Aerospace Propulsion Assignment 5 — On-Design Inlets  
Instructions
Write your solutions in single column format, with one statement following another vertically. Write your solutions neatly so that they are easy to read and verify. Don't write one line with two equal signs. Highlight your answers using a box. Solve the problems starting from the Aerospace Propulsion Tables. Do not use any other document to solve the problems.
05.22.14
Question #1
Consider that you are faced with designing a two-dimensional supersonic diffuser. The main challenge in designing a supersonic diffuser is to minimize the stagnation pressure losses while achieving a high compression ratio. This can be done by compressing the flow through a series of equal strength oblique shocks preceding a normal shock. To minimize the geometric complexity of the inlet, it is here desired to use only three shocks to decelerate the flow to subsonic conditions:
3shockdiffuser.png
The inlet is designed for a flight Mach number of $2.4$ and such that the pressure increases twofold across each oblique shock. Find the $x,~y$ coordinates of points A and B in the inlet depicted above for a diffuser height $h$ fixed to 1.0 m.
Question #2
After graduating from UArizona, your first design project consists of developing a suitable mixed-compression inlet for a supersonic combustion ramjet (scramjet) engine. In a mixed-compression inlet, some of the compression process takes place externally and some internally. Since the scramjet engine is intended to power a non-reusable hypersonic cruise missile, the geometrical complexity is desired to be kept to a minimum to keep the manufacturing costs low. For this reason, the compression process consists of only two oblique shocks, as depicted in the figure below:
scramjetinlet-scaled.png ./download/file.php?id=10874&sid=1f38b223aeed6252e02c0598dbeb8dc3 ./download/file.php?id=10874&t=1&sid=1f38b223aeed6252e02c0598dbeb8dc3
For an inlet exit temperature fixed to $1066$ K, design the inlet such that it yields optimal performance (i.e. minimal stagnation pressure loss) for a flight Mach number of 7.5 at an altitude of 15 km. Specifically, perform the following tasks:
(a)  Find the compression ratio and percent stagnation pressure loss through the inlet
(b)  Find the angles $\delta$ and $\theta$
(c)  Find the Mach number at the inlet exit
(d)  Find the $x,~y$ coordinates of points A and B as a function of the inlet height $h$
Assume frictionless and constant-$\gamma$ flow.
Question #3
Consider the following scramjet inlet composed of a Prandtl-Meyer compression fan and one oblique shock as follows:
A5Q3.png ./download/file.php?id=11813&sid=1f38b223aeed6252e02c0598dbeb8dc3 ./download/file.php?id=11813&t=1&sid=1f38b223aeed6252e02c0598dbeb8dc3
Knowing that the altitude is of 15 km, that the flight Mach number is of 7.5, that $M_2=4$, $M_3=2.73$, and $y_{\rm B}=1$ m, do the following:
(a)  Find the pressure in zones 2 and 3.
(b)  Find the stagnation pressure ratio in the inlet $P_{\circ 3}/P_{\circ 1}$.
(c)  Find the temperature in zone 3.
(d)  Find the angles $\phi$ and $\psi$.
(e)  Find the height of the flow in zone 2.
(f)  Find the $x$ and $y$ coordinates of point B.
(g)  Find the $x$ and $y$ coordinates of point A.
10.03.23
Answers
1.  1 m, 1.438 m, 0.916 m, 0.191 m.
2.  2.73, 57.7 , 78.1%, $14^\circ$, $8.3^\circ$, $2.73~h$, $h$, $3.27~h$, $0.82~h$.
3.  $27.7^\circ$, 512.5 kPa, $10.7^\circ$, 2188 kPa, 0.68, 1067 K, 7.44 m, 1 m, 0.0756 m, 0.797 m, 7.216 m.
Do Problems #1 and #3 only. Due on Tuesday October 22nd at 23:59.
10.10.24
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