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Reentry Air Data System for a Sub-orbital Spacecraft Based on X-34 ...

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2007 USU Industry Day<br />

Real Gas Effects<br />

• An “averaged” value <str<strong>on</strong>g>for</str<strong>on</strong>g> γ across the shockwave is<br />

calculated using Eckert’s empirical reference temperature<br />

Tref = T∞ + 1<br />

2 Tawall − T ( ∞)+<br />

0.22( T0 2 − T ) ∞<br />

where Tawal l = T ⎡ 3<br />

∞ 1 + Pr ⎣<br />

⎢<br />

γ − 1<br />

2 M 2<br />

∞<br />

⎤<br />

⎡<br />

⎦<br />

⎥ and T02 = T∞ 1 +<br />

⎣<br />

⎢<br />

P r is the Prandtl number <str<strong>on</strong>g>for</str<strong>on</strong>g> air μC p /κ<br />

γ − 1<br />

2 M 2<br />

∞<br />

• These equati<strong>on</strong>s are solved iteratively, with the gas<br />

properties coming from real gas tables<br />

⎤<br />

⎦<br />

⎥<br />

16

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