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Consistent Behavior of Eulerian Monte Carlo fields at Low Reynolds Numbers

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Abstract

A slightly different version of the Eulerian Monte Carlo method (EMC) (Valiño, Flow Turbul. Combust. 60, 157–172, (1998)) is presented in this paper. The EMC method is an effective stochastic numerical approach to solve the Probability Density Function (PDF) of reacting species in turbulent flows. In contrast with the original formulation, the spurious Wiener term associated with the molecular diffusion is removed, by splitting the micro-mixing into mean gradient and fluctuating contributions. The evolution of the EMC fields representing the PDF in the proposed formulation is then consistent in the laminar limit: the EMC fields follow the same standard convection-diffusion equation, without any stochastic terms.

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References

  1. Lundgren, T.S.: Distribution functions in the statistical theory of turbulence. Phys. Fluids 10, 969–975 (1967)

    Article  Google Scholar 

  2. Valiño, L.: A field monte carlo formulation for calculating the probability density function of a single scalar in a turbulent flow. Flow Turbul. Combust. 60, 157–172 (1998)

    Article  MATH  Google Scholar 

  3. Mustata, R., Valiño, L., Jiménez, C., Jones, W.P., Bondi, S.: A probability density function eulerian Monte Carlo field method for large-eddy simulations. Application to a turbulent piloted methane/air diffusion flame (Sandia D). Combust. Flame 145, 88–104 (2006)

    Article  Google Scholar 

  4. Dodoulas, I.A., Navarro-Martinez, S.: Large eddy simulation of premixed turbulent flames using the probability density function approach. Flow Turbul. Combust. 90(3), 645–678 (2013)

    Article  Google Scholar 

  5. Loth, E.: Progress in probability density function methods for turbulent reacting flows. Prog. Energy Combust. Sci. 36, 168–259 (2010)

    Article  Google Scholar 

  6. Soulard, O., Sabelnikov, V.A.: Rapidly decorrelating velocity-field model as a tool for solving one-point fokker-planequations for probability density functions of turbulent reactive scalars. Phys. Rev. E 72(016301), 1–20 (2005)

    Google Scholar 

  7. Jones, W.P., Launder, B.E.: The prediction of laminarization with a two-equation model. Int. J. Heat Mass Transf. 15, 301–314 (1972)

    Article  Google Scholar 

  8. Durbin, P.A., Petterson Reif, B.A.: Statistical Theory and Modeling for Turbulent Flows. Wiley (2001). ISBN 0-471-49744-4

  9. Valiño, L., Hierro, J.: Boundary conditions for probability density function transport equations in fluid mechanics. Phys. Rev. E 67(046310), 1–7 (2003)

    Google Scholar 

  10. Dopazo, C.: Probabilistic approach to tubulent mixing of a reactive scalar. Bull. Am. Meteorol. Soc. 57(5), 637 (1976)

    Google Scholar 

  11. Frisch, U.: Turbulence. Cambridge University Press (1995). ISBN 0-521-45713-0

  12. Pope, S.B.: Turbulent Flows. Cambridge University Press, 123–125 (2000)

  13. Dopazo, C.: Probability density function approach for an axisymmetric heated jet: centerline evolution. Phys. Fluids 18, 397 (1975)

    Article  MATH  Google Scholar 

  14. Valiño, L., Dopazo, C.: A binomial langevin model for turbulent mixing. Phys. Fluids A 3(13), 3034–3037 (1991)

    Article  MATH  Google Scholar 

  15. Dopazo, C.: Recent developments in PDF methods. In: Libby, P.A., Williams, F.A. (eds.) Turbulent Reactive Flows, chap 7, pp. 375–474. Academic Press, San Diego (1994). ISBN 0-12-447945-6

  16. Mustafa Kamal, M., Zhou, R., Balusamy, S., Hochgreb, S.: Favre- and Reynolds-averaged velocity measurements: interpreting PIV and LDA measurements in combustion. In: Proceedings of the Combustion Institute, vol. 35, pp. 3803–3811 (2015)

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Authors and Affiliations

  1. LIFTEC, CSIC - Universidad de Zaragoza, María de Luna 10, 50018, Zaragoza, Spain

    Luis Valiño & Radu Mustata

  2. 16, Bd Maréchal de Lattre, 21300, Chenôve, France

    Khaled Ben Letaief

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  1. Luis Valiño
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  2. Radu Mustata
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  3. Khaled Ben Letaief
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Correspondence to Luis Valiño.

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Valiño, L., Mustata, R. & Letaief, K.B. Consistent Behavior of Eulerian Monte Carlo fields at Low Reynolds Numbers. Flow Turbulence Combust 96, 503–512 (2016). https://doi.org/10.1007/s10494-015-9687-0

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  • DOI: https://doi.org/10.1007/s10494-015-9687-0

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