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Rate Processes
Published in Danny D. Reible, Fundamentals of Environmental Engineering, 2017
For mass transfer processes, R in Equation 5.1 is usually written as an expression for chemical flux, qm. A flux is simply the quantity per unit area per time as shown in Figure 5.1. A fluid velocity can be thought of as a volumetric flux, i.e., the volume of fluid moving per unit area per time. () VolumetricFlux=q={Volume}{area}{time}={length}{time}=Velocity(U)
Internal two-phase flow induced vibrations: A review
Published in Cogent Engineering, 2022
Samuel Gebremariam Haile, Elmar Woschke, Getachew Shunki Tibba, Vivek Pandey
The Mass Flux is defined as the mass flow rate of a phase per unit cross-sectional area occupied by that phase. It is denoted by G, where G = ρj, and ρ is the phase (liquid or gas) density. The total mass flux is given as G = GL + GG. Since G is the mass flow rate (in kg/s) divided by cross-sectional area (in m2), the SI units for G are kg-m−2s−1. The Volumetric Flux (or Superficial Velocity) for internal two-phase flow, is the volumetric flow rate per unit cross-sectional area of the pipe/conduit (compare this to the Mass Flux). It is denoted as jL or jG indicating the volumetric flux/superficial velocity of the liquid and gas phases, respectively. The measurement units for j are the same as the velocity, that is, m/s. The total superficial velocity is j = jL+ jG. The instantaneous, local velocities of the liquid and gas phases are denoted as uL and uG. The relative velocity between the phases is uL—uG. The Volume Fraction (Holdup) of a phase is the volume occupied by a phase to the total volume considered and is denoted by α. It follows that αL= 1 − αG. The Void Fraction is the volume of the gas phase for unit volume of the pipe. From the above definitions, it follows that the Volumetric Flux (or Superficial Velocity) of a phase has the following relation to its volume fraction, and its velocity. For example, for the gas phase, jG= αGuG. Therefore, the superficial velocity of a phase is the product of the phase volume fraction and the phase velocity. The Mass Fraction, xL, of the liquid phase is ρL α L/ρ. The Volumetric Quality of a phase is defined as the ratio of the Volumetric Flux of the phase (L or G) to the total volumetric flux. For the liquid phase, the Volumetric Quality for the liquid phase would be jL/j. The Mass Quality (or Quality), for the Liquid phase, χL, is the ratio of the liquid mass flux to the total mass flux, GL/G, or ρLjL/ρ j . The Drift Velocity, or Slip Velocity of a phase is defined as the velocity of that phase in a frame of reference moving at a velocity equal to the total volumetric flux, j. For example, the Drift Velocity for the Liquid phase (uLj) is written as uLj= uL−j.