Buoancy Driven Flow in a vertical pipe

[OzzieFlow]

I'm trying to obtain a proper understanding of buoyancy-driven flow. My main question is whether the shape of the temperature profile throughout the length of the pipe has any influence on the pressure difference created?

Consider a vertical pipe of length L (also equal to height difference h). In most textbooks and articles I've seen they use the normal stack effect, i.e. the pressure difference = (rho_ambient - rho_out)*g*height. This is also equal the weight difference between the air column in the pipe and the same volume of air column at the ambient temperature, IF it is assumed that the temperature in the pipe is constant and equal to T_out. This is typical of a stack/chimney where hot gas enters at the inlet and the temperature stays constant, assuming adiabatic walls. In terms of buoyancy forces it makes sense to me that the pressure difference is analogous to the weight difference between the air column in the pipe and an equivalent ambient air column.

HOWEVER, when ambient air enters the pipe and is progressively heated as it travels upwards, the weight of this air column will be less than the air column described above, where hot gas enters the pipe, thus, the pressure differential should be less?

I've seen one article where they've used a temperature profile factor ,which they said is 0.5 for a linear temperature profile. This makes sense to me. Is my thinking correct or am I missing something?

 

[BigInch]

If the weight of the continuously heated gas is even less than the usual volume of hot air within the chimney, then would not the difference in density between the continuously heated gas and the ambient air outside be even more. That causes a greater pressure differential and buoyant effect on continuously heated gas wold be greater.

you must get smarter than the software you're using.

 

[OzzieFlow]

Think I've found the answer thank you. Had a look at fluid statics and it appears to be all about the weight of the column of fluid, i.e. how manometers work. The profile of the temperature along the pipe will definitely influence the buoyancy pressure differential. Strange however that how many articles I've found, especially on cooling of PV cells with induced air, where they have not taken this into account.

 

[BigInch]

"Induced air" usually means forced flow, not free convection (buoyant flow), so the temperature profile is more uniform due to the typically turbulent mixing and higher velocity, as opposed to slow, laminar flows that are more prominent in convection driven flows.

you must get smarter than the software you're using.

 

[OzzieFlow]

Thank you BigInch, my use of "induced flow" was incorrect. I was meaning buoyant flow as you've correctly picked up.

 

[BigInch]

So the question seems to be, is there significant mixing between warmed and cool air next to PV panels, or would flow remain laminar with little or no mixing, as there is within a bounded warm air column, like what happens inside a chimney where density differences are significant. I suspect that might be possible on a still day, but with any kind of a breeze, probably not. If we think about it, the temperature difference inside a chimney is hundreds of degrees C. Temperatures along a PV panel wouldn't be more than 40C maximum. If you need to look closer at this, Reynolds, Grashoff and Nusselt numbers will help you evaluate the heat transfer coefficient of the air to PV panel boundary layer at various flow rates.

you must get smarter than the software you're using.

 

[davefitz]

ozzieflow:
Yes, if the heat is primarily absorbed in the bottom third of the pipe the "natural circulation" characteristic of the circuit will be come more positive , that is , dW/dQ|dp will increase ( ie the rate of increase in mass flow with increasing heat flux under conditions of fixed pressure drop will increase). Additional improvement is found by increasing the pipe diameter in the outlet third of the circuit. Other observations can be had using the type of analysis outlined in F Thelen's “Stromungsstabilitat in Verdampfern von Zwangdurchlaufdampferzeugern”, in VGB Kraftwerkstechnik 61 Jarhgang , heft 5, mai 1981 pp357-367.

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