Download 4262: Rockets and Mission Analysis

MAE 3241: Aerodynamics and Flight Mechanics
Distributed: April 28, 2010
Collected: Before Final Exam
Name: _________________
Exam #4
Directions:
1. Treat this exam as if you were taking it in class
2. Spend no more than 60 minutes on the exam and complete the exam all at once
3. Exam is open book and open notes, but do not consult anyone else in the class on the
solution or help with the specific problems
Exam is worth 110 points. Read each question carefully and show all your work.
Short Answer (5 points each): Use equations and/or no more than 3-4 short phrases to provide
answers to these questions.
1. Why is the flow across a shock wave non-isentropic, and yet the total temperature (for a
calorically perfect gas) remains constant and is described by:
T0
 1 2
 1
M
T
2
1
2. Qualitatively, how does the supersonic flow field over an airplane’s nose cone differ from
the supersonic flow over a sharp wedge?
3. The pictures below show two Russian airplanes.
MIG – 31: Inlet system mounted on side of airplane
MIG – 15: Inlet system integrated into
nose of airplane
Comment on why the designers of these aircraft took these approaches for the inlet design and
location. Specifically which airplane do you think flies faster and what is the impetus behind the
inlet design and location to help achieve these flight regimes.
1
Question 1 (5 points): An observer on the ground does not hear the sonic boom caused by an
airplane moving at 5 km altitude until it is 9 km past the observer’s location. What is the
approximate Mach number of the airplane? You may assume a small disturbance and neglect the
variation in speed of sound with altitude.
Question 2 (15 points): Consider the expansion of a sonic air flow.
Part 1: Calculate the maximum deflection angle through which this flow can be expanded via a
centered expansion fan.
Part 2: Which deflects a large angle, a monoatomic or diatomic gas?
2
Question 3 (10 points): The entropy increase across a normal shock wave is 200 J / (kg K).
What is the ratio of upstream to downstream Mach numbers?
Question 4 (20 points): Air flows at Mach 3 and 1 atmosphere toward a wedge of 16º at zero
angle of attack as shown in the picture below.
M=3
16º
A
M=3
B
Part 1: If the pointed edge is forward, what will be the pressure at a location 50% of the way
along the lower wall, at point A?
Part 2: If the blunt edge is forward (lower figure), what will be the pressure at point B?
3
Question 5 (20 Points): An explosion in air creates a spherical shock wave propagating radially
into still air at standard conditions. At the instant shown in the figure below, the pressure just
inside the shock is 200 psi.
C
200 psi
V
Part 1: Estimate the shock speed, C
Part 2: Estimate the air velocity, V, just inside the shock
4
Question 6 (25 Points): When an oblique shock strikes a solid wall, it reflects as a shock of
sufficient strength to cause the exit flow, M3, to be parallel to the wall, as in the figure shown
below.
1
2
M = 2.5
3

40º
For air at Mach 2.5 and pressure 1 atmosphere, compute the Mach number in region 3, the
pressure in region 3 and the angle .
5