Cooling propagation

Equation (5.98) has a stabilizing effect on T due to this condition any disturbance arising close to the chaimel inlet will be rapidly damped. Furthermore, if the stack temperature increases far from the inlet, Eq. (5.98) sooner or later will damp development of instability due to the wave of cooling propagating from the inlet. 

Above we have seen that thermal waves are transported along the stack at the velocity given by (5.95). Suppose that the stack temperature has increased by a constant value 6T (which is equivalent to the disturbance with zero k). The boundary condition (5.98) will initiate a wave of cooling propagating from the inlet to the outlet. This wave will reach the channel outlet at the time... 

Figure 5.11 shows the numerically calculated evolution of a small disturbance in stack temperature with time. As can be seen, the initial growth of T with time is then damped due to the wave of cooling propagating from the channel inlet. 

Figure 5.11 Evolution of disturbance in stack temperature. At time t = 0 s, stack temperature is disturbed by a constant value of 20 K. Note the very fast (in the order of 10 s) decay of disturbance at 5 = 0 (charmel inlet, frame 33 s). Due to the instability, the stack temperature at the outlet x = 1) grows by 30 K (frames 33-494 s). Further temperature growth is damped by a slow wave of cooling propagating from the inlet (frames 164-987 s).

Cool Flames. An intriguing phenomenon known as "cool" flames or oscillations appears to be intimately associated with NTC relationships. A cool flame occurs in static systems at certain compositions of hydrocarbon and oxygen mixtures over certain ranges of temperature and pressure. After an induction period of a few minutes, a pale blue flame may propagate slowly outward from the center of the reaction vessel. Depending on conditions, several such flames may be seen in succession. As many as five have been reported for propane (75) and for methyl ethyl ketone (76) six have been reported for butane (77). As many as 10 cool flames have been reported for some alkanes (60). The relationships of cool flames to other VPO domains are depicted in Figure 6. 

Below a certain critical temperature, which varies with pressure and stoichiometry, cool flames for several hydrocarbons propagate from the wall inward above this temperature, they propagate from the center of the vessel (78). This transition is interpreted as evidence for a changeover from a predominantly heterogeneous preflame mechanism to a homogeneous one. 

High temperature steam cools and eventually condenses as it propagates through the oil reservoir. To maintain foam strength as the steam cools, a noncondensible gas, usually nitrogen or methane, is often added to the injectant composition (196). Methods of calculating the optimum amount of noncondensible gas to use are available (197). 

The maximum velocity at the axis is twice the average, whereas the velocity at the wall is zero. The effect of the burner wall is to cool the flame locally and decrease the burning velocity of the mixture. This results in flame stabilization. However, if the heat-transfer processes (conduction, convection, and radiation) involved in cooling the flame are somehow impeded, the rate of heat loss is decreased and the local reduction in burning velocity may no longer take place. This could result in upstream propagation of the flame. 

Elame Arrester A flame arrester is a device permeable to gas flow but impermeable to any flame. It quenches the flame and cools the products sufficiently to prevent reignition at arrester outlet. Arresters are used to prevent a flame propagating into the system from outside (such as via a tank vent) or one part of the system to another (such as through connected piping). 

Equipment described as explosion-proof is equipment installed in enclosures that will withstand internal explosions and also prevent the propagation of flame to the external atmosphere. As the gases generated by the explosion expand, they must be cooled before reaching the surrounding atmosphere. 

EPR methods that allow a more direct determination of kv have been developed. These enable absolute radical concentrations to be determined as a function of conversion. With especially sensitive instrumentation, this can be done by direct measurement/57 160 An alternative method, applicable at high conversions, involves trapping the propagating species in a frozen matrix361 362 by rapid cooling of the sample to liquid nitrogen temperatures. 

The cooling effect of the channel walls on flame parameters is effective for narrow channels. This influence is illustrated in Figure 6.1.3, in the form of the dead-space curve. When the walls are <4 mm apart, the dead space becomes rapidly wider. This is accompanied by falling laminar burning velocity and probably lowering of the local reaction temperature. For wider charmels, the propagation velocity w is proportional to the effective flame-front area, which can be readily calculated. On analysis of Figures 6.1.2b and 6.1.3, it is evident that the curvature of the flame is a function of... 

The mechanism is based on strong cooling of the products adjacent to the walls and injection of the cooled products in the form of an annular jet behind the flame, reducing its width as soon as the speed of the annular jet, proportional to the circumferential speed of the gas at the flame location becomes larger than the propagation speed of the edge flame. 

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