Berechnung der Str�mung in Lavald�sen mit beliebig verteilter W�rmezufuhr

The mathematical theory of thermal choking in nozzle flows

“…Without entering into the difficult analysis of the supercritical flow solution, we attempt to set up a criterion that can predict whether or not for given initial reservoir conditions, nozzle geometry and Q~,,(x) the flow is supercritical. We restrict our discussion to supersonic heat addition (Xb > O) because subsonic heat addition (Xb < 0) requires the influence of the exit boundary conditions as well [for numerical solution of the differential theory with heat addition in the subsonic region see Jungclaus and van Raay (1967)]. It follows at once from Proposition 2.2.2 that the flow is subcritical if…”

“…(45)- (48) requires consideration of the nonequilibrium rate equation if g'r 0 and can only be achieved by numerical analysis. The numerical solutions of the system corresponding to heat addition from internal sources and from nonequilibrium condensation of wet steam are already available in the literature from the work of Jungclaus and van Raay (1967) and Barschdorff (1971). A better understanding of the nature of solution can be achieved qualitatively by applying the singularity theory of differential equations [e.g.…”

“…Such flows will be termed diabatic. A comprehensive discussion of diabatic flows is already available in the literature from the work of Shapiro (1953), Jungclaus and van Raay (1967), M6hring (1979), Zierep (1990) and its application to nozzle flows with nonequilibrium condensation can be found in Wegener and Mack (1958), Pouring (1965) and Barschdorff (1967). It is well-known that when the amount of internal heat release exceeds a certain limit the phenomenon usually referred to as thermal choking occurs.…”