By Frederick R. Riddell
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Thus = h - log " *4 * - log θχ 28 HYPERSONIC FLOW RESEARCH With these relations and with 4 . > n - 8 fT γ log Κ/λσ x yîTyl - e Eq. «) "e where within the present first-order approximation n^ involved in the integral has been replaced by n e . Here the variables n 0 and/30 are given by Eqs. 6a and 3«6e, respectively, and n^ is given by Eq. 15 with nj_ evaluated from Eq. 3 . l 4 . Therefore the number density along the stagnation line of molecules with velocities appropriate to the Ω 2 space can be evaluated from Eq.
1 3 ) , and merits investigation. Cheng (Ref. 13) has made that assumption in his interesting study of the present problem based on the approximation of a thin shock layer. SECOND-ORDER COMPRESSIBLE BOUNDARY LAYER THEORY Second-order boundary layer theory is developed in a general form, free of the restrictions associated with the problem just discussed (though with that application in mind). Thus the oncoming flow need not be isoenergetic, nor the viscosity vary as a power of temperature, nor the Mach number be infinite.
This is generalized to higher approximations by introducing a second asymptotic expansion that replaces the outer expansion near the surface. 27) p(s,n;e) - ρ ^ ε , Ν ) + e p 2( s , N ) + T ( s , n ; * ) - ^ ( β , Ν ) + e t 2( s , N ) + The leading terms represent conventional boundary layer theory, and secondary terms represent its extension with which the investigator is concerned here. 29e) which are the conventional compressible boundary layer equations. 30a) = 0 2 + v 2u N 1 ) + P 2( u 1u N + v 1u l s ) + p 2 s - ( μ ι ι 2 η+ l N P ^ l ^ N u ^ - V !