Combustion of liquid fuel inside inert porous media: an analytical approach

This paper presents a numerical analysis of combustion of liquid fuel droplets suspended in air inside an inert porous media. A one-dimensional heat transfer model has been developed assuming complete vaporization of oil droplets prior to their entry into the flame. The effects of absorption coefficient, emissivity of medium, flame position on radiative energy output efficiency and optimum oil droplet size at the entry, defined as the maximum size for complete vaporization before entering the combustion zone, have been presented. The inert porous medium with low absorption coefficient will produce high downstream radiative output with large oil droplet sizes.     

Modeling of a conceptual self-sustained liquid fuel vaporization – combustion system with radiative output using inert porous media

The present model is based on a combined self-sustained liquid fuel vaporization – combustion system, where the liquid fuel vaporization occurs on a wetted wall plate with energy transferred through the plate from the combustion of vaporized oil. The vaporization energy has been derived through the radiative interaction of the vaporizing plate and an upstream end surface of the porous medium. The inert porous medium, used in the flow passage of combustion gas, is allowed to emit and absorb radiant energy. The radiative heat flux equations for the porous medium have been derived using the two-flux gray approximation. The work analyzes the effect of emissivities of vaporizing plate and porous medium, the optical thickness of medium and equivalence ratio on the kerosene vaporization rate, combustion temperature and radiative output of the system. Combination of low and high emissivities of vaporizing plate and porous medium respectively with low optical thickness of medium makes the system operable over a wide range of power. The study covers the data concerning the design and operating characteristics of a practical system.     

Combustion of suspended fine solid fuel in air inside inert porous medium: A heat transfer analysis

Present work is a numerical analysis of combustion of submicron carbon particles inside an inert porous medium where the particles in form of suspension in air enter the porous medium. A one-dimensional heat transfer model has been developed using the two-flux gray radiation approximation for radiative heat flux equations. The effects of absorption coefficient, emissivity of medium, flame position and reaction enthalpy flux on radiative energy output efficiency have been presented. It is revealed that in porous medium the combustion of suspended carbon particles is similar to premixed single phase gaseous fuel combustion except the former has shorter preheating temperature zone length. Use of porous ceramic having high porosity and made of Al₂O₃ or ZrO₂ with stabilized flame position operated nearer to downstream end will ensure radiative output maximum and minimum at downstream and upstream end, respectively.     

Entropy production analysis of swirling diffusion combustion processes

A critical factor in the design of combustion systems for optimum fuel economy and emission performance lies in adequately predicting thermodynamic irreversibilities associated with transport and chemical processes. The objective of this study is to map these irreversibilities in terms of entropy production for methane combustion. The numerical solution of the combustion process is conducted with the help of a Fluent 6.1.22 computer code, and the volumetric entropy production rate due to chemical reaction, viscous dissipation, and mass and heat transfer are calculated as post-processed quantities with the computed data of the reaction rates, fluid velocity, temperature and radiative intensity. This paper shows that radiative heat transfer, which is an important source of entropy production, cannot be omitted for combustion systems. The study is extended by conducting a parametric investigation to include the effects of wall emissivity, optical thickness, swirl number, and Boltzmann number on entropy production. Global entropy production rates decrease with the increase in swirl velocity, wall emissivity and optical thickness. Introducing swirling air into the combustion system and operations with the appropriate Boltzmann number reduces the irreversibility affected regions and improves energy utilization efficiency.     

Entropy production analysis of swirling diffusion combustion processes

A critical factor in the design of combustion systems for optimum fuel economy and emission performance lies in adequately predicting thermodynamic irreversibilities associated with transport and chemical processes. The objective of this study is to map these irreversibilities in terms of entropy production for methane combustion. The numerical solution of the combustion process is conducted with the help of a Fluent 6.1.22 computer code, and the volumetric entropy production rate due to chemical reaction, viscous dissipation, and mass and heat transfer are calculated as post-processed quantities with the computed data of the reaction rates, fluid velocity, temperature and radiative intensity. This paper shows that radiative heat transfer, which is an important source of entropy production, cannot be omitted for combustion systems. The study is extended by conducting a parametric investigation to include the effects of wall emissivity, optical thickness, swirl number, and Boltzmann number on entropy production. Global entropy production rates decrease with the increase in swirl velocity, wall emissivity and optical thickness. Introducing swirling air into the combustion system and operations with the appropriate Boltzmann number reduces the irreversibility affected regions and improves energy utilization efficiency.     

A Numerical and Experimental Investigation of Performance of a Nonsprayed Porous Burner

The performance of a nonsprayed porous burner (NSPB) is investigated through both numerical and experimental studies. The major requirement of liquid fuel combustion systems is excellent fuel vaporization, which is accomplished by using porous medium. Instead of heterogeneous combustion, which occurs in free space of a conventional sprayed burner, a homogeneous combustion of vaporized kerosene and air takes place within a porous medium. The liquid kerosene is preheated and completely vaporized in the first porous medium before being mixed with preheated air in the mixing chamber (i.e., a small space between two porous media). Then the combustion occurs in the second porous medium. A subcooled boiling, single global reaction combustion, and local nonthermal equilibrium between fluid and solid phases with phase change under complex radiative heat transfer are considered. The model accuracy is validated by the experimental data before parametric study—that is, equivalence ratio and firing rate are performed. Result show that a self-sustaining evaporation without atomization and matrix-stabilized flame can be achieved in the NSPB by providing the radiant output efficiency in the same range as a conventional premixed gaseous porous burner. This indicates that the NSPB is one possible technology to replace conventional spray burners for future requirements.     

Radiative heat transfer in porous media with spatially-dependent heat generation

We report an investigation of radiative heat transfer in porous radiant burners. The combustion was modeled as a spatially-dependent heat generation. Using the spherical harmonics to solve the equation of transfer, we have obtained the P-11 solution for the net radiative heat flux. Results presented illustrate the radiant output as a function of the position of the combustion zone, the optical thickness and the type of scattering of the porous layer, and the amount of reflection from the distribution chamber.     

Multimode heat transfer in cyclic flow reversal combustion in a porous medium

Experimental and numerical studies of combustion and multimode heat transfer in a porous medium, with and without a cyclic flow reversal of a mixture through a porous medium, were performed. Parametric studies were done in order to understand combustion characteristics such as maximum flame temperature and radiative heat flux using a one‐ dimensional conduction, convection, radiation and premixed flame model. The porous medium was assumed to emit and absorb radiant energy, while scattering is ignored. Non‐local thermodynamic equilibrium between the solid an d gas is taken into account by introducing separate energy equations for the gas and the solid phase. As a prelimina ry study, the combustion regime was described by a one‐step global mechanism with an internal heat source uniformly dist ributed along the reaction zone. The effects of the flame position, cyclic flow reversal, period of the cyclic flow rever sal, the optical thickness and the flow velocity on the burner performance were clarified by a rigorous radiation analysis. Th e model was validated by comparing the theoretical results with the experiments. It was shown that, for maximizing the fl ame temperature and the net radiative heat flux feedback, the flame should be stabilized near the centre of the po rous medium with a cyclic flow reversal, the period of which should be as small as possible. A high optical thickness prod uced a high flame temperature and a high net radiative feedback. Also, a high flow velocity at low period of the cyclic f low reversal of mixture yielded a high value of both the flame temperature and the net radiative feedback. Thermal structure predictions in terms of the gas‐phase and the solid‐phase temperature distributions along the axis of the combustor show good agreement with the experimental ones. Copyright © 1999 John Wiley & Sons, Ltd.     

A universal model of opposed flow combustion of solid fuel over an inert porous medium

In this study, a universal model is developed to examine the behavior of combustion wave observed in porous solid matters (e.g., smoldering, self-propagating high-temperature synthesis (SHS), diesel particulate filter (DPF) regeneration process). Analytical expressions of the combustion characters of solid combustible (e.g., diesel particulate matters trapped in a DPF) deposited over an inert porous medium are obtained employing large activation energy asymptotic taking into account the sensible transport processes; namely, heat transfer between the porous medium and gas phases, radiation heat transfer from the porous medium, heat loss from the porous medium to the environment, mass transfer of oxygen from the gas stream to the surface of solid fuel and the effective diffusion in modeling the species diffusion. Then it has been validated that the present model is applicable and adaptable for predicting the characteristics of smoldering combustion and thus SHS process. As a result, the features of combustion wave of the present phenomena would be useful to other processes. From practical point of view and for deep understanding of the behavior of combustion wave of these processes, we investigate the effects of various physical parameters over a wide range of conditions. We observe that the moving speed of the reaction front increases with the increase of porosity of the porous medium, mass transfer coefficient and initial fuel mass fraction; while it decreases owing to the increase of heat transfer rate from the porous medium to the gas, heat loss to the environment and radiative heat transfer. Furthermore, the results reveal that extinction tends to occur due to lower porosity of the porous medium, higher radiative heat transfer from the porous medium, higher heat transfer rate from the porous medium to the gas and higher heat losses from the porous medium to the environment. Even the observed near-extinction behavior in reaction front speed versus heat loss diagram is found to be similar what we got in gaseous premixed flame propagating through the porous medium. An extinction limit diagram has been presented as a function of radiation-conduction parameter and the gas flow velocity. In addition to, the impact of radiation and the combined effect of the inclusion of Knudsen diffusion and tortuosity are demonstrated in terms of the spatial temperature and species profiles to examine how these two parameters modify the reaction front structure. Furthermore, the governing equations have been solved numerically and it is observed that asymptotic analysis gives a good agreement with the numerical solution.     

Asymptotic structure of planar nonadiabatic reverse combustion fronts in porous media

A leading-order analytic analysis of the structure of a planar nonadiabatic reverse combustion (RC) front in a combustible porous medium has been performed by use of matched asymptotic expansions in the activation energy of the combusion reaction. The model considers the irreversible reaction of oxygen in a feed gas flow with an excess of a single-component gaseous fuel devolatilized from the medium, according to one-step, first-order kinetics characterized by a large activation energy. A heat loss term linear in the local temperature difference and an infinite effective Lewis number are assumed for this two-phase combustion process. The analysis determines conditions for the extinction of the steady RC front in terms of the heat loss strength and oxidant flux, and shows the existence of two solutions for heat losses below the extinction value. The predicted dependence of the steady front velocity and temperature on the heat loss intensity agree qualitatively with experimental observations.     

Modeling the role of microstructural parameters in radiative heat transfer through disordered fibrous media

Understanding the influence of microstructural parameters on the rate of heat transfer through a disordered fibrous medium is important for the design and development of heat insulation materials. In this work, by generating virtual 3-D geometries that resemble the internal microstructure of fibrous insulation materials, we simulated the influence of diameter, orientation, and emissivity of the fibers, as well as the media’s porosity and thickness on the radiative heat transmittance. Our simulations are based on a Monte Carlo ray tracing algorithm that we have developed for studying radiative heat flow in 3-D disordered media. The media were assumed to be made up of cylindrical opaque fibers with specular surface. The advantage of our modeling approach is that it does not require any empirical input values, and can directly be used to isolate and study the role of individual microstructural parameters of the media. The major limitation of the model is that it is accurate as long as the fibers can be considered large relative to the wavelength of the incoming rays. Our results indicate that heat flux through a fibrous medium decreases by increasing the packing fraction of the fibers when the thickness and fiber diameter are kept constant. Increasing the fibers’ absorptivity (or emissivity) was observed to decrease the radiation transmittance through the media. Our simulations also revealed that for constant porosity and thickness, the heat flux transmitted across the medium can be reduced by using finer fibers. The steady state temperature profiles across the thicknesses of media with different properties were obtained and found to be independent of the fibers’ emissivity.     

Solution of radiative transfer in a one‐dimensional anisotropic scattering media with different boundary conditions using the DRESOR method

The DRESOR method was applied to analyze the radiative transfer process in anisotropic scattering media with different boundary conditions in this paper. The method was validated by the integral formulation of the radiative transfer equation at first. Some variation regulations about the emissivity were obtained by extensive numerical simulations. When the optical thickness of the media became very large, the emissivity converged to a constant value. The converged emissivity in the forward scattering medium was the largest and that for the backward scattering medium was the smallest. Also the converged emissivity was associated with the scattering albedo of the media. The greater the scattering albedo was, the smaller the converged emissivity was. When the scattering albedo decreased to zero the converged emissivity reached the blackbody emissivity at the same temperature. Furthermore, different boundary conditions were considered. The results showed that if the temperature of the medium and the boundary was equal, the intensity at boundary was the same as that for the blackbody emission at the same temperature, whether the boundary reflectivity was 1.0 or not. When the temperature of the boundary was lower than that of the medium, the boundary emissivity can reach 1.0 only if ρ=1.0. Finally, the radiation flux was studied with different phase functions and different boundary conditions. © 2008 Wiley Periodicals, Inc. Heat Trans Asian Res, 37(3): 138–152, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20198     

Combustion of methane in catalytic honeycomb monolith burners

The heat transfer efficiency, stability, and pollutant emissions characteristics of ultra‐lean methane–air combustion in some precious metal‐based honeycomb monoliths were investigated. The interpretation of the experimental results was assisted using numerical modelling of the gas‐phase combustion process. The thermal radiation output of the monoliths varied between 27 and 30 per cent of the thermal input, and this compared favourably with equivalent porous inert media burners. The minimum fuel concentrations for very‐low emission stable combustion were found to be significantly lower than for conventional gas‐phase combustion and were shown to vary with the nature and loading of the catalyst, as well as with flow rates. The palladium catalyst was found to have a larger window of mixture strengths and flow rates for stable operation than the platinum one. During all the runs under stable combustion conditions, only extremely small amounts of CO, NO_x and unburnt hydrocarbons were detected. Thus, the operating conditions verified ‘near‐zero’ pollutant emissions that only a catalytic combustion process can achieve at present. Temperature profiles inside the monoliths channels proved that the catalyst's role was not only to enable the ignition of fuel mixtures below flammability limits, but also to ensure the complete oxidation of the fuel to CO₂ via surface reactions in the steady state. The reaction zone inside the catalysts was found to end at about 10 mm from the monolith's entrance. The effect of monolith length was investigated and a reduction of 70 per cent in the original length was found possible. Copyright © 2000 John Wiley & Sons, Ltd.     

Numerical modelling of a three-zone combustion for heavy fuel oil in inert porous media reactor

Numerical model for heavy fuel oil and air mixtures combustion is presented to simulate the behavior of the fuel in an inert porous medium reactor for hydrogen production. Three-zone combustion of oil and petroleum cokes separated by temperature ranges starting from ambient temperature to 560 K, from 560 K to 673 K, and above 673 K, is presented. Hydrogen production is achieved using water gas shift equilibrium reaction on the combustion products at different temperatures. Results show a high enthalpy contribution due to coke combustion formed in the low temperature oxidation reaction, being the most important reaction in relation to its zone size. Simulations increasing filtration velocity (from 0.05 to 0.9 m/s) has a favorable effect on the maximum temperature and the combustion front velocity. The effect of the simplified combustion model lowers computational time, with acceptable results for temperature as well as hydrogen production in contrast to laboratory tests and other software simulation such as COMSOL Multiphysics.     

A theoretical analysis of the extinction limits of a methane-air opposed-jet diffusion flame

A theoretical analysis is described for a methane-air diffusion flame stabilized in the forward stagnation region of a porous metal cylinder in a forced convective flow. The analysis includes effects of radiative heat loss from the porous metal surface and finite rate kinetics but neglects the effects of gravity. The theoretically predicted extinction limits compare well with experimentally observed extinction limits from the literature.After the predicted limits compared well with the experimental limits, a parametric study of the effect of fuel surface emissivity and Lewis number was conducted with the numerical model. It was found that the computed blowoff limit is independent of radiative heat loss for high fuel blowing velocities but is a strong function of Lewis number. At low fuel blowing velocities, the extinction limit varies with both radiative heat loss and Lewis number. It is discovered, however, that even if thermal losses from the fuel surface are absent, the flame can extinguish at the fuel surface independently of Lewis number due to excessive reaction zone thinning.     

Radiative heat transfer in a participating medium with specular–diffuse surfaces

The results obtained by ray-tracing method can be regarded as benchmarks for its good accuracy. However, up to now, this method can be only used to solve radiative transfer within medium confined between two specular surfaces or two diffuse surfaces. This article proposes a hybrid ray-tracing method to solve the radiative transfer inside a plane-parallel absorbing–emitting–scattering medium with one specular surface and another diffuse surface (S–D surfaces). By the hybrid ray-tracing method, radiative transfer coefficients (RTCs) for S–D surfaces are deduced. Both surfaces of the medium under consideration are considered to be semitransparent or opaque. This paper examines the effects of scattering albedo, opaque surface emissivity and anisotropically scattering on steady-state heat flux and transient temperature fields. From the results it is found that the effects of anisotropic scattering is more for a bigger optical thickness medium; and keeping other optical parameters unchanged, anisotropic scattering affects transient temperature distributions so much in a small refractive index medium.     

TRANSIENT CONDUCTION AND RADIATION HEAT TRANSFER WITH VARIABLE THERMAL CONDUCTIVITY

The effect of variable thermal conductivity on transient conduction and radiation heat transfer in a planar medium is investigated. Thermal conductivity of the medium is assumed to vary linearly with temperature, while the other thermophysical properties and the optical properties are assumed constant. The radiative transfer equation is solved using the discrete transfer method, (DTM) and the nonlinear energy equation is solved using an implicit scheme. Transient as well as steady state results are found for an absorbing, emitting, and anisotropically scattering gray medium. Thermal conductivity has been found to have significant effects on both transient as well as steady state temperature and heat flux distributions. Some steady state results are compared with the results reported in the literature.     

Generalized radiative transfer equation for porous medium upscaling: Application to the radiative Fourier law

Many porous media cannot be homogenized as Beerian semi-transparent media. Effective extinction, absorption and scattering coefficients can indeed have no physical meaning for small or intermediate optical thicknesses. A generalized radiative transfer equation (GRTE), directly based on the extinction cumulative distribution function, the absorption and scattering cumulative probabilities and the scattering phase function is established for this optical thickness range. It can be solved by a statistical Monte Carlo approach. For a phase of a porous medium that is optically thick at local scale, the GRTE degenerates into a classical Beerian RTE. In these conditions, a radiative conductivity tensor is directly obtained, by a perturbation method, and expressed with the radiative coefficients of this RTE and temperature. As illustrations, exhaustive radiative conductivity results are given for a set of overlapping transparent spheres within an opaque phase and for opaque rod bundles.     

Application of the Conservative Discrete Transfer Radiation Method to a Furnace with Complex Geometry

ABSTRACT

A conservative form of the discrete transfer radiation method (DTRM) has been applied in a computational fluid dynamics (CFD) simulation of the radiative heat transfer in an experimental furnace with complex geometry. The furnace was operated under nonpremixed conditions, burning preheated heavy fuel oil. For combustion simulation a semiempiric oil combustion model has been applied, while for the flow field resolution an unstructured CFD code has been used. The simulation results are compared with available experimental data, showing acceptable level of prediction accuracy. The conservative DTRM formulation is shown to be superior to the original formulation in this particular case.