Is there any gas in the system?
Not counting friction in a closed loop, you can get any flow at zero pump head. No real closed system will have this characteristic though.
@Steven Bolgiano : this ^^
Thanks! I wanted to make sure I wasn't overlooking factors beyond friction.
So you are trying to design a real system.
Real. "Solar Assisted Anaerobic Digester"
"poor boy" solution...How much did it cost to make this system? It doesn't look cheap. I would imagine a hydronic expansion tank is chump change in comparison. But perhaps the change in temperatures in the system are not so great that you've experienced a problem.
A simple 'T' fitting at the high point in the system, would allow air to escape, while heated water would not flow through the small exposed reservoir tank.
You can work that out by knowing the temperature of the water around the system and computing the density. Compute a path around the loop, accumulating hydrostatic pressure and head.
Unless they are simple flaps, check valves will take more pressure to operate than is available from a thermal siphon. Check valves work well in pumped systems where backflow must be prevented.
It didn't really cost that much to build the system, but it's because this project is an exercise in designing alternative methods to construct and fabricate. So a cheap expansion tank design would be nice. Inside the peak of the greenhouse at the highest point of the system is a 4" schedule 80 PVC, that could act as the "tank", and I can mount a pressure relief valve there (do I set the threshold pressure just below what the pip's psi rating is?).
exactly what I suspected I observed
Why must it operate at great pressure, can you not just let it breathe ?
You study for a couple of years, so you can solve any general case.
Can you demonstrate the calculations for the simplest closed loop you can think of - a "text book problem" ? The calculations are completely novel to me.
The analyses I have been involved in studied the natural circulation flow in a system with a heat source down low and a heat sink up high. A closed loop with pumps installed but not running.
I was just thinking there must be some base model, where the heat input establishes the thermal gradient in the water column, and a free convection within a column is creating the flow. Warm fluid is less dense and rises, cold fluid sinks. I can see this happening vertically, but it's harder to swallow that a bulk flow is established in a loop as if there were a pump circulating the flow. What is the base model for this is what I'm asking...its probably going to be complicated even with simplifying assumptions; whatever they may be.
I'm imagining a single column joining a warm reservoir on bottom to a cold reservoir above. I can imagine a natural circulation occurring where heat is brought to the top cold reservoir by free convection in the column and is released to the environment in the top cold reservoir, that seems like it can have a steady state circulation. I can't see it happening with the hot reservoir on top, nor can I see it with two vertical columns establishing some kind of net clockwise\counterclockwise flow like a pump would provide around a loop.
It's pretty light in supporting theory, but it guess its legit if they are using it as a deep backup safety in nuclear plants. I still would like to see an analysis.