The adiabatic flame temperature

Fig. 1. The postulated flame stmcture for an AP composite propellant, showing A, the primary flame, where gases are from AP decomposition and fuel pyrolysis, the temperature is presumably the propellant flame temperature, and heat transfer is three-dimensional followed by B, the final diffusion flame, where gases are O2 from the AP flame reacting with products from fuel pyrolysis, the temperature is the propellant flame temperature, and heat transfer is three-dimensional and C, the AP monopropellant flame where gases are products from the AP surface decomposition, the temperature is the adiabatic flame temperature for pure AP, and heat transfer is approximately one-dimensional. AP = ammonium perchlorate.

Oxidizers. The characteristics of the oxidizer affect the baUistic and mechanical properties of a composite propellant as well as the processibihty. Oxidizers are selected to provide the best combination of available oxygen, high density, low heat of formation, and maximum gas volume in reaction with binders. Increases in oxidizer content increase the density, the adiabatic flame temperature, and the specific impulse of a propellant up to a maximum. The most commonly used inorganic oxidizer in both composite and nitroceUulose-based rocket propellant is ammonium perchlorate. The primary combustion products of an ammonium perchlorate propellant and a polymeric binder containing C, H, and O are CO2, H2, O2, and HCl. Ammonium nitrate has been used in slow burning propellants, and where a smokeless exhaust is requited. Nitramines such as RDX and HMX have also been used where maximum energy is essential. 

Flame Temperature. The adiabatic flame temperature, or theoretical flame temperature, is the maximum temperature attained by the products when the reaction goes to completion and the heat fiberated during the reaction is used to raise the temperature of the products. Flame temperatures, as a function of the equivalence ratio, are usually calculated from thermodynamic data when a fuel is burned adiabaticaHy with air. To calculate the adiabatic flame temperature (AFT) without dissociation, for lean to stoichiometric mixtures, complete combustion is assumed. This implies that the products of combustion contain only carbon dioxide, water, nitrogen, oxygen, and sulfur dioxide. 

Actual temperatures in practical flames are lower than calculated values as a result of the heat losses by radiation, thermal conduction, and diffusion. At high temperatures, dissociation of products of combustion into species such as OH, O, and H reduces the theoretical flame temperature (7). Increasing the pressure tends to suppress dissociation of the products and thus generally raises the adiabatic flame temperature (4). 

The radiation from a black body is proportional to the fourth power of the adiabatic flame temperature, according to the Stefan-Boltzmann s law ... 

For a gas containing combustibles, the adiabatic flame temperature is given by... 

K for lean methane/air = 0.455) flames, with and without RHL, respectively, indicated as nonadiabatic and adiabatic. Symbol indicates the adiabatic flame temperature Tad-... 

For the adiabatic condition in which RHL is suppressed, the flame response exhibits the conventional upper and middle branches of the characteristic ignition-extinction curve, with the upper branch representing the physically realistic solutions. It can be noted that the effective Le of this lean methane/air mixture is sub-unity. It can be seen from Figure 6.3.1 that, with increasing stretch rate, first increases owing to the nonequidiffusion effects (S > 0), and then decreases as the extinction state is approached, owing to incomplete reaction. Furthermore, is also expected to degenerate to the adiabatic flame temperature, when v = 0. 

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]

Calculate the adiabatic flame temperatures for the following mixtures initially at 25 °C ... 

Calculate the adiabatic flame temperature (at constant pressure) for ethane C2H6 in air ... 

A furnace used preheated air to improve its efficiency. Determine the adiabatic flame temperature (in K) when the furnace is operating at a mass air to mass fuel ratio of 16. Air enters at 600 K and the fuel enters at 298 K. Use the following approximate properties ... 

For our estimations and the adiabatic control volume in Figure 4.10, 7b should be the adiabatic flame temperature. Consider a fuel-lean case in which no excess fuel leaves the control volume. All the fuel is burned. Then by the conservation of species,... 

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... 

Given that the lower flammability limit of n-butane (w-C4H10) in air is 1.8 % by volume, calculate the adiabatic flame temperature at the limit. Assume the initial temperature to be 25 °C. Use Table 4.5. 

What is the LFL in air of a mixture of 80 % (molar) methane and 20 % propane by Le Chatelier s rule What is the adiabatic flame temperature of this system ... 

It is reported that the adiabatic flame temperature for H2 at the lower flammability limit (LFL) in air is 700 °C. From this information, estimate the LFL, in % by volume, for the hydrogen-air mixture at 25 °C. Assume water is in its vapor phase within the products. 

Using the assumption of a minimum flame temperature needed for ignition of the mixture, determine the minimum fuel mass loss rate per unit surface area (m l) to cause flame propagation through the boundary layer. The heat of combustion that the volatile wood produces (Ahc) is 15 kJ/g. (Hint the adiabatic flame temperature at the lower flammable limit for the mixture in the boundary layer must be at least 1300 °C.)... 

Turbulent fire plume temperatures do not generally exceed 1000 °C. This is well below the adiabatic flame temperature for fuels. Why ... 

The parameters essential for the evaluation of combustion systems are the equilibrium product temperature and composition. If all the heat evolved in the reaction is employed solely to raise the product temperature, this temperature is called the adiabatic flame temperature. Because of the importance of the temperature and gas composition in combustion considerations, it is appropriate to review those aspects of the field of chemical thermodynamics that deal with these subjects. 

Referring back to Eq. (1.10), when all the heat evolved is used to raise the temperature of the product gases, AH and Qp become zero. The product temperature T2 in this case is called the adiabatic flame temperature and Eq. (1.10) becomes... 

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