Inception criteria for droplet entrainment in concurrent gas-liquid film flow were developed from simple physical models. For film Reynolds number > 160, an entrainment model based on the shearing off of roll-wave crests was used. At lower film Reynolds numbers, a wave undercutting mechanism was introduced. Experimentally observed abrupt changes in the critical gas velocity corresponding to the onset of entrainment at a certain film Reynolds number have been explained by the shift in the entrainment mechanisms. An agreement of the present inception criteria with various experimental data is shown to be satisfactory, and significant improvements over the existing empirical correlations have been made.

One-dimensional Model of Wave Propagation 18 2. Comparison of Homogeneous Frozen and Homogeneous Equilibrium Model with Data of Ref. 11 for Pressure-pulse Propagation in Steam-Water Mixtures 26 3. Comparison of Homogeneous Frozen and Homogeneous Equilibrium Model with Data of Ref. 12 for Pressure-pulss Propagation in Steam-Water Mixtures 27 4. Illustration of Simple Separated-flow Regimes. 34 5. Illustration of (a) Possible Nonuniform Propagation and (b) Resulting Wave Form for a Simple Stratified Media ...... 34 6. Approximate Wave Form Employed to Describe Momentum Transfer in Wavy Annular Flow 37 7. Gas and Liquid Elements in (a) a Slug-flow Pattern and (b) Idealized Slug-flow Model. 42 8. Pressure Response of Gas Element in Slug Flow to Step Change Ahead of Liquid Element 45 9. Experimental Facility 49 10. Mixer Section for Experimental Facility 50 11. Test Section for Experimental Facility 51 12. Photo of Transducer, Oscilloscope, and Charge Amplifier ... 53 l.'j. Sample Oscilloscope Traces for Steaa-Water Compression and Rarefaction Pulses. 54 14. Correlation of Air-Water Data at Various Pressures ..... 55 15. Comparison of the Proposed Correlation and the Steam-Water Data 56 16. Comparison of the Frontal Velocities for Compression and Rarefaction Waves in Steam-Water Mixtures .57 17. Comparison of the Proposed Correlation and the Homogeneous Models with the Air-Water Data of Refs. 13 and 33 58 16. Comparison of the Homogeneous Adiabatic Model and Eq. 82 with the Steam-Water Data of Karplus 58 19. Comparison of the Homogeneous Adiabatic Model and Eq. 82 with the Steam-Water and Air-Water Data of Semenov and Kosterln 59 20. Comparison of the Homogeneous Models and Eq. 82 with the Weak-shock-wave Air-Water Data of Hamilton 21. Comparison of the Measurement Technique Used in This Study and that Employed by Hamilton 60 22. Comparison of Eq. 82 and the Steam-Water Data of Dejong and Firey • 62 23. Comparison of the Homogeneous Models and the Proposed Correlation with the Air-Water Velocity of Sound Data of Karplus ... ......... 24. Frequency Dependence of Velocity of Sound » 25. Comparison of the Smooth-interface Model with the Stratified Air-Water Data 26. Comparison of the Smooth-interface Model with the Stratified Steam-Water Data 27. Comparison of the Two-component Models with the Experimental Data of Refs. 7 and 9 65 28. Comparison of the Proposed Models with Air-Water Data of Garrard for (a) Void Fractions Determined from Film Thickness Measurements, (b) Calculated Void Fractions, and (c) Calculated Core Void Fractions 66 29. Comparison of the Proposed One-component Models with the Steam-Water Data of White and D'Arcy 67 30. Compression and Rarefaction Wave Data for (a) Air at 60°F and (b) a 50% Quality Steam-Water Mixture as Reported in Ref. 14 68 31. Comparison of the One-component Models with the Rarefaction Wave Data of England et_ al 68 32. Comparison of the One-component Models with the Rarefaction Wave Data of Collinghara e£ al. as a Function of Gross and Core Qualities 69 33.

This paper presents, for the first time, a generalized correlation for flashing choked flow of an initially subcooled liquid. The present approach is an extension of a previously published correlation for homogeneous equilibrium choked flow with two-phase (quality) inlet conditions (Leung, 1986). The model assumptions are:1. Isentropic flow 2. Thermal equilibrium 3. Equal phasic velocities once saturation is reached It should be noted that this model is only a limiting case, without consideration of nonequilibrium effects (Schrock et al., 1977). In this regard it gives a lower-bound estimate for the mass flow rate and should therefore serve as a useful reference model in many engineering applications. Model Development the following equation derived from the first and second lawsAs usual, the critical mass velocity G is found by maximizingFor a subcooled inlet condition the above integral can be partitioned into two parts, namely the subcooled region and the saturated two-phase region, thus: where w is given by (Leung, 1986) Here all physical properties are to be evaluated a t the saturation line corresponding to the inlet stagnation temperature To. P, is the saturation pressure. Upon substitution, the second integral becomes By defining and Eq. 2 yields an expression for the normalized mass velocity asIn the saturated two-phase region, we employ the approximate Maximization is accomplished by setting the derivative dGldP or dG *ldv to zero, thus yielding the following transcendental 688

For large atmospheric vessels the potential occurrence of sufficient liquid swell resulting in two‐phase flow is of special importance. Based upon an extension of analytical work it would appear justifiable to ignore two‐phase flow effects for non‐foamy systems.

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