Buoancy Driven Flow in a vertical pipe
Buoancy Driven Flow in a vertical pipe
(OP)
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 = (rhoambient - rhoout)*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 Tout. 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?
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 = (rhoambient - rhoout)*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 Tout. 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?





RE: Buoancy Driven Flow in a vertical pipe
you must get smarter than the software you're using.
RE: Buoancy Driven Flow in a vertical pipe
RE: Buoancy Driven Flow in a vertical pipe
you must get smarter than the software you're using.
RE: Buoancy Driven Flow in a vertical pipe
RE: Buoancy Driven Flow in a vertical pipe
you must get smarter than the software you're using.
RE: Buoancy Driven Flow in a vertical pipe
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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