13 High Speed Flight

Normal Shock Waves

(Normal meaning perpendicular to the upstream flow). In addition to the formation of a shock wave described overleaf, a shock wave can be generated in an entirely different manner when there is no object in the supersonic airflow. (We have now returned to the wind tunnel analogy of a stationary aircraft and moving air). Whenever supersonic airflow is slowed to subsonic speed without a change in direction, a ‘normal’ shock wave will form as a boundary between the supersonic and subsonic region. This means that some ‘compressibility effects’ will occur before the aircraft as a whole reaches Mach 1.0.

	AIR BEING ACCELERATED	NORMAL
		SHOCK
	TO SUPERSONIC SPEED	WAVE
13	LOCAL MACH NUMBER > 1
High
Speed		LOCAL MACH NUMBER < 1
Flight		(PRESSURE WAVES ABLE
		TO TRAVEL FORWARD)

Figure 13.5 Shock wave at subsonic free stream Mach number

Critical Mach Number

An aerofoil generates lift by accelerating air over the top surface. At small angles of attack the highest local velocity on an aircraft will usually be located at the point of maximum thickness on the wing. For example, at a free stream speed of M 0.84, maximum local velocity on the wing might be as high as M 1.05 in cruising level flight. At increased angles of attack the local velocity will be greater and further forward. Also, if the thickness/chord ratio were greater, the local speed will be higher.

As the free stream speed increases, the maximum speed on the aerofoil will reach the local speed of sound first. The free stream Mach number at which the local velocity first reaches Mach 1.0 (sonic) is called the Critical Mach number (MCRIT ).

Critical Mach number is the highest speed at which no parts of the aircraft are supersonic

Increased thickness/chord ratio and increased angle of attack cause greater accelerations over the top surface of the wing, so the critical

Mach number will decrease with increasing thickness/chord ratio or angle of attack.

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High Speed Flight

Accelerating beyond MCRIT

At speeds just above the critical Mach number there will be a small region of supersonic airflow on the upper surface, terminated by a shock wave, Figure 13.6.

		NORMAL
	AREA OF SUPERSONIC FLOW	SHOCK
		WAVE
	SUBSONIC FLOW	SUBSONIC FLOW

Figure 13.6 Mixed supersonic & subsonic airflow at transonic speeds

As the aircraft speed is further increased, the region of supersonic flow on the upper surface extends, and the shock wave marking the end of the supersonic region moves rearwards. A similar sequence of events will occur on the lower surface although the shock wave will usually form at a higher aircraft speed because the lower surface usually has less curvature so the air is not accelerated so much.

When the aircraft speed reaches Mach 1.0, the airflow is supersonic over the whole of both upper and lower surfaces, and both the upper and lower shock waves will have reached the trailing edge. At a speed just above Mach 1.0 the other shock wave previously described and illustrated in Figure 13.4, the bow wave, forms ahead of the leading edge.

The bow shock wave is initially separated (detached) from the leading edge by the build-up of compressed air at the leading edge, but as speed increases, it moves closer to the leading edge. For a sharp leading edge the shock eventually becomes attached to the leading edge. The Mach number at which this occurs depends upon the leading edge angle. For a sharp leading edge with a small leading edge angle the bow wave will attach at a lower Mach number than one with a larger leading edge angle.

Figure 13.8 on page 417, shows the development of shock waves on an aerofoil section at a small constant angle of attack as the airspeed is increased from subsonic to supersonic.

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High Speed Flight 13

A shock wave forms at the rear of an area of supersonic flow

At MCRIT there is no shock wave because there is no supersonic flow

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13 High Speed Flight

Pressure Distribution at Transonic Mach Numbers

Flight Speed High 13

Refer to Figure 13.8. The solid blue line represents upper surface pressure and the dashed blue line the lower surface. Decreased pressure is indicated upwards. The difference between the full line and the dashed line shows the effectiveness of lift production; if the dashed line is above the full line, the lift is negative in that area. Lift is represented by the area between the lines, and the Centre of Pressure (CP) by the centre of the area.

During acceleration to supersonic flight, the pressure distribution is irregular.

M 0.75 This is the subsonic picture. Separation has started near the trailing edge and there is practically no net lift over the rear third of the aerofoil section; the CP is well forward. Figure 13.7 shows that CL is quite good and is rising steadily; CD, on the other hand, is beginning to rise.

M 0.81 A shock wave has appeared on the top surface; notice the sudden increase of pressure (shown by the falling line) caused by decreasing flow speed at the shock wave. The CP has moved back a little, but the area is still large. Figure 13.7 shows that lift is good, but drag is now rising rapidly.

M 0.89 The pressure distribution shows very clearly why there is a sudden drop in lift coefficient before the aerofoil as a whole reaches the speed of sound; on the rear portion of the aerofoil the lift is negative because the suction on the top surface has been spoilt by the shock wave, while there is still quite good suction and high-speed flow on the lower surface. On the front portion there is nearly as much suction on the lower surface as on the upper. The CP has now moved well forward again. Figure 13.7 shows that drag is still increasing rapidly.

M 0.98 This shows the important results of the shock waves moving to the trailing edge and no longer spoiling the suction or causing separation. The speed of the flow over the surfaces is nearly all supersonic, the CP has moved aft again and, owing to the good suction over nearly all the top surface, with rather less on the bottom, the lift coefficient has actually increased. The drag coefficient is just about at its maximum, as shown Figure 13.7.

M 1.4 The aerofoil is through the transonic region. The bow wave has appeared. The lift coefficient has fallen again because the pressure on both surfaces is nearly the same; and for the first time since the critical Mach number, the drag coefficient has fallen considerably.

CL	M 0 81				CD			M 0 98
	M 0 75	M 0 98
							M 0 89		M 1 4
						M 0 81
		M 0 89	M 1 4			M 0 75
	0 5	1 0		1 5
					0		5	1 0	1 5
	Mach number
							Mach number

Figure 13.7 Changes in lift & drag in the transonic region

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High Speed Flight 13

	M 0 75	M 0 81
	CP	CP
			13
	M 0 89		M 0 98
	CP	CP	SpeedFlight
			High
		M 1 4
		CP
		Figure 13.8 Pressure distribution in the transonic region

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