CFD Online Discussion Forums - Pressure driven flow through a valve: pressure BCs clarification

Hello everyone,

I am a PHD student in mechanical engineering currently working on a simple 2D simulation of a pressure driven flow through an axial valve.
Unfortunately, due to the current pandemic, my mentor/professor is currently having hard times with the virus, so I decided to ask outside the academic environment for help to clarify the following doubts.

I want to thank in advance anyone who will kindly reply me.

I am currently using Ansys Fluent 2020 R2 Academic version.

The current computational domain is a cross-section of the 3D valve, since I preferred having a look at the results (in terms of mass flow rate, for further Cv/Kv calculation) before passing to the full 3D analysis.

The simulation is a 2D-axisymmetric one.

Please find attached a snap of the domain.

The fluid considered for this simulation is water at 20°C, just for the sake of simplicity and for understanding if everything's going right before starting complicating things.

I am using $\kappa$ - $\epsilon$ model, realizable version, with standard wall functions, sand roughness wall roughness model enabled, first coeff set to 0.0005 m (half a mil) , m coeff as per default (0.5).

I have already performed many runs, so grid independence has already been successfully achieved.
Pre-calculations on Boundary layer discretization, initialization for $\kappa$ and $\epsilon$ have been done as well.

My core question is: since this is a pressure driven flow, with known $\Delta p$ across the fluid domain from the up-stream point (INLET) and the downstream point (OUTLET), which should be the correct approach for setting up the pressure inlet - pressure outlet boundary conditions pair?

Clearly, the bigger the difference between total and static inlet pressure, the bigger would be the computed inlet velocity and, keeping the same outlet pressure, the mass flow rate would increase as well.

I have read a lot about the solution initialization sensitivity that this choice introduces, and that's what I am struggling with to be honest.

What I am confused about, probably because I still need to deepen my Fluent knowledge, is how to properly set up the pressure inlet and pressure outlet boundary conditions.
Since the $\Delta p$ is 20000 Pa, what should I set as total pressure at the inlet, as static gauge pressure at the inlet and as outlet pressure (static or total)?

Moreover, I have noticed that the volume flow rate varies depending on the reference values used and on the pressure operating condition so, since I am interested in computing the Cv coefficient, which may be a recommendation/reference or standard for setting these values as well?

Finally, how should I compute the $\Delta p$ to evaluate the Cv coefficient? Should I consider a theoretical one (0.2 bar [gauge] = 20000 Pa) or a volume/mass averaged values derived from the computational domain?

The formula I am currently using is the one as follows:

$C_{v}=1.15622 \cdot \frac{\dot{V} \cdot 3600}{\sqrt{\Delta p}}$

$\dot{V}$ is the computed Volume Flow rate exiting the computational domain (in short, $\dot{V}$ at the outlet).

Residuals, for steady-state simulation, have been set to $10^{-7}$ for continuity and $10^{-6}$ for [x,y] velocity and for TKE and TDR. In the simulations I have previously performed, I had no issues with convergence, the values successfully reached convergence in approx. 2500 iterations (5000 were set to be run).

SIMPLEC solver has been set, no skewness correction (hence = 0); spatial discretization: Least Squares cell base for Gradient, second order for pressure (if other algorithms are to be preferred, please let me know), Momentum, TKE and TDR all have second order upwinding applied.
Default Fluent over-relaxation factors, beside 0.9 instead of 1 for TDR.

In conclusion, what I am mostly concerned about, is to get my head round on how to properly use the pressure-inlet & pressure-outlet pair of boundary conditions in case of incompressible flow.

There's a big difference from knowing the theory alone and knowing how to apply the theory to real simulations/real case studies, so any help will be highly appreciated.

Any advice in terms of modelling techniques, simulation setup, others (ways to retrieve simulation data for Cv computation and so on) will be highly appreciated.

Thanks again in advance for your time and knowledge

Have a nice day

Kind regards,

Coraz94