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Show ' AFRC85-11 Using Eqs. (12), (13), (lOe) and (40), the solid energy equation, Eq. (6), is Integrated from y = 0 t o y = -«j to yield d(o - 9 )o s , w 3 , p' dt p c s p ?>: M M •••«•• + 3.79 ML2 A e S'P S'W (41) ,RJ LPeJ s,w s,p l^J' " {pV)»%.p+ "s.R^s -' + 3 7 9 3. SOLUTION 3.1 Ignition Criteria A considerable problem in the study of ignition is the question of ignition criterion. In experimental studies, ignition is detected by a light emission. The use of light emission as a theoretical ignition criterion is very difficult due to the lack of information on various physical properties associated with the chemical kinetics. Ignition is a combined chemical and physical process and ignition criteria must be determined relative to the physics of the problem. For the problem under consideration, the initial state of the fuel is in the condensed phase. When a convective heat source is applied, it is heated and fuel gases are produced. Therefore, the transport processes at the interface must be used to determine the occurrence of Ignition. These processes are simply the heat and mass transports. Figure 2 illustrates the temperature gradient at the surface as function of the blowing velocity and shows that an increase in the blowing velocity results In a decrease of the temperature gradient. But when f w is high enough, e'(0) increases abruptly indicating that the thermal runaway takes place in the gas phase. These points, therefore, can be used as Ignition points and expressed as da'(0) 1 APRC65-12 For the condensed phase, two processes are important: the rate of the solid heating and the rate of the chenical reaction at the surface. The competition of these processes Kill determine the onset of the flaming reaction of the condensed phase. Therefore, the ignition condition for the solid phase can be determined by fdo s, w dt do dt = 1.0 (43) IH 3.2. Prediction of Ignition Time Ignition time is defined as the time from exposure to the onset of the flame. For the surface ignition phase, this tine in determined simply by solving the energy equation of the solid from t = 0 until the condition expressed by Eq. (43) is reached. For the gas phase, ignition time is calculated as ig = t + t. (44) where t is the time required to heat the solid and t_ is referred to as reaction time. This time must be computed from the competition among the gasification rate, the reaction rate and the convection rate. Thus D l Y F Y 0 ( 2 a p M ) 1/2 Mpv), -E /o . g 45) 3.3. Numerical Procedures Equations (28)-(30) and (41) are coupled, hence required to be solved simultaneously. Because of quasi-steady approximation, the gas phase equations can be integrated Independently of the solid energy equation by specifying the surface temperature. |