ON COMBUSTION MODELING

There is a strong demand in applying combustion modeling for building fires, burning materials and of course for engines and furnaces. Most combustion flows, particularly those in fires, are very complicated to study. Concept on applied physics and chemistry would be applied. A review on combustion modeling will be presented in this paper. Effects of turbulence on flame propagation are focused. Some fundamental aspects of combustion modeling for numerical modeling of premixed and diffusion turbulent combustion are discussed. Eddy break-up model and its expansion, Eddy dissipation model, simplified PDF model with different reaction rate and flame surface, and flamelet model are included. 1. LAMINAR AND TURBULENT PREMIXED FLAMES Combustion process of premixed gases depends on the flow condition. The flow velocity of the combustible premixed gases is not high for laminar flames, and there are no fluctuations. The flame surface appears smooth, with combustion rather steady. The flame surface will supply heat and activated radicals to the nearby thin layer of combustible premixed gases which are not yet burnt, through heat transfer and molecular diffusion. The flame will then spread along the surface, called laminar flames. When the flow velocity of the combustible premixed gases is relatively high or the flow area is relatively large, a large quantity of large and small eddies with random rotations and movement are produced in the fluid flow. These eddies will fluctuate back and forth, up and down through the flow streamlines. The flame surface will be folded and deformed to be thicker and shorter, kept on rolling and making noises. Such flames are called turbulent flames. In contrast to laminar flames, the transport of heat and activated radicals from the turbulent flame surface to the not yet burnt premixed gases are governed by the eddy movement of the fluid to excite and intensify, which depends on the fluid flow. The spreading rate of turbulent flames is much faster than that for laminar combustion. 1.1 Spreading Rate of Laminar Flames The spreading rate of laminar flames is a basic characteristic parameter of the combustion process. To effectively control the combustion in practical processes, the mechanism of flame spreading and the influences of various physical and chemical factors on it should be clearly understood. That is to understand the specific transfer process of chemical reactions of combustion from one layer of reacted premixed gases to another layer of freshly premixed gases. At present, there are two schools of thought on the mechanism of flame spreading: thermal theory and diffusion theory. For thermal theory, chemical reactions in the flame are induced by the introduction of heat which thermally activate the molecules. The movement of the chemical reaction zone (called the flame front) in space depends on the heat transfer rate from the reaction zone to the freshly premixed gases. This theory does not deny that there are activated radicals and diffusion in the flame, but it is generally believed that the activated radicals in the combustion process do not have a dominant effect on the chemical reactions. On the contrary, the diffusion theory assumes that chemical reactions in the flame are mainly due to the diffusion of activated radicals (such as H and OH) to the freshly premixed gases, which enhances the chain reactions. Among these two theories, the thermal theory more resembles the practical situations. The thermal theory of laminar flame spreading proposed by the Russian scientist Zeldovich (1938) and his coworkers Frank-Kamenetkii (1940), Semenov et al. (1951), International Journal on Architectural Science 39 and based on the literature results of others as well, is considered the most widely accepted flame spreading theory at present. Zeldovich’s theory of flame propagation is described in the following. 1.1.1 Zeldovich’s analysis of flame propagation Based on the analysis of the flame front structure, the thermal theory of flame spreading was proposed by Zeldovich and coworkers with six assumptions: 1. Chemical reactions in the flame are the result of thermal activation of molecules. The movement of the flame front in space depends on the heat transfer between the burning gases and the freshly mixed gases. Although there will be some effects due to diffusion of activated radicals, the effect is not significant and can be neglected. 2. The combustion reactions studied are simple reactions and not chain reactions. The reactions have very high activation energies and take place at high temperature close to the combustion temperature. 3. The reactants and combustion products are both ideal gases, their physical parameters including heat transfer coefficient λ, heat diffusion coefficient a, diffusion coefficient D and caloric value are all constants in the process, taken as the average value in the temperature zone studied. The heat diffusion coefficient is equal to the diffusion coefficient, i.e. a = D, meaning that temperature field and concentration field are similar. 4. The reactions are of equal pressure and thermally insulated, i.e. pressure diffusion and heat loss are not considered. 5. Air flow is one-dimensional thermally insulated flow. The gas parameter is only a one-dimensional function of space with negligibly small variation of kinetic energy. 6. The flame front is a calm plane front. Under the above assumptions, the equation for the spreading rate of laminar flames can be derived based on the energy equation of gases. The heat transfer equations in the flame are derived in the following. The energy equations for onedimensional steady flow with chemical reactions are listed. Consider a small control volume in the flame front, with volume dv of dxdydz. When premixed combustible gases flow past the microvolume from left to right, its temperature T increases gradually along the flow direction. Heat dx x Q + is transferred from the high temperature zone on the right side to the left side of the control volume dv with x Q . Since there is air flow through the control volume, the heat enthalpy brought in is dx x H + . The changes in energy in the control volume depend on these three heat flows. The heat flow introduced would increase the enthalpy of the gas in the control volume, i.e. x x dx x x x Q Q Q Q dx Q x + ∂   − = + −   ∂   x Q T dx dydz dx x x x λ ∂ ∂  ∂    = =     ∂ ∂ ∂     2