Elsevier

Chemical Engineering Science

Volume 172, 23 November 2017, Pages 622-635
Chemical Engineering Science

Flow pattern and power consumption in a vibromixer

https://doi.org/10.1016/j.ces.2017.07.010Get rights and content

Highlights

  • The impact of agitator type on flow and power consumption in a vibromixer were studied.

  • Analysed quantities were determined both using CFD simulations and experimentally.

  • Power input was estimated using original measuring procedure.

  • Modified dimensionless numbers for vibro-mixing were proposed.

Abstract

The paper presents investigations of flow hydrodynamics and power consumption in a vibromixer (mixer with a reciprocating agitator). Solid or perforated discs different in diameter were used as agitators. Basing on CFD simulations and measurements flow parameters and power requirement for vibro-mixing were found. Power input was estimated using original measuring procedure with modified dimensionless numbers. Results were processed in quantitative correlations, describing an influence of process and operating conditions on vibromixer performance. Utilitarian effects of this study can be used for description and clarification of processes occurring in mixing vessels with reciprocating agitators as well as during design optimization of apparatuses of this kind.

Introduction

Vibromixers (mixers with reciprocating discs) are an interesting alternative for commonly used in industry conventional stirred vessels with a single or multiple turbine impellers (Harnby et al., 2001, Paul et al., 2004, Montante et al., 2006, Cullen, 2009, Kresta et al., 2016) that are applied for preparation of multiphase systems (Dyląg and Talaga, 1995, Talaga et al., 1996, Kamieński, 2004). Their advantages such as a simple design, versatility of application and easy modification of flow circulation can be used for formation of various multiphase systems, e.g. emulsions (Lo et al., 1998, Kamieński and Wójtowicz, 2003), conventional and “light” suspensions (Wójtowicz, 2014) and also during solid-liquid dissolving (Masiuk and Rakoczy, 2007). Vibromixers can be therefore applied as reactors in different industries, e.g. chemical and petrochemical (Yakovenko, 1994), food (Tkachenko et al., 2010), pharmaceutical and related to them, in polymerization, extraction, organic synthesis or plastic production and processing. Potential applications of vibromixers are also seen in environmental protection, e.g. in recycling (plastic regranulats rinsing in solvents) or sewage treatment (fermentation, flocculation). It is worth noting that a specific flow circulation occurs in vibromixers is different from that in typical stirred vessels. A reciprocating agitator generates intensive liquid flow in the whole volume of a vessel, without a central vortex (unfavorable aeration of a system) and without strong sheer stresses typical for rotational, high-speed impellers. Owing to these features, vibromixers should be preferred in biotechnology as bioreactors, where using high-speed turbines is often limited in view of bio-cell damage in strong, shear flow region (Brauer and Annachhrate, 1992) in particular occurring close to impeller blades and in an impeller discharge stream.

The main parameter that decides on the selection of mixing equipment for a particular process is its efficiency. A proper mixing equipment selection, its type, design, operating conditions, etc. affect process expenditure and production cost. In the case of mechanically agitated vessels their efficiency is estimated by a required power that should be delivered by an agitator to a mixed system to obtain an intended technological effect. Power input also influences a mixing vessel design, e.g. strength parameters of an impeller shaft, an applied driving system, seal choice etc. While, in the case of conventional stirred vessels a method of determination of power input is well known and rather uncomplicated, its calculation for vibromixers with solid or perforated reciprocating discs is more complex. This is because of variation of agitator motion, which periodically changes position, velocity and movement direction. It complicates analysis of the process and requires the use of more advanced methods and complex description methodology, e.g. modified criteria numbers in comparison with those, characterizing traditionally mixing processes.

First research on estimation of power requirement in mixing equipment with vibrating elements was focused on a reciprocating plate column performance (Hafez and Baird, 1978, Tojo et al., 1979, Baird and Rama Rao, 1995; Gagnon et al., 1998). Authors used usually several (two or more) discs, located on the same shaft in a slender vessel. Tojo et al. (1979) investigated power dissipation in a vibrating disc column. They analyzed forces exerted on a vibrating disc for two variants: in a single (liquid phase) system as well as in a two phase (gas-liquid) system. Experiments showed that the effect of aeration on power dissipation in the column was considerably smaller than that observed in classic stirred tanks with turbine impellers. Hafez and Baird (1978) examined power requirement for the Karr extraction reciprocating plate column. They used two methods for determination of power consumption and analyzed influence of amplitude and frequency of vibration on efficiency of the process. Finally, authors proposed a correlation for time-averaged power dissipation calculation. An interesting report on power consumption in reciprocating plate columns was published by Baird and Rama Rao (1995) and Gagnon et al. (1998). The former concerned an interesting design of a baffle-plate column. The authors observed flow pattern and measured power dissipation rate for selected process parameters. The latter (Gagnon et al., 1998) presented experiments on power consumption and mass transfer coefficients in a reciprocating plate column and a gas-liquid system. Results were compared to those obtained for a column equipped with Rushton turbines or helical ribbon impellers. The reciprocating plate column showed a slightly favorable mass transfer at a given power input compared to stirred tank reactors.

Subsequent research was focused on mixing vessels with different design reciprocating agitators (Osipov et al., 1980, Smelyagin, 1991, Lo et al., 1998, Masiuk, 1999, Komoda et al., 2000, Kordas et al., 2013, Prikhodko and Smelyagin, 2016).

Osipov et al. (1980) investigated power input in a vibromixer equipped with a single perforated disc. The disc moved with relatively small amplitudes A = 0.0005–0.005 m and high frequencies f = 20–60 Hz. Results were processed in dimensional correlations with the use of various operating and geometric parameters of the mixing device. Smelyagin (1991) analysed different machines and mechanisms with electromagnetic drive, including vibromixers.

Lo et al. (1998) analysed the process of emulsion preparation in the mixing vessel equipped with two solid reciprocating discs, located on the same shaft. They examined performance of the mixing vessel applied for formation of liquid-liquid system (drops break-up process). Research conducted by Masiuk (1999) was focused on measurement of power consumption in a vibromixer agitated by a single, perforated, reciprocating disc. The author determined the maximum power consumption for the agitator and proposed dimensionless correlations taking both mixing vessel geometry and its operating parameters into account. Komoda et al. (2000) investigated vibro-mixing process in a mixing vessel agitated by different diameter up-and-down moving discs. They visualized a mixing process in various flow regimes using decolorizing reaction and examined the influence of a disc diameter choice on vibromixer efficiency. Interesting investigations were reported by Kordas et al. (2013). The authors proposed a novel agitator moving reciprocating and rotating motion at the same time. They analysed an influence of agitator performance on time of liquid homogenization. Results were processed in dimensionless correlations using a mixing time number and a rotating and reciprocating Reynolds number. A novel reactor with a rotationally-reciprocating motion of impeller was analysed by Prikhodko and Smelyagin (2016). They proposed – taking into account the type of drive system – a dynamic model of such a mixer. Analysis was carried out using energy-mass method. A rule of an impeller motion was found and described.

The analysis of the state-of-the art in the discipline showed that literature lacks information on vibromixers. In particular on an issue of flow hydrodynamics analysis and power consumption estimation. The existing literature body is rather limited in comparison with classical stirred tanks with rotational impellers. It should be noted that studies on vibro-mixing so far presented in the literature were often conducted using relatively small units, operating in a narrow range of process parameters. Investigations were often limited to one, specific agitator. It considerably complicates a comparison between vibromixers and conventional stirred tanks of the same scale. Moreover, some authors presented their results only graphically without any quantitative correlations, using in their experiments incomplete and simplified measuring methodology, not taking into consideration impact essential parameters and phenomena, e.g. effect of inertial forces on power input measurements. Results presented in papers differ as a result of variously defined simplexes and criteria numbers. Some authors use in their description maximum agitator velocities and maximum power input, whereas others apply mean values. It substantially complicates and prevents a comparison between results.

The analysis of literature and my earlier work on dispersion of multiphase systems in vibromixers (Kamieński and Wójtowicz, 2003, Wójtowicz, 2014) justify the need for further research. Especially at the stage of identification of liquid flow in vibromixers as well as developing a uniform method of power requirement estimation for vibro-mixing. To this end, up-to-date research methods can be useful, e.g. recently very popular Computational Fluid Dynamics (CFD) packages, applied for simulations of mixing vessel performance (Marshall and Bakker, 2002, Wójtowicz et al., 2014).

Section snippets

Experimental

Investigations were conducted for vibromixer with a reciprocating agitator shown in Fig. 1a. The experimental system consisted of a cylindrical vessel 1 (internal diameter T = 0.286 m), closed at the top and a single reciprocating agitator 2. Circular (solid or perforated) flat discs (Fig. 2) were used as agitators, with discs of D1 = 0.260; D2 = 0.238; D3 = 0.220 and D4 = 0.204 m in diameter. The agitator diameter was selected so that T/D1.4 = 1.1–1.4. The thickness of discs was gd = 0.003 m. For

Methodology of numerical simulations

A model of the vibromixer was created using Gambit 2.4.6 (Fluent Inc., 2006) as a pre-processor. Numeric grids consisted of about 106 combined tetrahedral or hexahedral cells. The quality of grids was checked using normalized EquiAngle and EquiSize Skew criteria. The maximum values for all grids did not exceed 0.6 and modal values were in the range of 0.3–0.4. It confirms that all grids were of good quality (Fluent Inc., 2006). During numerical simulations grid density independency test was

Conclusions

The study described in this paper was focused on determination of a power input in a vibromixer equipped with solid or perforated, reciprocating agitators. For better explanation and description of processes and phenomena occurring in the vibromixer apart from measurements a CFD analysis of flow pattern was also performed.

This study demonstrated that:

  • (1)

    Flow circulation generated by a reciprocating (up-and-down moving) disc, whether it was solid or perforated, was completely different than

Acknowledgments

This research did not receive any specific grant from founding agencies in the public, commercial or not-for-profit sectors.

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