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# PressureDrop_web - ENU 4134 Pressure Drop Models D...

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ENU 4134 – Pressure Drop Models D. Schubring October 14, 2009

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Empirical Analysis of Two-Phase Fluid Mechanics Schedule I Flow Regime Maps – 1 I Annular Flow – 1.5 I Bubbly Flow – 0.75 I Other flow regimes (intermittent and horizontal) – 0.75 I Counter-current two-phase flow – 0.5 I Pressure drop models – 2.5
Pressure Drop Models Outline The total number of published pressure drop models for straight pipe flow easily extends into the 100’s. We’ll investigate the following four: I Lockhart-Martinelli I Martinelli-Nelson I Armand-Treschev I M¨uller-Steinhagen and Heck (not in text)

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Pressure Drop Models Outline (2) The text also provides the models of Thom (similar to M-N), Baroczy (similar to M-N), Jones, and Chisholm. These are no longer frequently used; they are not required for this course. You also have learned the HEM pressure drop and the general SFM equation, when φ 2 lo is given. On exams, the following are included in the scope: I Evaluation of the HEM I Evaluation of the SFM, given φ 2 lo I Evaluation of φ 2 lo from the Martinelli-Nelson or Armand-Treschev models and solving for dP / dz I Evaluation of φ 2 lo or φ 2 go from the Lockhart-Martinelli model and solving for dP / dz I Evaluation of the M¨uller-Steinhagen and Heck model
Lockhart-Martinelli Model Assumptions: 1. The pressure (gradient) of the two fluids is equal at any axial position ( i.e. , p l ( z ) = p v ( z )) 2. Single-phase relations can be applied without each phase

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Lockhart-Martinelli Parameter X 2 = ( dP / dz ) l fric ( dP / dz ) v fric (1) dP dz l fric = f l D e G 2 m (1 - x ) 2 2 ρ l (2) dP dz v fric = f v D e G 2 m x 2 2 ρ v (3) Note : These are not calculated by assuming all the flow is as liquid (or gas).
Lockhart-Martinelli Parameter (2) Most often, a turbulent smooth-tube relation is used to compute X 2 . When this is done, X 2 tt is usually used as the symbol. The most frequent relation is the McAdams (seen below) dP dz l fric = 0 . 184 Re - 0 . 2 l D e G 2 m (1 - x ) 2 2 ρ l (4) Re l = = G m (1 - x ) D e μ l (5) dP dz v fric = 0 . 184 Re - 0 . 2 v D e G 2 m x 2 2 ρ v (6) Re v = = G m xD e μ v (7)

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Lockhart-Martinelli Parameter (3) X 2 tt = Re v Re l 0 . 2 1 - x x 2 ρ v ρ l (8) X 2 tt = x μ l (1 - x ) μ v 0 . 2 1 - x x 2 ρ v ρ l (9) X 2 tt = μ l μ v 0 . 2 1 - x x 1 . 8 ρ v ρ l (10)
Lockhart-Martinelli Multiplier The L-M correlation is for the two-phase multipliers, φ 2 l and φ 2 v (not φ 2 lo and φ 2 vo ).

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