Subsonic Inflow/Outflow Boundarty Conditions
 

Hello,

I'm testing my code for solving the compressible inviscid Euler equations with very simple examples. Noy I'm testing the subsonic case.

I know that in the inflow total temperature, total pressure and the angle/s must to be specified. But, I'd like to know how to "translate" these conditions to the conservatives quantities (density, momentum and energy).

For the outflow I read that the most common quantity to be imposed is the pressure.

Many thanks!

Re: Subsonic Inflow/Outflow Boundarty Conditions
 

I presume that you may try to use the isentropic relations??

Re: Subsonic Inflow/Outflow Boundarty Conditions
 

I found the isentropic relations here

http://www.grc.nasa.gov/WWW/K-12/airplane/isentrop.html

but:

- how can I determine the Mach to compute the density, pressure and temperature. I pressume that I need the Riemann invariants but I don't know...

- what is the total density? Is it a given data?

Re: Subsonic Inflow/Outflow Boundarty Conditions
 

dear ruben,

with fixed total pressure and temperature the total density is also known (gas equation). To get the Mach number the most simple possibility is to extrapolate the pressure or the density from the inner flowfield. Together with the prescribed total state you can determine the Machnumber and from the Machnumber and then prescribed flow angle all conservation variables.

Re: Subsonic Inflow/Outflow Boundarty Conditions
 

Ok, thanks and excuse me for my trivial question about density...

About the Mach: I don't understand when the authors say "I impose a inlet Mach number of ..." Can I impose a inlet mach number?

Re: Subsonic Inflow/Outflow Boundarty Conditions
 

When you solve the compressible inviscid Euler equations at the inlet subsonic boundary you cannot set all values because 1) you have the characteristics in 1D case (or characteristics surface in 2D/3D cases) running to the inlet boundary from inside calculation region and 2) you don't know the inlet speed (or inlet Mach number). So you have to use total temperature T0, total pressure P0, angle(s) in 2D(3D) cases and Riemann invariant condition from characterictics coming from inside region from previous time step. Such conditions are called "non-reflecting" conditions because they allow disturbances of flow parameters to leave calculation region and so increase speed of convergence of numerical solution.

Above means that you write system of non-linear equations for every inlet grid point. For 2D case we have

P/P0 = Fp isoentopic (cappa) T/T0 = Ft isoentopic (cappa) v/u = angle( given funtion) f(u,v,p,t, parameters at the nearest points at previous time layer) = 0 (Riemann invariant for corresponding characteristic)

and solve it by Newton method, for example.

Hope, above answers your question.

Re: Subsonic Inflow/Outflow Boundarty Conditions
 

Thanks Peter!

Re: Subsonic Inflow/Outflow Boundarty Conditions
 

Ruben,

One correction about reflecting and non-reflecting boundary conditions (in my previous post I was non-correct). Non-reflecting boundary conditions mean that you set Riemann invariants along characteristics coming from outside calculation region. In 1D subsonic flow, for example, we have two such characteristics - C+ and C0. So we have to set 2 conditions like h+u2/2 = H0 = cpT0 (along C0) and u+2a/(cappa-1)= 2a0/(cappa-1) (along C+). I don't have textbook in front of me so better to verify these relations. If you simulate case when cappa is not constant (cp = cp(T)), then you can use similar approach but formulae would be slightly complicated (for Newton iterations it doesn't matter).

Re: Subsonic Inflow/Outflow Boundarty Conditions
 

My boundary conditions are working!!

Thanks a lot another time Peter.

Re: Subsonic Inflow/Outflow Boundarty Conditions
 

It is not possible to impose the Mach number at inlet. The precsibed total state at inlet does not fix the Mach number. The Machnumber depends also from the exit pressure, i.e. the boundary condition at outlet. It is like a test rig. At inlet you have a vessel with a total state and guide vanes for the inlet angle. At the end of the test rig the flow is blown for example in an exhaust pipe with given outlet pressure.