Continuous Thermodynamics Research Articles

Experimental analysis and modeling of the molecular architecture influence on the solid-liquid transition of ethylene/1-octene copolymer solvent systems

The knowledge of solid-liquid equilibria of polymer-solvent systems is particularly important for further clarifying and understanding polymer crystallization. The molecular architecture in terms of molecular weight and branching related to the semicrystallinity of the polymer plays a key role in solid-liquid equilibria in polyethylene-solvent systems. Recently, a new thermodynamic model based on the Lattice Cluster Theory and continuous thermodynamics was developed, which can capture the influence of molecular weight distribution and degree of branching on solid-liquid equilibria. The model was applied to ethylene/1-hexene copolymer-solvent systems. However, the experimental database for solid-liquid equilibria of polymer solvent systems, where comprehensive molecular information of the polymer is connected with morphological quantities, e.g., semicrystallinity, and solid-liquid phase equilibria, is scarcely available in the literature. Therefore, herein a concept for this structure-property relationship is developed for ethylene/1-octene copolymer-solvent systems. The experimentally determined structure-property relationships are then used for determining the parameters of the statistical thermodynamics model and for model validation. The thermodynamic model allows the investigation of the transition zone from branching to molecular weight-induced solid-liquid equilibrium in dependence on the polydisperse nature of ethylene/1-octene copolymers.

Modeling of the Deasphalting Process by a Residue–Solvent Equilibrium Calculation Using Continuous Thermodynamics

Modeling of the Deasphalting Process by a Residue–Solvent Equilibrium Calculation Using Continuous Thermodynamics

Thermodynamic Modeling of the Solid–Liquid Phase Transition in Polyethylene Copolymer–Solvent Systems Based on Continuous Thermodynamics and Lattice Cluster Theory

Thermodynamic Modeling of the Solid–Liquid Phase Transition in Polyethylene Copolymer–Solvent Systems Based on Continuous Thermodynamics and Lattice Cluster Theory

Thermodynamics and Problems of Taking into Account Deformations of Porous Adsorbents

An adsorbate can simultaneously affect the external and internal surfaces of an adsorbent, changing the volume of a sample with a fixed amount of the adsorbent. This process is discussed from the standpoints of mechanics of continuous media, thermodynamics, and molecular models. The microscopic theory of solids distinguishes between external and internal deformations, which makes it possible to associate mechanical characteristics with adsorption ones. Based on the lattice gas model, the principles of two-level structural models are formulated for deformable porous bodies. They enable the self-consistent description of changes in their volumes and adsorption isotherms as a function of the adsorbate external pressure at a fixed temperature. For the simple presentation of the calculation scheme, it is accepted that the atomic sizes of a solid and components of the adsorbate mobile phase are comparable. The molecular level reflects the volume of molecules and their lateral interaction in the quasi-chemical approximation. The supramolecular level of the model is presented as a granule/grain of a porous material with the set distribution function of different (in size and type) pores connected with each other. A relationship between internal deformations and the nonequilibrium state of a solid is shown. A calculation procedure for local mechanical modules with regard to internal and external deformations characterizing the mechanical properties of solids is exemplified by the compression modulus. The procedure takes into account the effect of the nonequilibrium of an adsorbent on adsorbent isotherms and its volume. The approach proposed can be also applied to related systems in which the adsorption of active mobile solutions by highly dispersed compounds changes their volume.

A hybrid droplet vaporization-adaptive surrogate model using an optimized continuous thermodynamics distribution

Liquid transportation fuels are composed of hundreds of species, necessitating the use of surrogates in CFD simulations. Surrogates composed of a few species are often formulated to emulate the combustion properties targets (CPTs) of pre-vaporized fuels but fail to reproduce their vaporization behavior, implying that such surrogates cannot replicate the CPTs in the presence of preferential vaporization. The prevailing approach to this problem proposes a physical–chemical surrogate formulated to match the fuel’s distillation curve in addition to its CPTs. However, the physical–chemical surrogate approach requires more species, may not reproduce the instantaneous (distillation-resolved) CPTs, and is not well-suited to conditions in which non-surrogate species surround the droplets. A recent hybrid approach addresses these shortcomings by combining a continuous thermodynamic model (CTM) for droplet vaporization with an adaptive chemical surrogate formulated using functional group matching (FGM). Whereas the hybrid model previously required a delumping calculation to recover discrete fluxes prior to FGM, the approach is modified here to directly predict the fluxes of functional groups using the CTM, increasing its flexibility for high-pressure applications. To this end, a novel, purely mathematical distribution variable is proposed to correlate key functional groups, in addition to thermophysical and transport properties. The accuracy and flexibility of both hybrid approaches compare favorably with the physical–chemical surrogate method. While droplet vaporization rates are well-represented by both methods, functional group fluxes and instantaneous CPTs are predicted more accurately by the hybrid methods, illustrating their potential for improving the accuracy of Eulerian-phase solvers in the presence of preferential vaporization.

Investigation of features of shock wave distribution in the rock massif at gas dynamic phenomena

When studying risk factors in coal mines, it is necessary, in the first place, to consider factors and properties of the rock massif occurred with the deepening of mining operations in the coal mines, and determine one of the main types of danger: risk of geodynamic phenomena. The geodynamic phenomena occur and develop under the influence of natural and technological factors. Natural factors determine the rock massif proneness of ato geodynamic manifestations or, in other words, its potential danger due to these phenomena. Occurrence of this danger depends on technological factors. Among the dangerous factors of underground coal production to which primarily belong the geodynamic phenomena, the main ones are gas-dynamic phenomena, which are the most complex by their nature and dangerous by consequences due to high dynamic power and release of great amount of gas during a short period of time. Their consequences can be accidents due to sudden gassing and blockage of workings by coal and rock, explosions of methane and coal dust, destruction of the roadway supports, damage of machines and mechanisms, equipment and devices. As the gas-dynamic phenomena in the rocks massif are accompanied by occurrence of various processes differed by their nature, therefore, risks caused by them should be taken into account at mining operations. When considering the gas-dynamic phenomena attention should be paid to the shock wave propagation, as it is one of the gas dynamic processes. Therefore, purpose of this research was to study specific features of the shock wave propagation in the rock massif in order to prevent dangerous consequences. In this article, the authors consider the processes which occur in the rock massif prone to dangerous gas-dynamic phenomena at the shock wave propagation. The methods of rock mechanics, mechanics of continuous media, gas and thermodynamics were used in the research. Analytical researches of processes and numerical analysis of the received results were carried out. It is shown that a sharp increase of thermodynamic parameters under the action of gas-dynamic phenomena can lead to occurrence of the shock waves. It is further established that an explosive air-methane mixture can be formed in cracks, cavities and pores of the face area. At opening the cavities and pores, cases of shock waves formation in air-methane mixture leading to its detonation are possible. Under adverse conditions, this phenomenon can lead to a fire in the roadway.

Uniaxial Damaged Plastic Constitutive Relation of Recycled Aggregate Concrete

This paper presents a proposed uniaxial damaged plastic constitutive relation of recycled aggregate concrete (RAC) based on the experimental studies. A total of five groups of RAC specimens with different recycled coarse aggregate (RCA) replacement percentages of 0, 25%, 50%, 75%, and 100%, respectively, are tested under both monotonic loading and cyclic loading. The effect of the RCA replacement percentage is thoroughly investigated on a variety of mechanical properties, including the compressive strength, the peak strain, and the elastic modulus. Based on the test results, a uniaxial damage plastic constitutive relation of the RAC is proposed within the continuous thermodynamics framework. After validated by the experimental results, the proposed damaged plastic constitutive relation of the RAC is applied to perform nonlinear analysis of the RAC columns under cyclic loading, which provides close predictions of the hysteresis behavior of the RAC columns.

A hybrid multicomponent model for the vaporisation simulation of gasoline drop

A Hybrid multicomponent drop vaporisation model inspired by both the continuous thermodynamics and discrete component approaches is developed to improve the simulation of drop vaporisation process of petroleum fuels. Using the hybrid model, the petroleum fuel is assumed to be the mixture of several hydrocarbon species groups, and the composition of each group is described by an individual gamma distribution about the molecular weight. Compared to a traditional continuous thermodynamics model based on a single gamma distribution, the hybrid model is first proved to be more adequate in the description of petroleum fuel composition. For each hydrocarbon species group, the normal boiling point is assumed to be linearly correlated with the molecular weight, and improved prediction of normal boiling point is obtained compared to a traditional model. On this basis, improved prediction of gasoline distillation curve is also achieved. The hybrid model is finally used to simulate the vaporisation of a single gasoline drop, and a more complex variation of liquid-phase composition is observed during the vaporisation process. The distribution of species composition in each group moves in the direction of increasing molecular weight, and a significant change in the overall molar proportion of the species groups in the liquid drop is also observed during the vaporisation.

A multi-field coupled mechanical-electric-magnetic-chemical-thermal (MEMCT) theory for material systems

A material system may have rich physical and chemical properties; it can respond to the action of multifields. This paper reports the development of a generalized constitutive theory, based on continuous thermodynamics, to describe the multifield nature and dissipative behaviors of a material system, which couples the mechanical, electric, magnetic, chemical, and thermal (MEMCT) aspects of material characteristics. This theory also deals with chemical diffusions at different time scales subjected to an electromagnetic field and subsequent chemical reactions occurring between the diffusive species and the host material, and the dynamic evolutions of charged species subjected to thermomagnetoelectric actions and related forces.Problems pertaining to a magnetoelectroelastic (MEE) body sensitive to thermal–chemical diffusions are analytically solved based on the proposed MEMCT theory. Transversely isotropic materials, which are widely encountered in MEE designs are modeled. With the assistance of the operator theory, a set of general solutions for elastic displacements, stresses, electric/magnetic potentials, electric displacements, magnetic inductions, temperature, and chemical potentials of involved species, subjected to MEMCT coupling, is derived. The presented MEMCT theory and the general solutions provide a basis for computing and simulating interfaces of complex material systems in MEMCT multifield interactions.

Simulation of diesel spray combustion using LES and a multicomponent vapourisation model

Diesel spray and combustion in a constant-volume engine cylinder was simulated by a large eddy simulation (LES) approach coupling with a multicomponent vapourisation (MCV) modelling. The simulation focused on the inclusion of the interaction between fuel spray and gas-phase turbulence flow at the sub-grid scale. The LES was based on the dynamic structure sub-grid model, and an additional source term was added to the filtered momentum equation to account for the effect of drop motion on the gas-phase turbulence. The multicomponent drop vapourisation modelling was based on the continuous thermodynamics approach using a gamma distribution to describe the complex diesel fuel composition and was capable of predicting a more complex drop vapourisation process. The effect of gas-phase turbulence flow on the fuel drop vapourisation process was evaluated through the solution of the gas-phase moments of the distribution in the present LES framework. A non-evaporative spray in a constant-volume engine cylinder was first simulated to examine the behaviours of LES, in comparison with a Reynolds-averaged Navier–Stokes (RANS) simulation based on the RNG k–ϵ model. More realistic diesel spray structures and improved agreement on liquid penetration length with the corresponding experimental data were predicted by the LES, using a grid resolution close to that of RANS. A more comprehensive simulation of diesel spray and combustion in cylindrical combustor was also performed. Predicted distributions of soot particles were compared to the experimental image, and improved agreement with the experimental data was also observed by using the present LES and MCV models. Consequently, results of the present models proved that improved overall performance of the fuel spray simulation can be achieved by the LES without a significant increase in the computational load compared to the RANS.

Extensive chemical characterization of a heavy fuel oil

This paper presents procedures for determining the fractions, chemical compositions and combustion characteristics of Heavy Fuel Oil (HFO). This chemical characterization is requisite for better prediction of thermodynamic behaviour of multicomponent fuel such as HFO which consist of thousands of different components. Detailed chemical and physical compositions, molecular weight range and mean molecular weight of individual fractions of fuel enable to use more advanced approaches such as continuous thermodynamics for simulation and modelling. Sequential elution solvent chromatography was used to separate a HFO into Saturates, Aromatics, Resins and Asphaltenes (SARA) as gas chromatographic analysis was unsatisfactory to reveal the overall composition of a HFO, due to the insufficient volatility in most of the heavy compounds. Subsequent mass spectrometric and elemental analysis showed a wide range of molecular weight distributions for the fractions. The results also indicate that the saturates fraction contains cyclic structures with aliphatic side chains while the aromatics fraction contains tetracyclic aromatic rings with aliphatic side chains. The degree of difference between the Thermo-Gravimetric Analysis (TGA) scans of the fractions in inert and oxidizing atmospheres observed at high temperatures also increases with the degree of functionality of the fractions due to the presumably greater extent of free radical chemistry occurring in an oxidizing environment. The Infrared spectra of the fractions are consistent with what would be expected from a consideration of the solvents used to elute them in column chromatography and supported the classification of the fractions.

Modeling multicomponent fuel droplet vaporization with finite liquid diffusivity using Coupled Algebraic-DQMoM with delumping

Multicomponent fuel droplet vaporization models for use in combustion CFD codes often prioritize computational efficiency over model complexity. This leads to oversimplifying assumptions such as single component droplets or infinite liquid diffusivity. The previously developed Direct Quadrature Method of Moments (DQMoM) with delumping model demonstrated a computationally efficient and accurate approach to solve for every discrete species in a well-mixed vaporizing multicomponent droplet. To expand the method to less restrictive cases, a new solution technique is presented called the Coupled Algebraic-Direct Quadrature Method of Moments (CA-DQMoM). In contrast to previous moment methods for droplet vaporization, CA-DQMoM solves for the evolution of two liquid distributions by coupling a monovariate, homogeneous DQMoM approach with additional algebraic moment equations, allowing for a more complex droplet vaporization model with finite rates of liquid diffusion to be solved with computational efficiency. To further decrease computational expense, an approximation that employs the same nodes for both distributions can be used in certain cases. Finally, a delumping technique is adapted to the finite diffusivity model to reconstruct discrete species information at minimal computational cost. The model is proven to be accurate relative to a full discrete component model for both a kerosene droplet comprised of 36 species and a multicomponent droplet of 200 species while maintaining the computational efficiency of continuous thermodynamics models. The combined accuracy and computational efficiency demonstrated by the CA-DQMoM with delumping model for a multicomponent fuel droplet with finite liquid diffusivity makes it ideal for incorporation into CFD models for complex combustion process.

Mesoscopic continuum thermodynamics for mixtures of particles with orientation

The aim of the present paper is a continuum theoretical framework for mixtures of different chemical components, including the possibility of chemical reactions. The molecules are assumed to have an orientational degree of freedom, i.e. they are needle-shaped or planar. In the first case the microscopic director is the orientation of the particle long axis, in the second case it is the unit vector normal to the disc. This orientation is introduced as an additional variable in the domain of the field quantities. On this enlarged domain, the mesoscopic space, balance equations are derived. Compared to usual continuum theory, additional fluxes in orientation space occur. These are constitutive functions, like internal energy, heat flux and stress tensor. The restrictions on constitutive functions imposed by the second law of thermodynamics are derived by the method of Liu. Therefore, this new approach is very promising, since microscopic features of the particles, discarded in traditional continuous thermodynamics, become now an important part in the understanding of chemical systems. In addition, the results presented here can be extended to the study of other complex materials such as alloys, ferrofluids, carbon fibers, etc.

Continuous Thermodynamics of Polydisperse Polymer/Solvent Systems: Polystyrene/Cyclohexane and Polystyrene/Methyl Acetate Mixtures

Various types of liquid–liquid equilibrium of polydisperse polymer solutions, including upper critical solution temperature (UCST), both UCST and lower critical solution temperature (LCST), and closed loop miscibility, are investigated. Determination of the cloud-point curves for polydisperse polystyrene (PS)/cyclohexane and PS/methyl acetate systems is conducted by thermal optical analysis. In addition, the molecular weight distribution of polydisperse PS is determined by a gel permeation chromatography technique. To describe the phase equilibria of polydisperse polymer solutions, a continuous thermodynamic approach is incorporated into the incompressible lattice model. This appropriately describes the characteristic phase behaviors of polydisperse polymer solutions, and the calculated results show good agreement with the experimental data.

Cloud point pressure in the system polyethylene + ethylene – Impact of branching

We propose here a simple theory for polydisperse, branched polyethylene dissolved in ethylene based on a cubic equation, namely the Sako-Wu-Prausnitz-equation of state, in combination with the Lattice Cluster Theory in the incompressible version, which is predictive concerning the branching, while using continuous thermodynamics to account for polydispersity with respect to the molecular mass. The new theory considers polymers to follow the Schulz-Flory distribution and to adopt an average degree of branching. It does not require different parameters for different molar masses, polydispersities or degrees of branching and hence, the number and mass average molar mass as well as average branch content are sufficient. We parameterize this theory for ethylene based on critical data and for polyethylene based on simple arguments and some experimental data of n-alkanes. The binary parameter describing the dispersion energy and its temperature dependence stemming from Lattice Cluster Theory is fit to experimental cloud point data from literature of one specific sample of polyethylene in ethylene. The theory is then used to predict the cloud point curves and critical properties of nine other polyethylene samples in ethylene. The fit and predicted cloud point curves show quantitatively correct temperature dependence. For high polydispersities, the concentration dependence is only qualitatively correct, which is most probably due to the oversimplified Schulz-Flory distribution. The influence of branching on cloud point pressures and critical pressures at constant temperature is predicted quantitatively correct.

Droplet evaporation behaviour of a liquid fuel from chicken litter

Experiments on the evaporation of single droplets of a refined fraction of a liquid fuel produced by fast pyrolysis of chicken litter are presented. A computational model for the evaporation of the fuel is devised using the techniques of continuous thermodynamics, with distribution functions selected to represent the five main chemical groups in the fuel (n-paraffins, 1-alkenes, n-alkylbenzenes, n-alkyl fatty acids and n-diols) as determined through Py-FIMS and other analyses. The distribution parameters are determined directly from these analyses. This model is found to give accurate predictions of droplet temperature and diameter histories during evaporation. At ambient temperatures of 500°C and above bubbling and disruption of the droplet surface was observed, with the bubbles exhibiting a thin skin like that of a balloon. This was attributed to polymerization of the surface layer, causing the underlying liquid to reach higher temperatures. Under most conditions a solid residue remained after evaporation, believed also to be the product of polymerization, and, at higher temperatures, of pyrolysis as well.

Modeling of the (liquid + liquid) equilibrium of polydisperse hyperbranched polymer solutions by lattice-cluster theory

The (liquid+liquid) equilibrium of solutions of hyperbranched polymers of the Boltorn type is modeled in the framework of lattice-cluster theory. The association effects are described by the chemical association models CALM (for self association) and ECALM (for cross association). For the first time the molar mass polydispersity of the hyperbranched polymers is taken into account. For this purpose continuous thermodynamics is applied. Because the segment-molar excess Gibbs free energy depends on the number average of the segment number of the polymer the treatment is more general than in previous papers on continuous thermodynamics. The polydispersity is described by a generalized Schulz–Flory distribution. The calculation of the cloud-point curve reduces to two equations that have to be numerically solved. Conditions for the calculation of the spinodal curve and of the critical point are derived. The calculated results are compared to experimental data taken from the literature. For Boltorn solutions in non-polar solvents the polydispersity influence is small. In all other of the considered cases polydispersity influences the (liquid+liquid) equilibrium considerably. However, association and polydispersity influence phase equilibrium in a complex manner. Taking polydispersity into account the accuracy of the calculations is improved, especially, in the diluted region.

Discrete multicomponent model for biodiesel spray combustion simulation

An important first step in spray combustion simulation is an accurate determination of the fuel properties which affects the modelling of spray formation and reaction. In a practical combustion simulation, the implementation of a multicomponent model is important in capturing the relative volatility of different fuel components. A Discrete Multicomponent (DM) model is deemed to be an appropriate candidate to model a composite fuel like biodiesel which consists of four components of fatty acid methyl esters (FAME). In this paper, the DM model is compared with the traditional Continuous Thermodynamics (CTM) model for both diesel and biodiesel. The CTM model is formulated based on mixing rules that incorporate the physical and thermophysical properties of pure components into a single continuous surrogate for the composite fuel. The models are implemented within the open-source CFD code OpenFOAM, and a semi-quantitative comparison is made between the predicted spray-combustion characteristics and optical measurements of a swirl-stabilised flame of diesel and biodiesel. The DM model performs better than the CTM model in predicting a higher magnitude of heat release rate in the top flame brush region of the biodiesel flame compared to that of the diesel flame. Using both the DM and CTM models, the simulation successfully reproduces the droplet size, volume flux, and droplet density profiles of diesel and biodiesel. The DM model predicts a longer spray penetration length for biodiesel compared to that of diesel, as seen in the experimental data. Also, the DM model reproduces a segregated biodiesel fuel vapour field and spray in which the most abundant FAME component has the longest vapour penetration. In the biodiesel flame, the relative abundance of each fuel component is found to dominate over the relative volatility in terms of the vapour species distribution and vice versa in the liquid species distribution.

Simulation of the compressible flow with mass transfer of semi-continuous mixtures using the direct quadrature method of moments

We developed a method for the solution of the compressible flow with mass transfer of semi-continuous mixtures and it is based on the quadrature method of moments (QMoM) for continuous thermodynamics. The method extends the adaptive characterization of the continuous mixture to field problems and solves the mass transport equation for the continuous component. The method is referred as direct QMoM, or DQMoM, for continuous thermodynamics. It was implemented in the OpenFOAM® as a compressible ideal gas flow solver. The DQMoM was applied to the mixing flow of two gas streams with different compositions of a mixture with 57 hydrocarbons diluted in nitrogen. We showed that 4 adaptive components reproduced the mixture properties within 3% accuracy. Furthermore, the DQMoM CFD solution was approximately two times faster than the solution using 58 discrete components.

The Association Thermodynamics Modeling of Asphaltene Precipitation

In this work, the authors introduce an association asphaltene deposition modeling through application of continuous thermodynamics for crude oil mixture. It is assumed that a binary system forms consist of a nonprecipitating crude oil solvent system and a precipitating asphaltene component in which pure asphaltene component only participate in deposition phase. A simple association factor as an association term has been incorporated in set of equations for minimization of Gibbs free energy, which was obtained from molecular weight distribution (fractional molecular weight) and association ability of system. For characterization of asphaltenes, asphaltene segment distribution function and the association term are applied at equilibrium condition. The association parameters of asphaltene component are adjusted with the experimental data at different conditions. In this study, experimental data from the Iranian crude oil reservoir was used to examine the proposed asphaltene model. It has been shown that the calculated results are in good agreement with experimental data.