A Fundamental Derivative in Gasdynamics

Abstract

The quantity which is here called the fundamental derivative has been defined as the nondimensional form Γ≡12ρ3c4(∂2Υ/∂P2)s. The relation of Γ to other thermodynamic variables is discussed. It is already known that the existence of conventional compression shocks requires Γ>0. It is shown that other dynamic behavior of compressible fluids is fixed by the sign of Γ. Particular emphasis is given to phenomena corresponding to negative Γ. These phenomena include the area variation of a transonic passage, the form of a Prandtl-Meyer wave, the behavior of adiabatic flow with friction, and nonlinear wave propagation. Formulas and numerical values are given for Γ in various substances.

Molecular interpretation of nonclassical gas dynamics of dense vapors under the van der Waals model

“…A nontrivial result from the thermodynamic theory of BZT vapors is that three different situations can possibly occur in the vapor phase. 20 In the classical regime and for ⌫Ͼ1, the speed of sound decreases across isentropic rarefactive processes and the well-known ideal gas dynamic behavior of compression shocks and isentropic rarefaction wave is encountered. For ⌫Ͻ0, nonclassical rarefaction shocks or isentropic compression wave are predicted.…”

“…Evolution of a compression-rarefaction profile for ⌫Ͼ0 ͑left͒, ⌫ =0 ͑center͒ and ⌫Ͻ0 ͑right͒, from Ref. 20. Dotted lines indicate characteristic lines belonging to the C + family in the x-t plane.…”

“…20,36,37 Many authors employed various equations of state with different levels of complexity and accuracy to demonstrate that, for some high molecular weight fluids, there exists a region at high reduced temperature and pressure close to saturation in which ⌫ becomes negative, see, e.g., Refs. 22, 33, and 38-40.…”

Bayesian quantification of thermodynamic uncertainties in dense gas flows

“…[27] and references cited therein). These peculiar behaviors occur when the fundamental derivative of gas dynamics [12] Γ := 1 + ρ a ∂a ∂ρ s…”

“…In thermodynamic regions close to the liquid-vapor coexistence curve, the thermodynamic behavior of fluids with high molecular complexities differs significantly from that of a perfect gas and can no longer be represented by the polytropic perfect gas law. The largest deviations are encountered in the so-called dense gas flows ( [7,8,9]) -for which a non-ideal dependence of the speed of sound on the fluid density is observed when the flow is submitted to isentropic perturbations-and most of all for a class of fluids known as the Bethe-Zel'dovich-Thompson (BZT) fluids ( [10,11,12]). Examples of gases exhibiting this special behavior are given by heavy hydro-and fluorocarbons and siloxanes, for which accurate and comprehensive thermodynamic data are scarce.…”