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Unformatted text preview: ENU 4134 Pressure Drop Models D. Schubring October 14, 2009 Empirical Analysis of TwoPhase 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 Countercurrent twophase 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 LockhartMartinelli I MartinelliNelson I ArmandTreschev I MullerSteinhagen and Heck (not in text) Pressure Drop Models Outline (2) The text also provides the models of Thom (similar to MN), Baroczy (similar to MN), 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 MartinelliNelson or ArmandTreschev models and solving for dP / dz I Evaluation of 2 lo or 2 go from the LockhartMartinelli model and solving for dP / dz I Evaluation of the MullerSteinhagen and Heck model LockhartMartinelli 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. Singlephase relations can be applied without each phase LockhartMartinelli 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). LockhartMartinelli Parameter (2) Most often, a turbulent smoothtube 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) LockhartMartinelli 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) LockhartMartinelli Multiplier The LM correlation is for the twophase 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.
 Spring '11
 Schubring

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