Adiabatic flame temperature, equations

When the reaction is conducted under adiabatic conditions, all of the heat generated, rijQj, is converted to the enthalpy of the products T2 then becomes Tji which is defined as the adiabatic flame temperature. Equation (2.17) becomes... 

The adiabatic flame temperature is defined as the maximum possible temperature achieved by the reaction in a constant pressure process. It is usually based on the reactants initially at the standard state of 25 °C and 1 atm. From Equation (2.20), the adiabatic temperature (7 i[Pg.30]

Note that when q" = 0, 7b is the adiabatic flame temperature. We can regard this equation as a balance between the net energy released and energy lost ... 

It is further found that the adiabatic flame temperature is approximately 1300 °C for mixtures involving inert diluents at the lower flammable limit concentration. The accuracy of this approximation is illustrated in Figure 4.19 for propane in air. This approximate relationship allows us to estimate the lower limit under a variety of conditions. Consider the resultant temperature due to combustion of a given mixture. The adiabatic flame temperature (7f ad), given by Equation (2.22) for a mixture of fuel (Xp), oxygen (Xo2) and inert diluent (Xd) originally at 7U, where all of the fuel is consumed, is... 

The heat of combustion amounts to 7483 cal/g of aluminum fuel and the adiabatic flame temperature calculated by the NASA chemical equilibrium program [6] is 4005 K. The combustion equation for aluminum and steam is... 

Though the above equations are nonlinear and complex, 1 and tij may be computed for any combustion reaction for which thermochemical data are available. In the following, the reaction -t Oj at 2 MPa is used to demonstrate a representative computation, illustrating the procedure for the determination of T)-and rij and reiterating the principles of thermochemical equilibrium and adiabatic flame temperature. Eirst, the following reaction scheme and products are assumed ... 

Solution of this algebraic equation yields T = 2146 K, which is the adiabatic flame temperature. 

The equation is correct because the total enthalpy is conserved and the enthalpy is a state function so that the enthalpy change is independent of the path the process takes as long as the initial and final states are kept unchanged. The adiabatic flame temperature 7 can be found by solving the equation for Tf. 

Among the assumptions that led to the equation above - TReact is equal to the adiabatic flame temperature, conversion is 100% and reference enthalpy is equal to the specific enthalpy of the feed streams - the last one represented by equation (7) seems to be the most questionable one. 

In terms of the adiabatic flame temperature that can be achieved with given inlet temperatures and fuel mass fractions, Tn.ad, eq. (12b) represents isotherms, lines of constant flame temperature. A proper interpretation of eq. (12a) may be as follows Solutions of eq. (12a) are lines of constant flame temperature taking the energy loss from the L.E. to the E.E. s into account. From fig. 6 it can be seen that the extinction line of the enhanced 3EM is a solution of the equation (12b) as well as the one according to the standard 3EM, is a solution of equation (12a). 

Assume an adiabatic flame temperature Te and calculate the corresponding equilibrium composition with the proper set of equilibrium and material balance equations. 

At 1 atmosphere pressure the adiabatic flame temperature is 2500°C (using equation (7.1), which results when the product is TiOa solid and the gases are fed at 100°C. When the product is TiOa liqviid the adiabatic flame temperature is 1350°C. These two temperatvires are above and below the fusion temperature for TiOa of 1825°C, and for this reason the TiOa produced is for the most part solid with a fraction liquid. But this fixes the flame temperature at the fusion temperature of 1825 C. At 1 atmosphere pressure and 1825 + 273 K, the initial 11 moles of reactants and final 11 moles of gaseous products will occupy 1892 liters of volume giving the initial reactant concentration 0.00053 moles/liter TiCU, 0.00423 moles/liter Na, and 0.00106 moles/liter Oa. 

As the hot boundary is approached (t 1), / goes to zero, causing X ) to approach zero [see equation (88)]. Since equation (90) then implies that X approaches zero at the hot boundary for n > 1, the series given in equation (96) should converge rapidly as the adiabatic flame temperature is approached. On the other hand, near the cold boundary b is small and, therefore, the series tends to converge slowly upstream [see equation (99)]. 

A thermodynamic quantity of considerable importance in many combustion problems is the adiabatic flame temperature. If a given combustible mixture (a closed system) at a specified initial T and p is allowed to approach chemical equilibrium by means of an isobaric, adiabatic process, then the final temperature attained by the system is the adiabatic flame temperature T. Clearly depends on the pressure, the initial temperature and the initial composition of the system. The equations governing the process are p = constant (isobaric), H = constant (adiabatic, isobaric) and the atom-conservation equations combining these with the chemical-equilibrium equations (at p, T ) determines all final conditions (and therefore, in particular, Tj). Detailed procedures for solving the governing equations to obtain Tj> are described in [17], [19], [27], and [30], for example. Essentially, a value of Tf is assumed, the atom-conservation equations and equilibrium equations are solved as indicated at the end of Section A.3, the final enthalpy is computed and compared with the initial enthalpy, and the entire process is repeated for other values of until the initial and final enthalpies agree. 

The calculation of an adiabatic flame temperature follows the general procedure outlined in Section 9.5b. Unknown stream flow rates are lirst determined by material balances. Reference conditions are chosen, specific enthalpies of feed components are calculated, and specific enthalpies of product components are expressed in terms of the product temperature, Finally, AH(Tiii) for the process is evaluated and substituted into the energy balance equation (Aw = 0), which is solved for... 

The following two-equation model [202], provides a better adiabatic flame temperature and a reasonable estimate of the CO concentration at equilibrium ... 

If all the heat liberated by a reaction goes into heating up the products of combustion (the flue gas), the temperature achieved is defined as the flame temperature. If the combustion process is conducted adiabatically, with no heat transfer loss to the surroundings, the final temperature achieved by the flue gas is defined as the adiabatic flame temperature. If the combustion process is conducted with theoretical or stoichiometric air (0% excess), the resulting temperature is defined as the theoretical adiabatic flame temperature (TAFT). TAFT represents the maximum temperature the products of combustion (flue) can achieve if the reaction is conducted both stoichiometrically and adiabatically. For this condition, all the energy liberated on combustion at or near standard conditions (A//° and/or A//298) appears as sensible heat in heating up the flue products, A/fp. This may be represented in equation form as... 

This expression may now be equated with the negative of the enthalpy of reaction (or combustion) to calculate the theoretical adiabatic flame temperature. This procedure is illustrated in the solution to this problem. 

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