ANALYTICAL SOLUTION FOR POTENTIAL FLOW AROUND A ROTATING SPHERE AND COMPARISON WITH CFD

Yıl 2024, Cilt: 8 Sayı: 1, 101 - 111, 30.06.2024

Tarıq Abraheem Mohammed Almıqasbı Ekrem Yılmaz Aydın Şalcı

https://doi.org/10.53600/ajesa.1424673

Öz

A three-dimensional analytical solution was derived for an incompressible steady potential at an initially uniform velocity flow around a sphere, which translates forward, backward, rotates longitudinally or transversally. The concept of relative velocity was used to analyze the flow around the transitionally moving sphere. To analyze the flow around the longitudinally rotating sphere, A formula of the circumferential velocity of the fluid is found at the equatorial plane of the sphere and then generalized to the whole sphere as an approximation. The superposition principle of velocities was used to analyze the flow around the transversely rotating sphere, the stagnation points were detected and analyzed, the pressure distribution at the equator was calculated and compared with the experimental and CFD results, and the lift coefficient was calculated and compared with the experimental results and a good agreement for C_p and C_L was found at low spin factors, In contrast, at high spin factors the results begin to diverge due to the viscous effects and eddy formation.

Anahtar Kelimeler

Potential Flow, Analytical Solution, Rotating Sphere, Superposition Principle, Stagnation Points

Kaynakça

• Anderson JD; Fundamentals of Aerodynamics, Sixth Edition, McGraw-Hill Book Company, 2017.
• Briggs LJ; Effect of Spin and Speed on the Lateral Deflection (Curve) of a baseball; and the Magnus effects for Smooth Spheres, American Journal of Physics, 1959; 27(8), 1959: 589 -596.
• F. B. Hildebrand; Advanced calculus for applications, Prentice-Hall, 1962.
• F. M. White; Fluid Mechanics, 7th edition, McGraw-Hill Series in Mechanical Engineering, 2011.
• Hydro-Aerodynamics Lecture Notes, Aydın ŞALCI, 2020.
• L. W. Alaways , M. Hubbard; Experimental determination of baseball spin and lift, Journal of Sports Sciences, 2001, 19, 349- 358.
• Mehta R. C., Aerodynamics of Spinning Sphere in Ideal Flow, Scholars Journal of Engineering and Technology (SJET), 2016; 4(5):215-219
• T. Nagami, T. Higuchi, H. Nakata, T. Yanai, and K. Kanosue; Relation Between Lift Force and Ball Spin for Different Baseball Pitches, Journal of Applied Biomechanics, 2016, 32, 196 -204.
• W.P. Graebel, Advanced Fluid Mechanics, Elsevier, New York, 2007