Lesson 6: Flow Effects and Flight
Section 3 - Transonic Flow
In our previous section, we covered motion at subsonic speeds. The air was treated as though it were incompressible and a study of the aerodynamics involved using this simplifying assumption was made. As the airplane speed increases, however, the air loses its assumed incompressibility and the error in estimating, for example, drag, becomes greater and greater.
COMPRESSIBILITY
The issue arises as to how to test an airplane that must be moving before one takes into account compressibility. One important quantity which is an indicator is the speed of sound of the air through which the airplane is flying. A disturbance in the air will send pressure pulses or waves out into the air at the speed of sound.
Consider the instance of a cannon fired at sea level. An observer situated some distance from the cannon will see the flash almost instantaneously but the sound wave is heard (or the pressure wave is felt) some time later.
The observer can easily compute the speed of sound by dividing the distance between him and the cannon by the time it takes the sound to reach him. The disturbance propagates out away from the cannon in an expanding hemispherical shell.
The speed of sound varies with altitude. In other words, it depends upon the square root of the absolute temperature. At sea level under standard conditions (To = 288.15 K) the speed of sound is 340.3 m/sec but at an altitude of 15 kilometers where the temperature is down to 216.7 K the speed of sound is only 295.1 m/sec.
This difference indicates that an airplane flying at this altitude encounters the speed of sound at a slower speed, and, therefore, comes up against compressibility effects sooner. An airplane flying well below the speed of sound creates a disturbance in the air and sends out pressure pulses in all directions. Air ahead of the airplane receives these "messages" before the airplane arrives and the flow separates around the airplane.
THE SPEED OF SOUND
But as the airplane approaches the speed of sound, the pressure pulses merge closer and closer together in front of the airplane and little time elapses between the time the air gets a warning of the airplane approach and the airplane's actual arrival time.
At the speed of sound, the pressure pulses move at the same speed as the airplane. They merge together ahead of the airplane into a "shock wave" which is an almost instantaneous line of change in pressure, temperature, and density.
The air has no warning of the impending approach of the airplane and abruptly passes through the shock system. There is a tendency for the air to break away from the airplane and not flow smoothly about it; as a result, there is a change in the aerodynamic forces from those experienced at low incompressible flow speeds.
MACH NUMBER
The Mach number is a measure of the ratio of the airplane speed to the speed of sound. In other words, it is a number that may relate the degree of warning that air may have to an airplane approach. The Mach number is named after Ernst Mach, an Austrian professor (1838 - 1916).
There are several Mach levels. For Mach numbers less than one, one has subsonic flow, for Mach numbers greater than one, supersonic flow, and for Mach numbers greater than 5 the name used is hypersonic flow.
Additionally, transonic flow pertains to the range of speeds in which flow patterns change from subsonic to supersonic or vice versa, about Mach 0.8 to 1.2. Transonic flow presents a special problem area as neither equations describing subsonic flow nor those describing supersonic flow may be accurately applied to this regime.
FLOW AT HIGH SPEEDS
Now, let us examine in a little more detail the flow at high speeds. Up to now, the airplane was considered to be in motion at subsonic speeds. Drag was composed of three main components -- skin-friction drag, pressure drag, and induced drag, or drag due to lift. At transonic and supersonic speeds there is a substantial increase in the total drag of the airplane due to fundamental changes in the pressure distribution.
This drag increase encountered at these high speeds is called wave drag. The drag of the airplane wing, or for that matter, any part of the airplane, rises sharply, and large increases in thrust are necessary to obtain further increases in speed.
This wave drag is due to the unstable formation of shock waves which transform a considerable part of the available propulsive energy into heat, and to the induced separation of the flow from the airplane surfaces.
Throughout the transonic range, the drag coefficient of the airplane is greater than in the supersonic range because of the erratic shock formation and general flow instabilities. Once a supersonic flow has been established, however, the flow stabilizes and the drag coefficient is reduced.
There is a variation of an airplane wing drag coefficient with Mach number. The total drag at transonic and supersonic speeds can be divided into two categories: (1) zerolift drag composed of skin-friction drag and wave (or pressure-related) drag of zero lift and (2) lift-dependent drag composed of induced drag (drag due to lift) and wave (or pressure-related) drag due to lift.
THE SOUND BARRIER
The infamous "sound barrier" occurs since to fly supersonically the airplane must provide enough thrust to exceed the maximum transonic drag that is encountered. In the early days of transonic flight, the sound barrier represented a real barrier to higher speeds.
Once past the transonic regime, the drag coefficient and the drag decreases, and less thrust is required to fly supersonically. However, as it proceeds toward higher supersonic speeds, the drag increases even though the drag coefficient may show a decrease.
A large loss in propulsive energy due to the formation of shocks causes wave drag. Up to a free-stream Mach number of about 0.7 to 0.8, compressibility effects have only minor effects on the flow pattern and drag. The flow is subsonic everywhere.
As the flow must speed up as it proceeds about the airfoil, the local Mach number at the airfoil surface will be higher than the free-stream Mach number. There eventually occurs a freestream Mach number called the critical Mach number at which a sonic point appears somewhere on the airfoil surface, usually near the point of maximum thickness and indicates that the flow at that point has reached Mach 1.
As the free-stream Mach number is increased beyond the critical Mach number and closer to Mach 1, larger and larger regions of supersonic flow appear on the airfoil surface. In order for this supersonic flow to return to subsonic flow, it must pass through a shock or what is considered to be pressure discontinuity.
This loss of velocity is accompanied by an increase in temperature, that is, a production of heat. This heat represents an expenditure of propulsive energy which may be presented as wave drag. These shocks appear anywhere on the airplane including wings, fuselage, engine, etc. where, due to curvature and thickness, the localized Mach number exceeds 1.0 and the airflow must decelerate below the speed of sound.
For transonic flow the wave drag increase is greater than would be estimated from a loss of energy through the shock. In fact, the shock wave interacts with the boundary layer so that a separation of the boundary layer occurs immediately behind the shock. This condition accounts for a large increase in drag which is known as shock-induced (boundary-layer) separation.
The free-stream Mach number at which the drag coefficient of the airplane increases markedly is called the drag-divergence Mach number. Large increases in thrust are required to produce any further increases in airplane speed. If an airplane has an engine of insufficient thrust, its speed will be limited by the drag-divergence Mach number.
A prototype Convair F- 102A was originally designed as a supersonic interceptor but early flight tests indicated that because of high drag, it would never achieve this goal. However, success was achieved later for this airplane through proper redesigning.
DRAG-DIVERGENCE
Now, let is discuss how the delay of the drag-divergence Mach number to a value closer to 1 can be achieved, as it is essential to aerodynamic designs. What this implies is the ability to fly at near-sonic velocities with the same available engine thrust before encountering large wave drag. There are a number of ways of delaying the transonic wave drag rise or increasing the drag-divergence Mach number closer to 1.
These include:
- Use of thin airfoils
- Use of sweep of the wing forward or back
- Low-aspect-ratio wing
- Removal of boundary layer and vortex generators
- Supercritical and area-rule technology
Thin airfoils: The wave drag rise associated with transonic flow is roughly proportional to the square of the thickness-chord ratio (t/c). If a thinner airfoil section is used, the flow speeds around the airfoil will be less than those for the thicker airfoil.
You may fly at a higher free-stream Mach number before a sonic point appears and before one reaches the drag-divergence Mach number. The disadvantages of using thin wings are that they are less effective concerning lift produced in the subsonic speed range and they can accommodate less structure (wing fuel tanks, structural support members, armament stations, etc.) than a thicker wing.
In the example of the F-104, it was designed to achieve the minimum possible wave drag but was penalized with low subsonic lift. As a result, the landing speed of this airplane was particularly high and landing mishaps were common among untrained pilots.
SWEEP
Sweep: It was Adolf Busemann in 1935 who proposed that sweep may delay and reduce the effects of compressibility. A swept wing will delay the formation of the shock waves encountered in transonic flow to a higher Mach number. Additionally, it reduces the wave drag over all Mach numbers.
You can consider the effect of sweep of a wing as effectively using a thinner airfoil section (t/c reduced). In the case of a modern jet airplane employing forward sweep, forward sweep can have disadvantages, in the stability and handling characteristics at low speeds.
A major disadvantage of swept wings is that there is a spanwise flow along the wing, and the boundary layer will thicken toward the tips for sweepback and toward the roots for sweepforward.
In the case of sweepback, there is an early separation and stall of the wing-tip sections and the ailerons lose their roll control effectiveness. The spanwise flow may be reduced by the use of stall fences, which are thin plates parallel to the axis of symmetry of the airplane. In this manner a strong boundary layer buildup over the ailerons is prevented.
LOW ASPECT RATIO
Low aspect ratio: The wing's aspect ratio is another parameter that influences the critical Mach number and the transonic drag rise. Substantial increases in the critical Mach number occur when using an aspect ratio less than about four. However from previous discussions, low-aspect-ratio wings are at a disadvantage at subsonic speeds because of the higher induced drag.
THE BOUNDARY LAYER
Removal or reenergizing the boundary layer: By bleeding off some of the boundary layer along an airfoil's surface, the drag-divergence Mach number can be increased. This increase results from the reduction or elimination of shock interactions between the subsonic boundary layer and the supersonic flow outside of it.
Vortex generators are small plates, mounted along the surface of a wing and protruding perpendicular to the surface. They are small wings, and by creating a strong tip vortex, the generators feed high-energy air from outside the boundary layer into the slow moving air inside the boundary layer.
This condition reduces the adverse pressure gradients and prevents the boundary layer from stalling. A small increase in the drag-divergence Mach number can be achieved. This method is economically beneficial to airplanes designed for cruise at the highest possible drag-divergence Mach number.
SUPERCRITICAL AND AREA-RULE TECHNOLOGY
Supercritical and area-rule technology: One of the more recent developments in transonic technology and destined to be an important influence on future wing design is the NASA supercritical wing developed by Dr. Richard T. Whitcomb of the NASA Langley Research Center. A substantial rise in the drag-divergence Mach number is realized.
The curvature of a wing gives the wing its lift. Because of the flattened upper surface of the supercritical airfoil, lift is reduced. However, to counteract this the new supercritical wing has increased camber at the trailing edge. There are two main advantages of the supercritical airfoil. First, by using the same thickness-chord ratio, the supercritical airfoil permits high subsonic cruise near Mach 1 before the transonic drag rise. And also, at lower drag divergence Mach numbers, the supercritical airfoil permits a thicker wing section to be used without a drag penalty. This airfoil reduces structural weight and permits higher lift at lower speeds.
