Flame Temperature and Species Calculations with an Excel/VBA Computer Code

Paper from the AFRC 2013 conference titled Flame Temperature and Species Calculations with an Excel/VBA Computer Code by David G. Lillley

As a contribution to applied combustion calculations with and without dissociation of H2O and CO2, a simple, easy-to-use calculation procedure has been developed that permits rapid generation of general fuel-air and fuel-oxygen combustion with many parameter variations. Many fuels and mixtures, including municipal solid wastes, plastic and nonplastic, may be easily handled in the developed computer code. It is written in Excel/VBA and the program calculations are with immediate graphics of the parameter effects on the results, thus permitting an extensive range of parameter effects to be quickly investigated and assessed. The very-general fuel is specified by way of its C-H-O-N-S content. Over 100 standard fuels are in the data base for immediate calculations. Percentages of these may be specified easily so that several of them (and/or new fuels added by the user) are combined for a single calculation. Additional water content is easily specified by the user. The "air" is specified by way of the volume percent of oxygen, and the other component of "air" (nitrogen and/or carbon dioxide) is specified by the user. So also is the temperature of each inlet, the inlet fuel and "air" streams. The methodology and computer code takes as input also the equivalence ratio. A computer code is described which calculates the adiabatic flame temperature under the following user choices:  Type of fuel (CHONS amounts and heating value on a mass basis specified)  Different equivalence ratios  Type of oxidant (air or oxygen)  With and without limited dissociation of CO2 and H2O, and more detailed dissociation reactions  With "air" as the oxidant, the volume fraction of oxygen is specified  The inlet temperatures of the fuel and oxidant streams individually are specified Two types of results are generated: (a) the adiabatic flame temperature with the equilibrium product species both with and without dissociation; and (b) with the products temperature specified then the heat transfer inside the combustor is calculated, on the basis of products both with and without dissociation. In both these cases, the calculation automatically includes combustion in "air" and oxygen alone. The computer code is very user friendly, with automatic nested loops for parameter variation and automatic generation of graphs, which are particularly useful in assessing the particular process under consideration.

1 Flame Temperature and Species Calculations with an Excel/VBA Computer Code David G. Lilley Lilley & Associates, 7221 Idlewild Acres, Stillwater, Oklahoma 74074 Email: [e-mail] As a contribution to applied combustion calculations with and without dissociation of H2O and CO2, a simple, easy-to-use calculation procedure has been developed that permits rapid generation of general fuel-air and fuel-oxygen combustion with many parameter variations. Many fuels and mixtures, including municipal solid wastes, plastic and non-plastic, may be easily handled in the developed computer code. It is written in Excel/VBA and the program calculations are with immediate graphics of the parameter effects on the results, thus permitting an extensive range of parameter effects to be quickly investigated and assessed. The very-general fuel is specified by way of its C-H-O-N-S content. Over 100 standard fuels are in the data base for immediate calculations. Percentages of these may be specified easily so that several of them (and/or new fuels added by the user) are combined for a single calculation. Additional water content is easily specified by the user. The "air" is specified by way of the volume percent of oxygen, and the other component of "air" (nitrogen and/or carbon dioxide) is specified by the user. So also is the temperature of each inlet, the inlet fuel and "air" streams. The methodology and computer code takes as input also the equivalence ratio. A computer code is described which calculates the adiabatic flame temperature under the following user choices:  Type of fuel (CHONS amounts and heating value on a mass basis specified)  Different equivalence ratios  Type of oxidant (air or oxygen)  With and without limited dissociation of CO2 and H2O, and more detailed dissociation reactions  With "air" as the oxidant, the volume fraction of oxygen is specified  The inlet temperatures of the fuel and oxidant streams individually are specified Two types of results are generated: (a) the adiabatic flame temperature with the equilibrium product species both with and without dissociation; and (b) with the products temperature specified then the heat transfer inside the combustor is calculated, on the basis of products both with and without dissociation. In both these cases, the calculation automatically includes combustion in "air" and oxygen alone. The computer code is very user friendly, with automatic nested loops for parameter variation and automatic generation of graphs, which are particularly useful in assessing the particular process under consideration. I. 0BIntroduction It is often necessary to know the adiabatic flame temperature and corresponding product species composition in a chemically reacting system. However, experimentation to determine this is very delicate, costly, and time consuming. For this reason, theoretical calculations are preferred, where results of calculations from a model can be 2 checked against a limited set of experimental data. Then extrapolations can be made to other conditions of interest. The effect of each parameter on the results may then be deduced theoretically. However, the theoretical prediction of temperature and product species amounts are neither easy nor quick, and available computer codes usually do not have the ease and range of application desired. Standard undergraduate thermodynamics courses present chemical reaction expressions and apply energy balance methods. Both dissociated and non-dissociated product species are also considered. Techniques are generally presented which permit the deduction of the flame temperature and the relative amounts of the individual species in the reaction products. But, the methods used by and large require ‘trial and error' iterative hand calculations, with student interpolation of values from thermodynamic tables and/or the assumption of known constant specific heats. A calculation procedure is described that permits rapid calculation of fuel-air combustion with a very large range of general fuels and conditions covering those for the use of alternative fuels in advanced power generation. Calculations are made via Excel/VBA with immediate graphics of the parameter effects on the results. A large range of useful results have been generated. Parameter variations include: 1. Type of fuel amounts specified via C-H-O-N-S amounts and/or molar (volume) or mass fractions of multi-component fuels 2. Different equivalence ratios 3. Type of oxidant (air or oxygen) 4. With and without limited dissociation of CO2 and H2O, and more detailed dissociation reactions 5. With "air" as the oxidant, the volume fraction of oxygen is specified, the other component of air may be nitrogen or carbon dioxide or a combination of the two, and an amount of water may accompany the inlet fuel and oxidant streams 6. The inlet temperatures of the fuel and oxidant streams individually are specified The most complicated case required nested half-interval searches for temperature and species. Results show the accuracy, robustness and versatility of the code, and its ease of applicability to realistic combustion situations. Useful illustrative calculations were also given for municipal solid wastes, and their adiabatic flame temperature and, alternatively, the combustor internal heat transfer when the exit temperature is known. Current application is to a vast range of additional reaction features. Significant energy savings, higher and uniform thermal field, lower pollution, and smaller size of equipment for a range of furnace applications - these have all been demonstrated via recent advances on High Temperature Air Combustion (HiTAC) or flameless oxidation. Burning of alternative fuels, and prospects of energy recovery from wastes and associated HiTAC technologies, are discussed in Tsuji et al (2003) and Gupta and Lilley (1999 and 2003). The thermal and chemical behavior of these flames depend on the precise fuel composition, preheat temperature, and oxygen concentration of air. Waste heat from a furnace using HiTAC is retrieved and introduced back into the furnace using a regenerator. These features help save energy, which subsequently also reduce the emission of CO2 (greenhouse gas) to the environment. Flames with high temperature air provide significantly higher and more uniform heat flux than normal air, which reduces the equipment size or increases the process material throughput for the same size of equipment. The high temperature air combustion technology can provide significant energy savings (up to about 60%), downsizing of the equipment (about 30%), and pollution reduction (about 25%). In the incineration of municipal solid waste for energy production and minimal pollution, new "high temperature air combustion" HiTAC technologies are evolving. As a contribution to this area of current research interest, a calculation procedure has been developed that permits rapid generation of general fuel-air combustion with many parameter variations. It is written in Excel/VBA and the program calculations are with immediate graphics of the parameter effects on the results, thus permitting an extensive range of parameter effects to be quickly investigated and assessed. The very-general fuel is specified by way of its C-H-O-N-S content. Additional water content is easily specified. The "air" is specified by way of the volume percent of oxygen, and the other component of "air" (nitrogen and/or carbon dioxide) is specified by the user. So also is the temperature of each inlet, the inlet fuel and "air" streams. The methodology and computer code takes as input also the equivalence ratio. Then, results of adiabatic flame temperature are calculated along with the equilibrium product species both with and without dissociation. Alternatively, the products temperature may be specified and the heat transfer in the combustor is then calculated. The computer code is very user friendly, with automatic nested loops for parameter variation and 3 automatic generation of graphs, which are particularly useful in assessing the particular process under consideration. The application now is to incineration of municipal solid waste for energy production and minimal pollution. The waste may consist of a variety of specified components, including plastics and non-plastics, cellulose, cardboard, wood, etc. and the relative amounts are given as inputs. II. 1BFlame Temperature and Product Species Calculation Typically, thermodynamics textbooks present the ideas of chemical reactions, dissociation, flame temperature, and product species; but the techniques given are often in a manner that is not computerizable. Often, even the computerized methods given lack generality and ease of use. On the other hand, combustion-oriented texts (for example, see Kuo (1986)) are not usually studied by engineering undergraduates or graduates who are not combustion specialists. Other texts concentrate on fuels, see Goodger (1975) and Odgers and Kretchmer (1986), and combustion aerodynamics and its applications, see Beer and Chigier (1972) and Gupta and Lilley (1985). None of these texts give general computerized methods for finding the adiabatic flame temperature and product species amounts, including some degree of dissociation. Only advanced research reports (for example, Gordon and McBride (1971)) give very general computerized methods with a significant sophistication given to the dissociation aspects of the calculation. Some combustion-oriented texts do include methods and results of computerized calculations of flame temperature (see, for example, Borman and Ragland (1998) and Turns (2001)) and some texts include a computer code, see, for example, Turns (2001). None of them present easily computerizable flame temperature and species calculation methodologies, with and without dissociation, with oxidizer air alone and pure oxygen, that can be used easily and quickly by the practicing applied combustion engineer. The present objective is to present a useful Exce/VBA code that permits easily a wide range of calculations to be accomplished and graphed easily by the practical man. A straightforward computer code has been developed and is now described which calculates the adiabatic flame temperature and product species amounts for general CHONS fuels. The program is named Adiabatic Flame Temperature Calculation (AFTC). It is useful for calculations within in a computational fluid dynamics reacting flow computation, and it is readily incorporated into undergraduate and graduate course studies. It is based on the methods of Goodger (1977) and Campbell (1979). The theoretical background and computational algorithms used in its development are presented. The parameters used are: fuel type, equivalence ratio, reactant temperatures and pressure, type of oxidant and air composition, and inclusion of dissociation effects. This work builds on previous papers, Lilley (2004) and Olinger and Lilley (2004a and b, and 2005a). Results are given for a range of input parameters so as to illustrate the versatility of the computer program. Associated results applicable to the new technology of high temperature air combustion are given in an associated paper; see Olinger and Lilley (2005b). The standard expression for general fuel-air combustion is: CxHyOzNuSv + m (O2 + f N2 + g CO2 ) + h H2O  n1CO + n2CO2 + n3H2O + n4N2 + n5O2 + n6H2 + n7SO2 The right hand side represents the major combustion product species. Without dissociation, the ni-values are readily specified (the so-called "cold" products of combustion). With dissociation, the more detailed ni-values are deducible via a half-interval search technique at a given temperature. Additionally, more complex dissociated product species may occur, including O, H, OH, and NO. For an oxidizer of standard dry air, f = 3.762. This occurs as standard dry air consists of 21 percent oxygen by volume, and nitrogen is reckoned to provide the other 79 percent. These values correspond to 23.2 percent oxygen by mass and 76.8 percent nitrogen by mass. The value of m is determined from the burning conditions (the amount of oxidant supplied relative to the amount of fuel supplied). It strongly controls the number of moles of product species (n1, n2 …, n7) by restricting complete fuel combustion of the fuel or by adding extra oxidizer for dissociation. Dissociation reactions absorb thermal energy, thus lowering the product's temperature. One of the simplest and most effective assumptions about dissociation is that at high temperatures some of the CO2 in the product stream will dissociate into CO and O2 and some of the H2O in the product stream will dissociate into H2 and O2. These primary reactions are represented by: 4 CO2 = O2 2 CO  1 H2O = 2 O2 2 H  1 The degree of dissociation is dependent on both the combustion pressure and temperature, and is such that the molar (volume) fractions obey the laws of mass action. Appendix A provides detailed information about the iterative solution procedure, with half-interval searches for temperature and species amounts. The methodology for solution of these equations for the adiabatic flame temperature and product species, with and without this limited dissociation, has been described in detail by Lilley (2004) and further development and application by Olinger and Lilley (2004a and b, and 2005a and b). Half interval search procedures in nested loops are used for both temperature and species calculations, using fitted curves for temperature variation of enthalpy and partial pressure chemical equilibrium constants. Energy balance and species conservation checks ensure convergence of the AFTC code. Problem specification, data input, and operation of the computer code are therefore not further discussed here. Half interval search procedures in nested loops are used for both temperature and species calculations, using fitted curves for temperature variation of enthalpy and partial pressure chemical equilibrium constants. Energy balance and species conservation checks ensure convergence of the AFTC code. Problem specification, data input, and operation of the computer code are therefore not further discussed here. Several additions to the core code have been included in two versions of AFTC: A. AFTC -Composite The first version of AFTC, called AFTC-composite, creates a composite fuel by merging a list of user selected fuels. The program allows the user to choose from an array of 200 fuels that are already on the spreadsheet with CHONS composition and lower heating value. The chosen fuels are automatically merged into a single fuel with correct representation of its chemical formula and heating value, and the flame temperature calculations ensue from this. In this way, the new fuel's properties are the respective proportional sums from that of each component fuel. To aid in data generation, this computer program includes additional nested loops for parameter variations. The inner loop runs the basic AFTC code seven times, each time changing the reactant temperatures as per the user's input. Furthermore, the iterated steps are displayed on succeeding pages within the spreadsheet, with each page showing convergence for each case. The outer loop then runs each of these inner loops over a series of seven oxygen percentages in the air, by volume. In this way, forty-nine sets of data for a given pressure and equivalence ratio may be generated quickly and easily, with seven automatically generated graphs. B. AFTC-Multifuel The second version of AFTC, called AFTC-multifuel, keeps the core loop structure of AFTC, and expands upon it to handle many different fuels. The same fuel listing used in the Composite program is used in this variation. Temperature and products are calculated for each fuel in turn, allowing automatic, fast generation of eight graphs and useful tables. These permit immediate comparison of different fuels and properties, such as how the adiabatic flame temperature varies with the carbon number of a fuel, equivalence ratio, inlet reactant (fuel and "air") temperatures, etc. III. 2BResults and Discussion A. Comparison with Other Methods Other methods exist that may offer a more direct solution to the above equations, but at the cost of guaranteed convergence, Campbell (1979). One such method for solving the flame temperature and product composition is to use a Newton-Raphson iteration procedure. This is the method used in both the well-known programs by Turns (2001) and Gordon-McBride (1971). It is also implemented in Ferguson and Kirkpatrick (2001). In addition to the dissociated species accounted for in AFTC, these programs also account for H, NO, O, OH, and N. Goodger (1977) also gives temperature predictions. The present code has been run for a variety of situations and compared very favorably, typically less than a one percent difference in temperature. The results for Turns were obtained by running the program. Results for Gordon-McBride were cited in Glassman (1987). Results for Goodger (1977) and 5 Ferguson and Kirkpatrick (2001) are from their respective books. Table 1 displays the adiabatic flame temperature found by each program. Table 2 then recalculates the results of Table 1 to give each program's percent difference in temperature, relative to the present AFTC calculations. Adiabatic flame temperature values for a variety of fuels found in the above works are listed in Table 1. Furthermore, Table 2 provides the percent differences in these temperatures In all cases where data was available, the percent difference in each work's results is less than two percent. This corresponds to a temperature difference of approximately 30K, despite the different dissociation constraints. Except for Gordon and McBride's result for methane, 1.68%, AFTC showed less than one percent difference with all the programs for the standard hydrocarbons This covers the range from the high temperature acetylene to the relatively low temperature methane. Additionally, the oxygen bearing and nitrogen bearing fuels see an extremely small temperature difference across the different programs. Methanol has a maximum difference of 0.63% and cyanogen has maximum difference of only 0.29%. Finally, hydrogen and carbon monoxide exhibit the greatest disparity across the different programs, both on the order of 1.5%. There are three primary reasons for these slight differences. We take standard air consisting of 21% oxygen, there are 3.762 moles of nitrogen for every mole of oxygen in the air. Some codes use 20.9% oxygen. Additionally, there are slightly different physical constants and different parametric curve-fits of enthalpy versus temperature. We use a simple three parameter curve over the temperature range 1600K to 6000K. And of course, each calculation method has to converge to an answer, but what degree of convergence is used. The precise specification is not well documented in the other methods mentioned here. B. Comparison of General HC Fuels After the comparison with other computer programs, AFTC was run for a variety of different fuels and equivalence ratios, the results of which are displayed at the end of this paper. For example, many fuels, grouped into acetylenes, paraffins, and olefins, are calculated for stoichiometric combustion. These results are given in Figure 1. The adiabatic flame temperature is graphed against the carbon number of the fuel. Notice all the curves, each representing a different class of fuels, converge to one temperature as the carbon number increases. This is justification for the common practice in industry of modeling complex fuels as composites of simpler fuels. After these results were displayed, the equivalence ratio was changed to fuel lean and fuel rich conditions. From Figures 2 and 3, one finds the temperatures are highest for nondissociated combustion. As the equivalence ratio shifts from unity, the temperature decreases. C. Comparison of CHON Fuels With AFTC run for basic HC fuels, the fuel listing was expanded to include fuels containing carbon and hydrogen, results of which are displayed in Figure 4. Once more, the dependency of the flame temperature, and thus dissociation, upon the carbon number is demonstrated. As the carbon number takes a larger fraction of the molecule, the flame temperatures approach a single value. Notice that these fuels have lower heat release on a mass basis than the HC-only fuels. D. Municipal Solid Waste Fuels The plastic/ versus non-plastic relative amounts in municipal solid waste has a dramatic effect on the heating value of the fuel, and the product species produced, and their adiabatic flame temperature or, alternatively, the amount of heat transferred internally in a furnace or boiler when the exit temperature is less than the adiabatic flame temperature. General results have been generated and discussed at length before, see Lilley (2004, 2008 and 2009) and Olinger and Lilley (2004a and b, and 2005a and b). The composition of the waste varies significantly from source to source and also from season to season. Typical composition of the dry MSW is given in Table 3. The presence of moisture (which can vary from 10 to 66%) can have a significant influence on the heating value of the waste. Dry Municipal Solid Waste MSW has an approximate heating value of 16.2 MJ/kg (or equivalently 6,968 Btu/lb), see Table 4. As an example, a 10% increase in moisture will reduce the heating value of waste by about 1.67 MJ/kg (or equivalently 717 Btu/lb). The decrease in heating value (in Btu/lb) with the increase in moisture content can reasonably be estimated from (6968- 71.7 x), where x is the moisture content in weight percent. The average moisture content in material depends on the material type. Food waste may have moisture content of about 70%, while plastic and leather have very low moisture content of about 2%. There are seasonal variations of the moisture and energy content of the wastes. 6 Therefore, the sorting of the material cannot only provide near uniform chemical composition but also energy content. A comparison of heating values of municipal waste with various other waste fuels and biomass is given in Table 4. The data shows that the energy content in the MSW is comparable with some wood material and wastes. 5BE. Calculations of Adiabatic Flame Temperature for Plastics and Non-Plastics Figure 5 shows the adiabatic flame temperature of a variety of plastics and non-plastics burning in fuel lean, standard air, from 25% excess air to stoichiometric, represented by equivalence ratio from 0.8 to 1. As expected, the maximum flame temperatures occur at stoichiometric conditions, and decrease with a decreasing fuel concentration. Polystyrene (C8H8, lower heating value of 39.75 MJ/kg of fuel) and cellulose (C6H10O5, lower heating value of 16.12 MJ/kg of fuel) are used to represent plastic and non-plastic, because their values approximate typical values for all plastics and non-plastics. Adiabatic flame temperatures of composite fuels with different mass fractions of the representative plastic and non-plastic are also calculated, the results of which are shown in Figure 6 and Table 5. As expected, the maximum adiabatic flame temperature occurs at an equivalence ratio of one, and decrease with greater amounts of excess air, as  reduces. Plastic/non-plastic mixtures are calculated for 100%(mass) plastic to 0%(mass) plastic, at intervals of 25%(mass). Notice that, the higher the plastic content, the higher the temperature, because of the higher heating value of the plastic-rich fuel. Also, it is seen that the curves are clustered towards the pure plastic case, indicating that the flame temperature is progressively more sensitive to changes in the non-plastic content, as that content becomes increasingly larger. 6BF. Calculations of Combustor Internal Heat Transfer versus Combustion Product Temperature for Plastics and Non-Plastics In Figures 7 through 9, the internal heat transfer from the flame in the combustor region (of the combustion chamber, furnace or boiler) is calculated, on the basis that the combustor exit temperature is specified. Figure 7 is for a 1500K exit temperature, Figure 8 is for a 1000K temperature, and Figure 9 is for a 500K temperature. Each figure shows the heat transfer from the flame within the furnace as a function of the equivalence ratio. The same variety of fuel plastic/non-plastic mixtures as before is considered. Numerical results for Figures 7 through 9 are given in Tables 6 through 8, respectively. As expected, the heat transfer from the flame is highest (among the range of different fuels and equivalence ratios considered) for pure plastic burning at stoichiometric conditions. This is because the pure plastic at stoichiometric conditions would have had the highest flame temperature. Thus, when the exit temperature is reduced to the specified value, the amount of energy transferred internally is highest. Additionally, comparing the three figures and noting that the ordinate scale changes, the heat transferred from a flame increases as the specified combustion products temperature decreases. That is, the lower the exit temperature, the greater is the internal heat transferred from the flame. Concepts of the specific heat increasing with temperature, more so with greater oxygen and nitrogen content in the combustion products, give rise to why the slope of the lines becomes flatter as the exit temperature is reduced, that is, over Figures 7 through 9. G. Pressure and Oxygen Fraction in "Air" Effects Finally, after varying the equivalence ratio and fuel type, the flame temperature's dependence on the pressure and oxidizer were explored. Figure 10 consists of two flame temperature curves, one for dissociation and one for no dissociation. The first graph has a low pressure of half an atmosphere and serves to illustrate the increased dissociation at below average pressures. As the pressure is increased, the temperatures increase correspondingly. Despite this however, high pressures suppress dissociation, as can be seen in the 5atm and 10atm graphs. This is most clearly seen by noting that the high-pressure temperature curves are closer together than the low-pressure temperature curves. Furthermore, separation of the two curves is delayed until higher temperatures associated with increasing oxygen percents in the "air" occur, with higher temperatures and greater dissociation. IV. 3BConclusions A computer code has been developed using Excel/VBA to permit the rapid calculation of adiabatic flame temperatures and product species compositions for a large variety of easily specified fuel and air reactant conditions. An equilibrium combustion calculator such as AFTC can be a powerful aid to the power generation industry. The most complicated case required nested half-interval searches for temperature and species. Results show the accuracy, robustness and versatility of the code, and its ease of applicability to realistic combustion situations. Useful illustrative calculations were also given for municipal solid wastes, and their adiabatic flame temperature 7 and, alternatively, the combustor internal heat transfer when the exit temperature is known. Results are calculated immediately for the cases of "air" (with specified oxygen volume percentage) as the oxidant, with and without dissociation. Alternatively, the product temperature may be identified, and then the heat transfer in the combustor is calculated. In the user input section, the reaction is simply specified by way of the fuel's CHONS formula and its lower heating value, and the oxidizer's makeup. Once the equivalence ratio is set, a variety of calculations are generated automatically, covering a spectrum of initial parameters. Current application is to a vast range of additional reaction features. 4BReferences Beer, J. M., and Chigier, N. A., (1972) "Combustion Aerodynamics," Wiley, New York, 1972. Borman, G. L., and Ragland, K. W., (1998) "Combustion Engineering," McGraw-Hill, New York, 1998. Campbell, A. S., (1979) "Thermodynamic Analysis of Combustion Engines," Wiley, New York, 1979. Ferguson, C.R. and Kirkpatrick, A.T., "Internal Combustion Engines, Applied Thermosciences 2nd Edition," John Wiley & Sons, New York, 2001 Glassman, I., "Combustion, 2nd Edition," Academic Press, Oralando , 1987 Goodger, E. M., (1975) "Hydrocarbon Fuels," MacMillan, London, 1975. Goodger, E. M., (1977) "Combustion Calculations," MacMillan, London, 1977. Gordon, S., and McBride, B. J., (1971) "Computer Program for Calculation of Complex Chemical Equilibrium Compositions, Rocket Performance, Incident and Reflected Shocks, and Chapman-Jouget Detonations," NASA SP-273, 1971. Gupta, A. K., and Lilley, D. G., (1985) "Flowfield Modeling and Diagnostics," Abacus Press, Tunbridge Wells, England, 1985. Gupta, A. K. and Lilley, D. G., (1999). "Energy Recovery Opportunities from Wastes," AIAA Journal of Propulsion and Power, Vol.15, No. 2, pp.175-180., March/April, 1999. Gupta, A. K. and Lilley, D. G., (2003). "Incineration of Plastics and Other Wastes for Efficient Power Generation: A Review," Paper AIAA-2003-0334, Reno, NV, Jan. 6-9, 2003. Kuo, K. K., (1986) "Principles of Combustion," Wiley, New York, 1986. Lilley, D. G., (2004) "Adiabatic Flame Temperature Calculation: A Simple Approach for General CHONS Fuels," Paper AIAA-2004-0817, Reno, NV, Jan. 5-8, 2004. Lilley, D. G. (2008) "Thermal Field Characteristics with Alternate Fuels in Advanced Power Generation," in Second International Energy 2030 Conference, Abu Dhabi, United Arab Emerites, November 4-5, 2008. Lilley, D. G., (2009) "Municipal Solid Waste Burning Under High temperature Air Combustion Conditions," Paper AIAA-2009-4648, Denver, CO, August 2-5, 2009. Odgers, J., and Kretchmer, D., (1986) "Gas Turbine Fuels and Their Influence on Combustion," Abacus Press, Tunbridge Wells, England, 1986. Olinger, D. S. and Lilley, D. G., (2004a) "Temperature and Product Species with Oxygen-Deficient "Air" Fuel Combustion," Paper ASME PWR2004-52100, Baltimore, MD, Mar. 30-Apr. 1, 2004. 8 Olinger, D. S. and Lilley, D. G., (2004b) "High Temperature Low Oxygen Concentration Flame Calculations," Paper AIAA-2004-5773, Providence, RI, Aug. 16-19, 2004. Olinger, D. S. and Lilley, D. G., (2005a) "Calculation of Temperature and Product Species with General Fuel-Air Combustion," Paper AIAA-2005-0166, Reno, NV, Jan. 10-13, 2005. Olinger, D. S. and Lilley, D. G., (2005b) "Flame Calculations for High Temperature Air Combustion," Paper AIAA- 2005-0171, Reno, NV, Jan. 10-13, 2005. Tsuji, H., Gupta, A. K., Hasegawa, T., Katsuki, M., Kishimoto, K. and Morita, M. (2003). "High Temperature Air Combustion", CRC Press, Boca Raton, FL, 2003. Turns, S. R., (2001) "An Introduction to Combustion," 2nd Edition, McGraw-Hill, New York, 2001. Table 1. Comparisons of the dissociated stoichiometric adiabatic flame temperature (K) as predicted by AFTC, Goodger (1977), Turns (2001), Ferguson and Kirkpatrick (2001), and Gordon and McBride (Glassman, 1987) in dry standard air Comparison of Adiabatic Flame Temperatures (K) Fuel Formula AFTC Goodger Turns F&K G&M Methane CH4 2248 2247 2226 2227 2210 Propane C3H8 2274 2289 2267 2268 - Heptane C7H16 2281 2298 2274 - 2290 Acetylene C2H2 2558 2583 2539 2540 - Methanol CH3OH 2229 2243 2221 - - Hydrogen H2 2419 2444 2382 2383 2400 Carbon Monoxide CO 2364 2399 2383 - 2400 Cyanogen C2N2 2588 - 2594 2596 - Table 2. Percent differences of the dissociated stoichiometric adiabatic flame temperature (K) as predicted by AFTC, Goodger (1977), Turns (2001), Ferguson and Kirkpatrick (2001), and Gordon and McBride (Glassman, 1987) in dry standard air Percent Differences in Adiabatic Flame Temperature Calculations Fuel Formula AFTC Goodger Turns F&K G & M Methane CH4 0 -0.03 -0.97 -0.92 -1.68 Propane C3H8 0 0.67 -0.30 -0.26 - Heptane C7H16 0 0.76 -0.30 - 0.40 Acetylene C2H2 0 0.99 -0.73 -0.69 - Methanol CH3OH 0 0.63 -0.35 - - Hydrogen H2 0 1.05 -1.52 -1.47 -0.77 Carbon Monoxide CO 0 1.46 0.78 - 1.50 Cyanogen C2N2 0 - 0.21 0.29 - 9 Table 3. Characteristic Composition of the Dry Municipal Solid Waste Component Average Content (% weight) Heating Value dry (Btu/lb) Food waste 33.5 6,528 Paper, Cardboard 33.5 7,500 Plastics 9.2 14,000 Ferrous metal 7.8 300 Glass 5.8 250 Leather and rubber 4.8 13,000 Textiles and rags 3.7 7,652 Stones and ceramics 1.5 652 Nonferrous metals 0.2 13,000 Table 4. A Comparison of Heating Values of Municipal Solid Waste with other wastes, Refuse derived Fuels, Biomass and Fossil Fuels Waste Type (Fuel) Heating value (Btu/lb) Heating value (MJ/kg) Cellulose 7,300 17.00 Lignin 9,111 21.20 Wood (Pine) 9,600 22.30 Wood (Oak) 8,296 19.30 Coal (Sub-Bituminous) 11,729 27.30 Peat 8,237 19.20 Municipal Solid Waste (dry) 6,968 16.20 Municipal Solid waste (50% moisture) 3,380 7.90 Refuse derived Fuel (RDF) 7,942 18.50 10 Table 5. Adiabatic Flame Temperature (K) of Mass Mixtures of Plastics (P) and Non-Plastics (NP) vs. Equivalence Ratio FLAME TEMPERATURE (K) Fuel Equivalence Ratio 0.80 0.85 0.90 0.95 1.00 100/0 mass P/NP 2116 2192 2255 2305 2340 75/25 mass P/NP 2103 2177 2240 2289 2324 50/50 mass P/NP 2084 2156 2218 2267 2300 25/70 mass P/NP 2055 2126 2186 2234 2266 Mass Composition 0/100 mass P/NP 2008 2074 2132 2178 2208 Table 6. Heat Transfer From Flame at 1500K vs. Equivalence Ratio for Various Mass Mixtures of Plastic/Non-Plastic HEAT RELEASED (MJ/kg of fuel) Fuel Equivalence Ratio 0.80 0.85 0.90 0.95 1.00 100/0 mass P/NP 14.9 16.2 17.3 18.4 19.3 75/25 mass P/NP 12.5 13.6 14.6 15.4 16.2 50/50 mass P/NP 10.1 11.0 11.8 12.5 13.2 25/70 mass P/NP 7.7 8.4 9.0 9.6 10.1 Mass Composition 0/100 mass P/NP 5.3 5.8 6.3 6.7 7.0 Table 7. Heat Transfer From Flame at 1000K vs. Equivalence Ratio for Various Mass Mixtures of Plastic/Non-Plastic HEAT RELEASED (MJ/kg of fuel) Fuel Equivalence Ratio 0.80 0.85 0.90 0.95 1.00 100/0 mass P/NP 25.9 26.7 27.3 27.9 28.4 75/25 mass P/NP 22.0 22.6 23.2 23.6 24.1 50/50 mass P/NP 18.0 18.5 19.0 19.4 19.8 25/70 mass P/NP 14.1 14.5 14.8 15.1 15.4 Mass Composition 0/100 mass P/NP 10.1 10.4 10.7 10.9 11.1 Table 8. Heat Transfer From Flame at 500K vs. Equivalence Ratio for Various Mass Mixtures of Plastic/Non-Plastic HEAT RELEASED (MJ/kg of fuel) Fuel Equivalence Ratio 0.80 0.85 0.90 0.95 1.00 100/0 mass P/NP 36.0 36.2 36.4 36.6 36.7 75/25 mass P/NP 30.6 30.8 31.0 31.1 31.2 50/50 mass P/NP 25.3 25.4 25.5 25.6 25.7 25/70 mass P/NP 19.9 20.0 20.1 20.2 20.3 Mass Composition 0/100 mass P/NP 14.5 14.6 14.7 14.7 14.8 11 Nondissociated Stoichiometric Combustion in Standard Air 2000 2200 2400 2600 2800 3000 0 5 10 15 20 Carbon Number Adiabatic Flame Temperature (K) ACETYLENES (CxH2x-2) OLEFINS (CxH2x) PARAFFINS (CxH2x+2) Dissociated Stoichiometric Combustion in Standard Air 2000 2200 2400 2600 2800 3000 0 5 10 15 20 Carbon Number Adiabatic Flame Temperature (K) ACETYLENES (CxH2x-2) OLEFINS (CxH2x) PARAFFINS (CxH2x+2) Figure 1. Stoichiometric Adiabatic Flame Temperature as a Function of the Fuel Carbon Number Nondissociated 20% Fuel Lean Combustion in Standard Air 2000 2200 2400 2600 2800 3000 0 5 10 15 20 Carbon Number Adiabatic Flame Temperature (K) ACETYLENES (CxH2x-2) OLEFINS (CxH2x) PARAFFINS (CxH2x+2) Dissociated 20% Fuel Lean Combustion in Standard Air 2000 2200 2400 2600 2800 3000 0 5 10 15 20 Carbon Number Adiabatic Flame Temperature (K) ACETYLENES (CxH2x-2) OLEFINS (CxH2x) PARAFFINS (CxH2x+2) Figure 2. 20% Fuel Lean Adiabatic Flame Temperature as a Function of the Fuel Carbon Number Nondissociated 20% Fuel Rich Combustion in Standard Air 2000 2200 2400 2600 2800 3000 0 5 10 15 20 Carbon Number Adiabatic Flame Temperature (K) ACETYLENES (CxH2x-2) OLEFINS (CxH2x) PARAFFINS (CxH2x+2) Dissociated 20% Fuel Rich Combustion in Standard Air 2000 2200 2400 2600 2800 3000 0 5 10 15 20 Carbon Number Adiabatic Flame Temperature (K) ACETYLENES (CxH2x-2) OLEFINS (CxH2x) PARAFFINS (CxH2x+2) Figure 3. 20% Fuel Rich Adiabatic Flame Temperature as a Function of the Fuel Carbon Number Nondissociated Stoichiometric Combustion in Standard Air 2000 2200 2400 2600 2800 3000 0 5 10 15 Carbon Number Adiabatic Flame Temperature (K) AROMATICS NAPHTHENES (CxH2x) PARAFFINS (CxH2x+2) ALIPHATIC ALCOHOLS Dissociated Stoichiometric Combustion in Standard Air 2000 2200 2400 2600 2800 3000 0 5 10 15 Carbon Number Adiabatic Flame Temperature (K) AROMATICS NAPHTHENES (CxH2x) PARAFFINS (CxH2x+2) ALIPHATIC ALCOHOLS Figure 4. Stoichiometric Adiabatic Flame Temperature as a Function of the Fuel Carbon Number 12 1500 1700 1900 2100 2300 2500 2700 2900 0.8 0.85 0.9 0.95 1 Fuel Equivalence Ratio Adiabatic Flame Temperature (K) polyethylene (s) acetate polyurethane polypropylene polystyrene nylon cardboard cellulose paper Figure 5. Adiabatic Flame Temperature (K) of Different Plastics and Non-Plastics vs. Equivalence Ratio 2000 2100 2200 2300 2400 0.80 0.85 0.90 0.95 1.00 Fuel Equivalence Ratio Adiabatic Flame Temperature (K) 100/0 mass P/NP 75/25 mass P/NP 50/50 mass P/NP 25/70 mass P/NP 0/100 mass P/NP Figure 6. Adiabatic Flame Temperature (K) of Mass Mixtures of Plastics (P) and Non-Plastics (NP) vs. Equivalence Ratio 0.0 5.0 10.0 15.0 20.0 0.80 0.85 0.90 0.95 1.00 Fuel Equivalence Ratio Q (MJ/kgfuel) 100/0 mass P/NP 75/25 mass P/NP 50/50 mass P/NP 25/70 mass P/NP 0/100 mass P/NP Figure 7. Heat Transfer From Flame at 1500K vs. Equivalence Ratio for Various Mass Mixtures of Plastic/Non-Plastic 13 0.0 10.0 20.0 30.0 0.80 0.85 0.90 0.95 1.00 Fuel Equivalence Ratio Q (MJ/kgfuel) 100/0 mass P/NP 75/25 mass P/NP 50/50 mass P/NP 25/70 mass P/NP 0/100 mass P/NP Figure 8. Heat Transfer From Flame at 1000K vs. Equivalence Ratio for Various Mass Mixtures of Plastic/Non-Plastic 0.0 10.0 20.0 30.0 40.0 0.80 0.85 0.90 0.95 1.00 Fuel Equivalence Ratio Q (MJ/kgfuel) 100/0 mass P/NP 75/25 mass P/NP 50/50 mass P/NP 25/70 mass P/NP 0/100 mass P/NP Figure 9. Heat Transfer From Flame at 500K vs. Equivalence Ratio for Various Mass Mixtures of Plastic/Non-Plastic 14 Stoichiomtric Methane Combustion in Air with Varying Oxygen Percentages at 298K and 0.5 Atm. Inlet Conditions 0 1000 2000 3000 4000 0 10 20 30 40 Oxygen Percentage in Air Adiabatic Flame Temperature (K) No Dissociation Burning in Air With Dissociation Burning in Air Stoichiomtric Methane Combustion in Air with Varying Oxygen Percentages at 298K and 1 Atm. Inlet Conditions 0 1000 2000 3000 4000 0 10 20 30 40 Oxygen Percentage in Air Adiabatic Flame Temperature (K) No Dissociation Burning in Air With Dissociation Burning in Air Stoichiomtric Methane Combustion in Air with Varying Oxygen Percentages at 298K and 5 Atm. Inlet Conditions 0 1000 2000 3000 4000 0 10 20 30 40 Oxygen Percentage in Air Adiabatic Flame Temperature (K) No Dissociation Burning in Air With Dissociation Burning in Air Stoichiomtric Methane Combustion in Air with Varying Oxygen Percentages at 298K and 10 Atm. Inlet Conditions 0 1000 2000 3000 4000 0 10 20 30 40 Oxygen Percentage in Air Adiabatic Flame Temperature (K) No Dissociation Burning in Air With Dissociation Burning in Air Figure 10. Flame Temperature for Methane Burning in Stoichiometric "Air", as a Function of Oxygen Percentage and for Varying Combustion Pressures 15 APPENDIX A ADIABATIC FLAME TEMPERATURE CALCULATION: Computational Methodology for General CHONS Fuels 1. PRODUCT SPECIES 1.1 Chemical Balance The discussion is restricted to typical hydrocarbon fuels of the form CxHy where x and y are known for the fuel of interest. Additionally, oxygen, nitrogen and sulfur may be specified as part of the fuel. The paraffins have y = 2x + 2 and include the most familiar fuels: methane CH4, propane C3H8, butane C4H10, and decane C10H22. The results will illustrate computations with these four fuels; other fuels can be handled in a similar fashion. Focusing on 1 kg-mole of fuel, the general expression for burning of a hydrocarbon fuel in air is CxHyOzNuSv+ m (O2 + f N2)  n1CO + n2CO2 + n3H2O + n4N2 + n5O2 + n6H2 + n7SO2 (1) The right hand side represents the major combustion product species. Without dissociation the ni-values are readily specified (so-called "cold" products of combustion), see Section 1.2. With dissociation the ni-values are deducible via a half-interval search technique at a given temperature, see Section 1.3. With more detailed dissociation consideration, additional right hand side product species occur, including O, H, OH, and NO. Information on handling these extra complexities is also given in Section 1.3. If burning takes place in oxygen alone, then f = 0 and n4 = u/2. If the oxidant is air, then f = 3.76 since oxygen represents 21 percent of air by volume and nitrogen is reckoned to provide the other 79 percent. These values are consistent with 23.2 percent oxygen by mass, and 76.8 percent nitrogen by mass. The value of m is determined from the burning conditions (the amount of oxidant supplied relative to the amount of fuel supplied). It controls strongly the amount of product species (the n1, n2, …, n7 values, the kg-mole amounts of product species produced from the burning of 1 kg-mole amounts of product species produced from the burning of 1 kg-mole of fuel). Two values of m have special significance in determination the nondissociated products produced (the products observed when their temperature is low). These two values are: 1. Stoichiometric m = ms = x + y/4 - z/2 + v This amount of oxidant produces entirely CO2 and H2O in the product stream and their amounts are determined. There is no CO or O2 in the products. The familiar stoichiometric (chemically-correct) reaction expression is Eq. (1) with m = ms n1 = n5 = n6 = 0 n2 = x n3 = y/2 n4 = mf + u/2 n7 = v 2. Minimum air m = mmin= x/2 + y/4 - z/2 + v This amount of oxidant is just enough to oxidize all the fuel to CO and H2O. There is no CO2 or O2 in the products. The familiar minimum oxidant reaction expression in Eq. (1) with 16 m = mmin n2 = n5 = n6 = 0 n1 = x n3 = y/2 n4 = mf + u/2 n7 = v The chemically-correct m for stoichiometric burning (ms = x + y/4 -z/2 + v) serves to define the equivalence ratio A0/ E Aof a particular reaction with user-specified m via: A0/ E A = ms/m For a given fuel or fuel blend, m and A0/ E A are related easily with each other. A general burn is either: 1. Fuel rich A0/ E A > 1 and m < ms 2. Fuel lean A0/ E A < 1 and m > ms 3. Stoichiometric A0/ E A = 1 and the nondissociated products are easily determined from x, y and m of the given problem, as illustrated in Section 1.2. Notice that n6 = 0 in all the nondissociated product cases. 1.2 Product Species Without Dissociation The hotter the product species are, the more the assumption of nondissociated products will be incorrect, and flame temperatures calculated with this assumption will also be increasingly in error. In the present section, product species are considered without dissociation; in Section 1.3, this restriction is removed and product species amounts with the inclusion of dissociation are calculated. The values of x, y, z, u, v and m determine the product species molar (volumetric) amounts. If Ufuel leanU m > ms and there is no CO or H2 in the products, and, see Borman and Ragland (1998) and Turns (2001), we have n1 = 0 n2 = x n3 = y/2 n4 = mf + u/2 n5 = m - ms n6 = 0 n7 = v If Ufuel richU m < ms and there is no O2 or H2 in the products, it is assumed that the lack of sufficient oxygen affects the CO2 only (part of the C oxidizing only as far as CO). The very reactive hydrogen H is assumed to fully oxidize to H2O. Then, again see Borman and Ragland (1998) and Turns (2001), we have n1 = 2 (ms - m) n2 = 2 (m - mmin) n3 = y/2 n4 = mf + u/2 17 n5 = 0 n6 = 0 n7 = v These equations hold for m  mmin only. The cases m < mmin are of limited interest, for then not all the fuel burns, flame temperatures are low, ignition is a problem, and poor flames result. These extreme fuel-rich flames will be excluded from further discussion. 1.3 Product Species with Dissociation One of the simplest, effective and most useful assumptions about dissociation is that at high temperatures some of the CO2 in the product stream will dissociate into CO and O2 and some of the H2O in the product stream will dissociate into H2 and O2. This dissociation absorbs energy and reduces the temperature of the product stream. This main dissociation is represented via CO2 = O2 2 CO  1 H2O = 2 O2 2 H  1 The amount of dissociation depends on pressure and temperature, and is such that the molar (volume) fractions obey the laws of mass action. Following Goodger (1977) and Campbell (1979), these can be written in the form   1 2 T 5 1 2 CO n n p n n K 2  (2)   1 2 T 5 6 3 H O n n p n n K 2  (3) where n1, n2, …, n7 are the molar species amounts (see Eq. (1)), p is the total pressure (in atmospheres), and nT = n1 + n2 + … + n7. The value of the partial pressure equilibrium constants KCO2 and H2O K can be expressed in terms of temperature T via K(T) = exp [ a/T + (b + c/T) lnT + d ] (4) where T is in degrees Kelvin, and the coefficients a, b, c and d are constants given in Table 1 (from Campbell, 1979) for the useful range 1600 < T < 6000. Table 1 Coefficients for Eq. (4) Constant a b c d KCO2 33,805.0 0.7422 165.8 -16.5739 H2O K 42,450.0 -1.074 -2,147.0 3.2315 18 The two equations, Eqs. (2) and (3), are supplemented by five chemical element balance equations from Eq. (1): n1 + n2 = x 2n3 + 2n6 = y n1 + 2n2 + n3 + 2n5 = 2m + z n4 = mf+ u/2 n7 = v These seven equations, at a given pressure and temperature, suffice to determine the product stream coefficients n1, n2, …, n7. If the temperature of the product stream is known, a half-interval search technique can be used (for the species molar amounts ni) as described in Goodger (1977). The initial estimate for the molar fraction of oxygen (taken as 0.4 is usually satisfactory) is sequentially refined until the seven n values simultaneously satisfy the required seven equations. A half-interval search technique is used; it is robust and converges rapidly. After the main dissociations of CO2 and H2O are established, further dissociation of the product species can be determined in a similar fashion, via: O2 = 2 O H2 = 2 H OH = O + H 2 NO = O2 + N2 with partial pressure equilibrium constants similar to Eqs. (2) and (3), and given by fitted curves like Eq.(4). Parameters for the calculation of the K values are available in a form similar to Table 1. If the product stream temperature is unknown, an outer loop with half-interval search for temperature is needed - it is described in the next section. 2. TEMPERATURE 2.1 Energy Balance Consider 1 kg-mole of fuel and other reactants entering and reacting inside a control volume fixed in space. The products of combustion leave the control volume. The process is supposed to be in steady state operation at constant pressure. No work is done by the gaseous mixture in the control volume, but heat is supplied to it in the amount of Q Joules per kg-mole of fuel entering. The appropriate steady flow energy equation version of the first law of thermodynamics (neglecting kinetic energy which is usually small in combustion cases relative to other changes) is simply Q = P - R =  ne he -  ni hi (5) where P = total energy in product stream, R = total energy in reactant stream, and the summations are over all species energies, ne = kg-moles of species e, and he = specific enthalpy of species e in Joules/kg-mole of species e (in exit stream), and ni and hi are similarly defined for the inlet stream. The he and hi depend on the species in question and temperature. The fuel stream enthalpy includes its chemical enthalpy (the energy it releases when burned), this being calculated in the computer code from its given "Heating Value" or "Heat of Combustion". 19 When Q equals zero, the temperature of the product stream is called the adiabatic flame temperature. When both reactants and products are at 298 K, the heat added (Q J/kg-mole of fuel - usually Q is negative since typical combustion reactions are exothermic) to achieve this is the negative of the heat of combustion of the fuel (J/kg-mole of fuel), quoted as the net (lower) value if the product species are considered to be in gaseous form, and as the gross (higher) value if product species condense to liquid form. Other names are: calorific value, heating value, and enthalpy of combustion (reaction). 2.2 Enthalpy Calculations Following Campbell (1979), the enthalpies (kJ/kg-mole of species) of the high temperature (1600 < T < 6000) gaseous product species may be expressed as h = A + BT + C ln T (6) with T in degrees Kelvin. Table 2 gives the constants for the six product species of interest. Table 2. Coefficients for Eq. (6) Species A B C CO 309,070. 39.29 -6,201.9 CO2 93,048. 68.58 -16,979.0 H2O 154,670. 60.43 -19,212.0 N2 44,639. 39.32 -6,753.4 O2 127,010. 46.25 -18,798.0 H2 461,750. 46.23 -27,649.0 For most hydrocarbon fuels, heating values are typically about 45 MJ/kg of fuel, tables of values are readily available in thermodynamics and combustion texts. For example: Methane 50.05 MJ/kg Propane 46.39 Butane 45.77 Decane 44.63 These values are input to the computer code, and then internally calculation is made of the "fuel enthalpy" which is easily calculated using a stoichiometric version of Eq. (5) with reactants and products at 298 K, and nondissociated gaseous species in the product stream. Table 3. Enthalpies of reactants at 298 K Species Enthalpy kJ/kg-mole CH4 887,166. C3H8 2,204,156 C4H10 2,856,436. C10H22 6,769,800. O2 17,200. N2 15,780 20 The so-calculated "enthalpies" of the reactant species are given in Table 3; these values include the chemical enthalpy of the fuel. If the reactants enter at temperatures higher than 298 K, additional enthalpy is calculated using appropriate specific heat values and the temperature range. Note that the fuel enthalpy includes the "chemical enthalpy" of the fuel, so that this amount of total reactant energy is all-important. For the adiabatic flame temperature, one seeks a temperature at which the total enthalpy of the products is equal to this reactant energy. When the product stream temperature is known, a calculation of the heat transferred inside the combustor/furnace is simply calculated as the difference between the energies of the reactants and the products. 2.3 Temperature Calculations Adiabatic flame temperatures are found using a half-interval search technique, seeking to find a product species temperature for which Q is zero, see Eq. (5). The method is described in Campbell (1979). The first trial for T is 4000 K, and the first T correction is 2000 K. The procedure is: 1. Guess T of products 2. Calculate Q = P - R 3. If Q is positive, take new T = T - T If Q is negative, take new T = T + T 4. Half T 5. Return to step 2 Steps 2 through 5 are repeated until Q is small. Typically, 15 such iterations are used to obtain the outlet temperature to within 1 degree Kelvin. When used with known nondissociated product species amounts of Section 2.2, the half-interval search for product temperature is the only iterative sequence required. When used with dissociated product species amounts, which depend on temperature, see Section 1.3, the half-interval search for temperature provides an outer loop. An inner loop is for the product species amounts, using another half-interval search described in Section 1.3. 3. THE COMPUTER CODE 3.1 The Computer Code Structure AFTC is a computer code that has two capabilities. One possibility is calculating the adiabatic flame temperature and the product species for the given reactants. The second possibility is that of calculating the amount of heat transferred within the combustor when a specified exit stream temperature is given. After the dimension and data segments, the code is divided into eight chapters: 1. Preliminaries and four problem loops 2. Outer loop for product outlet temperature 3. Inner loop for product species amounts 4. No dissociation case, product species are known 5. Dissociation calculations for product species 6. Check sum of product species for convergence 7. Check first law for adiabatic reaction 8. Storage, loop terminators and final print 21 3.2 Problem Specification/Data Input The situation considered in the computer code has the following data: 1. Enthalpy and fuel identification characters (x, y, z, u, v) 2. Enthalpy-temperature expression parameters 3. Inlet temperatures of the fuel and oxidant streams 4. In "air" as the oxidant, specification of the percent by volume in the air is permitted 5. Dissociation case: total pressure in atmospheres and partial pressure equilibrium constants of CO2 and H2O - these are calculated from fitted curves vs temperature The above data are input in the data segment. SI units are used exclusively. 3.3 Solution Algorithm The user specifies the fuel via the input table which has a range of fuels already included, and the molar amounts of each fuel component in the case of a composite fuel. Any new fuel can easily be specified via its C, H, O etc content and its lower heat of combustion. Internally, the stoichiometric and minimum air m values are then calculated. The multiplier m of the "air" or oxidant bracket of Eq. (1), with prompts as to the ms and mmin values for his specified fuel. The user also specifies the equivalence ratio from which the air bracket multiplier m is calculated. A further prompt requests the oxygen volume percent of the "air" stream, for the air-fuel reaction; from the value supplied, the f-value is calculated. If the default value of 21 percent is taken, a value of f = 3.76 results. The user is also prompted to supply inlet temperatures of the reactant streams (typically 298 degrees K. The combustor pressure is supplied in atmospheres. He is makes the choice for finding the adiabatic flame temperature (in which case this is calculated in the code) or specifying the outlet temperature (in which case the heat transferred inside the combustor is calculated). Internally, two nested loops control the solution procedure according to the problem situation. These loops handle the following parameters: 1. Dissociation effect loop - where this effect is to be considered or not 2. Oxidant loop - which determines the burning to be in "air" or oxygen The VBA code behind the Excel sheet is written and divided into "Chapters". The initial estimate of outlet temperature is given in Chapter 2 of the computer code, taken as 4000 degrees K. Two nested iteration loops are need to converge upon the correct temperature and species amounts. The outer loop of iterations provides a half-interval search for the correct outlet temperature for an adiabatic reaction is used; the first law is checked in Chapter 7 of the computer code, a revised estimate of the temperature is calculated, and control is returned to Chapter 2. This provides the outer loop. An inner loop for the product species molar amounts when dissociation is included; otherwise, no inner loop iterations are needed. With dissociation, an initial estimate of the ratio n5/nT is given in Chapter 3 of the computer code. This represents the number of moles in oxygen in the product divided by the total number of moles in the product. A half-interval search for the correction ratio and the product species amounts is used; the check is made in Chapter 6, a revised estimate is calculated, and control is returned to Chapter 3. This provides the inner loop.