Critical flow: General theory and spurious solutions

摘要

It is hardly necessary to emphasize the importance that an accurate prediction of the parameters of critical flow plays in a number of industries, notably in nuclear reactor safety calculations and in metering. In spite of its importance, the literature of the subject still contains erroneous statements. Many of them result from an unjustified belief in the generality of certain conclusions drawn in the elementary study of one-dimensional isentropic flow of a perfect gas with constant specific heats through a convergent-divergent (de Laval) nozzle. This lecture will present a complete and consistent theory of such flows, applicable to any fluid (single- or multiphase) and any channel shape. The study is restricted to the one-dimensional approximation, and, although only adiabatic conditions are discussed, the formalism can be extended to arbitrary conditions at the boundary of the channel. A scrutiny of some of the latest critical reviews of the state of the art of modelling thermal-hydraulic phenomena, especially in the context of LWR safety analysis, reveals the persistence of some misconceptions concerning the nature of the flow and of the relation between the preferred mathematical model and its discretized equivalent. It has recently become clear that the ensemble of trajectories in phase space of a mathematical model, expressed in the form of a set of differential equations, can be radically different from the ensemble of solutions implied in the numerical code, expressed as a set of linear algebraic equations employed in practical applications. This discrepancy becomes acute when critical flow rates are computed under conditions of choked flow.