OCR Text |
Show there is an upper stable curve, and a lower unstable curve. Also the analysis showed that there is a trivial solution for llr =0. For any initial condition, the solution will move on the upper stable curve, or to the trivial stable solution. The solutions will always move away from the meta-stable lower part of the curve. Hopf bifurcations were reported in the Baker and Essenhigh paper, which implied the existence of pulsating or unsteady state combustion. However, the bifurcation analysis on the new equations does not show the occurence of Hopf bifurcations. Thus the conclusion would seem to be that PSR's do not exhibit oscillatory behavior. Curves were also generated for several different values of:J and of temperature. Figure 2, shows that as the firing rate increases, then the range of 4>, for which operation is possible, increases, and the maximum attainable reaction efficiency also increases. The reduction in the range of 4> for small values of 3 can be due to the approaching of another limit, a firing limit. That is, if there exists a minimum firing rate, corresponding to :JOlin, such that there are no solutions, excepting the trivial case, then there will be no solutions for any 3 < 3min. The curves shown in Figure 3 show that as the temperature increases, then the range of 4> for the loop decreases. The next logical step would be to write Cp as a function of temperature, instead of being taken as a constant. 10 |