Thermodynamic fluid equations-of-state

As experimental measurements of thermodynamic properties have improved in accuracy, to five or six figures, over the decades, cubic equations that are widely used for modern thermodynamic fluid property data banks require ever-increasing numbers of terms with more fitted parameters. Functional forms with continuity for Gibbs density surface (p,T) which accommodate a critical-point singularity are fundamentally inappropriate in the vicinity of the critical temperature (T-c) and pressure (p(c)) and in the supercritical density mid-range between gas- and liquid-like states. A mesophase, confined within percolation transition loci that bound the gas- and liquid-state by third-order discontinuities in derivatives of the Gibbs energy, has been identified. There is no critical-point singularity at T-c on Gibbs density surface and no continuity of gas and liquid. When appropriate functional forms are used for each state separately, we find that the mesophase pressure functions are linear. The negative and positive deviations, for both gas and liquid states, on either side of the mesophase, are accurately represented by three or four-term virial expansions. All gaseous states require only known virial coefficients, and physical constants belonging to the fluid, i.e., Boyle temperature (T-B), critical temperature (T-c), critical pressure (p(c)) and coexisting densities of gas ((cG)) and liquid ((cL)) along the critical isotherm. A notable finding for simple fluids is that for all gaseous states below T-B, the contribution of the fourth virial term is negligible within experimental uncertainty. Use may be made of a symmetry between gas and liquid states in the state function rigidity (dp/d)(T) to specify lower-order liquid-state coefficients. Preliminary results for selected isotherms and isochores are presented for the exemplary fluids, CO2, argon, water and SF6, with focus on the supercritical mesophase and critical region.info:eu-repo/semantics/publishedVersio

Thermodynamic modeling for numerical simulations based on the generalized cubic equation of state

We further elaborate on the generalized formulation for cubic equation of state proposed by Cismondi and Mollerup [Fluid Phase Equilib. 232 (2005)]. With this formulation all well-known cubic equations of state can be described with a certain pair of values, which allows for a generic implementation of different equations of state. Based on this generalized formulation, we derive a complete thermodynamic model for computational fluid dynamics (CFD) simulations by providing the resulting correlations for all required thermodynamic properties. For the transport properties, we employ the Chung correlations. Our generic implementation includes the often used equations of state Soave-Redlich-Kwong and Peng-Robinson and the Redlich-Kwong-Peng-Robinson (RKPR) equation of state. The first two assume a universal compressibility factor and are therefore only suitable for fluids with a matching critical compressibility. The Redlich-Kwong-Peng-Robinson overcomes this limitation by considering the equation of state parameter as function of the critical compressibility. We compare the resulting thermodynamic modeling for the three equations of state for selected fluids with each other and CoolProp reference data. As supplementary material to this paper, we provide a Python tool called real gas thermodynamic python library (realtpl). This tool can be used to evaluate and compare the results for a wide range of different fluids. Additionally, we also provide the implementation of the generalized form in OpenFOAM

Bayesian quantification of thermodynamic uncertainties in dense gas flows

A Bayesian inference methodology is developed for calibrating complex equations of state used in numerical fluid flow solvers. Precisely, the input parameters of three equations of state commonly used for modeling the thermodynamic behavior of so-called dense gas flows, – i.e. flows of gases characterized by high molecular weights and complex molecules, working in thermodynamic conditions close to the liquid-vapor saturation curve–, are calibrated by means of Bayesian inference from reference aerodynamic data for a dense gas flow over a wing section. Flow thermodynamic conditions are such that the gas thermodynamic behavior strongly deviates from that of a perfect gas. In the aim of assessing the proposed methodology, synthetic calibration data –specifically, wall pressure data– are generated by running the numerical solver with a more complex and accurate thermodynamic model. The statistical model used to build the likelihood function includes a model-form inadequacy term, accounting for the gap between the model output associated to the best-fit parameters, and the rue phenomenon. Results show that, for all of the relatively simple models under investigation, calibrations lead to informative posterior probability density distributions of the input parameters and improve the predictive distribution significantly. Nevertheless, calibrated parameters strongly differ from their expected physical values. The relationship between this behavior and model-form inadequacy is discussed.ANR-11-MONU-008-00

Recent advances in the evolution of interfaces: thermodynamics, upscaling, and universality

We consider the evolution of interfaces in binary mixtures permeating strongly heterogeneous systems such as porous media. To this end, we first review available thermodynamic formulations for binary mixtures based on \emph{general reversible-irreversible couplings} and the associated mathematical attempts to formulate a \emph{non-equilibrium variational principle} in which these non-equilibrium couplings can be identified as minimizers. Based on this, we investigate two microscopic binary mixture formulations fully resolving heterogeneous/perforated domains: (a) a flux-driven immiscible fluid formulation without fluid flow; (b) a momentum-driven formulation for quasi-static and incompressible velocity fields. In both cases we state two novel, reliably upscaled equations for binary mixtures/multiphase fluids in strongly heterogeneous systems by systematically taking thermodynamic features such as free energies into account as well as the system's heterogeneity defined on the microscale such as geometry and materials (e.g. wetting properties). In the context of (a), we unravel a \emph{universality} with respect to the coarsening rate due to its independence of the system's heterogeneity, i.e. the well-known ${\cal O}(t^{1/3})$-behaviour for homogeneous systems holds also for perforated domains. Finally, the versatility of phase field equations and their \emph{thermodynamic foundation} relying on free energies, make the collected recent developments here highly promising for scientific, engineering and industrial applications for which we provide an example for lithium batteries

Model for an optically thick torus in local thermodynamic equilibrium around a black hole

We propose a simple model for an optically thick radiative torus in local thermodynamic equilibrium around a Kerr black hole. The hydrodynamics structure, which is not affected by the radiation field, is the same as for the so--called polish doughnuts. Under the assumption of isentropic fluid and polytropic equation of state, a simple stationary and axisymmetric solution to the relativistic radiation hydrodynamics equations is possible, for which the temperature of the torus scales like the specific enthalpy. The astrophysical relevance of the model is briefly discussed.Comment: With updated bibliographyc informatio

Full causal dissipative cosmologies with stiff matter

The general solution of the gravitational field equations for a full causal bulk viscous stiff cosmological fluid, with bulk viscosity coefficient proportional to the energy density to the power 1/4, is obtained in the flat Friedmann-Robertson-Walker geometry. The solution describes a non-inflationary Universe, which starts its evolution from a singular state. The time variation of the scale factor, deceleration parameter, viscous pressure, viscous pressure-thermodynamic pressure ratio, comoving entropy and Ricci and Kretschmann invariants is considered in detail.Comment: 6 pages, 6 figures, to appear in Int. J. Mod. Phys.