A multi‐scale theoretical model for gas–Liquid interface mass transfer based on the wide spectrum eddy contact concept

Han, Luchang; Luo, He’an; Liu, Yuejin; You, Kuiyi; Liu, Pingle

doi:10.1002/aic.12327

Cited by 13 publications

(15 citation statements)

References 43 publications

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“…The proposed model (i.e., the unsteady‐state model presented in Table ) shows a good agreement with the experimental data. The results predicted by the model of Han et al is not shown in Figure as the predicted results are very close to those predicted by the model of Lamont and Scott . Furthermore, the models of Harriott (i.e.,

k_{normalL} = 1 / [H / D + 0.885 \sqrt{t_{normale} / D}]

), Fortescue and Pearson (i.e.,

{\overset{k}{true}}_{Λ} = 1.46 \sqrt{D \sqrt{{\overset{U}{true}}^{2}} / Λ}

) and Seo and Lee 11 (i.e.,

k_{normalL} = 0.9 \sqrt{D}

\int_{0}^{\infty} \sqrt{t_{e} Φ (t_{e}) / 〈 t_{e} 〉 d t_{e}}

) are also not compared in this work since the parameters appearing in these models cannot be obtained directly from the known operating conditions.…”

Section: Resultssupporting

confidence: 52%

“…Then, λ e can be estimated by Eq. with a trial‐error method . That is, we can take different trial values of λ e from η to 2π/ n min and compare the turbulent energy dissipation rates calculated by Eq.…”

Section: Model Developmentmentioning

confidence: 99%

“…with the known value of ε . If the calculated value and the known value are equal or the difference between them is less than a certain limit (e.g., 10 −7 ), the corresponding trial value of λ e can be taken as the average scale of energy‐containing eddies …”

Section: Model Developmentmentioning

confidence: 99%

“…The interfacial mass‐transfer mechanism is the basis of understanding these processes, it can predict mass‐transfer rate and help to design proper equipments. Since the two‐film theory was proposed by Lewis and Whitman, many theories and models, such as penetration theory, surface renewal theory, and their improved models, eddy concept model, and statistics theory, have been presented. Furthermore, a large number of experiential correlations with regard to several key parameters, for example, per unit volume power and superficial gas velocity, have been presented .…”

Section: Introductionmentioning

confidence: 99%

“…They adopted s =( ε / υ ) 1/2 , and thus this model can also be written as

k_{L} = 2 \sqrt{D / π} {(ε / υ)}^{1 / 4} \approx 1.13 \sqrt{D} {(ε / υ)}^{1 / 4}

. Han et al proposed that k L =0.682 D 1/2

\int_{n_{\min}}^{n_{\max}} [E {(n)}^{5 / 4} n^{3 / 4} d n] / \int_{n_{\min}}^{n_{\max}} [E (n) d n]

, which is a steady‐state wide spectrum eddy contact model. Here, E ( n ) is the energy spectrum function and n is the wave number of eddy.…”

Section: Introductionmentioning

confidence: 99%

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A theoretical unsteady‐state model for k_L of bubbles based on the framework of wide energy spectrum

Han

et al. 2015

AIChE Journal

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An unsteady-state model for predicting mass-transfer coefficient k L of bubbles with mobile surface was developed for turbulent gas-liquid dispersions. This model was derived from an unsteady-state convection and diffusion equation through a characteristics method. Unlike the previous work, this model considered the contributions of the amount of fluid structures of different scales (i.e., eddies) existing in the turbulent flows, the frequency of eddies arriving at the surface, the deformation and oscillation of bubbles to mass transfer. This model was based on the framework of wide energy spectrum and can account for the role of eddies of different sizes in mass transfer. Thus the assumption adopted by the previous models that mass transfer was controlled by eddies of certain sizes is no more needed. The overall k L predicted by the proposed model showed a better agreement with the reported experimental data. Derivation of liquid-side mass-transfer coefficientAccording to the points of (1) and (3) mentioned above, the convection-diffusion equation for the solute concentration in the thin concentration layer close to surface can take the form of Ã c is the dimensionless distance. It can be seen from Figure 5a that this distance increases with the increasing s. Nevertheless, our calculations indicate that y c will not be changed obviously when s > 1.0 under the action of the convections of eddies, which are responsible to sweep the surface and remove the solute-enriched liquid to the bulk fluid. As shown in Figure 5b, the turbulent dissipation rate e, the diffusion coefficient D and the size of eddy k affect the solute concentration distribution Figure 4. The variation of R L with f min .

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k_{normalL} = 1 / [H / D + 0.885 \sqrt{t_{normale} / D}]

), Fortescue and Pearson (i.e.,

{\overset{k}{true}}_{Λ} = 1.46 \sqrt{D \sqrt{{\overset{U}{true}}^{2}} / Λ}

) and Seo and Lee 11 (i.e.,

k_{normalL} = 0.9 \sqrt{D}

\int_{0}^{\infty} \sqrt{t_{e} Φ (t_{e}) / 〈 t_{e} 〉 d t_{e}}

) are also not compared in this work since the parameters appearing in these models cannot be obtained directly from the known operating conditions.…”

Section: Resultssupporting

confidence: 52%

Section: Model Developmentmentioning

confidence: 99%

Section: Model Developmentmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…They adopted s =( ε / υ ) 1/2 , and thus this model can also be written as

k_{L} = 2 \sqrt{D / π} {(ε / υ)}^{1 / 4} \approx 1.13 \sqrt{D} {(ε / υ)}^{1 / 4}

. Han et al proposed that k L =0.682 D 1/2

\int_{n_{\min}}^{n_{\max}} [E {(n)}^{5 / 4} n^{3 / 4} d n] / \int_{n_{\min}}^{n_{\max}} [E (n) d n]

, which is a steady‐state wide spectrum eddy contact model. Here, E ( n ) is the energy spectrum function and n is the wave number of eddy.…”

Section: Introductionmentioning

confidence: 99%

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A theoretical unsteady‐state model for k_L of bubbles based on the framework of wide energy spectrum

Han

et al. 2015

AIChE Journal

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Consideration of low viscous droplet breakage in the framework of the wide energy spectrum and the multiple fragments

et al. 2015

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An improved model for low viscous droplet breakage has been developed. Unlike the previous work that considered the inertia subrange and adopted the assumption of binary breakage, this work considered the breakage of droplets in the framework of the multiple fragments and the wide energy spectrum (i.e., including the dissipation range, the inertia subrange, and the energy containing range simultaneously). The previous interactions between the droplet and the surrounding fluids have been considered through introducing the interaction forces. The effect of the surface deformation and oscillation resulting from these interactions on the constraints of multiple breakages has been accounted for. These factors have been neglected in the existing models. The wide energy spectrum distribution was found to have an important effect on the nonmonotone evolution of breakage frequency with increasing parent droplet size. The cumulative volume fractions predicted by this work showed a better agreement with the experimental data. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2147–2168, 2015

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Drag models coupled with CFD–PBM method for simulation in bubble columns

Jia

Chen

2022

Can J Chem Eng

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In this study, three-dimensional numerical simulation of gas-liquid flow in bubble columns was realized by using the computation fluid dynamics (CFD)population balance model (PBM). The new drag model improves the stabilityconstrained multi-fluid (SCMF-C) model because of the consideration of the wake accelerating and the hindering effects for calculating the drag correction factor. The gas holdup, axial liquid velocity, and bubble size distribution (BSD) predicted by four drag models at 0.02 and 0.1 m/s were compared. The results revealed that the proposed drag model can provide excellent predictions for both bubbly and heterogeneous flows. Because the wake accelerating and the hindering effects were considered, reliable predictions were achieved for the gas holdup, and the problem of uniform gas holdup distribution was mitigated.

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A multi‐scale theoretical model for gas–Liquid interface mass transfer based on the wide spectrum eddy contact concept

Cited by 13 publications

References 43 publications

A theoretical unsteady‐state model for k_L of bubbles based on the framework of wide energy spectrum

A theoretical unsteady‐state model for k_L of bubbles based on the framework of wide energy spectrum

Consideration of low viscous droplet breakage in the framework of the wide energy spectrum and the multiple fragments

Drag models coupled with CFD–PBM method for simulation in bubble columns

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A multi‐scale theoretical model for gas–Liquid interface mass transfer based on the wide spectrum eddy contact concept

Cited by 13 publications

References 43 publications

A theoretical unsteady‐state model for kL of bubbles based on the framework of wide energy spectrum

A theoretical unsteady‐state model for kL of bubbles based on the framework of wide energy spectrum

Consideration of low viscous droplet breakage in the framework of the wide energy spectrum and the multiple fragments

Drag models coupled with CFD–PBM method for simulation in bubble columns

Contact Info

Product

Resources

About

A theoretical unsteady‐state model for k_L of bubbles based on the framework of wide energy spectrum

A theoretical unsteady‐state model for k_L of bubbles based on the framework of wide energy spectrum