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

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Unformatted text preview: ENU 4134 Pressure Drop Models D. Schubring October 14, 2009 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 100s. Well investigate the following four: I Lockhart-Martinelli I Martinelli-Nelson I Armand-Treschev I Muller-Steinhagen and Heck (not in text) 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 2 lo is given. On exams, the following are included in the scope: I Evaluation of the HEM I Evaluation of the SFM, given 2 lo I Evaluation of 2 lo from the Martinelli-Nelson or Armand-Treschev models and solving for dP / dz I Evaluation of 2 lo or 2 go from the Lockhart-Martinelli model and solving for dP / dz I Evaluation of the Muller-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 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 l (2) dP dz v fric = f v D e G 2 m x 2 2 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- . 2 l D e G 2 m (1- x ) 2 2 l (4) Re l = = G m (1- x ) D e l (5) dP dz v fric = 0 . 184 Re- . 2 v D e G 2 m x 2 2 v (6) Re v = = G m xD e v (7) Lockhart-Martinelli Parameter (3) X 2 tt = Re v Re l . 2 1- x x 2 v l (8) X 2 tt = x l (1- x ) v . 2 1- x x 2 v l (9) X 2 tt = l v . 2 1- x x 1 . 8 v l (10) Lockhart-Martinelli Multiplier The L-M correlation is for the two-phase multipliers, 2 l and 2 v (not 2 lo and 2 vo )....
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This note was uploaded on 07/14/2011 for the course ENU 4133 taught by Professor Schubring during the Spring '11 term at University of Florida.

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

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