USE OF TWO -FLUID TECHNIQUES TO MODEL TURBULENT DIFFUSION FLAMES
Turbulent flames appear spotty to the eye; they contain luminous streaks, filaments and other distinct structures. Temperature and composition measurements confirm this, as they indicate temporal and spatial fluctuations ranging from ambient to the adiabatic flame maximum. In addition, velocity measurements suggest that hot and cold fluid parcels move at distinctly different velocities.
Conventional "mixture" models do not adequately represent the above physical
phenomena. In particular,
Radiation flux is proportional to the fourth power of temperature. Radical formation is
often marked by temperature thresholds (e.g. NOx, only formed above 2000K) Body forces
accelerate lighter "hot" fragments of fluid enhancing shear; this is important,
since reaction occurs at interfaces, and oxidant entrainment is a function of fragment
size and relative velocity.
So, mixture models average temperature peaks and smear interfaces - deficiencies that are particularly acute in large turbulent diffusion flames prevalent in fires. Some measure of this fragmentariness has been accounted for to some degree by the reaction limiting eddy-break-up model, suitable for premixed turbulent combustion.
The well known IPSA algorithm for the solution of two inter-penetrating continua satisfies the requirements stated earlier. The velocity, temperature, density and species concentration can be solved for separately in each "phase", with reaction, exchange of heat, mass and momentum occurring at the interface.
The distinction between the two fluids is based on physical grounds. Hence,
Fluid 1 = Hot, reacting and turbulent
Fluid 2 = Cold, irrotational, air only
Other definitions are of course possible. In a turbulent flame, fluid 2 is the ambient air. Fluid 1 is then made up of fragments of fuel and reaction products. These fragments are produced by turbulence and shear, increase by entraining air, and break by tearing.
The two-fluid model has been applied to three-dimensional domestic fires and buoyant atmospheric plumes. Although more complex than the mixture model which is universally used by fire modellers, it is not necessarily more expensive computationally. Convergence is improved by the additional degree of freedom given to buoyant fragments, and a sharper - more realistic - interface between air and smoke layer results.
The model is most suitable for pool fires and other scenarios were air and fuel are not premixed, and where large turbulent structures exist.
Reference:
K Pericleous and N C Markatos. A two-fluid approach to the modelling of three-dimensional turbulent flames, Proc. Eurotherm 17, Springer Verlag, Cascais Portugal, Oct 1990.
