Aerohydrodynamics Sample Questions

7/30/2019 Aerohydrodynamics Sample Questions

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SYLLABUS FOR THE WRITTEN PRELIMINARY EXAMINATION IN THE

CONCENTRATION OF AEROHYDRODYNAMICS.

The exam will be open book and notes. Students are also allowed to use a computer, calculator, any references orwritten materials as they see fit. Students may also find software referenced at

http://www.aoe.vt.edu/academics/software.php useful in solving some prelim problems. Students' solutions must be

strictly their own. No communication of any type, implicit or explicit is allowed during the exam. The honor codewill be strictly enforced.

Students are required to answer four of seven questions. Questions will require the student to effectively apply their

knowledge from across the area of concentration to familiar and unfamiliar situations. Questions may address a

single topic, or integrate material from different areas. Questions will draw on material contained within therecommended texts listed below.

1. LIST OF RECOMMENDED TEXTS

Text: Karamcheti K, 1980,Principles of Ideal Fluid Aerodynamics, 2nd Edition, Kreiger, Malabar.

Sections: All chapters except 7 and 20.

Text: Grossman B., 2000,Fundamental Concepts Of Real Gasdynamics, Lecture notes version 3.

Sections: All.

Text: Anderson J. D., 2003,Modern Compressible Flow with Historical Perspective, 4th Edition,

McGraw-Hill, New York.

Sections: Chapters 1-10 and 11.1-11.7, 14.1-14.2, 15.1-15.4, 16.8-16.12, 17.1-17.6

Text: Bertin, J.J, 2002,Aerodynamics for Engineers, 3rd Edition Prentice-Hall, Englewood Cliffs.

Sections: Chapters 1-7

Text: Schetz J. A., 1993,Boundary Layer Analysis, 2nd Edition, Prentice Hall, Englewood Cliffs.

Sections: Chapters 1 (except 1-8), 2 (except 2-9), 3, 4 (except 4-6 and 4-7-5), 5 (except 5-7, 5-9, 5-10, 5-12

and 5-14), 6 (except 6-6-6 and 6-6-8), 7 (except material on suction and injection, and 7-10through 7-15), 8 (except 8-2-3, 8-4-3, 8-4-4 and 8-5), 10 (except 10-4 and 10-5).

Text: Hill P G and Peterson C R, 1992,Mechanics and Thermodynamics of Propulsion, 2nd edition,Addison-Wesley

Sections: Chapters, 1, 2, 3, 4, 5, 6, 7.1-7.5, 10, 11, 12.1-12.3, 14.

Text: Ames Research Staff, 1953,Equations Tables and Charts for Compressible Flow, NACA Report

1135, published by AMTEC Engineering, Bellevue WA. Also available at

http://naca.larc.nasa.gov/reports/1953/naca-report-1135/naca-report-1135.pdf

Sections: All

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2. SAMPLE QUESTIONS (Note: Author initials will be removed in final version)

Consider a (2D) rocket motor on a test stand whose geometry is sketched below. The rocket has a chamber

pressure ofpc =107, a chamber temperature ofTc =500 K , and a nozzle area ratio ofAe /At=4. After the nozzle exit,

there is a base region denoted by the line A - B which is inclined at 15o to the axis. The external housing O - B maybe considered semi-infinite and is parallel to the axis. For the purpose of this problem, you may assume that the

internal and external flow is air, with =1.4.

a) For ambient conditions ofpb =4 .9 104 N/m2 and Tb =220K determine the flow in the vicinity of A -B.

i. Find the pressure along A - B.

ii. Determine the initial plume angle i.

iii. Carefully sketch the flow in this region, indicating all waves and contact surfaces.b) Determine the value of the ambient pressurepb such that the initial plume angle i will be zero. Sketch the flow

for this condition.

c) We wish to make a crude estimate of the surface temperature along A - B, including the effect of a laminar

boundary layer. (You may neglect the effect of the boundary layer inside the nozzle up to point A).

i. For an insulated wall, estimate the wall temperature for Prandtl number 1and 0.7.ii. If we fix the wall temperature at Tw , write a relationship which can be used to estimate the Stanton

number in terms of the skin friction coefficient. How can we determine the heat transfer rate from the Stanton

number?

______________________________

Turbulence is convected towards a stagnation point (see figure).

The velocity vector field of the convecting flow is V =Axi -Ayj

where i andj are unit vectors in the directions of the cartesian

coordinatesx andy andA is a dimensional constant. The velocityfluctuations associated with the turbulence are weak enough so as

not to significantly disturb this velocity field. We wish to

determine the fate of turbulent eddies approaching the stagnation

point. Consider a small segment of an eddy initially a distance h

from the stagnation point of length , angle to the horizontal

and average vorticity . Using inviscid vortex theorems,

determine expressions for the angle and average vorticity of theeddy as a function of time. Make clear what assumptions you are making.


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Consider a thin symmetric airfoil (e.g. NACA 0012) of 1m chord. The airfoil is traveling through a stationary sea-

level atmosphere at 100m/s and an angle of attack of 5 degrees.

(a) Estimate the maximum pressure on the airfoil (in Pascals) on the airfoil.

(b) Estimate the boundary layer thickness at the trailing edge of the airfoil.

The airfoil passes by a stationary vortex shed by a previous vehicle, as shown in the cartoon strip below. Outside its

core the velocity distribution of the vortex is close to that of an ideal two-dimensional point vortex with a strength of

500m2s.(c) Quantitatively estimate the lift coefficient on the airfoil as a function of time as it passes the vortex.

(d) Explain in detail the limitations and shortcomings of your time-history estimate, and therefore which

parts of the history you expect to be most accurate, and which least accurate.(e) Suppose the minimum pressure coefficient recorded on the airfoil surface during the encounter is -8.1.

Would you expect compressibility effects to be significant in this flow? Quantitatively justify your

answer.

1m

100m/s

Vortex Core


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Consider a circular shock tube 0.1m in diameter in which both driver and driven gases are air, initially at 300K. The

driven section of the tube is 3m long. A pressure probe is mounted in the driver section. The probe has a stem, 5mm

in diameter, that projects 5cm into the tube. The probe initially records a pressure of 500kPa. Exactly five

milliseconds after the diaphragm ruptures the probe pressure starts to drop. The drop in pressure followed by a short

period during which the pressure remains constant at 295kPa.

Estimate, as best you can

(a) The distance from the diaphragm location to the probe(b) The initial mass flow rate through the fractured diaphragm.

(c) The time taken for the shock to reach the closed end of the driven section.

(d) The drag on the probe stem, during the short period while it reads a pressure of 295kPa.

______________________________

(a) Analyze the flow over a 2 ft. circular cylinder traveling at 100 mph at sea level.

i) Write down the edge velocity distribution in a coordinate system appropriate for boundary layercalculations.

ii) What is the stagnation point velocity gradient?

iii) What is the best approximate method for this problem in the region of favorable pressure gradient?iv) What is the value of the momentum thickness at the stagnation point? At a point 60 deg around the

cylinder from the stagnation point?

v). Estimate the skin friction, displacement thickness, and shape factor for the caes in part iv.

vi). What criteria will be used to determine separation? Where do you expect it to occur?(b) Suppose a circulation is imposed around the cylinder such that the stagnation point is moved 20 deg. around the

surface. Reformulate the analysis in A above to incorporate the effects of circulation. What are the new valuesof the stagnation point velocity gradient and the momentum thickness at the stagnation point? Interpret this

result.

(c) Suppose this infinitely long cylinder is swept 45 deg. Explain how this changes the problem.

5cm

DRIVEN SECTION

3m

DRIVER SECTION

DIAPHRAGM LOCATION

PROBE


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Aerohydrodynamics Sample Questions