Suspiciously large pressure difference between DNS and LES modes

[mst-parkhachev]

Dear colleagues!

We considered a 96x100 mm panel located in the middle of a 40 cm long air duct. One end of the duct had a boundary condition corresponding to air flow at a speed of 1 m/s, while the other end was open.

The panel has 56 holes. The hole diameter is 5 mm. The panel thickness is 5 mm. The free area is 11.67%.
The mesh cell size in which the panel is located is 0.5 mm. Most of the duct volume has a 1 mm cell size.

The calculation was performed in DNS and LES modes. There are two identical projects, differing only in the calculation mode.
les.txt
dns.txt

2 sec was calculated. The figure below shows the air velocity graphs near the left VENT in LES and DNS modes. At this scale, they are identical.

However, the figure below shows that the pressure increases significantly faster in DNS mode. Why is the difference so large?

The estimates for the loss coefficient (zeta) at time 2 s (153 for DNS and 99 for LES) also do not match the expected value of about 176 (for FA=11.67%). https://www.design1st.com/Design-Resource-Library/engineering_data/AirFlowResistanceofPerforatedPlates.pdf

In an attempt to understand what was happening, additional research was conducted. The airflow through the VENT was obtained from the MLR_AIR column of the CHID_hrr file. The airflow through a section located 1 cm to the right of the panel was obtained using
&DEVC ID='MF_RIGHT_1', XB=0.01,0.01,0,0.096,0,0.1, QUANTITY='TOTAL MASS FLUX X', SPEC_ID='AIR', SPATIAL_STATISTIC='AREA INTEGRAL' /

The difference between these flows was integrated, and graphs were obtained for the mass accumulated to the left of the panel.

This graph shows that in LES mode a greater air mass accumulates to the left of the panel than in DNS mode. At the same time, the pressure graph shows that the pressure to the left of the panel is higher in DNS mode. This means that the pressure and mass graphs seem to contradict each other. According to the mass graph, the excess pressure should be approximately 60 Pa for DNS mode, while for LES mode it should be 116 Pa. These values ​​do not match the values ​​on the pressure graphs.

What is the reason for such a big difference in the pressure drop graphs in the DNS and LES modes?

[mcgratta]

I'll take a look, but at first glance, I'm not sure you can expect to match experimental results with a rectilinear grid that does not confirm to those small circular holes. Also, in LES mode, FDS uses empirical wall functions that may or may not be appropriate for a simulation like this.

[mcgratta]

I am running the cases now. Before discussing pressures, let's look at the mass issue. I suggest that you plot the mass fluxes (MF kg/s) from each case together. They should be similar, but probably not exactly the same. The reason for this is that there is some error in mass conservation initially as the gas begins flowing through the holes. To reduce these errors, you would want to increase the N_PRESSURE_ITERATIONS used to solve the Poisson equation for pressure. In theory, the mass of gas upstream of the barrier should be the same in both cases, regardless of the pressure rise. This is because the equation of state is $p_0=R \rho T / W$ where $p_0$ is the background pressure (101325 Pa), $R$ is the gas constant, $\rho$ is the density, $T$ the temperature, $W$ the molecular weight. These values are all constant, as is the free stream velocity.

As for pressure, 153 (DNS) vs 176 (exp) is not unexpected given that there are still resolution issues. If data exists for square holes, that might be a better case to look at. As for LES, there is probably still some issues related to treatment of the boundary using the empirical wall functions. We've never rigorously tested convergence of LES to DNS for a case like this. If you would like to do that, I would recommend square holes to eliminate the shape as a source of uncertainty.

[mst-parkhachev]

Thank you, Mr. McGrattan! We need to think about it. Perhaps we can consider another case, as you suggest.

I'm not sure I completely understood you about the air mass passing through the panel. Shouldn't air accumulate to the left of the panel if the pressure there increases? If not, then why does the pressure increase? If air accumulates there, then why doesn't the integral of the difference in air flow from the VENT and through the device to the right of the panel follow the pressure curve?

[mcgratta]

FDS uses a low-Mach number approximation. Specifically in this case, this means that the air is incompressible because its temperature and molecular weight do not change. If this were a compressible code (or reality), you are correct that the mass of air upstream would increase with pressure.

[rmcdermo]

Just so we are on the same page, the density would increase with pressure in a compressible simulation. No matter what, at steady state, the integrated mass flux is the same along any plane (normal to x) in the simulation.

[mcgratta]

Your cases are still running with the latest code (nightly build). So far, the pressures upstream seem closer than in your case. However, I will let them run further.

[mcgratta]

These cases are running slowly for me, but here is what I see today. I suggest that you run your case with the latest version of the source code (nightly build).

[mst-parkhachev]

Thank you, Mr. McGrattan! Indeed, your results differ significantly from those of FDS 6.10.1. We'll experiment with the nightly build.

[mcgratta]

This is very interesting work that you are doing. I have never done a simulation like this, and I would be interested in your results. One issue of interest is the convergence of a LES to DNS. As I said above, it is not a trivial exercise to demonstrate that an LES will naturally converge to a DNS.

[mst-parkhachev]

We'll take some time to choose a case for simulation. I'll try to find experimental data for a specific panel and reproduce its configuration for numerical calculations. If I find it, we'll be able to compare losses not only with the generalized data from the reference book.
Then I'll report here on the results of the DNS and LES comparison.

[mcgratta]