Question

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 = 1

I 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 1

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.