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HIGH SPEED AERODYNAMICS
Developments in aircraft and powerplants have produced high performance airplanes with capabilities for very high speed flight. The study of aerodynamics at these very high flight speeds has many significant differences from the study of classical low speed aerodynamics. Therefore, it is quite necessary that the Naval Aviator be familiar with the nature of high speed airflow and the characteristics of high performance airplane configurations.
GENERAL CONCEPTS AND SUPERSONIC
FLOW PATTERNS
NATURE OF COMPRESSIBILITY
At low flight speeds the study of aerodynamics is greatly simplified by the fact that air may experience relatively small changes in pressure with only negligible changes in density. This airflow is termed incompressible since the air may undergo changes
in pressure without apparent changes in density. Such a condition of airflow is analogous to the flow of water, hydraulic fluid, or any other incompressible fluid. However, at high flight speeds the pressure changes that take place are quite large and significant changes in air density occur. The study of airflow at high speeds must account for these changes in air density and must consider that the air is compressible and that there will be * ‘compressibility effects.’ ’
A factor of great importance in the study of high speed airflow is the speed of sound. The speed of sound is the rate at which small pressure disturbances will be propagated through the air and this propagation speed is solely a function of air temperature. The accompanying table illustrates the variation of the speed of sound in the standard atmosphere.
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TABLE 3-1. Variation of Temperature and Speed of Sound with Altitude in the Standard Atmosphere
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As an object moves through the air mass, velocity and pressure changes occur which create pressure disturbances in the airflow surrounding the object. Of course, these pressure disturbances are propagated through the air at the speed of sound. If the object is travelling at low speed the pressure disturbances are propagated ahead of the object and the airflow immediately ahead of the object is influenced by the pressure field on the object. Actually, these pressure disturbances are transmitted in all directions and extend indefinitely in all
directions. Evidence of this “pressure warning’’ is seen in the typical subsonic flow pattern of figure 3.1 where there is upwash and flow direction change well ahead of the leading edge. If the object is travelling at some speed above the speed of sound the airflow ahead of the object will not be influenced by the pressure field on the object since pressure disturbances cannot be propagated ahead of the object. Thus, as the flight speed nears the speed of sound a compression wave will form at the leading edge and all changes in velocity and pressure will take place quite sharply and suddenly. The airflow ahead of the object is not influenced until the air particles are suddenly forced out of the way by the concentrated pressure wave set up by the object. Evidence of this phenomenon is seen in the typical supersonic flow pattern of figure 3.1.
The analogy of surface waves on the water may help clarify these phenomena. Since a surface wave is simply the propagation of a pressure disturbance, a ship moving at a speed much less than the wave speed will not form a “bow wave.” As the. ship’s speed nears the wave propagation speed the bow wave will form and become stronger as speed is increased beyond the wave speed.
At this point it should become apparent that all compressibility effects depend upon the relationship of airspeed to the speed of sound. The term used to describe this relationship is the Mach number, M, and this term is the ratio of the true airspeed to the speed of sound.
M=Mach number F=true airspeed, knots a= speed of sound, knots
= Яо^в
Oo=speed of sound at standard sea level conditions, 661 knots 0 = temperature tatio
= r/re
Revised January 1965
It is important to note that compressibility effects are not limited to flight speeds at and above the speed of sound. Since any aircraft will have some aerodynamic shape and will be developing lift there will be local flow velocities on the surfaces which are greater than the flight speed. Thus, an aircraft can experience compressibility effects at flight speeds well below the speed of sound. Since there is the possibility of having both subsonic and supersonic flows existing on the aircraft it is convenient to define certain regimes of flight. These regimes are defined approximately as follows:
Subsonic—Mach numbers below 0.75
Transonic—Mach numbers from 0.75 to
1.20
Supersonic—Mach numbers from 1.20 to
5.00
Hypersonic—Mach numbers above 5.00 While the flight Mach numbers used to define these regimes of flight are quite approximate, it is important to appreciate the types of flow existing in each area. In the subsonic regime it is most likely that pure subsonic airflow exists on all parts of the aircraft. In the transonic regime it is very probable that flow on the aircraft components may be partly subsonic and partly supersonic. The supersonic and hypersonic flight regimes will provide definite supersonic flow velocities on all parts of the aircraft. Of course, in supersonic flight there will be some portions of the boundary layer which are subsonic but the predominating flow is still supersonic.
The principal differences between subsonic and supersonic flow are due to the compressibility of the supersonic flow. Thus, any change of velocity or pressure of a supersonic flow will produce a related change of density which must be considered and accounted for. Figure 3-2 provides a comparison of incompressible and compressible flow through a closed tube. Of course, the condition of continuity must exist in the flow through the closed tube; the mass flow at any station along the tube is constant. This qualification must exist in both compressible and incompressible cases.
The example of subsonic incompressible flow is simplified by the fact that the density of flow is constant throughout the tube. Thus, as the flow approaches a constriction and the streamlines converge, velocity increases and static pressure decreases. In other words, a convergence of the tube requires an increasing velocity to accommodate the continuity of flow. Also, as the subsonic incompressible flow enters a diverging section of the tube, velocity decreases and static pressure increases but density remains unchanged. The behavior of subsonic incompressible flow is that a convergence causes expansion (decreasing pressure) while a divergence causes compression (increasing pressure).
The example of supersonic compressible flow is complicated by the fact that the variations of flow density are related to the changes in velocity and static pressure. The behavior of supersonic compressible flow is that a convergence causes compression while a divergence causes expansion. Thus, as the supersonic compressible flow approaches a constriction and the streamlines converge, velocity decreases and static pressure increases. Continuity of mass flow is maintained by the increase in flow density which accompanies the decrease in velocity. As the supersonic compressible flow enters a diverging section of the tube, velocity increases, static pressure decreases, and density decreases to accommodate the condition of continuity.
The previous comparison points out three significant differences between supersonic compressible and subsonic incompressible flow.
(a) Compressible flow includes the additional variable of flow density.
(b) Convergence of flow causes expansion of incompressible flow but compression of compressible flow.
(r) Divergence of flow causes compression of incompressible flow but expansion of compressible flow.
Revised January 1965
DECREASING VELOCITY
INCREASING PRESSURE
INCREASING DENSITY
INCREASING VELOCITY
DECREASING PRESSURE
DECREASING DENSITY
Figure 3.2. Comparison of Compressible and Incompressible Flow Through a Closed Tube
When supersonic flow is clearly established, all changes in velocity, pressure, density, flow direction, etc., take place quite suddenly and in relatively confined areas. The areas of flow change are generally distinct and the phenomena are referred to as “wave” formations. All compression waves occur suddenly and are wasteful of energy. Hence, the compression waves are distinguished by the sudden “shock” type of behavior. All expansion waves are not so sudden in their occurrence and are not wasteful of energy like the compression shock waves. Various types of waves can occur in supersonic flow and the nature of the wave formed depends upon the airstream and the shape of the object causing the flow change. Essentially, there are three fundamental types of waves formed in supersonic flow: (1) the oblique shock wave (compression), (2) the normal shock wave (compression), (3) the expansion wave (no shock).
OBLIQUE SHOCK WAVE. Consider the case where a supersonic airstream is turned into the preceding airflow. Such would be the case of a supersonic flow “into a comer” as shown in figure 3.3- A supersonic airstream passing through the oblique shock wave will experience these changes:
(1) The airstream is slowed down; the velocity and Mach number behind the wave are reduced but the flow is still supersonic
(2) The flow direction is changed to flow along the surface
(3) The static pressure of the airstream behind the wave is increased
(4) The density of the airstream behind the wave is increased
(5) Some of the available energy of the airstream (indicated by the sum of dynamic and static pressure) is dissipated and turned into unavailable heat energy. Hence, the shock wave is wasteful of energy.
A typical case of oblique shock ■’wave formation is that of a wedge pointed into a supersonic airstream. The oblique shock wave will form on each surface of the wedge and the inclination of the shock wave will be a function of the free stream Mach number and the wedge angle. As the free stream Mach number increases, the shock wave angle decreases; as the wedge angle increases the shock wave angle increases, and, if the wedge angle is increased to some critical amount, the shock wave will detach from the leading edge of the wedge. It is important to note that detachment of the shock wave will produce subsonic flow immediately after the central portion of the shock wave. Figure 3-4 illustrates these typical flow patterns and the effect of Mach number and wedge angle.
The previous flow across a wedge in a supersonic airstream would allow flow in two dimensions. If a cone were placed in a supersonic airstream the airflow would occur in three dimensions and there would be some noticeable differences in flow characteristics. Three-dimensional flow for the same Mach number and flow direction change would produce a weaker shock wave with less change in pressure and density. Also, this conical wave formation allows changes in airflow that continue to occur past the wave front and the wave strength varies with distance away from the surface. Figure 3.5 depicts the typical three-dimensional flow past a cone.
Oblique shock waves can be reflected like any pressure wave and this effect is shown in figure 3-5- This reflection appears logical and necessary since the original wave changes the flow direction toward the wall and the reflected wave creates the subsequent flow change to cause the flow to remain parallel to the wall surface. This reflection phenomenon places definite restrictions on the size of a model in a wind tunnel since a wave reflected back to the model would cause a pressure distribution not typical of free flight.
NORMAL SHOCK WAVE. If a bluntnosed object is placed in a supersonic airstream the shock wave which is formed will be detached from the leading edge. This detached
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Figure 3.4. ShockWaves Formed by VariousWedge Shapes |
REFLECTED OBLIQUE WAVES
MOOEL IN WIND
TUNNEL WITH WAVES
REFLECTED FROM
WALLS
Figure 3.5. Three Dimensional and Reflected Shock Waves
Revised January 1965
wave also occurs when a wedge or cone angle exceeds some critical value. Whenever the shock wave forms perpendicular to the upstream flow, the shock wave is termed a ‘ ‘normal” shock wave and the flow immediately behind the wave is subsonic. Any relatively blunt object in a supersonic airstream will form a normal shock wave immediately ahead of the leading edge slowing the airstream to subsonic so the airstream may feel the presence of the blunt nose and flow around it. Once past the blunt nose the airstream may remain subsonic or accelerate back to supersonic depending on the shape of the nose and the Mach number of the free stream.
In addition to the formation of normal shock waves described above, this same type of wave may be formed in an entirely different manner when there is no object in the supersonic airstream. It is particular that whenever a supersonic airstream is slowed to subsonic without a change in direction a normal shock wave will form as a boundary between the supersonic and subsonic regions. This is an important fact since aircraft usually encounter some ‘‘compressibility effects” before the flight speed is sonic. Figure 3.6 illustrates the manner in which an airfoil at high subsonic speeds has local flow velocities which are supersonic. As the local supersonic flow moves aft, a normal shock wave forms slowing the flow to subsonic. The transition of flow from subsonic to supersonic is smooth and is not accompanied by shock waves if the transition is made gradually with a smooth surface. The transition of flow from supersonic to subsonic without direction change always forms a normal shock wave.
A supersonic airstream passing through a normal shock wave will experience these changes:
(1) 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
Mach number ahead of the wave is 1.25, the Mach number of the flow behind the wave is approximately 0.80.
(2) The airflow direction immediately behind the wave is unchanged.
(3) The static pressure of the airstream behind the wave is increased greatly.
(4) The density of the airstream behind the wave is increased greatly.
(5) The energy of the airstream (indicated by total pressure—dynamic plus static) is greatly reduced. The normal shock wave is very wasteful of energy.
EXPANSION WAVE. If a supersonic airstream were turned away from the preceding flow an expansion wave would form. The flow “around a corner” shown in figure 3 7 will not cause sharp, sudden changes in the airflow except at the corner itself and thus is not actually a “shock” wave. A supersonic airstream passing through an expansion wave will experience these changes:
(1) The airstream is accelerated; the velocity and Mach number behind the wave are greater.
(2) The flow direction is changed to flow along the surface—provided separation does not occur.
(3) The static pressure of the airstream behind the wave is decreased.
(4) The density of "the airstream behind the wave is decreased.
(5) Since the flow changes in a rather gradual manner there is no “shock” and no loss of energy in the airstream. The expansion wave does not dissipate airstream energy.
The expansion wave in three dimensions is a slightly different case and the principal difference is the tendency for the static pressure to continue to increase past the wave.
The following table is provided to summarize the characteristics of the three principal wave forms encountered with supersonic flow.
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TABLE 3-2. Supeitonic Wave Choracttrittict
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