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1. Averaging_web

# 1. Averaging_web - ENU 4134 – Averaging in Two-Phase Flow...

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Unformatted text preview: ENU 4134 – Averaging in Two-Phase Flow D. Schubring July 23, 2010 Learning Objectives I 1-a-i Average any well-defined flow parameters over volume, area, and time I 1-a-ii Identify frequently-used averaged parameters and develop competence in computing these efficiently I 5-a Develop familiarity with terminology and mathematical symbols common to nuclear TH, including those symbols which do not map one-to-one to terminology Averaging, Averaged Parameters I Averaging operators – volume, area, time (Chapter 5, Section 2) I Volume (and sometimes time) averaged parameters (Chapter 5, Section 3) I Area (and sometimes time) average parameters (Chapter 5, Section 4) Volume Averaging Notation: h c i = volumetric average of c (usually a scalar, doesn’t have to be). Computation in general volume V : h c i = RRR V c ( ~ r , t ) dV RRR V dV (1) h c i = 1 V ZZZ V c ( ~ r , t ) dV (2) Weighted Volume Averaging (not in text) For some application, it is useful to compute a volume average, weighted by some other parameter. Example: mass averaging, by weighting with the density. h c i mass = RRR V c ( ~ r , t ) ρ ( ~ r , t ) dV RRR V ρ ( ~ r , t ) dV (3) h c i mass = 1 M total ZZZ V c ( ~ r , t ) ρ ( ~ r , t ) dV (4) Averaging over Phase Volume Phase density function α k ( ~ r , t ) = 1 if ~ r occupied by phase k at t 0 otherwise (5) h c i k = RRR V c ( ~ r , t ) α k ( ~ r , t ) dV RRR V α k ( ~ r , t ) dV (6) The denominator is termed V k – the volume occupied by phase k . Any volume in V but not in V k is termed V k , the volume occupied by phase k . Average over Phase Volume (2) Divide the numerator into two parts – one is an integration over V k , the other an integration over V k : h c i k = RRR...
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1. Averaging_web - ENU 4134 – Averaging in Two-Phase Flow...

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