Non-premixed Flames (Diffusion Flames)

Abstract

In many combustion processes, the fuel and oxidizer are separated before entering the reaction zone where they mix and burn. The combustion reactions in such cases are called “non-premixed flames,” or traditionally, “diffusion flames” because the transport of fuel and oxidizer into the reaction zone occurs primarily by diffusion. Many combustors operate in the non-premixed burning mode, often for safety reasons. Since the fuel and oxidizer are not premixed, the risk of sudden combustion (explosion) is eliminated. Chemical reactions between fuel and oxidizer occur only at the molecular level, so “mixing” between fuel and oxidizer must take place before combustion. In non-premixed combustion the fuel and oxidizer are transported independently to the reaction zone, by convection and diffusion, where mixing of the fuel and oxidizer occurs prior to their reaction. Often the chemical reactions are fast, hence the burning rate is limited by the transport and mixing process rather than by the chemical kinetics. Consequently, greater flame stability can be maintained. This stable characteristic makes diffusion flames attractive for many applications, notably aircraft gas-turbine engines. Topics covered in this chapter include: (1) a detailed description of a candle flame, (2) the structure of non-premixed laminar jet flames, (3) theoretical and empirical expressions for laminar jet flame height, (4) Burke-Schumann jet diffusion flames, (5) turbulent jet flames including liftoff height and blowout limit, and (6) a short discussion of condensed fuel fires.

Exercises

• 7.1 Consider a laminar methane diffusion flame stabilized on a circular burner. The pressure is 1 atm and the ambient temperature is 25°C.

  • (a) For a fixed fuel mass flow rate, how does the flame height vary with ambient pressure? Hint: the diffusivity is inversely proportional to pressure.

  • (b) If the height of the diffusion flame is L _f , qualitatively sketch the axial (centerline) profiles of the following quantities from the base of the diffusion flame to a height of 2L _f : temperature, methane, and carbon dioxide concentrations.

• 7.2 Following exercise 7.1, if the height of the diffusion flame is L _f , qualitatively sketch the radial profiles of the following quantities at heights of L _f /4 and L _f /2: temperature, carbon dioxide concentration, and methane concentration. Assume that in both cases the flame sheet is located at radius r _f (radius is the distance from the centerline). If a quantity would be higher at one height make sure this is clearly indicated.

• 7.3 Consider the classic Burke-Schumann laminar jet flame with C₃H₈ as the fuel and standard air as the oxidizer. Both propane and air enter the burner at the standard temperature and pressure. Sketch the flame shape for the following conditions: $\dot{Q}{}_{fuel} = 1\;{\hbox{c}}{{\hbox{m}}^3}{\hbox{/s}}$ and $\dot{Q}{}_{air} = 20\;{\hbox{c}}{{\hbox{m}}^3}{\hbox{/s}}$, where $\dot{Q}{}_{fuel}$ and $\dot{Q}{}_{air}$ are the volumetric flow rates for the fuel and air.

• 7.4

  • (a) Consider a laminar diffusion flame stabilized on a circular burner. The burner Reynolds number is ${{Re}_d} = {V_{jet}}{d_{jet}}/\nu$ where V _jet is the exit velocity of the fuel from the burner, d _jet is the burner diameter, and ν is the kinematic viscosity that is assumed to be equal to D,the effective diffusivity. For a fixed burner exit velocity and kinematic viscosity, sketch the flame height as a function of the burner Reynolds number.

  • (b) Now consider a turbulent diffusion flame stabilized on a circular burner. Assume that the following empirical relation holds for the turbulent diffusivity: ${D_t} \propto {V_{jet}}{d_{jet}}$. For a fixed burner exit velocity and kinematic viscosity, sketch the flame height as function of Reynolds number.

• 7.5 A burner operates with a nonpremixed (diffusion) propane jet flame enclosed in a box. The box is designed for safe operation at P = 1 atm. The operator wishes to increase the pressure to P = 2 atm with the same burner. The fuel and air temperatures are kept the same. In order to avoid flame impingement (flame hitting the box), suggest what the operator should do for the following two cases assuming that the peak flame temperature remains the same:

  • (a) the flame is laminar.

  • (b) the flame is turbulent.