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Sphere

Example simulation of a sphere

The analytical solution for the potential flow around a sphere of radius R=1R=1R=1
m and a uniform flow of ∣Vref∣=1|\mathbf{V}_{ref}|=1∣Vref​∣=1
 m/s is known. The perturbation (or doublet) potential is given by:
ϕ=∣Vref∣cos(θ)R32r2,\phi=|\mathbf{V}_{ref}|cos(\theta)\frac{R^3}{2r^2}\text{,}ϕ=∣Vref​∣cos(θ)2r2R3​,
where ϕ\phiϕ
 is the perturbation (or doublet) potential, RRR
 is the radius of the sphere, rrr
is the distance from the sphere centre to any point of interest on its surface, ∣Vref∣|\mathbf{V}_{ref}|∣Vref​∣
is the freestream velocity magnitude, and θ\thetaθ
is the angle between the xxx
-axis and the projection of rrr
on the x−zx-zx−z
plane. An unstructured mesh of 532 elements is used. The image below shows the sphere pressure coefficient.
The images below compare the perturbation potential, the total potential, and the pressure coefficient with the analytical solution.
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Good agreement between the simulation and the analytical solution is observed.
Files
sphere.zip
12KB
Binary
References

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Output files

Ellipsoid

Last modified 2yr ago