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• W1656738984 abstract "HE governing equations for a continuous, homogeneous, compressible, viscous, heat conducting, Stokesian fluid are of considerable mathematical complexity. This fact coupled with the usual fluid dynamic boundary conditions has limited the number of known analytical solutions. Consequently a number of numerical solutions of these equations have been investigated. Reference 1 provides a recent survey of these investigations. These numerical investigations generally require the numerical specification of some upstream or far field parameter such as Mach number or Reynolds number. Alternately the numerical specification of some boundary condition parameter is required. Thus, each example of these numerical solutions is applicable for only the one value of the numerically specified parameter. Considering the large number of applicable parameters, a parametric analysis of the solutions is both formidable and expensive. The transformation presented below eliminates, to a large extent, the necessity of numerically specifying far field or boundary condition parameters. In deriving the transformation the flow is considered to be steady, two-dimensional and without body forces or bulk rate of heat addition. An ideal gas (P = pRT) is assumed along with a power law viscosity relation ijjir = C(T/T^f° where the r subscript denotes some reference state and C is the ChapmanRubesin constant.2 Finally a constant Prandtl number is assumed. For these specified conditions the compressible NavierStokes equations (continuity, momentum, and energy) in cartesian coordinates are well known.3 Extension to threedimensional flows with body forces and bulk rate of heat addition is straightforward. The analysis is begun by introducing a stream function i//y = pu;l/x = — pv which satisfies the continuity equation. The resulting forms of the momentum and energy equations are then transformed by introducing dependent variable stretchings * = p00V«V, H = H00H/, p = p^p', P = P»F, T=TaoT', k = kaokf. Using these transformations the diffusion term in the energy equation becomes (knTJUmHnpJ{VTx^x + (VTy')}. Using the definition of the stagnation enthalpy H = h+ U 2/2 where h is the static enthalpy and U2 = u2 + v2 along with the approximation that H^ = h^ + U^2/2 = U^2/2 in hypersonic flow allows writing this term as" @default.
• W1656738984 created "2016-06-24" @default.
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• W1656738984 date "1973-01-01" @default.
• W1656738984 modified "2023-09-27" @default.
• W1656738984 title "Transformation of the hypersonic compressible Navier-Stokes equations." @default.
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• W1656738984 doi "https://doi.org/10.2514/3.6685" @default.
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