Flame temperature, adiabatic

The adiabatic flame temperature is calculated for powdered solid fuel and liquid and gaseous fuel assuming that the standard enthalpy of the reaction is entirely absorbed adiabatically in Explosives the entire mass of combustion products (i.e., ashes, residues, and flue gases) exhibiting an 

The heat of reaction is given by the difference between the heat of formation of the reactants and that of the products. When the temperature of the reactant T0 becomes the temperature of the product Tlt the energy change due to chemical reaction is represented by the energy conservation law as[4 71 

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

Though the set of equations are nonlinear and complex, computations of Tf and rtj for any combustion reactions are possible as long as the thermochemical data are available. The reaction of 3H2 + 02 at 2 MPa is demonstrated as an example computation to identify the procedure for the determinations of Tf and rtj and to understand the principle of a thermochemical equilibrium and adiabatic flame temperature. First, the following reaction scheme and products are assumed  

The mass of the each chemical species is conserved before and after reaction. For the number of hydrogen atoms, 

The chemical species of the products are all in the chemical equilibrium state as 

A heat-flow calorimeter is a variation of an isothermal-jacket calorimeter. It uses a thermopile (Fig. 2.7) to continuously measure the temperature difference between the reaction vessel and an outer jacket acting as a constant-temperature heat sink. The heat transfer takes place mostly through the thermocouple wires, and to a high degree of accuracy is proportional to the temperature difference integrated over time. This is the best method for an extremely slow reaction, and it can also be used for rapid reactions. 

A flame calorimeter is a flow system in which oxygen, fluorine, or another gaseous oxidant reacts with a gaseous fuel. The heat transfer between the flow tube and a heat sink can be measured with a thermopile, as in a heat-flow calorimeter. 

With a few simple approximations, we can estimate the temperature of a flame formed in a flowing gas mixture of oxygen or air and a fuel. We treat a moving segment of the gas mixture as a closed system in which the temperature increases as combustion takes place. We assume that the reaction occurs at a constant pressure equal to the standard pressure, and that the process is adiabatic and the gas is an ideal-gas mixture. 

The principle of the calculation is similar to that used for a constant-pressure calorimeter as explained by the paths shown in Fig. 11.11 on page 334. When the combustion reaction in the segment of gas reaches reaction equilibrium, the advancement has changed hy and the temperature has increased from T to T2. Because the reaction is assumed to he adiabatic at constant pressure, A7/(expt) is zero. Therefore, the sum of A//(rxn, T ) and A7/(P) is zero, and we can write 

The value of T2 that satisfies Eq. 11.6.1 is the estimated flame temperature. Problem 11.9 presents an application of this calculation. Several factors cause the actual temperature in a flame to be lower the process is never completely adiabatic, and in the high temperature of the flame there may be product dissociation and other reactions in addition to the main combustion reaction. 

Equation (2.18) can be split into two separate equations as follows  

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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. 

Figure 4 illustrates the trend in adiabatic flame temperatures with heat of combustion as described. Also indicated is the consequence of another statistical result, ie, flames extinguish at a roughly common low limit (1200°C). This corresponds to heat-release density of ca 1.9 MJ/m (50 Btu/ft ) of fuel—air mixtures, or half that for the stoichiometric ratio. It also corresponds to flame temperature, as indicated, of ca 1220°C. Because these are statistical quantities, the same numerical values of flame temperature, low limit excess air, and so forth, can be expected to apply to coal—air mixtures and to fuels derived from coal (see Fuels, synthetic). 

Fig. 4. Variation of adiabatic flame temperature with heat of combustion where + i+i°yk— CO- Note change of scale at 46.5 MJ /kg (20,000...

The insensitivity of adiabatic flame temperature to heat of combustion does not necessarily apply to the operational flame temperature, T, which is the flame temperature found in an actual furnace (remembering that this refers to some average temperature). The higher excess air requirements at higher C/H ratios coupled with greater thermal loads on longer flames generally results in markedly lower operational temperatures as the C/H ratio increases. 

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). 

Adiabatic flame temperatures agree with values measured by optical techniques, when the combustion is essentially complete and when losses are known to be relatively small. Calculated temperatures and gas compositions are thus extremely useful and essential for assessing the combustion process and predicting the effects of variations in process parameters (4). Advances in computational techniques have made flame temperature and equifibrium gas composition calculations, and the prediction of thermodynamic properties, routine for any fuel-oxidizer system for which the enthalpies and heats of formation are available or can be estimated. 

Design of explosion suppression systems is clearly complex, since the effectiveness of an explosion suppression system is dependent on a large number of parameters. One Hypothesis of suppression system design identifies a limiting combustion wave adiabatic flame temperature, below which combustion reactions are not sustained. Suppression is thus attained, provided that sufficient thermal quenching results in depression of the combustion wave temperature below this critical value. This hypothesis identifies the need to deliver greater than a critical mass of suppressant into the enveloping fireball to effect suppression (see Fig. 26-43). 

Flame Temperature The heat released by the chemical reaction of fuel and oxidant heats the POC. Heat is transferred from the POC, primarily by radiation and convection, to the surroundings, and the resulting temperature in the reaction zone is the flame temperature. If there is no heat transfer to the surroundings, the flame temperature equals the theoretical, or adiabatic, flame temperature. 

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

If the reaction is conducted both adiabatically and witli stoichiometric air. tlie resulting temperature is defined as tlie theoretical adiabatic flame temperature (TAFT). It represents tlie nia.xinuuii temperature tliat tlie products of combustion (flue) can acliieve if the reaction is conducted both stoichionietrically and adiabatically. For tliis condition, all tlie energy liberated from combustion at or near standard conditions (AH°c and/or AH°29s) appears as sensible heat in raising tlie temperature of tlie flue products, AHp, tliat is ... 

AHp = entlialpy change of the products as tlie temperature increases from 25°C to tlie theoretical adiabatic flame temperature... 

Mf = molecular weiglit of fiael Ma = molecular weiglit of air Ta = adiabatic flame temperature (K)... 

Adiabatic Reaction Temperature (T ). The concept of adiabatic or theoretical reaction temperature (T j) plays an important role in the design of chemical reactors, gas furnaces, and other process equipment to handle highly exothermic reactions such as combustion. T is defined as the final temperature attained by the reaction mixture at the completion of a chemical reaction carried out under adiabatic conditions in a closed system at constant pressure. Theoretically, this is the maximum temperature achieved by the products when stoichiometric quantities of reactants are completely converted into products in an adiabatic reactor. In general, T is a function of the initial temperature (T) of the reactants and their relative amounts as well as the presence of any nonreactive (inert) materials. T is also dependent on the extent of completion of the reaction. In actual experiments, it is very unlikely that the theoretical maximum values of T can be realized, but the calculated results do provide an idealized basis for comparison of the thermal effects resulting from exothermic reactions. Lower feed temperatures (T), presence of inerts and excess reactants, and incomplete conversion tend to reduce the value of T. The term theoretical or adiabatic flame temperature (T,, ) is preferred over T in dealing exclusively with the combustion of fuels. 

Adiabatic flame temperature The highest possible temperature of combustion obtained under the conditions that the burning occurs in an adiabatic vessel, that it is complete, and that dissociation does not occur. 

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

Tf Absolute adiabatic flame temperature of propellant Tg Gas temperature Ti Initial gas temperature T0 Initial propellant temperature T, Propellant surface temperature t Time... 

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]

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