On the measuring of film thickness profiles and local heat transfer coefficients in falling films
Introduction
Falling liquid film is a special kind of flow where a liquid film with a distinct interface flows down an inclined or vertical wall, usually in the presence of a gas layer. High heat transfer at relatively low mass flow rates and small temperature differences, together with short product residence, makes this technique a popular choice for a wide range of engineering and technological applications. For instance, falling films are used for heat-sensitive fluids such as fruit juice, sugar and dairy products, where short residence time and temperature control during the heat transfer process are essential. The heat transfer in falling film units is often predominantly influenced by the hydrodynamics [1], hence it is important to study the two simultaneously when evaluating the performance of these units.
The flow in falling film units is often described using dimensionless numbers. The most important ones are the Reynolds number (Re), the Kapitza number (Ka), the Nusselt number (Nu), and the Prandtl number (Pr), defined as follows:where Γ is the specific mass flow rate per unit circumference, g is the gravitational acceleration, h is the heat transfer coefficient, and the following properties of the working fluid are: μ is the dynamic viscosity, ρ is the density, σ is the surface tension, k is the thermal conductivity, ν is the kinematic viscosity and cp is the specific heat capacity.
The hydrodynamics of falling films have been studied by numerous researchers, e.g. [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16] and are usually characterized by different flow regimes [17], [18]. The transitions between different flow regimes are often described as a function of the Reynolds and Kapitza numbers. Al-Sibai [19] determined conditions for the transitions under non-evaporative conditions, where the flow was mapped into five different zones, Laminar (L), Sinus-shaped waves (S), Wavy-laminar (WL), Transition region (TR) and Turbulent (T). These regimes describe how the flow is transitioning from a smooth laminar film into a fully turbulent one, see Fig. 1. Each flow regime impacts the heat transfer differently depending on the film thickness and the degree of turbulence.
The hydrodynamics of a falling film are usually further investigated by looking at the changes of the film thickness, since the emerging waves govern much of the underlying flow structure that affects the heat transfer [20]. Numerous studies have attempted to determine the local film thickness of the liquid film in different flow regimes, and a large variety of techniques exist. Charogiannis et al. [21] recently made a thorough review of different methods.
The available techniques can usually be classified as intrusive or non-intrusive. There are simple intrusive methods, such as drainage or hold-up [22], where the flow is stopped and the liquid on the surface is collected and weighted, capable of giving an estimate of the average film thickness. Hot wire anemometry [23] or needle-contact-probes [24] have also been used to measure the thickness in a single point.
As for non-intrusive methods, one can use conductance probe [25] or capacitance probe [26], [27], [28] to estimate the amount of liquid. There are also several optical methods, for example using shadow photographs, where the film thickness is estimated from images [8]. There is also laser focus displacement [29] or chromatic confocal imaging [30], where monochromatic light is continuously emitted onto the interface and the intensity of the reflective light is measured. Furthermore, there are studies using laser-induced fluorescence [31], [32], [33], [34], [35], [36], [37] or planar laser-induced fluorescence [38], [21], [39] where the target media is illuminated, usually by a laser, and the intensity of the fluorescence is captured by a detector and can be related to various medium properties. All techniques clearly have their advantages and disadvantages, but in general, they are either insufficiently accurate, have low spatial resolution, disturb the flow, need additives or require a fluorescent or transparent fluid.
Correlations that estimate the film thickness are based on the results from different measurements techniques. The film thickness for flat laminar falling films without surface evaporation can be obtained from the Nusselt film theory as [40]:
Lukach et al. proposed the following correlation for the mean film thickness under wavy-laminar conditions [41]:and Brötz [42] proposed the following correlation for turbulent conditions (Re > 600):
Local heat transfer measurements in a subcooled system are typically performed by measuring the temperature difference between the wall and the bulk [43] or the interface [44], [45], [46], [47]. Usually the most difficult property to obtain is the wall temperature, which, for example, can be measured by installing a thermocouple (e.g. by soldering) inside the tube wall [48], [49]. However, this approach requires considerable effort, the number of measurement points is limited, and the position of the thermocouples must be predetermined before the start of the experimental campaign.
The heat transfer in falling films is usually described as a function of the Reynolds and Prandtl numbers. The degree of influence of each dimensionless number depends on the flow regime. For Laminar flow regime (see Fig. 1), the heat transfer takes place by pure conduction, it is rate-determined by the film thickness and it thus decreases with the Reynolds number. In Turbulent regime, however, the Nusselt number increases with the Reynolds number [50] and is also dependent on the Prandtl number. For an intermediate regime (Transition regime), a superposition is often used. Schnabel and Schlünder [51] developed a correlation for non-evaporative conditions under a constant heat flux:
The above correlation can be used to estimate the magnitude of the heat transfer coefficient but it does not give any information on how that coefficient varies in the streamwise direction or how it relates to the film thickness. Therefore, the objective of this work is to investigate two novel experimental procedures for characterizing falling films. The procedures will help us to gain a deeper insight into the hydrodynamics and the heat transfer of falling films, but also into their interaction. A quantitative method is assessed for obtaining wave characteristics and film thicknesses over a section of the surface. In the same time, we evaluate a method to measure the local wall and bulk temperatures in order to obtain the local heat transfer coefficients. Both procedures are investigated in an experimental falling film setup designed to study falling film characteristics.
Section snippets
Experimental setup and materials
The proposed measuring procedures are evaluated in an atmospheric falling film facility, see Fig. 2(Left). A copper tube, with the length of L = 0.8 m, outer diameter do = 60 mm and 5 mm thickness, is connected to an overflow distributor, illustrated in Fig. 2 (Right) to achieve an evenly distributed liquid film on the outer side of the tube. A displacement pump recirculates the liquid over the tube. An electrical heater (SAS Steatite cartridge) is mounted inside the tube and heats the
Laser triangulation scanner
The procedure we propose in this work for measuring the film thickness uses an optical triangulation scanner (light intersection method) of the model scanCONTROL 2950-100 from Micro-Epsilon [54]. The scanner uses a 20 mW power source to produce a laser beam of the wave length 658 nm that is enlarged through special lenses to form a static laser line on the target surface. A sensor matrix detects the diffused light and measures the reflected angle at 1280 points along the projected line. The
Laser triangulation scanner
Fig. 11 presents a comparison between the film thickness measurement (left) and the high-speed image (right) at two separate times (top and bottom) for the dairy product fluid at conditions Ka = 97 and the wetting rate of 0.48 kg/(m s). In the figure, it can be seen that the laser triangulation scanner is indeed able to detect the fundamental features of the liquid film flow and that it captures the wave dynamics in the same way as does the high speed imaging. The laser is capable of detecting
Conclusion
In this paper, we develop and report on two novel procedures for studying a number of fundamental features of vertical falling films. The film thickness measurement procedure is proven to capture the wave dynamics accurately along an approximately 0.1 m long vertical line, with a high spatial (±1.2 · 10−5 m) and temporal resolution (500 Hz). No additives to the liquid are required as long as the fluid investigated is reflective. There is also an advantage that the measurement equipment is
Conflict of interest
The authors declared that there is no conflict of interest.
Acknowledgment
This work was co-funded by the Swedish Energy Agency (P40550-1), Valmet AB and Tetra Pak Processing systems.
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