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Unformatted text preview: ENU 4134 – Exam #1 – Fall 2011 – NAME: SOLUTION SET 1 1. Two-Phase Transport Equations (20 points) (a) The 1-D mixture momentum transport equation for includes 5 terms; reprinted below assuming A z is constant in z . Briefly (couple-few words) explain the physical significance of each term (3 points each, 15 total). ∂ ∂t [ G m ] + g cos( θ ) ρ m + ∂ ∂z [ p ] + F 000 wz = ∂ ∂z " G 2 m ρ + m # (1) Transient term, gravity term, pressure (gradient term), forces at fixed bound- aries term [interface(s) wall(s) force(s) ok], convective term (b) Why do no F 000 sz terms appear in this equation (5 points)? These inter-phase interface terms cancel out in derivation of the mixture equation. Not linked to phase change; cannot declare equal to zero without justification. 2. Flow Regimes and Regime-Specific Phenomena (24 points) (a) What does the acronym IATE stand for in two-phase flow modeling? (4 points) Interfacial area transport equation – 1 per word (b) In annular flow, the triangular relationship asserts that given any 2 (of 3) parameters, the 3rd can be computed. What are these 3 parameters? (6 points) Film thickness, film flow rate (or entrained fraction) [“film flow velocity” - 1/2], interfacial shear (or pressure gradient – wall shear tolerated) (c) Fill-in-the-blank (14 points total, 2 per blank): • The IATE is most frequently used in bubbly (bubbly/annular) flows. • In annular flow, most droplets are thrown from waves (waves/base film/the right fielder). • The wavy-annular regime is observed in horizontal flow (horizontal flow/vertical upflow/vertical downflow). • The transition from counter-current (gas upward, liquid downward) to mixed up- ward/downward liquid flow is termed flooding (flow reversal/flooding) • The cap-bubbly regime exists for flow areas with very large (large/small/asymmetric) hydraulic diameters only....
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- Fall '11
- Trigraph, −1, Vvj ρg