Transonic Flow

When an airplane is in motion at subsonic speeds, the air is treated as though it was incompressible. As airplane speed increases, however, the air loses its assumed incompressibility and the error in estimating, for example, drag, becomes greater and greater.

The question arises as to how fast an airplane must be moving before one must take into account compressibility.

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. More precisely, it depends upon the square root of the absolute temperature. At sea level under standard conditions (T_o = 288.15 K (degrees Kelvin)), the speed of sound is 340.3 meters per second (761.2 miles per hour), but at an altitude of 15 kilometers (9.3 miles or 49,212 feet) where the temperature is down to 216.7 K, the speed of sound is only 295.1 meters per second (660.2 miles per hour). 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. But as the plane 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 plane's approach and the plane's actual arrival time At the speed of sound, the pressure pulses move at the same speed as the plane. They merge ahead of the airplane into a "shock wave" that is an almost instantaneous line of change in pressure, temperature, and density. The air has no warning of the 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.

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's approach. The Mach number is named after Ernst Mach, an Austrian professor (1838 - 1916). 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 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 the regime.

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 that transforms 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.

The total drag at transonic and supersonic speeds can be divided into two categories: (1) zero-lift 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. 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 decrease, 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).

It is a large loss in propulsive energy due to the formation of shocks that 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 free-stream Mach number called the critical Mach number at which a supersonic 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 approaches 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 (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 that may be presented as wave drag. These shocks appear anywhere on the airplane (wing, fuselage, engine nacelles, 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 that is known as shock-induced (boundary-layer) separation.

The free-stream Mach number at which the drag 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. The 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. It later achieved its goal through a redesign.

At a free-stream Mach number greater than 1, a bow shock appears around the airfoil nose. Most of the airfoil is in supersonic flow. The flow begins to realign itself parallel to the body surface and stabilize, and the shock-induced separation is reduced.

This condition results in lower drag coefficients. Supersonic flow is better behaved than transonic flow and there are adequate theories that can predict the aerodynamic forces and moments present. Often, in transonic flow, the flow is unsteady, and the shock waves on the body surface may jump back and forth along the surface, thus disrupting and separating the flow over the wing surface. This sends pulsing, unsteady flow back to the tail surfaces of the airplane. The result is that the pilot feels a buffeting and vibration of both wing and tail controls. This condition occurred especially in the first airplane types to probe the sound barrier. With proper design, however, airplane configurations gradually evolved to the point where flying through the transonic region posed little or no difficulty in terms of wing buffeting or loss of lift.

The question arises as to whether one may delay the drag-divergence Mach number to a value closer to 1 so as to impart 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 equivalently, increasing the drag-divergence Mach number closer to 1). These include

(1) Use of thin airfoils;

(2) Use of a forward or backward swept wing;

(3) Low-aspect-ratio wing;

(4) Removal of boundary layer and vortex generators; and

(5) Supercritical and area-rule technology.

—Adapted from Talay, Theodore A. Introduction to the Aerodynamics of Flight. SP-367, Scientific and Technical Information Office, National Aeronautics and Space Administration, Washington, D.C. 1975. Available at http://history.nasa.gov/SP-367/cover367.htm

For Further Reading:

Anderson, Jr., John D. A History of Aerodynamics. Cambridge, England: Cambridge University Press, 1997.

Wegener, Peter P. What Makes Airplanes Fly? New York: Springer-Verlag, 1991.

“Air Force Supersonic Research Airplane XS-1 Report No. 1. January 1948. NASA Historical Reference Collection, NASA History Office, NASA Headquarters, Washington, D.C. http://www.hq.nasa.gov/office/pao/History/x1/afsrax.html