3241 Lecture 15

# 3241 Lecture 15 - MAE 3241: AERODYNAMICS AND FLIGHT...

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MAE 3241: AERODYNAMICS AND FLIGHT MECHANICS Overview of Compressible Flows: Critical Mach Number and Wing Sweep April 25, 2011 Mechanical and Aerospace Engineering Department Florida Institute of Technology D. R. Kirk

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EXAMPLES: INFLUENCE OF COMPRESSIBILITY M < 1 M > 1 M ~ 0.85
WHEN IS FLOW COMPRESSIBLE? 0 2 4 6 8 10 12 14 0 0.5 1 1.5 2 2.5 3 Mach Number Stagnation to Static Density Ratio Cp/Cv=1.4 1 1 2 0 2 1 1 - - + = γ ρ M

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WHEN IS FLOW COMPRESSIBLE? 0 2 4 6 8 10 12 14 0 0.5 1 1.5 2 2.5 3 Mach Number Stagnation to Static Density Ratio Cp/Cv=1.4 0.95 1 1.05 1.1 1.15 1.2 0 0.1 0.2 0.3 0.4 0.5 Mach Number Cp/Cv=1.4 1 1 2 0 2 1 1 - - + = γ ρ M
EXAMPLES: COMPRESSIBLE INTERNAL FLOW 77 * = = A A A A e throat exit ε

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EXAMPLE: H 2 VARIABLE SPECIFIC HEAT, C P
COMPRESSIBILITY SENSITIVITY WITH γ 0 5 10 15 20 25 30 0 0.5 1 1.5 2 2.5 3 Mach Number Stagnation to Static Density Ratio Cp/Cv=1.4 Cp/Cv=1.2

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PRESSURE COEFFICIENT, C P Use non-dimensional description instead of plotting actual values of pressure Pressure distribution in aerodynamic literature often given as C p So why do we care? – Distribution of C p leads to value of c l Easy to get pressure data in wind tunnel – Shows effect of M on c l 2 2 1 - = - V p p q p p C p ρ
EXAMPLE: C P CALCULATION See §4.10

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For M < 0.3, ρ ~ const C p = C p,0 = 0.5 = const COMPRESSIBILITY CORRECTION: EFFECT OF M ON C P 2 0 , 2 1 - = - V p p q p p C p ρ Flight Mach Number, M Cp at a point on an airfoil of fixed shape and fixed angle of attack
2 2 0 , 1 5 . 0 1 - = - = M M C C p p For M < 0.3, ρ ~ const C p = C p,0 = 0.5 = const Effect of compressibility (M > 0.3) is to increase absolute magnitude of C p as M increases Called: Prandtl-Glauert Rule Prandtl-Glauert rule applies for 0.3 < M < 0.7 COMPRESSIBILITY CORRECTION: EFFECT OF M ON C P M

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EXAMPLE: SUPERSONIC WAVE DRAG F-104 Starfighter
CRITICAL MACH NUMBER, M CR As air expands around top surface near leading edge, velocity and M will increase Local M > M Flow over airfoil may have sonic regions even though freestream M < 1 INCREASED DRAG!

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CRITICAL FLOW AND SHOCK WAVES M CR 0 . 1 < < - Divergence Drag CR M M Sharp increase in c d is combined effect of shock waves and flow separation Freestream Mach number at which c d begins to increase rapidly called Drag- Divergence Mach number
CRITICAL FLOW AND SHOCK WAVES ‘bubble’ of supersonic flow

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CRITICAL FLOW AND SHOCK WAVES M CR