Species Mass Conservation Equations Research Articles

A new stabilized formulation for the simulation of underwater explosions using isogeometric analysis

We develop a new formulation for the computational modeling of underwater explosions (UNDEX). The formulation is based on the Navier–Stokes equations of compressible flows augmented with the species mass conservation equations. We develop a stabilized formulation with discontinuity capturing for this multiphase model using the framework of advective–diffusive systems. Isogeometric Analysis is successfully employed to discretize the resulting stabilized formulation. Novel interface sharpening and mass correction procedures are also developed based on the invertible mapping between the level-set and volume fraction functions. Several numerical examples of increasing complexity and including experimental validation are presented in order to demonstrate the good performance of the new UNDEX modeling methodology.

Reprint of: Finite volume methods for multi-component Euler equations with source terms

A first-order well-balanced finite volume scheme for the solution of a multi-component gas flow model in a pipe on non-flat topography is introduced. The mathematical model consists of Euler equations with source terms which arise from heat exchange, and gravity and viscosity forces, coupled with the mass conservation equations of species. We propose a segregated scheme in which the Euler and species equations are solved separately. This methodology leads to a flux vector in the Euler equations which depends not only on the conservative variables but also on time and space variables through the gas composition. This fact makes necessary to add some artificial viscosity to the usual numerical flux which is done by introducing an additional source term. Besides, in order to preserve the positivity of the species concentrations, we discretize the flux in the mass conservation equations for species, in accordance with the upwind discretization of the total mass conservation equation in the Euler system. Moreover, as proposed in a previous reference by the authors, [5], the discretizations of the flux and source terms are made so as to ensure that the full scheme is well-balanced. Numerical tests including both academic and real gas network problems are solved, showing the performance of the proposed methodology.

Finite volume methods for multi-component Euler equations with source terms

A first-order well-balanced finite volume scheme for the solution of a multi-component gas flow model in a pipe on non-flat topography is introduced. The mathematical model consists of Euler equations with source terms which arise from heat exchange, and gravity and viscosity forces, coupled with the mass conservation equations of species. We propose a segregated scheme in which the Euler and species equations are solved separately. This methodology leads to a flux vector in the Euler equations which depends not only on the conservative variables but also on time and space variables through the gas composition. This fact makes necessary to add some artificial viscosity to the usual numerical flux which is done by introducing an additional source term. Besides, in order to preserve the positivity of the species concentrations, we discretize the flux in the mass conservation equations for species, in accordance with the upwind discretization of the total mass conservation equation in the Euler system. Moreover, as proposed in a previous reference by the authors, [5], the discretizations of the flux and source terms are made so as to ensure that the full scheme is well-balanced. Numerical tests including both academic and real gas network problems are solved, showing the performance of the proposed methodology.

Scale-up analysis of continuous cross-flow atomic layer deposition reactor designs

This paper presents the development of a non-dimensional model of a continuous cross-flow atomic layer deposition (ALD) reactor with temporally separated precursor pulsing and a structured model-based methodology for scaling up the substrate dimensions. The model incorporates an ALD gas–surface reaction kinetic mechanism for the deposition of thin ZnO films from Zn(C2H5)2 and H2O precursors that was experimentally validated in our previous work (Holmqvist et al., 2012, 2013a). In order to maintain dynamic similarity, a scaling analysis was applied based on the dimensionless numbers, appearing in non-dimensionalized momentum and species mass conservation equations, that describe the convective laminar flow, mass transfer and heterogeneous reaction. The impact on these dimensionless numbers and, more importantly, the impact on the limit-cycle deposition rate and its relative uniformity was thoroughly investigated when linearly scaling up the substrate dimensions. In the scale-up procedure, the limit-cycle precursor utilization was maximized by means of dynamic optimization, while ensuring that identical deposition profiles were obtained in the scaled-up system. The results presented here demonstrated that the maximum precursor yields were promoted at higher substrate dimensions. Limit-cycle dynamic solutions to the non-dimensionalized model, computed with a collocation discretization in time, revealed that it is a combination of the degree of precursor depletion in the flow direction and the magnitude of the pressure drop across the reactor chamber that governs the extent of the deposition profile non-uniformity. A key finding of this study is the identification of optimal scaling rules for maximizing precursor utilization in the scaled-up system while maintaining fixed absolute growth rate and its relative uniformity.

Investigation on the Simulation of SCR Chemical Reaction

Abstract. With the global environment worsening and the consciousness of protecting environment strengthening, the limitation of noxious gas from diesel engines is becoming more and more strictly. Selective catalytic reduction (SCR) aftertreatment system has been applied to reduce Nitrogen Oxides (NOx) as a key technology. The urea solution injected into the tailpipe decomposes to ammonia, which will react with NOx on the surface of SCR catalyst. The main purpose of this paper is to study the effect of different concentrations of NO, NO2 and NH3 on the reactions taking place with SCR catalyst by simulation. Based on mass transfer equations and chemical kinetics the simulation results predict the concentrations of NO, NO2 and NH3 accurately. The mass conservation equations of species are solved by the software MATLAB. Some regulations can be revealed to improve the NOx conversion efficiency and reduced the NH3 slip.

Sensitivity analysis of surface ozone to modified initial and boundary conditions in both rural and industrial zones

Abstract. A three-dimensional air quality model based on a set of chemical species mass conservation equations describes the time evolution of chemical species in the atmosphere. In order to solve this set of equations, proper choices of initial and boundary conditions are needed. Ideally, initial and boundary conditions should be determined on the basis of observations. However, since such high-resolution observations are generally not available, it becomes necessary to use other information sources to specify the initial and boundary values. The fact that both the initial and the boundary conditions are specified with some degree of presumption makes it important to evaluate their influence in the model results. In this paper we present a study of the impact of initial and boundary concentrations on the modelled surface ozone concentration over two environments: Huelva and Badajoz, an industrial and a rural zone, respectively. The impacts are analysed for the same meteorological period (10–15 August 2003).

Analysis of Assumptions Commanding Detailed Chemistry EDC-Based Model for Diesel Spray Combustion(Diesel Engines, Combustion Modeling II)

The new eddy dissipation concept (EDC) model based on the operator-splitting procedure applied to the mass conservation equations for species participating in reversible chemical reactions representing combustion in a PaSR partially stirred reactor (PaSR) volume is analyzed. The model has been implemented in the KTVA-3V code together with a new droplet collision procedure, and its application to spray combustion simulation is illustrated by the results of the 3-D modeling of the DI Diesel Volvo D12C engine. The chemical mechanism of diesel oil surrogate consisted of 68 species (including soot aromatic precursors) participating in 285 reversible reactions has been applied to simulation of MK (Modulated Kinetics) diesel spray combustion regime. Mean features of MK combustion under conditions of delayed injection when auto-ignition has much in common with the HCCI process are predicted in accordance with experimental data.

Supersonic O2-jet Impingement on Liquid Iron with Surface Chemistry

This paper describes numerical analysis of a supersonic O 2 -jet impingement on carbon-contained liquid iron under vacuum circumstances. The gas phase is assumed to be composed of O 2 , CO, CO 2 , O and C. Since gas temperature is elevated over 1 000 K in the vicinity of the surface of liquid iron, high-temperature gas effects, namely vibrational energy excitation and dissociation, are included in the analysis. Therefore, the flow field is expressed by Navier-Stokes equations consisting of mass conservation, momentum, overall energy, vibrational energy and species mass conservation equations. Furthermore, surface reactions for O 2 -C and O-C encounters are included in surface boundary conditions. Cavity geometry is determined from the balance of pressure, shear stress, surface tension and liquid buoyancy. Based on the numerical results, sensitivity of mass fraction for each species to the probability of surface reaction is discussed. In addition, the effect of the surface reactions on the cavity geometry is clarified.

Modeling and measurements of heat transfer phenomena in two-phase PbSn alloy solidification in an external magnetic field

The main aim of this work is to study numerically the influence of an external magnetic field on the solidification processes of two-component materials. Based on the continuum model of two-phase flow a mathematical model for the directional solidification of a binary alloy in a magnetic field is presented. The model includes mass, momentum, energy and species mass conservation equations written in compressible form and additional relationships describing the temperature-solute coupling. The geometry under study is a cylindrical mold with adiabatic walls and cooled bottom. The macroscale transport in the solidification of alloys is governed by the progress of the two-phase mushy zone, which is treated by means of a porous medium approach. The volume fraction of liquid and solid phases, respectively, is calculated from a 2D approximation of the phase diagram. The results of calculation are compared with experimental data.

超軌道速度再突入カプセル前方衝撃波層の数値解析

The calculation code originally developed for a hypersonic nonequilibrium flow is applied to the flowfield in front of a super orbital-velocity reentry capsule. The re-entry speed is assumed to be 12km/sec. The governing equations for a chemically and thermally nonequilibrium flow consist of the full Navier-Stokes equations, including the 11 chemical species mass conservation equations and the vibrational-electronic energy conservation equation. The Park's two-temperature model is used for the chemical reaction rates. A Harten-Yee type upwind TVD scheme is used to solve the governing equations with a fractional step method. A semi-implicit scheme is introduced because of the stiffness of chemical source terms. Under a super orbital-velocity re-entry conditions, the results of numerical calculations indicate that the vibrational excitation behind a strong bow shock is prevented by nitrogen molecule dissociation. The obtained distributions of vibrational and translational temperatures and species mass fractions are essentially sufficient to yield not only the convective but also the radiative heat transfer to the capsule surface using the existing NEQAIR code.

A Computational Model for the Study of Gas Turbine Combustor Dynamics

A dynamic combustor model is developed for inclusion into a one-dimensional full gas turbine engine simulation code. A flux-difference splitting algorithm is used to numerically integrate the quasi-one-dimensional Euler equations, supplemented with species mass conservation equations. The combustion model involves a single-step, global finite-rate chemistry scheme with a temperature-dependent activation energy. Source terms are used to account for mass bleed and mass injection, with additional capabilities to handle momentum and energy sources and sinks. Numerical results for cold and reacting flow for a can-type gas turbine combustor are presented. Comparisons with experimental data from this combustor are also made.

Thermochemical Nonequilibrium in Rapidly Expanding Flows of High-Temperature Air

Abstract • This paper describes a computational study of the thermal and chemical nonequilibrium occuring in a rapidly expanding flow of high-temperature air transported as a free jet from an orifice into low-density stationary air. Translational, rotational, vibrational and electron temperatures are treated separately, and in particular the vibrational temperatures are individually treated; a multi-vibrational temperature model is adopted. The governing equations are axisymmetric Navier-Stokes equations coupled with species vibrational energy, electron energy and species mass conservation equations. These equations are numerically solved, using the second order upwind TVD scheme of the Harten-Yee type. The calculations were carried out for two different orifice temperatures and also two different orifice diameters to investigate the effects of such parameters on the structure of a nonequilibrium free jet.

Multitemperature Model Effects on Numerical Analysis of a Supersonic Non-Equilibrium Free Jet.

This paper describes numerical results of a thermal and chemical nonequilibrium plume of high-temperature air. The gas is expanded from an orifice into low-density stationary air as a free jet. The gas considered here is high-temperature air composed of N2, O2, N, O, NO, NO+and e-, and translational-rotational and vibrational-electron temperatures are treated in a two-temperature model. In addition to this model, a six-temperature model using a multi-vibrational temperature model is adopted. The governing equations for computation are axisymmetric Navier-Stokes equations coupled with species vibrational energy, electron energy and species mass conservation equations. The equations have been numerically solved using the second-order upwind TVD scheme of the Harten-Yee type.

Improved flux-split algorithm applied to hypersonic flows in chemical equilibrium

An explicit, finite-difference, shock-capturing numerical algorithm is presented and applied to hypersonic flows assumed to be in thermochemical equilibrium. Real-gas chemistry is either loosely coupled to the gasdynamics by way of a Gibbs free energy minimization package or fully coupled using species mass conservation equations with finite-rate chemical reactions. A scheme is developed that maintains stability in the explicit, finite-rate formulation while allowing relatively high time steps. The codes use flux vector splitting to difference the inviscid fluxes and employ real-gas corrections to viscosity and thermal conductivity. Numerical results are compared against existing ballistic range and flight data. Flows about complex geometries are also computed.