RADIATIVE TRANSFER IN LAMINAR FLAMES
Following from: Radiative transfer in combustion systems; Combustion phenomena affected by radiation
Leading to: Radiative transfer in turbulent flames; Radiative transfer in combustion chambers; Radiative transfer in two-phase combustion; Thermal radiation in unwanted fires
The role of radiation in laminar and turbulent flames has recently been reviewed (Chan, 2005; Viskanta 2005), and computational methods for solving the RTE in combustion systems have been discussed (Viskanta, 2008). These methods allow one to simulate chemically reacting flow and heat transfer in multidimensional combustion systems.
In the vast majority of fundamental flame studies, radiation has been neglected, partly because in many instances radiation plays only a secondary role and partly also because the accounting for thermal radiation is a difficult task. Radiation from flames has also been thought to be important only in furnaces and in fires of sufficient size (DeRis, 1979; Sarofim, 1986). In the past two decades or so, a number of fundamental theoretical studies have demonstrated the key role of radiation in determining the combustion behavior. The effects include: (i) lowering flame temperature due to energy loss, (ii) a change in the flame structure due to flame temperature decrease, (iii) a heat feedback mechanism in addition to conduction and convection in condensed fuel combustion, and (iv) causing flame quenching. Some of the radiative effects are quantitative in nature, but others are caused by qualitative changes in the flame behavior. In the few subsections that follow, we discuss the laminar and turbulent flames as well as a few related topics.
Laminar Flames
The basic structure of simple (1D) laminar flames is understood and has been modeled (Dixon-Lewis, 1990; Williams, 1985; Turns, 2000). A distinguishing feature of a gaseous flame is that it is a localized reaction zone that is able to self-propagate through the gaseous mixture supporting it. Fundamental theoretical and experimental studies of radiative transfer effects in laminar opposed flow, diffusion, premixed, partially premixed, axisymmetric stagnation, and jet flames as well as others have been reviewed, and it is found that considerable progress has been made in understanding the effects of radiation on the flame structure, flame temperature, and minor species formation. The main advantage for accounting of radiation in laminar, nonsooty flames is that they are more readily amenable to analysis. The radiation from gaseous species carbon dioxide, water vapor, and fuel vapor can be analyzed using band models, at least in simple flames (e.g., 1D geometry) (Viskanta, 2005).
A comparison of several radiative transfer models for a laminar diffusion flame, with CO_{2} and H_{2}O as the participating media, has been made (Bedir et al., 1997). Computed results for the net radiant energy loss/gain for wideband, narrowband, and SLWSGG (spectral line-based weighted sum of gray gases) models show reasonable agreement with each other, but the results from the optically thin and gray gas models with Planck mean absorption coefficient are shown to underestimate the emission substantially for the low stretch flame. Generally, the use of the optically thin medium approximation or the gray gas approximation with the Planck mean absorption coefficient tend to underestimate self-absorption and to overestimate the emission. This is the conclusion of Bedir et al. (1997).
Radiative transfer needs to be accounted for in the conservation of energy equation. For a 1D flame, the energy equation is (Shih et al., 1999)
(1) |
The divergence of the radiative flux (last term in the equation) can be approximated by a number of different models to account for the spectral (nongray) nature of radiation. For the sake of concreteness, we use the weighted sum of gray gases (WSGG) model to approximate the total radiative flux divergence (i.e., volumetric radiant energy loss/gain) d/dy as (Kim et al., 2003)
(2) |
The two integral terms on the right-hand side of the equation represent absorption of radiation originating at location y' that reaches location y. The third term on the right-hand side represents emission of radiation at location y, and M is the number of equivalent gray gases. Depending on what kind of narrowband model is being used (Kim et al., 2003), the total weighting factors W_{i}(y') and W_{i}(y) are functions of wave number and temperature for the narrowband calculations, and only a function of temperature for the total calculations. In writing Eq. (2), the walls “surrounding” the flame have been assumed to be gray and cold.
It is expected that there is a net radiant energy loss from the high-temperature zone owing to a greater radiation emission resulting from the higher-temperature region that also contains more radiating species. Hence, radiant energy loss from the flame lowers its temperature. The magnitude of temperature drop depends on the ratio of radiant energy loss to the rate of combustion heat release. This ratio increases when advection decreases. The maximum flame temperature drop occurs at the quenching limit when advection (convection) is at the minimum (Shih et al., 1999; Wang and Niioka, 2002).
The change in temperature due to radiation is shown in Fig. 1 as a function of X - X_{stoic} and mixture fraction, respectively. For calculations, the temperature change shows the temperature difference from adiabatic case for emission-only and emission/absorption cases. As hypothetical measured temperature change, the temperature difference between adiabatic calculation and experimental data (Barlow et al., 2001) is also plotted as a symbol for the comparison. The large temperature change appears at the rich premixed flame zone due to the radiation effects on flame structure. The X - X_{stoic} location at which the temperature is about 1200 K on the fuel-rich side of the premixed flame changes by ~2.1 mm between the adiabatic and the emission-only model of radiation (Zhu et al., 2002). The peak temperature change is about 1030 K for the emission-only case, and 750 K for the emission/absorption case. The emission-only calculation shows high temperature change at both the rich premixed flame and the diffusion flame zone compared to the emission/absorption case. The emission/absorption calculation shows good agreement with measurement, except for a few points near the rich premixed side.
Figure 1. Change in temperature distribution caused by emission and self-absorption (Zhu et al., 2002).
Calculations have shown that radiative transfer can alter significantly chemical reactions and species concentrations in laminar, partially premixed and premixed flames. For example, Chan et al. (1998) studied the effects of radiative transfer on the structure in a CH_{4}-air flamlet with global and detailed chemistry. The laminar diffusion flame was studied using a complex reaction mechanism (GRI-Mech.2.11) that contains 49 species and 279 reversible chemical reactions for the methane-air reaction. Besides the major species (O_{2}, CH_{4}, CO_{2}, H_{2}O, etc.), the minor (NO, CO, etc.) and intermediate species (OH, O, H, etc.) are all presented. The maximum value of the radiative flux divergence (net volumetric rate of radiant energy loss/gain), the maximum chemical heat release rate due to the reaction to the total heat release for each flamlet, and the ratio of the total radiant heat loss due to the total heat release for each flamlet have been calculated. The results show that when the ratio is large (e.g., 60% for low stretches), this can cause flame extinction.
The effects of radiation energy loss on the flame structure and NO formation in opposed-flow diffusion and partially premixed flames have been studied (Gore et al., 1999; Zhu et al., 2002). It was found that radiation changes the quantitative and qualitative response of the temperature and mole fractions of CO, H_{2}, C_{2}H_{2}, and NO to the stretch rate and equivalence ratio. The effects of radiation are significant at lower stretch rates and low-equivalence ratio partially premixed flames.
Confined Laminar Diffusion Flames
A detailed numerical simulation of axisymmetric coflow partially premixed methane-air laminar flames (Fig. 2) has been carried out (Claramunt et al., 2004). Chemical reactions were modeled using GRI-Mech 3.0 (http:www.gri.org), which contains 53 species and 325 reactions. The mechanism is suitable for the description of pollutant formation because it includes NO_{x} reactions. Radiation transfer is modeled using the optically thin approximation. The radiating species considered included CO_{2}, H_{2}O, CH_{4}, and CO. The model predictions were validated by comparisons with experimental data (McEnally and Pfefferle, 1999). Consideration of radiative transfer has shown to affect considerably the flame temperature and therefore pollutant formation.
Figure 2. Confined coflow methane-air laminar flame: (a) burner idealized geometry and (b) definition of different zones for the nonequispaced cylindrical grid (after Claramunt et al., 2004).
A detailed numerical simulation of axisymmetric coflow partially premixed methane-air laminar flames (Fig. 2) has been carried out (Claramunt et al., 2004). Chemical reactions were modeled using GRI-Mech 3.0 (http:www.gri.org), which contains 53 species and 325 reactions. The mechanism is suitable for the description of pollutant formation because it includes NO_{x} reactions. Radiation transfer is modeled using the optically thin approximation. The radiating species considered included CO_{2}, H_{2}O, CH_{4}, and CO. The model predictions were validated by comparisons with experimental data (McEnally and Pfefferle, 1999). Consideration of radiative transfer has shown to affect considerably the flame temperature and therefore pollutant formation.
Simulation of combustion and soot formation in luminous diffusion flames has been reviewed, and progress made has been assessed (Viskanta, 2005). The major challenge appears to be soot production in sooting fuels. Computation of soot volume (mass) fraction from fundamental physics-chemistry principles is hindered by the difficulty of predicting soot formation. A comprehensive state-of-the-art review and discussion of the essential chemistry of soot formation has been prepared by Kennedy (1997). An experimental and computational study of soot formation in an axisymmetric laminar diffusion flame has been carried out (Smooke et al., 1999; Liu et al., 2004), in which equations for soot particle production have been coupled to the mass, momentum, and energy, and species conservation equations have been solved for an axisymmetric, laminar coflow diffusion flame. The 2D system couples detailed transport and finite rate chemistry (GRI Mech 2.11) in the gas phase. The treatment accounts for the transport, inception, surface growth, oxidation, and coalescence of soot particles. Radiative transfer and both contributions by soot and radiating gaseous species (CO_{2} H_{2}O, CO) were considered and approximated using the optically thin model. The temperature, soot volume fraction, and selected species predictions are compared to experimental data for a confined methane-air flame.
REFERENCES
Barlow, R. S., Karpetis, A. N., Frank, J. H., and Chen, J.-Y., Scalar Profiles and NO Formation in Laminar Opposed-Flow Partially Premixed Methane/Air Flames, Combust. Flame, vol. 127, pp. 2102-2118, 2001.
Bedir, H., T’ien, J. S., and Lee, H. S., Comparison of Different Radiation Treatments for a One-Dimensional Diffusion Flame, Combust. Theory Modeling, vol. 1, pp. 395-404, 1997.
Chan, S. H., Yin, J. Q., and Shi, B. J., Structure and Extinction of Methane-Air Flamlet with Radiation and Detailed Chemical Kinetic Mechanism, Combust. Flame, vol. 112, pp. 445-456, 1998.
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.
Claramunt, K., Consul, R., Pérez-Segarra, C. D., and Oliva A., Multidimensional Mathematical Modeling and Numerical Investigation of Co-Flow Partially Premixed Methane/Air Laminar Flames, Combust. Flame, vol. 137, pp. 444-457, 2004.
DeRis, J., Fire Radiation--A Review,Proc. Combust. Inst., vol. 17, pp. 1003-1015, 1979.
Dixon-Lewis, G., Structure of Laminar Flames, 23rd Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, pp. 305-324, 1990.
Kennedy, I. M., Models of Soot Formation and Oxidation, Prog. Energy Combust. Sci., vol. 23, pp. 95-132, 1997.
Liu, F., Guo, H., and Smallwood, G. S., Effects of Radiation on the Modeling of a Maninar Coflow Methane/Air Diffusion Flame, Combust. Flame, vol. 138, pp. 136-154, 2004.
Kim, O. J., Gore, J. P., Viskanta, R., and Zhu, X. L., Prediction of Self-Absorption of Radiation on an Opposed Flow Diffusion and Partially Premixed Flames Using Weighted Sum of Gray Gases Model (WSGGM)-Based Spectral Model, Numer. Heat Transfer, Part A, vol. 44, pp. 335-353, 2003.
McEnally, C. S. and Pfefferle, L. D., Experimental Study of Nonfuel Hydrocarbon Concentrations in CoFlowing Premixed Mehane/Air Flames,Combust. Flame, vol. 118, pp. 619-632, 1999.
Sarofim, A. F., Radiation Heat Transfer in Combustion: Friend or Foe, Proc. Combust.Inst., Vol. 21, The Combustion Institute, Philadelphia, pp. 1-23, 1986.
Shih, H. Y., Bedir, H. Tien, J. S., and Song, C. J., Computed Flammability Limits of Opposed- Jet H_{2}/O_{2}/N_{2} Diffusion Flames at Low Pressure, J. Propul. Power, vol. 15, no. 6, pp. 903-908, 1999.
Smooke, M. D., Mcenally, C. S., Pfefferle, L. D., Hall, R. J., and Colket, M. B., Computational and Experimental Study of Soot Formation in a Coflow, Laminar Diffusion Flame, Combust. Flame, vol. 117, pp. 117-139, 1999.
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.
Viskanta, R., Computation of Radiative Transfer in Combustion Systems, Int. J. Num. Methods for Heat and Fluid Flow, vol. 18, no. 3/4, pp. 415-442, 2008.
Williams, F. A., Combustion Theory: The Fundamental Theory of Chemically Reacting Flow Systems, 2nd ed., Benjamin/Cummings Publishing, Menlo Park, CA, 1985.
Wang, J. and Niioka, T., Numerical Study of Radiation Reabsorption Effect on No_{x} Formation in CH_{4}/Air Counterflow Premixed Flames, Proc. Combust. Inst., vol. 29, pp. 2211-2218, 2002.
Zhu, X. L., Gore, J. P., Karpetis, A. H., and Barlow, R. S., The Effects of Self-Absorption of Radiation on an Opposed Flow Partially Premixed Flame, Combust. Flame, vol. 129, pp. 342-345, 2002.
Zhu, X. L., Kim, O. J., Gore, J. P., Takeno, T., and Viskanta, R., The Radiation-Chemistry. Interactions in an Opposed Flow Methane/Air Partially-Premixed Flame, Proc. of 2002 Technical Meeting of the Central State Section of the Combustion Institute, The Combustion Institute, Pittsburgh, 2002.
References
- Barlow, R. S., Karpetis, A. N., Frank, J. H., and Chen, J.-Y., Scalar Profiles and NO Formation in Laminar Opposed-Flow Partially Premixed Methane/Air Flames, Combust. Flame, vol. 127, pp. 2102-2118, 2001.
- Bedir, H., T’ien, J. S., and Lee, H. S., Comparison of Different Radiation Treatments for a One-Dimensional Diffusion Flame, Combust. Theory Modeling, vol. 1, pp. 395-404, 1997.
- Chan, S. H., Yin, J. Q., and Shi, B. J., Structure and Extinction of Methane-Air Flamlet with Radiation and Detailed Chemical Kinetic Mechanism, Combust. Flame, vol. 112, pp. 445-456, 1998.
- 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.
- Claramunt, K., Consul, R., Pérez-Segarra, C. D., and Oliva A., Multidimensional Mathematical Modeling and Numerical Investigation of Co-Flow Partially Premixed Methane/Air Laminar Flames, Combust. Flame, vol. 137, pp. 444-457, 2004.
- DeRis, J., Fire Radiation--A Review,Proc. Combust. Inst., vol. 17, pp. 1003-1015, 1979.
- Dixon-Lewis, G., Structure of Laminar Flames, 23rd Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, pp. 305-324, 1990.
- Kennedy, I. M., Models of Soot Formation and Oxidation, Prog. Energy Combust. Sci., vol. 23, pp. 95-132, 1997.
- Liu, F., Guo, H., and Smallwood, G. S., Effects of Radiation on the Modeling of a Maninar Coflow Methane/Air Diffusion Flame, Combust. Flame, vol. 138, pp. 136-154, 2004.
- Kim, O. J., Gore, J. P., Viskanta, R., and Zhu, X. L., Prediction of Self-Absorption of Radiation on an Opposed Flow Diffusion and Partially Premixed Flames Using Weighted Sum of Gray Gases Model (WSGGM)-Based Spectral Model, Numer. Heat Transfer, Part A, vol. 44, pp. 335-353, 2003.
- McEnally, C. S. and Pfefferle, L. D., Experimental Study of Nonfuel Hydrocarbon Concentrations in CoFlowing Premixed Mehane/Air Flames,Combust. Flame, vol. 118, pp. 619-632, 1999.
- Sarofim, A. F., Radiation Heat Transfer in Combustion: Friend or Foe, Proc. Combust.Inst., Vol. 21, The Combustion Institute, Philadelphia, pp. 1-23, 1986.
- Shih, H. Y., Bedir, H. Tien, J. S., and Song, C. J., Computed Flammability Limits of Opposed- Jet H_{2}/O_{2}/N_{2} Diffusion Flames at Low Pressure, J. Propul. Power, vol. 15, no. 6, pp. 903-908, 1999.
- Smooke, M. D., Mcenally, C. S., Pfefferle, L. D., Hall, R. J., and Colket, M. B., Computational and Experimental Study of Soot Formation in a Coflow, Laminar Diffusion Flame, Combust. Flame, vol. 117, pp. 117-139, 1999.
- 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.
- Viskanta, R., Computation of Radiative Transfer in Combustion Systems, Int. J. Num. Methods for Heat and Fluid Flow, vol. 18, no. 3/4, pp. 415-442, 2008.
- Williams, F. A., Combustion Theory: The Fundamental Theory of Chemically Reacting Flow Systems, 2nd ed., Benjamin/Cummings Publishing, Menlo Park, CA, 1985.
- Wang, J. and Niioka, T., Numerical Study of Radiation Reabsorption Effect on No_{x} Formation in CH_{4}/Air Counterflow Premixed Flames, Proc. Combust. Inst., vol. 29, pp. 2211-2218, 2002.
- Zhu, X. L., Gore, J. P., Karpetis, A. H., and Barlow, R. S., The Effects of Self-Absorption of Radiation on an Opposed Flow Partially Premixed Flame, Combust. Flame, vol. 129, pp. 342-345, 2002.
- Zhu, X. L., Kim, O. J., Gore, J. P., Takeno, T., and Viskanta, R., The Radiation-Chemistry. Interactions in an Opposed Flow Methane/Air Partially-Premixed Flame, Proc. of 2002 Technical Meeting of the Central State Section of the Combustion Institute, The Combustion Institute, Pittsburgh, 2002.