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Pressure-Inlet Theory Question

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Old   September 26, 2017, 16:34
Default Pressure-Inlet Theory Question
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I'm trying to figure out the theory of the pressure-inlet boundary condition.

For example, say I have subsonic, incompressible flow, constant temperature, with air being the fluid. If I have a pressure-inlet with some small value of gauge pressure and a pressure outlet of zero gauge pressure with constricting geometry in between, does the area of the inlet play any important role?

Think of the simple Venturi tube:
For test 1, the inlet is 10 square inches, the restriction is 1 square inch, and the outlet is 10 square inches.
For test 2, the inlet is now 100 square inches, the restriction is still 1 square inch, and the outlet is still 10 square inches.

Will the flow velocity at the pressure-outlet be the same for test 1 and 2?
If so, can this be proven with the Bernoulli equation?
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Old   September 26, 2017, 17:31
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Originally Posted by klub View Post
Will the flow velocity at the pressure-outlet be the same for test 1 and 2?
If so, can this be proven with the Bernoulli equation?
If you take the limiting case and take the limit as the inlet/outlet areas tends towards infinity, it necessitates that the velocity tends towards zero at the inlet/outlet. This would suggest that test 1 and test 2 should both have zero velocity, which seems to be a counter-proof by contradiction since you would not have any flow despite a driving pressure difference.
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Old   September 26, 2017, 19:32
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take the limiting case and take the limit as the inlet/outlet areas tends towards infinity
I think you got us half way there; if we take only the inlet as going to infinity then the inlet velocity becomes zero.

So we start off with the Bernoulli equation:
p_1 + 1/2*rho*(v_1)^2 = p_2 + 1/2*rho*(v_2)^2

From the original post we know that that p_2 = 0 so we can get rid of that variable.

To get rid of v_1, we use A_1*v_1 = constant and if we take A_1 to infinity then v_1 must go to zero.

So, we're left with the equation: p_1 = 1/2*rho*(v_2)^2 which shows that A_1 doesn't affect v_2 as long as p_1 stays constant.
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Old   September 26, 2017, 19:45
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I didn't use Bernoulli, only mass conservation and assumed that there is a flow. Of course the no flow case is the degenerate case where nothing matters. You might be surprised to see that it has nothing to do with pressure.

A1*V1 = A2*V2 = A3*V3

where 1 is the inlet, 2 is the throat and 3 is the outlet

Assuming A2*V2 is finite and non-zero,

Taking the limit as A1 or A3 ==> inf implies V1=A2*V2/A1=1/inf=> 0 which contradicts A2*V2 being finite or non-zero. Thus, either there is no-flow (the degenerate case in which there is no contradiction) or infinite flow.

Bernoulli's equation assumes you have an isentropic flow along a streamline. If A1=A3 for example, you would conclude that V1=V3 and P1=P3 and that there is no pressure difference, which contradicts P1 being non-zero.

Btw, you should consider not the static pressure but the total pressure if you want to see what does or does not change.
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Old   September 27, 2017, 15:41
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So since I'm looking to understand the 'pressure-inlet' boundary condition, as opposed to the 'velocity-inlet' boundary condition, how can it be explained using only mass conservation?

Like you said, I have been considering the static pressure component in the Bernoulli equation as constant instead of looking at the whole equation and considering the total pressure as constant. Does Fluent see the 'pressure-inlet' boundary condition as being total pressure or static pressure?
Reading through some old posts, I discovered Fluent's odd pressure terminology:
static vs. total pressure
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Old   September 27, 2017, 17:45
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Just for the heck of it, I ran a quick simulation comparing two cases:

Case 1:
Inlet: 10mm dia.
Throat: 5mm dia.
Outlet: 10mm dia.

Case 2:
Inlet: 50mm dia.
Throat: 5mm dia.
Outlet: 10mm dia.

Distances between inlet and throat and between throat and outlet were each 100mm.

The boundary conditions for each case was the same:
Viscous - Standard k-omega
Pressure-inlet: 7 lb/ft^2
Pressure-outlet: 0 lb/ft^2

Solution Method: Coupled, Second Order Upwind

Convergence to default error of 1e-03 occurred around 350 iterations.

I created a mass flow rate monitor at the outlet.

For both Case 1 and Case 2, the flow rate started around 0.05 lbm/s and approached 0 lbm/s asymptotically.

It's difficult for me to wrap my brain around it but it looks like you were correct, LuckyTran. Thanks
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Old   September 27, 2017, 22:28
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In this case, the dimensions that matter is only the throat diameter
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