Mixture Of Ideal Gases Research Articles

An oscillation free shock-capturing method for compressible van der Waals supercritical fluid flows

Numerical solutions of the Euler equations using real gas equations of state (EOS) often exhibit serious inaccuracies. The focus here is the van der Waals EOS and its variants (often used in supercritical fluid computations). The problems are not related to a lack of convexity of the EOS since the EOS are considered in their domain of convexity at any mesh point and at any time. The difficulties appear as soon as a density discontinuity is present with the rest of the fluid in mechanical equilibrium and typically result in spurious pressure and velocity oscillations. This is reminiscent of well-known pressure oscillations occurring with ideal gas mixtures when a mass fraction discontinuity is present, which can be interpreted as a discontinuity in the EOS parameters. We are concerned with pressure oscillations that appear just for a single fluid each time a density discontinuity is present. The combination of density in a nonlinear fashion in the EOS with diffusion by the numerical method results in violation of mechanical equilibrium conditions which are not easy to eliminate, even under grid refinement.A cure to this problem is developed in the present paper for the van der Waals EOS based on previous ideas. A special extra field and its corresponding evolution equation is added to the flow model. This new field separates the evolution of the nonlinear part of the density in the EOS and produce oscillation free solutions. The extra equation being nonconservative the behavior of two established numerical schemes on shocks computation is studied and compared to exact reference solutions that are available in the present context. The analysis shows that shock conditions of the nonconservative equation have important consequence on the results. Last, multidimensional computations of a supercritical gas jet is performed to illustrate the benefits of the present method, compared to conventional flow solvers.

Engineering Model of High Pressure Moist Air

The article deals with the moist air equation of state. There are equations of state discussed in the article, i.e. the model of an ideal mixture of ideal gases, the model of an ideal mixture of real gases and the model based on the virial equation of state. The evaluation of sound speed based on the ideal mixture concept is mentioned. The sound speed calculated by the model of an ideal mixture of ideal gases is compared with the sound speed calculated by using the model based on the concept of an ideal mixture of real gases. The comparison of enthalpy end entropy based on the model of an ideal mixture of ideal gases and the model of an ideal mixture of real gases is performed. It is shown that the model of an ideal mixture of real gases deviates from the model of an ideal mixture of ideal gases only in the case of high pressure. An impossibility of the definition of partial pressure in the mixture of real gases is discussed, where the virial equation of state is used.

Ideal cycle of combustion engine with natural gas as a fuel

The aim of the paper is to present a detailed methodology of calculations of parameters of an ideal working cycle of spark-ignition combustion engine. Natural gas in the form of compressed natural gas (CNG) was used as a fuel. A theoretical ideal cycle is currently described in simplified way. The paper introduces calculations considering excess air, residual space in the cylinder of the engine and the course of properties of gases in dependence on temperature. The thermodynamics of ideal gas mixture was used. A computer program for clear, quick and accurate calculations of this relatively complicated system of relations was designed. The presented methodology of calculations broadens the scope of the theory of combustion engines and enables a precise determination of parameters of combustion engine with natural gas as a fuel.

Diffusion of Charged Species in Liquids

In this study the laws of mechanics for multi-component systems are used to develop a theory for the diffusion of ions in the presence of an electrostatic field. The analysis begins with the governing equation for the species velocity and it leads to the governing equation for the species diffusion velocity. Simplification of this latter result provides a momentum equation containing three dominant forces: (a) the gradient of the partial pressure, (b) the electrostatic force, and (c) the diffusive drag force that is a central feature of the Maxwell-Stefan equations. For ideal gas mixtures we derive the classic Nernst-Planck equation. For liquid-phase diffusion we encounter a situation in which the Nernst-Planck contribution to diffusion differs by several orders of magnitude from that obtained for ideal gases.

Improving Students’ Understanding of the Connections between the Concepts of Real-Gas Mixtures, Gas Ideal-Solutions, and Perfect-Gas Mixtures

In many textbooks of chemical-engineering thermodynamics, a gas mixture obeying the fundamental law pVm = RT is most often called ideal-gas mixture (in some rare cases, the term perfect-gas mixture can be found). These textbooks also define the fundamental concept of ideal solution which in theory, can be applied indifferently to liquid or gas mixtures but in practice, is nearly always introduced through the instance of liquid solutions. Undergraduate students are thus faced with different theoretical solution models that are all named “ideal” which can be a source of confusion. It is indeed often observed either that the connections between the concepts of perfect gas and ideal solution are missed by undergraduate students, or that they do not make any distinction between the concepts of gaseous ideal-solutions and perfect-gas mixtures. In this article, a simple example is proposed to pedagogically clarify all the misconceptions inherited from the multiple definitions of ideal mixtures and to explicate t...

Critical slot size for deflagration initiation by hot products discharge into hydrogen–air atmospheres

This computational study addresses deflagration initiation of lean, stoichiometric, and moderately rich hydrogen–air mixtures by the sudden discharge of a hot planar jet of its adiabatic combustion products. The objective is to determine the minimum slot size required for ignition, a relevant quantity of interest for safety and technological applications concerning the accidental ignition of hydrogen. For sufficiently small jet velocities, the numerical solution of the problem requires integration of the two-dimensional Navier–Stokes equations for chemically reacting ideal-gas mixtures, supplemented by standard descriptions of the molecular transport terms and a reduced chemical–kinetic mechanism suitable for hydrogen–air combustion. The computations provide the variation of the critical slot size for hot-jet ignition with both the jet Reynolds number and the equivalence ratio of the mixture. In particular, it is seen that, while the Reynolds number exerts only a relatively weak effect on the ignition process, the influence of the equivalence ratio is much more pronounced, with the smallest slot widths found for stoichiometric or slightly-rich conditions. The numerical results show three different ignition modes, with the flame developing from a clearly identified ignition kernel located either at the core of the leading vortex pair (mode 1), at the symmetry plane near the leading edge of the starting jet (mode 2), or at the jet stem connecting the jet exit with the starting vortex (mode 3).

Describing diffusion in fluid mixtures at elevated pressures by combining the Maxwell–Stefan formulation with an equation of state

Many operations of interest to chemical engineers require proper modeling of diffusion in fluid mixtures at operating pressures ranging to several megapascals. Examples include supercritical extraction, fractionation of natural gas liquids, enhanced oil recovery and exploitation of shale gas reserves. The Maxwell–Stefan (M–S) formulation, in combination with the Peng–Robinson equation of state, affords a convenient framework for modeling mixture diffusion. The primary objective of this article is to highlight a number of important and distinguishing diffusional characteristics of mixture diffusion at elevated pressures. For dense binary gas mixtures, the pressure-dependence of the M–S diffusivity Ðij requires additional correction for the compressibility factor, Z; this correction introduces a composition dependence for the Ðij that is absent for ideal gas mixtures. Also significant are influences of the thermodynamic correction factors Γij, that are related to the derivatives of the fugacity coefficients with respect to the compositions. For operations near critical pressures, or close to vapor/liquid and solid/liquid phase transition regions, the thermodynamic factor for binary mixtures tend to reduce to near-zero values; this reduction has a direct and proportional impact on the Fick diffusivities. For ternary fluid mixtures, the Γij cause the individual diffusion fluxes to be strongly coupled. Such coupling effects can be of significant importance even for hydrocarbon mixtures; this conclusion is not intuitively obvious. Strongly coupled diffusion leads to curvilinear equilibration trajectories, and may cause uphill diffusion of species.

Equation of state of silicon dioxide with allowance for evaporation, dissociation, and ionization

Based on a previously proposed modified van der Waals model for a mixture, a widerange semi-empirical equation of state for silicon dioxide with due allowance for evaporation, dissociation, and ionization is constructed. In the low-density limit, it transforms to Saha’s equation of state for a mixture of ideal gases consisting of ions and electrons. The model and simplifying assumptions used in constructing the equation of state are described. The values of constitutive parameters are given. Results of model calculations are compared with data obtained in experiments on shock compression of solid and porous quartz samples, isentropic unloading, etc.

Comparison of the entropy of ideal gas mixture with total entropy of the components obtained from it

This paper presents two expressions define the ideal gaseous mixture entropy via its components entropies, the components being in two different conditions after segregation. In one case the components have the mixture temperature and pressure, whereas in the second case they also have the mixture temperature but their own partial pressure.As follows of data analysis, the conditions under which the mixture entropy is equal to the sum of its components are derived. The complete analysis allows us to some controversies called “The Gibbs paradox”. Refs 4.

Experimental investigation and thermodynamic calculation of the Mg–Mn–Sr system

Both experimental investigation and thermodynamic modeling were performed for the Mg–Mn–Sr system. Four decisive alloys were selected and prepared using a powder metallurgy method to measure the isothermal section at 500°C via a combination of X-ray diffraction (XRD) and electron probe microanalysis (EPMA). No ternary compound has been observed for this ternary system. Four three-phase regions, (Mg)+(αMn)+Mg17Sr2, Mg17Sr2+(αMn)+Mg38Sr9, Mg38Sr9+(αMn)+Mg23Sr6, and Mg23Sr6+(αMn)+Mg2Sr, have been identified at 500°C. No appreciable ternary solubility has been detected in the binary Mg–Sr compounds. Phase transition temperatures of the Mg–Mn–Sr alloys were measured by means of differential scanning calorimetry (DSC) measurements. In the present modeling, the substitutional solution model was used to describe the liquid phase. Due to the high evaporability of Mg, Mn and Sr, the gas phase can affect higher temperature equilibria in the Mg–Mn–Sr system and thus was included and modeled as an ideal gas mixture. The thermodynamic calculations match well with the experimental data, indicating that no ternary thermodynamic parameters are needed for the thermodynamic description. In order to verify the reliability of the current thermodynamic modeling of the Mg–Mn–Sr system, five as-cast alloys in Mg-rich corner were prepared. The calculated liquidus projection is consistent with the observed primary phase regions. The present thermodynamic modeling is reliable and can be used in the development of the Mg alloys.

Loss of thermodynamic work at the cascade stages during the separation of a multicomponent mixture of ideal gases

Formulas for estimating the thermodynamic work during the separation of components of binary and multicomponent mixtures are discussed and generalized. The difference between the work of separation determined from the separation potential and the thermodynamically estimated work during the isobaric–isothermal mixing of fractions separated at the ends of a cascade is calculated and explained.

Teaching Thermodynamics of Ideal Solutions: An Entropy-Based Approach To Help Students Better Understand and Appreciate the Subtleties of Solution Models

The thermodynamic formalism of ideal solutions is developed in most of the textbooks postulating a form for the chemical potential of a generic component, which is adapted from the thermodynamics of ideal gas mixtures. From this basis, the rest of useful thermodynamic properties can be derived straightforwardly without further hypothesis. Although formally elegant, this approach to ideal solutions does not allow appreciation of subtle concepts embodied in the model such as requirements of molecular size and shape or the fact that equations that contain the universal gas constant (R) can be applied to describe liquid or solid solutions. As alternative, it is discussed here an approach centered on the behavior of the partial molar entropy of the component using the framework provided by the concept of accessible volume. It is shown that this way of presenting the topic allows a more natural flow and, particularly, analytical justification of all the hypothesis and ideas behind many fundamental solution models, including that of ideal solutions, with the extra advantage that it can almost entirely carried out from a macroscopic point of view.

Thermodynamics and kinetics of binary nucleation in ideal-gas mixtures.

The nonisothermal single-component theory of droplet nucleation [N. V. Alekseechkin, Physica A 412, 186 (2014)] is extended to binary case; the droplet volume V, composition x, and temperature T are the variables of the theory. An approach based on macroscopic kinetics (in contrast to the standard microscopic model of nucleation operating with the probabilities of monomer attachment and detachment) is developed for the droplet evolution and results in the derived droplet motion equations in the space (V, x, T)—equations for V̇≡dV/dt, ẋ, and Ṫ. The work W(V, x, T) of the droplet formation is obtained in the vicinity of the saddle point as a quadratic form with diagonal matrix. Also, the problem of generalizing the single-component Kelvin equation for the equilibrium vapor pressure to binary case is solved; it is presented here as a problem of integrability of a Pfaffian equation. The equation for Ṫ is shown to be the first law of thermodynamics for the droplet, which is a consequence of Onsager's reciprocal relations and the linked-fluxes concept. As an example of ideal solution for demonstrative numerical calculations, the o-xylene-m-xylene system is employed. Both nonisothermal and enrichment effects are shown to exist; the mean steady-state overheat of droplets and their mean steady-state enrichment are calculated with the help of the 3D distribution function. Some qualitative peculiarities of the nucleation thermodynamics and kinetics in the water-sulfuric acid system are considered in the model of regular solution. It is shown that there is a small kinetic parameter in the theory due to the small amount of the acid in the vapor and, as a consequence, the nucleation process is isothermal.

High performance of Cu/CeO2-Nb2O5 catalysts for preferential CO oxidation and total combustion of toluene

Copper-based catalysts supported on niobium-doped ceria have been prepared and tested in the preferential oxidation of CO in excess of H2 (PROX) and in total oxidation of toluene. Supports and catalysts have been characterized by several techniques: N2 adsorption, ICP-OES, XRF, XRD, Raman Spectroscopy, SEM, TEM, H2-TPR and XPS, and their catalytic performance has been measured in PROX, with an ideal gas mixture (CO, O2 and H2) with or without CO2 and H2O, and in total oxidation of toluene. The effects of the copper loading and the amount of niobium in the supports have been evaluated. Remarkably, the addition of niobia to the catalysts may improve the catalytic performance in total oxidation of toluene. It allows us to prepare cheaper catalysts (niobia it is far cheaper than ceria) with improved catalytic performance.

Equilibrium and stability properties of detonation waves in the hydrodynamic limit of a kinetic model

A shock wave structure problem, like the one which can be formulated for the planar detonation wave, is analyzed here for a binary mixture of ideal gases undergoing the symmetric reaction . The problem is studied at the hydrodynamic Euler limit of a kinetic model of the reactive Boltzmann equation. The chemical rate law is deduced in this frame with a second-order reaction rate, in a chemical regime such that the gas flow is not far away from the chemical equilibrium. The caloric and the thermal equations of state for the specific internal energy and temperature are employed to close the system of balance laws. With respect to other approaches known in the kinetic literature for detonation problems with a reversible reaction, this paper aims to improve some aspects of the wave solution. Within the mathematical analysis of the detonation model, the equation of the equilibrium Hugoniot curve of the final states is explicitly derived for the first time and used to define the correct location of the equilibrium Chapman–Jouguet point in the Hugoniot diagram. The parametric space is widened to investigate the response of the detonation solution to the activation energy of the chemical reaction. Finally, the mathematical formulation of the linear stability problem is given for the wave detonation structure via a normal-mode approach, when bidimensional disturbances perturb the steady solution. The stability equations with their boundary conditions and the radiation condition of the considered model are explicitly derived for small transversal deviations of the shock wave location. The paper shows how a second-order chemical kinetics description, derived at the microscopic level, and an analytic deduction of the equilibrium Hugoniot curve, lead to an accurate picture of the steady detonation with reversible reaction, as well as to a proper bidimensional linear stability analysis.

Effects of radiative heat transfer on the turbulence structure in inert and reacting mixing layers

We use large-eddy simulation to study the interaction between turbulence and radiative heat transfer in low-speed inert and reacting plane temporal mixing layers. An explicit filtering scheme based on approximate deconvolution is applied to treat the closure problem arising from quadratic nonlinearities of the filtered transport equations. In the reacting case, the working fluid is a mixture of ideal gases where the low-speed stream consists of hydrogen and nitrogen and the high-speed stream consists of oxygen and nitrogen. Both streams are premixed in a way that the free-stream densities are the same and the stoichiometric mixture fraction is 0.3. The filtered heat release term is modelled using equilibrium chemistry. In the inert case, the low-speed stream consists of nitrogen at a temperature of 1000 K and the highspeed stream is pure water vapour of 2000 K, when radiation is turned off. Simulations assuming the gas mixtures as gray gases with artificially increased Planck mean absorption coefficients are performed in which the large-eddy simulation code and the radiation code PRISSMA are fully coupled. In both cases, radiative heat transfer is found to clearly affect fluctuations of thermodynamic variables, Reynolds stresses, and Reynolds stress budget terms like pressure-strain correlations. Source terms in the transport equation for the variance of temperature are used to explain the decrease of this variance in the reacting case and its increase in the inert case.

Low Mach number fluctuating hydrodynamics of multispecies liquid mixtures

We develop a low Mach number formulation of the hydrodynamic equations describing transport of mass and momentum in a multispecies mixture of incompressible miscible liquids at specified temperature and pressure, which generalizes our prior work on ideal mixtures of ideal gases [Balakrishnan et al., “Fluctuating hydrodynamics of multispecies nonreactive mixtures,” Phys. Rev. E 89 013017 (2014)] and binary liquid mixtures [Donev et al., “Low mach number fluctuating hydrodynamics of diffusively mixing fluids,” Commun. Appl. Math. Comput. Sci. 9(1), 47-105 (2014)]. In this formulation, we combine and extend a number of existing descriptions of multispecies transport available in the literature. The formulation applies to non-ideal mixtures of arbitrary number of species, without the need to single out a “solvent” species, and includes contributions to the diffusive mass flux due to gradients of composition, temperature, and pressure. Momentum transport and advective mass transport are handled using a low Mach number approach that eliminates fast sound waves (pressure fluctuations) from the full compressible system of equations and leads to a quasi-incompressible formulation. Thermal fluctuations are included in our fluctuating hydrodynamics description following the principles of nonequilibrium thermodynamics. We extend the semi-implicit staggered-grid finite-volume numerical method developed in our prior work on binary liquid mixtures [Nonaka et al., “Low mach number fluctuating hydrodynamics of binary liquid mixtures,” arXiv:1410.2300 (2015)] and use it to study the development of giant nonequilibrium concentration fluctuations in a ternary mixture subjected to a steady concentration gradient. We also numerically study the development of diffusion-driven gravitational instabilities in a ternary mixture and compare our numerical results to recent experimental measurements [Carballido-Landeira et al., “Mixed-mode instability of a miscible interface due to coupling between Rayleigh–Taylor and double-diffusive convective modes,” Phys. Fluids 25, 024107 (2013)] in a Hele-Shaw cell. We find that giant nonequilibrium fluctuations can trigger the instability but are eventually dominated by the deterministic growth of the unstable mode, in both quasi-two-dimensional (Hele-Shaw) and fully three-dimensional geometries used in typical shadowgraph experiments.

Transport-shifted multi-component non-ideal acid dew-point predictions and generalization/application of the mist-onset “tangency condition” for ideal vapor mixtures near cool surfaces

Anticipating condensation conditions at solid surfaces or within thermal boundary layers is important in many industrial applications involving condensible vapor flows in contact with cooler solid surfaces. In the case of hydrocarbon fuel/air combustion products at moderate pressures containing acid-precursor species (like NO2, SO3, HCl, etc.) surfaces that operate below the prevailing “acid dew point” (ADP) temperature (which can be significantly higher than the DP expected for H2O alone) become vulnerable to chemical attack. Surfaces cold enough to cause acid “mist” onset (AMO) in the vapor phase create potential environmental problems and become much less efficient for condensate capture. Previous methods for estimating ADP and AMO have several drawbacks, the most prominent of which are: limitation to one acid precursor species, dependence on a local curve-fit to earlier thermodynamic ADP-calculations, absence of systematic transport effects associated with the local temperature gradient, and “silence” about the resulting liquid acid composition. Our present, more fundamental, approach overcomes each of these limitations and yet, will be seen to remain tractable from an engineering viewpoint. While we illustrate our methods for the case of a prototypical ternary (N=3) acid condensate (highly non-ideal liquid mixture of H2O + HNO3 + H2SO4) produced from a high temperature ideal gas mixture containing H2O(g) and much smaller concentrations of the aqueous acid precursors: NO2, SO3 (or HNO3(g) and H2SO4(g)), our methods can be formally extended to N=4,5,… if one has access to VLE data for each of the N(N−1)/2 participating binary systems (if the resulting N-component liquid mixture does not itself phase-separate). Our present results also properly reduce from the N-component case to the N−1 case, hence even to the singular case: N=1 (i.e., the DP- and MO-conditions for pure water in the absence of any acid precursor). Because some of the vapor species of interest (e.g., H2O, HNO3, and H2SO4) have molecular weights rather different from the mean molecular weight of the flue gases, Ludwig–Soret transport effects can become non-negligible (in the presence of the temperature gradients expected for high temperature combustion products) both Tw(ADP) and Tw(AMO) will often be seen to be “transport-shifted”, although, as discussed in Appendices A, B, in many cases these effects are complicated by the thermal instability of the largest precursor molecules. Further extensions of likely future interest (e.g., effects of homogeneous chemistry within the thermal boundary layer where molecules like HNO3 and H2SO4 may have to be assembled from their lighter precursors; the effects of nucleation kinetic barriers and/or vapor phase non-ideality) are also identified and are the subject of our ongoing research.

Preferential oxidation of CO in excess of H2 on Pt/CeO2–Nb2O5 catalysts

A series of CeO2–Nb2O5 mixed oxides with different Nb content, as well as the pure oxides, have been synthesized by co-precipitation with excess urea. These materials have been used as supports for platinum catalysts, with [Pt(NH3)4](NO3)2 as precursor. Both supports and catalysts have been characterized by several techniques: N2 physisorption at 77K, X-ray diffraction, Raman spectroscopy, X-ray photoelectron spectroscopy, UV–vis spectroscopy, scanning electron microscopy, transmission electron microscopy, temperature-programmed reduction and temperature-programmed desorption (CO and H2), and their catalytic behaviour has been determined in the PROX reaction, both with an ideal gas mixture (CO, O2 and H2) and in simulated reformate gas containing CO2 and H2O. Raman spectroscopy analysis has shown the likely substitution of some Ce4+ cations by Nb5+ to some extent in supports with low niobium contents. Moreover, the presence of Nb in the supports hinders their ability to adsorb CO and to oxidize it to CO2. However, an improvement of the catalytic activity for CO oxidation is obtained by adding Nb to the support, although the Pt/Nb2O5 catalyst shows very low activity. The best results are found with the Pt/0.7CeO2–0.3Nb2O5 catalyst, which shows a high CO conversion (85%) and a high yield (around 0.6) after a reduction treatment at 523K. The effect of the presence of CO2 and H2O in the feed has also been determined.

Reviewing Some Crucial Concepts of Gibbs Energy in Chemical Equilibrium Using a Computer-Assisted, Guided-Problem-Solving Approach

G, G°, ΔrG, ΔrG°, ΔG, and ΔG° are essential quantities to master the chemical equilibrium. Although the number of publications devoted to explaining these items is extremely high, it seems that they do not produce the desired effect because some articles and textbooks are still being written with some of these quantities that appear to be identical to others. This work attempts to clarify the differences between the six quantities using a guided-problem-solving approach instead of a more conventional expository style. A very simple chemical equilibrium, N2O4(g) ⇌ 2NO2(g), has been chosen as an example. Furthermore, it has been treated in the simplest possible way (as an ideal gas mixture, to thereby avoid fugacities), because the important issue is to sort out concepts and not get entangled in laborious calculations that many times obscure the didactic objective pursued. It is complemented with a small computational tool (a MATLAB script) to quickly perform calculations and graphs. In addition, the script...