Pressure Required to Circulate Liquid in a Closed System?

[erobz]

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.

We did this numerically with a computer program that divides the system up into ~50 "nodes" and solves mass, energy, and momentum conservation. This allows for temperature & pressure-varying physical properties (eg, density), and flow-dependent resistance, etc. as well as varying the heat input and removal rates.

It can be done by hand but you have to make simplifying assumptions.

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.

 

[Steven Bolgiano]

Ah! So while the pump may need very little force to circulate water in the circuit ..... I see what you mean, ... without a pump, a thermal siphon generating heat transference on the downward link of the circuit is difficult to envision..... How could that happen?

 

[erobz]

Ah! So while the pump may need very little force to circulate water in the circuit ..... I see what you mean, ... without a pump, a thermal siphon generating heat transference on the downward link of the circuit is difficult to envision..... How could that happen?

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.

 

[gmax137]

It can work if heat is added at a lower elevation and removed at a higher elevation. The elevation difference has to be sufficient, otherwise the density difference between the "up leg" and the "down leg" won't be enough to overcome the flow resistance (friction, bends, change of area).

EDIT: this looks like it might help:
https://www.nuclear-power.com/nucle...nvection-free-convection/natural-circulation/

 

[erobz]

EDIT: this looks like it might help:
https://www.nuclear-power.com/nucle...nvection-free-convection/natural-circulation/

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.

 

[Baluncore]

The elevation difference has to be sufficient, otherwise the density difference between the "up leg" and the "down leg" won't be enough to overcome the flow resistance (friction, bends, change of area).

The flow velocity self regulates, as a slower fluid flow, has longer to heat, to a higher operating temperature, with a greater density change, resulting in a greater hydrostatic drive pressure difference.

A crude guide to the optimum arrangement of the components in a thermal siphon, is "Heat Rises".

 

[gmax137]

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.

For a real plant the analysis is more sophisticated than these hand calcs. Also, the startup testing done during plant commissioning includes a natural circulation test to verify the analytical results. Plus, several plants in the US have lost forced circulation (loss of power to the coolant pumps). This causes an immediate shutdown of the reactor, so the flow requirement is much lower than that required at power.

But this is pretty far afield from the greenhouse unit discussed in the OP; the nuclear plant link was just a convenient place to find a schematic drawing of the basic configuration and the pressure balance equations.

 

[erobz]

But this is pretty far afield from the greenhouse unit discussed in the OP; the nuclear plant link was just a convenient place to find a schematic drawing of the basic configuration and the pressure balance equations.

It seems like the OP's system has the cold reservoir lower than the hot reservoir.

 

[Baluncore]

It seems like the OP's system has the cold reservoir lower than the hot reservoir.

Part of the design optimisation process involves finding ways to invert that situation.

 

[gmax137]

I was hoping the OP would provide a schematic elevation sketch, I didn't take the time to figure it out from the video.