Thermodynamics Question About Steam

[jesmitter]

How long does it take for 500 degree F - 1000 psi steam to move through 24" of 3/16 ID pipe and fill a 1 cubic inch volume cylinder to 1000 psi? Can it be modeled mathematically or with the help of Steam Tables?

 

[anorlunda]

That sounds like a school assignment. Is it?

 

[jesmitter]

No, I am trying to characterize a single cylinder steam engine that I want to design and build to see what the RPM limit will be.

 

[Chestermiller]

What is in the tube and cylinder before you start?

 

[jesmitter]

The 3/16" tube is connected to an electronically controlled steam valve at the cylinder which will open at top dead center of the piston inside the cylinder. So, the tube will theoretically be filled with steam produced by the boiler (assume an unlimited steam supply), at least for the first cycle. Then as the RPM increases, the tubing will reach its limit caused by the diameter of the tubing causing "steam Starvation". In addition, the cylinder has a fill time that may not be satisfied by the amount of steam that the tubing can supply at the higher RPM. These are the unknown variables I'm trying to figure out -
1. What is the flow/volume limit through 3/16" stainless steel tubing?
2. What is the "fill time" required for the cylinder to completely fill with steam at full pressure (1000 psi)?

 

[jrmichler]

Yes, it can be modeled. You can calculate pressure drop vs flow rate through pipe for any Newtonian fluid, gas or liquid, using a Moody chart (search the term). However, that calculation only works for steady state flow. Your application will only have steady state flow at extremely low speed.

At any speed over about 10 to 100 RPM, a flow calculation will need to include the time to move the valve from closed to open, the volume of the tube, and the position of the piston. I once wrote a simulation for a high speed air cylinder. That simulation accurately predicted acceleration, deceleration, and presence/absence of bouncing. The simulation treated the valve as a variable orifice, and the connecting tube as a dead volume lumped with the piston position. Your case has a very long tube, which adds a complicating factor.

I suggest start with simplifying assumptions:
1) Valve opens instantly.
2) Piston at TDC, not moving.
3) Ignore pressure drop down the length of the tube.
4) Valve starts to open at TDC.
5) Ignore the speed of sound in the steam.

Then the only pressure drop in the system is the $C_V$ or equivalent orifice area of the valve. Then you can calculate the initial flow rate through the valve. Calculate the time for the downstream pressure to increase about 10%, then recalculate the flow rate at that time step until downstream pressure is almost equal to supply pressure. This can be done with a spreadsheet.

When you get that iterative calculation working, it's easy to add sophistication. Based on your results, decide which simplifying assumption you want to remove. If, for example, the time to fill the tube with steam is about equal to the valve opening time, that would be a good variable to add to your model.

IMPORTANT: Start as simple as possible, then add only one variable at a time.