On the implementation of the κ-ε turbulence model in incompressible flow solvers based on a finite element discretisation

Kuzmin, Dmitri; Mierka, Otto; Turek, Stefan

doi:10.1504/ijcsm.2007.016531

Cited by 115 publications

(106 citation statements)

References 10 publications

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“…The choice of fixed bubble pivot volumes and fixed class widths offers the advantage of expressing the discretized transport equation (20) in terms of class holdups α i instead of the number probability density, f i = α i υ i ∆υ i (see (1)). Doing so enforces only mass conservation, however the bubble number density may not be conservative.…”

Section: Implementation Of Pbementioning

confidence: 99%

“…Regarding the arising inconsistency we subscribe to the argument of [5], who reported that the difference in the predicted values of interfacial area and Sauter mean bubble diameter obtained with only mass conservation and obtained with mass and bubble number conservation was less than 1%. Multiplying equation (20) with υ i ∆υ i results in conservative source and sink terms, since the overall gas-holdup cannot be changed due to coalescence or breakup procedures 1 . Additionally, any sink (source) term of a given rate associated to a particular breakup or coalescence procedure induces a source (sink) term with the same rate but in a different class.…”

Section: Implementation Of Pbementioning

confidence: 99%

“…Since the continuous transport equation (4) is positivity preserving for nonnegative initial and boundary conditions the same property needs to be satisfied by its discrete counterpart (20). This can be achieved by an implicit treatment of the sink terms resulting in the following set of equations…”

Section: Integration Of Pbe Into Cfdmentioning

confidence: 99%

“…Therefore, in subsection 5.2.1, we aim to reconstruct the underlying turbulent flow field as a prerequisite for a subsequent population balance modeling in the framework of dispersed flows. For this reason, the open-source software package FeatFlow extended with Chien's Low-Reynolds number k−ε model was utilized to perform the flow simulations, which has already been successfully validated for channel flow problems (Re τ = 395) [20].…”

Section: Coupling With Cfdmentioning

confidence: 99%

“…In most of the present studies which consider implementation of CFD coupled with PBE, it is preferred to work with commercial codes like FLUENT [1,6,32,38] or CFX [5,7,28,27], naming just two of the most important CFD software packages. However, a commercial code is not the only option and opensource software packages such as FeatFlow (see http://www.featflow.de) extended with additional modules (such as turbulence model [20], multiphase model [22], subgrid-scale mixing model [35] or a population balance model in the present case) possess the advantages of higher flexibility and robustness.…”

Section: Introductionmentioning

confidence: 99%

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Numerical aspects and implementation of population balance equations coupled with turbulent fluid dynamics

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Section: Implementation Of Pbementioning

confidence: 99%

Section: Implementation Of Pbementioning

confidence: 99%

Section: Integration Of Pbe Into Cfdmentioning

confidence: 99%

Section: Coupling With Cfdmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Numerical aspects and implementation of population balance equations coupled with turbulent fluid dynamics

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Bed Surface Adjustments to Spatially Variable Flow in Low Relative Submergence Regimes

Monsalve

Yager

2017

Water Resources Research

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In mountainous rivers, large relatively immobile grains partly control the local and reach‐averaged flow hydraulics and sediment fluxes. When the flow depth is similar to the size of these grains (low relative submergence), heterogeneous flow structures and plunging flow cause spatial distributions of bed surface elevations, textures, and sedimentation rates. To explore how the bed surface responds to these flow variations we conducted a set of experiments in which we varied the relative submergence of staggered hemispheres (simulated large boulders) between runs. All experiments had the same average sediment transport capacity, upstream sediment supply, and initial bed thickness and grain size distribution. We combined our laboratory measurements with a 3‐D flow model to obtain the detailed flow structure around the hemispheres. The local bed shear stress field displayed substantial variability and controlled the bed load transport rates and direction in which sediment moved. The divergence in bed shear stress caused by the hemispheres promoted size‐selective bed load deposition, which formed patches of coarse sediment upstream of the hemisphere. Sediment deposition caused a decrease in local bed shear stress, which combined with the coarser grain size, enhanced the stability of this patch. The region downstream of the hemispheres was largely controlled by a recirculation zone and had little to no change in grain size, bed elevation, and bed shear stress. The formation, development, and stability of sediment patches in mountain streams is controlled by the bed shear stress divergence and magnitude and direction of the local bed shear stress field.

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Characterization of a membrane‐separated and a membrane‐less electrobioreactor for bioelectrochemical syntheses

Krieg

Phan

Wood

et al. 2018

Biotech & Bioengineering

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Bioelectrochemical systems (BESs) have the potential to contribute to the energy revolution driven by the new bio-economy. Until recently, simple reactor designs with minimal process analytics have been used. In recent years, assemblies to host electrodes in bioreactors have been developed resulting in so-called "electrobioreactors." Bioreactors are scalable, well-mixed, controlled, and therefore widely used in biotechnology and adding an electrode extends the possibilities to investigate bioelectrochemical production processes in a standard system. In this work, two assemblies enabling a separated and non-separated electrochemical operation, respectively, are designed and extensively characterized. Electrochemical losses over the electrolyte and the membrane were comparable to H-cells, the bioelectrochemical standard reaction system. An effect of the electrochemical measurements on pH measurements was observed if the potential is outside the range of -1,000 to +600 mV versus Ag/AgCl. Electrobiotechnological characterization of the two assemblies was done using Shewanella oneidensis as an electroactive model organism. Current production over time was improved by a separation of anodic and cathodic chamber by a Nafion® membrane. The developed electrobioreactor was used for a scale-up of the anaerobic bioelectrochemical production of organic acids and lysine from glucose using an engineered Corynebacterium glutamicum. Comparison to a small-scale custom-made electrobioreactor indicates that anodic electro-fermentation of lysine and organic acids might not be limited by the BES setup but by the biocatalysis of the cells.

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On the implementation of the κ-ε turbulence model in incompressible flow solvers based on a finite element discretisation

Cited by 115 publications

References 10 publications

Numerical aspects and implementation of population balance equations coupled with turbulent fluid dynamics

Numerical aspects and implementation of population balance equations coupled with turbulent fluid dynamics

Bed Surface Adjustments to Spatially Variable Flow in Low Relative Submergence Regimes

Characterization of a membrane‐separated and a membrane‐less electrobioreactor for bioelectrochemical syntheses

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