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RADIATIVE TRANSFER IN COMBUSTION PHENOMENA AFFECTED BY RADIATION

R. Viskanta

Following from: Radiative transfer in combustion systems

Leading to: Radiative transfer in laminar flames; Radiative transfer in turbulent flames; Radiative transfer in combustion chambers; Radiative transfer in two-phase combustion; Thermal radiation in unwanted fires

A number of physicochemical phenomena encountered in combustion systems are influenced by radiation. Some of the phenomena such as ignition of solids, burning velocity, flammability, extinction, flame quenching, flame spread, etc., have been recognized for some time (Gaydon and Wolfhard, 1979), while others such as the effect of radiative transfer on the flame structure itself have not been discussed in combustion textbooks (Williams, 1985; Kuo, 1986; Turns, 2000). For example, in diffusion flames, the flame structure depends on the energy release, rates of transport of fuel and oxidizer, and rates of heat transfer to the flame front. Hence, radiative transfer is expected to play a role in establishing the necessary conditions for the existence and extinction of a flame. Examples of phenomena affected by radiation include ignition of opaque and semitransparent exothermic solids, flame spread and extinction, flame structure, minor species formation (i.e., CO), pollutant emission, soot formation, and others. Reference is made to a recent monograph (Viskanta, 2005; Chan, 2005) for a more complete discussion of the affected phenomena.

Ignition is inherently a transient process that is usually triggered by external stimuli such as heating. The processes are complex, and usually involve many physical and chemical steps. There are a variety of methods to achieve ignition of a combustible gas, liquid, or solid, and include exposure to a hot gas or a flame (pilot), discharge of electrical spark, application of radiant energy input, and many others. An exhaustive and up-to-date resource on fundamentals of ignition including stimuli, devices, criteria, and phenomenology has recently been published (Babrauskas, 2003). Thermal ignition of solids as well as liquid layers by radiation has been discussed, and an extensive list of references dealing with fundamental principles, empirical data, and applications has been provided. The interested reader is referred to this massive resource for the details. Here, we discuss the ignition of a vertical slab, and the effects of radiation on the process.

Ignition of a Solid

Ignition of solids that are exposed to intense external radiation is an important topic of investigation relevant to fire safety and hazards. Ignition of a solid by a hot gas stream has been discussed, and in the boundary layer model neither gas-phase nor solid radiation has been considered (Kuo, 1986). This idealization is justifiable under most forced convection conditions when the hot gas stream velocity is sufficiently high. For example, at the stagnation point, absorption of radiation by the fuel vapor is a potential source of ignition of fuel-oxidizer mixture during radiant heating of a combustible material (Amos and Fernandez-Pello, 1988). The ignition of a pyrolizing solid fuel is a very complex physicochemical phenomenon involving heat and mass transfer as well as chemical reactions (Williams, 1985).

To elucidate the radiation-induced ignition of solid fuels, we present a model problem for simulating the process. As a concrete example, we consider a vertical slab of a solid fuel that is ignited by an intense external thermal radiation source (Fig. 1). Starting initially from isothermal conditions, as the heating continues, the temperature rises due to the absorption of external radiation by the combustible solid. After the surface has reached the pyrolysis temperature, an endothermic decomposition (gasification) reaction begins to take place at the surface, and the surface temperature quickly ceases to rise. The pyrolized gases start to diffuse away from the surface into the gas-phase region and mix with the oxidizers in the boundary layer. Absorption of incident external radiation and heat release from chemical reactions in the mixed gases accelerate the gas-phase reactions. Eventually a thermal runaway condition is reached and ignition occurs. During the process, buoyancy-driven boundary layer flow and transport is induced along the surface. This flow enhances the cooling of the surface and dilutes the radiatively participating gases. Cooling, dilution, and flushing of the gas mixture by free convection flow retard the ignition, whereas absorption of external radiation in the gas phase shortens the ignition delay times.

Figure 1. Schematic of a solid slab ignition model with buoyancy-driven boundary layer flow.

Assuming transient 2D heat conduction and radiation, and considering a homogeneous solid in which scattering is negligible in comparison to absorption, the energy equation for the solid phase can be written as

(1)

where the total (conductive + radiative) heat fluxes in the two directions are defined as

(2)

It should be noted at this point that the axial (x-direction) heat conduction may be important near the leading edge and for thin slabs. This term has been included in Eq. (2) for generality.

Considering the buoyancy-induced flow to be laminar and taking boundary layer approximations to be valid, the conservation equations for the gas phase can be given as follows (Williams, 1985):

Mass

(3)

Momentum

(4)

Energy

(5)

Species

(6)

where i stands for F (fuel), O (oxygen), or P (product). It should be noted that the boundary layer approximation does not include radiative transfer, and the component due to axial radiative flux in the energy equation [Eq. (5)] has been neglected.

The combustion is modeled as a one-step chemical reaction of the form

(7)

The resulting relation between mass and energy source terms is

(8)

The overall mass reaction rate is assumed to be of the Arrhenius form and is modeled as

(9)

where Ag and Eg are the pre-exponential factor and the activation energy in the gas phase reaction, respectively.

The conservation of radiant energy equation can be used to express the divergence of the radiation fluxes as (Viskanta, 2005)

(10)

The RTE can be used to solve for the radiation intensity Iλ(x,x,s,t) in both the solid and gas phases by accounting for the radiation in the two phases as well as for reflection and transmission of radiation at the solid-gas interface. For the limiting case when the solid fuel is opaque, radiation in the solid is a “surface” phenomenon, and can be treated accordingly by accounting for absorption, reflection, and emission of radiation at the “surface.” For example, radiative transfer in the volatile gas phase on a vertical fuel plate of polymethyl-methacrylate (PMMA) exposed to an external radiation source has been calculated by solving the RTE using the discrete ordinates method (DOM). The pyrolized gas and the combustion products were treated as gray, and the local absorption coefficient was taken to be proportional to the mass fraction of fuel and combustion products.

The initial and boundary conditions are standard for transient natural convection, except the conditions at the solid-gas interface (y = 0), and are therefore not given. For t > 0 and y = 0 (interface), the energy balance yields the temperature boundary condition,

(11)

where mp and ΔHp are the mass flux of pyrolyzed gases and heat of pyrolysis, respectively. Note that radiation terms are absent in the equation. At the solid-gas interface of a semitransparent material, radiation is not absorbed or emitted, and therefore should not appear in the energy balance. The fuel, oxygen, and product mass balances at the interface are

(12)

(13)

and

(14)

Radiation from gaseous species such as CO2, H2O, and fuel vapor are spectral in nature, and can be analyzed using band models, at least in simple (e.g., 1D) flames (Olson and Tien, 2000). Probably the most detailed treatment of radiative transfer in the gas-phase boundary layer along a vertical solid plate is due to Han and Baek (1995), except that the PMMA was considered to be opaque and was approximated accordingly. A comparison of the calculated surface temperature history with experimental data showed a reasonable agreement. Despite the induced free convection flow that takes energy from the fuel surface, the locally absorbed radiation, which is converted to internal energy, is found to play an important role in the onset of gas-phase ignition.

Many practical ignition and fire safety situations occur in confined geometry in which material advection plays an important role. The ignition of a solid fuel constituting one vertical wall of a compartment is relevant to fire spread and safety, and has been studied (Baek et al., 1997). A solid fuel is placed on the right vertical wall, and radiant heat source is located on the opposite (left) vertical wall. The radiation leaving the heat source is incident on the solid, heats and pyrolyzes the fuel, and releases volatile gases that are radiatively participating. A solid is exposed to the radiant energy source and is heated up, and volatile gases are evolved. The gases mix with air in the enclosure due to buoyancy-driven natural convection and diffusion, and finally they would be thermally ignited when the ignition condition was met. The volatiles are considered to be radiatively participating. The pyrolyzing rate of the solid and the gas-phase reaction rate are assumed to be given by the Arrhenius law. Initially, the air in the enclosure is taken to be stagnant and the enclosed air as well as all the surrounding boundaries are assumed to be held at ambient temperature.

The ignition of a solid fuel (PMMA) in a rectangular enclosure when it is suddenly exposed to radiation has been studied both theoretically and experimentally (Kwon et al., 2001). In the numerical simulations, both the surface (heater) and gas-phase radiation were considered. The rapid heating of the adiabatic floor made the flow very unstable, creating complex secondary recirculating flows. Depending on the hot source temperature, the ignition process of the PMMA wall was either controlled by transport of fuel vapor and oxidizer in the vicinity of the hot wall, or by infiltration of hot air into the region near the PMMA wall.

Flame Extinction

It is well established that when the ratio of heat loss rate by conduction and/or radiation to the chemical heat release rate becomes too large, the flame cannot sustain itself (Williams, 1985). Since radiant energy loss decreases flame temperature, one expects that the flame would quench if the temperature drop becomes too great. A review of radiative extinction (quenching) is available (T’ien and Bedir, 1997). Probably the most detailed analysis of radiation (both surface and gas phase) effects on the burning and extinction of a solid fuel in PMMA in a stagnation flow geometry has been performed by Rhatigan et al. (1998). A statistical narrowband model with carbon dioxide and water vapor as the radiating gaseous species was used, and the RTE was solved using the discrete ordinates method. This model was coupled to the conservation equation for energy, and the equations for mass, momentum, and species transport were solved numerically using a one-step overall gas-phase reaction and Arrhenius solid pyrolysis relation.

Figure 2 shows the predicted extinction boundaries for the solid (PMMA) combustion using oxygen mass fraction and stretch rate as the coordinates (Rhatigan et al., 1998). The extinction boundary is U-shaped. The flammability boundaries for surface radiation only and with both gas and surface radiation have the same shape. With gas radiation accounted for, the flammable domain is smaller, and the lowest oxygen limit occurs at a slightly higher stretch rate. The largest difference between these two boundaries occurs at low stretch rates, consistent with findings of other researchers (Maruta et al., 1998; Ju et al., 1999). The other branch of the flammability boundary is by blowoff extinction, as a result of insufficient gas residence time to complete chemical reaction. In the absence of radiant energy loss (adiabatic), the model does not predict an extinction limit.

Figure 2. Comparison of dimensionless maximum temperature (nondimensionalized by Te = 300 K) for a solid fuel (PMMA) stagnation-point diffusion flame (18% O2, 82% N2 mole fraction, p = 1 atm) with different radiation models (from Rhatigan et al., 1998).

REFERENCES

Amos, B. and Frenandez-Pello, A. C., Model for Ignition and Flame Development on a Vaporizing Combustible Surface in a Stagnation Flow: Ignition by Vapor Fuel Radiation Absorption, Combust. Sci. Technol., vol. 62, pp. 331-334, 1988.

Babrauskas, V., Ignition Handbook, Fire Science Publishers, Issaquah, WA, 2003.

Baek, S. W., Kim T. Y., and Kaplan, C. R., Ignition Phenomenon of Solid Fuel in a Confined Rectangular Enclosure, Int. J. Heat Mass Transfer, vol. 40, pp. 89-99, 1997.

Chan, S. H., Combined Radiation and Combustion, Annual Review of Heat Transfer, Vol. 14, C. L. Tien (ed.), Begell House, New York and Redding, CT, pp. 49-64, 2005.

Gaydon, A. G. and Wolfhard, H. G., Flames, 4th ed., Chapman and Hall, London, 1979.

Han, C. Y. and Baek, S. W., Radiation Ignition of Volatile Gases on a Vertical Fuel Plate, Combust. Sci. Technol., vol. 109, pp. 309-325, 1995.

Kuo, K. K., Principles of Combustion, Wiley, Hoboken, NJ, 1986.

Kwon, G. H., Baek, S. W., and Sohn, Y. M., Ignition of Solid Fuel by Thermal Radiation in Confined Rectangular Enclosure: Experiment and Numerical Analysis, Combust. Sci. Technol., vol. 165, pp. 85-110, 2001.

Ju, Y., Guo, H., Liu, F., and Maruta, K., Effects of the Lewis Number and Radiative Heat Loss on the Bifurcation and Extinction of CH4/O2-N2-He Flames, J. Fluid Mech., vol. 379, pp. 165-190, 1999.

Maruta, K., Yoshida, M., Guo, H., Ju, Y., and Niioka, T., Extinction of Low-Stretched Diffusion Flame in Microgravity, Combust. Flame, vol. 112, pp. 181-187, 1998.

Olson, S. L. and Tien, J. S., Buoyant Low-Stretch Diffusion Flames Beneath Cylindrical PMMA Samples, Combust. Flame, vol. 121, pp. 439-452, 2000.

Rhatigan, J. L., Bedir, H., and T’ien, J. S., Gas-Phase Radiative Effects on the Burning and Extinction of a Solid Fuel, Combust. Flame, vol. 112, pp. 231-241, 1998.

T’ien, J. S. and Bedir, H., Radiative Extinction of Diffusion Flames--A Review, Proceedings of 1st Asia-Pacific Conference on Combustion, May 12-15, Osaka, pp. 345-352, 1997.

Turns, S. R., An Introduction to Combustion, 2nd ed., McGraw-Hill, New York, 2000.

Viskanta, R., Radiative Transfer in Combustion Systems. Fundamental and Applications, Begell House, New York and Redding, CT, 2005.

Williams, F. A., Combustion Theory: The Fundamental Theory of Chemically Reacting Flow Systems, 2nd ed., Benjamin/Cummings Publishing, Menlo Park, CA, 1985.

References

  1. Amos, B. and Frenandez-Pello, A. C., Model for Ignition and Flame Development on a Vaporizing Combustible Surface in a Stagnation Flow: Ignition by Vapor Fuel Radiation Absorption, Combust. Sci. Technol., vol. 62, pp. 331-334, 1988.
  2. Babrauskas, V., Ignition Handbook, Fire Science Publishers, Issaquah, WA, 2003.
  3. Baek, S. W., Kim T. Y., and Kaplan, C. R., Ignition Phenomenon of Solid Fuel in a Confined Rectangular Enclosure, Int. J. Heat Mass Transfer, vol. 40, pp. 89-99, 1997.
  4. Chan, S. H., Combined Radiation and Combustion, Annual Review of Heat Transfer, Vol. 14, C. L. Tien (ed.), Begell House, New York and Redding, CT, pp. 49-64, 2005.
  5. Gaydon, A. G. and Wolfhard, H. G., Flames, 4th ed., Chapman and Hall, London, 1979.
  6. Han, C. Y. and Baek, S. W., Radiation Ignition of Volatile Gases on a Vertical Fuel Plate, Combust. Sci. Technol., vol. 109, pp. 309-325, 1995.
  7. Kuo, K. K., Principles of Combustion, Wiley, Hoboken, NJ, 1986.
  8. Kwon, G. H., Baek, S. W., and Sohn, Y. M., Ignition of Solid Fuel by Thermal Radiation in Confined Rectangular Enclosure: Experiment and Numerical Analysis, Combust. Sci. Technol., vol. 165, pp. 85-110, 2001.
  9. Ju, Y., Guo, H., Liu, F., and Maruta, K., Effects of the Lewis Number and Radiative Heat Loss on the Bifurcation and Extinction of CH4/O2-N2-He Flames, J. Fluid Mech., vol. 379, pp. 165-190, 1999.
  10. Maruta, K., Yoshida, M., Guo, H., Ju, Y., and Niioka, T., Extinction of Low-Stretched Diffusion Flame in Microgravity, Combust. Flame, vol. 112, pp. 181-187, 1998.
  11. Olson, S. L. and Tien, J. S., Buoyant Low-Stretch Diffusion Flames Beneath Cylindrical PMMA Samples, Combust. Flame, vol. 121, pp. 439-452, 2000.
  12. Rhatigan, J. L., Bedir, H., and T’ien, J. S., Gas-Phase Radiative Effects on the Burning and Extinction of a Solid Fuel, Combust. Flame, vol. 112, pp. 231-241, 1998.
  13. T’ien, J. S. and Bedir, H., Radiative Extinction of Diffusion Flames--A Review, Proceedings of 1st Asia-Pacific Conference on Combustion, May 12-15, Osaka, pp. 345-352, 1997.
  14. Turns, S. R., An Introduction to Combustion, 2nd ed., McGraw-Hill, New York, 2000.
  15. Viskanta, R., Radiative Transfer in Combustion Systems. Fundamental and Applications, Begell House, New York and Redding, CT, 2005.
  16. Williams, F. A., Combustion Theory: The Fundamental Theory of Chemically Reacting Flow Systems, 2nd ed., Benjamin/Cummings Publishing, Menlo Park, CA, 1985.
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