Mixture Of Ideal Gases Research Articles

Understanding the thermodynamic effects of chemically reactive working fluids in the Stirling heat pump

Within the realm of sustainable heating technologies, this study examines the performance of a Stirling heat pump employing chemically reactive working fluids in contrast to conventional inert counterparts. Reactive working fluids are energy vectors that enable the conversion of not only thermal but also chemical energy within the heat pump. The investigation spans a wide range of theoretical reactive gaseous mixtures, leveraging the ideal gas mixture thermodynamic model. Each fluid is characterized by an equilibrated chemical reaction, denoted as A2(g)⇄2A(g), and distinguished by a set of reaction coordinates: the standard entropy change of reaction and standard enthalpy change of reaction. The chemical reaction evolution and thermodynamic properties are observed in each transformation, and the overall coefficient of performance (COP) of the system is evaluated and benchmarked against that of comparable inert working fluids. It is observed that the exothermic reaction during isothermal compression significantly increases the thermal energy supplied to the heat sink, as well as the thermal energy density per unit maximum volume, by up to 269 %, compared to an inert gas system. However, for the majority of reactive fluids studied, chemical reactions introduce irreversibility in the internal regenerator due to heat transfer across a finite temperature difference, contrary to the case of inert working fluids, penalizing the COP. Consequently, a reduction of up to 28 % in the COP is observed. Nevertheless, there exists a range of reactive fluids, characterized by reversible heat exchange in the internal regenerator, offering increased thermal energy transfer to the heat sink without compromising the COP.

Direction of Spontaneous Processes in Non-Equilibrium Systems with Movable/Permeable Internal Walls.

We consider three different systems in a heat flow: an ideal gas, a van der Waals gas, and a binary mixture of ideal gases. We divide each system internally into two subsystems by a movable wall. We show that the direction of the motion of the wall, after release, under constant boundary conditions, is determined by the same inequality as in equilibrium thermodynamics dU-đQ≤0. The only difference between the equilibrium and non-equilibrium laws is the dependence of the net heat change, đQ, on the state parameters of the system. We show that the same inequality is valid when introducing the gravitational field in the case of both the ideal gas and the van der Waals gas in the heat flow. It remains true when we consider a thick wall permeable to gas particles and derive Archimedes' principle in the heat flow. Finally, we consider the Couette (shear) flow of the ideal gas. In this system, the direction of the motion of the internal wall follows from the inequality dE-đQ-đWs≤0, where dE is the infinitesimal change in total energy (internal plus kinetic) and đWs is the infinitesimal work exchanged with the environment due to the shear force imposed on the flowing gas. Ultimately, we synthesize all these cases within a general framework of the second law of non-equilibrium thermodynamics.

Experimental and numerical investigations of cake baking in mold

This article deals with the in-mold cake baking process. The methodology relies on numerical and experimental investigations to validate a multiphysics developed model. This numerical model is next exploited to enhance the comprehension of the physical processes that occur during a typical cake baking phase. Based on the governing equations for heat and mass transport and under few assumptions (deformable porous medium, local thermodynamic equilibrium, ideal gas mixture …), the problem consists in solving a system of five coupled partial derivative equations. Temperature, moisture content, total gas pressure, porosity and displacement are used as state variables in this study. The swelling of the dough caused by the increase in total gas pressure is predicted by a viscoelastic model. This thermo-hydro-mechanical model is implemented in a finite element code. Moreover, an experimental laboratory set-up was developed to continually acquire temperatures, water losses and gas pressure inside the product. The browning kinetic is also studied. Furthermore, the cake deformation is tracked by camera. The numerical model is validated based on the conducted experiments. Different operating conditions are tested to verify the robustness of the model. Finally, a sensitivity analysis is performed to understand the impact of estimated parameters on the outputs of the developed model.

A spectroscopic study of ternary gas diffusion

The unsteady diffusion of the ternary gas mixture CH4(α) – CO2(β) – C3H8(γ) is measured with FTIR Spectroscopy in the transmission mode at 308.15 K, 0.1 MPa and equilibrium compositions xα,∞=0.333 and xβ,∞=0.363. A parallel is drawn between the experimental approach and the classical Two-Bulb method. The geometry of the setup is calibrated by measuring the equimolar counter-diffusion of C3H8/CO2 at 308.15 K and 0.1 MPa. Then, analogous experiments are conducted for the gas pairs CH4/CO2, CH4/C2H6, CH4/C3H8 and C2H6/C3H8 to measure their mutual diffusivity. Last, the ternary diffusion of CH4(α) – CO2(β) – C3H8(γ) is measured and modelled with the Maxwell – Stefan theory of multicomponent equimolar diffusion for ideal gas mixtures. Osmotic, reverse and barrier diffusion are observed and predicted for methane before reaching equilibrium.

Numerical modelling of heat and mass transfer during cake baking

This article deals with the development of a numerical multiphysics model to study heat and mass transfer phenomena as well as the swelling during the baking of a cake contained in mold. The aim of this study is to provide an effective numerical tool, experimentally validated, for a better understanding of mechanisms leading to the desired end product. Based on the governing equations for heat and mass transport and under few assumptions (homogenous medium, local thermodynamic equilibrium, ideal gas mixture…), the problem consists in solving a system of five coupled partial derivative equations. Temperature, moisture content, total gas pressure, porosity and displacement are used as state variables in this study. The swelling of dough caused by the increase of total gas pressure is predicted by a viscoelastic model. This thermo-hydro-mechanical model is implemented in finite elements code. Moreover, an experimental laboratory set-up was developed in order to continually acquire temperatures, water losses, deformation and to correctly apprehend the boundaries conditions. The numerical results are then compared with experimental data. They are overall in good agreement. Various operating conditions are tested to check the robustness of predictions.

Numerical Simulations of Thermoacoustic Binary Gas Mixture Batch Separation

In this paper, 2D simulations were carried out to prove the potential of thermoacoustic technology in separating a binary gas mixture. A 2D model of a gas mixture separator was developed, including a loudspeaker responsible for producing acoustic waves in the separation pipe. As a result of the imposed sound waves propagating inside the separator, main parameters including pressure, temperature, and density undergo oscillations, which in turn drive the light and heavy gas components in opposite directions. Through time, one end of the separator is enriched with the light component while the other end is enriched with the heavy one. Simulations were all performed using ANSYS Fluent. The aim was to separate an ideal gas mixture of Helium–Argon and study the impact of different parameters on the separation process.

Understanding the thermodynamic effects of chemically reactive working fluids in the Stirling engine

The Stirling engine, renowned for its high theoretical efficiency, is capable of partaking an active role in the current energy transition. Given its closed-cycle operation, the choice of the working fluid is pivotal in designing the Stirling engine. Dinitrogen tetroxide N2O4 has been extensively investigated in the past, based on the ideal gas thermodynamic model, as a chemically reactive working fluid for Stirling cycles. This molecule reversibly and rapidly dissociates into nitrogen dioxide NO2–and recombines into N2O4–under the influence of thermodynamic transformations throughout the cycle, in accordance with chemical equilibrium. Addressing discrepancies in previous studies, this work aims at assessing a wide range of theoretical chemically reactive gases as working fluids in a Stirling cycle, employing the ideal gas mixture model. The behavior of each reactive fluid is examined throughout the cycle, and the thermodynamic performance is evaluated. Therefore, this work quantifies and analyzes the thermodynamic performance of a chemically reactive Stirling engine. Results indicate a slight increase in the net specific work output with certain reactive fluids, offering a thermal efficiency comparable to that of inert working fluids. In addition, it is emphasized that for chemically reactive working fluids, the isochoric heat exchange within the internal regenerator is incomplete due to chemical reactions, in contrast to the case of inert fluids. To address this, either a supplementary heat source, heat sink, or both are required during the isochoric processes. Furthermore, chemically reactive fluids in the Stirling engine induce irreversibility in the internal regenerator, stemming from heat exchange across a finite temperature difference, penalizing the thermal efficiency of the engine for the majority of reactive fluids studied.

Minimum work associated with separating nitrogen from air: An exergy analysis

Background Nitrogen is essential for a variety of industries, including heat treatment, laser cutting, fire protection, and food packaging. Many companies in these industries obtain nitrogen via on-premises air separation processes. The three main processes for separating nitrogen from ambient air are cryogenic distillation, membrane separation, and pressure-swing adsorption (PSA). Improvements to these processes will likely focus on increasing efficiency, resulting in reduced environmental impact owing to less electrical power demand and opportunities for economic incentives. Regardless of the process utilized, a minimum theoretical amount of work input is required to obtain nitrogen gas at different pressures and concentrations compared to ambient conditions. Methods An equation was derived to evaluate the total exergy (including thermo-mechanical and chemical exergy) of product and exhaust mixtures resulting from air separation, indicating the minimum theoretical work input as a function of the product pressure, purity, and process recovery rate. This analysis considered an air separation system as a black box, with the input, output, and exhaust assumed to be ideal gas mixtures of nitrogen and oxygen at 15°C. The analysis applies to cryogenic distillation if the product and exhaust mixtures return to the gas phase. Results In general, the minimum required work input increases with product purity and recovery rate. Plots of minimum theoretical work versus product purity and recovery rate were made for two product pressures (atmospheric and 800 kPa) to show the behavior of the derived equation. Conclusions The analysis allows for direct efficiency (based on the second law of thermodynamics) comparisons between existing processes and future technological innovations in the field of air separation. Actual air separation systems have low efficiencies compared to ideal systems; actual PSA systems were estimated to have second law efficiencies of 5.5–11.2%. Therefore, there is great potential for improvements to current air separation systems.

Parameters of State in the Global Thermodynamics of Binary Ideal Gas Mixtures in a Stationary Heat Flow.

In this paper, we formulate the first law of global thermodynamics for stationary states of the binary ideal gas mixture subjected to heat flow. We map the non-uniform system onto the uniform one and show that the internal energy U(S*,V,N1,N2,f1*,f2*) is the function of the following parameters of state: a non-equilibrium entropy S*, volume V, number of particles of the first component, N1, number of particles of the second component N2 and the renormalized degrees of freedom. The parameters f1*,f2*, N1,N2 satisfy the relation (N1/(N1+N2))f1*/f1+(N2/(N1+N2))f2*/f2=1 (f1 and f2 are the degrees of freedom for each component respectively). Thus, only 5 parameters of state describe the non-equilibrium state of the binary mixture in the heat flow. We calculate the non-equilibrium entropy S* and new thermodynamic parameters of state f1*,f2* explicitly. The latter are responsible for heat generation due to the concentration gradients. The theory reduces to equilibrium thermodynamics, when the heat flux goes to zero. As in equilibrium thermodynamics, the steady-state fundamental equation also leads to the thermodynamic Maxwell relations for measurable steady-state properties.

Towards systematic approach to boundary conditions in mixture and multiphasic incompressible models: Maximum Entropy principle estimate

The single continuum model formulation, no matter how complex the considered constitutive relations are, cannot describe important phenomena stemming from constituents’ interactions. In contrast, mixture theory is a successful framework for providing thermodynamically consistent governing equations in the bulk allowing for the inclusion of details in the material structure and interactions. Despite its ubiquitous applications, a fundamental open problem, a framework for the assessment of boundary conditions, persisted.Our objective is to relate these boundary conditions of mixtures to those of a single continuum and, hence, derive their possible form. To obtain such an estimation, we suggest using the Maximum Entropy (MaxEnt) principle yielding the least biased estimate (when measured by the entropy) of the values of the state variables on the more detailed level based on the knowledge of the state on the less detailed level. In the case of mixtures, the total mixture quantities represent the less detailed description, whereas the quantities related to each phase of the mixture represent the more detailed level, and the mapping (projection) connecting the two levels usually follows from the conservation of total mixture quantities. Therefore, once we have entropy on the detailed level and the aforementioned projection, from the MaxEnt principle, we get the least biased estimate of the decomposition of the total mixture state variables into variables corresponding to each constituent.These estimates can be used to obtain the interfacial conditions between two mixtures: we consider the decomposition of the total mixture quantities to partial quantities on both sides of the interface independently and match the mixture quantities at the interface using classical boundary conditions for a single phase. In this way, we may connect the well-developed theory for single continuum boundary conditions to the boundary conditions in mixtures. The generality of such an approach is discussed together with an explicit example of a binary system of ideal gases illustrating the whole procedure explicitly. The outlined MaxEnt procedure results in a decomposition of total pressure in accordance with Dalton’s law of partial pressures in a mixture of ideal gases. Finally, we apply the method numerically to a mixture of van der Waals gases demonstrating the versatility of the proposed framework. We obtain a nontrivial prediction which differs from the decomposition of mixture pressure according to Dalton’s law.

Advances in 1D thermo-fluid dynamic simulation of SI hydrogen-fueled engine

This work has the objective to describe the improvement introduced in the 1D thermo-fluid dynamic simulation code developed to simulate hydrogen-fueled Internal Combustion Engines. Two main topics have been analyzed. The first regarding the simulation of unsteady flows in the whole intake and exhaust system and the injection process of the fuel, considering a mixture of ideal gases as working fluid with specific heats depending on both gas temperature and composition. The second one focused on the combustion process, where the correlation-based approach used to compute the laminar flame speed for the homogeneous air-hydrogen mixture has been substituted by a Tabulated Kinetic approach. New correction factors that account for surface instabilities have been also added to obtain a more accurate prediction of the combustion process. The modifications introduced have been validated against experimental values comparing in-cylinder pressure trends, intake and exhaust instantaneous pressure pulses taken at different locations. Finally, the results obtained from the simulations of a novel hydrogen-fueled heavy-duty engine are presented.

Consistent lattice Boltzmann model for reactive mixtures

A new lattice Boltzmann model (LBM) for chemically reactive mixtures is presented. The approach capitalizes on the recently introduced thermodynamically consistent LBM for multicomponent mixtures of ideal gases. Similar to the non-reactive case, the present LBM features Stefan–Maxwell diffusion of chemical species and a fully on-lattice mean-field realization of the momentum and energy of the flow. Besides introducing the reaction mechanism into the kinetic equations for the species, the proposed LBM also features a new realization of the compressible flow by using a concept of extended equilibrium on a standard lattice in three dimensions. The full thermodynamic consistency of the original non-reactive multicomponent LBM enables us to extend the temperature dynamics to the reactive mixtures by merely including the enthalpy of formation in addition to the sensible energy considered previously. Furthermore, we describe in detail the boundary conditions to be used for reactive flows of practical interest. The model is validated against a direct numerical simulation of various burning regimes of a hydrogen/air mixture in a microchannel, in two and three dimensions. Excellent comparison in these demanding benchmarks indicates that the proposed LBM can be a valuable and universal model for complex reactive flows.

A variable time step self-consistent mean field DSMC model for three-dimensional environments.

A self-consistent mean field direct simulation Monte Carlo (SCMFD) algorithm was recently proposed for simulating collision environments for a range of one-dimensional model systems. This work extends the one-dimensional SCMFD approach to three dimensions and introduces a variable time step (3D-vt-SCMFD), enabling the modeling of a considerably wider range of different collision environments. We demonstrate the performance of the augmented method by modeling a varied set of test systems: ideal gas mixtures, Poiseuille flow of argon, and expansion of gas into high vacuum. For the gas mixtures, the 3D-vt-SCMFD method reproduces the properties (mean free path, mean free time, collision frequency, and temperature) in excellent agreement with theoretical predictions. From the Poiseuille flow simulations, we extract flow profiles that agree with the solution to the Navier-Stokes equations in the high-density limit and resemble free molecular flow at low densities, as expected. The measured viscosity from 3D-vt-SCMF is ∼15% lower than the theoretical prediction from Chapman-Enskog theory. The expansion of gas into vacuum is examined in the effusive regime and at the hydrodynamic limit. In both cases, 3D-vt-SCMDF simulations produce gas beam density, velocity, and temperature profiles in excellent agreement with analytical models. In summary, our tests show that 3D-vt-SCMFD is robust and computationally efficient, while also illustrating the diversity of systems the SCMFD model can be successfully applied to.

Continuum Thermodynamics of Constrained Reactive Mixtures.

Mixture theory models continua consisting of multiple constituents with independent motions. In constrained mixtures, all constituents share the same velocity but they may have different reference configurations. The theory of constrained reactive mixtures was formulated to analyze growth and remodeling in living biological tissues. It can also reproduce and extend classical frameworks of damage mechanics and viscoelasticity under isothermal conditions, when modeling bonds that can break and reform. This study focuses on establishing the thermodynamic foundations of constrained reactive mixtures under more general conditions, for arbitrary reactive processes where temperature varies in time and space. By incorporating general expressions for reaction kinetics, it is shown that the residual dissipation statement of the Clausius-Duhem inequality must include a reactive power density, while the axiom of energy balance must include a reactive heat supply density. Both of these functions are proportional to the molar production rate of a reaction, and they depend on the chemical potentials of the mixture constituents. We present novel formulas for the classical thermodynamic concepts of energy of formation and heat of reaction, making it possible to evaluate the heat supply generated by reactive processes from the knowledge of the specific free energy of mixture constituents as well as the reaction rate. We illustrate these novel concepts with mixtures of ideal gases, and isothermal reactive damage mechanics and viscoelasticity, as well as reactive thermoelasticity. This framework facilitates the analysis of reactive tissue biomechanics and physiological and biomedical engineering processes where temperature variations cannot be neglected.

On the thermodynamic consistency of non-random hydrogen bonding lattice-fluid model for multicomponent mixtures

Compressible lattice-fluid Equation of State (EoS) models have been widely used to interpret phase equilibria and related properties of pure fluids and their mixtures, including polymer solutions. One of the first models of this family has been proposed by Sanchez and Lacombe (SL), providing useful expressions for EoS and chemical potentials for both pure components and mixtures. The assessment of the thermodynamic consistency of the expressions provided by these models for the chemical potential of each component in a mixture is a relevant issue, to which has seldom been devoted the attention it deserves. In fact, it has been demonstrated in the literature that the equations provided by the SL theory for the equilibrium chemical potential of a component in a mixture exhibits a thermodynamic inconsistency emerging from the adopted mixing rules for the close packed volume. Consequently, these expressions do not converge to the proper form in the limit of ideal gas mixtures. Later, the Non-Random Hydrogen Bonding (NRHB) lattice-fluid model was introduced to overcome some limitations of the SL model, by accounting for possible presence of strong specific intermolecular interactions, such as hydrogen bonding, as well as for non-random distribution of intermolecular contacts. In the present work, using a thermodynamic framework endowed with internal state variables, it is shown that the expressions of the chemical potential provided by the NRHB model for a multicomponent mixture at equilibrium, converge consistently to the correct form in the limit of ideal gas mixtures, thus overcoming the inconsistency implicit in the most common corresponding formulations of the SL model. We demonstrate that this feature is essentially related to the assumption of a constant value of the segmental volume, v*, that takes the same ‘universal’ value (9.75/NA cm3/molecular segment, where NA is the Avogadro number) for all pure fluids as well as for their mixtures. In addition, we have re-examined also the inconsistency issue of the SL model proving that this model recovers the thermodynamic consistency if it is assumed again a constant value of v* or if a particular type of mixing rule is assumed for v*.

A lattice Boltzmann model for reactive mixtures.

A new lattice Boltzmann model for reactive ideal gas mixtures is presented. The model is an extension to reactive flows of the recently proposed multi-component lattice Boltzmann model for compressible ideal gas mixtures with Stefan–Maxwell diffusion for species interaction. First, the kinetic model for the Stefan–Maxwell diffusion is enhanced to accommodate a source term accounting for the change in the mixture composition due to chemical reaction. Second, by including the heat of formation in the energy equation, the thermodynamic consistency of the underlying compressible lattice Boltzmann model for momentum and energy allows a realization of the energy and temperature change due to chemical reactions. This obviates the need for ad-hoc modelling with source terms for temperature or heat. Both parts remain consistently coupled through mixture composition, momentum, pressure, energy and enthalpy. The proposed model uses the standard three-dimensional lattices and is validated with a set of benchmarks including laminar burning speed in the hydrogen–air mixture and circular expanding premixed flame.This article is part of the theme issue ‘Progress in mesoscale methods for fluid dynamics simulation’.

Irreversible thermodynamics of multicomponent fluids and its statistical mechanics basis.

The irreversible thermodynamics of a multicomponent fluid is reviewed. This includes a discussion of the role of individual component fluxes. It is argued that their differences vanish on the same time scale as that which establishes local thermodynamic equilibrium and thus do not play an independent role in fluid dynamics, but only arise in response to gradients in conserved thermodynamic variables. The contributions to the energy flux are examined and it is argued that there should be explicit contributions associated with the various component fluxes, which are not mentioned in standard kinetic theory presentations. Three different thermodynamic perspectives are discussed as to their form, with the respective equations for the entropy flux and production described and contrasted. The Onsager reciprocal relations are considered to be a consequence of the single-valuedness of the entropy production with the chemical potential gradients as the driving forces for diffusion. These are specialized to ideal gas mixtures using the component density gradients associated with Fick's laws and to using the mole fraction gradients that are standardly used in gas kinetic theory. The ideal gas Onsager relations are identical to those deduced from the Boltzmann equation. Irving and Kirkwood's statistical mechanics treatment of the evolution equations of a one-component fluid [J. Chem. Phys. 18, 817 (1950)JCPSA60021-960610.1063/1.1747782] is generalized to multicomponent fluids and agrees with the thermodynamic perspective that treats the energy transfers as reversible.

Limit of the buoyancy ratio in Boussinesq approximation for double-diffusive convection in binary mixture

This paper deals with a mathematical and numerical investigation of double-diffusive natural convective heat and mass transfer in a cavity filled with Newtonian fluid with significant density and mass diffusivity changes. In such a situation, the assumption of the Boussinesq approximation is not justified, and an appropriate model based on a set of Low Mach Number equations is used. The active parts of two vertical walls of the cavity are maintained at fixed but different temperatures and concentrations, while the other two walls, as well as inactive areas of the sidewalls, are considered to be adiabatic and impermeable to mass transfer. The coupled momentum, energy, and solute transfer equations in binary mixtures of ideal gases are solved through a global iterative procedure based on the finite volume methods in the context of the low Mach number approximation. The study includes the effect of the buoyancy ratio N with the aim to find its application limit in the Boussinesq conditions. The results show that if we use the Boussinesq approximation to study double-diffusive convection, the value of parameter N must be between −6 and 27.

Thermodynamic Discrimination between Energy Sources for Chemical Reactions

Summary Chemical transformations traverse large energy differences, yet the comparison of energy sources to drive a reaction is often done on a case-by-case basis; there is no fundamentally driven, universal framework with which to analyze and compare driving forces for chemical reactions. In this work, we present a reaction-independent expression for the equilibrium constant as a function of temperature, pressure, and voltage. With a specific set of axes, all reactions are represented by a single ( x , y ) point, and a quantitative divide between electrochemically and thermochemically driven reactions is visually evident. Additionally, we show that our expression has a strong physical basis in work and energy fluxes to the system, although specific data about operating conditions are necessary to provide a quantitative energy analysis. Overall, this universal equation and facile visualization of chemical reactions provides a consistent thermodynamic framework for comparing electrochemical versus thermochemical energy sources without knowledge of detailed process parameters.

Consistent lattice Boltzmann model for multicomponent mixtures

Abstract