Theoretical Investigations of Real Gas Effects in Cryogenic Wind Tunnels

Abstract

Real gas effects in cryogenic nitrogen flows have been calculated using the Beattie-Bridgeman equation of state. The investigations include Prandtl-Meyer expansions; oblique shocks, transonic small perturbation theory, transonic flow past a NACA 0012 aerofoil, and shock-wave/boundary-layer interaction. The last two cases mentioned have been treated with the aid of finite volume techniques. The results show som noticeable deviations from the behavior of an ideal gas, not only at cryogenic conditions but also at normal temperatures and high pressures. Within the operating range of cryogenic wind tunnels the deviations remain very small; only the friction coefficient exhibits a considerable amount of systematic variation.

Numerical simulation of dense gas flows on unstructured grids with an implicit high resolution upwind Euler solver

“…which are satisÿed for any node i or k (notice that E @ ik = 0 and^@ i = 0 if i or k are internal nodes). These properties guarantee that the metric vectors behave similar to the integrated normal vectors ] ik previously deÿned in the context of ÿnite volume methods and that, apart from the second-order boundary terms corresponding to the last summations appearing in Equation (11) or (12), the FE discretization (11) can be interpreted as a node-centred FV discretization in which the cell shapes are deÿned so that,…”

“…Fluids exhibiting non-classical behaviour are called BZT after the initials of the scientists who ÿrst formulated the theory.CFD simulations of dense gases in the classical regime are reported in the literature. Several works describe the study of ows through nozzles [10] or around simple airfoil geometries [11][12][13]. Two-dimensional simulations of the ow through turbine cascades are treated in References [14,15].…”

“…Two-dimensional simulations of the ow through turbine cascades are treated in References [14,15]. The complexity of the numerical methods varies from an explicit ÿnite volume method (FVM) applied to the two-dimensional Euler and Navier-Stokes equations [11], to an upwind scheme for the solution of the Euler equations in the axisymmetric form [10], to an implicit, ÿnite-volume upwind scheme for the solution of the two-dimensional Euler and Navier-Stokes equations [12,15]. Fluid thermodynamic models also varies in complexity from the Van der Waals [10] and Redlich-Kwong-type equations of state (EOS) [14] to the Beatty-Bridgemann [11], 13] and BWR [10] EOSs.Other documented simulations are focused speciÿcally on BZT e ects in uid ows.…”

On the suppression of shock-induced separation in Bethe–Zel'dovich–Thompson fluids

“…The authors are not aware of any computations of the present kind which involve shock-boundary layer interactions in dense gases. The interactions presented by Wagner & Schmidt (1978) correspond to a free-stream pressure of one bar. The Navier-Stokes computations of Anderson (1991a) involve transonic flow and nearly normal shocks on airfoils; as result, no direct comparisons are appropriate.…”

“…dense-gas, effects must be considered include the design of subcritical and supercritical power cycles (Reynolds &Perkins 1977 andHawkins 1986) and chemical and fuel transport (Leung &Epstein 1988 andBober &Chow 1990). Further examples include the design of hypersonic and transonic wind tunnels as described by Enkenhus & Parazzoli (1970), Wagner & Schmidt (1978), Simeonides (1987Simeonides ( , 1990, Anderson (1991a, b), and Anders (1993). Dziedzic et al (1993) described the use of supercritical hydrogen to cool hypersonic aircraft.…”