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06_PressureDrop_web - ENU 4134 Pressure Drop Models D...

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ENU 4134 – Pressure Drop Models D. Schubring Fall 2011
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Learning Objectives I 1-e-i Use empirical models (including those not based on the HEM or SFM) to estimate pressure drop I 1-e-ii Develop a correlation for adiabatic, two-component two-phase pressure drop and compare to literature models (in project) I 1-e-iii Identify issues related to experiments on two-phase flow (mostly in project) I 1-e-iv Estimate design requirements and propose system for acquisition of pressure drop data (in project) I 5-b Use correlations and/or models to analyze problems in nuclear thermal hydraulics I 5-c Use appropriate software (EES, TK Solver; scripting/compiled languages) to automate evaluation of correlations for a range of conditions or for more complex problems such as single-channel analysis (mostly in project) I 5-d Identify assumptions used in development of models and critically evaluate the applicability of these assumptions for the TH conditions being modeled
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Remarks Course: I In the next 5-6 weeks, the emphasis will shift from lecture-driven theoretical understanding to problem-driven empirical analysis. I Topics covered: pressure drop (these notes, HW 3, Project 1); two-phase convective heat transfer (HW 4 and 5); and nuclear heat generation/transfer and SCA (HW 6, Project 2). Pressure Drop Models Considered: I The total number of published pressure drop models for straight pipe flow easily extends into the 100’s. I Different correlations are advised for steam-water (most nuclear-relevant), refrigerants (de-emphasized in this course), and two-component flows ( e.g., air-water). I Most industrial applications are pure-fluid; most experiments are two-component (why is this?).
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Pressure Drop Models Outline I Lockhart-Martinelli (mostly two-component) I M¨uller-Steinhagen and Heck (two-component or refrigerants) I Review of HEM (pure fluids, steam-water at high G ) I Martinelli-Nelson (steam-water at low-to-moderate G ) I Armand-Treschev (steam-water, BWR-type conditions) The text also provides the models of Thom (similar to M-N), Baroczy (similar to M-N), Jones, and (one of the correlations by) Chisholm. These are no longer frequently used; they are not required for this course.
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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 within 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).
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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, n = 0 . 2) 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)
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