Abstract
The non-monotone dependence of the speed of sound along adiabatic transformations is demonstrated to result in the admissibility of non-ideal increase of the flow Mach number across oblique shock waves, for pre-shock states in close proximity of the liquid-vapour saturation curve. This non-ideal behaviour is primarily associated with a less-than-unity value of the fundamental derivative of gasdynamics and, therefore, non-ideal shock waves are expected to be observed in flows of fluids with moderate molecular complexity. The simple yet qualitatively sound van der Waals model is used to confirm the present findings and to provide exemplary non-ideal shock waves.
Highlights
The gasdynamics of single-phase flows of molecularly complex fluids in close proximity of the liquid-vapour equilibrium, for pressures on the order of those corresponding to the critical point, can significantly differ from its dilute-gas counterpart
The fundamental derivative plays a central role in delineating the qualitative behaviour of fluid flows in many contexts, including, for instance, shock formation in unsteady flows, steady isentropic flow, steady duct flow with friction and steady oblique shock waves, which is the focus of the present work [1, 2, 3, 4, 5]
Steady oblique shock waves were investigated in the non-ideal thermodynamic framework
Summary
The gasdynamics of single-phase flows of molecularly complex fluids in close proximity of the liquid-vapour equilibrium, for pressures on the order of those corresponding to the critical point, can significantly differ from its dilute-gas counterpart. Conventional treatments of gasdynamics assume, either explicitly or implicitly, that Γ > 1 This is the case, for instance, for the ideal gas model, for which the fundamental derivative is a constant larger than unity. From the qualitative point of view, the behaviour of any fluid with constant Γ > 1 resembles that of ideal gases, see for instance reference [6]. In the non-ideal fluid-dynamic context, it is standard practice to distinguish between the cases Γ ≤ 0 and 0 < Γ ≤ 1 In the former case, one rather speaks of non-classical gasdynamics, as opposed to classical gasdynamics if Γ > 0, because unconventional phenomena such as expansion shocks, isentropic compression fans, split shocks and composite waves are allowed, see for instance
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