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This article considers the application of flame emission models used for predicting the thermal radiation fluxes from flames and fires within a computational fluid dynamic framework, used in conjunction with the discrete transfer method. The flame emission models differ in their generality, sophistication, accuracy and computational cost, and are assessed in terms of their ability to predict radiation transfer in idealised situations, as well as flames in tubes representative of burner systems, laboratory-scale jet flames and wind-blown jet fires. It is concluded that the implementation of simple flame emission models, based on the grey gas assumption, must be treated with caution due to convergence problems. The key problem occurs when the grey absorption coefficient is based on a length scale linked to the size of the control volume. This issue is well known in the radiation modelling community, but not so in the combustion modelling community. Use of models based on the banded mixed grey gas, TTNH, wide and narrow band approaches yield satisfactory results for all the simulated flames and fires considered, typically being within 20% of the measured radiation heat flux.

The mathematical modelling of high temperature processes requires an ability to predict the thermal radiation fields with confidence. The fundamental quantity of interest, the spectral intensity, depends in a complex way on the temperature and participating species distributions. This, together with the fact that the spectral intensity is a function of location, orientation and wavelength, makes the simulation of combusting flows a challenging scientific computation. Even with today’s computer hardware and the routine use of parallel computing facilities choices have to be made regarding the balance between the levels of sophistication of the radiation model relative to other sub-models that form the composite flame or fire model. In this article a number of radiation models are evaluated with respect to their accuracy and suitability to be combined with a computational fluid dynamic (CFD) model for simulating a number of idealised and generic flows. Example areas of application are as part of mathematical models used in the safety analysis of high-pressure plant and pollution control in heating plant. The safe design and operation of high-pressure plant and pipe work requires that provision be made for the relief of pressure under certain operational and emergency conditions. The consequences of a release must also be evaluated so that appropriate safety measures can be adopted during the relief process. In addition, assessments of the consequences associated with accidental releases of flammable material are required as the basis of safety reports and risk assessments on existing and proposed installations. For flammable gases and vapours it is necessary to be able to predict the thermal radiation fluxes that any fire might impose on its surroundings—either by direct flame impingement of the fire on an item of plant or at distance from the fire by radiation transmitted through the atmosphere. This information is in turn used to provide estimates, for example, of vessel survival times, building burning distances and escape times for personnel. In addition to the safety analysis of fires, increasing concerns over the environmental impact of heating plant such as boilers and furnaces requires that the energy balance during their operation is evaluated accurately. Insight into the energy transfer processes of heating plant is necessary to ensure that the temperature sensitive reaction rates relevant to pollution production, such as NOx and SOx, can be estimated. In this way it is possible to predict pollution concentrations such that they can be assessed and minimised by good design. Radiation heat transfer in fires and flame tubes differs significantly in a number of ways. For the natural gas combustion processes considered in the present work, the thermal radiation field in a jet fire, for example, is highly anisotropic with significant levels of radiation in discrete spectral windows determined by the emitting species present in the combustion products and fuel. In an enclosed flame such as that present in a flame tube the radiation field is more isotropic and if significant levels of soot are present then the spectral radiation has a more continuous distribution in wave number space. However, for both types of flame a number of modelling issues are common, such as the flame structure used as input to the radiation model. Predictions of the structure of fires using either integral [1] or numerical [2] techniques require that some representation be made of the absorption and emission characteristics of the products of combustion to allow solution of the radiation transfer equation. In particular, flame emission models are required for the gaseous species and unburned carbon particulates that occur within the fire. As an example, recent experimental and theoretical work [2] which considered a number of jet fires (up to 2.7 GW in size) stabilised on subsonic releases of natural gas demonstrated that the contribution from soot particles to total radiation fluxes measured about these fires was at most 40% and likely to be much less than this. In the case of sonic natural gas jet fires the residence time is sufficiently small for soot production to be significantly reduced as insufficient time is available for the particles of soot to form before being advected out of the high temperature region of the fire [3]. The visible flame envelope for sonic natural gas jet fires has a bluish colour, suggesting that the contribution of emissions from soot particles to the total radiation flux is insignificant. This article considers the application of a number of flame emission models to predict the radiation fluxes from jet fires and within flame tubes. Each flame emission model is applied in conjunction with the discrete transfer method [4] for solving the equation of radiation transfer where appropriate or a discretisation of the radiation heat transfer equation in its integral form. All implementations use a numerical quadrature to evaluate the incident radiation flux integral and in that respect they are similar to the discrete transfer method. The discrete transfer method has been adopted due to its frequent use in fire modelling codes, as well as its computational economy, ease of implementation and conceptual simplicity [4], although in its original form there are issues relating to the accuracy of the radiation source field [5]. However, some of the conclusions drawn are independent of the radiation solution algorithm implemented and can therefore be considered equally relevant to the discrete-ordinates method, the finite-volume method and the Monte Carlo method, and these issues will be considered further in later sections. The flame emission models considered differ in their generality, sophistication, accuracy and computational cost, and are each assessed in terms of their ability to predict radiation transfer from one-dimensional idealised representations of the internal structure of non-premixed flames, as well as from laboratory and field-scale jet fires and flame tube simulations. Of particular interest is the accuracy and computational cost of the various modelling approaches and their suitability for application in combination with a CFD model to predict the flow fields. The present work considers the appropriate choice of flame emission model to achieve the optimum balance between model accuracy and computational cost. An additional interest is how the degree of in-homogeneity and soot level influences a flame emission model’s accuracy and generality. Whilst this might be expected to be the case, the question of quantification remains.

Comparing the performance of the flame emission models for the jet flames/fires and the flame tube simulation, broadly speaking the speed-up characteristics are consistent and any differences are associated with the different finite-volume meshes used. In previous comparisons of the wide band model and the narrow band model, typically the wide band model is shown to be an order of magnitude faster with predictions of integrated intensity, and hence radiation flux, within 10% of the narrow band prediction. The disappointing speed-up of the wide band model is due to its use of an expression for the spectral transmissivity rather than the grey band assumption implemented by Edwards, necessary for use in a CFD framework. This means the spectral intensity distribution must be evaluated using a numerical quadrature rather than a relatively simple evaluation of a piecewise constant spectral distribution. This problem could be partially resolved by implementing the adaptive quadrature technique used successfully by Cumber [40] and [42] to evaluate the incident flux integral. Another factor is that the ray trace is included in the run-time of both models, tending to reduce the speed-up factor for the wide band model. One conclusion from this study is the implementation of simple participating media models within the discrete transfer method, based on the assumption of grey gas behaviour is not appropriate for non-homogeneous systems as radiation fluxes predicted using this approach do not converge as the representation of a non-homogeneous path is refined. In general, the banded grey gas, TTNH, wide and narrow band models yield satisfactory results for flame and fire applications, with an adequate level of agreement between the various models, and with experimental data. This article highlights the significant overhead of the ray trace used in the discrete transfer method, and in particular how the type of finite-volume mesh employed to represent the flame structure modifies the run-time of any radiation model implemented. For computations of fires obtained in conjunction with Cartesian meshes, the TTNH and banded grey gas models give speed-up factors, respectively, of one and two orders of magnitude relative to the wide and narrow band approaches. The performance of all models relative to the narrow band approach is, however, dramatically reduced when more complex, non-Cartesian meshes are employed. Results for the idealised test case indicate that only a relatively small number of homogeneous cells are required by some models to represent a non-homogeneous profile. This suggests that radiation calculations for fires, depending on the flame emission model, could be performed on meshes that are coarser than those generally used for the fluid dynamic computations. Use of the wide band model should be treated with some caution due to the large number of control volumes required to give converged results. This situation can be improved with some thought given to the computer implementation of the model in the context of a CFD framework, or through use of wide band scaling techniques. However, wide band-scaling techniques are likely to introduce a significant computational overhead even though fewer control volumes may be required to achieve finite-volume mesh independent predictions.