3241 Lecture 14 - MAE 3241 AERODYNAMICS AND FLIGHT...

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MAE 3241: AERODYNAMICS AND FLIGHT MECHANICS Overview of Shock Waves and Shock Drag Mechanical and Aerospace Engineering Department Florida Institute of Technology D. R. Kirk
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PERTINENT SECTIONS Chapter 7: Overview of Compressible Flow Physics Reads very well after Chapter 2 (§2.7: Energy Equation) §7.5, many aerospace engineering students don’t know this 100% Chapter 8: Normal Shock Waves §8.2: Control volume around a normal shock wave §8.3: Speed of sound Sound wave modeled as isentropic Definition of Mach number compares local velocity to local speed of sound, M=V/a Square of Mach number is proportional to ratio of kinetic energy to internal energy of a gas flow (measure of the directed motion of the gas compared with the random thermal motion of the molecules) §8.4: Energy equation §8.5: Discussion of when a flow may be considered incompressible §8.6: Flow relations across normal shock waves
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PERTINENT SECTIONS Chapter 9: Oblique shock and expansion waves §9.2: Oblique shock relations Tangential component of flow velocity is constant across an oblique shock Changes across an oblique shock wave are governed only by the component of velocity normal to the shock wave (exactly the same equations for a normal shock wave) §9.3: Difference between supersonic flow over a wedge (2D, infinite) and a cone (3D, finite) §9.4: Shock interactions and reflections §9.5: Detached shock waves in front of blunt bodies §9.6: Prandtl-Meyer expansion waves Occur when supersonic flow is turned away from itself Expansion process is isentropic Prandtl-Meyer expansion function (Appendix C) §9.7: Application t supersonic airfoils
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EXAMPLES OF SUPERSONIC WAVE DRAG F-104 Starfighter
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DYNAMIC PRESSURE FOR COMPRESSIBLE FLOWS Dynamic pressure is defined as q = ½ ρ V 2 For high speed flows, where Mach number is used frequently, it is convenient to express q in terms of pressure p and Mach number, M, rather than ρ and V Derive an equation for q = q(p,M) 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 1 2 1 = = = = = = = = M p q pM a V p q p a V p p V p p V q V q γ γ γ ρ γ ρ γ ρ γ γ ρ ρ
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