Computation of transport coefficients of chemically reacting systems

A new method is proposed for computing the thermal conductivity of a gaseous mixture with regard for chemical reactions occurring therein, which enables the estimation of the thermal conductivity from each separate reaction to the chemical component of thermal conductivity. The method for determining the paired collision integrals, which is used in the work, is also briefly presented. The results computed by the proposed method are compared with experimental data and the data obtained by the existing computational methods in the temperature range from 500 to 2500 K under atmospheric pressure. The comparison was done both for pure gases and for the gaseous mixtures, including the combustion products of solid fuels. The obtained results may be applied for the development and design of systems related to heat exchange, gas dynamics, processing of solid and liquid fuels, for example, boiler aggregates, aviation engines, and in other applications.     

Enskog’s kinetic theory of dense gases for chemically reacting binary mixtures, II: Light scattering and sound propagation

Enskog’s kinetic theory for a symmetric moderately dense reaction A+A?B+B is used to determine Fick’s and Fourier’s law. The transport coefficients of diffusion, thermal-diffusion rate and thermal conductivity are represented graphically for endothermic and exothermic reactions and are analyzed as a function of the activation energy and of the density of the mixture. The Onsager reciprocity relations are numerically investigated and verified. The problems related to sound propagation and light scattering are investigated for such a mixture and it is shown that the influence of chemical reactions on phase velocity, attenuation coefficient and light scattering spectra is more pronounced for rarefied gases although there is a considerable change in these quantities as the mixture becomes denser.     

Theory of sound propagation in superfluid-filled porous media

The theory of sound propagation in macroscopically isotropic and homogeneous porous media saturated with superfluid ⁴He has been developed neglecting all damping processes. The case when the normal fluid component is locked inside a porous medium by viscous forces is investigated in detail. It is shown that in this case one shear wave and two longitudinal, fast and slow, waves exist. Fast wave as well as slow wave is accompanied with temperature oscillations. The velocities of these waves are obtained.     

Generation of vorticity motion by sound in a chemically reacting gas and inversion of acoustic streaming in the non-equilibrium regime

Nonlinear stimulation of the vorticity mode caused by losses in the momentum of sound in a chemically reacting gas is considered. The instantaneous dynamic equation for the vorticity mode is derived. It includes a quadratic nonlinear acoustic source, which reflects the fact that the reason for the interaction between sound and the vorticity mode is nonlinear. Both periodic and aperiodic sound may be considered as the origin of the vorticity flow. The equation governing the mean flow (the acoustic streaming) in the field of periodic sound is also derived. In the non-equilibrium regime of a chemical reaction, there may exist streaming vortices whose direction of rotation is opposite to that of the vortices in the standard thermoviscous flows. For periodic sound, this is illustrated by an example. The theory and the example describe both equilibrium and non-equilibrium chemical reactions.     

Diffusion-induced instability in chemically reacting systems: Steady-state multiplicity,oscillation, and chaos

The dynamical behavior of two coupled cells or reactors is described. The cells are coupled by diffusion, e.g., through a semipermeable membrane, and the chemical reactions and initial or feed concentrations of all species are the same in the two cells. Each cell has only a single stable steady state in the absence of coupling, and the coupled system may exhibit multiple steady states, periodic oscillation, or chaos. The attractors of the coupled system may be either homogeneous (the two cells have equal concentrations) or inhomogeneous. Three two-variable kinetic models are examined: the Brusselator, a model of the chlorine dioxide-iodine-malonic acid reaction, and the Degn-Harrison model. The dynamical behavior of the coupled system is determined by the nonlinearities in the uncoupled subsystems and by two ratios, that of the diffusion constants of the two species and that of the area of the membrane to the product of the membrane thickness and the volume of a cell.     

Growth of discontinuities in chemically reacting relativistic fluids

A relativistic theory is developed to study the growth of weak discontinuities propagating in a chemically reacting fluid mixture. The velocity of propagation is determined, which fully agrees with classical results in the nonrelativistic limit. The growth equation for the wave propagation in relativistic fluid flows with nonequilibrium effects is obtained and solved. The wave amplitude is determined as a function of time. The relativistic and relaxation effects on the global behavior of the wave amplitude are studied analytically. It is concluded that if the wave is of a compressive nature and its initial amplitude is greater than a critical value, then the discontinuity grows until it develops into a shock wave after a finite critical timet _c . But on the other hand if the initial wave amplitude is less than the critical one, the wave decays and damps out ultimately. It is shown that both relativistic and relaxation effects help in stabilizing the wave propagation by increasing the critical timet _c for the breakdown of the wave due to nonlinear steepening.     

The propagation of an ion sound wave in the presence of a large neutral background

The case is taken of an ion wave in a single component weakly ionised plasma. Collisional effects on the ions are also included.     

A high-order low-Mach number AMR construction for chemically reacting flows

A high-order projection scheme was developed for the study of chemically reacting flows in the low-Mach number limit. The numerical approach for the momentum transport uses a combination of cell-centered/cell-averaged discretizations to achieve a fourth order formulation for the pressure projection algorithm. This scheme is coupled with a second order in time operator-split stiff approach for the species and energy equations. The code employs a fourth order, block-structured, adaptive mesh refinement approach to address the challenges posed by the large spectrum of spatial scales encountered in reacting flow computations. Results for advection–diffusion-reaction configurations are used to illustrate the performance of the numerical construction.     

Finite elastic coupling effects in critical sound propagation in dilute Ising systems

The nonasymptotic critical properties of sound propagation induced by finite spin-strain coupling are studied in dilute Ising model aboveT _c by means of renormalization group methods and expansion. It is shown that effective hydrodynamic sound attenuation exponent is lower in compressible systems than in the almost rigid ones. Scaling functions for sound attenuation and dispersion are obtained in the crossover region to the first order.     

A thermodynamic framework for thermo-chemo-elastic interactions in chemically active materials

In this paper, a general thermodynamic framework is developed to describe the thermo-chemo-mechanical interactions in elastic solids undergoing mechanical deformation, imbibition of diffusive chemical species, chemical reactions and heat exchanges. Fully coupled constitutive relations and evolving laws for irreversible fluxes are provided based on entropy imbalance and stoichiometry that governs reactions. The framework manifests itself with a special feature that the change of Helmholtz free energy is attributed to separate contributions of the diffusion-swelling process and chemical reaction-dilation process. Both the extent of reaction and the concentrations of diffusive species are taken as independent state variables, which describe the reaction-activated responses with underlying variation of microstructures and properties of a material in an explicit way. A specialized isothermal formulation for isotropic materials is proposed that can properly account for volumetric constraints from material incompressibility under chemo-mechanical loadings, in which inhomogeneous deformation is associated with reaction and diffusion under various kinetic time scales. This framework can be easily applied to model the transient volumetric swelling of a solid caused by imbibition of external chemical species and simultaneous chemical dilation arising from reactions between the diffusing species and the solid.     

Determination of equivalent sound speed profiles for ray tracing in near-ground sound propagation

The determination of appropriate sound speed profiles in the modeling of near-ground propagation using a ray tracing method is investigated using a ray tracing model which is capable of performing axisymmetric calculations of the sound field around an isolated source. Eigenrays are traced using an iterative procedure which integrates the trajectory equations for each ray launched from the source at a specific direction. The calculation of sound energy losses is made by introducing appropriate coefficients to the equations representing the effect of ground and atmospheric absorption and the interaction with the atmospheric turbulence. The model is validated against analytical and numerical predictions of other methodologies for simple cases, as well as against measurements for nonrefractive atmospheric environments. A systematic investigation for near-ground propagation in downward and upward refractive atmosphere is made using experimental data. Guidelines for the suitable simulation of the wind velocity profile are derived by correlating predictions with measurements.     

Long-range sound propagation in the northeastern Atlantic

Experimental data on the long-range propagation of explosion-generated signals are analyzed. The experiments were performed in the northeastern Atlantic under the conditions of a two-axis underwater sound channel. The sound field in the upper channel was governed by the vertical redistribution of the ray structure and sound energy under the influence of a smooth increase in the depth of the channel’s axis along the propagation path. The explosions were produced in the upper sound channel at a depth of 200 m, which was constant along the path. The time structure of the sound field is analyzed for the upper channel (a reception depth of 200 m) and for deeper layers lying somewhat below the boundary between the upper and lower sound channels (a reception depth of 1200 m). The deviation of the decay law obtained for the sound field level in the upper channel from the cylindrical law is used to estimate the attenuation coefficient. The low-frequency (several hundreds of hertz) attenuation coefficients experimentally determined with allowance for the sound field redistribution agree well with the calculated sound absorption in seawater. The attenuation coefficients determined by the differential method also agree well with the absorption calculated by the formulas proposed earlier. The analysis of the time structure of the sound field near the boundary between the upper and lower channels reveals a permanent insonification of this horizon by weak water-path signals propagating with the velocity typical of the signals traveling in the upper channel.     

Long-range sound propagation in the Mediterranean Sea

The data of several experiments on the long-range propagation of explosion-generated and tonal sound signals are analyzed. The experiments are performed by the Acoustics Institute in the Mediterranean Sea with a fully developed sound channel. A substantial difference is observed for the propagation conditions in the western and eastern parts of the sea. This difference concerns the vertical sound speed profiles, the time structures of the sound field in the underwater sound channel, the duration of the explosion-generated signal, and the positions of the convergence zones. The experiment is compared with calculations. The observed difference in the experimental and calculated positions of the first convergence zone is explained by the imperfection of the relation used to recalculate the salinity, water temperature, and hydrostatic pressure to the sound speed. In spite of substantial difference in the propagation conditions on two 600-km paths, the experimental low-frequency attenuation coefficients on these paths (and on some shorter ones) agree well with each other for the frequency band of several kilohertz. The data are also close to those published for another 600-km path. All the paths mentioned run in different parts of the Mediterranean Sea. The frequency dependence of sound attenuation (absorption) can be well described by the relation that accounts for the absorption caused by the boron present in the sea water.     

Long-range sound propagation in the norwegian sea

The data of repeated experiments on the long-range propagation of explosion-generated and cw signals in the Norwegian Sea in summer conditions (with a fully-developed underwater sound channel) are presented. These data are used to analyze the spatial and time structures of the sound field, as well as to estimate the attenuation coefficient at frequencies within 63–630 Hz and to determine its frequency dependence. The spatial variability of the propagation conditions is analyzed on the basis of the experimental data obtained for the propagation of explosion-generated signals along a 815-km-long path crossing the Norwegian and Lofoten Hollows.     

Study of mass consistency LES/FDF techniques for chemically reacting flows

A hybrid large eddy simulation/filtered density function (LES/FDF) approach is used for studying chemically reacting flows with detailed chemistry. In particular, techniques utilised for ensuring a mass consistent coupling between LES and FDF are discussed. The purpose of these techniques is to maintain a correct spatial distribution of the computational particles representing specified amounts of fluid. A particular mass consistency technique due to Y.Z. Zhang and D.C. Haworth (A general mass consistency algorithm for hybrid particle/finite-volume PDF methods, J. Comput. Phys. 194 (2004), pp. 156–193) and their associated algorithms are implemented in a pressure-based computational fluid dynamics code suitable for the simulation of variable density flows, representative of those encountered in actual combustion applications. To assess the effectiveness of the referenced technique for enforcing LES/FDF mass consistency, two- and three-dimensional simulations of a temporal mixing layer using detailed and reduced chemistry mechanisms are carried out. The parametric analysis performed focuses on determining the influence on the level of mass consistency errors of parameters such as the initial number of particles per cell and the initial density ratio of the mixing layers. Particular emphasis is put on the computational burden that represents the use of such a mass consistency technique. The results show the suitability of this type of technique for ensuring the mass consistency required when utilising hybrid LES/FDF approaches. The level of agreement of the computed results with experimental data is also illustrated.     

Acoustic propagation in the subsurface sound channel

Experimental data obtained in the kilohertz frequency band for the sound propagation in the subsurface channel formed by the wind-caused mixing of subsurface waters are discussed. The data were obtained in different years in the northeastern region of the Atlantic Ocean, where the subsurface waters down to the depths of 40–70 m are mixed by both wind waves and the swell that arrives from distant ocean areas. The hydrological conditions in the subsurface waters of this region are characterized by a good reproducibility. The spatial structure of the sound field and the attenuation of sound propagating in the subsurface channel are analyzed. The origin of the additional attenuation (in comparison with the absorption in sea water) is discussed. The data of our experiments are compared with those obtained by other experimenters and with the calculations performed using the computer code by Avilov. The necessity of improving the computer codes to allow for the scattering of sound beyond the channel under the influence of the swell, whose parameters are unrelated to the wind regime at the experimental site, is emphasized.     

Fluctuating hydrodynamic equations of mixed and of chemically reacting gases

The method of the nonlinear Langevin equation is generalized to ordinary mixed and to chemically reacting gases. The stochastic Boltzmann equations of these gases, the fluctuating hydrodynamic equations of mixed gases, and the Langevin equations for the number density of each component of a reaction-diffusion system are obtained.This work was supported financially by the Alexander von Humboldt Foundation. The main part of the paper was written during the author's stay at the Max-Planck Institut für Festkörperforschung (Stuttgart) as a Humboldt fellow.