Compressible Inviscid Flow 18 - Shock Boundary Layer Interaction and Drag Divergence

Question 1

What is the critical Mach number?

Answer 1

Freestream Mach number for an aerofoil when the Mach number starts to reach sonic on the aerofoil

Question 2

Define critical pressure coefficient

Answer 2

Pressure coefficient when Mach number on aerofoil is sonic

Question 3

What happens on an aerofoil beyond critical Mach number

Answer 3

Supersonic pocket forms
As M increases further, normal shock forms, terminating supersonic pocket and producing the wave drag

Question 4

Critical Mach number vs aerofoil thickness

Answer 4

Critical M is higher for a thinner aerofoil compared to a thicker aerofoil

Question 5

Shock boundary layer interaction on convex surface

Answer 5

Due to viscous effect, BL forms on aerofoil surface
Shock wave presents strong adverse pressure gradient on BL, which can induce BL separation
Shock induced BL separation leads to transonic drag divergence, a sudden substantial increase of drag

Question 6

Drag divergence and the sound barrier

Answer 6

As shock gets stronger, induces BL separation, increases drag
This presents itself as a barrier as an aircraft is approaching the sonic speed with limited propulsion

Question 7

Sound barrier and aerofoil thickness

Answer 7

Thinner aerofoil to address problem of drag divergence as sound barrier is approached
Higher critical M implies higher drag divergence M

Question 8

Supercritical aerofoil

Answer 8

Purpose is to increase drag divergence M
Relatively flat top, encouraging region of supersonic flow with lower local M, so terminating shock is weaker, creating less drag
Therefore, drag divergence M is higher
Because top is relatively flat, forward 60% of aerofoil has negative camber which lowers the lift
To compensate, lift is increased by having extreme positive camber on behind 30%

Question 9

Swept wing

Answer 9

Originally proposed by Busemann in 1935
For reducing large drag increase at supersonic speeds, reasoned that flow over wing is governed mainly by velocity component perpendicular to leading edge - if wing is swept, this component will decrease
Therefore supersonic wave drag will decrease
If sweep angle is large enough, normal velocity component will be subsonic (‘subsonic leading edge’) with dramatic reduction of wave drag

Question 10

Swept wing + supercritical aerofoil for modern aircraft

Answer 10

A380 - largest civil transport aircraft
Cruise at M = 0.85
Wing span = 79.75m
Wing aspect ratio = 7.53
Wind sweep = 33.5 degrees

Question 11

Area rule to deal with compressibility effect

Answer 11

Planview, cross-section and area distribution (CSA vs distance along axis of plane) are sketched
CSA experiences some abrupt changes along axis, with discontinuities in both A and dA/dx in wing regions
CSA should be smooth, so fuselage CSA should decrease to compensate for addition of wing and tail CSA (‘coke bottle’ fuselage shape)
Reduces peak drag
Alleviates compressibility effects around aircraft, as sudden compression is likely to lead to shock formation and therefore drag