THICKNESS OF LIQUID FILM FORMED IN SLUG FLOW IN MICRO TUBE

Slug flow is the representative flow regime of two-phase flow in micro tubes. It is well known that the evaporation of thin liquid film formed between the tube wall and the vapor bubble plays a important role in micro conduits heat transfer. In the present study, experiments are carried out to clarify the effect of parameters that affect the formation of the thin liquid film. Laser focus displacement meter is used to measure the thickness of the thin liquid film. Air, ethanol, water and FC-40 are used as working fluids. Circular tubes with five different diameters, D = 0.3, 0.5, 0.7, 1.0 and 1.3 mm, are used. It is confirmed that the liquid film thickness is determined only by capillary number at small capillary number and the effect of inertia force on the liquid film thickness is negligible. But as capillary number increases, the effect of inertia force is not neglected. At relatively high capillary number, liquid film thickness shows minimum against Reynolds number. The effects of bubble length, liquid slug length and gravity on liquid film thickness are investigated. Experimental correlation based on the capillary number, Reynolds number and Weber number is proposed. INTRODUCTION Micro scale evaporation heat transfer attracts much attention due to its many advantages, e.g., high efficiency, miniaturization, etc. However, the characteristics of flow boiling in micro tube is quite different from those in conventional tube and they are not fully understood. Flow regime is also different in micro tube due to surface tension, and slug flow becomes the dominant flow pattern. It is known that the evaporation of thin liquid film formed between the tube wall and the vapor bubble plays a important role in micro tube heat transfer. It is reported that the thickness of the liquid film is one of the important factors for the prediction of flow boiling heat transfer in micro tubes [1][2]. Many researches on the liquid film formed in slug flow in micro tube have been conducted both experimentally and theoretically. Taylor [3] experimentally obtained the mean liquid film thickness remaining on the wall by measuring the difference of the bubble velocity and the fluid mean velocity. He used highly viscous fluid, e.g., glycerine, syrup-water mixture and lubricating oil, so wide range of capillary number was covered in his experimental data. Bretherton [4] suggested a scaling analysis of the liquid film thickness with the lubrication approximation. He showed that the liquid film thickness can be scaled with Ca2/3. Moriyama et al. [5] obtained the liquid film thickness formed by a vapor bubble expansion in a narrow gap by measuring the temperature change of the channel wall, which was superheated initially. In his experiment, the heat is assumed to be consumed by the evaporation of the liquid film. His experimental data was correlated in terms of capillary number and Bond number based on the interface acceleration. Heil [7] investigated the effect of inertia force on the liquid film thickness numerically. It is shown that the liquid film thickness and the pressure gradient are dependent on the Reynolds number. Aussillous and Quere [6] measured the liquid film thickness using fluids of relatively low surface tension. It was found that the liquid film thickness deviates from the Taylor’s data at relatively high capillary number. Visco-inertia regime, where the effect of inertia force on the liquid film thickness becomes significant was demonstrated. Kreutzer et al. [8] investigated the liquid film thickness and the pressure drop in a micro tube both numerically and experimentally. Their predicted liquid film thickness showed almost the same trend with that of Heil [7]. Utaka et al. [9] measured the liquid film thickness formed by a vapor bubble in a narrow gap mini-channel with laser extinction method. They investigated heat transfer characteristics quantitatively. It was concluded that the boiling phenomena were determined by two kinds of characteristic periods, i.e., the micro-layer dominant and the liquid saturated periods. Although many experiments have been carried out to measure the liquid film thickness in micro tubes, quantitative data of the liquid film thickness and the varying liquid film thickness are still limited. To develop a good flow boiling heat transfer model in micro tube, it is crucial to know the characteristics of the local liquid film thickness. In the present study, the local liquid film thickness and varying liquid film thickness are measured directly with laser focus displacement meter. Series of experiments is conducted to investigate the effects of important parameters that affect the formation of liquid film in micro tubes. EXPERIMENTAL SETUP AND PROCEDURE Experimental Setup Circular tubes made of Pyrex glass with 0.3, 0.5, 0.7, 1.0 and 1.3 mm inner diameter were used as test tubes. Tube diameter was measured by microscope and the inlet and outlet inner diameters were averaged. Table 1 and Fig. 1 show the dimensions 1 Table 1. Dimensions of test tubes Tube I.D. (mm) O.D. (mm) Length (mm) A 1.305 1.6 250 B 0.995 1.6 250 C 0.715 1.0 250 D 0.487 0.8 250 E 0.305 0.5 250 Figure 1. Photograph of 0.995 mm inner diameter tube and the photograph of the test tubes. The difference of inlet and outlet inner diameters is less than 1% for all tubes. Ethanol, water, FC-40 (Fluorinert, 3M) and air were used as working fluids. All experiments were conducted under conditions of room temperature and 1 atm. Table 2 shows the properties of each fluid at 25◦C and 1 atm. Figures 2 and 3 show the schematic diagram and the photograph of the experimental setup. One edge of Pyrex glass tube was connected to the syringe and the actuator motor. Actuator motor (EZHC6A-101, Oriental motor) was used to move the liquid inside the test conduits. The velocity range of actuator motor is 0 to 0.6 m/s. Syringes with several cross sectional areas were used to control the liquid velocity in micro tube. The range of liquid velocity in present experiments was 0 to 6 m/s. The velocity of the gas-liquid interface was measured from the images captured by the high speed camera (Phantom 7.1). The images were taken at several frame rates according to the bubble velocity. For maximum bubble velocity, frame rate was 10000 frames per second with a shutter time of 10 μs. Laser focus displacement meter (LT9010M, Keyence) was used to measure the thickness of the liquid film. Figure 4 shows the principle of the laser focus displacement meter. The displacement of target surface can be determined by the displacement of objective lens moved by the tuning fork. The received light intensity becomes highest in the light-receiving element when focus is obtained on the target surface. The resolution is 0.01 μm, the laser spot diameter is 2 μm and the response time is 640 μs. Thus, it is possible to measure the varying local thickness of liquid film. Laser focus displacement meter has been used by several researchers for the measurement of liquid film thickness [10][11]. It is reported that the laser focus displacement meter can measure the liquid film thickness very accurately, within 1% error [11]. Liquid film thickness is transformed to DC voltage signal in the range of ±10V. Output signal was sent to PC through GPIB interface and recorded with LabVIEW. Table 2. Properties of the working fluids at 25◦C and 1 atm Water Ethanol FC-40 ρ (kg/m3) 997 785 1849 μ (μ Pa · s) 889 1088 3260 σ (mN/m) 70.0 22.3 16.0 Figure 2. Schematic diagram of the experimental setup Figure 3. Photograph of experimental setup Experimental Procedure The experimental procedure is described in this section. Cover glass and glycerol were used to remove the focus scattering caused by the curvature of the outer wall. Refractive index of glycerol (n = 1.47) is almost the same with that of the Pyrex glass (n = 1.474), so the refraction of laser between glycerol and Pyrex glass can be neglected. Figure 5 shows the schematic diagram of the micro tube with cover glass and glycerol. It is difficult to detect the interface of the inner wall and the liquid film at the same time, because the difference of both two refractive indexes is small. Therefore, the distance from the cover glass to the inner wall is initially measured without liquid film. Then, the thickness including liquid film is measured. The liquid film thickness is calculated from the difference of these two values. Although the focus scattering caused by the curvature of the outer wall is removed, there is another focus scattering due to the curvature of the inner wall. To compensate for this 2 Figure 4. Principle of laser focus displacement meter Figure 5. Schematic of micro tube and images of bubble movement