Spatial distributions of mean age and higher moments in steady continuous flows

Liu, M.; Tilton, J.N.

doi:10.1002/aic.12151

Cited by 55 publications

(98 citation statements)

References 17 publications

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“…Then UDF (user-defined function) code of the equation for particle age (Liu and Tilton, 2010;Baléo and Cloirec, 2000;and Simcik et al, 2012) is used to calculate the age of the bubbles (a) in the dilutor cell. The mean age function and its multiphase scalar transport representation are (Simcik et al, 2012)…”

Section: Modelingmentioning

confidence: 99%

CFD analysis of laboratory scale phase equilibrium cell operation

Jama

Nikiforow

Qureshi

et al. 2017

Review of Scientific Instruments

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For the modeling of multiphase chemical reactors or separation processes, it is essential to predict accurately chemical equilibrium data, such as vapor-liquid or liquid-liquid equilibria [M. Šoóš et al., Chem. Eng. Process.: Process Intensif. 42(4), 273–284 (2003)]. The instruments used in these experiments are typically designed based on previous experiences, and their operation verified based on known equilibria of standard components. However, mass transfer limitations with different chemical systems may be very different, potentially falsifying the measured equilibrium compositions. In this work, computational fluid dynamics is utilized to design and analyze laboratory scale experimental gas-liquid equilibrium cell for the first time to augment the traditional analysis based on plug flow assumption. Two-phase dilutor cell, used for measuring limiting activity coefficients at infinite dilution, is used as a test case for the analysis. The Lagrangian discrete model is used to track each bubble and to study the residence time distribution of the carrier gas bubbles in the dilutor cell. This analysis is necessary to assess whether the gas leaving the cell is in equilibrium with the liquid, as required in traditional analysis of such apparatus. Mass transfer for six different bio-oil compounds is calculated to determine the approach equilibrium concentration. Also, residence times assuming plug flow and ideal mixing are used as reference cases to evaluate the influence of mixing on the approach to equilibrium in the dilutor. Results show that the model can be used to predict the dilutor operating conditions for which each of the studied gas-liquid systems reaches equilibrium.

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Section: Modelingmentioning

confidence: 99%

CFD analysis of laboratory scale phase equilibrium cell operation

Jama

Nikiforow

Qureshi

et al. 2017

Review of Scientific Instruments

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show abstract

“…The method introduced here modifies the inlet and outlet boundaries which are typically applied towards mean age (Liu & Tilton, 2010). The boundaries used here apply solely to the bottom of the vessel, Zone C, which is the region of interest.…”

Section: Open Vs Closed System Resultsmentioning

confidence: 99%

“…Mean age theory as a means of modeling the time dependent behavior of a passive scalar in a steady-state CFD simulation has been derived elsewhere for a single phase system (Liu & Tilton, 2010;Sandberg, 1981;Spalding, 1958). The theory is extended here for application to multiphase systems.…”

Section: Multiphase Mean Age Theorymentioning

confidence: 99%

“…The theory is extended here for application to multiphase systems. Liu & Tilton (2010) begin with the assumption that C(x,t) is the concentration of the scalar tracer at a given location x and time t, without further definition. It is reasonable to assume that their C(x,t) could be defined as:…”

Section: Multiphase Mean Age Theorymentioning

confidence: 99%

“…the derivation transfers directly (Liu & Tilton, 2010). Multiplying both sides by time t and integrating yields: (28) The first term on the left can be integrated by parts to give:…”

Section: Multiphase Mean Age Theorymentioning

confidence: 99%

See 2 more Smart Citations

Mixing and mean age in multiphase systems.

Russ¹

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Multi‐impeller mixing performance prediction in stirred tanks using mean age theory approach

Wu,

Jurtz,

Hohl

et al. 2023

AIChE Journal

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The mixing performance and power consumption for four dual‐impeller configurations in a stirred tank are studied using the mean age theory (MAT) approach, the fully transient techniques (FTT), and experiments. A novel method is developed based on the scaled mean age probability distribution curve, allowing the MAT method to be applied to multi‐impeller systems for the first time. The MAT approach provides three‐dimensional tracer distribution within the vessel, which is confirmed by FTT and experiments. Compared to the experimental data, the predicted mixing time from the MAT approach shows a deviation within 20%. This is a good degree of accuracy compared to FTT and correlations. For steady‐state predicted power numbers, a 20% deviation from the experimental data is observed, while the transient approach exhibits a lower deviation at 10%. However, the computational time can be reduced significantly using the steady‐state MAT approach.

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Spatial distributions of mean age and higher moments in steady continuous flows

Cited by 55 publications

References 17 publications

CFD analysis of laboratory scale phase equilibrium cell operation

CFD analysis of laboratory scale phase equilibrium cell operation

Mixing and mean age in multiphase systems.

Multi‐impeller mixing performance prediction in stirred tanks using mean age theory approach

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