Critical Mach Number 632s3f

CLASS

CRITICAL MACH NUMBER

CRITICAL MACH NUMBER

In aerodynamics, the critical Mach number (Mcr) of an aircraft is the lowest Mach number at which the airflow over some point of the aircraft reaches the speed of sound.

CRITICAL MACH NUMBER

For all aircraft in flight, the airflow speed around the aircraft is not exactly the same as the airspeed of the aircraft due to the airflow speeding up and slowing down to travel around the aircraft structure.

CRITICAL MACH NUMBER

At the Critical Mach number, local airflow in some areas near the airframe reaches the speed of sound, even though the aircraft itself has an airspeed lower than Mach 1.0. This creates a weak shock wave

CRITICAL MACH NUMBER At speeds faster than the Critical Mach number:  in an aircraft not designed for transonic or supersonic speeds, changes to the airflow over the flight control surfaces lead to the problem in control of the aircraft  the drag coefficient increases suddenly, causing dramatically increased drag

PROBLEMS AT THE CRITICAL MACH  The

phenomena associated with problems at the Critical Mach number became known as compressibility. Compressibility led to a number of accidents involving high-speed military and experimental aircraft in the 1930s and 1940s.

CRITICAL MACH NUMBER (SOUND BARRIER) Although unknown at the time, compressibility was the cause of the phenomenon known as the sound barrier. Subsonic aircraft hase relatively thick, unswept wings and are incapable of reaching Mach 1.0.  In 1947 the sound barrier was finally broken. 

CRITICAL MACH NUMBER Early transonic military aircrafts were designed to fly satisfactorily faster than their Critical Mach number.  They did not possess sufficient engine thrust to reach Mach 1.0 in level flight but could be dived to Mach 1.0.  Modern enger-carrying jet aircraft such as Airbus and Boeing aircraft have Maximum Operating Mach numbers slower than Mach 1.0. 

CRITICAL MACH NUMBER Supersonic aircraft, such as Concorde, Lockheed F-104, and MiG 21 are designed to exceed Mach 1.0 in level flight and therefore are designed with very thin wings.  Their Critical Mach numbers are higher than those of subsonic and transonic aircraft but still less than Mach 1.0. 

CRITICAL MACH NUMBER The actual Critical Mach number varies from wing to wing.  In general a thicker wing will have a lower Critical Mach number, because a thicker wing accelerates the airflow to a faster speed than a thinner one.  For instance, the fairly thick wing on the P-38 Lightning has a Critical Mach number of about .69. 

P-38 LIGHTNING

CRITICAL MACH NUMBER, MCR

Flow over airfoil may have sonic regions even though freestream M∞ < 1 INCREASED DRAG!

14

Stagnation to Static Density Ratio

/Cv=1.4 12 10

0    1 2   1  M    2 

8

1  1

6 4 2 0 0

0.5

1

1.5 Mach Number

2

2.5

3

14 WHEN IS FLOW COMPRESSIBLE? /Cv=1.4

1.2

12 Stagnation to Static Density Ratio

Stagnation to Static Density Ratio

/Cv=1.4

10 8 6 4

0    1 2   1  M    2 

1.15

1.1

1  1

1.05

1

0.95 0

0.1

0.2

0.3

0.4

0.5

Mach Number

2 0 0

0.5

1

1.5 Mach Number

2

2.5

3

COMPRESSIBILITY SENSITIVITY WITH G 30

Stagnation to Static Density Ratio

/Cv=1.4 /Cv=1.2 25

20

15

10

5

0 0

0.5

1

1.5 Mach Number

2

2.5

3

CRITICAL FLOW AND SHOCK WAVES

M CR  M Drag Divergence  1.0

MCR • Sharp increase in cd is combined effect of shock waves and flow separation • Freestream Mach number at which cd begins to increase rapidly called DragDivergence Mach number

CRITICAL FLOW AND SHOCK WAVES ‘bubble’ of supersonic flow

CRITICAL FLOW AND SHOCK WAVES

MCR

AIRFOIL THICKNESS SUMMARY



Which creates most lift? 



Which has higher critical Mach number? 



Thicker airfoil

Note: thickness is relative to chord in all cases Ex. NACA 0012 → 12 %

Thinner airfoil

Which is better? 

Application dependent!

CAN WE PREDICTA MCR?

C p, A

2  M 2

  1 2  1 M  p0  pA 2    p  p  1   1 M 2  A  p0  2  pA

• Pressure coefficient defined in of Mach number (instead of velocity) PROVE THIS FOR CONCEPT QUIZ

 pA    1  p  

 1

• In an isentropic flow total pressure, p0, is constant • May be related to freestream pressure, p∞, and static pressure at A, pA

CAN WE PREDICT MCR?

C p, A

    1   1  2   1  M  2  2     1 2  M   1    1 M 2  A    2   

C P ,CR 

2 2 M CR

    1   1  2   1   M CR  2    1  1    1      2   

• Combined result – Relates local value of to local Mach number – Can think of this as compressible flow version of Bernoulli’s equation

• Set MA = 1 (onset of supersonic flow) • Relates ,CR to MCR

HOW DO WE USE THIS? 1. 2. 3.

Plot curve of ,CR vs. M∞ Obtain incompressible value of at minimum pressure point on given airfoil Use any compressibility correction (such as P-G) and plot vs. M∞  

Intersection of these two curves represents point corresponding to sonic flow at minimum pressure location on airfoil Value of M∞ at this intersection is MCR 1

3

2

C P ,CR 

2 2 M CR

    1   1  2   1   M CR  2    1  1    1      2   



C p,0 1  M 2

IMPLICATIONS: AIRFOIL THICKNESS

Note: thickness is relative to chord in all cases Ex. NACA 0012 → 12 %

  

Thick airfoils have a lower critical Mach number than thin airfoils Desirable to have MCR as high as possible Implication for design → high speed wings usually design with thin airfoils 

Supercritical airfoil is somewhat thicker

ROOT TO TIP AIRFOIL THICKNESS TRENDS Boeing 737

Root

Mid-Span

http://www.nasg.com/afdb/list-airfoil-e.phtml

Tip

SWEPT WINGS 

All modern high-speed aircraft have swept wings: WHY?

PAKFA T – 50

F - 35

WHY WING SWEEP?

V∞

V∞

Wing sees component of flow normal to leading edge

WHY WING SWEEP?

V∞

V∞,n V∞

W

W

V∞,n < V∞ Wing sees component of flow normal to leading edge

SWEPT WINGS: SUBSONIC FLIGHT  



 

Recall MCR If M∞ > MCR large increase in drag Wing sees component of flow normal to leading edge Can increase M∞ By sweeping wings of subsonic aircraft, drag divergence is delayed to higher Mach numbers

SWEPT WINGS: SUBSONIC FLIGHT 

Alternate Explanation:   



Airfoil has same thickness but longer effective chord Effective airfoil section is thinner Making airfoil thinner increases critical Mach number

Sweeping wing usually reduces lift for subsonic flight

WING SWEEP DISADVANTAGE • At M ~ 0.6, severely reduced L/D • Benefit of this design is at M > 1, to sweep wings inside Mach cone

 

Wing sweep beneficial in that it increases drag-divergences Mach number Increasing wing sweep reduces the lift coefficient