OCR Text |
Show - 12 - The intersection of the $ = 0.5 curve in Figure 2 with 1 msec at f = 0 provides an estimate of a critical value of x for this particular system. That is, a value of x which is significantly greater than 1 msec will result in unstable or no operation of the pulse combustor, since the time required for reignition is too long. Allowing for a variability in operation and uncertainties in computed results of a factor of 2, a band has been drawn in Figure 2 about this limiting value of x. The interpretation of the model results in terms of this limiting band relies very heavily on the need for the combustor to operate at a nearly constant frequency and an assumption that the reignition time remains an effectively fixed fraction of that operating period. If the ignition of a given mixture is too rapid (i.e. a shorter time than that indicated in Figure 2), then the system will adjust by drawing a larger amount f of fresh reactants into the combustion chamber. Because this lowers T0, the next ignition delay time will be longer, leading to a value of x which is closer to the optimal value of 1 msec. Conversely, too long a time delay will lead to a reduced fraction f of fresh reactants and a subsequent reduction in x. In this sense, the band at x = 1 msec represents a region of stability, with the dynamics of the reignition and intake processes tending to maintain that stability. Only for mixtures with $ less than the lean limit or greater than the rich limit does this feedback mechanism lead to extinction. In these cases the ignition delay time is above the shaded band in Figure 2. However, the reduction in the mixture fraction f to provide smaller values of x cannot continue because the limiting value of f = 0 is achieved before x is sufficiently reduced. |