Correct Answer : Windward surface
Explanation : When a cone is at an angle of attack, the windward streamline is at φ = 0 deg and the leeward streamline is at φ = 180 deg. The flow through leeward streamline acquires an entropy of s1 which curves toward the windward surface thus wetting the entire cone. The flow through windward surface has an entropy of s2 as well as entropy s1 from the streamlines that curve upward to the windward side. This leads to the windward portion of the cone with two values of entropy which is known as a vortical singularity.
φ = 0 deg
φ = 180 deg
Correct Answer : Away from the surface
Explanation : When the angle of attack of the cone with free stream flow is more than the shock wave angle, the flow converges at a point that is not on the surface, rather it is slightly away. When the angle of attack is less than the shock wave angle, the vortical singularity lies on the windward surface.
Correct Answer : True
Explanation : On the top surface of the cone, the streamlines with different entropies come together and meet at a point known as vortical singularity. This leads to an entropy layer on or above the surface of the cone depending on the relation between angle of attack and shock wave angle. This layer leads to a large gradient of entropy normal to the streamlines.
Correct Answer : Angle of attack > half cone angle
Explaination : Embedded shock waves appear over the leeward surface of the cone when the cross – flow velocity increases thus becoming supersonic. These waves are prevalent only when the angle of attack is greater than the half – cone angle and are usually weak in nature.
Correct Answer : Embedded shock waves on the leeward side
Explanation : When the cross – flow velocity (Vθ, V?) increases and Vθ2 + V?2 becomes greater than the square of free – stream velocity i.e. the cross – flow velocity becomes supersonic, then there is formation of embedded shock waves on the leeward portion of the cone.
Correct Answer : 2
Explanation : Unlike right – circular cone kept at zero angle of attack with respect to the free stream, fluid properties over an elliptical cone at zero angle of attack is dependent on two factors – Azimuth angle and polar angle.
Correct Answer : Vθ2 + Vφ2 = 0
Explaination : 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 Vθ2 + Vφ2 = 0 is met.
Correct Answer : Azimuth angle
Explanation : Shock wave angle is the angle formed between the shock wave and the axis of the conical surface. This angle is a function of azimuth angle ? and varies for every different meridian plane. Streamlines that move through various points on the shock wave undergo various changes in entropy around the shock since the shock wave angle of the shock wave is different.
?
Correct Answer : Polar angle
Explanation : When a right – circular cone is kept at a zero angle of attack in a supersonic flow, the flow properties are only a function of polar angle θ. It is independent of the azimuth angle φ and the distance from the vertex along conical ray.
θ
φ
Correct Answer : Three – dimensional
Explanation : When the right – circular cone is kept at a zero angle of attack to the free – stream, it is known to be axisymmetric and is known to be a two – dimensional flow. But, when it is kept at an angle of attack, the flow no longer remains two – dimensional. The shock wave more or less remains the same but the flow becomes three – dimensional.
Explanation : For axisymmetric flow (flow over a cone at zero angle of attack), the flow field is only dependent on polar angle whereas when the cone is kept at some angle of attack, the flow field is a function of both polar angle θ and the azimuth angle φ.
