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By Jakob Yngvason, Elliott H.Lieb

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To get a feeling for the involved heat fluxes and temperatures there consider the example in Fig. 4, which, however, covers only a small and low Mach number flight span. We look first at the Moo-Tw surface dit q^j = 0. The recovery temperature is smaller everywhere than the total temperature. 0 K compared to the recovery temperature. At smaller flight Mach numbers, and hence flight altitudes, the radiation cooling loses fast its effectiveness. This is due to the high unit Reynolds numbers. Fig.

0 km altitude. 0 km altitude. Regarding the aerothermodynamic simulation means, which will be discussed shortly in Chapter 10, we note t h a t ground-test facilities are available for all flow regimes. However, in almost no case is a full simultaneous simulation of all relevant parameters possible for hypersonic flows. Computational simulation for the continuum and for the slip-flow regime can be made with the classical tools, to which now the methods of numerical aerothermodynamics for the solution of the Euler equations, the Navier^ In [11] it is shown, that with a "locally" defined Knudsen number more precise statements can be made.

3 Flow Regimes Kn = J. 13) The characteristic length L can be a body length, a nose radius, a boundary-layer thickness, or the thickness of a shock wave, depending on the problem at hand. Take for instance the thickness <5 of a laminar, incompressible flat-plate (Blasius) boundary layer [12]: as characteristic length, with Rcoo^x = poo'^oo^lf^oo, then: A A Kn = - - — y S ^ . eoo,L> L being for instance the vehicle length: For a laminar boundary layer like above then it holds: Kn ~ - ^ . 20) - free molecular flow (gas particles colHde only with the body surface, Newton limit [13]): 10 < Kn.

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A Guide To Entropy And The Second Law Of Thermodynamics (Princeton) by Jakob Yngvason, Elliott H.Lieb


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