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Properties of a Normal Shock Wave

	NORMAL
	SHOCK WAVE
SUBSONIC	SUPERSONIC
	SUBSONIC

Figure 13.9 Normal shock wave formation

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C

STRONG OBLIQUE

SHOCK WAVE

A

NORMAL SHOCK WAVE B

WEAK OBLIQUE

SHOCK WAVE

MACH LINE

Figure 13.10 Normal & oblique shock waves

When a shock wave is perpendicular (normal) to the upstream flow, streamlines pass through the shock wave with no change of direction. A supersonic airstream passing through a normal shock wave will also experience the following changes:

•The airstream is slowed to subsonic; the local Mach number behind the wave is approximately equal to the reciprocal of the Mach number ahead of the wave e.g. if the Mach number ahead of the wave is 1.25, the Mach number of the flow behind the wave will be approximately 0.80. (The greater the Mach number above M 1.0 ahead of the wave, the greater the reduction in velocity).

•Static pressure increases.

•Temperature increases.

•Density increases.

•The energy of the airstream [total pressure (dynamic plus static)] is greatly reduced.

Minimum energy loss through a normal shock wave will occur when the Mach number of the airflow in front of the shock wave is small but supersonic.

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Oblique Shock Waves

An oblique shock wave is a slightly different type of shock wave.

Referring to Figure 13.10, at ‘A’ the air is travelling at supersonic speed, completely unaware of the approaching object.

The air at ‘B’ has piled up and is subsonic, trying to slip around the front of the object and merge with the airflow.

Through the shock wave supersonic air from ‘A’ slows immediately, increasing in pressure and density as it does so. As previously pointed out, a rise in temperature also occurs. The centre part of the shock wave, lying perpendicular or normal to the direction of the airstream, is the strong normal shock wave.

Notice that ‘above’ and ‘below’ the normal shock wave, the shock wave is no longer perpendicular to the upstream flow, but is at an oblique angle; the airstream strikes the oblique shock wave and is deflected.

Like the normal shock wave, the oblique shock wave in this region is strong. The airflow will be slowed down; the velocity and Mach number of the airflow behind the wave are reduced, but the flow is still supersonic. The primary difference is that the airstream passing though the oblique shock wave changes direction. (The component of airstream velocity normal to the shock wave will always be subsonic downstream, otherwise no shock wave).

The black dashed lines in Figure 13.10 outline the area of subsonic flow created behind the strong shock wave.

Particles passing through the wave at ‘C’ do not slow to subsonic speed. They decrease somewhat in speed and emerge at a slower but still supersonic velocity. At ‘C’ the shock wave is a weak oblique shock wave. Further out from this point the effects of the shock wave decrease until the air is able to pass the object without being affected. Thus the effects of the shock wave disappear, and the line cannot be properly called a shock wave at all; it is called a ‘Mach line’.

ShockWave Summary

•The change from supersonic to subsonic flow is always sudden and accompanied by rapid and large increases in pressure, temperature and density across the shock wave that is formed. A normal shock wave marks the change from supersonic to subsonic flow.

•If the shock wave is oblique, that is, at an angle to the upstream flow, the airflow is deflected as it passes through the shock and may remain supersonic downstream of the shock wave. However, the component of velocity normal to the shock wave will always be subsonic downstream of the shock.

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Effects of Shock Wave Formation

The formation and development of shock waves on the wing have effects on lift, drag, stability and control. Many of these effects are caused by shock induced separation. As the air flows through the shock wave, the sudden rise in pressure causes the boundary layer to thicken and often to separate. This increases the depth of the turbulent wake behind the wing.

Effect of ShockWaves on Lift

At low subsonic speeds the lift coefficient CL is assumed to be constant at a given angle of attack. With increasing Mach number, however, it will vary as shown in Figure 13.11.

		C L	M 0 81
			M 0 75
				M 0 98
	13			M 0 89
	High	0 4	MCRIT	1 2	1 4
	Speed
			SHOCK	MACH NUMBER
	Flight		STALL

Figure 13.11 Variation of CL with Mach number at Constant α

At high subsonic speed CL increases. This is the result of the changing pattern of streamlines. At low speeds the streamlines begin to diverge well ahead of the aerofoil, Figure 13.3 and Figure 13.12. At high subsonic speeds they do not begin to deflect until closer to the leading edge, causing greater acceleration and pressure drop around the leading edge. It will be remembered from Chapter 7 that this phenomena causes the stall speed to increase at high altitudes.

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HIGH SPEED

LOW SPEED

Figure 13.12 Streamlines at low & high subsonic speeds

At speeds above MCRIT a shock wave will have formed on the upper surface. This may cause boundary layer separation aft of the shock wave, causing loss of lift (above M 0.81, as shown

in Figure 13.8 and Figure 13.11).

SHOCK WAVE

SEPARATED AIRFLOW

Figure 13.13 Shock stall

This is known as the shock stall because it results from a separated boundary layer just as the low speed stall does. Shock stall occurs when the lift coefficient, as a function of Mach number, reaches its maximum value (for a given angle of attack). The severity of the loss of lift depends on the shape of the wing sections. Wings not designed for high speeds may have a severe loss of lift at speeds above MCRIT (Figure 13.11), but wings designed specifically for high speed flight, with sweepback, thinner sections and less camber will have much less variation of lift through the transonic region.

Separated airflow caused by a shock stall can cause severe damage to the airframe, particularly the empennage. This will be fully discussed on page 427.

The lower end of the transonic region is where most modern high speed jet transport aircraft operate and a small shock wave will exist on the top surface of the wing in the cruise.

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Effect of ShockWaves on Lift Curve Slope and CLMAX

At a constant angle of attack, the increase of CL as speed increases from about M 0.4 into the low end of the transonic region gives a steeper lift curve slope, i.e. the change of CL per degree angle of attack will increase. However, because of earlier separation resulting from the formation of the shock wave, CLMAX and the stalling angle will be reduced. Figure 13.14 and Figure 13.15 illustrate these changes.

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	HIGH
CL	SUBSONIC SPEEDS
	INCOMPRESSIBLE
	FLOW

ANGLE OF ATTACK

Figure 13.14 Effects of Mach number on lift curve

CLMAX

0 4	1 0	MFS

Figure 13.15 Effect of Mach number on CLMAX.

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Effect of ShockWaves on Drag

As speed increases above MCRIT shock waves begin to form and drag increases more rapidly than it would have done without the shock waves. The additional drag is called wave drag and is due to energy drag and boundary layer separation.

The Mach number at which the aerodynamic drag begins to increase rapidly is called THE DRAG DIVERGENCE MACH NUMBER. The Drag Divergence Mach Number is usually close to, and always greater than, the Critical Mach Number, as shown in Figure 13.16.

Energy Drag

Energy drag stems from the irreversible nature of the changes which occur as an airflow crosses a shock wave. Energy has to be used to provide the temperature rise across the shock wave and this energy loss is drag on the aircraft. The more oblique the shock waves are, the less energy they absorb, but because they become more extensive laterally and affect more air, the energy drag rises progressively as MFS increases.

Boundary Layer Separation

In certain stages of shock wave movement there is a considerable flow separation, as shown in Figure 13.8 and Figure 13.13. This turbulence represents energy lost to the flow and contributes to the drag. As M FS increases through the transonic range, the shock waves move to the trailing edge and the separation decreases; hence, the drag coefficient decreases.

M 0 98

CD

M 0 89

M 0 75

M 0 81

MCRIT			1 2
DRAGDIVERGENCE			MACH NUMBER
MACHNUMBER

Figure 13.16 Variation of CD with Mach number

The change in drag characteristics is shown by the CD curve for a basic section at a constant angle of attack in Figure 13.16. The ‘hump’ in the curve from M 0.89 to M 1.2 is caused by:

•The drag directly associated with the trailing edge shock waves (energy loss).

•Separation of the boundary layer.

•The formation of the bow shock wave above M 1.0.

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Effect of ShockWaves on the CL/ CD Drag Polar Curve

Although the curve of CL / CD is unique at low speeds, at transonic speeds when compressibility becomes significant, the curve will change. Figure 13.16 shows the variation of CL / CD with Mach number. The point at which the tangent from the origin touches the curve corresponds to the maximum CL / CD or maximum L / D. In the transonic region, the L/D ratio is reduced.

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CL

LOW MACH NUMBERS

HIGH MACH NUMBERS

L DMAX

CD

Figure 13.17 Effects of Mach number on CL / CD polar

Effect of ShockWaves on the Centre of Pressure

The centre of pressure of an aerofoil is determined by the pressure distribution around it. As the speed increases through the transonic region, the pressure distribution changes and the

centre of pressure will move. It was shown in Figure 13.8 that above MCRIT the upper surface pressure continues to drop on the wing until the shock wave is reached. This means that a

greater proportion of the ‘suction’ pressure will come from the rear of the wing, and the centre of pressure is further aft. The rearward movement of the CP, however, is irregular as the pressure distribution on the lower surface also changes. The shock wave on the lower surface usually forms at a higher free stream Mach number than the upper surface shock, but it reaches the trailing edge first. The overall effect on the CP is shown in Figure 13.18. As the aircraft accelerates to supersonic speed, the overall movement of the CP is aft to the 50% chord position.

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1 4
1 0
MCRIT
50%	100%

PERCENTAGE CHORD

Figure 13.18 CP movement in the transonic region

The wing root usually has a thicker section than the wing tip so will have a lower MCRIT and shock induced separation will occur at the root first. The CP will move towards the tip, and

if the wing is swept, this CP movement will also be rearward. This effect will be discussed in detail later.

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Figure 13.19 Low pressure area in front of shock wave

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Effect of ShockWaves on CP Movement

Rearward CP movement with increasing Mach number in the transonic region produces a nosedown pitching moment. This is known as ‘Mach Tuck’, ‘High Speed Tuck’ or ‘Tuck Under’.

A further factor contributing to the nose-down pitching moment is decreased downwash at the tail resulting from reduced lift at the wing root. If the tailplane is situated in the downwash, its effective angle of attack is increased, giving an increase in the nose-down pitching moment.

For a stable aircraft a push force is required on the stick to produce an increase in speed, but as a result of Mach tuck, the push force required may decrease with speed above MCRIT giving an unstable stick force gradient, Figure 13.20.

PUSH
	UNSTABLE STICK
STICK	FORCE GRADIENT
FORCE
0
PULL
MCRIT	MACH NUMBER

Figure 13.20 Reduction in stick force with increasing Mach number

The Effect of ShockWaves on Flying Controls

A conventional trailing edge control surface works by changing the camber of the aerofoil to increase or decrease its lift. Deflecting a control surface down will reduce MCRIT. If the control is moved down at high subsonic speed and a shock wave forms on the aerofoil ahead of the control surface, shock induced separation could occur ahead of the control, reducing its effectiveness. At low speed, movement of a control surface modifies the pressure distribution over the whole aerofoil. If there is a shock wave ahead of the control surface, movement of the control cannot affect any part of the aerofoil ahead of the shock wave, and this will also reduce control effectiveness.

Conventional trailing edge control surfaces may suffer from greatly reduced effectiveness in the transonic speed region and may not be adequate to control the changes of moment affecting the aircraft at these speeds. This can be overcome by incorporating some or all of the following into the design: an all moving (slab) tailplane (Figure 11.2), roll control spoilers, making the artificial feel unit in a powered flying control system sensitive to Mach number or by fitting vortex generators.

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