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An experimental investigation on the developing wavy falling film in the presence of electrohydrodynamic conduction phenomenon
Accepted Manuscript An experimental investigation on the developing wavy falling film in the presence of electrohydrodynamic conduction phenomenon R. Gharraei, M. Hemayatkhah, S. Baheri Islami, E. Esmaeilzadeh PII: DOI: Reference:
S0894-1777(14)00203-9 http://dx.doi.org/10.1016/j.expthermflusci.2014.08.005 ETF 8284
To appear in:
Experimental Thermal and Fluid Science
Received Date: Revised Date: Accepted Date:
18 March 2014 9 August 2014 9 August 2014
Please cite this article as: R. Gharraei, M. Hemayatkhah, S. Baheri Islami, E. Esmaeilzadeh, An experimental investigation on the developing wavy falling film in the presence of electrohydrodynamic conduction phenomenon, Experimental Thermal and Fluid Science (2014), doi: http://dx.doi.org/10.1016/j.expthermflusci.2014.08.005
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An experimental investigation on the developing wavy falling film in the presence of electrohydrodynamic conduction phenomenon R. Gharraei1*, M. Hemayatkhah2, S. Baheri Islami3, E. Esmaeilzadeh4 1. Mechanical Engineering Department, Azarbaijan Shahid Madani University, Tabriz, Iran, email: [email protected] 2. North-West Steel Industries Co., Tabriz, Iran. email: [email protected] 3. Mechanical Engineering Department, University of Tabriz, Tabriz, Iran, email: [email protected] 4. Mechanical Engineering Department, University of Tabriz, Tabriz, Iran, email: [email protected]
* Corresponding author, Assistant Professor, Mechanical Engineering Department, Azarbaijan Shahid Madani University, Tabriz, Iran, phone: +984113392458, fax: +984113354153 , email: [email protected]
An experimental investigation on the developing wavy falling film in the presence of electrohydrodynamic conduction phenomenon R. Gharraei1*, M. Hemayatkhah2, S. Baheri Islami3, E. Esmaeilzadeh4 1. Mechanical Engineering Department, Azarbaijan Shahid Madani University, Tabriz, Iran. 2. North-West Steel Industries Co., Tabriz, Iran. 3. Mechanical Engineering Department, University of Tabriz, Tabriz, Iran. 4. Mechanical Engineering Department, University of Tabriz, Tabriz, Iran.
* Corresponding author, Assistant Professor, Mechanical Engineering Department, Azarbaijan Shahid Madani University, Tabriz, Iran, phone: +984113392458, email: [email protected]
Abstract Hydrodynamic behavior of developing laminar wavy falling film has been studied, experimentally, in the presence of electrohydrodynamic conduction phenomenon. Electric field has been applied using nine pairs of flush mounted electrodes which can generate an EHD conduction pumping effect in the liquid film. Statistical characteristics of wavy falling film have been extracted and the effect of EHD conduction phenomenon on the wavy falling film behavior has been investigated in various Re numbers and applied voltages for two different inclination angles. Furthermore, two different operation cases for conduction pumps have been considered. The results show that applying of electric field on falling film using flush mounted electrodes, which does not alter the flow geometry and film original structure, can intensify the wavy behavior of laminar falling film. This effect is considerable for high Reynolds numbers in which large waves appear on the film surface. Comparison of operation cases show that the case with narrower high voltage electrode decreases the substrate thickness and can be the better choice for enhancement of heat/mass transfer. Keywords: Falling film, EHD, Conduction, Dielectric 1. Introduction Falling films are encountered in various industrial applications such as condensers, evaporators and wetted wall absorbers. So many studies have been performed on the behavior of falling films. Experimental studies approve the increase of heat and mass transfer from falling film by waves [1, 2]. The heat/mass transfer is enhanced by turbulence for Re>270 and by waves, which appear on the film surface, for lower Re numbers (10
convection is more intensive in the film surface and outer layers of falling film. This effect has a crucial role because the molecular diffusion coefficients are very small [2]. Experimental measurements of Roberts and Change [3] showed that the surface waves in the wavy laminar film flow regime may enhance the mean mass transfer coefficient 2-3 times of that for flat film at the 0.3 – 0.65 m from flow entry. Hydrodynamic behavior of waves on falling film depends on film Reynolds number, plate inclination and distance from entry [1, 4-8]. In a certain distance from entry, waves are appeared on the smooth film surface. These small waves coalesce to develop and form large waves which move on the substrate of film with higher velocity [9]. There are some studies on the electrohydrodynamic enhancement of heat/mass transfer from falling films. Yabe et al. [10] reported an experimental study on augmentation of condensation heat transfer by applying the non-uniform electric field. The cooled vertical pipe was connected to ground and non-uniform electric field was generated by a helical wire high voltage electrode around the pipe. This mechanism enhanced the heat transfer by removing the condensate liquid from the pipe surface. Wawazynik and Seyed-Yagoobi[11] applied fluid extraction technique for augmentation of condensation heat transfer on a single Turbo CII enhanced tube. Furthermore Yabe et al. [12] and Yamashita et al. [13] reported augmentation of condensation heat transfer using EHD extraction and psedodropwise condensation. They used a helical wire high voltage electrode for removal of condensate film from the surface of cooled pipe. Pseudodropwise condensation accrued in film thicknesses below 200 μm. So, the EHD extraction which removes the bulk of condensate from the pipe surface was followed by EHD psedodropwise condensation on thin film which enhanced the heat transfer even more [14]. Darabi et al. [15] studied the heat transfer enhancement for falling film evaporation. They used wire and plate electrode system for applying the electric field on the plane and enhance tubes. Extraction of liquid toward the outer helical or cylindrical (plate) high voltage electrode leads to augmentation of the heat transfer from film up to four folds. In the mentioned studies, application of electric field on falling film has been performed by adding the electrodes to falling film system and leads to distortion of original structure of film and alters the flow geometry. There are some studies on electrified falling films without distortion of the structure of falling film. For example, Gonzalez and Castellanos [16] studied the flow of conducting falling film in the presence of electric field, theoretically. Electric field was applied normal to flow direction by two parallel plates which ground electrode was placed far from the film surface. They determined the critical electric field intensity by inception of instabilities on the film. Tseluiko and Papageorgiou [17] studied creation and development of waves on falling film in the presence of electric field, theoretically and numerically. Their results showed that application of intense electric field normal to film flow direction lead to the instability of film at Reynolds numbers below the linear stability limit for non-electrified falling films. Furthermore, there are some other studies on the instability of falling films in the presence of electric field which is applied normal to the flow direction [18-21]. EHD conduction pumping of liquid film using flush mounted electrodes studied by Seyed-Yagoobi et al. [22,23] for the first time. EHD conduction pumping is based on the non-equilibrium behavior of dissociation-recombination processes related to a neutral space and its corresponding positive and negative ions in the dielectric liquid for electric fields exceeding from certain limit. The advantage of EHD conduction pumping of dielectric liquids is the lack of working fluid degradation in comparison with application of electric field using sharp high voltage electrodes in the ion drag
pumps. Flush mounted electrode design for pumping of liquid film does not alter the flow geometry and this is a considerable advantage for this kind of pumps. Numerical studies presented by Yazdani, Seyed-Yagoobi [23, 24] and Gharraei et al. [25] and flow pattern visualization for conduction pumping of liquid film conducted by Hemayatkhah et al. [26], approve the generation of vortices by EHD conduction phenomenon in film flow. Gharraei et al. [25, 27], conducted comprehensive experimental and numerical studies on the hydrodynamic behavior of horizontal film which was pumped using the flush mounted conduction pumps. Considering the studies conducted by Jeong and Seyed-Yagoobi [28], Yazdani and Seyed-Yagoobi [23,24] and Hanaoka et al. [29-31] and experimental and numerical studies of Gharraei et al. [25, 27], it can be concluded that there are two effective factors which determine the flow rate and direction of conduction pumping: asymmetry of electrode design and mismatch of mobilities for positive and negative ions generated in fluid. So, Gharraei et al. [27] defined two different cases for operation of conduction pumps. Case 1, which has a narrower ground electrode and asymmetry factor and mismatch of mobilities strengthen each other and case 2, which narrower electrode is high voltage and asymmetry and mismatch of mobilities have a weakening effect on each other. The visualized and computed flow pattern by the authors, has been presented in Fig. 1 for the pumping of silicon oil in cases 1 and 2 [25, 26]. As can be seen, conduction pumping generates two counter rotating vortices, which are named as primary and secondary vortices. In the present study, the hydrodynamic behavior of inclined falling film in the presence of electric field applied by flush mounted electrodes has been studied. The motivation for this study was the role of large waves on enhancement of heat/mass transfer from falling films. The investigation on the interaction between vortices generated by conduction pumps and surface waves or vortices, which would be generated in the large waves, is very interesting in order to enhance the heat/mass transfer using waviness of film surface. 2. Experimental apparatus and method Fig. 2, shows a schematic view of test section which has been used for this study. The flow loop has been designed to feed a steady constant head flow to the test section. The test section consists of a 180 cm length plexiglass plate with 22 cm width and plate copper electrodes constructed flushed with test section bottom. The distance of first electrode from film entry is 15.8 cm. The plate can be inclined with various angles. The liquid flow rate has been controlled by flow meter in the upstream of upper plenum. The upper plenum reduces the fluid velocity and allows a smooth entry of film to test section. In order to distinguish the film/air interface, a sheet of light passing from a slot has been used. Refraction of light in the liquid/gas interface leads to luminance of interface so; the interface is distinguished from the dark ambient. Interface has been captured using a high speed camera (Casio Exlime EX-F1) with 300 fps and the thickness of film has been determined with image processing of recorded movies from flow. As can be seen from Fig. 2, nine pairs of electrodes have been constructed on the test section in the developing region of falling film. The camera has been directed to the seventh pair of electrodes which captures the film interface on this pump. The working fluid was transformer oil (Nynas, Nytro-10GBN) with physical and electrical properties presented in Table 1.
In order to investigate the dynamic behavior of falling film in the presence of EHD conduction phenomenon, the recorded movies from the studying region have been analyzed using an image processing code which has been written in Matlab software. The movies in “.mov” format have been captured to separated frames. Then, the image of every frame converted to “HSI” field (Hue, Saturation and Intensity). The illuminated surface can be distinguished from dark surrounding by the highest intensity in the every column of image tensor in the Matlab. Data have been analyzed by statistical methods and important parameters in the dynamic behavior of falling film have been extracted. The mean film thickness, δmean , has been calculated by averaging the instantaneous thickness data: (1)
n
δ mean =
∑δ
i
i =1
n
where δi is the instantaneous thickness and n is the number of samples. The main difficulty of comparison of falling film data reported in literature is the variety of inclination angles and fluid properties. It can be overcome by definition of suitable dimensionless parameters. The dimensionless mean film thickness, δ*, is defined as [34] 1
δ*mean
⎡ g sin θ ⎤ 3 = δ mean ⎢ 2 ⎥ ⎣ ν ⎦
(2)
θ, νare inclination angle and kinematic viscosity, respectively. The general wave frequency composition can be described by power spectral density of local instantaneous film thickness [1,35,36]. So characteristic wave frequency, f, has been determined as the frequency corresponding to maximum magnitude of power spectral density for instantaneous film thickness at the 39 cm distance from entry. The non-dimensional frequency has been defined by Miyara [37] as:
f* =
fδ Nu u Nu
(3)
where δ Nu and u Nu are mean film thickness and mean flow velocity predicted by Nusselt theory as [38]: 1
δ Nu
⎡ 3 ν 2 Re ⎤ 3 =⎢ ⎥ ⎣ 4 g sin θ ⎦
(4)
δ 2 g sin θ 3ν
(5)
and
u Nu =
The film Reynolds number has been defined as: 4Q Re = νw
(6)
Q is volumetric flow rate and w represents the channel width. Calculation of wave velocity for non-electrified falling film has been performed by applying the discrete cross-covariance function [39, 40] on the instantaneous film thickness data in two separated points. The average time shift, τ*, between two points by separation distance of Lsep (=34 mm), corresponds to the time shift for maximum magnitude of cross-covariance. So, average wave velocity is determined by: uw =
Lsep
(7)
τ
*
Further study on the effect of EHD conduction on the falling film behavior could be performed by considering the probability density function (PDF) for instantaneous local falling film thickness data. From the statistical basis PDF could be defined as [35]:
PDF =
dFδ dδ
(8)
where Fδ is probability for occurrence of thicknesses lower than δ and
Fδ = Pr ob[δ( t ) < δ]
(9)
For Re<25 falling film can be interpreted as smooth film, for 25
therefore agreement between present results and the results of Brauner and Moalem Maron[1] and Moran et al. [41] is better. For low Re numbers, small waves form on the film. Because of low velocity, the probability of coalescence for these small waves with low mass content is very lower than large waves which appear in higher Re numbers. So, these waves have developed in a shorter distance of entry and there is a good agreement between present results and other data in low Re numbers. By increasing the Re number, the wave inception occurs in the larger distances. The frequency of fully developed waves is lower than developing waves which have been measured in this study, because of acceleration and coalescence of waves. The present results have a good agreement with Jones and Whitaker [44] measurements in the entry region. It can be concluded from Figs. 3 and 4 that the measurement technique has an acceptable accuracy. Fig. 5 shows the variation of mean film thickness versus Re number, in the presence of electric field for two different inclination angles. Application of electric field by flush mounted electrodes leads to electrohydrodynamic conduction phenomenon which can generate a pumping effect on the fluid [22, 27].The operation of pumps can be changed from case 1 to case 2, by altering the polarity of electrodes (Fig. 1). It is clear that for all of the cases, EHD conduction increases the mean film thickness for low Re numbers because of generation of fixed ripples on the electrodes. These ripples are generated by primary and secondary vortices which are created on the electrodes of a conduction pump as shown by Gharraei et al.[25] and Hemayatkhah etal. [26]. In this circumstance the small waves slip on the fixed ripples on electrodes which leads to the increasing of mean and maximum film thicknesses. For Re numbers higher than 100 at both of inclinations, the natural waves have a relatively sharp front (especially for inclination of 45◦). This can be related to the generation of a recirculating zone in the large wave. By increasing the Re number this recirculation generates a strong vortex in the wave. Interaction of vortex of moving wave by primary and secondary vortices on the electrodes leads to sweeping of these vortices because of higher momentum of large waves. The shear stresses generated from primary vortices on two adjacent electrode pairs and a weak pumping effect of neighbor electrodes from two adjacent electrode pairs create the secondary vortices [26, 32]. So these vortices are very weaker than primary vortices and have not a considerable effect on the dynamic behavior of moving waves. Fig. 6 illustrates the process of passing of a large wave from the electrode pair region. As mentioned before, primary and secondary vortices hold a volume of fluid in the ripples, when a large wave by a strong vortex passes from the region of primary vortex it sweeps this volume of fluid and this leads to increment of wave height and maximum thickness of film. Increasing the wave height associated by decreasing the thickness of film in the tail of the wave [32]. After the passing of large wave from the primary vortex region and passing the tail of generated large wave, when the thickness of film reached to a suitable size, the primary vortex is created and increases the film thickness, by preserving the volume of fluid, again. These preservations and sweepings of fluid lead to considerable fluctuations in the local film thickness. Considering the statistical results the increment of fluctuations of local film thickness have a tendency to lower thicknesses and decreases the mean film thickness. This process is similar for operation of conduction pumps as case 1 or case 2, and Fig. 5 shows this similarity. Furthermore, Fig. 5 shows that increasing the inclination angle decreases the film thickness as nonelectrified falling films [1] and increasing the applied voltage strengthen the effect of
EHD in the most of the cases. Fig. 7, shows the variation of dimensionless maximum film thickness versus Re number for wavy falling films in two different inclination angles in the presence of EHD conduction with two different operations (Maximum film thickness determination is based on the probability of 5% or less). As illustrated before, EHD conduction phenomenon increases the maximum wave thickness for all of the cases. Fig. 8 presents the PDF of local film thickness for two different Re numbers and two different inclination angles with and without EHD conduction. Chu and Dukler [35, 36] used the PDF for definition of a special thickness named substrate thickness. They defined the substrate thickness as the limit of most probable thicknesses of film which corresponds to the peak of PDF curve. This thickness can be interpreted as the main thermal resistance against the heat transfer between wall and gas stream in the condensers or other falling film heat exchangers. This figure shows that for low Re number, application of EHD through conduction pumps increases the substrate thickness of film. For low Re numbers the primary vortex of conduction pump holds a volume of fluid as a ripple and prevents from the penetration of weak disturbances and sweeping effect of moving waves to the inner layers of film. Considering the stronger primary vortex for case 1 [26], increasing of substrate thickness is higher for this case in comparison with case 2. On the other hand, PDF curves show that application of EHD conduction expands the range of fluctuations of thickness and this expansion is toward higher thicknesses. For high Re numbers, because of the interaction between recirculating flow of strong large waves and primary vortex, disturbances penetrate to the inner layers of film. So expansion of the range of fluctuations toward lower thicknesses can be seen in the Fig.8. Case 2, creates the weaker primary vortex relative to case 1, so penetration of disturbances to inner layers of film is higher for Case2 and this case decreases the substrate thickness. It should be noted that the vortices generated by EHD conduction phenomenon have two different effects on the falling film behavior: these vortices could intensify the disturbances by transferring their energy to recirculating flow of waves and on the other hand they prevent from penetration of disturbances to the inner layers of film specially at low Re numbers. The increasing of the range of fluctuations is higher for inclination angle of 45◦ than the one of 26◦. Fig. 9 represents the frequency of waves versus Re number for two different inclination angles with and without EHD conduction. This figure shows that for low Re numbers application of EHD increases the frequency of waves by accelerating (case 1) or decelerating (case 2) of wave passing from the primary vortex region. This effect can decrease the wave length and increase the wave frequency. For Re>100 resistance of primary vortices against the sweeping by large waves, decelerates this waves in the region above the electrode pairs, for both cases. Therefore, the subsequent wave with higher velocity approaches the decelerated wave and collision and coalescence of waves decreases the frequency of waves. Increasing the applied voltage strengthen this effect. Fig. 10 shows the variation of wave velocity versus Re number for various inclination angles and voltages. Primary and secondary vortices generated by conduction pumps, deform the waves of falling film and application of cross-covariance method for estimation of wave migration time is not accurate, so the direct data inspection method [45] has been used for evaluating the wave velocity. Comparison of the results of direct data inspection method by cross-covariance method for nonelectrified falling film wave velocity in Fig. 11 approved the accuracy of this method.
As mentioned before, for low Re numbers, application of EHD increases amplitude of thickness fluctuation and the size of waves ( Figs. 5,7) and leads to the higher wave velocities as conducted by Brauner and Moalem Maron [1] for non-electrified falling films. In spite of the small waves which slip on the conduction pump vortices, large waves, which tend to sweep the vortices, are decelerated by primary vortices. Increasing the voltage strengthen these effects. Fig. 12 presents the variation of standard deviation of local film thickness versus Re number for various inclination angles and voltages. For all of the cases standard deviation increases by application of EHD conduction which approves the intensification of disturbances and strengthening of wavy behaviors by application of EHD. 4. Conclusions Hydrodynamic behavior of developing wavy laminar falling film in the presence of electric field, applied by flush mounted electrodes, has been investigated. The results show that EHD conduction increases the mean film thickness, wave velocity and frequency for the films with low Re number. For higher Re numbers in which the large waves appear on the surface of film, applying the electric field decreases the mean film thickness, wave frequency and wave velocity and enlarge the surface waves. Furthermore, applying the electric field on the film increases the substrate thickness at low Re numbers but decreases it for higher Re numbers. This decrement occurs in the case 2 of operation. For the whole range of Re numbers, by applying the electric field standard deviation of local film thicknesses increases which approves the intensification of wavy behavior of film in the presence of EHD conduction phenomenon. Considering the extracted statistical characteristics for falling film, it can be concluded that applying the electric field using flush mounted electrodes can enhanced the heat/mass transfer from falling films and the case 2 is the suitable choice for this purpose. This conclusion is based on the hydrodynamic behavior of waves and other experiments about the heat/mass transfer enhancement are required for accurate judgment about effectiveness of this technique. 5. References [1] N. Brauner, D. Moallem Maron, Characteristics of inclined thin films, waviness and the associated mass transfer, Int. J. Heat and Mass Transfer, 25 (1982) 99-110. [2] C. D. Park, T. Nosoko, S. Gima, S. T. Ro, Wave-augmented mass transfer in a liquid film falling inside a vertical tube, Int. J. Heat and Mass Transfer, 47 (2004) 2587-2598. [3] R. M. Roberts, H. C. Chang, Wave enhanced interfacial Transfer, Chemical Engineering Science, 55 (2000) 1127–1141. [4] S. Portalski, A.J. Clegg, An experimental study of wave inception on falling liquid films, Chemical Engineering Science, 27 (1972) 1257–1265. [5] D.R. Webb, G.F. Hewitt, Downwards co-current annular Flow, Int. J. Multiphase Flow, 2 (1975) 35–49. [6] H. Takahama, S. Kato, Statistical characteristics of thin, vertical, wavy, liquid films without concurrent gas flow, Int. J. Multiphase Flow, 6 (1980) 203–215. [7] R.P. Salazar, E. Marschall, Time-average local thickness measurement in falling liquid film flow, Int. J. Multiphase Flow, 4 (1978) 405–412.
[8] T.D. Karapantsios, A.J. Karabelas, Longitudinal characteristics of wavy falling films, Int. J. Multiphase Flow, 21 (1995) 119–127. [9] C.D. Park, T. Nosoko, Three-dimensional wave dynamics on a falling film and associated mass transfer, AIChE J. 49 (2003) 2715–2727. [10] A. Yabe, T. Taketani, K. Kikuchi, Y. Mori, K. Hijikata, Augmentation of condensation heat transfer around vertical cooled tubes provided with helical wire electrodes by applying nonuniform electric fields, Heat Transfer Science and Technology, Proc. Int. Symp. (1987) 812-819. [11] M. Wawzyniak, J. Seyed-Yagoobi, Augmentation of condensation heat transfer with electrohydrodynamics on vertical enhanced tubes, ASME J. Heat Transfer, 118 (1996) 499-502. [12] A. Yabe, T. Taketani, K. Kikuchi,Y. Mori, H. Miki, Augmentation of conduction heat transfer by applying electro-hydro-dynamic pseudo-drop-wise condensation, Proc. of the Int. Heat Transfer Conf., 6 (1986) 2957-2962. [13] K. Yamashita, M. Kumagai, S. Sekita, Heat transfer characteristics on an EHD condenser, Proc. 3rd ASME/JSME Thermal Engineering Conf., (1991) 61–67. [14] J. Seyed-Yagoobi, J. E. Bryan, Enhancement of heat and mass transport in single-phase and two phase flows with electrohydrodynamics, Advances in Heat Transfer, 33 (1999) 95-18. [15] J. Darabi, M. Ohadi, S. V. Desiatoun, Falling film and spray evaporation enhancement using an applied electric field, ASME J. Heat Transfer. 122 (2000) 741748. [16] A. Gonzalez, A. Castellanos, Nonlinear electrohydrodynamic waves on films falling down an inclined plane, Physical Review E. 53 (1996) 3573-3578. [17] D. Tseluiko, D. T. Papageorgiou, Wave evolution on electrified falling Films, J. Fluid Mechanics. 556 (2006) 361–386. [18] G. I. Taylor, A. D. McEwan, The stability of a horizontal fluid interface in a vertical electric field, J. Fluid Mechanics. 22, part 1 (1965) 1-15. [19] D. Tseluiko, M. G. Blyth, D. T. Papageorgiou , J. M. Vanden-Broeck, Electrified falling-film flow over topography in the presence of a finite electrode, J. Engineering Mathematics, 68 (2010) 339–353. [20] A. W. Wray, O. Matar, D. T. Papageorgiou, Non-linear waves in electrified viscous film flow down a vertical cylinder, IMA J. Applied Mathematics, 77 (2012) 430–440. [21] A. Samanta, Shear wave instability for electrified falling films, Physical Review E, 88 (2013) 053002. [22] M. Siddiqui, J. Seyed-Yagoobi, Experimental study of pumping of liquid film with electric conduction phenomenon, IEEE Trans. Industry Applications, 45 (2009) 3-9. [23] M. Yazdani, J. Seyed-Yagoobi, Electrically induced dielectric liquid film flow based on electric conduction phenomenon, IEEE Trans. Dielectrics and Electrical Insulation, 16 (2009) 768-777. [24] M. Yazdani, J. Seyed-Yagoobi, Numerical investigation of electrohydrodynamicconduction pumping of liquid film in the presence of evaporation, ASME J. Heat Transfer, 131 (2009) 011602. [25] R. Gharraei, E. Esmaeilzadeh, M. R. Heirani Nobari, Numerical investigation of conduction pumping of dielectric liquid film using flush-mounted electrodes, Theoretical and Computational Fluid Dynamics, 28 (2014) 89-106.
[26] M. Hemayatkhah, R. Gharraei, E. Esmaeilzadeh, Flow pattern visualization of liquid film conduction pumping using flush mounted electrodes, Experimental Thermal and Fluid Science , 35 (2011) 933-938. [27] R. Gharraei, E. Esmaeilzadeh, M. Hemayatkhah, J. Danaeefar, Experimental investigation of electrohydrodynamic conduction pumping of various liquid films using flush electrodes, J. Electrostatics , 69 (2011) 43-53. [28] S. I. Jeong, J. Seyed-Yagoobi, P. Atten, Theoretical/numerical study of electrohydrodynamic pumping through conduction phenomenon, IEEE Trans. Industry Applications, 39 (2003) 355-361. [29] R. Hanaoka, S. Takata, M. Murakumo, H. Anzi, Properties of liquid jet induced by electrohydrodynamic pumping in dielectric liquids, Electrical Engineering in Japan 138 (2002) 224-230. [30] R.Hanaoka, H. Nakamichi, S. Takata, T. Fukami, Distinctive flow properties of liquid jet generated by EHD pump and conical nozzle, Electrical Engineering in Japan, 154 (2006) 399-406. [31] R. Hanaoka, I. Takahashi, S. Takata, T. Fukami, Y. Kanamaru, Properties of EHD pump with combination of rod-to-rod and meshy parallel plates electrode assemblies, IEEE Trans. Dielectrics and Electrical Insulation, 16 (2009) 440-447. [32] R. Gharraei, Hydrodynamic investigation of falling film in the presence of electric field, Ph.D. Thesis, Department of Mechanical Engineering, University of Tabriz, 2011. [33] Nynas, Nytro 10GBN, Naphthenics product data sheet, 2005. [34] V. V. Lel, F. Al-Sibai, A. Leefken, U. Renz, Local thickness and wave velocity measurement of wavy films with a chromatic confocal imaging method and a fluorescence intensity technique, Experiments in Fluids, 39 (2005) 856–864. [35] K.J. Chu, A.E. Dukler, Statistical Characteristics of Thin, Wavy Films: Part II. Studies of the Substrate and its Wave Structure, AIChE J. , 20 (1974) 695-706. [36] K.J. Chu, A.E. Dukler, Statistical Characteristics of Thin, Wavy Films: Part III. Structure of the Large Waves and their Resistance to Gas Flaw, AIChE. J. , 21 (1975) 583-593. [37] A. Miyara, Numerical Analysis in Flow Dynamics and Heat Transfer of Falling Liquid Films with Interfacial Waves, Heat and Mass Transfer, 35 (1999) 298-306. [38] W. Nusselt, Die oberflachenkondensation des wasserdamphes, VDI-Zs 60 (1916) 541. [39] W. Ambrosini, N. Forgione, F. Oriolo. P. Vigni, S. Baessler, Experimental investigation on wave velocity in a falling film, 2nd Int. Symp. Two-Phase Flow Modeling and Experimentation, (1999) 23–26. [40] W. Ambrosini, N. Forgione, F. Oriolo., Statistical characteristics of a water film falling down a flat plate at different inclinations and temperatures, Int. J. Multiphase Flow, Vol. 28, pp. 1521–1540. [41] K. Moran, J. Inumaru, M. Kawaji, Instantaneous hydrodynamics of a laminar wavy liquid film, Int. J. Multiphase Flow, 28 (2002) 731– 755. [42] M. L. Jackson, Liquid films in viscous flow, AIChE. Journal, 1 (1955) 231-240. [43] H. Brauer, VDI Forschungsheft 457B, 22 (1956) 1–40. [44] L. O. Jones, S. Whitaker, An Experimental Study of Falling Liquid Films, AIChE J. , 12 (1966) 525-529. [45] M. Kostoglou, K. Samaras, T. D. Karapantsios, Large wave characteristics and their downstream evolution at high Reynolds number falling films, AIChE J., 56 (2010) 11-23.
Highlights •
Hydrodynamic behavior of electrified developing wavy falling film has been studied.
•
The electric field applied using flush electrodes which does not alter the geometry. EHD decreases the film thickness, wave velocity and frequency for high Re numbers.
•
Secondary vortex
Secondary vortex
Primary vortex
Primary vortex
(a)
(b) Fig.1: Flow pattern for conduction pumping of Silicone oil: Right (case1), Left (case2), (a) Flow visualization [26] ,(b) Numerical simulation [25]
Flush mounted electrode pairs
Upper plenum
Test section
HV. power supply
Collection vessel
2 mm
Capturing 4 mm section
Flow
220 mm
16 mm
Side walls ( Plexiglass)
160 mm
350 mm
12 mm
7th. electrode pair
Fig. 2: Schematic diagram of falling film test section 8
7
5
δ*
mean
6
4 Present study (26 deg) Present study (45 deg) Moran et al. [40] Jackson et al. [41] Brauer [42] Nusselt Lel et al. [34]
3
2
1
0
50
100
150
200
Re
Fig. 3: Comparison of dimensionless film thickness with other experimental studies
Present study (26 deg) Present study (45 deg) Brauner & Moalem Maron [1] (26 deg) Moran et al. [40] (45 deg) Jones & Whitaker [43] (90 deg, x=6.35 cm) Jones & Whitaker [43] (90 deg, x=20.32 cm)
0.08
f*
0.06
0.04
0.02
0
0
50
100
150
200
Re
2
2
1.8
1.8
δmean (mm)
δmean(mm)
Fig. 4: Comparison of dimensionless wave frequency with other experimental studies
1.6
1.4
V=0 V=9 kV V=12 kV V=15 kV
1
0
50
100
150
V=0 V=9 kV V=12 kV V=15 kV
1
0.8
200
0
100
150
200
θ= 26° 2
1.8
1.8
δmean (mm)
2
1.6
1.4
1.6
1.4
1.2
1.2 V=0 V=9 kV V=12 kV V=15 kV
1
0.8
50
Re
Re
δmean(mm)
1.4
1.2
1.2
0.8
1.6
0
50
100
150
V=0 V=9 kV V=12 kV V=15 kV
1
0.8
200
0
50
100
150
Re
Re °
θ= 45 Fig. 5: Variation of mean film thickness versus Re number for various applied voltages, left: Case1, Right: Case2.
200
G
HV
(a )
HV
G
(b) Fig. 6: Creation of large waves in the presence of conduction phenomenon, θ= 45°
2.8
2.8
2.6
2.6
2.4
2.4
2.2
2.2
δmax / δNu
δmax / δNu
a: Case1, b: Case2
2 1.8 1.6
1.6
1.4
1.4 V=0 V=9 kV V=12 kV V=15 kV
1.2 1 0.8
2 1.8
0
50
100
150
V=0 V=9 kV V=12 kV V=15 kV
1.2 1 0.8
200
0
50
Re
100
150
200
Re
3
3
2.8
2.8
2.6
2.6
2.4
2.4
δmax / δNu
δmax / δNu
θ= 26°
2.2 2 1.8
2 1.8 1.6
1.6
1.4
1.4 V=0 V=9 kV V=12 kV V=15 kV
1.2 1 0.8
2.2
0
50
100
Re
150
200
V=0 V=9 kV V=12 kV V=15 kV
1.2 1 0.8
0
50
100
150
200
Re
θ= 45° Fig. 7: Variation of dimensionless Maximum film thickness versus Re number for various applied voltages, left: Case1, Right: Case2.
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
PDF
PDF
0.9
0.4 0.3
0.3 V=0 Case 1 Case 2
0.2 0.1 0
0.4
0
0.6
1.2
1.8
δ (mm)
2.4
3
V=0 Case 1 Case 2
0.2 0.1 0
3.6
0
0.6
1.2
1.8
δ (mm)
2.4
3
3.6
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
PDF
PDF
θ= 26°
0.4
V=0 Case 1 Case 2
0.2 0.1 0
0.4 0.3
0.3
0
0.6
1.2
1.8
δ (mm)
2.4
3
V=0 Case 1 Case 2
0.2 0.1
3.6
0
0
0.6
1.2
1.8
δ (mm)
2.4
θ= 45° Fig. 8: PDF.s of local film thickness, left: Re=58, right: Re=140.
3
3.6
16
16 V=0 V=9 kV V=12 kV V=15 kV
12
12
10
10
8
6
4
4
2
2
0
50
100
150
0
200
50
100
150
200
150
200
°
θ= 26
16
16 V=0 V=9 kV V=12 kV V=15 kV
14
10
10
f (Hz)
12
8
8
6
6
4
4
2
2
0
50
V=0 V=9 kV V=12 kV V=15 kV
14
12
0
0
Re
Re
f (Hz)
8
6
0
V=0 V=9 kV V=12 kV V=15 kV
14
f (Hz)
f (Hz)
14
100
Re
150
200
0
0
50
100
Re
θ= 45° Fig. 9: Variation of wave frequency versus Re number for various applied voltages, left: Case1, Right: Case2.
0.7
0.7 V=0 V=9 kV V=12 kV V=15 kV
0.6
0.4
(m/s)
0.3
u
0.5
0.4
w
w
(m/s)
0.5
u
V=0 V=9 kV V=12 kV V=15 kV
0.6
0.3
0.2
0.2
0.1
0.1
0
0
50
100
150
0
200
0
50
100
Re
150
200
150
200
Re
θ= 26° 0.7
0.7 V=0 V=9 kV V=12 kV V=15 kV
0.6
0.3
0.4
w
0.4
(m/s)
0.5
u
w
(m/s)
0.5
u
V=0 V=9 kV V=12 kV V=15 kV
0.6
0.3
0.2
0.2
0.1
0.1
0
0
50
100
150
0
200
0
50
100
Re
Re
θ= 45° Fig. 10: Variation of wave velocity versus Re number for various applied voltages, left: Case1, Right: Case2. 0.7 26 26 45 45
0.6
deg (Covariance) deg (Direct method) deg (Covariance) deg (Direct method)
w
u (m/s)
0.5
0.4
0.3
0.2
0.1
0
0
50
100
150
200
Re
Fig. 11: Comparison of wave velocity calculated by cross-covariance and direct data inspection methods
1.6 1.4 1.2
1.2
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
0
50
V=0 V=9 kV V=12 kV V=15 kV
1.4
S
S
1.6
V=0 V=9 kV V=12 kV V=15 kV
100
150
0
200
0
50
100
150
200
150
200
Re
Re °
θ= 26
1.6
1.6 V=0 V=9 kV V=12 kV V=15 kV
1.2
1.2
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
0
50
V=0 V=9 kV V=12 kV V=15 kV
1.4
S
S
1.4
100
150
0
200
0
50
Re
100
Re
θ= 45° Fig. 12: Variation of standard deviation of local film thickness versus Re number for various applied voltages, left: Case1, right: Case2.
Table1: Physical and electrical properties of Transformer oil (20 ◦C)
Density (kg/m3) [33]
Viscosity (10-3Pa.s) [33]
895.5
11
Mobility (10-8 m2/Vs) [32] positive negative 0.18
0.35
Electrical conductivity (10-12 S/m) [32]
Dielectric constant [32]
1.2
2.08
S0894-1777(14)00203-9 http://dx.doi.org/10.1016/j.expthermflusci.2014.08.005 ETF 8284
To appear in:
Experimental Thermal and Fluid Science
Received Date: Revised Date: Accepted Date:
18 March 2014 9 August 2014 9 August 2014
Please cite this article as: R. Gharraei, M. Hemayatkhah, S. Baheri Islami, E. Esmaeilzadeh, An experimental investigation on the developing wavy falling film in the presence of electrohydrodynamic conduction phenomenon, Experimental Thermal and Fluid Science (2014), doi: http://dx.doi.org/10.1016/j.expthermflusci.2014.08.005
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An experimental investigation on the developing wavy falling film in the presence of electrohydrodynamic conduction phenomenon R. Gharraei1*, M. Hemayatkhah2, S. Baheri Islami3, E. Esmaeilzadeh4 1. Mechanical Engineering Department, Azarbaijan Shahid Madani University, Tabriz, Iran, email: [email protected] 2. North-West Steel Industries Co., Tabriz, Iran. email: [email protected] 3. Mechanical Engineering Department, University of Tabriz, Tabriz, Iran, email: [email protected] 4. Mechanical Engineering Department, University of Tabriz, Tabriz, Iran, email: [email protected]
* Corresponding author, Assistant Professor, Mechanical Engineering Department, Azarbaijan Shahid Madani University, Tabriz, Iran, phone: +984113392458, fax: +984113354153 , email: [email protected]
An experimental investigation on the developing wavy falling film in the presence of electrohydrodynamic conduction phenomenon R. Gharraei1*, M. Hemayatkhah2, S. Baheri Islami3, E. Esmaeilzadeh4 1. Mechanical Engineering Department, Azarbaijan Shahid Madani University, Tabriz, Iran. 2. North-West Steel Industries Co., Tabriz, Iran. 3. Mechanical Engineering Department, University of Tabriz, Tabriz, Iran. 4. Mechanical Engineering Department, University of Tabriz, Tabriz, Iran.
* Corresponding author, Assistant Professor, Mechanical Engineering Department, Azarbaijan Shahid Madani University, Tabriz, Iran, phone: +984113392458, email: [email protected]
Abstract Hydrodynamic behavior of developing laminar wavy falling film has been studied, experimentally, in the presence of electrohydrodynamic conduction phenomenon. Electric field has been applied using nine pairs of flush mounted electrodes which can generate an EHD conduction pumping effect in the liquid film. Statistical characteristics of wavy falling film have been extracted and the effect of EHD conduction phenomenon on the wavy falling film behavior has been investigated in various Re numbers and applied voltages for two different inclination angles. Furthermore, two different operation cases for conduction pumps have been considered. The results show that applying of electric field on falling film using flush mounted electrodes, which does not alter the flow geometry and film original structure, can intensify the wavy behavior of laminar falling film. This effect is considerable for high Reynolds numbers in which large waves appear on the film surface. Comparison of operation cases show that the case with narrower high voltage electrode decreases the substrate thickness and can be the better choice for enhancement of heat/mass transfer. Keywords: Falling film, EHD, Conduction, Dielectric 1. Introduction Falling films are encountered in various industrial applications such as condensers, evaporators and wetted wall absorbers. So many studies have been performed on the behavior of falling films. Experimental studies approve the increase of heat and mass transfer from falling film by waves [1, 2]. The heat/mass transfer is enhanced by turbulence for Re>270 and by waves, which appear on the film surface, for lower Re numbers (10
convection is more intensive in the film surface and outer layers of falling film. This effect has a crucial role because the molecular diffusion coefficients are very small [2]. Experimental measurements of Roberts and Change [3] showed that the surface waves in the wavy laminar film flow regime may enhance the mean mass transfer coefficient 2-3 times of that for flat film at the 0.3 – 0.65 m from flow entry. Hydrodynamic behavior of waves on falling film depends on film Reynolds number, plate inclination and distance from entry [1, 4-8]. In a certain distance from entry, waves are appeared on the smooth film surface. These small waves coalesce to develop and form large waves which move on the substrate of film with higher velocity [9]. There are some studies on the electrohydrodynamic enhancement of heat/mass transfer from falling films. Yabe et al. [10] reported an experimental study on augmentation of condensation heat transfer by applying the non-uniform electric field. The cooled vertical pipe was connected to ground and non-uniform electric field was generated by a helical wire high voltage electrode around the pipe. This mechanism enhanced the heat transfer by removing the condensate liquid from the pipe surface. Wawazynik and Seyed-Yagoobi[11] applied fluid extraction technique for augmentation of condensation heat transfer on a single Turbo CII enhanced tube. Furthermore Yabe et al. [12] and Yamashita et al. [13] reported augmentation of condensation heat transfer using EHD extraction and psedodropwise condensation. They used a helical wire high voltage electrode for removal of condensate film from the surface of cooled pipe. Pseudodropwise condensation accrued in film thicknesses below 200 μm. So, the EHD extraction which removes the bulk of condensate from the pipe surface was followed by EHD psedodropwise condensation on thin film which enhanced the heat transfer even more [14]. Darabi et al. [15] studied the heat transfer enhancement for falling film evaporation. They used wire and plate electrode system for applying the electric field on the plane and enhance tubes. Extraction of liquid toward the outer helical or cylindrical (plate) high voltage electrode leads to augmentation of the heat transfer from film up to four folds. In the mentioned studies, application of electric field on falling film has been performed by adding the electrodes to falling film system and leads to distortion of original structure of film and alters the flow geometry. There are some studies on electrified falling films without distortion of the structure of falling film. For example, Gonzalez and Castellanos [16] studied the flow of conducting falling film in the presence of electric field, theoretically. Electric field was applied normal to flow direction by two parallel plates which ground electrode was placed far from the film surface. They determined the critical electric field intensity by inception of instabilities on the film. Tseluiko and Papageorgiou [17] studied creation and development of waves on falling film in the presence of electric field, theoretically and numerically. Their results showed that application of intense electric field normal to film flow direction lead to the instability of film at Reynolds numbers below the linear stability limit for non-electrified falling films. Furthermore, there are some other studies on the instability of falling films in the presence of electric field which is applied normal to the flow direction [18-21]. EHD conduction pumping of liquid film using flush mounted electrodes studied by Seyed-Yagoobi et al. [22,23] for the first time. EHD conduction pumping is based on the non-equilibrium behavior of dissociation-recombination processes related to a neutral space and its corresponding positive and negative ions in the dielectric liquid for electric fields exceeding from certain limit. The advantage of EHD conduction pumping of dielectric liquids is the lack of working fluid degradation in comparison with application of electric field using sharp high voltage electrodes in the ion drag
pumps. Flush mounted electrode design for pumping of liquid film does not alter the flow geometry and this is a considerable advantage for this kind of pumps. Numerical studies presented by Yazdani, Seyed-Yagoobi [23, 24] and Gharraei et al. [25] and flow pattern visualization for conduction pumping of liquid film conducted by Hemayatkhah et al. [26], approve the generation of vortices by EHD conduction phenomenon in film flow. Gharraei et al. [25, 27], conducted comprehensive experimental and numerical studies on the hydrodynamic behavior of horizontal film which was pumped using the flush mounted conduction pumps. Considering the studies conducted by Jeong and Seyed-Yagoobi [28], Yazdani and Seyed-Yagoobi [23,24] and Hanaoka et al. [29-31] and experimental and numerical studies of Gharraei et al. [25, 27], it can be concluded that there are two effective factors which determine the flow rate and direction of conduction pumping: asymmetry of electrode design and mismatch of mobilities for positive and negative ions generated in fluid. So, Gharraei et al. [27] defined two different cases for operation of conduction pumps. Case 1, which has a narrower ground electrode and asymmetry factor and mismatch of mobilities strengthen each other and case 2, which narrower electrode is high voltage and asymmetry and mismatch of mobilities have a weakening effect on each other. The visualized and computed flow pattern by the authors, has been presented in Fig. 1 for the pumping of silicon oil in cases 1 and 2 [25, 26]. As can be seen, conduction pumping generates two counter rotating vortices, which are named as primary and secondary vortices. In the present study, the hydrodynamic behavior of inclined falling film in the presence of electric field applied by flush mounted electrodes has been studied. The motivation for this study was the role of large waves on enhancement of heat/mass transfer from falling films. The investigation on the interaction between vortices generated by conduction pumps and surface waves or vortices, which would be generated in the large waves, is very interesting in order to enhance the heat/mass transfer using waviness of film surface. 2. Experimental apparatus and method Fig. 2, shows a schematic view of test section which has been used for this study. The flow loop has been designed to feed a steady constant head flow to the test section. The test section consists of a 180 cm length plexiglass plate with 22 cm width and plate copper electrodes constructed flushed with test section bottom. The distance of first electrode from film entry is 15.8 cm. The plate can be inclined with various angles. The liquid flow rate has been controlled by flow meter in the upstream of upper plenum. The upper plenum reduces the fluid velocity and allows a smooth entry of film to test section. In order to distinguish the film/air interface, a sheet of light passing from a slot has been used. Refraction of light in the liquid/gas interface leads to luminance of interface so; the interface is distinguished from the dark ambient. Interface has been captured using a high speed camera (Casio Exlime EX-F1) with 300 fps and the thickness of film has been determined with image processing of recorded movies from flow. As can be seen from Fig. 2, nine pairs of electrodes have been constructed on the test section in the developing region of falling film. The camera has been directed to the seventh pair of electrodes which captures the film interface on this pump. The working fluid was transformer oil (Nynas, Nytro-10GBN) with physical and electrical properties presented in Table 1.
In order to investigate the dynamic behavior of falling film in the presence of EHD conduction phenomenon, the recorded movies from the studying region have been analyzed using an image processing code which has been written in Matlab software. The movies in “.mov” format have been captured to separated frames. Then, the image of every frame converted to “HSI” field (Hue, Saturation and Intensity). The illuminated surface can be distinguished from dark surrounding by the highest intensity in the every column of image tensor in the Matlab. Data have been analyzed by statistical methods and important parameters in the dynamic behavior of falling film have been extracted. The mean film thickness, δmean , has been calculated by averaging the instantaneous thickness data: (1)
n
δ mean =
∑δ
i
i =1
n
where δi is the instantaneous thickness and n is the number of samples. The main difficulty of comparison of falling film data reported in literature is the variety of inclination angles and fluid properties. It can be overcome by definition of suitable dimensionless parameters. The dimensionless mean film thickness, δ*, is defined as [34] 1
δ*mean
⎡ g sin θ ⎤ 3 = δ mean ⎢ 2 ⎥ ⎣ ν ⎦
(2)
θ, νare inclination angle and kinematic viscosity, respectively. The general wave frequency composition can be described by power spectral density of local instantaneous film thickness [1,35,36]. So characteristic wave frequency, f, has been determined as the frequency corresponding to maximum magnitude of power spectral density for instantaneous film thickness at the 39 cm distance from entry. The non-dimensional frequency has been defined by Miyara [37] as:
f* =
fδ Nu u Nu
(3)
where δ Nu and u Nu are mean film thickness and mean flow velocity predicted by Nusselt theory as [38]: 1
δ Nu
⎡ 3 ν 2 Re ⎤ 3 =⎢ ⎥ ⎣ 4 g sin θ ⎦
(4)
δ 2 g sin θ 3ν
(5)
and
u Nu =
The film Reynolds number has been defined as: 4Q Re = νw
(6)
Q is volumetric flow rate and w represents the channel width. Calculation of wave velocity for non-electrified falling film has been performed by applying the discrete cross-covariance function [39, 40] on the instantaneous film thickness data in two separated points. The average time shift, τ*, between two points by separation distance of Lsep (=34 mm), corresponds to the time shift for maximum magnitude of cross-covariance. So, average wave velocity is determined by: uw =
Lsep
(7)
τ
*
Further study on the effect of EHD conduction on the falling film behavior could be performed by considering the probability density function (PDF) for instantaneous local falling film thickness data. From the statistical basis PDF could be defined as [35]:
PDF =
dFδ dδ
(8)
where Fδ is probability for occurrence of thicknesses lower than δ and
Fδ = Pr ob[δ( t ) < δ]
(9)
For Re<25 falling film can be interpreted as smooth film, for 25
therefore agreement between present results and the results of Brauner and Moalem Maron[1] and Moran et al. [41] is better. For low Re numbers, small waves form on the film. Because of low velocity, the probability of coalescence for these small waves with low mass content is very lower than large waves which appear in higher Re numbers. So, these waves have developed in a shorter distance of entry and there is a good agreement between present results and other data in low Re numbers. By increasing the Re number, the wave inception occurs in the larger distances. The frequency of fully developed waves is lower than developing waves which have been measured in this study, because of acceleration and coalescence of waves. The present results have a good agreement with Jones and Whitaker [44] measurements in the entry region. It can be concluded from Figs. 3 and 4 that the measurement technique has an acceptable accuracy. Fig. 5 shows the variation of mean film thickness versus Re number, in the presence of electric field for two different inclination angles. Application of electric field by flush mounted electrodes leads to electrohydrodynamic conduction phenomenon which can generate a pumping effect on the fluid [22, 27].The operation of pumps can be changed from case 1 to case 2, by altering the polarity of electrodes (Fig. 1). It is clear that for all of the cases, EHD conduction increases the mean film thickness for low Re numbers because of generation of fixed ripples on the electrodes. These ripples are generated by primary and secondary vortices which are created on the electrodes of a conduction pump as shown by Gharraei et al.[25] and Hemayatkhah etal. [26]. In this circumstance the small waves slip on the fixed ripples on electrodes which leads to the increasing of mean and maximum film thicknesses. For Re numbers higher than 100 at both of inclinations, the natural waves have a relatively sharp front (especially for inclination of 45◦). This can be related to the generation of a recirculating zone in the large wave. By increasing the Re number this recirculation generates a strong vortex in the wave. Interaction of vortex of moving wave by primary and secondary vortices on the electrodes leads to sweeping of these vortices because of higher momentum of large waves. The shear stresses generated from primary vortices on two adjacent electrode pairs and a weak pumping effect of neighbor electrodes from two adjacent electrode pairs create the secondary vortices [26, 32]. So these vortices are very weaker than primary vortices and have not a considerable effect on the dynamic behavior of moving waves. Fig. 6 illustrates the process of passing of a large wave from the electrode pair region. As mentioned before, primary and secondary vortices hold a volume of fluid in the ripples, when a large wave by a strong vortex passes from the region of primary vortex it sweeps this volume of fluid and this leads to increment of wave height and maximum thickness of film. Increasing the wave height associated by decreasing the thickness of film in the tail of the wave [32]. After the passing of large wave from the primary vortex region and passing the tail of generated large wave, when the thickness of film reached to a suitable size, the primary vortex is created and increases the film thickness, by preserving the volume of fluid, again. These preservations and sweepings of fluid lead to considerable fluctuations in the local film thickness. Considering the statistical results the increment of fluctuations of local film thickness have a tendency to lower thicknesses and decreases the mean film thickness. This process is similar for operation of conduction pumps as case 1 or case 2, and Fig. 5 shows this similarity. Furthermore, Fig. 5 shows that increasing the inclination angle decreases the film thickness as nonelectrified falling films [1] and increasing the applied voltage strengthen the effect of
EHD in the most of the cases. Fig. 7, shows the variation of dimensionless maximum film thickness versus Re number for wavy falling films in two different inclination angles in the presence of EHD conduction with two different operations (Maximum film thickness determination is based on the probability of 5% or less). As illustrated before, EHD conduction phenomenon increases the maximum wave thickness for all of the cases. Fig. 8 presents the PDF of local film thickness for two different Re numbers and two different inclination angles with and without EHD conduction. Chu and Dukler [35, 36] used the PDF for definition of a special thickness named substrate thickness. They defined the substrate thickness as the limit of most probable thicknesses of film which corresponds to the peak of PDF curve. This thickness can be interpreted as the main thermal resistance against the heat transfer between wall and gas stream in the condensers or other falling film heat exchangers. This figure shows that for low Re number, application of EHD through conduction pumps increases the substrate thickness of film. For low Re numbers the primary vortex of conduction pump holds a volume of fluid as a ripple and prevents from the penetration of weak disturbances and sweeping effect of moving waves to the inner layers of film. Considering the stronger primary vortex for case 1 [26], increasing of substrate thickness is higher for this case in comparison with case 2. On the other hand, PDF curves show that application of EHD conduction expands the range of fluctuations of thickness and this expansion is toward higher thicknesses. For high Re numbers, because of the interaction between recirculating flow of strong large waves and primary vortex, disturbances penetrate to the inner layers of film. So expansion of the range of fluctuations toward lower thicknesses can be seen in the Fig.8. Case 2, creates the weaker primary vortex relative to case 1, so penetration of disturbances to inner layers of film is higher for Case2 and this case decreases the substrate thickness. It should be noted that the vortices generated by EHD conduction phenomenon have two different effects on the falling film behavior: these vortices could intensify the disturbances by transferring their energy to recirculating flow of waves and on the other hand they prevent from penetration of disturbances to the inner layers of film specially at low Re numbers. The increasing of the range of fluctuations is higher for inclination angle of 45◦ than the one of 26◦. Fig. 9 represents the frequency of waves versus Re number for two different inclination angles with and without EHD conduction. This figure shows that for low Re numbers application of EHD increases the frequency of waves by accelerating (case 1) or decelerating (case 2) of wave passing from the primary vortex region. This effect can decrease the wave length and increase the wave frequency. For Re>100 resistance of primary vortices against the sweeping by large waves, decelerates this waves in the region above the electrode pairs, for both cases. Therefore, the subsequent wave with higher velocity approaches the decelerated wave and collision and coalescence of waves decreases the frequency of waves. Increasing the applied voltage strengthen this effect. Fig. 10 shows the variation of wave velocity versus Re number for various inclination angles and voltages. Primary and secondary vortices generated by conduction pumps, deform the waves of falling film and application of cross-covariance method for estimation of wave migration time is not accurate, so the direct data inspection method [45] has been used for evaluating the wave velocity. Comparison of the results of direct data inspection method by cross-covariance method for nonelectrified falling film wave velocity in Fig. 11 approved the accuracy of this method.
As mentioned before, for low Re numbers, application of EHD increases amplitude of thickness fluctuation and the size of waves ( Figs. 5,7) and leads to the higher wave velocities as conducted by Brauner and Moalem Maron [1] for non-electrified falling films. In spite of the small waves which slip on the conduction pump vortices, large waves, which tend to sweep the vortices, are decelerated by primary vortices. Increasing the voltage strengthen these effects. Fig. 12 presents the variation of standard deviation of local film thickness versus Re number for various inclination angles and voltages. For all of the cases standard deviation increases by application of EHD conduction which approves the intensification of disturbances and strengthening of wavy behaviors by application of EHD. 4. Conclusions Hydrodynamic behavior of developing wavy laminar falling film in the presence of electric field, applied by flush mounted electrodes, has been investigated. The results show that EHD conduction increases the mean film thickness, wave velocity and frequency for the films with low Re number. For higher Re numbers in which the large waves appear on the surface of film, applying the electric field decreases the mean film thickness, wave frequency and wave velocity and enlarge the surface waves. Furthermore, applying the electric field on the film increases the substrate thickness at low Re numbers but decreases it for higher Re numbers. This decrement occurs in the case 2 of operation. For the whole range of Re numbers, by applying the electric field standard deviation of local film thicknesses increases which approves the intensification of wavy behavior of film in the presence of EHD conduction phenomenon. Considering the extracted statistical characteristics for falling film, it can be concluded that applying the electric field using flush mounted electrodes can enhanced the heat/mass transfer from falling films and the case 2 is the suitable choice for this purpose. This conclusion is based on the hydrodynamic behavior of waves and other experiments about the heat/mass transfer enhancement are required for accurate judgment about effectiveness of this technique. 5. References [1] N. Brauner, D. Moallem Maron, Characteristics of inclined thin films, waviness and the associated mass transfer, Int. J. Heat and Mass Transfer, 25 (1982) 99-110. [2] C. D. Park, T. Nosoko, S. Gima, S. T. Ro, Wave-augmented mass transfer in a liquid film falling inside a vertical tube, Int. J. Heat and Mass Transfer, 47 (2004) 2587-2598. [3] R. M. Roberts, H. C. Chang, Wave enhanced interfacial Transfer, Chemical Engineering Science, 55 (2000) 1127–1141. [4] S. Portalski, A.J. Clegg, An experimental study of wave inception on falling liquid films, Chemical Engineering Science, 27 (1972) 1257–1265. [5] D.R. Webb, G.F. Hewitt, Downwards co-current annular Flow, Int. J. Multiphase Flow, 2 (1975) 35–49. [6] H. Takahama, S. Kato, Statistical characteristics of thin, vertical, wavy, liquid films without concurrent gas flow, Int. J. Multiphase Flow, 6 (1980) 203–215. [7] R.P. Salazar, E. Marschall, Time-average local thickness measurement in falling liquid film flow, Int. J. Multiphase Flow, 4 (1978) 405–412.
[8] T.D. Karapantsios, A.J. Karabelas, Longitudinal characteristics of wavy falling films, Int. J. Multiphase Flow, 21 (1995) 119–127. [9] C.D. Park, T. Nosoko, Three-dimensional wave dynamics on a falling film and associated mass transfer, AIChE J. 49 (2003) 2715–2727. [10] A. Yabe, T. Taketani, K. Kikuchi, Y. Mori, K. Hijikata, Augmentation of condensation heat transfer around vertical cooled tubes provided with helical wire electrodes by applying nonuniform electric fields, Heat Transfer Science and Technology, Proc. Int. Symp. (1987) 812-819. [11] M. Wawzyniak, J. Seyed-Yagoobi, Augmentation of condensation heat transfer with electrohydrodynamics on vertical enhanced tubes, ASME J. Heat Transfer, 118 (1996) 499-502. [12] A. Yabe, T. Taketani, K. Kikuchi,Y. Mori, H. Miki, Augmentation of conduction heat transfer by applying electro-hydro-dynamic pseudo-drop-wise condensation, Proc. of the Int. Heat Transfer Conf., 6 (1986) 2957-2962. [13] K. Yamashita, M. Kumagai, S. Sekita, Heat transfer characteristics on an EHD condenser, Proc. 3rd ASME/JSME Thermal Engineering Conf., (1991) 61–67. [14] J. Seyed-Yagoobi, J. E. Bryan, Enhancement of heat and mass transport in single-phase and two phase flows with electrohydrodynamics, Advances in Heat Transfer, 33 (1999) 95-18. [15] J. Darabi, M. Ohadi, S. V. Desiatoun, Falling film and spray evaporation enhancement using an applied electric field, ASME J. Heat Transfer. 122 (2000) 741748. [16] A. Gonzalez, A. Castellanos, Nonlinear electrohydrodynamic waves on films falling down an inclined plane, Physical Review E. 53 (1996) 3573-3578. [17] D. Tseluiko, D. T. Papageorgiou, Wave evolution on electrified falling Films, J. Fluid Mechanics. 556 (2006) 361–386. [18] G. I. Taylor, A. D. McEwan, The stability of a horizontal fluid interface in a vertical electric field, J. Fluid Mechanics. 22, part 1 (1965) 1-15. [19] D. Tseluiko, M. G. Blyth, D. T. Papageorgiou , J. M. Vanden-Broeck, Electrified falling-film flow over topography in the presence of a finite electrode, J. Engineering Mathematics, 68 (2010) 339–353. [20] A. W. Wray, O. Matar, D. T. Papageorgiou, Non-linear waves in electrified viscous film flow down a vertical cylinder, IMA J. Applied Mathematics, 77 (2012) 430–440. [21] A. Samanta, Shear wave instability for electrified falling films, Physical Review E, 88 (2013) 053002. [22] M. Siddiqui, J. Seyed-Yagoobi, Experimental study of pumping of liquid film with electric conduction phenomenon, IEEE Trans. Industry Applications, 45 (2009) 3-9. [23] M. Yazdani, J. Seyed-Yagoobi, Electrically induced dielectric liquid film flow based on electric conduction phenomenon, IEEE Trans. Dielectrics and Electrical Insulation, 16 (2009) 768-777. [24] M. Yazdani, J. Seyed-Yagoobi, Numerical investigation of electrohydrodynamicconduction pumping of liquid film in the presence of evaporation, ASME J. Heat Transfer, 131 (2009) 011602. [25] R. Gharraei, E. Esmaeilzadeh, M. R. Heirani Nobari, Numerical investigation of conduction pumping of dielectric liquid film using flush-mounted electrodes, Theoretical and Computational Fluid Dynamics, 28 (2014) 89-106.
[26] M. Hemayatkhah, R. Gharraei, E. Esmaeilzadeh, Flow pattern visualization of liquid film conduction pumping using flush mounted electrodes, Experimental Thermal and Fluid Science , 35 (2011) 933-938. [27] R. Gharraei, E. Esmaeilzadeh, M. Hemayatkhah, J. Danaeefar, Experimental investigation of electrohydrodynamic conduction pumping of various liquid films using flush electrodes, J. Electrostatics , 69 (2011) 43-53. [28] S. I. Jeong, J. Seyed-Yagoobi, P. Atten, Theoretical/numerical study of electrohydrodynamic pumping through conduction phenomenon, IEEE Trans. Industry Applications, 39 (2003) 355-361. [29] R. Hanaoka, S. Takata, M. Murakumo, H. Anzi, Properties of liquid jet induced by electrohydrodynamic pumping in dielectric liquids, Electrical Engineering in Japan 138 (2002) 224-230. [30] R.Hanaoka, H. Nakamichi, S. Takata, T. Fukami, Distinctive flow properties of liquid jet generated by EHD pump and conical nozzle, Electrical Engineering in Japan, 154 (2006) 399-406. [31] R. Hanaoka, I. Takahashi, S. Takata, T. Fukami, Y. Kanamaru, Properties of EHD pump with combination of rod-to-rod and meshy parallel plates electrode assemblies, IEEE Trans. Dielectrics and Electrical Insulation, 16 (2009) 440-447. [32] R. Gharraei, Hydrodynamic investigation of falling film in the presence of electric field, Ph.D. Thesis, Department of Mechanical Engineering, University of Tabriz, 2011. [33] Nynas, Nytro 10GBN, Naphthenics product data sheet, 2005. [34] V. V. Lel, F. Al-Sibai, A. Leefken, U. Renz, Local thickness and wave velocity measurement of wavy films with a chromatic confocal imaging method and a fluorescence intensity technique, Experiments in Fluids, 39 (2005) 856–864. [35] K.J. Chu, A.E. Dukler, Statistical Characteristics of Thin, Wavy Films: Part II. Studies of the Substrate and its Wave Structure, AIChE J. , 20 (1974) 695-706. [36] K.J. Chu, A.E. Dukler, Statistical Characteristics of Thin, Wavy Films: Part III. Structure of the Large Waves and their Resistance to Gas Flaw, AIChE. J. , 21 (1975) 583-593. [37] A. Miyara, Numerical Analysis in Flow Dynamics and Heat Transfer of Falling Liquid Films with Interfacial Waves, Heat and Mass Transfer, 35 (1999) 298-306. [38] W. Nusselt, Die oberflachenkondensation des wasserdamphes, VDI-Zs 60 (1916) 541. [39] W. Ambrosini, N. Forgione, F. Oriolo. P. Vigni, S. Baessler, Experimental investigation on wave velocity in a falling film, 2nd Int. Symp. Two-Phase Flow Modeling and Experimentation, (1999) 23–26. [40] W. Ambrosini, N. Forgione, F. Oriolo., Statistical characteristics of a water film falling down a flat plate at different inclinations and temperatures, Int. J. Multiphase Flow, Vol. 28, pp. 1521–1540. [41] K. Moran, J. Inumaru, M. Kawaji, Instantaneous hydrodynamics of a laminar wavy liquid film, Int. J. Multiphase Flow, 28 (2002) 731– 755. [42] M. L. Jackson, Liquid films in viscous flow, AIChE. Journal, 1 (1955) 231-240. [43] H. Brauer, VDI Forschungsheft 457B, 22 (1956) 1–40. [44] L. O. Jones, S. Whitaker, An Experimental Study of Falling Liquid Films, AIChE J. , 12 (1966) 525-529. [45] M. Kostoglou, K. Samaras, T. D. Karapantsios, Large wave characteristics and their downstream evolution at high Reynolds number falling films, AIChE J., 56 (2010) 11-23.
Highlights •
Hydrodynamic behavior of electrified developing wavy falling film has been studied.
•
The electric field applied using flush electrodes which does not alter the geometry. EHD decreases the film thickness, wave velocity and frequency for high Re numbers.
•
Secondary vortex
Secondary vortex
Primary vortex
Primary vortex
(a)
(b) Fig.1: Flow pattern for conduction pumping of Silicone oil: Right (case1), Left (case2), (a) Flow visualization [26] ,(b) Numerical simulation [25]
Flush mounted electrode pairs
Upper plenum
Test section
HV. power supply
Collection vessel
2 mm
Capturing 4 mm section
Flow
220 mm
16 mm
Side walls ( Plexiglass)
160 mm
350 mm
12 mm
7th. electrode pair
Fig. 2: Schematic diagram of falling film test section 8
7
5
δ*
mean
6
4 Present study (26 deg) Present study (45 deg) Moran et al. [40] Jackson et al. [41] Brauer [42] Nusselt Lel et al. [34]
3
2
1
0
50
100
150
200
Re
Fig. 3: Comparison of dimensionless film thickness with other experimental studies
Present study (26 deg) Present study (45 deg) Brauner & Moalem Maron [1] (26 deg) Moran et al. [40] (45 deg) Jones & Whitaker [43] (90 deg, x=6.35 cm) Jones & Whitaker [43] (90 deg, x=20.32 cm)
0.08
f*
0.06
0.04
0.02
0
0
50
100
150
200
Re
2
2
1.8
1.8
δmean (mm)
δmean(mm)
Fig. 4: Comparison of dimensionless wave frequency with other experimental studies
1.6
1.4
V=0 V=9 kV V=12 kV V=15 kV
1
0
50
100
150
V=0 V=9 kV V=12 kV V=15 kV
1
0.8
200
0
100
150
200
θ= 26° 2
1.8
1.8
δmean (mm)
2
1.6
1.4
1.6
1.4
1.2
1.2 V=0 V=9 kV V=12 kV V=15 kV
1
0.8
50
Re
Re
δmean(mm)
1.4
1.2
1.2
0.8
1.6
0
50
100
150
V=0 V=9 kV V=12 kV V=15 kV
1
0.8
200
0
50
100
150
Re
Re °
θ= 45 Fig. 5: Variation of mean film thickness versus Re number for various applied voltages, left: Case1, Right: Case2.
200
G
HV
(a )
HV
G
(b) Fig. 6: Creation of large waves in the presence of conduction phenomenon, θ= 45°
2.8
2.8
2.6
2.6
2.4
2.4
2.2
2.2
δmax / δNu
δmax / δNu
a: Case1, b: Case2
2 1.8 1.6
1.6
1.4
1.4 V=0 V=9 kV V=12 kV V=15 kV
1.2 1 0.8
2 1.8
0
50
100
150
V=0 V=9 kV V=12 kV V=15 kV
1.2 1 0.8
200
0
50
Re
100
150
200
Re
3
3
2.8
2.8
2.6
2.6
2.4
2.4
δmax / δNu
δmax / δNu
θ= 26°
2.2 2 1.8
2 1.8 1.6
1.6
1.4
1.4 V=0 V=9 kV V=12 kV V=15 kV
1.2 1 0.8
2.2
0
50
100
Re
150
200
V=0 V=9 kV V=12 kV V=15 kV
1.2 1 0.8
0
50
100
150
200
Re
θ= 45° Fig. 7: Variation of dimensionless Maximum film thickness versus Re number for various applied voltages, left: Case1, Right: Case2.
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.9
0.4 0.3
0.3 V=0 Case 1 Case 2
0.2 0.1 0
0.4
0
0.6
1.2
1.8
δ (mm)
2.4
3
V=0 Case 1 Case 2
0.2 0.1 0
3.6
0
0.6
1.2
1.8
δ (mm)
2.4
3
3.6
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
θ= 26°
0.4
V=0 Case 1 Case 2
0.2 0.1 0
0.4 0.3
0.3
0
0.6
1.2
1.8
δ (mm)
2.4
3
V=0 Case 1 Case 2
0.2 0.1
3.6
0
0
0.6
1.2
1.8
δ (mm)
2.4
θ= 45° Fig. 8: PDF.s of local film thickness, left: Re=58, right: Re=140.
3
3.6
16
16 V=0 V=9 kV V=12 kV V=15 kV
12
12
10
10
8
6
4
4
2
2
0
50
100
150
0
200
50
100
150
200
150
200
°
θ= 26
16
16 V=0 V=9 kV V=12 kV V=15 kV
14
10
10
f (Hz)
12
8
8
6
6
4
4
2
2
0
50
V=0 V=9 kV V=12 kV V=15 kV
14
12
0
0
Re
Re
f (Hz)
8
6
0
V=0 V=9 kV V=12 kV V=15 kV
14
f (Hz)
f (Hz)
14
100
Re
150
200
0
0
50
100
Re
θ= 45° Fig. 9: Variation of wave frequency versus Re number for various applied voltages, left: Case1, Right: Case2.
0.7
0.7 V=0 V=9 kV V=12 kV V=15 kV
0.6
0.4
(m/s)
0.3
u
0.5
0.4
w
w
(m/s)
0.5
u
V=0 V=9 kV V=12 kV V=15 kV
0.6
0.3
0.2
0.2
0.1
0.1
0
0
50
100
150
0
200
0
50
100
Re
150
200
150
200
Re
θ= 26° 0.7
0.7 V=0 V=9 kV V=12 kV V=15 kV
0.6
0.3
0.4
w
0.4
(m/s)
0.5
u
w
(m/s)
0.5
u
V=0 V=9 kV V=12 kV V=15 kV
0.6
0.3
0.2
0.2
0.1
0.1
0
0
50
100
150
0
200
0
50
100
Re
Re
θ= 45° Fig. 10: Variation of wave velocity versus Re number for various applied voltages, left: Case1, Right: Case2. 0.7 26 26 45 45
0.6
deg (Covariance) deg (Direct method) deg (Covariance) deg (Direct method)
w
u (m/s)
0.5
0.4
0.3
0.2
0.1
0
0
50
100
150
200
Re
Fig. 11: Comparison of wave velocity calculated by cross-covariance and direct data inspection methods
1.6 1.4 1.2
1.2
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
0
50
V=0 V=9 kV V=12 kV V=15 kV
1.4
S
S
1.6
V=0 V=9 kV V=12 kV V=15 kV
100
150
0
200
0
50
100
150
200
150
200
Re
Re °
θ= 26
1.6
1.6 V=0 V=9 kV V=12 kV V=15 kV
1.2
1.2
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
0
50
V=0 V=9 kV V=12 kV V=15 kV
1.4
S
S
1.4
100
150
0
200
0
50
Re
100
Re
θ= 45° Fig. 12: Variation of standard deviation of local film thickness versus Re number for various applied voltages, left: Case1, right: Case2.
Table1: Physical and electrical properties of Transformer oil (20 ◦C)
Density (kg/m3) [33]
Viscosity (10-3Pa.s) [33]
895.5
11
Mobility (10-8 m2/Vs) [32] positive negative 0.18
0.35
Electrical conductivity (10-12 S/m) [32]
Dielectric constant [32]
1.2
2.08