FLAME PROCESSES FROM POSITIONS OF PROBABILITY THEORY

To solve the problem of determining the flame temperature in  the working space of the thermal units it is proposed to calculate the  change of adiabatic enthalpy by using methods of probability theory.  It is shown that the normal function of the fuel cells distribution allows to obtain the integral function of enthalpy and adiabatic temperature along the length of flame distribution, including at asymmetrical  distribution function. The problem is solved regarding homogeneous  diffusive gaseous flames, associated with the combustion of sprayed  liquid fuel. Transfer equations solutions regularization’s conditions are  defined, homochronic number and Bio mass transfer number relation’s  approximations are proposed. For synthesis of the solution on canals  of initial forms the corresponding linear connections are proposed;  the limits of change of the mass transfer Bio number and the convergence of series sums in the regularization of solutions of the surface  combustion equation are defined according to the method of BurkeSchumann. Flame length’s dispersion factor’s variability is considered.  The explanation of the S-shaped temperature curve observed by the  burning of nearly all fuels in installations of various types is proposed.  Flame processes generally examined by probability theory with various density of normal distribution function φ(U) for homogenic flame  by normal integral function Ф(U) are described. The steady form Ф(U)  significantly explains the S-shaped longitudinal temperature function  observed in practice and which serves as a basis for thermal and nonstationary theory of ignition. Actual flame’s temperature determination  is possible on flare’s continuum adiabatic temperature placement taking into account the radiative properties of all heat transfer system’s  elements. Likewise the task of heterogenic flame’s axial temperature’s  description with variable dispersion factor σ can be solved.

 flame,  homogeneous,  probability theory,  distribution of fractions,   dispersion factor,  integral function,  enthalpy,  adiabatic temperature

1. Williams Forman A. Combustion theory. Addison-Wesley Publishing Company, 1965, 447 p. (Russ.ed.: Williams F.A. Teoriya goreniya. Moscow: Nauka, 1971, 616 p.).

2. Spalding D.B. Some fundamentals of combustion. London: Butterworth  Scientific  publications,  1955,  250  p.  (Russ.ed.:  Spalding  D.B. Osnovy teorii goreniya: Fizika. Moscow: Izd-vo Kniga po  Trebovaniyu, 2012, 320 p.).

3. Zel’dovich  B.Ya.,  Barenblatt  G.I.,  Librovich  V.B.,  Makhviladze  G.M. Matematicheskaya teoriya goreniya i vzryva [Mathematical theory of combustion and explosion]. Moscow: Nauka, 1980,  478 p. (In Russ.).

4. Lisienko V.G. Lobanov V.I., Kitaev B.I. Teplofizika metallurgicheskikh protsessov [Thermal physics of metallurgical processes]. Moscow: Metallurgiya, 1995, 240 p. (In Russ.).

5. Lisienko  V.G.  Volkov  V.V.,  Goncharov  A.L.  Matematicheskoe mode lirovanie teploobmena v pechakh i agregatakh [Mathematical  modeling of heat transfer in furnaces and aggregates]. Kiev: Naukova dumka, 1984, 232 p. (In Russ.).

6. Lisienko V.G., Volkov V.V., Malikov Yu.K. Uluchshenie toplivoispol’ zovaniya i upravleniya teploobmenom v metallurgicheskikh pechakh [Improving fuel consumption and management of heat transfer in metallurgical furnaces]. Moscow: Metallurgiya, 1988, 230 p.  (In Russ.).

7. Lisienko V.G. Shchelokov Ya.M., Ladygichev M.G. Khrestomatiya energosberezheniya: Spravochnoe izdanie: V 2­kh knigakh. Kniga 2  [Energy saving readings: Ref.: In 2 books. Book 2]. Moscow:  Teploenergetik, 2003, 768 p. (In Russ.).

8. ANSYS: Products. Available at URL: http://www.ansys.com/products.

9. Spalding D.B. Vychislitel’naya gidrodinamika (CFD): proshloe, nastoyashchee i budushchee: Problemy gazodinamiki i teploobmena v energeticheskikh ustanovkakh. V 2­kh tomakh. Tom 1 [Computational fluid dynamics (CFD): past, present and future: Problems of  gas dynamics and heat exchange in power plants. In 2 vols. Vol. 1].  Moscow: Izdatel’skii dom MEI, 2007, pp. 9–13. (In Russ.). 

10. Korn Granino A., Korn Theresa M. Mathematical handbook for scientists and engineers. Definitions, theorems and formulas for reference and review. 2nd ed. New York: McGraw – Hill, 2000. (Russ.ed.:  Korn G.A., Korn T.M. Spravochnik po matematike dlya nauchnykh rabotnikov i inzhenerov. St. Petersburg: Lan’, 2003, 831 p.).

11. Toropov E.V . Influence of shape and thermal massiveness of the  bodies on the accumulation processes efficiency. Vestnik YuUrGU. Seriya Metallurgiya. 2016, vol. 16, no. 2, pp .117–121. (In Russ.).

12. Toropov E.V., Osintsev K.V . Concentration of flare continuum for  the intensive burning zone in boiler unit. Vestnik YuUrGU. Seriya Energetika. 2015, vol. 15, no. 3, pp. 5–10. (In Russ.).

13. Toropov E.V., Osintsev K.V. Main characteristics of the flare  continuum  in  intensive  burning  zone  in  boiler  unit.  Vestnik YuUrGU. Seriya Energetika. 2016, vol. 16, no. 2, pp. 14–21. (In  Russ.).

14. Kutateladze S.S. Teploperedacha i gidrodinamicheskoe soprotivlenie: Spravochnoe posobie [Heat transfer and flow resistance:  Refe rence manual]. Moscow: Energoatomizdat, 1990, 367 p. (In  Russ.).

15. Telegin A.S., Shvydkii V.S., Yaroshenko Yu.G. Teplomassoperenos: Uchebnik dlya vuzov [Heat and mass transfer: Textbook for universities]. Moscow: Akademkniga, 2002, 455 p. (In Russ.). 

16. Toropov E.V., Osintsev K.V . Mathematical model for determining  the initial zone of heterogeneous torch and its adaptation. Vestnik YuUrGU. Seriya Energetika. 2016, vol. 16, no. 3, pp. 15–22. (In  Russ.).

17. Harrje D.T., Reardon F.H. Liquid propellant rocket combustion instability. Washington D.C.: NASA, 1972, 657 p. (Russ.ed.: Harrje  D.T., Reardon F.H. Neustoichivost’ goreniya v ZhRD. Moscow:  Mir, 1975, 869 p.).

18. Vintovkin A.A., Ladygichev M.G., Goldobin Yu.M., Yasnikov G.P.  Tekhnologicheskoe szhiganie i ispol’zovanie topliva [Technological  combustion and use of fuel]. Moscow: Teplotekhnik, 2005, 288 p.  (In Russ.).