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Aviation History
1945
1945 - 0498.PDF
286 FLIGHT MARCH 15TH, 1945 Shock Wmq wake after fl breakaway Shock wave with flow breakaway •Shock wave 'hock waves? Shock wave becoming oblique and moving back Fig. Breakaway partially suppressed Second shock wave formed 3; Illustrations of shock-wavepatterns for an aerofoil as Mach number approaches unity. pressure differences will theoretically exceed atmospheric pressure, and vacuums may appear in the flow. In the case of a comparatively incompressible fluid, such as water, this phenomenon is usually called cavitation. However, with a fluid such as air, which can expand to fill any space, we find a different situation. Instead of cavitation we find the air becoming more and more attenu- ated in the regions of low pressure. Unfortunately for' the mathematician the attenuation of the air lessens the density, so that the inertia forces are decreased, in turn decreasing the required pressures, thereby unbalancing the * force system, causing the flow to undergo further read- justment, etc. This ends in a headache. Energy Loss from Sound Waves in addition to the expansion of air ia regions of low pressure, a second phenomenon occurs at the speed of sound, It can be shown, theoretically, that a steady reciprocating motion of a piston in a pipe can be main- tained without unergy IOKS SO long as the motion is below u certain frequency. Above this frequency, increasing amounts of energy are sent down the pipe in the form of sound waves. Similarly, at low speeds, the steady motion of a body requires no energy input, while at and above the speed of sound energy is continuously radiated out- ward in the form of a wave. This wave is very similar to the bow wave of a boat. However, such waves would be unimportant at present- day speeds were it not for the fact that a complicated interaction occurs between the first phenomenon of fluid expansion and the second phenomenon of wave motion. This interaction causes the shock waves which occur approximately midway of the length of the aerofoil chord (Fig. 3). An example of very similar occurrence is given by the well-known hydraulic jump in the spillways of dams. Theoretically, little can be said about shock waves, but from a practical aspect they cause much greater head- arhes than either of the first two phenomena. The task of estimating compressibility effects from a 0.9 06 COMPRESSI Bl LITY mathematical viewpoint presents many in- terrelated difficulties such as: — (1) Absence of exact mathematical solu- tions of practical interest. (2) Questionable convergence of approxi- mate methods. (3) Uncertainty as to the criterion for occurrence of shock waves. (4) Considerable inaccuracy of experi- mental verification. When mathematical studies are made, a steady adiabatic flow-field of an ideal gas about a two-dimensional body is assumed. When shocks are present, the assumption of 06 0.5 Q4 05 0.2 0.1 0 \ \ Me \ i. Co —V.P U 2 - ,*•• ~Criticctf Mach number rw,2 — CPO*M 2 ... M,2 r! + Vl-M,2) 7=1 k-= 1.405 U * I 14 1.8 2.2 2.6 Fig. 4 3 3.4 35 42 4.6 Aerofoil critical velocity v. coefficient S 5.4 5.8 b2 Ua 1 maximum pressure irrotationality no longer exists. Through the demands of structural and aerodynamic design, the interest of aircraft manufacturers has become more and more sharply focused on the attempts to find a satisfactory and practical solution to the problems out- lined previously. We shall start with the diagram of pressure distribution over a wing as obtained from low-speed wind tunnelsyp* The pressures are proportional to the velocity squared. On this basis then, the higher the pressure, the higher will be the local velocity, and as a result, trie sQoner we will run into trouble. (Fig 4.) This suggests immediately 0.029 0.027 0.025 0023 0.021 Qints fr spsec//t omuts / 1/ I // 0.42 04b 050 0.54 058 v/vc 062 0.6b 070 074 Fig. 5. Apparent variation 01 total drag coefficient with Machnumber. that we should be very caieful of curvature. The smaller the curvature, the better will be the flow conditions over the body. Small radii of curvature should be avoided when designing radial engine cowls, aerofoil section,, canopy, and fuselage lines. It is important that the f lage lines be as nearly straight as possible in the vicinity of the wing juncture, since we have superposition of fuselage and wing airflows. ' Efforts to determine, theoretically, the irffluence of the Mach number on the pressure distribution and total lift of a wing have already been made. The answer, although not applicable up to the speed of sound, is relatively simple. The expression determined by Glauert-Prandtl is as fol- lows: Increase all ordinates of the aerofoil by 1/v'i-M2. The air forces are then equivalent to those of an incom- pressible flow acting on the modified profile. In particular, since angle of attack and camber also in- crease with the factor 1/v'i-M2, the lift will increase proportionately to i/Vi-M!. The drag will increase in degree indicated by the increased angle of attack and especially the increased thickness of the profile. Such con- ditions apply only in the case of relatively low Mach num- bers, for example, up to M=o.6. Thick profiles, however, should be avoided. According to the factor 1/ ^i-M1, we have for M = o.6 (i.e., V = 455 nj.p'.h. at sea level) a profile with 15 per cent, thickness which corresponds to 18.8 per cent, thickness in an incompressible flow. Such a thickness
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