A supersonic aerofoil is given a sharp leading edge chiefly to
Answer: A
A sharp edge asks only a small deflection, which an attached weak oblique shock can supply, so the wave drag is small. A rounded edge would force a detached bow shock with a strong nearly normal portion ahead of it and a heavy drag penalty at supersonic speed.
Please log in or register to report this question.
Wave drag on a supersonic aerofoil arises because
Answer: B
In supersonic flow the pressures on forward-facing and rearward-facing surfaces no longer balance, and the residue is a drag that exists even with no viscosity and no finite span. It is quite distinct from induced drag, which needs a finite wing, and from friction drag, which needs viscosity.
Please log in or register to report this question.
An expansion fan crossing an oblique shock
Answer: C
The two waves interact: the expansion reduces the pressure ratio the shock has to sustain and so weakens it, while the shock refracts the characteristics of the fan. This is why the trailing-edge shocks of a supersonic aerofoil are weakened by the expansion coming off the surface ahead of them.
Please log in or register to report this question.
A convex corner in a supersonic stream can turn the flow through, at most,
Answer: D
Expansion is limited by the pressure falling to zero, at which point the gas has reached its maximum possible speed and cannot expand further. Turning beyond that leaves a vacuum region between the flow and the surface, so the flow simply separates from the corner.
Please log in or register to report this question.
In a Prandtl-Meyer expansion, the flow properties depend only on
Answer: A
The corner is treated as sharp and the fan as centred, so no length scale enters and the solution is self-similar. Everything downstream follows from the upstream Mach number and the angle turned through, which is what makes the Prandtl-Meyer function such an economical piece of bookkeeping.
Please log in or register to report this question.
For air, the Prandtl-Meyer function evaluated at \( M = 2 \) is nearest to
Answer: B
The standard value is \( \nu(2) = 26.38 \) degrees. It says that a sonic stream must be turned through just over twenty-six degrees to reach Mach 2. The other options are the function evaluated at Mach 1.5 and Mach 3, and the Mach angle at Mach 2.
Please log in or register to report this question.
A stream at \( M_1 = 1.5 \), for which \( \nu = 11.90 \) degrees, is turned through \( 14.48 \) degrees round a convex corner. The downstream Mach number is
Answer: C
Turning angles add in the Prandtl-Meyer function, so \( \nu_2 = 11.90 + 14.48 = 26.38 \) degrees. Reading that value back gives \( M_2 = 2.0 \). This additivity is the whole reason the function is tabulated: no iteration is required.
Please log in or register to report this question.
Air already at \( M = 2 \), where \( \nu = 26.38 \) degrees, negotiates a convex corner of \( 23.38 \) degrees. What Mach number does it reach?
Answer: D
Adding the turn gives \( \nu_2 = 26.38 + 23.38 = 49.76 \) degrees, which corresponds to \( M = 3.0 \). Note how much turning the second unit of Mach number costs compared with the first: the function flattens as the Mach number rises.
Please log in or register to report this question.
The maximum angle through which a sonic stream of air can theoretically be turned by expansion is nearest to
Answer: A
The limit is \( \nu(\infty) = 90^\circ (\sqrt{(\gamma+1)/(\gamma-1)} - 1) \). With \( \gamma = 1.4 \) the square root is \( \sqrt{6} = 2.449 \), so the value is \( 90 \times 1.449 = 130.45 \) degrees. At that point the pressure has fallen to zero and no further expansion is possible.
Please log in or register to report this question.
The leading Mach line of an expansion fan in a stream at \( M_1 = 2 \) lies at what angle to the oncoming flow?
Answer: B
The leading characteristic is a Mach wave in the undisturbed flow, so it lies at the upstream Mach angle \( \arcsin(1/2) = 30 \) degrees. The distractor 19.5 degrees is the Mach angle at Mach 3, which would bound the fan if the flow were expanded to that speed.
Please log in or register to report this question.
