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SFM_Example_SOLUTIONS

# SFM_Example_SOLUTIONS - An Example with the SFM 1 Saturated...

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An Example with the SFM 1 Saturated steam water at 270 C flows in a round tube of diameter 0.05 m. The mass flow rate is 1.5 kg s - 1 . The flow is vertical upflow. Assume that the quality is increasing (there is boiling) at a rate of 0.06 m - 1 ( i.e. , dx/dz = 0 . 06 m - 1 ). After 1 meter (assume fully developed flow), the flow quality is therefore 0.06. Void-Quality-Slip Relations Using steam tables (E-1 in T&K): ρ v = 28 . 1 kg m - 3 (1) ρ f = 768 kg m - 3 (2) P sat = 5 . 505 MPa (3) σ = 0 . 02144 N m - 1 (4) Estimate the void fraction, { α } with: 1. HEM HEM implies S = 1. The equation for void fraction is then { α } = 1 1 + 1 - x x ρ v ρ l S (5) { α } = 1 1 + 1 - 0 . 06 0 . 06 28 . 1 768 1 (6) { α } = 0 . 636 (7) 2. The correlation of Bankoff (Equation 11-42) { α } = K { β } (8) { α } = K { α } HEM (9) K = 0 . 71 + 0 . 0001 p (10) K = 0 . 71 + 0 . 0001 (5 . 505 × 147) (11) K = 0 . 791 (12) { α } = 0 . 791 × 0 . 636 (13) { α } = 0 . 503 (14) 3. Use Figure 11-7 to determine the flow regime, then use the appropriate Zuber and Findlay drift flux model with Dix’s correlation to estimate { α } . Mapping coordinates are ρU 2 s for liquid and liquid U sl = ˙ m (1 - x ) l (15) U sl = 2 × 0 . 94 0 . 025 2 π × 768 (16)

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An Example with the SFM 2 U sl = 0 . 936 m s - 1 (17) ρ l U
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SFM_Example_SOLUTIONS - An Example with the SFM 1 Saturated...

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