Numerical investigation of combustion with non-gray thermal radiation and soot formation effect in a liquid rocket engine

A numerical analysis was carried out in order to investigate the combustion and heat transfer characteristics in a liquid rocket engine in terms of non-gray thermal radiation and soot formation. Governing gas and droplet phase equations with PSIC model, turbulent combustion model with liquid kerosene fuel, soot formation, and non-gray thermal radiative equations are introduced. A radiation model was implemented in a compressible flow solver in order to investigate the effects of thermal radiation. The finite-volume method (FVM) was employed to solve the radiative transfer equation, and the weighted-sum-of-gray-gases model (WSGGM) was applied to model the radiation effect by a mixture of non-gray gases and gray soot particulates. After confirming the two-phase combustion behavior with soot distribution, the effects of the O/F ratio, wall temperature, and wall emissivity on the wall heat flux were investigated. It was found that the effects of soot formation and radiation are significant; as the O/F ratio increases, the wall temperature decreases. In addition, as the wall emissivity increases, the radiative heat flux on the wall increases.     

Combined non-gray radiative and conductive heat transfer in solar collector glass cover

A rigorous approach for the radiative heat transfer analysis in solar collector glazing is developed. The model allows a more accurate prediction of thermal performance of a solar collector system. The glass material is analysed as a non-gray plane-parallel medium subjected to solar and thermal irradiations in the one-dimensional case using the Radiation Element Method by Ray Emission Model (REM by REM).This method is used to analyse the combined non-gray convective, conductive and radiative heat transfer in glass medium. The boundary surfaces of the glass are specular. The spectral dependence of the relevant radiation properties of glass (i.e. specular reflectivity, refraction angle and absorption coefficient) are taken into consideration. Both collimated and diffuse incident irradiation are applied at the boundary surfaces using the spectral solar model proposed by Bird and Riordan. The optical constants of a commercial ordinary clear glass material have been used. These optical constants (100 values) of real and imaginary parts of the complex refractive index of the glass material cover the range of interest for calculating the solar and thermal radiative heat transfer through the solar collector glass cover. The model allows the calculation of the steady-state heat flux and temperature distribution within the glass layer. The effect of both conduction and radiation in the heat transfer process is examined. It has been shown that the real and imaginary parts of the complex refractive index have a substantial effect on the layer temperature distribution. The computational time for predicting the combined heat transfer in such a system is very long for the non-gray case with 100 values of n and k. Therefore, a simplified non-gray model with 10 values of n and k and two semi-gray models have been proposed for rapid computations. A comparison of the proposed models with the reference non-gray case is presented. The result shows that 10 bandwidths could be used for rapid computation with a very high level of accuracy.     

Mixed Convection and Non-Gray Radiation in a Horizontal Rectangular Duct

Numerical studies for fluid flow and heat transfer in a horizontal rectangular duct are carried out. The flow is considered to be laminar, hydrodynamically and thermally developing. Heat transfer by both forced and natural convection is taken into account. The radiation from the gas is modeled with weighted sum of gray gases (WSGG) model. While considering non-gray radiation with WSGG, the fluid is considered to be a mixture of CO₂ and H₂O. Simulations are carried out with lower wall temperature than the inlet temperature of the gas. The effect of buoyancy and radiation on bulk mean temperature and Nusselt number are studied. The effects of temperature dependent properties are discussed. Comparative studies are carried out among forced convection, mixed convection, gray and non-gray gas radiation. It is found from the simulations that the assumption of gray gas can produce an error of ±10% over a non-gray model with WSGG for the cases studied.     

Radiative and conductive transfer for a real gas in a cylindrical enclosure with gray walls

The purpose of this study is to examine the interaction of radiative and conductive transfer for a radiatively participating real gas stagnant in a cylindrical enclosure with gray diffuse walls. Consideration of reflecting boundaries represents an extension of previous black wall studies. Examination of radiative transfer was made by the zone method with gas radiative properties furnished by the weighted sum of gray gases model. Directed flux areas are expressed as the weighted sum of gray gas total exchange areas which are evaluated using the matrix formulation method from direct exchange areas. Axial and radial gas temperatures are examined along with wall heat flux or temperature for respective cases of either specified wall temperatures or heat fluxes. Emphasis is placed on examining results to show the effects of wall emittance and duct diameter. Results for heat generation within the gas are also presented.     

Theoretical approach of a flat-plate solar collector taking into account the absorption and emission within glass cover layer

A rigorous theoretical approach of a flat-plate solar collector with a black absorber considering the glass cover as an absorbing–emitting media is presented. The glass material is analyzed as a non-gray plane-parallel medium subjected to solar and thermal irradiations in one-dimensional case using the Radiation Element Method by Ray Emission Model (REM²). The optical constants of a clear glass window proposed by Rubin have been used. These optical constants, 160 values of real part n and imaginary part k of the complex refractive index of a clear glass, cover the range of interest for calculating the solar and thermal radiative transfer through the glass cover. The computational time for predicting the thermal behavior of solar collector was found to be prohibitively long for the non-gray calculation using 160 values of n and k. Therefore a suitable semi-gray model is proposed for rapid calculation. The profile of the efficiency curve obtained in the present study was found to be not linear in shape. Indeed, the heat loss from the collector is a combination of convection and radiation and highly non linear. The effect of the outside convective heat transfer on the efficiency curve is also studied. In fact, when the convection is the dominant heat transfer mode compared with the radiation one, the profile of the efficiency curve is more or less straight line. Consequently, the heat loss coefficient could be calculated using Klein model. It has been also shown that the effect of the wind speed on the glass cover mean temperature is very important. This effect increases with the increase of the mean absorber temperature.     

Inverse Boundary Design Problems in Enclosures With Non-Gray Media

In this work, the inverse analysis is applied to radiative heat transfer boundary design problems with non-gray media. The objective of the inverse problem is to find the power of the heaters on the heater surface that produces the desired output, that is, temperature and heat flux distribution over the design surface. The inverse problem is formulated as an optimization problem for minimization of an objective function, which is defined by the sum of the squared difference between estimated and desired heat flux distributions over the design surface. The non-gray optimization problem is solved using the conjugate gradient method, which is a gradient-based optimization method. The spectral line weighted-sum-of-gray-gases model (SLW) is used to account for non-gray gas radiation properties. The radiative transfer equation is solved by the discrete ordinates method combined with two models for simulation of non-gray media. Enclosures with diffuse and gray walls are considered. Radiation is assumed the dominant mode of heat transfer. Example problems including homogeneous/nonhomogeneous, isothermal/nonisothermal media are considered. The results obtained using the SLW model and the gray model are compared.     

Transient thermal analysis of semitransparent composite layer with an opaque boundary

Transient coupled radiative and conductive heat transfer in a two-layer, absorbing, emitting, and isotropically scattering non-gray slab is investigated by the ray tracing method in combination with Hottel's zonal method. One outer boundary is opaque, and another is semitransparent. The radiative energy transfer process in a semitransparent composite is divided into two sub-processes, one of which considers scattering, the other does not. The radiative transfer coefficients of the composite are deduced under specular and diffuse reflection and combined specular and diffuse reflection, respectively. The radiative heat source term is calculated by the radiative transfer coefficients. Temperature and heat flux are obtained by using the full implicit control-volume method in combination with the spectral band model. The method presented here needs only to disperse the space position, instead of the solid angle. A comparison with previous results shows that the results are more accurate.     

Theoretical approach of a flat plate solar collector with clear and low-iron glass covers taking into account the spectral absorption and emission within glass covers layer

Accurate modeling of solar collector system using a rigorous radiative model is applied for the glass cover which represents the most important component of the system and greatly affects the thermal performance. The glass material is analyzed as a non-gray plane-parallel medium subjected to solar and thermal irradiations in one dimensional case using the radiation element method by ray emission model (REM²). The optical constants of a clear and low-iron glass materials proposed by Rubin have been used. These optical constants, 160 values of real part n and imaginary part k of the complex refractive index of such materials, cover the range of interest for calculating the solar and thermal radiative transfer through the glass cover. The computational times for predicting the thermal behavior of solar collector were found to be prohibitively long for the non-gray calculation using 160 values of n and k for both glasses. Therefore, suitable semi-gray models have been proposed for rapid calculation. The temperature distribution within the glass cover shows a good agreement with that obtained with iterative method in case of clear glass. It has been shown that the effect of the non-linearity of the radiative heat exchange between the black plate absorber and the surroundings on the shape of the efficiency curve is important. Indeed, the thermal loss coefficient is not constant but is a function of temperature, due primarily to the radiative transfer effects. Therefore, when the heat exchange by radiation is dominant compared with the convective mode, the profile of the efficiency curve is not linear. It has been also shown that the instantaneous efficiency of the solar collector is higher in case of low-iron glass cover.     

Reconstruction of Temperature Distribution in the Combustion Region of a Non-Gray Medium

Two-dimensional temperature distribution in the combustion region of a radiant furnace with non-gray gaseous products is reconstructed in an inverse manner. The discrete ordinate method is used to solve the radiative transfer equation, and the non-gray behavior of gaseous medium is modeled by the spectral line weighted sum of gray gas model. Conjugate gradient method is employed for the inverse analysis. The domain of interest is divided into two regions: the unknown- and known-temperature zones. The temperature distribution in the unknown-temperature zone, near the flame, is recovered in an inverse manner by the measurement of heat fluxes over the opposite walls in the direction of flame diffusion. Effects of the size of unknown-temperature zone, variable concentrations, and measurement errors in temperature reconstruction are discussed.     

Physico-chemical processes occurring inside a degrading two-dimensional anisotropic porous medium

A lumped-parameter kinetic model is applied to simulate the pyrolysis of lignocellulosic particles, exposed to a high temperature environment. Physical processes account for radiative, conductive and convective heat transport, diffusion and convection of volatile species and pressure and velocity variations across a two-dimensional (2-D) , anisotropic, variable property medium. The dynamics of particle degradation are found to be strongly affected by the grain structure of the solid. A comparison is made between the total heat transferred to the virgin solid (conduction minus convection) along and across the grain. Notwithstanding the lower thermal conductivities, because of the concomitant slower convective transport (lower gas permeabilities) , the largest contribution is that across the solid grain. The role played by convective heat transport is successively less important as the particle size is increased. Finally, the 2-D and the widely applied one-dimensional (1-D) predictions are compared.     

A mathematical model of a solar chimney

A simple mathematical model of a solar chimney is proposed. The physical model is similar to the Trombe wall. One side of the chimney is provided with a glass cover which with the other three solid walls of the chimney form a channel through which the heated air could rise and flow by natural convection. Openings provided at the bottom and top of the chimney allow room air to enter and leave the channel. Steady state heat transfer equations were set up to determine the boundary temperatures at the surface of the glass cover, the rear solar heat absorbing wall and the air flow in the channel using a thermal resistance network. The equations were solved using a matrix-inversion solution procedure. The thermal performance of the solar chimney as determined from the glass, wall and air temperatures, air mass flow rate and instantaneous heat collection efficiency of the chimney are presented. Satisfactory correlation was obtained with experimental data from other investigators. Further experimental investigation is currently under way.     

Conjugate Heat Transfer Analysis in a Glazed Room Modeled as a Square Cavity

A numerical study of conjugate heat transfer by turbulent natural convection in a room with three different glazed configurations is presented. The room is modeled as a square closed cavity, where the lower wall is adiabatic, the right wall is semitransparent, and the upper and left walls are opaque conductive surfaces. Governing equations of mass, momentum, and energy were solved by the finite volume method with a two equation turbulence model. The results are presented in terms of streamlines, isotherms, heatlines, turbulent viscosity isolines, and thermal parameters, such as indoor temperatures and heat transfer coefficients. From the three cases considered in this study, the reflective glass window was the optimal configuration from the thermal comfort point of view for both design days. On the contrary, the glass-film configuration showed the worst indoor thermal performance inside the cavity despite of being the configuration that allows lower energy transferred into the room through the glazed surface. A set of useful heat transfer correlations are obtained for building design applications and energy codes in temperate climates.     

Numerical study on the importance of radiative heat transfer in building energy simulation

ABSTRACT

A neural network-based model for interior longwave radiative heat transfer has been developed and implemented into a new computer code, BERHT (Building Energy with Radiative Heat Transfer). The model accounts for the non-gray effect of absorbing species in a building environment and the geometric effect of a three-dimensional building structure. Numerical studies have been carried out on a rectangular single-story building. For nominal concentration of CO₂, H₂O, and small particulates, results show that the effect of radiative heat transfer is important. The surface emissivity of enclosure walls and optical properties of the absorbing/emitting medium are demonstrated to have significant effects on the distribution of heat transfer between convection and radiation, as well as the transient behavior of the indoor air temperature. Supplemental studies provide an insight that the one-zone, well-mixed model used in building energy simulation generates a “fictitious” non-local heat transfer behavior, leading to uncertainties in the understanding of the radiative heat transfer effect.     

A Universal Performance Chart for CPU Cooling Devices

This article deals with performance evaluation of the discrete ordinates method in terms of its capacity to provide accurate results in solving radiation mode problems with different complexities. The problem formulation is done keeping in view the heat transfer process in an evaporator used in a coal-based thermal power station. The hot gas mass in the evaporator is assumed to be a heat source with two different shapes, spherical and conical. The evaporator walls that are covered with a water cooling jacket are modeled with a convective boundary condition. The gas is assumed to be gray and absorbing–emitting. The solution of the radiative transport equation is carried out using the discrete ordinates method. Parametric studies are performed for a wide range of aspect ratio, extinction coefficient, and convective heat transfer coefficient. The code is validated by comparing the result of discrete ordinates method with the exact and the discrete transfer method for nonradiative as well as radiative equilibrium conditions.     

Entropy Generation due to Combined Natural Convection and Thermal Radiation within a Rectangular Enclosure

ABSTRACT

The present work investigates entropy production due to coupled natural convection/radiation heat transfer phenomenon in an inclined rectangular enclosure, isothermally heated from the bottom side and isothermally cooled from the other sides. The discrete-ordinate method is used in modeling the radiative transport equation while the statistical narrow band correlated-k model is adopted to deduce the radiative properties of the medium. The influence of pertinent parameters such as aspect ratio, inclination angle and walls emissivities on entropy generation is studied. It is found that the volumetric entropy generation is reduced when increasing the inclination angle of the enclosure. Moreover, it is shown that the minimum entropy production due to radiation heat transfer in participating media occurs at aspect ratio equal to unity.     

RAD-NNET,a neural network based correlation developed for a realistic simulation of the non-gray radiative heat transfer effect in three-dimensional gas-particle mixtures

A neural network correlation, RAD-NNET, is developed to simulate the realistic effect of non-gray radiative absorption by a homogeneous mixture of combustion gases (CO₂ and H₂O) and soot using numerical data generated by RADCAL. RAD-NNET is then applied to assess the accuracy of some commonly accepted approximate approaches to evaluate radiative heat transfer in three-dimensional non-gray media. Results show that there are significant errors associated with the current approximate approaches. RAD-NNET can be readily implemented in commercial CFD codes to greatly enhance the accuracy of simulation of radiative heat transfer in practical engineering systems.     

The lattice Boltzmann modeling on the nanofluid natural convective transport in a cavity filled with a porous foam

In this work, the natural convective transport was numerically investigated for nanofluids in a metal-foam cavity. A lattice Boltzmann (LB) model for the nanofluid natural convection in a porous medium was established by using the volume-averaging method. The velocity and temperature fields were obtained, and flow and thermal characteristics of the nanofluid convection in a porous medium were presented. The effects of the Rayleigh Number, the Darcy Number, the porosity, the solid thermal conductivity of porous medium, the nanoparticle thermal conductivity and the nanoparticle concentration on natural convection were examined. The average velocity was put forward to evaluate the convection effect and the natural convection onset was also discussed. It is shown that the Nusselt number of the natural convection increases with an increase in the Darcy number, the Rayleigh number, the porosity and the effective thermal conductivity. The change from the heat conduction regime to the convection regime is clearly shown from the numerical result, which verifies the onset point of the nanofluid natural convection in a porous medium. The highly conductive porous foam and the nanofluid can promote the thermal performance of the natural convection, which own great potential in practical thermal applications.     

Experimental results and a user-friendly model of heat transfer from a thin film resistance temperature detector

The research reported in this paper has focused on the different modes of heat transfer – conductive (to the substrate), conductive and convective (to the environment) and radiative (to the environment) – from an on-chip resistance temperature detector (RTD). The study has been carried out at various input voltages, various pressures ranging from atmospheric to vacuum, and for two classes of platforms for the device – thermal insulators (glass wool and ceramic), and a thermal conductor (aluminum block). The transient temperature–time response of the RTD under the various conditions stated above was recorded. A heat transfer model approximately accounting for all the modes of heat transfer was introduced. The calibration parameters of the model allowed us to quantify the different modes of heat transfer. The model uncovers the fact that the heat losses to the environment via conduction and convection are almost as much as the heat lost by radiation (radiative effects were unequivocally confirmed experimentally). Compared to these losses, conductive heat losses from the RTD to its underlying substructure are far more dominant (almost five times). We also give an analysis originating from the exact form of conservation of energy and demonstrate that the use of the simplified model has led to the most dominant heat transfer mode of conduction to the substrate being underestimated by no more than 7.89% (at the highest input power tested).     

Modeling the radiation of anisotropically scattering media by coupling Mie theory with finite volume method

A new mathematical model and code for radiative heat transfer of particulate media with anisotropic scattering for 2-D rectangular enclosure is developed. The model is based on the coupling of (i) finite volume method for the solution of radiative transfer equation with (ii) Mie equations for the evaluation of scattering phase function. It has not been done before to the authors’ best knowledge. The predictions were compared against the only found results, published 15 years ago. For those results the S-N discrete ordinates method for the solution of radiative transfer equation and the Legendre polynomials expansions for the evaluation of scattering phase function were used. The agreement between the results is very good. The advantages of new model and code are in their straight forward application to any given particles parameters without the need for previously designed analytical expression for scattering phase function. In addition, that analytical expression, with generated expansion coefficients, is restricted and can be used only for that particular case of particle parameters. The new model was applied to the solid particles of several various coals and of an ash and the series of 2-D predictions are performed. The effects of particle size parameter and of scattering albedo on radiative heat flux and on incident radiation were analyzed. It was found that the model developed is reliable and very accurate and thus suitable for extension towards: (i) 3-D geometries, (ii) mixtures of non-gray gases with particles as well as for (iii) incorporation in computational fluid dynamics codes.     

Entransy flux of thermal radiation and its application to enclosures with opaque surfaces

Entransy is a new concept developed in recent years to measure the transport ability of heat at a temperature in conduction and convection. This paper develops the concept of entransy flux for thermal radiation in enclosures with opaque surfaces. The entransy balance equation and entransy dissipation function are derived. The minimum principle of radiative entransy loss is developed. The potentials and the heat fluxes distribution which meet the Stefan–Boltzmann’s law and the energy balance equation would make the radiative entransy loss minimum if the net heat flux of each surface or the thermal potentials of the surfaces are given. The extremum entransy dissipation principles (EEDP) for thermal radiation are developed. The minimum radiative entransy dissipation leads to the minimum average radiative thermal potential difference for prescribed total heat exchange and the maximum radiative entransy dissipation leads to the maximum heat exchange for prescribed average radiative thermal potential difference. The minimum and maximum principle can be concluded into the minimum thermal resistance principle (MTRP) for thermal radiation by defining the thermal resistance with the entransy dissipation. The EEDP or MTRP is proved to be reliable when they are used to optimize some radiative heat transfer problems, and a comparison is made between the minimum principle of entropy generation and the EEDP.