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# MCQs on Cones at Angle of Attack

For a supersonic flow over a right – circular cone at zero angle of attack, what are the flow properties a function of?

a) Polar angle

b) Azimuth angle

c) Mach number

d) Conical ray distance

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a

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.

When the right – circular cone is kept at an angle of attack to the free – stream, what is it considered to be?

a) One – dimensional

b) Two – dimensional

c) Three – dimensional

d) Four – dimensional

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c

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.

How many variables is the flow field dependent on in case of flow over a cone at an angle of attack?

a) 1

b) 2

c) 3

d) 4

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b

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.

Streamlines curl from the leeward to the windward surface along the conical surface when kept at an angle to the free stream.

a) True

b) False

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b

Explanation: The incoming streamlines move along the conical surface curve from the windward surface which is the bottom portion of the cone to the leeward surface which is the upper portion of the cone.

For a cone at an angle of attack, what is the shock wave a function of?

a) Polar angle

b) Azimuth angle

c) Angle of attack

d) Conical ray distance

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b

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 ϕ 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.

Vortical singularity exists at which part of the conical surface?

a) Leeward surface

b) Windward surface

c) Axis of the cone

d) Vertex of the cone

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b

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.

When the angle of attack of the cone with free stream flow is greater than the shock wave angle where is the vortical singularity present?

a) On the windward surface

b) Away from the surface

c) Inside the conical surface

d) On the leeward surface

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b

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.

There is a large gradient of entropy near the surface of the cone.

a) True

b) False

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a

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.

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) Vθ2 + Vϕ2 = 0

d) (Vθ + Vϕ)2 = 1

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c

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 Vθ2 + Vϕ2 = 0 is met.

Find the condition of stagnation point on conical surface from given diagram

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.

Flow over an elliptical cone at zero angle of attack, the fluid properties are a function of how many elements?

a) 1

b) 2

c) 3

d) 4

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b

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.

What happens when the cross – flow velocity becomes supersonic?

a) Embedded shock waves on windward side

b) Embedded shock waves on the leeward side

c) Expansion shock waves on the windward side

d) Oblique shock waves on the leeward side

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b

Explanation: When the cross – flow velocity (Vθ, Vϕ) increases and Vθ2 + Vϕ2 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.

When does embedded shock wave appear on the cone kept at an angle?

a) Angle of attack = half cone angle

b) Angle of attack > half cone angle

c) Angle of attack < half cone angle

d) Shock wave angle = 90 degrees

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b

Explanation: 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.