Module code: MECH$379001$

$2.$ This question requires you to demonstrate your knowledge and understanding of shock$-$expansion theory.

Consider an experimental supersonic aerofoil shown in Figure Q$2$ below. The aerofoil is subjected to a Mach $2\mathrm{.}0$ free stream airflow and the angle of attack is $10$ degrees.

a$)$ Sketch the flow structure around the aerofoil, showing all shock waves and expansion fans that form on the aerofoil. b$)$ Assuming a freestream static pressure, po $=10\mathrm{.}0$ kPa and the heat capacity ratio y$=1\mathrm{.}4,$ Use Shock$-$Expansion theory to calculate flow Mach number and static pressure for each surface on the aerofoil. Only consider the weak shock solution.

c$)$ With the aid of a diagram and without calculation, explain what would happen if the angle of attack of the supersonic aerofoil is increased from $10$ to $30$ degrees?

$[5$ marks$]$

$[15$ marks$]$

$[5$ marks$]$

Mo$=2\mathrm{.}0$

$0,5$

Surface $1$

Surface $3$

$02-170$

Surface $2$

c$=1\mathrm{.}0$m

angle of attack $10\backslash$deg

Figure Q$2$: A supersonic aerofoil subjected to a Mach $2\mathrm{.}0$ freestream $($not to scale$).$