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Calculating Discharge Coefficients Through Restriction and Mesh Convergence

Question asked by Jordan Truitt on Feb 2, 2019
Latest reply on Feb 2, 2019 by Mark Keown

I'm looking for some some help interpreting my results and making sure they are correct. I'm running a flow simulation where my volumetric flow rate in is 1 L/min and my exit is a pressure opening at 0.5 MPa. The fluid is flowing through a tight, rectangular restriction of 0.005 mm height and 72 mm width. I'm using a local mesh with equidistant with a 0.05mm offset distance and checking for mesh convergence by increasing the refinement level.


My goal is to calculate the discharge coefficient as it varies with flow rate and changes with restriction height. I'm using this basic equation to calculate the discharge coefficient:

Mass flow rate is known from my boundary condition. Density for the fluid is known. I'm calculating the total restriction area based off the dimensions. For delta P (P1-P2) I'm using the probe to actually measure the pressure, P1, before the restriction and I'm assuming P2 should be my exit pressure boundary condition of 0.5 MPa.


This is what my local mesh convergance results look like right now.

Refinement Level 5, P1 = 1.609 MPa, Discharge Coefficient = 0.4857

Refinement Level 6, P1 = 1.465 MPa, Discharge Coefficient = 0.5208

Refinement Level 7, P1 = 1.615 MPa, Discharge Coefficient = 0.4845

Refinement Level 8, P1 = 1.506 MPa, Discharge Coefficient = 0.5100

Refinement Level 9, P1 = 1.581 MPa, Discharge Coefficient = 0.4920


So there's no real clear trend. One thing that happened during refining was that the global min kept decreasing and the global max kept increasing. They occur at a sharp corner though so I'm assuming its a similar type of singularity issue with FEA where mesh refinement trends the value towards infinity.


Here are my questions though,

-Is this still too coarse of a mesh at the restriction to have confidence in? This is refinement level 9. I've seen rule of thumb that about 5 fluid cells across a restriction should be good, however my results don't appear to change even though I appear to be below 5 cells across.


-Is the local mesh refinement based off of the basic mesh? So in order to refine it anymore would I need to make the basic fluid cell mesh smaller (not more refined); packing more refinement level 0 fluid cells inside the computational domain so refinement levels have an increased resolution.


-For the calculation is it accurate to just assume P2 is exit pressure? Or should I be probing around the restriction exit for a reasonable minimum? The pressure does dip down a bit below the exit pressure boundary condition to around 0.3-0.4 MPa but from my understanding that's the vena contracta.


-Could someone explain a little bit about negative pressure warnings? I'm modifying this restriction and I will get that warning occasionally. Is a negative pressure warning caused because the volumetric flow rate forced through the restriction causes such a high exit velocity that the pressure drop is extreme?


Thank you.