Aero Engineering 315

Lesson 20

Supersonic Flow Part II

Supersonic Flow Objectives Define speed of sound

Calculate speed of sound in air Calculate Mach Number Describe the different “Mach” regimes Describe how lift and drag curves vary with

Mach number Define critical Mach number and drag

divergence Mach number Describe how A.C. moves with increasing

Mach Describe ways to increase critical Mach Describe ways to minimize wave drag

As an aircraft approaches Mach 1, the flow at some point on the aircraft will reach Mach 1 before the freestream velocity (V∞) does, since the flow accelerates over the aircraft’s surface. The freestream Mach number (M∞) where this occurs is called the critical Mach number. Mcrit is always less than 1.

Critical Mach number

MM=1

MM=1

= Mcrit

MM < 1

TerminatingShock

SeparatedWake

As Mach number increases beyond Mcrit, shock waves form on the wings, fuselage and other surfaces. The shock moves aft as Mach continues to increase.

Normal Shock

M > 1

Shock-induced separation- Huge increase in drag- Significant loss of lift

Transonic Region

Normal Shock Parameters

Po1 > Po2

V1 > V2

P1 < P2

T1 < T2

1 < 2

Bow Shock

When the freestream Mach number > 1, bow shocks form on bodies with blunt leading edges

M > 1

M > 1

Bow Shock

M < 1

Oblique Shock

M > 1

Oblique Shock

When the freestream Mach number > 1, oblique shocks form on bodies with sharp leading edges. M > 1 everywhere in the flowfield.

M > 1 M > 1

M > 1

Oblique Shocks

Mach Sweep Video

Effect of Mach on Lift

TransonicSubsonic

Mach Number, M

Supersonic

1.0 2.0

Lif

t Coe

ffic

ient

Cur

ve S

lope

, CL

Theoretical

TransonicSubsonic

Mach Number, M

Supersonic

1.0 2.0

Lif

t Coe

ffic

ient

Cur

ve S

lope

, CL

Theoretical

2

)0(

1

M

CC ML

L

Prandtl-Glauert( 0.3 < M < 0.7 )

Mach Effects

NACA 0012 – 3 degrees AOA

Mach

M = 0.6 = MCR

Cl

Local Mach = 1.0Mach

Shock moves to TE

Prandtl-Glauert

Shock Stall

M

C Do

Profile Drag

Wave Drag

MCRIT

Effect of Mach on Drag

M=1

MDrag Divergence

Mach Effects

NACA 0012 – 3 degrees AOA

Mach

M=0.8

Shock Separated Flow

Shock Wave

Cd MCR

MDD

Effect of Mach on A.C.

When the Mach number > 1, the aerodynamic center of all aerodynamic surfaces moves from approximately the quarter chord point (c/4) to the half chord (c/2) point.

c/4Subsonic

c/2 Supersonic

Mach Effects

NACA 0012 – 3 degrees AOA

Xac

Trailing Edge Shock

Detached Bow Shock

M=1.6

Mach

Ways to Increase MCRIT

In order to fly faster before shock waves form, we need to increase MCRIT. This requires that the flow accelerate less over the aircraft.

The drawback of these methods is that less lift is generated, so high Mach aircraft must have effective high lift devices.

Thin wings (F-16) Less camber (T-38) Swept wings (F-15) Sharp, slender leading edges and fuselage (F-104)

Supercritical airfoil (C-17)

Wing Sweep

Anderson, J. D., Introduction to Flight, 4th Edition, page 300

Wing sweep increases the critical Mach number by decreasing the velocity component the airfoil “sees”

Supercritical Wings

Anderson, J. D., Introduction to Flight, 4th Edition, page 274

Stretching MCRIT

Boeing 707 – Mach .80 727 – Mach .82 767 – Mach .80 747 – Mach .85 777 – Mach .84 Sonic Cruiser – Mach .95-.98

Airbus A320 – Mach .82 A380 – Mach .89

Boeing Sonic Cruiser

Minimizing Wave Drag Blended wing-body

Eliminates sharp corners which cause shock waves to form Area-ruled (coke bottle) fuselage

Smooth transition of aircraft cross-sectional area (T-38) Tailplane offset above or below wing

Gets tailplane out of separated, turbulent wake from shock and reduces vibration (F-104)

Sharp, slender wing leading edges and fuselage Causes oblique shocks to form, which produce less wave

drag than bow shocks (F-106, F-104 etc) Variable geometry wings (F-111, B-1)

Wings swept increases MCRIT and allows aircraft to fly faster Wings unswept increases Aspect Ratio and improves lift

characteristics for slower flight conditions such as takeoff and landing

Penalties in weight, cost, and reliability

Blended wing-body

Area Rule

Tailplane Offset & Sharp, Slender Shapes

Variable Geometry Wings

Next Lesson (21)… Prior to class

Review 3.5.1 – 3.5.8, 3.5.10, and 4.1- 4.6 Review/rework problems 16 - 25

In Class Review for GR#2