Flow around a plate - pressure distribution

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NewJoker
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Flow around a plate - pressure distribution

Post by NewJoker »

Hi,

I'm working on a simple benchmark problem. It involves a plate in a wind tunnel:

flow geom.JPG
flow geom.JPG (61.13 KiB) Viewed 1290 times

My goal is to obtain accurate pressure distribution on the surface of the plate for subsequent bending calculations.

The simulation is laminar with an inlet velocity of 200 m/s and outlet pressure of 0 Pa. Initially no-slip wall boundary condition was used for the walls of the plate but then I also tried the slip condition and it seems that the agreement with the analytical solution is better. Does it make sense ? The remaining walls use the default slip wall condition.

I calculated the pressure analytically using this basic formula:

F_D=0.5*rho*C_D*U^2*A

I assumed drag coefficient C_D=1.28 but it seems to vary a lot in the literature and I couldn't find a reliable source for this type of object subjected to flow. My results still don't agree well with this analytical solution, hence my doubt regarding the drag coefficient. I got 30720 Pa from hand calculation with this value of C_D and around 34000 Pa at maximum from OpenFOAM (after multiplying by the density since OpenFOAM calculates pressure in m^2/s^2) with some lower values on the sides (even negative around the edges):

press v2.JPG
press v2.JPG (32.04 KiB) Viewed 1290 times

Do you think that a better agreement and more uniform pressure distribution in simulation is possible ? Is that drag coefficient correct or should I use a different value for analytical calculations ? Maybe this way I would get closer to simulation results.

Here's the FreeCAD file:
Flow around a plate.FCStd
(21.47 KiB) Downloaded 32 times
thschrader
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Re: Flow around a plate - pressure distribution

Post by thschrader »

I get cf=1,3 when using DIN1055 "Wind loads".
Calculate the cf0-value, then the slenderness reduction factor.

We use cf=1,3 - 1,4 when calculating buildings.
Are you sure the inlet-speed is 200m/s =720 km/h?
simpleFOAM is not valid for speeds > 0,3*Ma = 100 m/s
cf_coeff_plate_DIN1055.JPG
cf_coeff_plate_DIN1055.JPG (117.43 KiB) Viewed 1235 times
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Re: Flow around a plate - pressure distribution

Post by NewJoker »

thschrader wrote: Sun Mar 05, 2023 9:22 am I get cf=1,3 when using DIN1055 "Wind loads".
Thanks, I wasn't sure about that but it turns out that my assumption was close to the value recommended by DIN. Still, the biggest issue is nonuniform distribution of the pressure in simulation results . Do you think that it can be improved ? Most likely, that's the reason why my analytical results (especially deflection) are still a bit too far from the simulation results. Mesh refinement doesn't seem to help anymore and it only makes the analysis run too long for my needs. Perhaps better agreement is not possible and simulation will always give such nonuniform pressure distribution but I'm still hoping that it can be improved.

thschrader wrote: Sun Mar 05, 2023 9:22 am Are you sure the inlet-speed is 200m/s =720 km/h?
simpleFOAM is not valid for speeds > 0,3*Ma = 100 m/s
Initially, I used 2 m/s but the stress and deflection were too low. Even with 200 m/s, it's only around 9 MPa and 0.02 mm but I could decrease the speed to 100 m/s or change the geometry to less stiff if needed.
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Re: Flow around a plate - pressure distribution

Post by thschrader »

I scaled up the model by a factor of 10 (which still gives cf=1,3 for the plate)
and used more reasonable boundary conditions. And half of the model, xz-plane is symmetry.

Inlet v=28 m/s (100 km/h), far-field pressure 490 MPa.
FC gives somewhere below 150 N for the half plate, theory gives 130N.
When plotting the p field along a vertikal line, you can see that the distribution along the line
is nearly a rectangle. So the location of the resulting x-force vector should be near +0,5 m above x-Axis.
That gives a momentum of 2*63=126 Nm at the base of the complete plate.

You can also see that at the edges of the "building" the pressure drops (and therefore the v rises),
which is in accordance to DIN1055. The flow is highly unsteady and the mesh is still too rough,
for a Phd-thesis not the best work. But for calculating clumsy buildings it is ok.

BTW:
I can compute resulting forces from the p-field in paraview.
But how to compute momentum?

"Real" building test case:
viewtopic.php?t=68164

my file:
cf_coeff_plate.FCStd
(29.13 KiB) Downloaded 32 times
forces_half_body.JPG
forces_half_body.JPG (46.64 KiB) Viewed 1161 times
pressure_plot.JPG
pressure_plot.JPG (78.98 KiB) Viewed 1161 times
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NewJoker
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Re: Flow around a plate - pressure distribution

Post by NewJoker »

@thschrader Thank you very much for your help. I changed my model to utilize symmetry, decreased the speed to 80 m/s, made the plate thinner and higher to get larger stress and deflection and now the agreement is sufficient for me. Apparently, it can’t be much better because of that non-uniform distribution of the pressure in the simulation.
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Re: Flow around a plate - pressure distribution

Post by herbk »

thschrader wrote: Sun Mar 05, 2023 3:44 pm ...
FC gives somewhere below 150 N for the half plate, theory gives 130N.
...
Atm i'm not shure what you and FC takes into account for the calculations.
If i remember right, the DIn calculates only with the pressure at the front of the plate. ?
But at real there is a additional force at the backside of the plate. If FC adds this force it explanes the different to me (but don't know if FC this do...).
Gruß Herbert
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Re: Flow around a plate - pressure distribution

Post by thschrader »

herbk wrote: Wed Mar 08, 2023 8:54 am
thschrader wrote: Sun Mar 05, 2023 3:44 pm ...
FC gives somewhere below 150 N for the half plate, theory gives 130N.
...
Atm i'm not shure what you and FC takes into account for the calculations.
If i remember right, the DIn calculates only with the pressure at the front of the plate. ?
But at real there is a additional force at the backside of the plate. If FC adds this force it explanes the different to me (but don't know if FC this do...).
The cf0-curve from DIN1055 above is made for practical daily use. From a practical point of view there is no
difference between FC-result and "theory". The FC-result gives the resulting total force of the complete pressure
distribution of the body, not only the front face.
When doing statics for a building, you can split the cf-value 1,3 into 0,8 (front) and 0,5 (back) of the building.
pressure.JPG
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Re: Flow around a plate - pressure distribution

Post by thschrader »

Hi @NewJoker,

FYI:
here is a nice tutorial from @FEAnalyst, how to project the
calculated OF-pressure field onto the FEM-mesh for static calculation. It is your plate problem.
https://www.youtube.com/watch?v=76gqtkEhFwg

He uses the prepomax-interface (with ccx-solver) for statics:
https://prepomax.fs.um.si/

You can import the p-field via the pv.foam file.
When running multi cpu with cfdof, you must merge the cpu-results
with "reconstructPar" command in OF-console before importing in prepomax.

Importing pressure-fields into FEM would be a nice feature for FC.
import_pressure_openfoam.JPG
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NewJoker
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Re: Flow around a plate - pressure distribution

Post by NewJoker »

thschrader wrote: Sat Mar 11, 2023 4:53 pm here is a nice tutorial from @FEAnalyst
Yeah, that's actually my tutorial ;-)
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