8 Compressibility Effects EAS 4101 S11

8 Compressibility Effects EAS 4101 S11 - EAS 4101, S11...

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EAS 4101, S11 University of Florida 4/1/11 1/52 Section 8, Compressibility Effects 8 Compressibility Effects 8.1 Introduction to Compressibility Effects in Aerodynamics To date, we have been studying incompressible aerodynamics which is generally limited to 0.3 U Ma a  , where a is the isentropic speed of sound. The assumption of incompressibility (i.e., treating the density as being a known constant, ) allowed us to solve for the aerodynamic forces and moments by essentially decoupling the energy equation from the continuity and momentum equations. Before getting into specifics, let’s discuss some of the qualitative aspects of different flow regimes (note that the numbers are just guidelines) :

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EAS 4101, S11 University of Florida 4/1/11 2/52 Section 8, Compressibility Effects Flow visualization is nice, but what are the consequences of these flow regimes? o For this class, we will not discuss hypersonic flow, but will discuss compressible subsonic, transonic and supersonic flows. : cr M aM a compressibility correction, d’Alembert holds. cr Ma occurs when sonic flow is obtained at the maximum velocity (minimum pressure) point of the airfoil drag divergence : cr Ma Ma Ma wave drag starts to appear drag divergence : Ma Ma d c can increase by a factor of 10 (thrust requirement!) 8.1.1 Fear of “Sound Barrier” Why the fear of breaking the “sound barrier”? o Prandtl-Glauert compressibility corrections (just a coordinate transform) state ,0 22 ; 11 Pl cc M a    , both go to infinity as 1 Ma . Experimental data regarding drag divergence indicates a dramatic increase in drag (due to shocks) as 1 Ma . o Thinner wings were noted to reduce the drag divergence o Remember, increased drag translates into increased loading on wings People died trying! o DeHavilland (UK) built the DH 108 and his son was the test pilot…plane disintegrated near speed of sound. o Poorly designed aircraft that couldn’t withstand additional loading.
EAS 4101, S11 University of Florida 4/1/11 3/52 Section 8, Compressibility Effects 8.1.2 Defeating sound barrier Bell XS-1 (Experimental Sonic 1) piloted by Chuck Yeager achieved 1.06 Ma on 10/14/47 Design issues to overcome sound barrier: o Prandtl-Glauert compressibility corrections are invalid as 1 Ma . o Swept wings (structural improvement as well as aerodynamic) o Improved power plant, etc. Richard Whitcomb (NASA Langley Research Center) had two great ideas to reduce “wave drag”: o Area rule : decrease cross-sectional area of fuselage to mitigate area increase of wings, “motivated by bullet aerodynamics” Conventional design:

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EAS 4101, S11 University of Florida 4/1/11 4/52 Section 8, Compressibility Effects Area rule design: Payoff in reducing wave drag, ~ factor of 2: o Supercritical airfoil: Reduce strength of rear shock via airfoil shape Try to increase cr Ma by modifying the shape of the airfoil This will also lead to an increase in drag divergence Ma Longer, more gradual, favorable pressure gradient leads to a larger region of supersonic flow over airfoil Weaker terminating shock!
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This note was uploaded on 09/05/2011 for the course EAS 4101 taught by Professor Sheplak during the Spring '08 term at University of Florida.

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8 Compressibility Effects EAS 4101 S11 - EAS 4101, S11...

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