Newbie to compressible, viscous flow. Advice on approach to problem?

bzz77 · December 1, 2012, 05:17

Hello everyone:

Until now, I have only dealt with incompressible flow. I am interested in a problem involving compressible flow of a viscous fluid. It seems like most of the practical guides I've found are aimed at inviscid compressible fluids. Would anyone be willing to get me started on the right track--either by directing me to a resource I've missed or offering advice on how to approach this problem?

I can frame my problem in terms of fluid in a tank where there is an outlet pipe. I can't view the fluid in the tank. When fluid leaves the tank through the outlet pipe, I want to figure out where (approximately) it came from in the tank. So I would want to calculate streamlines and, if possible, the depth at which the fluid was in the tank...

So far I can solve this problem if I assume that the fluid is inviscid, but I want to come up with a more realistic approach. Here is the reality; could I deal with the full complexity of this problem computationally? Are there any examples out there where people have come up with the governing equations for this kind of problem? I'd like to use OpenFoam, if possible.

-The fluid is viscous. The viscosity can change with temperature and when bubbles are present in the fluid.
-The fluid may be stratified in the tank according to density and viscosity. It may contain bubbles, which would make flow compressible.
-Flow probably is not laminar, but I could live with that assumption.

Any advice would be very much appreciated. Thanks.

Rami · December 4, 2012, 04:18

The term "incompressible" is somewhat misleading. If your Mach number is less than 0.3, you actually better use an incompressible flow solver (and possibly relate the density to temperature). Compressible solvers usually perform poorly in this region, since the spectral radius is high (there is a lot of literature on this topic, if you are interested).

bzz77 · December 4, 2012, 05:57

Hi Rami:

Thanks a lot for your reply. My Mach number would be <0.3 in some situations, but greater in others.

The reason I am thinking about compressible flow is that (1) my fluid can be bubbly (although I'd like to run some calculations for non-bubbly fluid) and (2) it can be stratified by density, with the densest fluid at the bottom of the tank.

I'm not sure whether temperature change would be that important for my system.

I will do a search on "spectral radius." Never heard that term! Thanks a lot.

Rami · December 4, 2012, 08:56

Quote:

Originally Posted by bzz77

Hi Rami:

Thanks a lot for your reply. My Mach number would be <0.3 in some situations, but greater in others.

The reason I am thinking about compressible flow is that (1) my fluid can be bubbly (although I'd like to run some calculations for non-bubbly fluid) and (2) it can be stratified by density, with the densest fluid at the bottom of the tank.

I'm not sure whether temperature change would be that important for my system.

I will do a search on "spectral radius." Never heard that term! Thanks a lot.

I should have use "condition number" rather than "spectral radius". The two are related, though.

bzz77 · December 4, 2012, 08:59

OK thanks. I'll look it up. I;m just trying to get a sense of what the state-of-the-art is for dealing with this kind of problem.

December 1, 2012, 05:17	Newbie to compressible, viscous flow. Advice on approach to problem?	#1
bzz77 New Member Join Date: Jan 2010 Posts: 28 Rep Power: 16	Hello everyone: Until now, I have only dealt with incompressible flow. I am interested in a problem involving compressible flow of a viscous fluid. It seems like most of the practical guides I've found are aimed at inviscid compressible fluids. Would anyone be willing to get me started on the right track--either by directing me to a resource I've missed or offering advice on how to approach this problem? I can frame my problem in terms of fluid in a tank where there is an outlet pipe. I can't view the fluid in the tank. When fluid leaves the tank through the outlet pipe, I want to figure out where (approximately) it came from in the tank. So I would want to calculate streamlines and, if possible, the depth at which the fluid was in the tank... So far I can solve this problem if I assume that the fluid is inviscid, but I want to come up with a more realistic approach. Here is the reality; could I deal with the full complexity of this problem computationally? Are there any examples out there where people have come up with the governing equations for this kind of problem? I'd like to use OpenFoam, if possible. -The fluid is viscous. The viscosity can change with temperature and when bubbles are present in the fluid. -The fluid may be stratified in the tank according to density and viscosity. It may contain bubbles, which would make flow compressible. -Flow probably is not laminar, but I could live with that assumption. Any advice would be very much appreciated. Thanks.

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December 4, 2012, 04:18		#2
Rami Senior Member Rami Ben-Zvi Join Date: Mar 2009 Posts: 155 Rep Power: 17	The term "incompressible" is somewhat misleading. If your Mach number is less than 0.3, you actually better use an incompressible flow solver (and possibly relate the density to temperature). Compressible solvers usually perform poorly in this region, since the spectral radius is high (there is a lot of literature on this topic, if you are interested).

December 4, 2012, 05:57		#3
bzz77 New Member Join Date: Jan 2010 Posts: 28 Rep Power: 16	Hi Rami: Thanks a lot for your reply. My Mach number would be <0.3 in some situations, but greater in others. The reason I am thinking about compressible flow is that (1) my fluid can be bubbly (although I'd like to run some calculations for non-bubbly fluid) and (2) it can be stratified by density, with the densest fluid at the bottom of the tank. I'm not sure whether temperature change would be that important for my system. I will do a search on "spectral radius." Never heard that term! Thanks a lot.

December 4, 2012, 08:59		#5
bzz77 New Member Join Date: Jan 2010 Posts: 28 Rep Power: 16	OK thanks. I'll look it up. I;m just trying to get a sense of what the state-of-the-art is for dealing with this kind of problem.