Premixed Flames

Abstract

Premixed flames refer to the combustion mode that takes place when a fuel and oxidizer have been mixed prior to their combustion. Premixed flames are present in many practical combustion devices. Two such applications are a home heating furnace and a spark ignited internal combustion engine. In premixed flame combustors, the fuel and oxidizer are mixed thoroughly before being introduced into the combustor. Combustion is initiated either by ignition from a spark or by a pilot flame, creating a ‘flame’ that propagates into the unburned mixture. It is important to understand the characteristics of such a propagating flame in order to design a proper combustor. Some relevant engineering questions arise, such as: How fast will the flame consume the unburned mixture? How will flame propagation change with operating conditions such as equivalence ratio, temperature, and pressure? From a fire protection viewpoint, how can flame propagation be stopped? Topics covered in this chapter include: (1) the physical processes in a premixed flames, (2) flame speed and flame thickness, (3) flammability limits, (4) flame quenching, (5) minimum energy for sustained ignition and subsequent flame propagation, and (6) turbulent premixed flames.

Exercises

• 6.1 For a propane/air adiabatic laminar premixed flame with single-step global kinetics, calculate the laminar flame speed S _L and flame thickness δ for an equivalence ratio φ = 0.7. Assume a pressure of 1 atm, an unburned gas temperature of 300 K, a mean molecular weight of 29 g/mol, an average specific heat of 1.2 kJ/kg-K, an average thermal conductivity of 0.09 W/m-K, and a heat of combustion of 46 MJ/kg. The kinetics parameters you will need for propane (C₃H₈) are a = 0.1, b = 1.65, T _ig  = 743 K, E = 125.6 kJ/mol, and A = 8.6 × 10¹¹ cm^2.25/(s-mole^0.75). When calculating the reaction rate, be sure to evaluate the molar concentrations in units of moles/cm³.

• 6.2 For a stoichiometric adiabatic laminar premixed propane flame with single-step global kinetics propagating through a gaseous mixture of fuel, oxygen, and nitrogen, how does the reaction rate R vary with the ratio $X_{{N_2}}^\infty /X_{{O_2}}^\infty$ where $X_{{N_2}}^\infty$ is the ambient nitrogen concentration and $X_{{O_2}}^\infty$ is the ambient oxygen concentration? In other words, indicate the proportionality $R \propto f\left( \psi \right)$ where $\psi = X_{{N_2}}^\infty /X_{{O_2}}^\infty$. Does the reaction rate increase or decrease with increasing $\psi$ and why?

• 6.3 A flame arrestor (a plate with small circular holes) is to be installed in the outlet of a vessel containing a stoichiometric mixture of propane and air, initially at 20°C and 1 atm, to prevent the potential of flame propagation (flashback) to the interior of the vessel. (a) Calculate the diameter of the flame arrestor holes. (b) Based on your previous calculations, estimate the hole diameter if the pressure is 5 atm. (c) From a safety point of view, would you change the hole diameter of the flame arrestor if the mixture is made richer or leaner? (explain).

• 6.4 The pilot light has blown out on your gas heater at home. Your heater is defective so natural gas continues to enter your home. The natural gas (assume 100% methane) enters at a rate of 30 L/s. If your house has a volume of 350 m³, how long will it be before your house is in danger of blowing up (lean limit)? How much longer until it is no longer in danger of blowing up (rich limit)? Assume the gases are always perfectly mixed and that methane is flammable in air for methane concentrations between 5% and 15% by volume.