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Aerodynamics - Oblique Shock and Expansion Waves Quiz(MCQ)
A)
Across an oblique shock, pressure and temperature increases
B)
Across an oblique shock, Mach number and total pressure decreases
C)
Across an oblique shock, Mach number increases whereas pressure and density decreases
D)
Across an oblique shock, Mach number decreases whereas pressure and temperature increases

Correct Answer :   Across an oblique shock, Mach number increases whereas pressure and density decreases


Explanation : Across an expansion fan, Mach number increases, pressure, density, and temperature decreases. Since the process is isentropic, stagnation properties like total pressure and temperature remain constant.

A)
Across an oblique shock, pressure and temperature decreases
B)
Across an oblique shock, Mach number and total pressure increases
C)
Across an oblique shock, Mach number increases whereas density and pressure decrease
D)
Across an oblique shock, Mach number decreases whereas pressure and temperature increases

Correct Answer :   Across an oblique shock, Mach number decreases whereas pressure and temperature increases


Explanation : Across an oblique shock, due to its non-isentropic nature, Mach number decreases, pressure, density, and temperature increases. Total pressure across the shock wave decreases

3 .
Which of the following is true regarding the θ-β-M relation?
A)
There are two values of deflection angle for a given Mach number and shock angle
B)
There are two possible solutions for any given deflection angle and Mach number
C)
The θ-β-M relation has a solution only when the Mach number of the flow downstream is less than unity
D)
There is a maximum value of deflection angle for a given Mach number for a straight oblique wave

Correct Answer :   There is a maximum value of deflection angle for a given Mach number for a straight oblique wave


Explaination : The minimum value of the deflection angle is 0 and the maximum value is attained at M1 = ∞. There are two possible solutions (shock angles), within the limiting values of the deflection angle and Mach number.

A)
Circle
B)
Ellipse
C)
Parabola
D)
Hyperbola

Correct Answer :   Circle


Explanation : When Mach number reaches infinity the shock polar is a circle. The circle lies between 0.41 to 2.45 characteristic Mach number values, which gives the diameter of the circle. This is the only circular curve other than the sonic circle in shock polar.

A)
Higher Mach number represents stronger shock
B)
Inside the sonic circle in shock polar, all velocities are supersonic
C)
Dimensionless shock polar is not very compact and hence is not used often
D)
Characteristic Mach number is used to represent the velocity of the flow ahead and behind the shock

Correct Answer :   Characteristic Mach number is used to represent the velocity of the flow ahead and behind the shock


Explanation : Characteristic Mach Number is used instead of only velocity or Mach number because when Mach number becomes infinity, characteristic Mach number becomes 2.45, which makes the graph more compact. All velocities inside the sonic circle are subsonic and outside it, are supersonic.

A)
Shock polar is the graphical representation of weak shocks properties
B)
Shock polar is the locus of all the velocities behind the shock for varying deflection angle from zero to the maximum deflection angle
C)
Shock polar is the graphical representation of normal shock properties
D)
Shock polar is the locus of all the shock angles behind the shock for varying Mach number from one to infinity

Correct Answer :   Shock polar is the locus of all the velocities behind the shock for varying deflection angle from zero to the maximum deflection angle


Explanation : Shock polar is a graphical representation of oblique shock properties. It is the loci of all such points for deflection angle from zero to maximum deflection, representing all the velocities behind the shock.

A)
Weaker shocks are observed in 3D than in 2D
B)
The pressure is constant over the surface of the cone
C)
Adiabatic nature of the wave is absent in 3-dimensional flow
D)
Streamlines are straight and parallel to the conical surface behind the shock

Correct Answer :   Weaker shocks are observed in 3D than in 2D


Explanation : 3D provides extra space for the flow to move and hence relieving the flow from stress concentration. Hence weaker shocks are observed in 3D than in 2D. Streamlines are curved and pressure is not constant over the surface of the cone.

8 .
What are the values of shock angles (β), when the deflection (θ) is zero, for a given Mach number?
A)
β = μ, 90°
B)
β = μ, 60°
C)
β = 0, 90°
D)
β = 0, 60°

Correct Answer :   β = μ, 90°


Explaination : When the deflection is zero, the θ-β-M equation reduces to (M1sin?β)2? = 1. Two solutions obtained for shock angles from the above relation are, β = -90°, 90°. When the shock angle is 90°, a normal shock is observed. But -90° is not possible and hence it takes some limiting value, μ.

9 .
The ratio of the densities of the flow downstream and upstream of the oblique shock is 1.5157. If the normal component of the velocity of the upstream flow is 445.9 m/s, then what is the normal component of the velocity downstream of the shock?
A)
306 m/s
B)
294.18 m/s
C)
269.6 m/s
D)
255 m/s

Correct Answer :   294.18 m/s

10 .
What is the Mach number of the flow after the shock and normal to the oblique shock? Mach number downstream of the flow is, M2 = 1.1, shock angle, β = 60°, and wall deflection angle, θ = 4.018°.
A)
0.77
B)
0.912
C)
0.952
D)
1.270

Correct Answer :   0.912


Explaination : The Mach number of the flow after the shock and normal to the oblique shock is given by, My = M2sin?(β – θ) = 1.1 × sin?(60 – 4.018) = 0.912.

A)
Weak oblique shocks occur at small deflection angles
B)
The flow downstream of the weak shock is supersonic
C)
Weak oblique shocks are considered as Mach waves with same shock angle
D)
Weak oblique shocks can compress the flow with an infinitesimal increase in entropy

Correct Answer :   Weak oblique shocks are considered as Mach waves with same shock angle


Explanation : Weak shock angle is not equal to Mach angle, also they differ by a finite amount. Mach waves compress the supersonic flow without increasing entropy, whereas in weak oblique shock there is a small increase in entropy to compress the supersonic flow.

12 .
Find the shock strength of a weak oblique shock with flow Mach number of 2 and a small deflection angle of 1°. Assume that the flow is isentropic and shock angle is almost equal to the Mach angle. Take heat capacity ratio (?) of gas as 1.4.
A)
0.0356
B)
0.0564
C)
3.5
D)
4.5

Correct Answer :   0.0564

A)
Change in entropy is directly proportional to the small deflection angle in a weak shock
B)
Total temperature and pressure are directly proportional to the small deflection angle in a weak shock
C)
Static density and temperature are directly proportional to the small deflection angle in a weak shock
D)
Stagnation pressure and temperature are directly proportional to the small deflection angle in a weak shock

Correct Answer :   Static density and temperature are directly proportional to the small deflection angle in a weak shock


Explanation : For very small deflection angle, static pressure, temperature, and density are directly proportional to the deflection angle. Change in entropy is proportional to the third power of the deflection angle. Stagnation properties are constant since the flow is isentropic in nature.

A)
Change in flow velocity is achieved in a shorter distance when closer to the wall than further away
B)
Mach lines formed due to small deflection are divergent
C)
Velocity downstream of the smooth supersonic compression is subsonic
D)
Increase in entropy by a number of weak shocks is greater than the increase by one single shock for a given deflection

Correct Answer :   Change in flow velocity is achieved in a shorter distance when closer to the wall than further away


Explanation : Increase in entropy by a number of weak shocks is smaller than a single shock for a given deflection angle. Reduction in entropy is of factor 1/n2, for ‘n’ weak shock waves. Also, the Mach lines are convergent in nature and hence, the change in flow velocity is achieved in a shorter distance when further away from the wall than closer to it. The deflection angle is taken to be small for smooth supersonic compression to obtain supersonic flow downstream.

A)
True
B)
False
C)
Can Not Say
D)
None of the above

Correct Answer :   False


Explanation : There is a combination of Mach lines for a small deflection. These Mach lines then converge at a point further away from the wall. Above the convergence point, there is a strong oblique shock formation.

A)
The two velocity components normal to the first and last Mach waves are equal
B)
The upstream velocity component parallel to the first Mach wave is not equal to the downstream velocity component parallel to the last Mach wave
C)
The upstream velocity component normal to the first Mach wave is greater than the downstream velocity component normal to the last Mach wave
D)
The upstream velocity component normal to the first Mach wave is smaller than the downstream velocity component normal to the last Mach wave

Correct Answer :   The upstream velocity component normal to the first Mach wave is smaller than the downstream velocity component normal to the last Mach wave


Explanation : During a supersonic expansion at a convex corner, the velocity components parallel to the Mach waves are equal. Since expansion follows an isentropic process, the normal component of the velocity downstream is greater than upstream normal velocity component.

A)
Mach lines diverge from the point where the deflection corner starts
B)
The Mach lines in a centered expansion wave are curved
C)
The last Mach line created at the corner is called the Prandtl – Meyer expansion fan
D)
The first Mach line created at the corner is called the Prandtl – Meyer expansion fan

Correct Answer :   Mach lines diverge from the point where the deflection corner starts


Explanation : In a centered expansion fan, Mach lines diverge from the corner. There is a fan of straight Mach lines from the corner which makes up the Prandtl – Meyer expansion fan.

A)
Flow velocity reduces across the flow
B)
There is an entropy decrease across the flow
C)
Static properties are instantly increased across the flow
D)
Pressure, temperature, and density decreases gradually throughout the flow

Correct Answer :   Pressure, temperature, and density decreases gradually throughout the flow


Explanation : When flow turns away from itself, expansion waves are created which follows an isentropic process. Pressure, density, and temperature are gradually decreased through a series of waves.

19 .
What are the values of expansion angle and deflection angle, when the radial component of the flow is zero and the expansion angle is maximum? Assume heat capacity ratio = 1.4.
A)
Expansion angle = 120° and deflection angle = 90°
B)
Expansion angle = 180° and deflection angle = 90°
C)
Expansion angle = 220.5° and Deflection angle = 130.5°
D)
Expansion angle = 130.5° and deflection angle = 220.5°

Correct Answer :   Expansion angle = 220.5° and Deflection angle = 130.5°

20 .
If the polar components of the expansion flow are Vr and V then what is true about the properties of these polar components?
A)
At the beginning of the expansion fan, the r component of the velocity is equal to the sonic velocity
B)
Vr is maximum at the beginning of the expansion fan and becomes zero for maximum expansion
C)
The ∅ component of the flow is constant and flow the properties are only dependent upon the r component
D)
The radial component of the flow is constant and flow the properties are only dependent upon the ∅ component

Correct Answer :   The radial component of the flow is constant and flow the properties are only dependent upon the ∅ component


Explaination : Flow properties do not change along any radial line and vary with ∅ only. At the beginning of the fac, the ∅ component of velocity is equal to the local speed of sound. Vr is maximum at the end of the expansion fan where the expansion angle is maximum.

21 .
A uniform flow of Mach number 2 passes over an expansion corner with wall deflection angle as 10°. What is the Mach number of the flow downstream of the expansion fan? Assume ? = 1.4.
A)
1.652
B)
2.015
C)
2.386
D)
3.258

Correct Answer :   2.386


Explaination : From the Prandtl-Meyer function table, for M1 = 2, ϑ1 = 26.38°. Now ϑ2 = θ + ϑ1 = 26.38 + 10 = 36.38°. Again from the table, we get, M2 = 2.386.

A)
When a simple wave is reflected by a wall
B)
When two simple waves of opposite family (+ or -) interact
C)
When two simple waves of the same family (+ only or – only) interact
D)
When the flow is isentropic in nature there is a single relation between Prandtl-Meyer function and flow deflection

Correct Answer :   When two simple waves of opposite family (+ or -) interact


Explanation : A non-simple is created when two simple waves of a different family (+ or -) interact. The relation between ν and θ is not simple anymore and calculation for such regions is done through methods of characteristics.

A)
When the motion is described by two variables
B)
When the motion preserves its geometry in space
C)
When the motion preserves its geometry in space or time
D)
When the motion preserves its geometry in space or time or both

Correct Answer :   When the motion preserves its geometry in space


Explanation : When the motion preserves its geometry in space or time or both, it is known to be self-similar. Prandtl-Meyer is a self-similar motion, and Prandtl-Meyer function is a similarity variable.

A)
Mach wave angle of the centered expansion fan wave
B)
The wall deflection angle measured from the vertical axis perpendicular to the upstream flow
C)
The inclination angle of the wave with respect to the Mach line corresponding to Mach 1
D)
The flow inclination of the wave with respect to the horizontal axis parallel to the upstream flow

Correct Answer :   The inclination angle of the wave with respect to the Mach line corresponding to Mach 1


Explanation : The Prandtl-Meyer function denoted by ν(M) is a function of the Mach number of the flow. Physically it represents the flow inclination angle of the wave corresponding to the line with zero turning angle (∅ = 0). When Mach number is equal to 1 the function becomes zero and hence the angle is measured with respect to this line.

A)
Static pressure and temperature
B)
Static temperature and wave angle
C)
Static density and pressure ratios
D)
Flow deflection angle and shock strength

Correct Answer :   Flow deflection angle and shock strength


Explanation : For any shock reflected from the surface, flow deflection angle before the incident shock and after the reflected shock doesn’t change. In weak shocks, shock strength is assumed to be equal since the change in pressure is very small.

A)
Only the deflection angle
B)
Pressure ratios and shock strength
C)
Flow deflection angle and shock strength
D)
Flow Mach number and shock wave angle

Correct Answer :   Only the deflection angle


Explanation : When a strong shock is reflected from a surface, the flow directions before and after the shocks are parallel and hence deflection angle is the same. The pressure ratios for each shock is different and the overall strength is the product of these two pressure ratios.

A)
Shock wave angles of incident and reflected shock waves are equal
B)
Shock wave angles of incident and reflected shock waves are not equal
C)
Shock wave angle of reflected shock is always greater than the incident wave angle
D)
Reflected shock wave angle is greater than the incident shock wave angle when the Mach number of the flow is high

Correct Answer :   Shock wave angles of incident and reflected shock waves are not equal


Explanation : When a shock wave is reflected from a rigid surface, the waves angles are not equal. For low Mach numbers, the reflected shock wave angle is greater than the incident shock wave angle. For high Mach numbers, the shock wave angle of reflected shock is always greater than the incident wave angle.

A)
Pressure
B)
Flow direction
C)
Temperature
D)
Flow Mach number

Correct Answer :   Temperature


Explanation : The contact surface can be idealized as a surface of discontinuity. It separates flow into two flow fields, with different temperature and density. Pressure, flow direction, and Mach number are the same.

29 .
What is the shock wave angle of the reflected shock with respect to the horizontal, when a shock is reflected from the surface with shock wave angle given as β=40 and flow Mach number is 2?
A)
37.9°
B)
39.7°
C)
45.6°
D)
50.2°

Correct Answer :   39.7°


Explaination : From θ-β-M graph, for M1=2 and β1=40, θ=10.5°. Now from oblique shock relation tables, we can find M2=1.63. Since the flow direction is unchanged after crossing the reflected wave, from the θ-β-M graph, for M2=2 and θ=10.5°, β2=50.2°. So the reflected shock wave angle w.r.t the ground is βr2-θ=50.2-10.5=39.7°.

A)
The shocks will coalesce and form one single stronger shock
B)
Shock waves will coalesce and form into many stronger shocks
C)
The shocks will pass through and create multiple shock systems
D)
Slipstream line will be created perpendicular to the flow direction

Correct Answer :   The shocks will coalesce and form one single stronger shock


Explanation : When two shocks of the same family interact, they coalesce and form one bigger shock wave. The slipstream line is parallel to the flow downstream of the shock and at the point of intersection of all the waves.

A)
Slipstream
B)
Vortex sheet
C)
Entropy boundary
D)
Tangential discontinuity

Correct Answer :   Entropy boundary


Explanation : In literature, the contact surface is referred to as material boundary, entropy discontinuity, slipstream or slip surface, vortex sheet, and tangential discontinuity. The contact surface is a surface of discontinuity. It can be stationary or moving.

A)
The downstream flow direction is equal to freestream flow direction
B)
The flow is always parallel to the ground due to multiple shock formation
C)
The downstream flow deflection angle of the portion above the slipstream is not equal to the portion below the slipstream
D)
The two portions downstream, below and above the slipstream of the shock system, have equal pressure

Correct Answer :   The two portions downstream, below and above the slipstream of the shock system, have equal pressure


Explanation : The interaction of two shock waves of opposite sign and unequal strength leads to the division of the flow into two portions by a slipstream. The downstream flow deflection angle and pressure are equal in these two portions. The downstream flow direction is may not be always equal to the freestream flow direction.

A)
Flow downstream is deflected more towards the positive direction family of the shock interaction
B)
There is a slight bend in the flow inside the shock system but flow direction doesn’t change before and after the interaction
C)
Flow direction downstream of the shock system is deflected towards the negative direction family of the shock system
D)
Flow direction before and after the shock interaction is same and there is no bent in the flow throughout the shock system

Correct Answer :   There is a slight bend in the flow inside the shock system but flow direction doesn’t change before and after the interaction


Explanation : When two shock waves of the opposite family but same strength interact, the flow direction upstream and downstream of the shock system doesn’t change. The flow bents a little between the reflected shocks by some angle but again is bent back to the previous direction.

A)
Like reflection takes place in a free boundary of the supersonic flow
B)
Unlike reflection takes place in the solid boundary of the exhaust nozzle
C)
Supersonic flow diffuses into the atmosphere without any shock interaction
D)
An imaginary free boundary preserves the atmospheric pressure along its length

Correct Answer :   An imaginary free boundary preserves the atmospheric pressure along its length


Explanation : When supersonic flow exits from the nozzle, an imaginary free boundary is created so as to preserve the atmospheric surrounding pressure along its length. From this free jet boundary, unlike reflections take place whereas from a solid boundary like reflections takes place.

35 .
A uniform supersonic flow at Mach number 2 expands through two convex corners of 10° each. What is the angle of the second expansion fan?
A)
14.16°
B)
26.38°
C)
36.38°
D)
46.38°

Correct Answer :   14.16°


Explaination : From Prandtl-Meyer functions table for M1 = 2, ν1 = 26.38°. We have ν2 = ν1 + θ = 36.38°. Again referring to the table, we get M2 = 2.38. The Prandtl-Meyer function after the second fan is ν3 = ν2 + θ = 46.38° and corresponding Mach number M3 = 2.83. The Mach angles are μ1 = 30, μ2 = 24.84, μ3 = 20.69. The angle of the second fan is μ23 = θ + μ2 – μ3 = 14.16°.

36 .
Which of the following statements correctly describes the shock waves when flow deflection angle is, θ > θmax?
A)
Detached curved shock is formed ahead of the nose
B)
The normal shock wave is formed attached to the nose
C)
Attached shock waves are formed when Mach number is low
D)
Normal shock is formed over the nose and around and later the shock gets curved and detached

Correct Answer :   Detached curved shock is formed ahead of the nose


Explaination : When the flow deflection angle, θ > θmax, then curved and detached shock wave is formed ahead of the nose as there is no solution for a straight oblique shock. Even for a streamlined body, the shock wave is detached for any Mach number.

A)
When wedge angle is equal to maximum flow deflection angle, the shock is attached but it is curved
B)
For a given wedge angle, when Mach number increases, the detachment point gets away from the nose
C)
When wedge angle is equal to maximum flow deflection angle, the shock gets detached but it is straight
D)
For a given wedge angle, when Mach number decreases, the detachment point gets away from the nose

Correct Answer :   When wedge angle is equal to maximum flow deflection angle, the shock is attached but it is curved


Explanation : For a given wedge angle, when the Mach number decreases, the shock angle increases and the detachment point gets away from the nose. When wedge angle is equal to maximum flow deflection angle, the shock is attached but it is curved, which represents the region between the lines the M1 = 1 and θ = θmax in θ-β-M graph.

A)
Like reflections
B)
Unlike reflections
C)
Opposite reflections
D)
Solid boundary reflections

Correct Answer :   Unlike reflections


Explanation : When shock waves reflect from a boundary and give rise to expansion waves, it is called as, unlike reflections. Unlike reflections take place from the free boundary and like reflections from the solid boundary.

A)
Formation of lower strength normal shock
B)
Formation of higher strength normal shock
C)
It gives rise to a reflected left running oblique shock
D)
It gives rise to a reflected right running oblique shock

Correct Answer :   It gives rise to a reflected left running oblique shock


Explanation : Intersection of a normal shock and right running oblique shock gives rise to a left running reflected shock in order to bring the flow to its original direction. The reflected oblique shock is of lesser strength than the right running oblique shock.

40 .
Considering Mach reflections, what is the relation between Mach numbers of different regions? Consider upstream of 1st shock as region 1, upstream of reflected shock as region 2 and downstream of the reflected shock as region 3.
A)
M1 > M2 > M3
B)
M1 < M2 < M3
C)
M1 < M2 > M3
D)
M1 = M2 > M3

Correct Answer :   M1 > M2 > M3


Explaination : When Mach reflections are considered, there is no simple oblique shock wave but the reflection of waves and the strength of the reflected shock reduces due to deflection involved in the process. This leads to the reduction in flow Mach number between different regions.

A)
Strong shock solution is observed
B)
Straight shock system can be seen
C)
Detached curved shock is observed behind and ahead of the normal shock
D)
Detached curved shock is observed ahead of the normal shock and straight shock is observed ahead of the normal shock

Correct Answer :   Detached curved shock is observed behind and ahead of the normal shock


Explanation : A strong shock solution is physically impossible for the scenario, but detached shock is part of the strong shock solution. The curved shock system is observed when two oblique shocks of the opposite family intersect.

A)
Pressure increases and becomes constant
B)
Pressure decreases linearly in a straight line thought the length of the edge of the plate
C)
Pressure increases and becomes constant on the top surface and on the bottom surface
D)
The pressure curve is of square shape with unequal pressure value on top and bottom surfaces

Correct Answer :   The pressure curve is of square shape with unequal pressure value on top and bottom surfaces


Explanation : According to shock expansion theory, shock wave interactions determine the aerodynamic loads on the surface of the airfoil. We can see that when a flat plate is at an angle of attack, the pressure on either side of the airfoil is unequal and hence the shape of the pressure curve is square.

A)
Pressure first increases instantly and then decreases linearly in a straight line
B)
Pressure increases and becomes constant till the trailing edge of the airfoil
C)
Pressure increases and becomes constant, and then becomes negative instantly
D)
Pressure decrease follows a parabolic path and then becomes atmospheric pressure again

Correct Answer :   Pressure first increases instantly and then decreases linearly in a straight line


Explanation : According to shock expansion theory, shock wave interactions determine the aerodynamic loads on the surface of the airfoil. Detached shock is formed on the blunt edge which increases the pressure and then it is linearly decreased along the upper length of the airfoil.

A)
Pressure increases and becomes constant
B)
Pressure decrease follows a parabolic path
C)
Pressure decreases linearly in a straight line
D)
Pressure increases instantly and becomes constant, and then suddenly becomes negative and becomes constant

Correct Answer :   Pressure increases instantly and becomes constant, and then suddenly becomes negative and becomes constant


Explanation : According to shock expansion theory, shock wave interactions determine the aerodynamic loads on the surface of the airfoil. Oblique shock and expansion waves decrease and increase the pressure respectively.

A)
The pressure on both sides are different
B)
The pressure on both sides are equal
C)
The flow direction of both sides are different
D)
The density and temperature are the same on both the sides

Correct Answer :   The pressure on both sides are equal


Explanation : On either side of the discontinuity the flow direction needs to be same. The pressure is also same on both sides as the flow is not turning.

A)
On the blunt edge point
B)
Far away from the edge
C)
Just above the blunt edge point
D)
Near the trailing edge of the section

Correct Answer :   Just above the blunt edge point


Explanation : In a detached shock, the normal shock is observed on the blunt edge and then slowly loses strength and becomes an oblique shock just above the edge point. Finally the detached shock becomes a Mach line far away from the edge.