Theoretical analysis of Ledinegg instability and density wave oscillation using dimensionless numbers

Abstract

• Dimensionless number criteria determining two phase flow stability is established. • Flow direction on stability is non-monotonic, the turning point expression is given. • Increasing flow rate and power proportionally can be good or bad for stability. • Contrary conclusions of flow direction and power level on stability are clarified. • The influences of tube length and diameter on stability are discussed and presented. Two-phase flow instability is influenced by many factors. The reported parameter effects on instability boundary are incomplete and sometimes conflict. Dimensionless numbers are more effective to reveal the mechanisms and describe the instability boundary. In this paper, dimensionless numbers are used to systematically analyze various parameters’ effects. One-dimensional governing equations describing the convective boiling process in a tube are simplified to a set of linear ordinary differential equations through integration and small perturbation methods. The judging inequalities expressed by six dimensionless numbers are obtained by the Routh stability criterion. The relationship between the judging inequalities and the instability types are identified theoretically for the first time. The boundary of density wave oscillation obtained from the fourth dimensionless number inequality agrees well with experimental data. The effects of Froude number, friction number, inlet temperature, inlet and outlet flow resistances, tube length and tube diameter are discussed in detail. Some contrary conclusions presented by previous investigators are clarified. The effect of varying Froude number (or flow orientation) on system stability is non-monotonic, and the turning point expression is given. The effects of geometric parameters are complex. The effects of tube length and tube diameter on the instability boundary are discussed systematically based on Froude number and friction number when operation parameters keep unchanged. Though many of the parameters’ influences are non-monotonic, some new universal laws or findings are extracted. For example, according to the conclusions of friction number effect, increasing the steam generator working power levels (heating power and mass flow rate increase proportionally) can be good or bad for stability according to different inlet flow resistances.