aerodynamics of aircraft

5/26/2018 AERODYNAMICS OF AIRCRAFT

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MA6621

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NANYANG TECHNOLOGICAL UNIVERSITY

SEMESTER 1 EXAMINATION 2009-2010

MA6621 Aerodynamics

November/December 2009 Time Allowed: 2hours

INSTRUCTIONS

1. This paper contains FIVE (5)questions and comprises FIVE (5)pages.2. Answer ALL questions. Support your answers with formulae and figures whenever

appropriate.

3. Write the answers for all questions in a separate answer book.4. All questions carry equal marks.5. This is an OpenBook Examination.6. Please start new questions on a new page.___________________________________________________________________________

1 Consider an incompressible, viscous fluid contained between two infinite plates

separated by a distance H. One plate is stationary and the other is moving at a

constant velocity U as shown in Figure 1. A pressure gradientp

x 0 is driving the

flow.

Figure 1: Flow between two plates.

Note: Question No. 1 continues on page 2.


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(i) Starting with the 2D-incompressible Navier-Stokes equations, determine thevelocity distribution of the flow.

(8 marks)

(ii) Determine the shear stress profile of the flow for the case that px

= 0 and

U0.Sketch the velocity and shear stress distribution for this case.

(4 marks)

(iii) Determine the shear stress profile of the flow for the case that px

0 and

U=0.Sketch the velocity and shear stress distribution for this case.

(4 marks)

(iv) Sketch the velocity field for a non-zero Uand a non-zero p

, so that the total

mass flow rate is zero.

(4 marks)

Be sure to clearly indicate your assumptions, as valid assumptions will vastly simplify

the problem. You can neglect effects of gravity. The flow is fully developed, steady

and quasi-2D.

2(a) For a given airplane, the drag of the aircraft can be expressed as:

CD =CD,0+ kCL2

with ka constant.

(i) Derive an expression for CL at maximum lift-to-drag ratio in terms of k andCD,0.

(6 marks)

(ii) Derive an expression for the maximum lift-to-drag ratio in terms of kand CD,0.(4 marks)

(b) Explain the need and the working mechanisms of high-lift devices such as flaps andslats. How do these devices fulfill their aerodynamic objectives?

(5 marks)

(c) Explain stages of laminar-turbulent transition. When is it useful to extend laminarsections and when is it useful to encourage transition?

(5 marks)


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3(a) Consider a supersonic wind tunnel consisting of a pressure vessel, a variable area

throat and a test section (Figure 2). The Mach number in the test section is controlled

by changing the throat area. The volume of the pressure vessel is V=12 m3 and the

pressure inside the vessel ispt=35 bar. At a speed of MachM=2.0 in the test section,

the pressure vessel empties in 15 seconds.

Figure 2: Setup of supersonic wind tunnel.

(i) Based on your engineering experience in gas dynamics, give an estimate inwhat time the pressure vessel will empty at a speed of MachM=4.0 in the test

section and substantiate your estimate briefly in words. You do not need to

perform any calculations.

(5 marks)

(ii) Calculate the velocity, density, speed of sound, and pressure in the test sectionif the speed in the test section is MachM=2.0. The temperature in the pressure

vessel is 320K.

(5 marks)

(b) Modern airliners travel at cruise conditions at transonic speeds.

(i) Describe the main difference in the velocity and pressure distribution forsubsonic and transonic aerofoils on the upper side. Use a sketch to show the

velocity and pressure distribution.(5 marks)

(ii) Explain, why the wing moment increases when attaining transonic speeds.(5 marks)


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4(a) Consider the following two configurations in a supersonic flow of speedM=2.3. In

the first case (Figure 3a), a flat plate of chord length cis at an angle of attack of =5,

leading to an expansion angle on the upper side of =5. In the second case

(Figure 3b), the aerofoil has a flap with its hinge at x/c=0.5. The first section of the

aerofoil has no angle of attack, and the flap is lowered to =10.

(i) Sketch the shock and expansion waves of both configurations.

(4 marks)

(ii) Calculate the lift coefficient for both configurations using shock relations and

Prandtl-Meyer expansion theory.

(8 marks)

(iii) Calculate the lift coefficient for both configurations using linear theory

assuming that only small angles are involved (tan).

(4 marks)

(iv) Comment on the result, especially with regards of your result from (iii).

(4 marks)

Figure 3(a) and 3(b): Plate configurations in supersonic flow.


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5(a) Discretize the following equation using finite differences on an equidistant mesh inx

andy.

f

t=k

2f

x 2 + k

2f

y 2

(i) Using explicit time advancement.

(ii) Using implicit time advancement.

(4 marks)

(b) Give each two advantages and disadvantages of CFD vs. experimental methods and

comment briefly.

(8 marks)

(c) Assume you are tasked to improve the design a projectile. Explain options to reduce

drag.

(8 marks)

End of Paper

aerodynamics of aircraft

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