I want to calculate the drag force over a sphere i need a formulation to do that ..using CFD
For Hypersonic Flows over say Mach 8, we can use Newton Theory (A local surface inclination method ) for Rough Estimate
From Newton Theory, we directly get Cd = 1; It is independent of Mach and simply assumes High Hypersonic Machs. The Formulation is attached.
For more accuracy you can use the Modified Newton theory, obtain the Cp and use the Cp to get the pressure distribution or directly the Drag.
I can assure you that you cannot use other surface inclination methods like tangent wedge and tangent cone methods. As the shock will be detached in sphere
For Research Stuff
Hypersonic flow past a sphere
Proceedings of the Indian Academy of Sciences - Section A
December 1964, Volume 60, Issue 6, pp 396-415
by
Girishwar Nath
http://download.springer.com/static/pdf/148/art%253A10.1007%252FBF03047420.pdf?auth66=1424411480_117cc5e1aa042305be6d08bec4544f67&ext=.pdf
A precise correlation f(Mach,Reynolds) is given by Henderson in
Henderson, C. B., “Drag Coefficients for Spheres in Continuum and Rarefied Regimes,” AIAA Journal , Vol. 14, No. 6, June 1976, pp. 707–708
I agree with Aditya but since you are using CFD codes to evaluate Cd you can't be direct like the local inclination methods. Obtain the surface pressure distribution and then the surface pressure coefficient from it. Numerically integrate it taking infinitesimally small strips. Non dimensionalise it with base are and viola!!! you have the coefficient of drag
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