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1.1. Definitions

To model multi-phase flows one is sometimes required to describe properties averaged over the phase both spatially and temporally. A certain familiarity is required with these definitions before we discuss specific phenoma. The multiple phases (and/or components) are usually distinguished by numerical subscripts (1,2...) or for two-phases by subscripts f and g for a liquid-gas system of f and s for a liquid-solid system. (The second phase, component, is usually chosen as the dispersed phase.) For illustration, consider a two-phase air-water flow in a vertical pipe. The total mass flow rate is tex2html_wrap_inline525 with volumetric flowrate given by

equation30

Every part of the multiphase flow is occupied by one phase or another. One can consider the symbol tex2html_wrap_inline527 , as the fraction of an element of volume which is occupied over some time interval by phase i. Obviously, if the volume element and the time interval is chosen to be small enough (infinitesimal) tex2html_wrap_inline531 would be 0 and 1 at any instant. However, in actual practice tex2html_wrap_inline531 is an average quantity over some macroscopic volume (e.g., channel cross-sectional area) and time interval, and tex2html_wrap_inline531 is the "volume fraction" of tex2html_wrap_inline537 . For a gas the term void fraction is used. It can also be defined over a cross-sectional area or chord length. Another average flow quantity of interest particularly in boiling or condensation applications is the mass fraction of phase i

equation45

where, for liquid-gas flows, tex2html_wrap_inline541 is called the "quality". This quantity should not be confused with the thermodynamic quality, the ratio of the vapor mass (not mass flow rate) to the total mass. Only if the velocity of the phases are equal do the two definitions become the same; e.g., this is done in the homogeneous equilibrium model. One can also define a mass flux or mass velocity, G, by

equation53

and volumetric flux, i, as

equation69

With these definitions one can derive a number of useful physical quantities, e.g., the relation between the volume fraction tex2html_wrap_inline531 , and mass fraction, tex2html_wrap_inline549 . For a liquid-gas flow

equation90


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Next: Flow Patterns Up: INTRODUCTION AND CONCEPTS Previous: INTRODUCTION AND CONCEPTS


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