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This paper presents a numerical modeling study of one ethanol spray flame from the Delft Spray-in-Hot-Coflow (DSHC) database, which has been used to study Moderate or Intense Low-oxygen Dilution (MILD) combustion of liquid fuels (Correia Rodrigues et al. Combust. Flame 162, 759-773, 2015). A "Lagrangian-Lagrangian" approach is adopted where both the joint velocity-scalar Probability Density Function (PDF) for the continuous phase and the joint PDF of droplet properties are modeled and solved. The evolution of the gas phase composition is described by a Flamelet Generated Manifold (FGM) and the interaction by exchange with the mean (IEM) micro-mixing model. Effects of finite conductivity on droplet heating and evaporation are accounted for. The inlet boundary conditions starting in the dilute spray region are obtained from the available experimental data together with the results of a calculation of the spray including the dense region using ANSYS Fluent 15. A method is developed to determine a good estimation for the initial droplet temperature. The inclusion of the "1/3" rule for droplet evaporation and dispersion models is shown to be very important. The current modeling approach is capable of accurately predicting main properties, including mean velocity, droplet mean diameter and number density. The gas temperature is under-predicted in the region where the enthalpy loss due to droplet evaporation is important. The flame structure analysis reveals the existence of two heat release regions, respectively having the characteristics of a premixed and a diffusion flame. The experimental and modeled temperature PDFs are compared, highlighting the capabilities and limitations of the proposed model.

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Elsevier Naud, B.; Novella Rosa, R.; Pastor Enguídanos, JM.; Winklinger, JF. (2015). RANS modelling of a lifted H2/N2 flame using an unsteady flamelet progress variable approach with presumed PDF. Combustion and Flame. 162 (4) AbstractAn unsteady flamelet / progress variable (UFPV) approach is used to model a lifted H 2 /N 2 flame in a RANS framework together with presumed PDF. We solve the unsteady flamelets both in physical space and in mixture fraction space. We show that in the former case, the scalar dissipation rate profile strongly varies in time (while it is assumed to be fixed in time in the latter). However, this does not result in significant qualitative differences in the corresponding flamelet libraries. The progress variable is carefully defined, including both the main combustion product (H 2 O) and a key radical species in ignition process (HO 2 ). The presumed-PDF model is proposed in terms of the non-normalised progress variable, without assuming its statistical independence with mixture fraction. We introduce a modelled transport equation for the mean progress variable which is consistent with the basic underlying UFPV assumption, derived from the Lagrangian flamelet model. The influence of different model parameters on the results for the mean temperature and mean species mass fractions and their fluctuations is discussed. Good results are obtained for the conditions of the considered lifted flame where detailed experimental data is available. However, at low coflow temperature the modelled flame lift-off height is shorter than expected.

Abstract.A numerical investigation of a bluff-body stabilised nonpremixed flame, and the corresponding nonreacting flow, has been performed with differential Reynolds-stress models (DRSMs). The equilibrium chemistry model is employed and an assumed-shape beta function PDF approach is used to represent the interaction between turbulence and chemistry. The Reynolds flux of the mixture fraction is obtained from a transport equation, hence a full second moment closure is used. To clarify the applicability of the existing DRSMs in this complex flame, several models, including LRR-IP model, JM model, SSG model as well as a modified LRR-IP model, have been applied and evaluated. The existing models, with default values of the coefficients, cannot provide overall satisfactory predictions for this challenging test case. The standard LRR-IP model over predicts the centreline velocity decay rate, and therefore does not perform satisfactory. The modified LRR-IP model, with model constant C 1 = 1.6 instead of the standard value 1.44 (here named BM-M1), gives better results for the mean velocity. However in the nonreacting case this does not lead to improvement in predicting rms fluctuating velocities especially downstream of the recirculation zone. Motivated by the need to improve the prediction, a new modification of the LRR-IP model is proposed (BM-M2), with model constant C 2 = 0.7 in the pressure strain correlation rather than the standard value 0.6. With the new modified model, a very significant improvement of the prediction of flow field is obtained in the nonreacting case, whereas in the reacting case the prediction of the flow field is of the same overall quality as with BM-M1. This shows that some DRSMs have different behaviour in the nonreacting case and the reacting case. In the reacting case also the mean and variance of mixture fraction are considered and it is found that the best results are obtained with the BM-M1 model, with SSG as second best. Combining the results for flow field and mixture fraction field it is concluded that the BM-M1 model is recommended for further studies of this bluff-body stabilised flame. Grid independence of the result is demonstrated.

Abstract. Numerical simulation results are presented for 'Delft Flame III', a piloted jet diffusion flame with strong turbulence-chemistry interaction. While pilot flames emerge from 12 separate holes in the experiments, the simulations are performed on a rectangular grid, under the assumption of axisymmetry. In the first part of the paper, flow and mixing field results are presented with a non-linear first order k-ε model, with the transport equation for ε based on a modeled enstrophy transport equation, for cold and reactive flows. For the latter, the turbulence model is applied in combination with pre-assumed β-PDF modeling for the turbulence-chemistry interaction. The mixture fraction serves as conserved scalar. Two chemistry models are considered: chemical equilibrium and a steady laminar flamelet model. The importance of the turbulence model is highlighted. The influence of the chemistry model is noticeable too. A procedure is described to construct appropriate inlet boundary conditions. Still, the generation of accurate inlet boundary conditions is shown to be far less important, their effect being local, close to the nozzle exit. In the second part of the paper, results are presented with the transported scalar PDF approach as turbulencechemistry interaction model. A C 1 skeletal scheme serves as chemistry model, while the EMST method is applied as micro-mixing model. For the transported PDF simulations, the model for the pilot flames, as an energy source term in the mean enthalpy transport equation, is important with respect to the accuracy of the flow field predictions. It is explained that the strong influence on the flow and mixing field is through the turbulent shear stress force in the region, close to the nozzle exit.

In the context of transported joint velocity-scalar probability density function methods, the correspondence between Generalised Langevin Models (GLM) for Lagrangian particle velocity evolution and Eulerian Reynolds-stress turbulence models has been established in the 1990's by S.B. Pope. It was shown that the GLM representation of a given Reynolds stress model is not unique. It was also shown that a given GLM together with a given mixing model for particle composition evolution implies a differential scalar-flux model. In this paper, we study how extra constraints can be applied on the choice of the GLM coefficients in order to imply a chosen scalar-flux model. This correspondence between GLM-implied and standard scalar-flux models is based on the linear relaxation term and on the mean velocity gradient contributions in the rapid term. In general, GLM-implied models possibly involve more terms (including anisotropy effects in the scalar-flux decay rate and some high-order terms in the rapid-pressure-scrambling term). The proposed form of the GLM supposes a non-constant value for the diffusion coefficient C0, originally identified as a Kolmogorov constant. Here, the value of C0 is determined in order to yield the Monin model for linear relaxation of the scalar-flux, and the constant in the rapid-pressure contribution is related to the choice of the parameter β in the GLM. We finally show how GLM-implied scalar-flux models are in general dependent on the choice of the mixing model and how the proposed GLM can reduce this dependency. These developments are illustrated by results obtained from calculations of the Sydney bluff-body stabilised flame HM1.Response to Reviewers: First of all, we would like to thank the reviewers for their comments which helped to improve the paper. #1We included all the suggestions of Reviewer #1. About remark 5: we used the more general formalism introduced by Wouters [REF. 4] that allows to deal with variable density flows, and with Reynoldsstress models that include cubic terms (we added a remark in the text after Equation (27) at the beginning of Section 4.1). #2The remarks of Reviewer #2 allowed us to distinguish more clearly in the text two aspects: 1. setting the C_0 value depending on the Monin linear relaxation term and 2. removing the effect of the mixing model as much as possible. This lead to some modifications of the text. The modification of β in order to be in agreement with Launder's model for the rapid-pressure-scrambling term is indeed pragmatic. We added some clarifications on this aspect on page 12 in the paragraph "Rapid-pressure-scrambling term". About the "philosophical questions" raised by the reviewer, here are some remarks on the modification of C_0 in order to lead the Monin linear return to isotropy (the main contribution of this paper). As mentioned by the reviewer "the scalar field is dynamically passive". With Taylor's hypothesis, we see the relation between the Monin constant and the GLM coefficient C_0. As discussed in the paper, there is no re...