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Sphere

Example simulation of a sphere

PreviousOutput filesNextEllipsoid

Last updated 11 months ago

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The analytical solution for the potential flow around a sphere of radius R=1R=1R=1m 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, rrris 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\thetaθis the angle between the xxx-axis and the projection of rrron the x−zx-zx−zplane. 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.

Good agreement between the simulation and the analytical solution is observed.

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References

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sphere.zip
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