Nonlinear wave propagation in dense vapor of Bethe–Zel'dovich–Thompson fluids subjected to temperature gradients

N B Chandrasekaran,B Mercier,P Colonna

doi:10.1063/5.0063226

N B Chandrasekaran, B Mercier + Show 1 more

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https://doi.org/10.1063/5.0063226

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Abstract

Flows of fluids made of complex organic molecules exhibit unconventional fluid dynamic behavior in the vapor phase if their thermodynamic state is close to that of the vapor–liquid critical point. If the molecule is sufficiently complex, this thermodynamic domain is characterized by negative values of the fundamental derivative of gasdynamics Γ, the fluid is called Bethe–Zel'dovich–Thompson (BZT) fluid, and atypical phenomena, such as rarefaction shockwaves, are theoretically admissible. The nature of the steepening of nonlinear waves in dense vapor flows of organic fluids evolving in this thermodynamic region can be significantly affected by the presence of temperature gradients in the flow. This study investigates the evolution of finite-amplitude acoustic waves in these conditions. The steepening of the wavefront is analyzed using the wavefront expansion technique, and the deformation of the wavefront is simulated numerically by solving the Westervelt equation. The results of simulations of wave propagation in dense vapors indicate that, though Γ governs the nature of steepening waves, local gradients in sound speed and density can alter the rate of steepening and can enhance or delay shock formation in the medium, a result relevant also to the envisaged experiments aimed at proving the existence of nonclassical gasdynamics phenomena in BZT vapors.

Highlights

The thermodynamic states of a fluid with temperatures and pressures close to the values at the vapor–liquid critical point form a region characterized by changing values of the fundamental derivative of gasdynamics C, defined as C 1 þ q @c ; (1)c @q s where q is the density, c is the sound speed, and s is the entropy
The results of simulations of wave propagation in dense vapors indicate that, though C governs the nature of steepening waves, local gradients in sound speed and density can alter the rate of steepening and can enhance or delay shock formation in the medium, a result relevant to the envisaged experiments aimed at proving the existence of nonclassical gasdynamics phenomena in BZT vapors
The wavefront expansion method was used to investigate the propagation of waves in the dense vapor of dodecamethylcyclohexasiloxane, D6, a complex organic molecule considered in recent theoretical, numerical, and experimental studies on nonclassical gasdynamics

Summary

Introduction

The thermodynamic states of a fluid with temperatures and pressures close to the values at the vapor–liquid critical point form a region characterized by changing values of the fundamental derivative of gasdynamics C, defined as C 1 þ q @c ; (1)c @q s where q is the density, c is the sound speed, and s is the entropy. The thermodynamic states of a fluid with temperatures and pressures close to the values at the vapor–liquid critical point form a region characterized by changing values of the fundamental derivative of gasdynamics C, defined as C 1 þ q @c ; (1). It has been shown that, for organic fluids made by large and complex molecules, C may have a value lower than 1 and may even become negative at thermodynamic conditions close to those of the critical point of the fluid. This set of thermodynamic states characterized by negative values of the fundamental derivative is referred to in gasdynamics as the nonclassical thermodynamic region. Fluids featuring thermodynamic states for which C < 0 are known collectively as Bethe–Zel’dovich–Thompson (BZT) fluids. Unconventional gasdynamic phenomena, such as rarefaction shockwaves, which cannot be observed in classical flows because they violate fundamental principles, are instead theoretically admissible in flows of BZT fluids and for the stated thermodynamic conditions.

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