Semi-analytical modeling of non-premixed counterflow combustion of metal dust

  • Seyed Amir Hossein MadaniEmail author
  • Mehdi Bidabadi
  • Nafiseh Mohammadian Aftah
  • Abolfazl Afzalabadi


In this study, a semi-analytical model is developed for non-premixed combustion of metal dusts in counterflow configuration. Combustion domain is divided into three separate zones, each of which possesses corresponding mass and energy conservation equations as well as boundary and jump conditions. Metal dust, assumed to be aluminum, undergoes an Arrhenius-type reaction with oxidizer, when it is heated enough to reach the ignition temperature. Dimensionless forms of conservation equations are derived and utilized to elucidate the combustion characteristics. The effects of oxidizer Lewis number and fuel mass concentration on the flame position and temperature are discussed thoroughly. In addition, temperature distribution of the whole domain is calculated by numerically solving the system of partial differential equations. In order to track particles through combustion domain, Lagrangian equations of motion are solved either mathematically or numerically, considering thermophoretic, weight, buoyancy and drag forces. The effects of thermophoretic force on the particle path are investigated, and the deviation of particle from carrier neutral gas direction is obtained. The results showed a great agreement with the data reported in the literature highlighting the fact that the presented model is an efficient one to accurately model the non-premixed counterflow combustion of metal dust.


Non-premixed combustion Aluminum dust cloud Mathematical modeling Counterflow configuration Thermophoresis effect Particle tracking 

List of symbols


Strain rate (s−1)


Gas heat capacity (J kg−1 K−1)


Drag coefficient


Particle heat capacity (J kg−1 K−1)


Mean thermal velocity of gaseous molecules (m s−1)


Oxidizer diffusion coefficient (m2 s−1)


Particle diameter (m)


Thermal diffusion coefficient (m2 s−1)


Activation energy (J)


Buoyancy force (N)


Drag force (N)


Gravity force (N)


Thermophoretic force (N)


Knudsen number


Lewis number


Particle mass (kg)


Number of particles per unit volume (m−3)


Heat released per unit mass of fuel (J kg−1)


Universal gas constant (J mol−1 K−1)


Temperature (K)


Dimensionless activation energy


Velocity in x-direction (m s−1)


Particle velocity (m s−1)


Velocity in y-direction (m s−1)


Burning velocity (m s−1)


Molecular weight of fuel (kg mol−1)


Initiation point of flame


Oxidizer mass fraction


Solid fuel mass fraction

\(Y_{{{\text{s}} - \infty }}\)

Primary mass fraction of solid fuel

Greek symbols


Viscosity (Pa s)


Particle mean free path (m)


Dimensionless temperature


Stoichiometric mass ratio


Density (kg m−3)





Solid fuel






  1. 1.
    Matveeva EG, Gryczynski Z, Lakowicz JR. Myoglobin immunoassay based on metal particle-enhanced fluorescence. J Immunol Methods. 2005;302:26–35.CrossRefPubMedPubMedCentralGoogle Scholar
  2. 2.
    Lee YK, Kim J, Kim Y, Kwak JW, Yoon Y, Rogers JA. Room temperature electrochemical sintering of Zn microparticles and its use in printable conducting inks for bioresorbable electronics. Adv Mater. 2017;29:1702665.CrossRefGoogle Scholar
  3. 3.
    Hemmat Esfe M, Saedodin S, Bahiraei M, Toghraie D, Mahian O, Wongwises S. Thermal conductivity modeling of MgO/EG nanofluids using experimental data and artificial neural network. J Therm Anal Calorim. 2014;118:287–94.CrossRefGoogle Scholar
  4. 4.
    Sarafraz M, Nikkhah V, Madani SA, Jafatian M, Hormozi F. Low-frequency vibration for fouling mitigation and intensification of thermal performance of a plate heat exchanger working with CuO/water nanofluid. Appl Therm Eng. 2017;121:388–99.CrossRefGoogle Scholar
  5. 5.
    Toghraie D, Chaharsoghi VA, Afrand M. Measurement of thermal conductivity of ZnO–TiO2/EG hybrid nanofluid. J Therm Anal Calorim. 2016;125:527–35.CrossRefGoogle Scholar
  6. 6.
    Zadkhast M, Toghraie D, Karimipour A. Developing a new correlation to estimate the thermal conductivity of MWCNT–CuO/water hybrid nanofluid via an experimental investigation. J Therm Anal Calorim. 2017;129:859–67.CrossRefGoogle Scholar
  7. 7.
    Toghraie D, Abdollah MMD, Pourfattah F, Akbari OA, Ruhani B. Numerical investigation of flow and heat transfer characteristics in smooth, sinusoidal and zigzag-shaped microchannel with and without nanofluid. J Therm Anal Calorim. 2018;131:1757–66.CrossRefGoogle Scholar
  8. 8.
    Hemmat Esfe M, Ahangar MRH, Toghraie D, Hajmohammad MH, Rostamian H, Tourang H. Designing artificial neural network on thermal conductivity of Al2O3–water–EG (60–40%) nanofluid using experimental data. J Therm Anal Calorim. 2016;126:837–43.CrossRefGoogle Scholar
  9. 9.
    Pandas HM, Fazli M. Fabrication of MgO and ZnO nanoparticles by the aid of eggshell bioactive membrane and exploring their catalytic activities on thermal decomposition of ammonium perchlorate. J Therm Anal Calorim. 2018;131:2913–24.CrossRefGoogle Scholar
  10. 10.
    Dumitru R, Manea F, Lupa L, Păcurariu C, Lanculecsa A, Baciu A, Negria S. Synthesis, characterization of nanosized CoAl2O4 and its electrocatalytic activity for enhanced sensing application. J Therm Anal Calorim. 2017;128:1305–12.CrossRefGoogle Scholar
  11. 11.
    Arya A, Sarafraz MM, Shahmiri S, Madani SAH, Nikkhah V, Nakhjavani SM. Thermal performance analysis of a flat heat pipe working with carbon nanotube-water nanofluid for cooling of a high heat flux heater. Heat Mass Transf. 2018;54:985–97.CrossRefGoogle Scholar
  12. 12.
    Subramani J, Nagarajan PK, Mahian O, Sathyamurthy R. Efficiency and heat transfer improvements in a parabolic trough solar collector using TiO2 nanofluids under turbulent flow regime. Renew Energy. 2018;119:19–31.CrossRefGoogle Scholar
  13. 13.
    Bergthorson J, Goroshin S, Soo M, Julien P. Direct combustion of recyclable metal fuels for zero-carbon heat and power. Appl Energy. 2015;160:368–82.CrossRefGoogle Scholar
  14. 14.
    Li G, Yang H, Yuan C, Eckhoff R. A catastrophic aluminium-alloy dust explosion in China. J Loss Prev. 2016;39:121–30.CrossRefGoogle Scholar
  15. 15.
    Li Q, Wang K, Zheng Y, Mei X, Lin B. Explosion severity of micro-sized aluminum dust and its flame propagation properties in 20 L spherical vessel. Powder Technol. 2016;301:1299–308.CrossRefGoogle Scholar
  16. 16.
    Abbasi T, Abbasi SA. Dust explosions–cases, causes, consequences, and control. J Hazard Mater. 2007;140:7–44.CrossRefGoogle Scholar
  17. 17.
    Dreizin EL, Trunov MA. Surface phenomena in aluminum combustion. Combust Flame. 1995;101:378–82.CrossRefGoogle Scholar
  18. 18.
    Tang F-D. Reaction-diffusion fronts in heterogeneous combustion. Montreal: McGill University; 2011.Google Scholar
  19. 19.
    Goroshin S, Higgins A, Kamel M. Powdered metals as fuel for hypersonic ramjets. In: 37th joint propulsion conference and exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics; 2001.Google Scholar
  20. 20.
    Beckstead MW. A summary of aluminum combustion. Provo: Brigham Young University; 2004.Google Scholar
  21. 21.
    Goroshin S, Fomenko I, Lee J. Burning velocities in fuel-rich aluminum dust clouds. Symp Combust. 1996;26:1961–7.CrossRefGoogle Scholar
  22. 22.
    Trunov M, Schoenitz M, Dreizin E. Ignition of aluminum powders under different experimental conditions. Propellants Explos Pyrotech. 2005;30:36–43.CrossRefGoogle Scholar
  23. 23.
    Risha GA, Huang Y, Yetter RA, Yang V. Experimental investigation of aluminum particle dust cloud combustion. In: Proceedings of 43rd aerospace science meeting and exhibit, Reno, Nevada; 2005.Google Scholar
  24. 24.
    Huang Y, Risha GA, Yang V, Yetter RA. Effect of particle size on combustion of aluminum particle dust in air. Combust Flame. 2009;156:5–13.CrossRefGoogle Scholar
  25. 25.
    Bidabadi M, Biouki SA, Afzalabadi A, Dehghan AA, Poorfar AK, Rouboa A. Modeling propagation and extinction of aluminum dust particles in a reaction medium with spatially uniform distribution of particles. J Therm Anal Calorim. 2017;129:1855–64.CrossRefGoogle Scholar
  26. 26.
    Bidabadi M, Mohebbi M, Poorfar A. Modeling quenching distance and flame propagation speed through an iron dust cloud with spatially random distribution of particles. J Loss Prev Process Ind. 2016;43:138–46.CrossRefGoogle Scholar
  27. 27.
    Afzalabadi A, Poorfar AK, Bidabadi M, Moghadasi H, Hochgreb S, Rahbari A, et al. Study on hybrid combustion of aero-suspensions of boron-aluminum powders in a quiescent reaction medium. J Loss Prev Process Ind. 2017;49:645–51.CrossRefGoogle Scholar
  28. 28.
    Bidabadi M, Zadsirjan S, Mostafavi SA. Radiation heat transfer in transient dust cloud flame propagation. J Loss Prev Process Ind. 2013;26:862–8.CrossRefGoogle Scholar
  29. 29.
    Seshadri K, Trevino C. The influence of the Lewis numbers of the reactants on the asymptotic structure of counterflow and stagnant diffusion flames. Combust Sci Technol. 1989;64:243–61.CrossRefGoogle Scholar
  30. 30.
    Guo H, Ju Y, Maruta K, Niioka T, Liu F. Radiation extinction limit of counterflow premixed lean methane-air flames. Combust Flame. 1997;109:639–46.CrossRefGoogle Scholar
  31. 31.
    Seiser R, Pitsch H, Seshadri K, Pitz WJ, Gurran HJ. Extinction and autoignition of n-heptane in counterflow configuration. Proc Combust Inst. 2000;28:2029–37.CrossRefGoogle Scholar
  32. 32.
    Bidabadi M, Akbari Vakilabadi M, Khoeini Poorfar A, Monteiro E, Rouboa A, Rahbari A. Mathematical modeling of premixed counterflow combustion of organic dust cloud. Renew Energy. 2016;92:376–84.CrossRefGoogle Scholar
  33. 33.
    Mohammadi M, Bidabadi M, Khalili H. Modeling counterflow combustion of dust particle cloud in heterogeneous media. J Energy Eng. 2016. Scholar
  34. 34.
    Bidabadi M, Ramezanpour M, Mohammadi M, Fereidooni J. The effect of thermophoresis on flame propagation in nano-aluminum and water mixtures. Period Polytech Chem Eng. 2016;60(3):157–64.CrossRefGoogle Scholar
  35. 35.
    Bidabadi M. An experimental and analytical study of laminar dust flame propagation. Doctoral dissertation. McGill University; 1995.Google Scholar
  36. 36.
    Bergman TL, Incropera FP. Fundamentals of heat and mass transfer. London: Wiley; 2011.Google Scholar
  37. 37.
    Marino T. Numerical analysis to study the effects of solid fuel particle characteristics on ignition, burning, and radiative emission. Doctoral dissertation. The George Washington University; 2008.Google Scholar
  38. 38.
    Law CK. Combustion physics. Cambridge: Cambridge University Press; 2010.Google Scholar
  39. 39.
    Allen MD, Raabe OG. Re-evaluation of Millikan’s oil drop data for the motion of small particles in air. J Aerosol Sci. 1982;13:537–47.CrossRefGoogle Scholar
  40. 40.
    Talbot L, Cheng RK, Schefer RW, Willis DR. Thermophoresis of particles in a heated boundary layer. J Fluid Mech. 1980;101:737–58.CrossRefGoogle Scholar
  41. 41.
    Batchelor GK, Shen C. Thermophoretic deposition of particles in gas flowing over cold surfaces. J Colloid Interface Sci. 1985;107:21–37.CrossRefGoogle Scholar
  42. 42.
    Julien P, Whiteley S, Soo M, Goroshin S. Flame speed measurements in aluminum suspensions using a counterflow burner. Proc Combust Inst. 2017;36:2291–8.CrossRefGoogle Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  • Seyed Amir Hossein Madani
    • 1
    Email author
  • Mehdi Bidabadi
    • 1
  • Nafiseh Mohammadian Aftah
    • 2
  • Abolfazl Afzalabadi
    • 1
  1. 1.School of Mechanical EngineeringIran University of Science and Technology (IUST)Narmak, TehranIran
  2. 2.Faculty of New Sciences and TechnologiesUniversity of TehranTehranIran

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