Aerodynamics - Numerical Techniques for Steady Supersonic Flow Quiz(MCQ)

1 .

How are the streamlines for a conical flow behind a shock wave?

A)

Conical

B)

Parallel throughout

C)

Curved till surface tends to infinity

D)

Curved at the beginning, parallel as surface tends to infinity

Correct Answer : Curved at the beginning, parallel as surface tends to infinity

Explanation : For a conical flow at a given Mach number, the shock formation occurs at the vertex of the cone. The streamlines behind the shock wave are initially curved due to 3 – dimensional space unlike streamlines behind the shockwave on a wedge which is parallel. These streamlines eventually become parallel at the cone’s surface tends to infinity.

2 .

For which of these flows is methods of characteristics limited to?

A)

Inviscid flow

B)

Viscous flow

C)

One � dimensional flow

D)

Quasi � two � dimensional flow

Correct Answer : Inviscid flow

Explanation : For computing supersonic steady inviscid flows, there are two major numerical techniques that are used. The first being the methods of characteristics which is an older technique limited to inviscid flows. The other method is the finite – difference method which is applicable for both viscous and inviscid flows.

3 .

Which of these methods is employed to find solution using method of characteristics?

A)

Fourier series

B)

Laurent series

C)

Taylor series

D)

McLaurin series

Correct Answer : Taylor series

Explanation : The flow field properties such as the pressure, density at the discrete points in a grid (xy coordinate plane) are found out by expanding these properties in using Taylor series. If we know the pressure at some point (i,j), then the pressure at the point (i + 1,j) point can be computed using this series as follows:

4 .

What causes 'round off' error in numerical solution?

A)

Finite grid points

B)

Solving nonlinear equation

C)

Incoherent boundary conditions

D)

Rounding number to a significant figure

Correct Answer : Rounding number to a significant figure

Explanation : Numerical solutions are obtained using the computers which often rounds off every number to a certain significant digit. Each of these rounding off results in small errors. If we decrease the truncation errors, the round – off error increases and these errors is a function of step size ?x.

5 .

Where is the application of method of characteristics?

A)

Optimizing the wing

B)

Designing contour of nozzle

C)

Designing the compressor

D)

Optimizing the shape of the fuselage

Correct Answer : Designing contour of nozzle

Explanation : Despite the method of characteristics being highly intensive in terms of the computational load, the invention of high speed computers have made the possibility to use method of characteristics in designing the contour of the supersonic nozzle.

6 .

Method of characteristics is applicable for which of these flows?

A)

Inviscid, subsonic flow

B)

Steady, supersonic flow

C)

Unsteady, subsonic flow

D)

Unsteady supersonic flow

Correct Answer : Steady, supersonic flow

Explanation : Method of characteristics is a type of numerical technique used today for computing flow field of steady supersonic flows. This method was developed in the year of 1920s which is a very classical numerical approach.

7 .

Which grid is used to find the flow field properties using finite difference solutions?

A)

Rectangular grid

B)

Circular grid

C)

Square grid

D)

Non � rectangular grid

Correct Answer : Rectangular grid

Explanation : For computing the flow field properties at points in the flow, there is often grid considered in a plane with known properties at one of the grid point. Using that, properties at other grid points can be computed. In the method of characteristics, non – rectangular grid point is considered and for finite – difference solution, rectangular grid is considered.

8 .

What is the cause of truncation error in numerical solution?

A)

Solving nonlinear equation

B)

Incoherent boundary conditions

C)

Neglecting higher order terms

D)

Rounding number to significant figure

Correct Answer : Neglecting higher order terms

Explanation : In numerical solution, while expanding flow field properties in terms of Taylor series, higher order terms are often neglected. When these terms are neglected, it leads to errors known as truncation error.

9 .

What is the value of derivative of flow field along characteristic line?

A)

0

B)

0.5

C)

1

D)

Indeterminate

Correct Answer : Indeterminate

Explanation : If we consider the direction along the flow field and take the derivatives of these flow properties, the value takes the form of numerator/denominator=0/0 or indeterminate form along the characteristic lines.

10 .

Which partial differential equation is used to define the characteristic at sonic condition?

A)

Elliptic partial differential equation

B)

Circular partial differential equation

C)

Parabolic partial differential equation

D)

Hyperbolic partial differential equation

Correct Answer : Parabolic partial differential equation

Explanation : At sonic condition, when Mach number is equal to 1, there is only one characteristic that passes through the flow field point. This is defined by the parabolic partial differential equation.

11 .

Characteristic curves passing through a point in a flow field are straight lines.

A)

True

B)

False

C)

Can Not Say

D)

None of the above

Correct Answer : False

Explanation : The right and left running characteristic curves are generally curved as it is given by tan?(θ ± μ). Since the value of the Mach angle and the angle θ vary at each point in the flow field, the characteristics are curved instead of being a straight line.

12 .

For subsonic flows, the characteristics through a flow field point are imaginary.

A)

True

B)

False

C)

Can Not Say

D)

None of the above

Correct Answer : True

Explanation : When the Mach number is less than 1 i.e. the flow is subsonic, the numerator in the characteristic curve is imaginary as the terms inside the square root sign is negative. Thus, methods of characteristics is not used for subsonic flows.

13 .

Which of these represents K₊ constant along the C₊ characteristic line?

A)

θ – ν(M) = const

B)

θ + ν(M) = const

C)

θ – 2ν(M) = const

D)

θ + 2ν(M) = const

Correct Answer : θ + ν(M) = const

Explaination : The K₊ constant along the C₊ characteristic line is obtained by integrating the compatibility equation

Where, ν(M) is the Prandtl – Meyer function and we obtain the K+ constant as θ + ν(M) = const.

14 .

Which of these is not an application of a hodograph?

A)

Determining temperature

B)

Swinging Artwood�s machine

C)

Obtaining motion of celestial objects

D)

Solution for method of characteristics

Correct Answer : Determining temperature

Explanation : Hodograph is a velocity diagram which has its applications in finding the graphical solution of the methods of characteristics in high tech computers as it related velocity to characteristic lines, obtaining the position of stars, planets, swinging Artwood’s machine as well as in metrological department.

15 .

Where is methods of characteristics used?

A)

Designing supersonic nozzle

B)

Designing fuselage�s bulkhead

C)

Computing optimum wing camber

D)

Designing diamond airfoil for supersonic flow

Correct Answer : Designing supersonic nozzle

Explanation : Methods of characteristics are used in designing the supersonic nozzle. For this, a line with known supersonic flow fields is required. Upon going downstream, depending on where the point lies (internal/wall) the method of characteristics is applied to find the flow field.

16 .

Disturbances in the case of steady supersonic flow are felt in the entire flow field region.

A)

True

B)

False

C)

Can Not Say

D)

None of the above

Correct Answer : False

Explanation : Unlike subsonic flow where the disturbances are felt in the entire flow field, this is not the case in supersonic flow. In steady supersonic linearized flow, the disturbances/perturbations are felt only in limited regions.

17 .

In which region will the disturbances be felt in a steady supersonic flow?

A)

Point A only

B)

Point C only

C)

Point C and D

D)

Point A and B

Correct Answer : Point A and B

Explaination : When a conical body is placed in a supersonic flow, there is a formation of shock waves. When the points lie within the Mach waves, the disturbances introduce are felt otherwise it is not. Since point A and B lies inside the Mach wave, any perturbations will be felt at these two points.

18 .

What is the domain of dependence?

A)

Area outside the left running wave

B)

Area within the downstream characteristics

C)

Area within the upstream characteristics

D)

Area which does not lie within the characteristic lines

Correct Answer : Area within the upstream characteristics

Explanation : If we consider a point A in the flow field through which two characteristic lines pass (C₊ and C_–) then area which is between the two upstream characteristics of both left and right running waves is known as domain of dependence.

19 .

On which of these points does the properties of flow field at point A depend?

A)

Point B

B)

Point C

C)

Point D

D)

Point P

Correct Answer : Point P

Explaination : Point P lies at the intersection of the two characteristic lines. Point A lies in the region of influence thus its flow properties depend on the properties generated due to disturbances at point P which is the intersection point.

20 .

For a point in the supersonic flow lying at the intersection of the characteristics, its flow field properties depend on change in which of these regions?

A)

Region of influence

B)

Domain of dependence

C)

Region outside the characteristics

D)

Intersection points of the characteristics

Correct Answer : Domain of dependence

Explaination : If a point P lies at the intersection of the left and right running waves, the flow field properties at point P is dependent on the flow field information in the region upstream i.e. domain of dependence.

21 .

What is the region of influence?

A)

Area outside right running wave

B)

Area outside the left running wave

C)

Area within the upstream characteristics

D)

Area within the downstream characteristics

Correct Answer : Area within the downstream characteristics

Explanation : For a point A which is present in a flow field with incoming steady supersonic flow, there will be two characteristic lines passing through them. The area formed between these two characteristics in the downstream region is known as region of influence.