The influence of molecular complexity on expanding flows of ideal and dense gases

This paper presents an investigation about the effect of the complexity of a fluid molecule on the fluid dynamic quantities sound speed, velocity, and Mach number in isentropic expansions. Ideal-gas and dense-gas expansions are analyzed, using the polytropic ideal gas and Van der Waals thermodynamic models to compute the properties of the fluid. In these equations, the number of active degrees of freedom of the molecule is made explicit and it is taken as a measure of molecular complexity. The obtained results are subsequently verified using highly accurate multiparameter equations of state. For isentropic expansions, the Mach number does not depend on the molecular weight of the fluid but only on its molecular complexity and pressure ratio. Remarkably enough, the Mach number can either increase or decrease with molecular complexity, depending on the considered pressure ratio. The exit speed of sound and flow velocity, however, are dependent on both molecular complexity and weight, as well as on the inlet total temperature. The exit flow velocity is found to be a monotonically increasing function of molecular complexity for all expansion ratios, whereas the speed of sound monotonically increases with molecular complexity only at high pressure ratios. The speed of sound is not monotone for pressure ratios around 3, which leads to the Mach number being nonmonotone at pressure ratios around 10. It should be noted that the sound speed and flow velocity depend much more strongly on molecular weight than on molecular complexity, which in realistic expansions often obscures the influence of the latter. Quantitative differences are observed between ideal and dense-gas expansions, which are dependent on the reduced inlet conditions. The present study concludes with the numerical simulation of two-dimensional expansions in a turbine nozzle to document the occurrence of real-gas effects and their dependence on molecular complexity in realistic applications. (C) 2009 American Institute of Physics. [DOI: 10.1063/1.3194308]