help with compressible flow BC's (need subsonic flow)
 

Dear all,

I am new to compressible flow and I need to learn the basics fast. My adviser wants me to run a simulation of a nearly sonic speed jet expanding from a pipe. I am trying to operate in the regime of Mach number ~ 0.9. I am having a really hard time trying to figure out exactly what I need to do with the boundary conditions in order to get it to converge. Here is my problem:
I have fully developed flow in a pipe expanding into the atmosphere. I want to model at least 3 inches of pipe and then the expansion of the jet into a box (outlets on the side and top of the box). I cant even get the flow in the pipe to converge. I dont want any shocks inside of the pipe (well, I guess in the end I dont care, bc I care more about the convergence!).
So far what I understand: I need to define the inlet pressure and inlet mass flow (or mass flux), I know the pressure ratio of this to the atmospheric must be below or above 1.8 or something - I think this may be where I am having problems.

if I have a straight pipe with a diameter of 0.402 in and a (nitrogen) gas velocity around 320 m/s (so i have a mass flux of about 364 kg/(m^2*s).The pipe outlet is into atmospheric pressure.

*now to sum up my problem:
How do I defined the inlet conditions so that I can maintain subsonic flow through the pipe and avoid any shocks and choke? Do I need to change the pressure ratio and pipe length?

Subsonic Boundary Conditions
 

Boundary conditions are decided based on characteristics, so in subsonic flow we need to prescribe 3 in 1D and 5 in 3D. Out of 3 in 1d problem it is known that two conditions have to be prescribed so we prescribe Pressure and Temperature and extrapolate velocity from inside at inlet. similarly at outlet we need to extrapolate 2 from inside and prescribe one at exit. usually Pressure is prescribe at exit and either velocity, temperature or velocity , density are extrapolated but velocity - temperature is preferred.

Thanks for your input, but I am still confused about what pressure to put at the inlet so that I dont have any shocks in the pipe. if my pipe outlet is atmospheric pressure, my temperature at the inlet is 298 and the ambient temp at the outlet is 298. What pressure should I use at the inlet so I dont get a shock or supersonic flow in the pipe or at the exit?

U can give Po at inlet some ranges, which I know for sure is 1.2 atm total pressure at inlet and 1 atm at exit will give u a mach of 0.5 similarly u can go ahead with other pressures or just check out fanno flow chart u may get some idea regarding P0/P ratios

Thanks Ramesh
So when I look at a fanno flow chart, Po is the inlet pressure and P is the outlet pressure?

Anyone who needs help with this I think I figured it out: For fanno flow

When you have subsonic (but compressible flow) the mach number will increase through the pipe b.c Ma = 1 is an entropic maximum. So if you want your outlet to not have a shock, but you know what you want your outlet Ma to be, you can look at a fanno flow chart to get the inlet BC/pipe length. So if you want your outlet pipe Ma to be 0.9, depending on your pipe conditions (friction factor, diameter, length) you would need a LOWER mach number at the inlet. For my case I have a pipe diameter of 0.402 in and a pipe length of 3 in, outlet into the atmosphere with a Ma = 0.9, so I set my inlet Ma = 0.75 and used the fanno flow chart with the appropriate gamma to get the P/Po and T/To to find my inlet conditions.

Hope this help someone else!