1. Local instantaneous equations

Summary

• Subject: Governing equations and jump conditions

• Key idea Inteface bring discontinuity from a macroscopic view; therefore, the conservation laws there become algebraic relationships between the two phase states.

• References

  • Prosperetti [Pro79]: Comprehensive derivation of jump conditions. Highly recommended.

  • Tomiyama and Hayashi [TH18]: Easy-to-follow derivation of jump conditions and averaged eqs.

Two-phase flows exhibit various flow structures depending on the fluid properties of the two phases, flow rates, the inlet conditions, the geometry of channels, and so on. The interface between fluids, e.g., gas-liquid interface, takes a wide variety of structures such as bubbly, slug, and annular flow patterns. However, in spite of the complex structure of the flows, the number of equations governing the two-phase flow dynamics is limited, i.e. the continuity and momentum equations of the two phases and the interface transport equation. We shall begin by discussing the governing equations.

• 1.1. Governing equations
• 1.2. Jump conditions
• 1.3. Interface tracking