Ensemble Averaged Conservation Equations for Multiphase, Multi-component, and Multi-material Flows

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Many important “fluid” flows involve a combination of two or more materials having different properties. The multiple phases or components often exhibit relative motion among the phases or material classes. The microscopic motions of the individual constituents are complex and the solution to the micro-level evolutionary equations is difficult. Characteristic of such flows of multi-component materials is an uncertainty in the exact locations of the particular constituents at any particular time. For most practical purposes, it is not possible to exactly predict or measure the evolution of the details of such systems, nor is it even necessary or desirable. Instead, ... continued below

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Berry, Ray A. August 1, 2003.

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Description

Many important “fluid” flows involve a combination of two or more materials having different properties. The multiple phases or components often exhibit relative motion among the phases or material classes. The microscopic motions of the individual constituents are complex and the solution to the micro-level evolutionary equations is difficult. Characteristic of such flows of multi-component materials is an uncertainty in the exact locations of the particular constituents at any particular time. For most practical purposes, it is not possible to exactly predict or measure the evolution of the details of such systems, nor is it even necessary or desirable. Instead, we are usually interested in more gross features of the motion, or the “average” behavior of the system. Here we present descriptive equations that will predict the evolution of this averaged behavior. Due to the complexities of interfaces and resultant discontinuities in fluid properties, as well as from physical scaling issues, it is essential to work with averaged quantities and parameters. We begin by tightening up, or more rigorously defining, our concept of an average. There are several types of averaging. The published literature predominantly contains two types of averaging: volume averaging [Whitaker 1999, Dobran 1991] and time averaging [Ishii 1975]. Occasionally combinations of the two are used. However, we utilize a more general approach by adopting what is known as ensemble averaging.

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  • Report No.: INEEL/EXT-03-01011
  • Grant Number: DE-AC07-99ID-13727
  • DOI: 10.2172/910743 | External Link
  • Office of Scientific & Technical Information Report Number: 910743
  • Archival Resource Key: ark:/67531/metadc880937

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  • August 1, 2003

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  • Sept. 22, 2016, 2:13 a.m.

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  • Nov. 7, 2016, 7:37 p.m.

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Berry, Ray A. Ensemble Averaged Conservation Equations for Multiphase, Multi-component, and Multi-material Flows, report, August 1, 2003; [Idaho Falls, Idaho]. (digital.library.unt.edu/ark:/67531/metadc880937/: accessed August 21, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.