How do I simulate a mass flux into a closed subdomain in time-dependent mode?

I would like to simulate an injector pumping gas at a certain ρ into a box and watch the resulting pressure rise over time. I was unable to find any examples (with time-dependency) in the documentation and keep getting the following error:
"High-order time stepping schemes not supported with integral constraints."

Any help you could lend would be greatly appreciated.

Thanks

jerrodbouchard wrote

I was unable to find any examples (with time-dependency) in the documentation

Although probably not directly related to your application, there are several tutorials involving time-dependency, for example:

  Quickstart > Wave Equation on a Circle
  Heat Transfer > Transient Heat Diffusion in a Rod
  Heat Transfer > Shrink Fitting of an Assembly
  Fluid Dynamics > Vortex Flow
  Multiphysics > Heat Induced Stress in a Brake Disc
  Multiphysics > Thermo-Mechanical Bending of a Beam
  Multiphysics > Fluid-Structure Interaction - Elastic Beam
  Multiphysics > Electro-Osmotic Flow
  Classic PDE > Shallow Water Equations

jerrodbouchard wrote

 and keep getting the following error:
"High-order time stepping schemes not supported with integral constraints."

Any help you could lend would be greatly appreciated.

Without really knowing any details about your model it is hard to say, but I suspect you have set up a model with the Navier-Stokes equations without an outflow. In this case a integral pressure constraint (the integral of the pressure over the domain is zero) is added implicitly in order to mathematically ensure a well posed problem (define a unique pressure). As the error message indicates, such an integral constraint does not work with higher order time-discretization/stepping schemes, and a solution would be to select a low order/1st order time stepping scheme (such as Backward-Euler) in the solver settings. Alternatively, you can avoid having to use a pressure integral constraint by fixing the pressure with a point constraint at at least one point.

That said, if you are using the Navier-Stokes they are only valid for incompressible fluids, and as such would probably not apply to the problem you're investigating. But then again, I'm not sure what you have modeled exactly.

Thank you very much for the reply.

I started with a “pressure vessel” defined as a 2-D unit square (1m x 1m) with boundaries labeled as 1 [bottom], 2 [right], 3 [top], 4 [left]. I assigned the physics mode as Navier-Stokes and I assigned the domain as initially filled with air at ambient conditions (277 degrees K, 101325 Pa, and Gas Constant 287 J/Kg*K). I’ve entered rho as ideal gas law (p/(R*T)), miu just as fixed 17.34e-6 Pa*s, and Fy as -gy*(p/(R*T)). I defined R in the model constants and expressions tab with the value noted above as well as defined gy as 9.81 m/s2 to account for gravity.
I then added the heat transfer physics mode so I can couple the dependent variable T and also coupled u and v. I used specific heat as 1e3 J/Kg*K and used k = 1.4. I assigned T0 as 277K. I left Q as 0 assuming no added heat flux.
My goal is to add a mass source to flow additional air into the pressure vessel through a boundary or somewhere in the domain at some m_dot value for X seconds and be able to observe the tank pressurizing as a function of time.
How do I assign a mass source and tie into the continuity, momentum, and energy equations in FEATool. In other tools, there is simply an option to assign a mass source/sink and define subsequent parameters.


Thanks again for all of your help!

jerrodbouchard wrote

I’ve entered rho as ideal gas law (p/(R*T)), miu just as fixed 17.34e-6 Pa*s, and Fy as -gy*(p/(R*T)). I defined R in the model constants and expressions tab with the value noted above as well as defined gy as 9.81 m/s2 to account for gravity.

Thank you for explaining your model. Are you sure this is a valid approach to model compressibility. My understanding of the Navier-Stokes equations is that it would only be valid for very weakly compressible fluids with modifications such as the Boussinesq equations (for modeling buoyancy effects)? In other cases the fully compressible equations would be more suitable?