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.
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
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.
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.
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.
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.
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.
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.
Correct Answer : 294.18 m/s
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.
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.
Correct Answer : 0.0564
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.
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.
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.
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.
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.
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.
Correct Answer : Expansion angle = 220.5° and Deflection angle = 130.5°
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.
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.
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.
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.
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.
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.
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.
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.
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.
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 βr=β2-θ=50.2-10.5=39.7°.
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.
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.
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.
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.
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.
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°.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.