Microsoft Word - 001.docx CHEMICAL ENGINEERINGTRANSACTIONS VOL. 66, 2018 A publication of The Italian Association of Chemical Engineering Online at www.aidic.it/cet Guest Editors:Songying Zhao, Yougang Sun, Ye Zhou Copyright © 2018, AIDIC Servizi S.r.l. ISBN978-88-95608-63-1; ISSN 2283-9216 Study in the Approach Prediction Ability of the Euler PDF Transport by Different Models of Turbulence Rouan Serik Habiba, Abdelhamid Bounifa,Mohamed Bouzita, Ahmed Amine Larbib a Faculté de Génie Mécanique, Université des Sciences et de la Technologie Mohamed Boudiaf d'Oran, BP. 1505 Oran El M’naouar, Oran 31000, Algeria b Unité de Recherche en Energies renouvelables en Milieu Saharien, URERMS, Centre de Développement des Energies Renouvelables, CDER 01000, Adrar, Alegria habib.rouanserik@univ-usto.dz The main objective of this study is the evaluation of the numerical capacity of the RANS-EPDF hybrid method, by comparing different turbulence models, with numerical simulations in a turbulent jet flame (hydrogen / air), using the method of Eulerian multi-environment transport to model the turbulence-chemistry interaction. And predict take-off height, flame ignition and extinction, as well as kinetic control of NOX species. The study was applied with three turbulence models, the modified k-ε, k-ε and the RSM. Numerical results are compared and discussed with experimental data. It was concluded that predictions of the modified k-ε model are more credible than other turbulence models and favor more impact on the optimization of computational methods. 1. Introduction For the numerical study of a turbulent diffusion flame of H2 injected into a flow of air preheated to the temperature of 1045K; we used the RANS-PDFT hybrid method (Muradoglu et al., 2001). The approach presented is based on the use of reduced kinetic schemes in order to limit the cost of calculation by unnecessarily avoiding the transport of reaction intermediates and to improve the numerical stability during the integration of the transport equations of the species. Over the last decade, Haworth (2010) has attracted a lot of attention by developing the probability density function in turbulent reactive flows. The goal of RANS-PDFT Hybrid was to consider the appropriate chemistry for any burning regime. Specifically, all terms characterized in a variable were defined by the average rate of chemical reaction. According to research carried out on this RANS-PDFT approach, there are two methods to solve its equations: the Lagrangian method (LPDF) and the multi-environment method with the Eulerian method (MEPDF). Numerous studies on the Lagrangian method have been conducted (Cabra et al., 2005; Cao et al., 2005) use a configuration of hybrid RANS–LPDF for studying lifted flames as well as the problem of auto-ignition in a vitiated coflow. Cao (2005) performed a sensitivity study in a turbulent flame of lifted vitiated coflow on different mixing constant (1.5,2.0,2.5) and by applying the three mixing models (IEM, EMST, MC) using LPDF concluded that lift-off height is largely unaffected to the mixing parameters. On the other hand, OH production is influenced by the three mixing models as the EMI model is more accurate than EMST and MC. (Senouci et al., 2013) used this method by comparing different mixing models (MC, EMI and EMST) to highlight the effect of the mixing model. A few publications to study the resolution of equations of the PDFT have appeared in recent years on the MEPDF. Fox suggest the hypothesis of devlopper the method (MEPDF) presumed in a turbulent reaction flow. Tang et al. (2007) by a numerical study uses the method of the moments in direct quadrature (DQMOM) with finite rates of chemistry, tested on a modeling of stabilized bluff-body flames; found that the PDF model accurately predicted. this type of flames. Yadav et al. (2014) used this method of MEPDF in two lifted diffusion flames of H2/N2 and CH4/air injected in vitiated coflow for numerical search introduced between different values of mixing constant and he found a good adequacy with experimental data. Another study by Yadav et al. (2013) uses the same approach for the non-gray radiation simulation with using WSGG method demonstrated that the prompt of a steady flame for lower estimations (Cphi=2). On the other side, LPDF approach found that an estimation of (Cphi=2) prompts global extinction, the estimation of (Cphi=3) prompts most precise outcomes DOI: 10.3303/CET1866069 Please cite this article as: Habib R.S., Bounif A., Bouzit M., Larbi A.A., 2018, Study in the approach prediction ability of the euler pdf transport by different models of turbulence, Chemical Engineering Transactions, 66, 409-414 DOI:10.3303/CET1866069 409 mailto:habib.rouanserik@univ-usto.dz (Yadav et al., 2013). Dongre et al. (2014) studied two different burners imitating Moderate and Intense Low Oxygen Dilution MILD by multi environment PDF and showed that the difference in the predictions for higher Re number is expanded and that is principally because of the errors in the turbulence model and wrong reaction of the micro-mixing term. Conduct a comparative study between the two Eulerian/Lagrangian methods in a hydrogen flame, and find insufficient results because of the weakness of the reaction mechanism of H2 .Another comparative investigation by Jaishree et al. (2012) use The same comparison and demonstrated that the lagrangian model is much more accurate than eulerian. In this article, the hybrid RANS- EPDF approach is presented. The Eulerian method is otherwise called the multi-environment or just Eulerian method that is determined and developed. in a turbulent reactive flow. Although the accuracy of the Eulerian PDF approach model has been well developed during in recent years, there are nevertheless still areas of research to be developed in parallel improving the accuracy of prediction of the zones of the flames by the EPDF model with the evolution of the numerical performances of the various models of turbulence, in particular in the prediction of major phenomena such as that the detachment, extinction and ignition of the flame (Larbi et al., 2018). It is for this purpose that this work is devoted. 2. Theoretical Formulation of Eulerian PDF transport method (EPDF) The complex phenomena of turbulent combustion are mainly governed by the Navier-Stokes equations and the transport equations of the majority chemical species, associated with a fast chemistry where the reaction rate is very high. all the variables are modeled by the diffusion gradient or by the average rate of reaction, with an invariable expression of its nonlinear function; For that, the modeling of the combustion must necessarily imply the resolution of the purely linear equations based on simplifying hypotheses. 𝜕 𝜕𝑡 (𝜌𝑝) + 𝜕 𝜕𝑥𝑖 (𝜌𝑢𝑖𝑝) + 𝜕 𝜕𝜓𝑘 (𝜌𝑆𝑘𝑝) = 𝜕 𝜕𝑥𝑖 [𝜌⟨𝑢𝑖 "|𝜓⟩𝑃] + 𝜕 𝜕𝜓𝑘 [𝜌 ⟨ 1 𝜌 𝜌𝑗𝑖,𝑘 𝜕𝑥𝑖 |𝜓⟩ 𝑃] (1) Equation (1) shows the equation of the transport PDF composition, it is not a closure problem, it is the main advantage of the PDFT equation that does not require modelling. The turbulent scalar flow in the first term of the equation is modeled by the term gradient - diffusion (2). − 𝜕 𝜕𝑥𝑖 [𝜌⟨𝑢𝑖 "|𝜓⟩𝑝] = 𝜕 𝜕𝑥𝑖 ( 𝜌𝜇𝑡 𝑆𝑐𝑡 𝜕𝑝 𝜕𝑥𝑖 ) (2) For the resolution there are two methods to close the second term of the PDF transport equation (1), multi- environment eulerian (MEPDF) method or lagrangian method (LPDF) based on the stochastic method of monte-carlo.(Larbi et al., 2018) shows in the table1 a comparison between the two methods LPDF and MEPDF. EPDF it is an associated approach between the composition space and the physical space. The composition space is defined by a smaller number of interactive environments by coexistence in the physical space. p(ψ; x⃑ , t) = ∑ pn( Ne n=1 x⃑ , t) ∏ δ [ψK −< ϕK >n (x⃑ , t)] Ns k=1 (3) So; The IEM will model the micro-mixture, and the diffusion gradient will model the turbulent scalar in the transport equation for a multi-dimensional associated composition space PDF, the MEPDF will take off from this equation with the closures of the terms in eq. (3), but there are still unknown terms. 𝜕𝜌𝑝𝑛 𝜕𝑡 + 𝜕 𝜕𝑥𝑖 (𝜌𝑢𝑖𝑝𝑛) = ∇(𝜌Γ∇𝑝𝑛) (4) 𝜕𝜌𝑠𝑘,𝑛 𝜕𝑡 + 𝜕 𝜕𝑥𝑖 (𝜌𝑢𝑖𝑠𝑘,𝑛) = ∇(𝜌Γ∇𝑠𝑘,𝑛)+ 𝜌(𝑀𝑘,𝑛 + 𝑆𝑘,𝑛 + 𝐶𝑘,𝑛) (5) FOX (2005) proposes the DQMOM model (direct quadrature method of moments) as a method of effective resolution to this problem. This proposal will allow the resolution of unknown terms,pn and <ɸk>n. in equation (3) the DQMOM approach, is used to present the resulting equations of MEDF in eq.(4) and (5), when Sk,n describe the reaction, Mk,n is the mixing and Ck,n is terms of correction 𝑆𝑘,𝑛 = 𝑝𝑛𝑆(< ϕK >n)𝑘 (6) 𝑀𝑘,𝑛 = 𝐶ϕ 𝜏 (< ϕK >n− ψK) (7) ∑ ϕK𝑛 𝑚𝑘−1𝑁𝑒 𝑛=1 𝐶𝑘,𝑛 = ∑ (𝑚𝑘 − 1 𝑁𝑒 𝑛=1 ) < ϕK >𝑛 𝑚𝑘−2 𝑝𝑛𝑐𝑘,𝑛 (8) 3. Turbulence modeling The approach used for numerical modeling of turbulent combustion is the Reynolds Means Techniques (RANS) for the purpose of predicting the behavior of the mean values of the reacting flow properties. 410 3.1 Standard K-ԑ model Launder and splanding propose this model as a simpler and faster reference in the computation, based on the resolution of the turbulent length and the scalar time. This model is a first-order model based on the concept of turbulent viscosity introduced by Boussinesq. 𝜕 𝜕𝑡 (𝜌𝑘) + 𝜕 𝜕𝑥𝑖 (𝜌𝑘𝑢𝑖) = 𝜕 𝜕𝑥𝑗 [(𝜇 + 𝜇𝑡 𝜎𝑘 ) 𝜕𝑘 𝜕𝑥𝑗 ] + 𝐺𝑘 + 𝐺𝑏 − 𝜌ԑ − 𝑌𝑀 + 𝑆𝑘 (9) 𝜕 𝜕𝑡 (𝜌ԑ) + 𝜕 𝜕𝑥𝑖 (𝜌ԑ𝑢𝑖) = 𝜕 𝜕𝑥𝑗 [(𝜇 + 𝜇𝑡 𝜎ԑ ) 𝜕ԑ 𝜕𝑥𝑗 ] + 𝐺1ԑ ԑ 𝑘 (𝐺𝑘 + 𝐺3ԑ𝐺𝑏) − 𝐶2ԑ𝜌 ԑ2 𝑘 + 𝑆𝑘 (10) This model is obtained by the derivation of a global equation of energies and transport, defined by the two terms turbulent kinetic energy k; and its dissipation rate called ԑ. Obtained from the two equations (9 and 10). 𝜇𝑡 = 𝜌𝐶𝜇 𝑘2 ԑ (11) The term Gb represents the turbulence production due to buoyancy. The term Gk represents the kinetic energy of turbulence generated by the average velocity gradients. The turbulence model kε has five constants to cite. For k on the nondimensional number called turbulent Schmidt number σ_k and 𝜎𝑘. For the term ε there is Cε1 (dissipation production), Cε2 (dissipation of the energy dissipation) and 𝐶𝜇 in the expression of the turbulent viscosity which appears in equation 11. 3.2 RSM model The Reynolds stress model is a second-order RANS turbulence model that has been designed for accurate predictions of complex flows. The closure of this model is performed by solving the Reynolds constraints and the dissipation rate equation. So here are the transport equations for the RSM model. 𝜕 𝜕𝑡 (�̅�𝑢𝑖 "𝑢𝑗 "̅̅ ̅̅ ̅̅ ) + 𝜕 𝜕𝑥𝑘 (�̅�𝑢�̃�𝑢𝑖 "𝑢𝑗 "̅̅ ̅̅ ̅̅ ) = 𝐷𝑖𝑗 𝑇 + 𝐷𝑖𝑗 𝐿 − 𝑃𝑖𝑗 − 𝐺𝑖𝑗 + 𝜑𝑖𝑗 − ԑ𝑖𝑗 (12) A simplified linear equation is used to model turbulent diffusion in the form of a scalar as follows: 𝐷𝑖𝑗 𝑇 = 𝜕 𝜕𝑥𝑘 ( 𝜇𝑡 𝜎𝑘 𝜕𝑢𝑖 "𝑢𝑗 "̅̅ ̅̅ ̅̅ 𝜕𝑥𝑘 ) (13) To model the term 𝜑𝑖𝑗 we break down it as follows: 𝜑𝑖𝑗 = 𝜑𝑖𝑗,1 + 𝜑𝑖𝑗,2 (14) 𝜑𝑖𝑗,1 This term is known as: slow pressure-strain, and this term 𝜑𝑖𝑗,2 is known as rapid pressure constraint 𝜑𝑖𝑗,1 = −𝐶1�̅� ԑ̃ �̃� [𝑢𝑖 "𝑢𝑗 "̅̅ ̅̅ ̅̅ − 2 3 𝛿𝑖𝑗 �̃�] (15) 𝜑𝑖𝑗,2 = −𝐶2 [(𝑃𝑖𝑗 + 𝐹𝑖𝑗 + 𝐺𝑖𝑗 − 𝐶𝑖𝑗) − 2 3 𝛿𝑖𝑗(𝑃 + 𝐺 − 𝐶)] (16) and the dissipation rate in (Ional et al. 1989). ԑ𝑖𝑗 = 2 3 𝛿𝑖𝑗�̅�ԑ̃ (17) 4. Turbulent flame of (hydrogen/air) Figure1: Burner schematic and computational field of calculation of Flame In this simulation Hydrogen flames chosen were experimentally studied by Cabra et al. (2005). The burner consists of a horizontal tube with an internal diameter of 4.57mm and an outside diameter of 6.35mm, centered in a cross-section with an internal diameter of 210 mm (Fig.1). In computational domain shown above contains fuel flow, pilot co-flow, surrounding air; with a mesh grid of 25440 cells in fine-1. To validate our choice of mesh a study of independence is proposed with three different meshes: base with 18220 cells and fine-2 with 35320 cells (Cabra et al., 2005; Larbi et al., 2018). 411 Table 2: The different entry conditions of H2 /Air Parameters Re D(mm) V(m/s) T(k) XH2 XO2 XN2 H2 (Jet) 23,600 4,57 107 305 0,2537 0,0021 0,7427 Air(Co-flow) 18,600 210 3.5 1045 0.0005 0,15 0,75 This configuration has an axisymmetric geometry, using ANSYS Fluent 15.0 as the calculation code. The refinement of the mesh in the areas close to the outlet of the ejection nozzle was considered to take into account the various phenomena due to the premixing and contact of the reagents. The mesh has been realized with the software Gambit 15.0. the method used in this calculation is the EPDF with a mixing constant of 1.8 using the ISAT approach as a tabulation method (Larbi et al., 2018). The reaction mechanism chosen is GRI-Mech2.1. Table 2 gives us the different entry conditions. 5. Results and discussion The study of the turbulent (H2/Air) flame; using the Eulerian Transport PDF approach, with a hot coflow that is nessaisaire for the stabilization of this flame. It should be noted that the quality of numerical simulation of turbulent diffusion flames depends essentially on the performance of the selected turbulence model. For it, three different turbulence models were used for this study. The first is the standard k-ε model; the RSM is the second model. The last is the modified k-ε that we modify in these constants and parameters. 5.1. GRID-Independent study 0,0 0,1 0,2 0,3 0,4 0,5 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 D e n si ty X/D fine-2 fine-1 base 0,0 0,1 0,2 0,3 0,4 0,5 0 20 40 60 80 100 120 140 V e lo ci ty X/D fine-2 fine-1 base Figure 2: Axial evolution of density and velocity for approach of MEPDF We show here the effect of the mesh, with a comparison of the axial evolution of density and velocity along the central axis of the flame for the EPDF approach. The two graphs compare the evolution of the velocity and density profiles for each mesh which are in refinement level difference for more precision (Base, Fine, Fine). Each plot shows three profiles for meshes 1, 2 and 3. Mesh 2 shows in both profiles slight differences from 5.2. Flame of hydrogen in a hot vitiated Co-flow 0 20 40 60 80 100 200 400 600 800 1000 1200 1400 1600 T e m p e ra tu re X/D EXP KEmd RSM KE 0 20 40 60 80 100 0,0000 0,0002 0,0004 0,0006 0,0008 0,0010 0,0012 O H m a ss f ra ct io n X/D EXP KEmd RSM KE 0 20 40 60 80 100 0,000 0,005 0,010 0,015 0,020 0,025 H 2 m a ss f ra ct io n X/D EXP KEmd RSM KE Figure 5: Axial profiles of temperature, and species mass fractions for different turbulence models Figure 5 shows the axial evolution of the temperature profiles and the mass fractions of the species (OH, H2) along the flame jet. According to the figure, the area of calculation is divided into three zones, the first one where (X/D<10) is the mixing and preheating zone and the point of (X/D=10) represents the beginning of the production of 'chemical species. Subsequently (10