Comparisons of LPDF and MEPDF for lifted H2/N2 jet flame in a vitiated coflow

Comparisons of LPDF and MEPDF for lifted H2/N2 jet flame in a vitiated coflow

Ahmed A. LarbiAbdelhamid Bounif Mohamed Bouzit 

Faculté de Génie Mécanique, Université des Sciences et de la Technologie Mohamed Boudiaf d'Oran, BP. 1505 Oran El M’naouar, 31000 Oran, Algeria

Unité de Recherche en Energies renouvelables en Milieu Saharien, URERMS, Centre de Développement des Energies Renouvelables, CDER 01000, Adrar, Alegria

Institut des Sciences et de la Technologie, Centre Universitaire Ahemd Zabana -Relizane, Bourmadia, BP 48000, Relizane, Algeria

Corresponding Author Email:
July. 09, 2017
Mar. 07, 2018
31 March 2018
| Citation



Transported probability density function (PDF) approach have been applied broadly and effectively for modelling turbulent reacting flows. The discretization of this approach is done with two methods, Multi-Environment Eulerian (MEPDF) and Lagrangian Monte-Carlo (LPDF) which each method has advantages and disadvantages. The aim of this work is to investigate the capabilities of each method in predicting hydrogen combustion in a turbulent flame. A comparative study has been adopted between the two methodsby equivalent physical models and numerical parameters. The study was applied in the diffusion turbulent flame of hydrogen into a vitiated of hot coflow with modified K-epsilon model of turbulence. The chosen mixture model is the IEM (Interaction by Exchange with the Mean) with mixing constant (2.1). The number of environment in the first approach is (2.0). The model was solved in this work by the commercial CFD code, ANSYS fluent and the chemical reaction mechanism injected is GRI mech 2.1. The numerical results for temperature and species mass fractions are presented and compared with the experimental data.  The comparison shows that the eulerian method gives better predictions than the lagrangian method. The advantages and disadvantages of both models are discussed in detail in relationship to the results.


PDF transport, MEPDF, LPDF, vitiated coflow, k-epsilon modified

1. Introduction
2. Theoretical Formulation of PDF Transport Approach
3. Flame of Vitiated Coflow
4. Results and Discussion
5. Conclusions

[1] Pope SB. (1985). PDF methods for turbulent reactive flows, Prog. Energy Combust. Sci. 11: 119–193.

[2] Fox RO. (2003). Computational models for turbulent reacting flows. Chem. Eng. 51(2): 215–243. 10.2516/ogst:1996020

[3] Haworth DC. (2010). Progress in probability density function methods for turbulent reacting flows. Prog. Energy Combust. Sci. 36(2): 168–259. 10.1016/j.pecs.2009.09.003

[4] Cabra R, Chen JY, Dibble RW, Karpetis AN, Barlow RS. (2005). Lifted methane-air jet flames in a vitiated coflow. Combust. Flame 143(4): 491–506. 10.1016/j.combust flame.2005.08.019

[5] Saxena V, Pope SB. (1998). PDF calculations of major and minor species in a turbulent piloted jet flame. Symp. Combust 27(1): 1081–1086. 10.1016/S0082-0784(98)80509-2

[6] Muradoglu M, Pope SB, Caughey DA. (2001). The hybrid method for the PDF equations of turbulent reactive flows: Consistency conditions and correction algorithms. J. Comput. Phys. 172(2): 841–878. 10.1006/ jcph.2001.6861

[7] Muradoglu M, Liu K, Pope SB. (2003). PDF modeling of a bluff-body stabilized turbulent flame. Combust. Flame 132(1–2): 115–137. 10.1016/S0010-2180(02)00430-3

[8] Cao R, Pope SB. (2003). Numerical integration of stochastic differential equations: Weak second-order mid-point scheme for application in the composition PDF method. J. Comput. Phys. 185(1): 194–212. 10.1016/S0021-9991(02)00054-2

[9] Masri AR., Cao RR., Pope SB., Goldin GM. (2004). PDF calculations of turbulent lifted flames of H2/N2 fuel issuing into a vitiated co-flow. Combust. Theory Model 8(1): 1–22. 10.1088/1364-7830/8/1/001

[10] Liu K, Pope SB, Caughey DA. (2005). Calculations of bluff-body stabilized flames using a joint probability density function model with detailedchemistry. Combust. Flame 141(1–2): 89–117. 10.1016/j.combust flame .2004.12.018

[11] Senouci M, Benchatti T, Bounif A, Oumrani N, Merouane H. (2016). A hybrid rans-Rsm/composition PDF-transport method for simulation of hydrgen-air turbulent diffusion flame. Int. J. Heat Technol. 34(2): 268–274. 10.18280/ijht.340216

[12] Cao RR., Pope SB. (2005). The influence of chemical mechanisms on PDF calculations of nonpremixed piloted jet flames. Combust. Flame 143(4): 450–470. 10.1016/j.combustflame.2005.08.018

[13] Gordon RL., Masri AR., Pope SB., Goldin GM. (2007). Transport budgets in turbulent lifted flames of methane autoigniting in a vitiated co-flow. Combust. Flame 151(3): 495–511. 10.1016/j.combustflame.2007.07.001

[14] Cao RR., Wang H, Pope SB. (2007). The effect of mixing models in PDF calculations of piloted jet flames. Proc. Combust. Inst. 31: 1543–1550. 10.1016/j.proci.2006.08.052

[15] Cao RR., Pope SB., Masri AR. (2005). Turbulent lifted flames in a vitiated coflow investigated using joint PDF calculations. Combust. Flame 142(4): 438–453. 10.1016/j.combustflame.2005.04.005 

[16] Senouci M, Bounif A, Abidat M, Belkaid NM, Mansour C, Gokalp I. (2013). Transported-PDF (IEM, EMST) micromixing models in a hydrogen-air nonpremixed turbulent flame. Acta Mech. 224(12): 3111–3124. 10.1007/s00707-013-0911-5.

[17] Fox RO. (2003). Computational Models for Turbulent Reacting Flows. Cambridge Univ Pr., 10.2277/0521659078

[18] Tang Q, ZhaoW, Bockelie M, Fox RO. (2007). Multi-environment probability density function method for modelling turbulent combustion using realistic chemical kinetics. Combust. Theory Model. 11(6): 889–907. 10.1080/13647830701268890

[19] Akroyd J, Smith AJ, Mcglashan LR, MKÃ. (2010). Numerical investigation of DQMoM-IEM as a turbulent reaction closure.Chem. Eng. Sci. 65(6): 1915–1924. 10.1016/j.ces.2009.11.010

[20] Yadav R, Kushari A, Eswaran V, Verma AK. (2013). A numerical investigation of the Eulerian PDF transport approach for modeling of turbulent non-premixed pilot stabilized flames. Combust. Flame 160(3): 618–634. 10.1016/j.combustflame.2012.11.010

[21] Dongre A, De A, Yadav R. (2014). Numerical investigation of MILD combustion using multi-environment Eulerian probability density function modeling. International Journal of Spray and Combustion Dynamics 6(4): 357–386.

[22] Yadav R, Kushari A. (2014). International journal of heat and mass transfer modeling of turbulent lifted flames in vitiated co-flow using multi environment Eulerian PDF transport approach. Heat Mass Transf. 77: 230–246. 10.1016/j.ijheatmasstransfer.2014.05.001

[23] Mo H, Gerlinger P, Bru D. (2001). Comparison of eulerian and lagrangian monte carlo PDF methods for turbulent diffusion flames. Combustion and Flame 124(3): 519-534.

[24] Pope S. (1994). Lagrangian PDF methods for turbulent flows. Annu. Rev. Fluid Mech. 26(1): 23–63. 10.1146/annurev.fluid.26.1.23

[25] Fox RO, Stiles HL, Uni IS. (2003). Computational models for turbulent reacting flows. Cambridge Univ Pr.

[26] Marchisio DL., Fox RO. (2005). Solution of population balance equations using the direct quadrature method of moments. 36: 43–73.

[27] Cabra R, Dibble RW. (2002). Vitiated coflow combustor website. 10.1016/j.jaerosci.2004.07.009 

[28] FLUENT 15.0.7 for the ANSYS 2014release version 15.0

[29] Pope SB. (1997). Computationally efficient implementation of combustion chemistry using in situ adaptive tabulation. 1: 1–63.