RADIATION TRANSFER IN COMBUSTION CHAMBERS
Following from: Radiative transfer in combustion systems; Combustion phenomena affected by radiation; Radiative transfer in laminar flames; Radiative transfer in turbulent flames
Leading to: Radiative transfer in two-phase combustion; Thermal radiation in unwanted fires
Radiative heat transfer plays an important role since it controls charge heating in furnaces and is a key mechanism in thermal heat losses and wall heat fluxes. Examples of combustion systems (usually large in scale) in which radiation is the prime mode of heat transfer include different types of furnaces for materials processing (Viskanta and Bergman, 1998), boilers (furnaces) for steam and power generation using gaseous fuels, fuel sprays and pulverized coal as fuels, and numerous others. An earlier review of radiative transfer in combustion systems is available (Viskanta and Mengüç, 1987), and a newer account can be found in a recent book (Viskanta, 2005). It is beyond this brief account to discuss the simulation of practical combustion devices, including radiative transfer, and only three broad areas of significant research effort are highlighted here. They include gas-fired combustion chambers and furnaces for materials processing. Boilers for steam generation are important combustion systems. Heat transfer (including radiation) in shell and immersion boilers for low- and high-temperature plants are discussed by Rhine and Tucker (1991), and reference is made to this account for detailed discussion.
Gas-Fired Combustion Chambers
Combustion and radiation are very different phenomena. Combustion is described through balances of mass, momentum, energy, and species over small (elementary) volumes, whereas radiative transfer involves long-range interaction. Thus, taking radiation into account in numerical simulations of combustion systems lead to two main difficulties. The first one is linked to limited computer resources (CPU requirements), and the second one is a more theoretical one requiring the solving of the RANS balance equations, which give access to local mean temperature and species concentrations. Whereas, radiative transfer requires information on the instantaneous local temperature and radiating species concentrations along the optical paths that usually are not available from RANS calculations.
As a concrete example simulation a combustion chamber (i.e., a device for converting chemical energy), consider a typical axisymmetric chamber for gas combustion. Two reactant streams emerge from two separate coaxial jets producing a diffusion flame. The fuel is injected from the central jet, whereas the oxidizer (combustion air) enters from the outer annular jet. The combustor is modeled by a cylindrical enclosure containing radiatively absorbing-emitting, but nonscattering, gases. The presence of soot particles can be accounted for if needed, since models for the spectral absorption coefficient are available (Viskanta, 2005) in terms of the soot volume fraction. The flow field, temperature, and species concentration distributions are to be calculated. The temperature of the combustion chamber walls bounding the products and heat transfer in and through the walls to the ambient environment are to be accounted for.
Turbulent flow, chemical reactions, and radiative transfer are simulated using the Favre-averaged transport equations and the Reynolds-averaged Navier-Stokes (RANS) equations with the standard k-ε turbulence model used (Pope, 2000). The conservation equations of mass, species, momentum, and energy can be expressed in generalized form as
(1) |
where is any of the variables, Γ_{ϕ} is the general diffusion coefficient, and S_{ϕ} is the source for the variable and is given in Viskanta (2005).
The most important condition that couples the gas phase to the solid (chamber wall) phase is the interface condition. This condition (at n = 0) can be expressed in terms of a local energy balance as
(2) |
where n stands for a coordinate normal to the boundary. The second term on the left-hand side of the equation represents the net local radiative flux, which can be calculated by solving the (total) radiant energy equation. The right-hand side of Eq. (2) represents the heat loss rate through the combustion chamber wall, with U being the overall heat transfer coefficient. This coefficient accounts for the thermal resistances of the (composite) wall as well as for the convective and radiative resistances on the outside (i.e., between the chamber wall and the ambient surroundings). The other boundary and inflow as well as outflow conditions must be specified to close the problem mathematically.
Turbulence and chemical reaction models for gaseous combustion processes have been extensively reviewed (Magnussen and Hjertager, 1976; Khalil, 1982; Veynante and Vervisch, 2002). By employing simplifying assumptions to achieve feasible solutions of chemical reaction equations, coupled with the turbulent fluid mechanics, a number of models have been developed based on the hypothetical time scales associated with chemical reaction and turbulent mixing time scales. The two simplest and commonly accepted models are the eddy breakup (EBU) (Magnuseen and Hjertager, 1976) and the mixture fraction/PDF (Khalil, 1982; Brewster et al., 1999). Only a brief discussion of the approaches that have been and are being used to simulate combustion systems is presented, and reference is made to publications for applications of the models (Louis et al., 2001; Orsino et al., 2001). The laminar flamelet, the conditional closure, the large eddy simulation (LES), and other advanced models are promising methods, and are becoming practical for non-premixed and premixed combustor simulations with radiative transfer.
In the EBU modeling approach, the reacting species are assumed to be premixed or the turbulent mixing time scale is taken to be very fast compared with the reaction time scale (Magnussen and Hjertager, 1976; Orsino et al., 2001). In this case, turbulent mixing can be ignored, and the fuel is burned instantaneously after it has been mixed.
Numerous approaches for modeling radiative transfer in turbulent unconfined and confined flames have been developed for self-absorbing media and include directional averaging, differential approximation, energy (zonal, statistical Monte Carlo, numerical), and hybrid methods. Reference is made to recent accounts (Viskanta 2005, 2008) for methods used in combustion systems. Different methods such as mean property, stochastic, and other approaches have been used to account for turbulence-radiation interaction (TRI) in combustion chambers. For example, the mean property model neglects TRI and underestimates the emission from the gas because of the nonlinearity of the spectral blackbody radiance with temperature. Radiative transfer in turbulent combustion systems can be treated using stochastic methods (Faeth et al., 1989). However, the stochastic approach is not practical for combustion chambers because it is too time consuming, whereas the TRI methods are as of yet not sufficiently general or developed for application in practical combustor simulations. More recently, a numerical simulation of non-premixed combustion of natural gas in atmospheric air in an axisymmetric cylindrical chamber has been reported (Silva et al., 2007). Turbulence is modeled by the standard k-εmodel, and chemical reactions by EDU. Thermal radiation is handled by the weighted sum of gray gases (WSGG) model, but TRI is neglected. The results indicate that while thermal radiation has a strong effect on temperature and heat transfer, its effect on chemical reactions is of less importance.
Existing multidimensional combustion chamber simulation models have been assessed and predictions compared with experimental (operating) data (Viskanta, 2005). The gas turbine combustor is a very important technological device, and during the last several decades has received major attention owing to growing concerns about atmospheric pollution and global warming (Lefebvre, 1983; Lefebvre and Ballal, 2010). Detailed radiative transfer (including TRI) studies and experimental measurements have been undertaken, and the interested reader is referred elsewhere (Viskanta, 2005) for the accounts.
Combustion and Heat Transfer in Furnaces
In the context of this discussion, “furnaces” refer to all fossil fuel-fired combustion systems in which heat is to be imparted from the hot combustion products to the “load” (sink). The load could be an inert solid, or fluid circulated in tubes located in the combustion chamber (i.e., boiler), or can take other forms (i.e., material being heated and melted). Release of gases into the combustion space owing to the transformations and/or chemical reactions in the load undergoing heating is not considered. It is beyond the scope of this limited account to discuss the large array of different furnaces encountered in materials processing (i.e., metal in a metallurgical furnace), manufacturing, steam generation, process heating, and other applications (Khalil, 1982; Blokh, 1988; Rhine and Tucker, 1991). This section is focused on a limited class of gas-fired, high-temperature furnaces that are more generic in nature. A discussion of low-temperature furnaces such as kilns, ovens, etc., can be found in Rhine and Tucker (1991).
A fossil fuel-fired furnace is typically comprised of three essential elements, namely, an enclosure with a heat source (i.e., a burner with flows of air or some oxidizer and the flow of exhaust gases) in which the load is located, a load (sink) to which heat is transferred, and the walls of the enclosure. A rigorous mathematical description of radiative transfer in enclosures describing a combustion system is available (Viskanta, 2005). The numerical calculations to be carried out on the spectral or even gray bases are very tedious and not practical for typical engineering analysis and design purposes. In addition, the temperature and concentration distributions needed as inputs to calculate radiative transfer quantities are not known a priori and must be calculated from the energy and species conservation equations simultaneously. The presence of the load complicates matters even further. Simulation of furnace dynamics and performance involves modeling of three essential components of the system, which are the combustion chamber, the walls of the chamber, and the load. The three models are intimately coupled, and this is indicated schematically in Fig. 1.
Figure 1. Schematic representation of a furnace simulation model (Viskanta, 2005).
The three components of a furnace require physical descriptions as well as the thermodynamic and thermophysical properties of the materials. The enclosure with its structural elements as well as the load are intimately coupled through the heat and mass transfer processes between the three components of the combustion system. As a concrete example, consider a metal reheating furnace. The most important elements of such a system, including the flame/combustion products, load, furnace walls, and waste gases, and some of the more important thermal interactions among the elements, are illustrated schematically in Fig. 1. The complexity of the processes and the interactions occurring in the furnace are apparent and indicate the difficulty in simulating realistically the processes, the dynamics, and the thermal performance of the system.
The models for analyzing heat transfer in furnaces are essentially of four types and are classified and briefly summarized in order of their complexity (Viskanta, 2005) as follows.
Zero-Dimensional (“well-stirred furnace”) Model. In this model, it is assumed that the gas temperature, the radiating species concentrations, and the system walls are at a uniform temperature, but the temperatures of the gas and the walls are considered to be different. In addition, the gas is taken as gray. The assumption of uniform temperature and composition of the combustion products implies a “well-stirred” system and may be appropriate if gas recirculation is included. The steady state version of the well-stirred furnace model is described by algebraic equations only. The model has been found to make substantially correct predictions of the relation among the global dominant variables for a wide range of furnaces (Hottel, 1974; Viskanta and Mengüç, 1987). The model served well its purpose during the time when digital computers were not available. The unsteady state version of the model may include ordinary differential equations, and this relative simplicity makes it particularly useful for simulating systems that are dynamic in nature.
One-Dimensional (“plug flow furnace”) Model. This model is appropriate when the temperature, the gas composition, and the system walls vary predominantly in one direction only. It is a reasonable representation of a long furnace or a tube in which variations over the cross section are small. If radiative transfer along the system is ignored, the steady state model is described by a first-order differential equation, while the unsteady state model is described by partial differential equations for combustion products, load, and walls (Hottel, 1974; Chapman et al., 1991).
Two-Dimensional Model. In this model, the variations in gas temperature as well as composition and wall temperatures occur in two directions. An example of such a system is an axisymmetric furnace. The model is described by a system of partial differential equations that can be solved numerically using explicit “marching integration” if there is no recirculation in the system. In the presence of axial recirculation, iterative methods are required (Khalil, 1982; Viskanta and Mengüç, 1987).
Three-Dimensional Model. This is the most general case and variations of gas temperature and species compositions as well as wall temperatures occur in all directions. This situation arises in most practical and small furnaces. The model is described by a system of partial differential and integral and/or integrodifferential equations that require numerical solution.
In combustion chambers, the load (sink) is absent. Owing to limited computer resources, the earlier furnace simulation models used the Hottel zone method for treating radiative transfer (Hottel, 1961, 1974). Unfortunately, the method is not readily adaptable and requires a large amount of input data and exchange areas for simulating multidimensional and often complex industrial furnace geometries. In addition, the currently available CFD algorithms for solving the conservation equations are incompatible with the nature of the zone method for treating radiative transfer. Finally, the zone method requires large amount of computer memory, and long run times, particularly using WSGG and other more realistic nongray gases models for simulating practical furnaces.
REFERENCES
Blokh, A. G., Heat Transfer in Steam Boiler Furnace, Hemisphere Publishing, Washington (1988).
Brewster, B. S., Cannon, J. R., Farmer, J. R., and Meng, F., Modeling of Lean Premixed Combustion Stationary Gas Turbines, Prog. Energy Combust. Sci., vol. 25, pp. 353-385, 1999.
Chapman, K. S., Ramadhyani, S., and Viskanta, R., Modeling and Parametric Studies of Heat Transfer in a Direct-Fired Continuous Reheating Furnace, Metal. Trans. B., vol. 22, pp. 513-521, 1991.
Faeth, G. M., Gore, J. P., Church, S. G., and Jeng, S.-M., Radiation from Turbulent Diffusion Flames, Annual Review of Numerical Fluid Mechanics and Heat Transfer, C. L. Tein and T. C. Chawla (eds.), Hemisphere Publishing, New York, pp. 1-38, 1989.
Hottel, H. C., Radiative Transfer in Combustion Chambers, J. Inst. Fuel, vol. 34, pp. 220-233, 1961.
Hottel, H. C., First Estimates of Industrial Furnace Performance--The One-Zone Model Re-Examined, Heat Transfer in Flames, N. H. Afgan and J. H. Beer (eds.), Scripta Book Co., New York, pp. 5-54, 1974.
Khalil, E. E., Modeling of Furnaces and Combustors, Abacus Press, Kent, 1982.
Lefebvre, A. H., Gas Turbine Combustion, Hemisphere Publishing, Washington, 1983.
Lefebvre, A. H. and Ballal, D. R., Gas Turbine Combustion: Alternative Fuels and Emissions, 3rd ed., CRC Press, Boca Raton, 2010.
Louis, J. J. J., Kok, J. B. W., and Klein, S. A., Modeling and Measurements of a 16-kW Turbulent Nonadiabatic Syngas Diffusion Flame in a Cylindrical Combustion Chamber, Combust. Flame, vol. 125, pp. 1012-1031, 2001.
Magnussen, B. I. and Hjertager, B. H., On Mathematical Modeling of Turbulent Combustion with Special Emphasis on Soot Formation and Combustion, 16th Symposium International on Combustion, The Combustion Institute, Pittsburgh, pp. 719-729, 1976.
Orsino, S., Weber, R., and Bolletini, U., Numerical Simulation of Combustion of Natural Gas with High-Temperature Air, Combust. Sci. Technol., vol. 170, pp. 1-34, 2001.
Pope, S. B., Turbulent Flows, Cambridge University Press, Cambridge, 2000.
Rhine, J. R. and Tucker, R. J., Modelling of Gas-Fired Furnaces and Boilers, British Gas plc, London, 1991.
Silva, C. V., France, F. H. R., and Vilmo, H. A., Analysis of the Turbulent, Non-Premixed Combustion of Natural Gas in a Cylindrical Chamber with and without Thermal Radiation Combust. Sci. Technol., vol. 179, pp. 1605-1630, 2007.
Veynante, D. and Vervisch, L., Turbulent Combustion Modeling, Prog. Energy Combust. Sci., vol. 28, pp. 193-266, 2002.
Viskanta, R. and Mengüç, M. P., Heat Transfer in Combustion Systems, Prog. Energy Combust. Sci., vol. 13, pp. 97-160, 1987.
Viskanta, R. and Bergman, T. L., Heat Transfer in Materials Processing, Handbook of Heat Transfer, 3rd ed., W. M. Rohsenow, J. P. Hartnett, and Y. I. Cho (eds.), McGraw Hill, New York, Chap. 18, 1998.
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. Numer. Methods Heat Fluid Flow, vol. 18, no. 3/4, pp. 415-442, 2008.
Referencias
- Blokh, A. G., Heat Transfer in Steam Boiler Furnace, Hemisphere Publishing, Washington (1988).
- Brewster, B. S., Cannon, J. R., Farmer, J. R., and Meng, F., Modeling of Lean Premixed Combustion Stationary Gas Turbines, Prog. Energy Combust. Sci., vol. 25, pp. 353-385, 1999.
- Chapman, K. S., Ramadhyani, S., and Viskanta, R., Modeling and Parametric Studies of Heat Transfer in a Direct-Fired Continuous Reheating Furnace, Metal. Trans. B., vol. 22, pp. 513-521, 1991.
- Faeth, G. M., Gore, J. P., Church, S. G., and Jeng, S.-M., Radiation from Turbulent Diffusion Flames, Annual Review of Numerical Fluid Mechanics and Heat Transfer, C. L. Tein and T. C. Chawla (eds.), Hemisphere Publishing, New York, pp. 1-38, 1989.
- Hottel, H. C., Radiative Transfer in Combustion Chambers, J. Inst. Fuel, vol. 34, pp. 220-233, 1961.
- Hottel, H. C., First Estimates of Industrial Furnace Performance--The One-Zone Model Re-Examined, Heat Transfer in Flames, N. H. Afgan and J. H. Beer (eds.), Scripta Book Co., New York, pp. 5-54, 1974.
- Khalil, E. E., Modeling of Furnaces and Combustors, Abacus Press, Kent, 1982.
- Lefebvre, A. H., Gas Turbine Combustion, Hemisphere Publishing, Washington, 1983.
- Lefebvre, A. H. and Ballal, D. R., Gas Turbine Combustion: Alternative Fuels and Emissions, 3rd ed., CRC Press, Boca Raton, 2010.
- Louis, J. J. J., Kok, J. B. W., and Klein, S. A., Modeling and Measurements of a 16-kW Turbulent Nonadiabatic Syngas Diffusion Flame in a Cylindrical Combustion Chamber, Combust. Flame, vol. 125, pp. 1012-1031, 2001.
- Magnussen, B. I. and Hjertager, B. H., On Mathematical Modeling of Turbulent Combustion with Special Emphasis on Soot Formation and Combustion, 16th Symposium International on Combustion, The Combustion Institute, Pittsburgh, pp. 719-729, 1976.
- Orsino, S., Weber, R., and Bolletini, U., Numerical Simulation of Combustion of Natural Gas with High-Temperature Air, Combust. Sci. Technol., vol. 170, pp. 1-34, 2001.
- Pope, S. B., Turbulent Flows, Cambridge University Press, Cambridge, 2000.
- Rhine, J. R. and Tucker, R. J., Modelling of Gas-Fired Furnaces and Boilers, British Gas plc, London, 1991.
- Silva, C. V., France, F. H. R., and Vilmo, H. A., Analysis of the Turbulent, Non-Premixed Combustion of Natural Gas in a Cylindrical Chamber with and without Thermal Radiation Combust. Sci. Technol., vol. 179, pp. 1605-1630, 2007.
- Veynante, D. and Vervisch, L., Turbulent Combustion Modeling, Prog. Energy Combust. Sci., vol. 28, pp. 193-266, 2002.
- Viskanta, R. and Mengüç, M. P., Heat Transfer in Combustion Systems, Prog. Energy Combust. Sci., vol. 13, pp. 97-160, 1987.
- Viskanta, R. and Bergman, T. L., Heat Transfer in Materials Processing, Handbook of Heat Transfer, 3rd ed., W. M. Rohsenow, J. P. Hartnett, and Y. I. Cho (eds.), McGraw Hill, New York, Chap. 18, 1998.
- 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. Numer. Methods Heat Fluid Flow, vol. 18, no. 3/4, pp. 415-442, 2008.