Quantitative methods in fire safety engineering 5 U01620 9. Introduction to combustion modelling

1. Quantitative methods in fire safety engineering 5 (U01620)  9. Introduction to combustion modelling Stephen Welch S.Welch@ed.ac.uk School of Engineering and Electronics University of Edinburgh

2. Introduction to combustion � Scope Combustion processes Premixed Diffusion flames Combustion chemistry Equilibrium Finite rate Combustion models Mixing controlled pdf methods

3. Introduction to combustion � Scope Toxic minor species Carbon monoxide Smoke Flame spread Solid-phase pyrolysis

4. Example application

5. Combustion processes Premixed flames Deflagration Detonation Diffusion flames Laminar Turbulent Typical of natural fire Fairly long time scales Buoyancy dominated

6. Turbulent diffusion flames Combustion chemistry/heat release Essentially �mixing controlled� Chemical kinetics can be assumed fast Useful simplifying assumption Species yields (e.g. toxic emissions) Products of incomplete combustion Non-equilibrium/slow chemistry important High heat loss Thermal radiation from carbon particles May influence �flame spread�

7. Combustion chemistry Equilibrium Thermodynamic equilibrium Unphysically high yields of intermediates Finite-rate chemistry Typically described by Arrhenius expressions: EA is the activation energy (typically very high!) Even for simple fuels can be hundreds of reactions and dozens of intermediate species

8. Methane mechanism

9. Combustion modelling Want to describe: Energy release Species yields, especially toxic products Distinguish controlling mechanisms: Mixing control Chemical reaction rate Damkohler number: Basis for simplified treatments Da>>1 (�fast chemistry�)

10. Combustion modelling Transport equation for species: Reynolds averaged form: Chemical source term Highly non-linear in instantaneous gas temperature Problem of �closure�

11. Chemical source term closure Consider simplified chemical reaction: Fuel + Oxidant Products k is rate constant for reaction: Source term for fuel consumption: If expanded get unknown cross-products

12. Favre averaging Density-weighted time averaging simplifies mathematical description Reynolds average: Favre average: where:

13. Reynolds averaging Time averaging Reynolds (1895):

14. Favre averaging Continuity equation: Reynolds average: Favre average:

15. Chemical source term closure Expand mean chemical source term:

16. Chemical source term closure Rate term can also be expanded: cross correlations are unknown and highly non-linear!

17. Does it matter? Consider temperature fluctuating between 500K and 2000K (e.g. reactants and products) Mean temperature = 1250K Typical activation energy/R=20,000K; A=1 Rate from mean T: Rate from exact T: Ratio 0.5%!

18. Does it matter? Using mean temperatures Significant underestimate of reaction rates If we have to model finite-rate chemistry Need a method of accommodating influence of temperature fluctuations Solve additional transport equations for each species of interest Soon becomes intractable!

19. Mixing controlled combustion If we can�t model reaction rate, just assume it�s infinitely fast: Constrained by microscopic mixing rate Need a model to describe mixing Eddy breakup (EBU version 1) Spalding (1971): k, ? = turbulent kinetic energy and dissipation Yf� = fluctuation of fuel mass fraction CEBU = empirical constant

20. Mixing controlled combustion Eddy breakup (EBU version 2) Magnussen & Hjertager (1976) For turbulent diffusion flame: Assuming isotropic turbulence: Usually taken to equal 4

21. Eddy breakup models Reasonably successful across a range of combustion systems Relatively simple formulation Provides for distributed heat release e.g. flame lengthening under ventilation control arises automatically Tracks composition evolution in terms of Oxidant, reactant and products BUT, detailed chemistry neglected No good if require other minor species: Toxic products of combustion, CO and smoke

22. PDF methods Chemical source term closure requires Knowledge of all cross-correlations Can be solved using Monte Carlo method Introduce large number of fluid �particles� Track progress of each in time Adjust particle composition as it interacts Hence Obtain the joint-pdf numerically Hugely demanding computationally!

23. Mixture fraction A variable can be defined as: where, ?: Assuming one-step chemistry: the rate of change of each term is equal and opposite ? is not affected by chemical change

24. Mixture fraction Call ? a �conserved scalar� Measure of the local mass which originated in fuel stream Value varies between 0 and 1 Cannot be created or destroyed Affected by other mixing processes Convection and diffusion Can track in space by solving an additional transport equation for ? If we can relate other chemistry to this parameter alone there is no need to close chemical source term!

25. Fast chemistry

26. Laminar flamelet models Imagine the mixture consists of an ensemble of �laminar flamelets� Chemistry of each is defined for full range of mixture fraction values found in a laminar diffusion flame Obtain instantaneous species concentrations: Y(?) defined by the state relationship Need only model the evolution of P(?)

27. Laminar flamelet models How can we determine P(?)!? Solve additional transport equations Mean: Variance: Ties in effect of turbulence

28. Laminar flamelet models Prescribed pdf�s, of fixed general shape: Beta function Gaussian Shape evolves with local conditions Expressed in terms of computed mean and variance of mixture fraction (beta function):

29. Laminar flamelet models Flamelet chemistry Equilibrium (gross overprediction) Experimental measurements Opposed diffusion flame modelling Chemical kinetics limited only by knowledge of mechanisms and computer power

30. Laminar flamelet - example Compared mechanisms: Simple 41 species 274 reactions Held et al. Complex 160 species 1540 reactions Seiser et al.

31. Toxic minor species Represent detailed chemistry in flamelet Obtain by quadrature: OK provided chemistry is sufficiently fast Probably not true for CO Definitely not true for smoke

32. Carbon Monoxide prediction Yield is a balance between Rate of formation (relatively slow) Turbulent transport Oxidation Flamelet methods robust for many cases May be necessary to parameterise to include: Heat loss Strain rate Degree of vitiation Requires huge libraries of pre-computed flamelets! Only works for pure fuels

33. Smoke prediction Fast chemistry assumption invalid Construct flamelet descriptions of the rate of formation Solve additional balance equations for soot particle number density and soot mass Flamelet rates provide source terms Consider oxidation where necessary May be a mixing-controlled rate

34. Smoke prediction Heat loss very important Multiple radiative loss libraries Looks up appropriate flamelet according to overall energy balance Function of local soot concentration Coupled problem

35. Flame spread modelling Ignition criterion Surface temperature Requires very accurate modelling of solid phase heat transfer Critical accumulated flux Requires some approximations for unknown heat losses from rear of specimen Cone calorimeter data Take HRR direct from cone test Will only apply to that flux Further complicated by radiation from flames

36. Critical accumulated flux Defined as: qmin is a minimum heat flux below which no ignition occurs

37. Example application Flame spread over full-scale corner wall 10 different materials Cellulosics Plastics With/without fire retardant

38. Heat release rate

39. CO production rate

40. Smoke production rate

41. Sensitivity

42. Sensitivity

43. Sensitivity

44. Sensitivity

46. Summary (1) Eddy breakup Mixing controlled Laminar flamelet Relaxes fast chemistry assumption Overcomes problem of turbulent closure of chemical source terms Slow chemistry processes, e.g. for toxic products like CO and smoke, require solution of additional transport equations

47. Summary (2) Flame spread predictions require Accurate smoke predictions Radiative feedback to surface controls volatilisation rate Need a comprehensive model which links all phenomena This is the strength of CFD over simpler models which are essentially more empirical

48. References Chung, T.J. �Computational Fluid Dynamics�, Cambridge University Press, 2002 Cox, G �Combustion Fundamentals of Fire�, Academic Press, 1995 Moss, J.B. �Turbulent diffusion flames�, chapter 4 in above, 1995 Wilcox, D.C. �Turbulence modelling for CFD�, DCW Industries, 1998 McGrattan, K. (ed.) Fire Dynamics Simulator (Version 4) � Technical Reference Manual, NIST special publication 1018, 2004