A discussion on the validity domain of the weighted residuals model including the Marangoni effect for a thin film flowing down a uniformly heated plate

Liu, Jiebin; Jiang, Shengyao; Duan, Riqiang

doi:10.1080/19942060.2017.1322148

Cited by 3 publications

(4 citation statements)

References 26 publications

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“…The inclination angle of the substrate is set to 90°(between the substrate and the horizon), and thus the inclination number is taken to be Ct = 0. On the Bi and Bi w values taken, Our previous paper (Liu et al, 2017), Kobov experiments (Kabov, Scheid, Sharina, & Legros, 2002), and Kallidasis et al (2012) have all shown that as Bi and Bi w are less than 1, their effects on the Marangoni effect for film flow instability is small. Due to poor heat transfer characteristics at the liquid-gas interface and solid-gas interface, the actual Bi and Bi w values are very small.…”

Section: Linear Stability Analysismentioning

confidence: 92%

“…They discovered that a rivulet pattern is formed and aligned with the mean flow at small Reynolds numbers. The RWRM method, based on a weighted residuals model, is applicable for small to moderate Reynolds numbers (Liu, Jiang, & Duan, 2017;Ruyer-Quil et al, 2005). Compared with other methods, the RWRM model is simpler than the three-dimensional integration method of the conservation equations and is more accurate than either the BE or lubrication approximation models at moderate Reynolds numbers (Kalliadasis, Ruyer-Quil, Scheid, & Velarde, 2012).…”

Section: Introductionmentioning

confidence: 99%

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Rivulet formulation in the flow of film down a uniformly heated vertical substrate

Wang

Zhao

Duan

2019

Engineering Applications of Computational Fluid Mechanics

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Three-dimensional regularized weighted residuals model is developed to study vertical falling film on a uniformly substrate with constant heat flux. The model is verified through linear stability analyses in both the stream and the span directions. It is shown that rivulet formation is due to the dominance of the thermocapillary Marangoni effect in the span direction, i.e., the component in the span direction of the surface temperature gradient is much larger than the component in the stream direction, which results from the different heat transfer modes in the stream and the span directions. Four types of initial disturbance are separately imposed on the film flow. It is shown that the initial disturbance does have an influence on the rivulet formation process, but it has no effect on the eventual film structure. Rivulet formation on the film enhances the heat transfer on a wavy film surface, which is attributed for the most part to the increase in the surface area of the film. On the effect of the Reynolds and the Marangoni numbers on rivulet formation, an increase in the former results in an increase in rivulet width, while an increase in the latter causes an advance in the film rupture. ARTICLE HISTORY

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Section: Linear Stability Analysismentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Rivulet formulation in the flow of film down a uniformly heated vertical substrate

Wang

Zhao

Duan

2019

Engineering Applications of Computational Fluid Mechanics

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“…F x denotes an additional acceleration term. The drag force per unit droplet mass, namely, F D ( v − v p ), where F D can be written as follows:

F_{D} = \frac{3 {italicμC}_{D} {Re}_{p}}{4 ρ_{P} D_{P}^{italic2}}

The dimensionless relative Reynolds number [ 22 ] (Re p ) is used to characterize the fluid flow and it can be expressed as follows [ 23 ] :

{Re}_{p} = \frac{{italicρD}_{p} |\overset{true\to}{v} - \overset{true\to}{v_{p}}|}{μ}

where D p is the particle diameter, and it follows Rosin–Rammler's distribution law.…”

Section: Methodsmentioning

confidence: 99%

“…The dimensionless relative Reynolds number [22] (Re p ) is used to characterize the fluid flow and it can be expressed as follows [23] :…”

Section: Governing Equationsmentioning

confidence: 99%

Multi‐objective optimization of drainage‐plates in wave‐plate mist eliminators using experiment and data‐driven modelling for lower water loss and energy requirement

et al. 2022

Can J Chem Eng

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Wave-plate mist eliminators are widely employed as gas-liquid separation devices to prevent the liquid escaping from thermal power plants or other cooling towers. In this study, the wave-plate mist eliminator with drainage plates was numerically analyzed and the effects between geometrical variables on two objectives, namely, pressure drop (ΔP) and separation efficiency (η), were revealed. Plate spacing, width, and length, as well as the relative position of the drainage plate, were thoroughly investigated. A combined strategy was developed for multi-objective optimization of the wave-plate mist eliminator by integrating computational fluid dynamics (CFD) simulation, response surface methodology (RSM), non-dominated sorting genetic algorithm-II (NSGA-II), and a technique for order of preference by similarity to ideal solution (TOPSIS) method. The results demonstrated that the relative position of drainage plates has a greater impact on the overall performance, whereas the width of drainage plates has the minimum effect. With the implementation of NSGA-II and the TOPSIS method, an optimal solution for the design of the mist eliminator was obtained. After comparing with the baseline case, the optimized case presents promising characteristics with high separation efficiency (enhanced by 3.6% ~9.06%) and a low energy consumption coefficient (reduced by 72.30% at η = 45%).

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Numerical simulation of thin film flowing down a vertical uniformly heated plane using the regularized weighted residuals model

Zhao

Duan

2019

IOP Conf. Ser.: Earth Environ. Sci.

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With the developed three-dimensional Regularized Weighted Residuals Model (RM), discussion on its accuracy and simulation work are conducted. It is shown that for small to moderate Reynolds number, the accuracy of RM decreases with increasing Marangoni number and decreasing Biot number of the plane. The streamwise error ratios are larger than spanwise ones and reach a maximum when Reynolds number equals 3, which is due to underestimate of Marangoni instability. The increase of Reynolds number or introducing streamwise most unstable disturbance makes film duration time longer. With increasing Reynolds number, the early stage of wave evolution becomes faster and ripples are more intensive; the final pattern is more unstable and disordered. Heat transfer efficiency reaches two peaks with increasing Reynolds number, one due to the interaction between thermal condition and flow rate, the other due to film no-rupture. Introducing streamwise most unstable disturbance makes the early stages of wave evolution longer and wave amplitude smaller in later stages. Unless Reynolds number is small enough, heat transfer efficiency decreases with the introduction of streamwise most unstable disturbance.

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A discussion on the validity domain of the weighted residuals model including the Marangoni effect for a thin film flowing down a uniformly heated plate

Cited by 3 publications

References 26 publications

Rivulet formulation in the flow of film down a uniformly heated vertical substrate

Rivulet formulation in the flow of film down a uniformly heated vertical substrate

Multi‐objective optimization of drainage‐plates in wave‐plate mist eliminators using experiment and data‐driven modelling for lower water loss and energy requirement

Numerical simulation of thin film flowing down a vertical uniformly heated plane using the regularized weighted residuals model

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