Pressure inlet for M=1

chri · September 1, 2015, 09:59

Dear guys!

I am dealing with compressible flow and I was trying to design inlets with a velocity of Mach=1, using pressure inlets. I calculated an isentropic flow with a critical pressure drop and drawed an inlet of critical surface, according to the theory.

Gauge inlet pressure/Supersonic pressure is therefore 0.8939 and inlet temperature is 235.95 K (comes from isentropic formula). For that setup I should get sonic velocity I think

As I get velocities of approx 40 m/s, there must have gone something wrong, so maybe you can tell me where my mistake is?!

All the best,
Christian

LuckyTran · September 1, 2015, 16:21

Your inlet stagnation pressure would depend on your geometric area. You just need to calculate the stagnation pressure that you need given the duct dimension and using the critical flow function.

But what are the knowns? There are various ways to get Mach=1 by changing both Pressure & Temperature, e.g. what velocity does Mach=1 correspond to exactly? This would depend on the thermodynamic state of the fluid at the inlet. Is the inlet stagnation temperature fixed?

chri · September 2, 2015, 05:31

Why does the stagnation pressure depend on the duct dimension? I thought, only the massflow depends on the duct surface and the stagnation pressure is fixed at 1,8939?

in this case M=1 corresponds to 307.903014 m/s. Temperature at the inlet is fixed, yes!

What I don't understand is why my FLUENT solution is that far away from what I calculated through isentropic expansion?!

For pressure inlet bc the User's guide shows formulas for isentropic conditions, so I dont know where that substantial error should be?!

Thanks for help!

LuckyTran · September 3, 2015, 02:11

The 1.8 pressure ratio is in terms of absolute static pressure. Your stagnation pressure at the inlet will therefore need to be higher than 1.8 bar for M=1 at the inlet.

In general, with Mach=1 the velocity is fixed, but the mass flux is not fixed, as density can still increase. And density can increase with increased pressure. Hence increasing your static & total pressure is not yet unique. Your static & total pressure at the inlet cannot yet be determined until the mass-flux is known (so you must know massflowrate and duct dimensions). If you want to test the minimum flowrate needed for M=1 at the inlet then you can use the Pinlet=1.8bar.

Similarly, also note that the inlet stagnation temperature must be specified and not the inlet static temperature.

chri · September 3, 2015, 08:04

I would like to have 1 bar at the inlet, so my stagnation pressure is exactly
p0 =ps*(1+(k-1)/2*M^2)^(k/k-1) which is 1,8939 .

I am sure that about my calculations of surface and mass-flux to be correct, because they work with mass-flow inlets. But where can be the mistake using pressure inlets?

I'll list my Input numbers:

Total Gauge Pressure :89393.93 Pa
Initial/Supersonic Gauge Pressure: 0
Total Temperature: 283.15
Direction: Normal to Boundary

I am quite sure my equations are right and I think the problem is at the input into FLUENT.

LuckyTran · September 3, 2015, 11:52

Those are correct. But then your outlet would need to be at 0 Pa absolute pressure, so do you have a pressure outlet at -101325 Pa, or something equivalent ?

In order for the flow to be M=1 at the inlet, the stagnation pressure must be 1.8bar and static pressure 1 bar. The boundary condition you are imposing in Fluent fixes only the stagnation pressure, the static pressure at the inlet is not fixed simultaneously (as it depends on the flow solution). As you know, you can specify that the inlet stagnation pressure is 1.8 bar, but you do not specify M=1.

This isn't a problem specific to Fluent, but it is the nature of boundary value problems. If you fix both stagnation and static pressure (and hence Mach number at the inlet) then you end up with an ill-posed boundary value problem (it starts to resemble an initial value problem). Your understanding of the theory is correct, but keep in mind Fluent is solving a pde (Navier-Stokes) with boundary conditions.

chri · September 3, 2015, 15:40

Why is it like that having the outlet condition?! can't it be at 1bar absolute pressure?!

Hm...well, stagnation pressure is Total gauge pressure and Initial/Supersonic Gauge Pressure is the static pressure, which I leave at 0, so it is calculated through the PDEs including the inlet boundary.
Do you know how I can work out to specify a certain Mach Number?! The thing is that I would like to avoid sonic shocks, therefore I am trying to get an inlet like that!

thanks a lot so far, christian

September 1, 2015, 09:59	Pressure inlet for M=1	#1
chri New Member Christian Mahr Join Date: Aug 2015 Posts: 11 Rep Power: 10	Dear guys! I am dealing with compressible flow and I was trying to design inlets with a velocity of Mach=1, using pressure inlets. I calculated an isentropic flow with a critical pressure drop and drawed an inlet of critical surface, according to the theory. Gauge inlet pressure/Supersonic pressure is therefore 0.8939 and inlet temperature is 235.95 K (comes from isentropic formula). For that setup I should get sonic velocity I think As I get velocities of approx 40 m/s, there must have gone something wrong, so maybe you can tell me where my mistake is?! All the best, Christian

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September 1, 2015, 16:21		#2
LuckyTran Senior Member Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,675 Rep Power: 66	Your inlet stagnation pressure would depend on your geometric area. You just need to calculate the stagnation pressure that you need given the duct dimension and using the critical flow function. But what are the knowns? There are various ways to get Mach=1 by changing both Pressure & Temperature, e.g. what velocity does Mach=1 correspond to exactly? This would depend on the thermodynamic state of the fluid at the inlet. Is the inlet stagnation temperature fixed?

September 2, 2015, 05:31		#3
chri New Member Christian Mahr Join Date: Aug 2015 Posts: 11 Rep Power: 10	Why does the stagnation pressure depend on the duct dimension? I thought, only the massflow depends on the duct surface and the stagnation pressure is fixed at 1,8939? in this case M=1 corresponds to 307.903014 m/s. Temperature at the inlet is fixed, yes! What I don't understand is why my FLUENT solution is that far away from what I calculated through isentropic expansion?! For pressure inlet bc the User's guide shows formulas for isentropic conditions, so I dont know where that substantial error should be?! Thanks for help!

September 3, 2015, 02:11		#4
LuckyTran Senior Member Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,675 Rep Power: 66	The 1.8 pressure ratio is in terms of absolute static pressure. Your stagnation pressure at the inlet will therefore need to be higher than 1.8 bar for M=1 at the inlet. In general, with Mach=1 the velocity is fixed, but the mass flux is not fixed, as density can still increase. And density can increase with increased pressure. Hence increasing your static & total pressure is not yet unique. Your static & total pressure at the inlet cannot yet be determined until the mass-flux is known (so you must know massflowrate and duct dimensions). If you want to test the minimum flowrate needed for M=1 at the inlet then you can use the Pinlet=1.8bar. Similarly, also note that the inlet stagnation temperature must be specified and not the inlet static temperature.

September 3, 2015, 08:04		#5
chri New Member Christian Mahr Join Date: Aug 2015 Posts: 11 Rep Power: 10	I would like to have 1 bar at the inlet, so my stagnation pressure is exactly p0 =ps(1+(k-1)/2M^2)^(k/k-1) which is 1,8939 . I am sure that about my calculations of surface and mass-flux to be correct, because they work with mass-flow inlets. But where can be the mistake using pressure inlets? I'll list my Input numbers: Total Gauge Pressure :89393.93 Pa Initial/Supersonic Gauge Pressure: 0 Total Temperature: 283.15 Direction: Normal to Boundary I am quite sure my equations are right and I think the problem is at the input into FLUENT.

September 3, 2015, 11:52		#6
LuckyTran Senior Member Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,675 Rep Power: 66	Those are correct. But then your outlet would need to be at 0 Pa absolute pressure, so do you have a pressure outlet at -101325 Pa, or something equivalent ? In order for the flow to be M=1 at the inlet, the stagnation pressure must be 1.8bar and static pressure 1 bar. The boundary condition you are imposing in Fluent fixes only the stagnation pressure, the static pressure at the inlet is not fixed simultaneously (as it depends on the flow solution). As you know, you can specify that the inlet stagnation pressure is 1.8 bar, but you do not specify M=1. This isn't a problem specific to Fluent, but it is the nature of boundary value problems. If you fix both stagnation and static pressure (and hence Mach number at the inlet) then you end up with an ill-posed boundary value problem (it starts to resemble an initial value problem). Your understanding of the theory is correct, but keep in mind Fluent is solving a pde (Navier-Stokes) with boundary conditions.

September 3, 2015, 15:40		#7
chri New Member Christian Mahr Join Date: Aug 2015 Posts: 11 Rep Power: 10	Why is it like that having the outlet condition?! can't it be at 1bar absolute pressure?! Hm...well, stagnation pressure is Total gauge pressure and Initial/Supersonic Gauge Pressure is the static pressure, which I leave at 0, so it is calculated through the PDEs including the inlet boundary. Do you know how I can work out to specify a certain Mach Number?! The thing is that I would like to avoid sonic shocks, therefore I am trying to get an inlet like that! thanks a lot so far, christian