surface_inclination_01

surface_inclination_01 - heat shield and the toroidal...

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1 (From Anderson)
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2 Windward side Leeward side r n c p = 2 r V " # r n ( ) 2 V " 2 c p = 0 Shadow region r V " # r n > 0 ( ) Geometry for 3-D Application of the Newtonian Theory r n : Unit normal vector
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3 Panel the surface with finite-sized elements Find the unit normal vector (pointing outwards) and the area for each element Calculate the pressure coefficient on each panel using: Calculate the local pressure using Sum up forces on the object to find the total force Normalize with appropriate reference area to obtain aerodynamic coefficients Numerical Implementation of Newtonian Models c p i = c p max r V " # r n i ( ) 2 V " 2 p i = 1 2 " # V # 2 c p i + p # r F = " p i A i r n i i # ( Cp max =2 for Newtonian Theory)
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4 Newtonian Results for a flat plate
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5 (From Anderson)
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6 (From Bertin)
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7 (From Bertin)
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8 (From Anderson)
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9 (From Bertin)
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10 x y (From Bertin) Apollo Command Module Geometry s / R b = 0.965 ( " b = 67 o ) : Tangency point of the spherical
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Unformatted text preview: heat shield and the toroidal surface s / R b = 1.082 ( b = o ) : Maximum body radius 11 (From Bertin) s / R b = 0.965 ( " b = 67 o ) : Tangency point of the spherical heat shield and the toroidal surface s / R b = 1.082 ( b = o ) : Maximum body radius Modified Newtonian Theory Applied to Apollo Command Module at AoA=0 deg. 12 Newtonian Theory provides useful results when the Mach number is large and/or the flow deflection angle is large (indicates strong shock assumption): Modified Newtonian theory works better for blunt bodies Newtonian Theory works better for wedges and cones (more accurate for cones than wedges) M " Sin # >> 1 (Figure 6.8 from Bertin) Applicability Region of Newtonian Theory 13 (From Anderson)...
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surface_inclination_01 - heat shield and the toroidal...

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