Analysis of the state equations of a real gas at high pressures with the virial coefficients obtained from controlled chaotic oscillations

Abstract

This paper investigates several cubic and non-cubic state equations of real gases at high pressures by using the virial coefficients estimated from chaotic oscillations with a mechanical-thermal device. The mechanical part is formed by a cylinder with a piston whose motion is limited by means of a nonlinear spring, a damper and a nonlinear control force to decouple the mechanical and thermal subsystems. To maintain the gas temperature approximately constant, a linear PI controller and a nonlinear control law which manipulates the flow rate of two heating coils inside the cylinder are added. The stability of the mechanical subsystem is analyzed through the first Lyapunov value, whose harmonic variation leads to chaotic behavior with great pressures and an almost constant temperature. The chaotic simulations for nonpolar gases are treated like experimental data to obtain an arbitrary number of virial coefficients which reproduce the state equation in a prescribed pressure range. The validity of the proposed device has been corroborated by using another alternative route to chaos and calculating the fugacity coefficient. The analytical calculations are in good agreement with the numerical simulations.

Optimization of goose breast meat tenderness by rapid ultrasound treatment using response surface methodology and artificial neural network

“…The value of adjusted determination coefficient ( R 2 Adj ) was 0.961, which was close to R 2 , indicating a high degree of adjustment between the observed and predicted values. Furthermore, the low coefficient value (C.V.% = 0.50) indicated low variation in the mean value and a high degree of precision and reliability of the experimental values (Pérez‐Polo, Pérez‐Molina, Varó, & Chica, ). Therefore, this model can reliably predict the response for the purposes of optimization.…”

Novel Cylinder Movement Modeling Method Based on Aerodynamics

“…In the subsequent operation process, cylinder's running time without considering aerodynamic is lower than the actual cylinder movement time and combined simulation running time, and the time gap continue increasing with the increase of displacement. This is because the gas viscosity resistance acts against the cylinder and the heat loss during the cylinder operation lead to the increase of cylinder movement time [21][22][23][24][25][26][27].…”

Estimation of the virial coefficients by means of chaotic oscillations of pressure and density: Application to quantum gases with cubic equations of state

“…additional system to maintain the gas temperature constant, thus providing a procedure to study the virial coefficients which is simpler than others previously published in the literature [10][11].…”

“…A probe which provides the output pressure of the control valve and expels gas out of the device towards the vessel is connected to the latter through a T-shaped connection. It should be pointed out that this device constitutes a simplification of a real i PI (t) The equations of the mechanical subsystem including the control valve and the PI controller are given by [1][2][3][4][5], [10][11]: dx t dx t x t…”

“…Eqs (11) describe the dynamic behavior of the system formed by the control valve (the first four equations) and the accumulation vessel (the last two equations).…”