Experimental investigation of the temperature field in the gas-liquid ...

Thermophysics and Aeromechanics, 2015, Vol. 22, No. 6

Experimental investigation of the temperature field in the gas-liquid two-layer system* 1

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E.Ya. Gatapova , R.A. Filipenko , Yu.V Lyulin , I.A. Graur , 1,2 1,4 I.V. Marchuk , and O.A. Kabov 1

Kutateladze Institute of Thermophysics SB RAS, Novosibirsk, Russia

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Novosibirsk State University, Novosibirsk, Russia

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Aix-Marseille Universite, Marseille, France

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Tomsk Polytechnic University, Tomsk, Russia

E-mail: [email protected] (Received November 5, 2014; in revised form December 5, 2014) Results of an experimental investigation of the temperature field across the liquid-gas two-layer system are presented. The liquid layer is locally heated from the bottom substrate, and the intensive liquid evaporation is observed. A technique for measuring the temperature profile across the liquid and gas layers (including their interface) is developed. To do these measurements, the microthermocouple is moved across the layers with the help of precision micropositioner with a step of 1 µm. The temperature jump at the liquid-gas interface is measured, and its value increases with the temperature increase. Detailed information on the temperature field near the interface is obtained by using the precise thermocouple displacement with a small step. Key words: microthermocouple, liquid-gas interface, temperature jump, evaporation.

In the electronic systems, such as multiprocessors computer centers and mobile devices, there are many problems associated with thermal loads. The devices of the next generation can have high heat fluxes and pulse loads [1], whose combination will require a new level of thermal management. The two-phase cooling systems are of a particular interest for the use in cooling systems because of the high heat transfer coefficients [2]. The latent heat of vaporization in the two-phase flow provides usually the greater cooling capacity as compared with the same capabilities of the single-phase flow, and this allows the use of the low mass flow rates. However, there are a number of problems related to reliability and efficiency of the two-phase cooling systems; therefore, a thorough study of the heat and mass transfer processes is required. Investigation of heat transfer in a two-layer system with phase transitions is one of the topical scientific problems, for instance, in developing the technologies for heat pipe production. The study of the heat transfer in two-phase systems is also the fundamental challenge in terms of the determination of correct boundary conditions *

The work was financially supported by the Russian Ministry of Education and Science (Project identifier RFMEFI61614X0016). © E.Ya. Gatapova, R.A. Filipenko, Yu.V. Lyulin, I.A. Graur, I.V. Marchuk, and O.A. Kabov, 2015

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E.Ya. Gatapova, R.A. Filipenko, Yu.V. Lyulin, I.A. Graur, I.V. Marchuk, and O.A. Kabov

and investigation of the gas phase effect on the surface phenomena and convective flows. The temperature and pressure jumps at the interface (in the Knudsen layer) at phase transition are known for a long time in the kinetic theory, since the phase transitions occur under the non-equilibrium conditions [3, 4]. Recently, an approach to the description of heat and mass transfer in the two-phase system, based on the Navier– Stokes equations with the temperature and pressure jumps boundary conditions, was suggested in [5]. The analysis showed good agreement between the solutions proposed in [5] and temperature and pressure profiles obtained from the solution of the Boltzmann equations. However, there is a lack of the experimental data on the pressure and temperature jumps at the gas-liquid interface. One of the first experiments on the measurement of temperature profile during the evaporation from the liquid surface to vapor in a closed system is presented in [6]; several thermocouples were used with the bead diameter of 0.3 mm, arranged successively at a certain distance from each other. The results of the temperature profile measurement obtained with the help of microthermocouple with the wire diameter of 25.4 µm are presented in [7]. In these studies, the temperature jumps at the liquid-vapor interface were measured under the saturation conditions at a reduced pressure. In [8], the measurements were carried out by the thermocouple of 50-µm diameter at a longitudinal temperature gradient on the liquid surface (liquid was heated from the lateral side of a pan). To obtain the temperature distribution at the interface further experimental study of the interfacial region is required. Then the measured temperature jumps can be compared with the results predicted by the kinetic theory. This direction is essential for heat transfer enhancement processes in microsystems. The current work deals with the experimental study of the temperature profile in the liquid-gas two-layer system when liquid is heated from the bottom substrate. The main aim is the development of experimental methods for investigation of the temperature jumps in the interfacial region. The experiments are performed on the setup shown in Fig. 1. This setup consists of the following items: working section, syringe pump, power supply, microthermocouples, precision micropositioner, control-measuring system, personal computer, video camera, and optical system for the shadow technique. The components of setup are located on the optical table inside a transparent box to prevent dust penetration and air disturbances. To study heat transfer in the two-layer liquid-gas system, the working section on a fluorocarbon base with the heating element is used. The base with a slot for liquid with the diameter of 35 mm and height of 1 mm has a circular shape. At the center of the base, there is a round hole with the diameter of 1.6 mm. The heating element is a brass core with a round head with the diameter of 1.6 mm. The tip of the core is tightly inserted into the hole in the fluorocarbon base and leveled with it in a single plane. The heat source is a Nichrome tape wound on the core shank. To minimize the heat losses, the heating element is carefully insulated with fiberglass layers wrapped around the core of the heating element. To measure and control the temperature, three standard microthermocouples of Omega production (1, 2, and 3 in Fig. 1) are mounted into the heating element. The thermocouple 1 is located on the heater surface contacting with liquid. Thermocouples 2 and 3 are installed in the thickest part of the core under the Nichrome tape. Temperatures measured by thermocouples 1, 2, and 3 in various locations of the heating element differ by no more than 1°C within the temperature range from 20 to 92°C. Data from these thermocouples obtained under different heating conditions are shown in Figs. 2а and 2b. The temperature is shown along the ordinate axis, and time is shown along the horizontal axis. It is evident that the temperature in the heater can be considered homogeneous with the sufficient accuracy. The temperature for each experimental regime was measured at least three times. The power of the heating element was controlled by the power supply. Heat flux density qw was determined in two ways: by the power of Joule heat generated 702


Fig. 1. Scheme of experimental setup (а) and test section design (b) where all dimensions are in mm.

by a Nichrome tape as qw = UI/S, where U is voltage, I is current strength, S is the area of the heater tip cross section, and by the temperature difference between the readings of the thermocouples 2 and 3 mounted along the cylindrical part of the heater. According to the authors’ estimations, the difference between the heat flux densities increases with heating and is no more than 15 % for the considered heating regimes. The temperatures of the heater, liquid, and environment are measured by microthermocouples. Acquisition of data on temperatures is performed by means of the control-measuring system consisting of data acquisition system and software. The temperature profiles across the liquid-gas system are measured by the standard calibrated microthermocouples of type K (Omega) with the beam diameter of 150 µm. Thermocouple readings were checked by two standard resistance temperature detectors ETS-100, whose error within the studied temperature ranges was 0.05 °С. They were calibrated by the KS-100-1 calibrator. The calibration curve was approximated by the fourth-degree polynomial. The accuracy of temperature measurements was 0.1 °С. The measurement errors were also estimated by the formulas of [9] and solving the problem of heat transfer in a thin rod being in atmosphere/liquid with the linear temperature distribution. Moreover, the boundary conditions of the 3rd kind were set on the wire side walls and at some distance from the bead upstream. The heat transfer coefficient was calculated by the formulas given in [9], and it was 120 W/(m2K). It was found that for a microthermocouple with the wire diameter of 100 µm and temperature difference of 5 K at a distance of 2 mm, the temperature difference between the thermocouple and atmosphere (measurement error) for the considered regimes was less than 1 % of the measured data. We should also mention Ref. [10], where 703


Fig. 2. Readings of thermocouples 1, 2, and 3 mounted into the heating element: no heating (а), 2 heating power of 0.35 W and heat flux density qw = 17.5 W/cm (b).

the thermocouple with the hot junction size of 5−10 µm was used to measure the temperature in a turbulent water flow under the non-isothermal conditions, and the measurement errors were evaluated. Specially prepared purified deionized Ultrapure Water (Merck Millipore) with no salt content is used as the working fluid. Water is fed by a syringe pump into the working section, where the horizontal liquid layer is formed. The layer thickness is varied depending on the operating parameters of experiment, and it is always less than 2 mm. The horizontal layer remains 2 open to the atmosphere inside the transparent permeable box with the base of 80×50 cm and height of 35 cm, so the pressure inside the box is atmospheric. At the center of the working section substrate, there is constant local heating, which formed the flow of water vapor from the central part of the liquid layer surface. Several stationary regimes are studied in the range of the heater temperatures from 20 to 92°C. Three microthermocouples are used to measure the temperature across the liquid and air layers. The distance between the microthermocouples 4 and 5 is about 5 mm, between the microthermocouples 5 and 6 it is about 12.5 mm, so the microthermocouple 4 is located over the heated center of the axisymmetric working section (Fig. 1). The position of microthermocouples is determined by Zaber precision micropositioner connected to a PC and controlled with the special software. The range of microthermocouple movement is 50 mm with a step of 1 micron. The velocity of microthermocouple motion in experiments is 100 μm/s. The surface shape and liquid layer level, position and motion of microthermocouple over and across the horizontal layer of liquid are observed by means of the shadow technique using the video camera with resolution of 640x480 pixels. Figure 3 shows the measurements of temperature profile for the gas phase and liquid layer at the heater temperature of 52°C. The position of microthermocouple is shown along the abscissa axis. Since the size of the microthermocouple sensor Fig. 3. Temperature profiles across the gas and liquid layers obtained by thermocouples 4, 5, 6. Heater temperature is 52 °С.

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is 150 μm, the position at −75 μm corresponds to the microthermocouple contact with the liquid surface, the mark 0 corresponds to the moment when the middle of microthermocouple sensor is at the interface, and 75 μm corresponds to the moment when the end of the microthermocouple bead is at the interface. The liquid layer thickness is controlled by the shadow technique as well as with the help of a micropositioner with microthermocouple and special software, which detects the position points at a given moment. The initial height is determined first, then, the point of a new interface for the next experimental iterations is identified by the first touch of the liquid surface by the microthermocouple. Microthermocouples 4, 5, and 6 move from the gas phase to liquid; the temperature in the gas phase is measured first, then, it is measured in liquid, and finally, thermocouple 4 reaches the heater, measuring the average value between the temperatures of the heater and liquid layer at the distance of a thermocouple bead size. Thermocouples 5 and 6 measure the temperature of the lower wall of the working section. We should note that the temperature near the heater measured from liquid is 4 °С lower than thermocouple readings in the heating element (Fig. 2b). Within the whole range of heater temperatures from 20 to 92°C, good local heating is observed throughout the liquid and gas layers as shown in Fig. 3. The temperature at the center of the liquid layer was always much higher. In the whole range of heater temperatures from 20 to 92°C, a bend of the temperature profile related likely to the different thermal conductivities of liquid and gas, is always observed at liquid-gas interface. Figures 4а−4c show the temperatures measured near the interface at different heater temperatures. It can be seen that there is a characteristic temperature difference (jump)

Fig. 4. Temperature profiles across the gas and liquid layers obtained by microthermocouples 4. Liquid layer thickness is 1750 μm; heater temperature: 31 °С (а), 52 °С (b), 92 °С (c).

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at the liquid-gas interface. The jump value increases with the heater temperature, and accordingly with increasing evaporation rate. The measurements are performed several times, and data are consistently repeated. The evaporation rate is defined as u = (ql − qg)/rρv, where ql is the heat flux at the interface from liquid, qg is the heat flux at the interface from gas (both characteristics are determined by the experimental temperature differences), r is the latent heat of vaporization, ρv is the vapor density. At the heater temperature of 92°C, the averaged value of jump is about 1.3°C, and the evaporation rate is about 20 mm/s. The precision micropositioner with a small step (1 μm) allows us to get the detailed data at the interface. Thus, the technique for measuring the temperature field at the interface is developed. We should note that the order of interface thickness equals few molecular free paths, which depends on the specified conditions (pressure, temperature). Under the normal conditions (atmospheric pressure) of the performed experiment, this value is about 1 µm for water vapors. These results should be analyzed further with more accurate measuring system (a smaller size of the microthermocouple) or under the reduced pressure conditions. In conclusion, we note that one of the main achievements of this work is the development of the measurement technique, which allows the characterization of the temperature profile at the interface by means of microthermocouple and precision micropositioner with the step of 1 µm under intensive evaporation condition. Using the developed method, the temperature jump at the interface is detected, whose value increases with interface temperature increasing. The detailed information on the temperature field at the interface is obtained with the help of precision micropositioner with a small step. References 1. A. Bar-Cohen and P. Wang, Thermal management of on-chip hot spot, J. Heat Transfer, 2012, Vol. 134, No. 5, P. 051017-1−051017-11. 2. S.G. Kandlikar, S. Colin, Y. Peles, S. Garimella, R.F. Pease, J.J. Brandner, and D.B. Tuckerman, Heat transfer in microchannels ⎯ 2012 status and research needs, J. Heat Transfer, 2013, Vol. 135, No. 9, P. 091001-1−091001-18. 3. R.Ya. Kucherov and L.E. Rikenglaz, On hydrodynamic boundary conditions for evaporation and condensation, J. Exp. Theor. Phys., 1960, Vol. 37, Iss. 10, No. 1, P. 88−89. 4. Y.-P. Pao, Temperature and density jumps in the kinetic theory of gases and vapors, Phys. Fluids, 1971, Vol. 14, No. 7, P. 1340−1346. 5. E.Ya. Gatapova, I.A. Graur, F. Sharipov, and O.A. Kabov, The temperature and pressure jumps at the vapor-liquid interface: application to a two-phase cooling system, Int. J. Heat Mass Transfer, 2015, Vol. 83, P. 235−243. 6. P.N. Shankar and M.D. Deshpande, On the temperature distribution in liquid–vapor phase change between plane liquid surfaces, Phys. Fluids A, 1990,Vol. 2, No. 6, P. 1030−1038. 7. C.A. Ward and D. Stanga, Interfacial conditions during evaporation or condensation of water, Phys. Rev. E, 2001, Vol. 64, P. 051509-1−051509-9. 8. Z.-Q. Zhu and Q.-S. Liu, Interfacial temperature discontinuities in a thin liquid layer during evaporation, Microgravity Sci. Technol., 2013, Vol. 25, P. 243−249. 9. N.A. Yaryshev, Theoretical Fundamentals of Non-Stationary Temperature Measurements, Energoatomizdat, Leningrad, 1990. 10. E.M. Khabakhpasheva, B.V. Perepelitsa, Yu.M. Pshenichnikov, and A.M. Nasibulov, The effect of flow velocity on non-stationary heat transfer at a drastic change in the heat flux, Structure of Hydrodynamic Flows (Forced Flow, Heat Convection), IT SO AN SSSR, 1986, P. 25–39.

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