Numerical investigation of large wave interactions on free falling films

Wasden, Frederic K.; Dukler, A. E.

doi:10.1016/0301-9322(89)90006-2

Cited by 36 publications

(3 citation statements)

References 10 publications

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“…The peak of the wall shear stress appears prior to the peak of the film thickness a bit. This phenomenon is also observed by Miya's, et.al., (1971), Wasden and Dukler (1989) and Moran, et.al., (2002) experimentally. The dimensionless wall shear stress τ w /ρgδ may be helpful to explain the flow behavior in the solitary wave (figure14).…”

Section: Wall Shear Stressmentioning

confidence: 96%

Three-dimensional simulation on behavior of water film flow with and without shear stress on water–air interface

Cheng

2014

International Journal of Heat and Mass Transfer

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In this paper, the simulations of falling film behaviour on a flat plate with and without interfacial gas-liquid shear stress were carried out. A three-dimensional numerical model was established based on film flow characteristics. A source term was implanted into the numerical model to take into account the interfacial gas-liquid shear stress. The model was validated by the experimental data. Both continuous film flow and film breakup were simulated. The film thickness, velocity distribution and wall shear stress at different Reynolds numbers were presented to understand the film flow behaviour comprehensively. The influence of water-air shear stress on film flow behaviour was revealed. A reasonable prediction on both MWR (Minimum Wetting Rate: Δ min) and MLFT (Minimum Liquid Film Thickness: Γ min) were obtained. The model proposed in this study ought to be profitable for studies on mechanism of film breakup.

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Section: Wall Shear Stressmentioning

confidence: 96%

Three-dimensional simulation on behavior of water film flow with and without shear stress on water–air interface

Cheng

2014

International Journal of Heat and Mass Transfer

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“…The statement of the problem in the electrolyte layer (4), (5), and its solutions (9)-(11) remain in the same form, but the equilibrium and boundary values for concentrations of both types of ion are found from balance equations porous layer, the ion current j(z) drops from j 0 to zero and is substituted by electron current j E that grows from zero to j 0 , i.e., the condition j(z) + j E (z) = j 0 always holds. In this case, in the equations of diffusion in the porous layer appear sources related to variation of the ion current:…”

Section: Approximation Of Finite Thickness Of Porous Anodementioning

confidence: 99%

“…The quantitative content of iodide electrolytes in Gratzel solar cells is not cited in [1][2][3][4]. At the same time, according to [5,6], the concentration of KI in electrolytes used for electrodiffusion methods of investigating the hydrodynamics of flows is C 0 = 0.1 M, whereas the iodine concentration varies in a wide range C 20 ≈ 0.004 ÷ 0.1 M, i.e., all limiting relations between concentrations are possible: C 10 C 20 , C 10 C 20 , and C 10 ∼ C 20 . Let us introduce mass transfer coefficients by relationships…”

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confidence: 96%

The maximum current in Gratzel photocells

Sigfusson

Nakoryakov

Gasenko

2011

J. Engin. Thermophys.

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The Gratzel solar cell [1], as a low-cost alternative to silicon solar cells, which was proposed for the first time in 1991, has a simple structure consisting of two electrodes and an iodine electrolyte that contains potassium iodide KI or lithium iodide LiI, iodine I 2 , and a small quantity of hypochlorous acid HClO 4 . The anodic electrode is coated with an active photosensitive layer of porous n-type semiconductor of titanium dioxide TiO 2 saturated with metal-complex ruthenium dye (see Fig. 1). The light coming from the anode is absorbed by the dye and transits one of electrons of its molecule to excited state. The excited electron moves from the dye to the conduction band of the semiconductor and then, via the anode circuit, loads the external load. The dye molecule is reduced to the initial state by receiving an electron from iodide ion I − in the oxidation reaction, transforming it to triiodide ion I − 3 , which, in its turn, diffuses to the opposite electrode and there, during the reduction reaction, receives an electron from the external circuit and again becomes the iodide ion I − . Thus, the I − ions diffuse from the cathode to anode through the electrolyte layer and the porous semiconductor layer, whereas the I − 3 ions diffuse in the opposite direction.We are sure that the diffusion current restrictions are the main ones.THIN ANODE APPROXIMATION Let us consider an electrolyte layer with a thickness d s with a constant density value of ion current j 0 that is determined by the counter diffusive motion of iodide and triiodide ions:where C 1 and C 2 are concentrations, D 1 and D 2 are diffusion coefficients of I − and I − 3 , respectively; F = 96500 K/mol is the Faraday constant. At the cathode (z = 0) occurs reaction of triiodides reduction to iodide ions due to electrons coming from the external circuit:At the anode (z = d s ), occurs oxidation of iodides to triiodide ions with electron transfer to the dye:Let us assume that the anode is a sufficiently thin TiO 2 layer in order that to avoid at this stage consideration of processes that occur inside the porous layer. The value of mass fluxes of iodides and triiodides in (1) is found from the diffusion equations D 1 d 2 C 1 dz 2 = 0, C 1 (0) = C 1c , dC 1 dz z=0 = 3j 0 2F D 1 (4) *

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A numerical study of mass transfer in free falling wavy films

Wasden

Dukler

1990

AIChE Journal

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Numerical simulations of mass transfer into falling liquid films, both through the wavy interface and from the wall, have been performed for experimentally measured large waves within which the flow fields have been computed. Experiments have shown that the occurrence of waves on free falling films causes dramatic increases in mass transfer into the film, even under laminar flow conditions. Wave effects have been modeled in several ways, none of which predicts the observed rate of enhancement. The present numerical procedure includes solving the convective-diffusion equation for wavy films by extending a technique developed for hydrodynamic simulation. The presence of waves is shown to cause significant velocities normal to each interface. In conjunction with recirculation within the large waves, these flow patterns produce transfer rates for large waves that are several times larger than predicted for quasiparallel velocity fields. Experimental wave structure data were used to define the dimensions and frequency of an average large wave and surrounding substrate. Computed transfer rates at both the gas-liquid interface and the wall for a film composed of a periodic sequence of average waves agree well with published data. These simulations confirm the inadequacy of parabolic, or Kapitza-type velocity profiles in formulating transport models.

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Numerical investigation of large wave interactions on free falling films

Cited by 36 publications

References 10 publications

Three-dimensional simulation on behavior of water film flow with and without shear stress on water–air interface

Three-dimensional simulation on behavior of water film flow with and without shear stress on water–air interface

The maximum current in Gratzel photocells

A numerical study of mass transfer in free falling wavy films

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