23.cfm

Another problem is you need heat transfer. As the gas leaves the supply vessel, it cools. In fact, the gas remaining in the vessel cools exactly as if it were doing work, so if it were adiabatic (ie: we ignore Qin), the gas remaining in the vessel would follow a line of constant entropy. So yea, it will get very cold as pressure drops and just the thermal mass of the vessels walls will be enough to warm it up. Heat flux from ambient isn't nessesary because the thermal mass of the vessel will be so high that it won't change temperature significantly. And that's actually a good thing for your analysis, because it means you can ignore all the extra work determining heat flux from ambient and only look at convective heat transfer from the inside wall of the vessel to the bulk gas to determine Qin. I typically use just a common value for convective heat transfer coefficients in this case because I'm too lazy to do all the work necessary to calculate h and because even if you do, I have little faith they will be any more accurate than the values I typically use. I'd suggest looking at the range of 0.5 to 1.5 Btu/hr-ft[sup]2[/sup]-F. Once you create a program (or spreadsheet) to do this, you can do a sensitivity analysis by sticking in that range of values.

Next, look at the gas flowing through your pipe. If you have a ball valve as you suggest, I'd recommend looking at the entire pipe including an entrance and exit loss as well as straight pipe and elbows. You can reduce all that as per Crane TP410 or just calculate a few values over the range you'll be working with and set up an equivalent Cv valve equation, similar to what you're doing now with just the one valve. But you said you have a ball valve which I generally consider to be a piece of pipe, so you really should take a look at the entire pipe run.

If you put a control volume around this pipe, you'll find you have Hin = Hout. It's isenthalpic. Which is great because it makes your job determining what happens in the receiving vessel much easier. Note I'm assuming you can ignore heat transfer for the pipe so this is adiabatic. If you don't think heat transfer can be ignored, just add that in so that Hin = Hout + Qin (ie: temperature is going to be below ambient so heat is entering the gas).

Similar to the supply vessel, the first law for the receiving vessel becomes dU = U2-U1 = Qout + Hin
or U2 = U1 + Hin - Qout
Note that in both these vessels I'm assuming an increase in energy is in and hotter while a decrease in energy is out and colder. As gas enters this vessel, it compresses what is already in it so that gas gets hotter. Again, you will have a heat tansfer term that you need to solve based on the above convective heat transfer value and bulk gas temperature. As per the supply vessel, you need a computerized thermo database to do the analysis.

I would typically do this using a spreadsheet with each line being some small time step and each column being part of the above analysis. I've done this before and it works out fairly well. What little experience I have with REFPROP is good - I think it will do what you need here.

Hope that gets you started,
PS: I also post under Q_Goest at PhysicsForums. So yes, this is a very similar problem to that one and I'd recommend doing those iterative steps the same, basic way. Except if you are a professional engineer, your company should give you the proper tools for this and that includes REFPROPS.