M. El Hafi

Benchmark numerical solutions for radiative heat transfer in two-dimensional axisymmetric enclosures with nongray sooting media

Accurate numerical solutions for radiative heat transfer in two-dimensional axisymmetric black enclosures with nongray sooting media have been obtained using three different methods. The ray tracing method together with the statistical narrow-band model is used to obtain highly accurate solutions for benchmark purposes. The Monte Carlo method using a net exchange formulation and the statistical narrow-band correlated k -distribution method also yield very accurate solutions, in excellent agreement with the ray tracing results. The discrete ordinates method combined with the correlated k -distribution method provides less accurate, but more economical, solutions, which are adequate for most practical applications. The solution accuracy of the methods is investigated and demonstrated, and results suitable for benchmarking are given in tabular form.

A net-exchange Monte Carlo approach to radiation in optically thick systems

A Monte Carlo approach to radiative transfer in participating media is described and tested. It solves to a large extent the well known problem of Monte Carlo simulation of optically thick absorption configurations. The approach which is based on a net-exchange formulation and on adapted optical path sampling procedures is carefully designed to insure satisfactory convergence for all types of optical thicknesses. The need for such adapted algorithms is mainly related to the problem of gaseous line spectra representation in which extremely large ranges of optical thicknesses may be simultaneously encountered. The algorithm is tested against various band average computations for simple geometries using the Malkmus statistical narrow band model.

Monte Carlo method and sensitivity estimations

It is shown that, starting from any existing Monte Carlo algorithm for estimation of a physical quantity A, it is possible to implement a simple additional procedure that simultaneously estimates the sensitivity of A to any problem parameter. The corresponding supplementary cost is very low as no additional random sampling is required. The principle is presented on a formal basis and simple radiative transfer examples are used for illustration.

Numerical investigation of the effect of soot aggregation on the radiative properties in the infrared region and radiative heat transfer

Abstract The effect of aggregation on soot radiative properties in the infrared region of the spectrum is numerically investigated using Rayleigh–Debye–Gans theory for fractal aggregates (RDG-FA). In order to use the RDG-FA theory for a wide range of aggregate sizes and wavelengths, the predicted phase functions, scattering and absorption coefficients are compared with a more accurate theory, the integral equation formulation for scattering—IEFS. The importance of scattering when compared with absorption is investigated, as well as the effect of aggregation on the phase function shape and on the scattering cross section. It is concluded that in the case of small aggregates formed with small primary particles the scattering coefficient is negligible compared with the absorption coefficient, and scattering and aggregation of primary particles can be ignored. Thus, the Rayleigh approximation can be used leading to isotropic scattering. In the case of large aggregates constituted by large primary particles, aggregation becomes important and the scattering cross section is of the same order of magnitude of the absorption cross section. Moreover, the phase function becomes highly peaked in the forward direction. Therefore, the Rayleigh and the equivalent volume Mie sphere approximations are not valid, and the RDG-FA method emerges as a good compromise between accuracy and simplicity of application. However, radiative transfer calculations between two infinite, parallel, black walls show that scattering may always be neglected in the calculation of total radiative heat source and heat fluxes to the walls. The minor influence of scattering on the accuracy of the predictions is explained by the shift between the spectral region where scattering is important and the region where the spectral radiative heat source is large.

ACCURATE SOLUTIONS FOR RADIATIVE HEAT TRANSFER IN TWO-DIMENSIONAL AXISYMMETRIC ENCLOSURES WITH GAS RADIATION AND REFLECTIVE SURFACES

ABSTRACT Accurate solutions for benchmarking purposes in two-dimensional axisymmetric enclosures with reflective surfaces have been obtained using the Monte Carlo method (MCM) based on the net exchange formulation (NEF). Previous applications of the MCM-NEF have been restricted to multidimensional problems with black boundaries or one-dimensional problems with gray boundaries. Here, the extension to multidimensional enclosures with gray boundaries is presented. The medium is a mixture of H2O, CO2, N2, and soot at atmospheric pressure, and its radiative properties are computed using the correlated k -distribution method. Predictions obtained using the discrete ordinates method are included, showing good agreement with the benchmark MCM/NEF solutions.

Monte Carlo Sensitivity Calculations Applied to Radiative Transfer-Combustion Coupling

In several applications such as meteorology or combustion, it is difficult to consider detailed radiative transfer modeling because of the high computing cost due to the numerous coupled physical phenomena such as fluid mechanics, heat transfer and chemistry. The aim of this work is to present an attempt to couple a highly accurate radiative transfer model to an advanced combustion code. This approach is based on a recently identified specific feature of Monte Carlo Methods. They provide not only the radiative source field but also its sensitivities to temperatures and concentrations with no additional random procedure. To illustrate this approach, a coupled simulation applied to a 1-D counterflow flame is presented.Copyright

Assessment of the Single-Mixture Gas Assumption for the Correlated K-Distribution Fictitious Gas Method in H2O–CO2–CO Mixture at High Temperature

This paper deals with the comparison of spectral narrow band models based on the correlated-K (CK) approach in the specific area of remote sensing of plume signatures. The CK models chosen may or may not include the fictitious gas (FG) idea and the single-mixture-gas assumption (SMG). The accuracy of the CK and the CK-SMG as well as the CKFG and CKFG-SMG models are compared, and the influence of the SMG assumption is inferred. The errors induced by each model are compared in a sensitivity study involving the plume thickness and the atmospheric path length as parameters. This study is conducted in two remote-sensing situations with different absolute pressures at sea level (105Pa) and at high altitude (16.6km, 104Pa). The comparisons are done on the basis of the error obtained for the integrated intensity while leaving a line of sight that is computed in three common spectral bands: 2000–2500cm−1, 3450–3850cm−1, and 3850–4150cm−1. In most situations, the SMG assumption induces negligible differences. Furthermore, compared to the CKFG model, the CKFG-SMG model results in a reduction of the computational time by a factor of 2.