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Which condition is to be met for occurrence of stagnation point on a conical surface at an angle of attack with free stream? (Vθ, Vϕ are cross flow velocities)(a) Vθ + Vϕ = 1(b) Vθ + Vϕ = 0(c) Vθ^2 + Vϕ^2 = 0(d) (Vθ + Vϕ)^2 = 1I got this question in semester exam.I would like to ask this question from Cones at Angle of Attack in portion Three-Dimensional Flow of Aerodynamics

Answer»

Right option is (c) Vθ^2 + Vϕ^2 = 0

Explanation: While working with three – DIMENSIONAL flow over a cone kept at an angle of attack with the free stream, we look at the cross – flow plane to analyze the STREAMLINES. The velocity on this plane is called cross – flow velocity. Stagnation point on the cone is SITUATED where the condition Vθ^2 + Vϕ^2 = 0 is met.

In the figure, the shaded portion is the X – y plane of the cone with the outer black boundary being the SHOCK wave. The blue lines are the streamlines with different entropies. Point A is the vortical singularity and point S is the stagnation point.



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