Closed-Form Local Stability of a Pressure-Phase-Coordinate Control-Volume Model

Abstract

This paper studies the local stability of a pressure–phasecoordinate control-volume model for one-dimensional compressible flow. Using pressure and a generalized phase coordinate as the state variables, the model retains the essential effects of compressibility, phase change, flow restriction, and wall heat transfer while remaining simple enough for closed-form analysis. Starting from the mass and energy balances, explicit state equations are derived and linearized about an equilibrium operating point. The analysis yields a closed-form factorization of the Jacobian determinant, showing that saddle versus non-saddle behavior is governed by a single phase-coordinate sensitivity term in the energy balance. In strictly single-phase regions, and in the bulk of the two-phase region under the present approximation, the model is non-saddle. By contrast, sharp heat-transfer variation near phase boundaries can drive direct stable-to-saddle transitions. In a higherpressure regime, the analysis also identifies conditions under which a Hopf candidate may arise. These results provide a simple and physically interpretable framework for understanding how heat transfer influences local stability in two-phase flow models.