Research PaperFalling film on a vertical flat plate – Influence of liquid distribution and fluid properties on wetting behavior
Introduction
Falling film units for heat or mass transfer are widely used in various industrial processes, such as rectification, distillation, absorption, evaporation or cooling. They provide a large specific surface with small specific liquid load, resulting in high heat and mass transfer. To ensure the efficiency of these applications, the heat or mass transfer surface must be wetted completely and evenly with a thin liquid film. This requires both the liquid being distributed sufficiently and evenly at the top of the surface and establishing a thin liquid film over the complete surface. This wetting process is influenced by the properties of the liquid film and the surface, the apparatus and operational parameters (see Fig. 1). Some of the recent studies addressed various liquid properties such as ionic liquid films [1], [2] or liquids with nanoparticles [3]. Also various surfaces like pillow plate [4], micro-baffled plate [5] or packings [6], [7], [8], [9], [10], [11], [12] were investigated. Although falling films on wetted surfaces represent a generic geometry for a multifold of heat and mass transfer operations, wall design differs significantly in mass vs. heat transfer application. Structured packings in distillation [6] or absorption [7] services are designed to maximize mass transfer interface between liquid and gas phase. These packings show corrugations, macro and micro structures, holes etc. to enforce liquid spreading and minimize pressure drop of the countercurrent gas flow. Adiabatic heat transfer occurs from condensation of vapor phase to partial evaporation of liquid. A high wetted coverage of the geometric packing surface is beneficial but not mandatory. In contrast, the surface coverage of falling films in heat transfer services aims at two distinct optima. In condensation applications [13], [14], [15], a spreading of the condensed phase is disadvantageous as it hinders direct contact of vapor with the cold condenser surface. In falling film evaporation [2], [16], [17], [18] or chiller applications [19], a full coverage of the heat transfer surface is mandatory to maximize utilization of the surface and – in evaporation services – minimize thermal stress to the product. Therefore, knowledge about minimum wetting rates, film thickness and its distribution is crucial for proper design and operation of the respective equipment.
Typical shell and tube falling film evaporators or absorbers are designed with a feed entering at the top and flowing down under gravity. The initial formation of the film significantly influences the wetting behavior of the tubes. To optimize the wetting behavior, falling film units are generally implemented with a distributor for the entering liquid. Some rules for the design of liquid distribution in shell and tube falling film evaporators are published in [20]. In a frequently used type of distributor, a perforated plate is arranged horizontally above the upper tube sheet. Distributor hole diameters are typically between 4 and 9 mm. Perforated plate distributors have three or six distributor holes around each tube. Six holes per tube arrangement is usually used for high liquid loads and large tube diameters [20] and was observed by Morison et al. [21] to lead to a qualitative better wetting behavior. Besides this work, little information on the effectiveness of using three or six holes on forming liquid films is available in the open literature.
Falling film transfer units are often operated with liquid recirculation. The pump-around flow is determined by the requirement of a completely wetted transfer surface. The specific liquid load (kg m−1 s−1) and (m3 m−1 s−1) are defined as the mass or volumetric flow per unit length of the feed surface (m), respectively [20].
The minimum specific liquid load required to establish or maintain a full liquid coverage of the surface is known as the minimum wetting rate . The minimum wetting rate is measured for two different cases; in wetting operations the specific liquid load is increased until a dry plate is wetted completely, while for dewetting conditions the liquid load is reduced starting from full coverage to film break-up [4], [22], [23]. Hartley and Murgatroyd [24] analyzed the stability of an existing dry patch und their approach by using a theoretical force balance is the most used foundation for later investigations [21], [25], [26], [27]. Dreiser and Bart [23] identified that the equation of Hartley and Murgatroyd [24] can be applied for polymeric surfaces wetted with water as well as with 50 wt.% water/glycerol. Morison et al. [21] have compared the measured correlation of minimum wetting rate with Hartley and Murgatroyd [24]. An overview of the equations is shown in Table 1. The equations can be expressed in a dimensionless form as and a function of the Kapitsa number Ka, which is the inverse of the film number KF and is defined in Eq. (2) [28].
Nevertheless, even for isothermal conditions a significant discrepancy of the minimum wetting rate appears in the predictions as well as in the measured values [22]. As shown in Table 1, the contact angle plays an important role in most predictions of the minimum wetting rate. However, the type of contact angle is not clearly defined in these equations. While the advancing contact angle could represent the wetting process and the receding contact angle the dewetting process [21], [27], [29], the equilibrium contact angle can be defined as the mean value of those [30] or be calculated with the function of Tadmor [31] or be defined as the static contact angle [27]. El-Genk and Saber [27] have reviewed measurements of contact angles for different liquid/surface material combinations, reporting that the value of the contact angle depends not only on the liquid and surface material, but also on the roughness of the surface, the liquid dispensing, the operation temperature and the air humidity.
A falling film can be characterized by the film thickness and film flow regime. The average film thickness is necessary for calculating the liquid hold-up and average flow velocity of the falling film and is therefore essential for designing an evaporator [20]. The first model of thin film was developed by Nusselt [32] (Eq. (3)), which is still the basis of film fluid dynamics as well as heat and mass transfer studies.
The film Reynolds number of the falling film is defined as the specific liquid load per viscosity , see Eq. (4). The characteristic length (m) is a quantity of physical properties as Eq. (5).
The Nusselt equation has proven to be a good estimation for , including not only laminar smooth but also laminar wavy films [32]. Laminar smooth films occur only at very low film Reynolds numbers. While Brauer [33] observed the critical film Reynolds number for laminar smooth films at without any dependency on liquid physical properties, some alternative models [28], [34], [35] considered the influence of the physical properties of liquid films by using the Kapitsa number (Eq. (2)). Al-Sibai [34] determined the range of laminar films experimentally for water and silicon oil on vertical and inclined plates and gives Eq. (6) as the critical film Reynolds number for laminar smooth films.
At higher film Reynolds numbers, laminar smooth films are observed at the inlet [34]. With increasing flow length, horizontal sinus-shaped waves, two-dimensional waves with a distinct amplitude as well as three-dimensional waves with different amplitudes and velocities are formed, consecutively [34], [36]. The last two wave patterns are summarized as stable wavy film flow. Al-Sibai [34] classified those flow regimes depending on the Kapitsa number, see Eqs. (7), (8).
The average thickness of laminar wavy films was found to be smaller than calculated with the function of Nusselt (Eq. (3)), because the velocity of a laminar wavy film is higher than that of a laminar smooth film [28], [33], [37]. Brauer [33] gives a reduction ratio of 0.93 relative to Eq. (3) for the laminar wavy film.
The transition to turbulent flow was found to occur typically at and the fully developed turbulent regime starts at [33]. With regards to the fluids physical properties, Al-Sibai [34] suggests Eq. (9) for the upper limit of the transition regime.
Various correlations for the film thickness were determined for the transition and turbulent regime, see review in Siebeneck et al. [4]. They are all based on the Nusselt function and are determined empirically. For all correlations, the exponent of the film Reynolds number is higher than 1/3 which is the exponent for laminar films. One established equation is given by Goedecke [20], see Eq. (10).
The specific liquid load, the minimum wetting rate and the film thickness are studied in this paper to present the wetting behavior on a vertical flat plate at single phase flow conditions of water and water/glycerol mixtures. Two liquid distribution devices were used. Kapitsa numbers of 1.6 · 10−11 ≤ Ka ≤ 3.9 · 10−6 were investigated at specific liquid loads varying between 0.03 kg m−1 s−1and 0.48 kg m−1 s−1 to determine the film thickness and wetted coverage of viscous mixtures.
Section snippets
Used materials
The effectiveness of the liquid distribution device was investigated with water as working fluid at 25 °C. The influence of the physical properties was determined by comparing water at 25 °C and water/glycerol mixtures at 20 °C. The fluorescein sodium salt (, FSS) with a mass loading of 5 ⋅ 10−5 gFSS gWasser−1 was mixed to all working fluids to enable an optical analysis of the film. Although influence of fluorescein on the mixture is negligible at this low concentration, the physical
Results
Following, the results of the wetted coverage, film thickness and minimum wetting rate are presented. The liquid distribution and the physical properties as primary influences on the wetting behavior are discussed.
Conclusions
In the present study, falling films on a vertical flat plate under open-air and isothermal condition were investigated experimentally with the fluorescence intensity technique. The wetting behavior characterized as wetted coverage, minimum wetting rate, film thickness and film thickness distribution was analyzed. Two different film distribution devices with the same total cross-sectional area have been compared using water as working fluid. At small specific liquid loads, the distributor with
Acknowledgements
Funding: This work was supported by the German Federal Ministry for Economic Affairs and Energy based on a Resolution of the German Bundestag through the Zentrales Innovationsprogramm Mittelstand ZIM [Project KF2614405ST4].
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