March 23-27, 2015, Campinas, SP, Brazil Copyright 2015 by ABCM Paper ID: JEM-2015-0076 THE EFFECT OF THE CROSS-SECTIONAL GEOMETRY ON SATURATED FLOW BOILING HEAT TRANSFER IN HORIZONTAL MICRO-SCALE CHANNELS Daniel Sempertegui-Tapia Escola de Engenharia de Sao Carlos, University of Sao Paulo (USP), Av. Trabalhador São Carlense, 400, Sao Carlos-SP, Brazil. dsempertegui@hotmail.com Gherhardt Ribatski Escola de Engenharia de Sao Carlos, University of Sao Paulo (USP), Av. Trabalhador São Carlense, 400, Sao Carlos-SP, Brazil. ribatski@sc.usp.br Abstract. In the present paper, convective boiling heat transfer results of R134a for circular, square and triangular tubes are presented. The evaluated channels present the same external perimeter and equivalent diameters of 1.1, 0.977 and 0.835 mm, respectively. Experiments were performed for mass velocities ranging from 200 to 800 kg/m²s, heat fluxes from 15 to 95 kw/m², saturation temperatures of 31 and 41 C, and vapor qualities from 0.05 to 0.95. In order to perform reasonable comparisons among the two test sections, the tests were run under similar mass velocities for the three geometries. The experimental data were carefully analyzed and discussed focusing on the effect of the cross-sectional geometry. Subsequently, they were compared with predictive methods from literature which are usually developed based only on circular channel experimental data. Overall, the model of Saitoh et al. (2007) modified by Ribatski (2014) and the method developed by Kim and Mudawar (2013) provided accurate predictions of the present database. Keywords: heat transfer coefficient, geometry effect, micro-channels, convective boiling. 1. INTRODUCTION In the last two decades, the number of studies concerning flow boiling in micro-scale channels has increased because of the need of dissipating high amounts of heat. In the last years, several experimental studies on two-phase heat transfer coefficient and pressure drop have been performed. However, as pointed out by Sempértegui-Tapia and Ribatski (2013), several aspects are still unclear due to the fact that studies from independent laboratory provide quite different behaviors. Besides, according to the literature review by Tibiriçá and Ribastki (2013), almost 97% of the studies on single channels were performed for circular cross sections, while 87% of the studies concerning micro-scale multi-channels were performed for rectangular cross sections and 9% for triangular cross sections. These facts indicates the need of performing careful experiments and obtaining accurate data for single-channels with non-circular geometries in order to support the development of precise predictive methods for multi-channels configurations. In this sense, the present paper focus on the study of the effect of the channel geometry on saturated flow boiling in horizontal micro-channels. For this purpose, heat transfer experimental data were collected for circular, square and triangular single channels. The evaluated channels present the same perimeter and equivalent diameters of 1.1, 0.977 and 0.855 mm, respectively. Experiments were performed for mass velocities ranging from 200 to 800 kg/m²s, heat fluxes from 0 to 85 kw/m², saturation temperatures of 31 and 41 C and vapor qualities from 0.05 to 0.95. Additionally, the experimental results were compared against the most quoted predictive methods from the literature including methods developed for conventional channels and methods specially developed for micro-scale channels. The methods were evaluated according to two criteria: the mean absolute error (MAE) and the parcel of data predicted within ±30% of error band. The results are carefully analyzed and discussed. 2. EXPERIMENTS 2.1 Experimental apparattus The experimental setup is comprised of refrigerant and water circuits. The water circuit is intended to condense and subcool the working fluid. The refrigerant circuit is schematically shown in Figure 1. It comprises a micropump to drive the test fluid through the circuit, a Coriolis mass flow meter, a preheater to establish the experimental conditions at the inlet of the test section, a test section, a visualization section, a tube-in-tube heat exchanger to condense the vapor created in the heated sections and a refrigerant tank. In the refrigerant circuit, the test fluid is driven by a self-lubricating oil-free micropump through the circuit. The liquid flow rate is set by a frequency inverter acting on the micropump. Downstream the micropump, the mass flow rate
Sempertegui-Tapia D and Ribatski G. The effect of the cross-sectional geometry on saturated flow boiling heat transfer in horizontal micro-scale channels. is measured with a Coriolis flow meter. Just upstream de pre-heater and test section, the inlet conditions are determined by a thermocouple and an absolute pressure transducer. Figure 1. Schematic diagram of the refrigerant circuit. The pre-heater and the test section are formed by a 490 mm horizontal stainless-steel tube. The test sections were fabricated from the same circular tube with internal diameter of 1.1 mm. Their shape was obtained through a process of conformation using a steel matrix composed of two-block with grooves designed especially for each cross section. A uniform pressure was provided to the matrix in order to get the desired shape. The pre -heater and the test sections are 200 and 150 mm long, respectively. Both sections are heated by applying direct DC current to their surface and are thermally insulated. The power is supplied to them by two independent DC power sources controlled from the data acquisitions system. A detailed scheme of the pre-heater and test section is shown in Fig. 2. Figure 2. Scheme of the pre-heater section and the test section. Figure 3a and 3b illustrates the profiles of the square and triangular channels, respectively. These profiles were obtained with Wiko NT1100 equipment and treated with the software Version Vision 4.20, Copyright Veeco Instruments, Inc. 2
Figure 3. Cross-sectional geometries, a) Square, b) Triangular. 2.2 Data reduction 2.2.1 Mass velocity Mass velocity is calculated as the ratio between the mass flow rate and the internal cross sectional area of the tube, according to the following equation: M G (1) A int The cross-sectional area of the circular tube is calculated as follows: 2 D Aint circ (2) 4 The cross-sectional area of the square and triangular channels were estimated through the image processing of the geometries displayed in Figs. 3a and 3b, respectively, using the software MATLAB R2010a. 2.2.2 Vapor quality The local vapor quality was determined through an energy balance over the pre-heater and the test section according to the following equation: 1 Pph Pts( z) x( z) i L, in il( z) i ( z) LG M (3) where i L,in is the enthalpy of the liquid at the inlet of the pre-heater, i L (z) and i LG (z) are the enthalpy of the saturated liquid and the latent heat of vaporization corresponding to the local saturation at the position z, respectively. 2.2.3 Heat transfer coefficient The local heat transfer coefficients were calculated according to the Newton s cooling law as follows: h( z) T w ts ( z) T sat ( z) (2) where T w (z) is the inner wall temperature estimated according to Fourier s law based on the outer wall temperatures measurements. T sat (z) is the local saturation temperature of the refrigerant, which is estimated through a prorated method based on the values of the local saturation pressure along the test section, obtained during the adiabatic pressure drop tests.
Sempertegui-Tapia D and Ribatski G. The effect of the cross-sectional geometry on saturated flow boiling heat transfer in horizontal micro-scale channels. 2.3 Validation of the Experimental Facility Experimental tests for single-phase flow were previously performed in order to assure the accuracy of the measurements and evaluate the effective rate of heat losses. Figure 4a illustrates the single-phase pressure drop results for the three geometries. As shown in the figure, the laminar experimental data for pressure drop agree reasonably well with the theory for laminar flow. For turbulent flow, the experimental data were compared to the method of Blasius (1913). The correlation of Blasius over-predicted the experimental data for the square channel around 20% while provides accurate predictions for circular and triangular channels. Figure 4. Single-phase flow results, a) Pressure drop, b) Heat transfer coefficient. Figure 4b illustrates the experimental single-phase heat transfer coefficient for the three geometries. As noted in the figure, the laminar theory for the three geometries under-predict the experimental values. For turbulent flow, the correlation of Gnielinski (1976) agrees quite well with the experimental values for square and triangular channels, but under predict the experimental data for the triangular cross section. Temperature measurements were calibrated and the temperature uncertainty was evaluated according to the procedure suggested by Abernethy and Thompson (1983). Accounting for all instrument errors, uncertainties for the calculated parameter were estimated using the method of sequential perturbation according to Moffat (1988). All the experimental uncertainties associated with the sensors and calculated parameters are listed in Table 1. Table 1. Uncertainties of measured and calculated parameters Parameter Uncertainty Parameter Uncertainty D 20 µm G 1.7% L 1 mm x < 5% p 4.5 kpa h < 30% Δp 3. RESULTS AND DISCUSSION 3.1 Two-phase heat transfer coefficent 150 Pa P ph, P ts 0.8 % T 0.15 C 3.1.1 Effect of the cross-sectional geometry Figure 5 illustrates the effect of the cross-sectional geometry on the heat transfer coefficient. As observed in this figure, for low heat fluxes the HTC for circular channel is higher than the one for square and triangular channels at high vapor quality conditions, while for low vapor qualities the HTC of the three geometries are almost similar. On the other hand, for high heat fluxes the heat transfer coefficient for triangular channel is higher than the one for circular and square channels independent of the any vapor quality. 4
Figure 5. Effect of the geometry on the heat transfer coefficient 3.1.2 Effect of the heat flux and vapor quality According to Figure 6, the heat transfer coefficient increases with heat flux independently of the geometry and mass velocity range (not shown). For square channels, the heat transfer coefficient increases with increasing vapor quality. This effect is more evident at low heat fluxes and is almost negligible for the experimental data for triangular channels (see Figure 6b). Figure 6. Effect of the mass velocity on the heat transfer coefficient for: a) Square channel, b) Triangular channel.
Sempertegui-Tapia D and Ribatski G. The effect of the cross-sectional geometry on saturated flow boiling heat transfer in horizontal micro-scale channels. 3.1.3 Effect of the saturation temperature Figure 7 illustrates the effect of the saturation temperature on the heat transfer coefficient. According to Figure 7a, for a circular channel, the HTC increases between 5 to 15% with increasing saturation temperature from 31 to 41 C. On the other hand, an earlier dryout seems to occur for the triangular channel the HTC for a saturation temperature of 31 C and heat fluxes of 25 and 55 kw/m 2 (see Figure 7b). Figure 7. Effect of the saturation temperature on the heat transfer coefficient for: a) Circular channel, b) Triangular channel. 3.2 Assessment of predictive methods for heat transfer coeficcient Table 2 lists de mean absolute errors (MAE) and the parcels of data predicted within ±30 % of error band (η) obtained from the comparisons between predictive methods and the experimental database. The comparisons were performed considering the data for each cross-sectional geometry and the overall database. Table 2. Mean absolute error (MAE) and the percentage of predictions (η) which fall within 30% of the measurements from each data set* Predictive method Experimental Database Circular Channel Data points 762 Lazareck and Black (1982) Liu and Winterton (1991) Zhang et al. (2004) Thome et al. (2004) Saitoh (2007) modified by Ribatski (2014) Bertsch et al. (2009) Kim and Mudawar (2013) MAE 22.1% 27.7% 21.3% 20.5% 11.2% 38.1% 11.0% Η 76.6% 59.2% 82.0% 77.7% 92.5% 17.2% 96.1% Square Channel 382 MAE 25.1% 20.3% 17.3% 23.1% 5.4% 36.5% 7.2% Η 68.8% 92.1% 88.2% 70.9% 100.0% 34.3% 100.0% Triangular Channel 376 MAE 38.5% 20.2% 17.8% 31.2% 6.4% 35.0% 10.2% Η 18.9% 79.8% 91.0% 44.3% 99.2% 32.0% 96.7% MAE 26.8% 24.1% 19.5% 23.7% 8.6% 37.0% 9.9% Overall 1520 Η 60.3% 72.0% 85.2% 67.4% 95.4% 24.9% 96.6% *Bold numbers indicate a Mean Average Error (MAE) below 25% and more than 75% of the data predicted within the ±30% of the measurement. 6
For the comparisons involving the overall database, the models of Saitoh et al. (2007) modified by Ribatski (2014) and Kim and Mudawar (2013) provided very accurate results of the present experimental database. Saitoh et al. (2007) modified by Ribatski (2014) obtained the lowest MAE (8.6%) and Kim and Mudawar (2013) the highest η (96.6 %). This result is not surprising considering that Ribatski (2014) adjusted the empirical constants of the method of Saitoh et al. (2007) based on three experimental databases including the experimental database of Tibiriçá (2011), which was obtained using the same experimental facility considered for the present study. The accomplishment of the method developed by Kim and Mudawar (2013) is probably explained by the fact that the authors used an experimental database containing 10,805 points in order to adjust their empirical constants. The methods of Zhang et al. (2004), and Liu and Winterton (1991) also provided reasonable agreement predicting 85.2% and 72% of the overall database within an error band of ±30%, respectively. Thome et al. (2004) and Lazareck and Black (1982) perform relatively well providing a MAE between 23 and 27%. The method by Berstch et al. (2009) provided a MAE higher than 30% and a η less than 25%. The methods of Saitoh et al. (2007) modified by Ribatski (2014), Kim and Mudawar (2013) and Zhang provided accurate predictions of the experimental databases of the three geometries. Liu and Winterton (1991) provided reasonable prediction of the square and triangular databases. Thome et al. (2004) and Lazareck and Black (1982) performed relatively well for the circular channel experimental database, but completely fail to predict the triangular channel database. The model of Berstch et al. (2009) wasn t able of providing reasonable predictions of any of geometries evaluated in the present study. Figure 8 illustrates comparisons between the experimental database segregated according cross-sectional geometry and the model by Kim and Mudawar (2013) and Saitoh et al. (2007) modified by Ribatski (2014). According to this figure, both methods can be considered reasonably accurate independent of the heat transfer coefficient range. It should be also mentioned the fact that both methods mostly under-predict the experimental database. Figure 8. Comparison of the experimental databases of the three geometries with predictive methods by: a) Kim and Mudawar (2013), b) Saitoh modified by Ribatski (2014). Since a good predictive method should be not only statistically accurate, but also be able of capturing the main trends of the experimental results. Figure 9 displays the evolution of the heat transfer coefficient with the vapor quality according to the predictive methods and the experimental data. According to Fig. 9, Saitoh et al. (2007) modified by Ribatski (2014), Kim and Mudawar (2013), Liu and Winterton (1982) and Zhang et al. (2004) captures the behavior that the heat transfer coefficient increases with increasing vapor qualities. However, only Saitoh et al. (2007) modified by Ribatski (2014) and Kim and Mudawar (2013) were able of predicting the heat transfer coefficient trends especially for the circular and square channel (Figure 9a and 9b). It should be also highlighted the fact that most of the correlations present a huge divergence between the predicted absolute values and the experimental trends. For these methods, different trends were observed over the entire vapor quality range achieving deviation higher than 200%.
Sempertegui-Tapia D and Ribatski G. The effect of the cross-sectional geometry on saturated flow boiling heat transfer in horizontal micro-scale channels. Figure 9. Comparison of the heat transfer coefficient trends according to the predictive methods and the experimental data. 4. CONCLUSIONS The following remarks summarize the conclusions of the present investigation: For high heat fluxes the heat transfer coefficient for a triangular channel ends up being superior to the ones obtained for square and circular channels under the same experimental conditions. The heat transfer coefficient increases with increasing the heat flux for the three geometries. The heat transfer coefficient increases with increasing vapor quality. This effect is more evident at low heat fluxes and is almost negligible for the experimental data for triangular channel. The heat transfer coefficient increases with increasing saturation temperature before dryout conditions. The method proposed by Saitoh et al. (2007) later modified by Ribatski (2014) and the method proposed by Kim and Mudawar (2013) provided the best predictions, resulting MAEs of only 8.6% and 9.9%, respectively. These methods were also able of predicting the HTC trends especially for the circular and square experimental data. 5. ACKNOWLEDGEMENTS The authors gratefully acknowledge FAPESP (The State of São Paulo Research Foundation, Brazil) for the financial support under contract numbers 2010/17605-4 and 2011/50176-2. The authors also thanks to CNPq (National Counsel of Technological and Scientific Development of Brazil) to the grant contract number 303852/2013-5. The technical support given to this investigation by Mr. José Roberto Bogni is also appreciated and deeply recognized. The authors also thank Prof. Renato Goulart Jasinevicius for the support in obtaining the profiles of the test sections. 8
6. REFERENCES Abernethy, R.B. and Thompson, 1983, J.W. Handbook, Uncertainty in gas turbine measurement. National Technical Information Service. Blasius, H., 1913. Das ahnlichkeitsgesetz bei reibungsvorg/ingen in fltissigkeiten. Forschg. Arb. Ing-Wes., Vol. 131. Bertsch, S.S., Groll, E. and Garimella, S.V., 2009, A composite heat transfer correlation for saturated flow boiling in small channels, International Journal of Heat and mass Transfer, Vol. 52, pp. 2110-2118. Gnielinski, V., 1976. New equations for heat and mass transfer in turbulent pipe and channel flow. International Chemical Engineering, Vol. 16, No. 2, pp. 359-368. Kim, S.M. and Mudawar, I., 2013, Universal approach to predicting saturated flow boiling heat transfer in mini/microchannels Part II. Two-phase heat transfer coeffcient, Int. J. Heat Mass Transfer, Vol. 64, pp. 1239-1256. Lazareck, G.M. and Black, S.H., 1982, Evaporative heat transfer, pressure drop and critical heat flux in a small vertical tube with R-113, Int. J. Heat Mass Transfer, Vol. 25, pp. 945-960. Liu, Z. and Winterton, R.H., 1991, A general correlation for saturated and subcooled flow boiling in tubes and annuli, based on a nucleate pool boiling equation, International Journal of Heat and Mass Transfer, Vol. 34, pp. 2759-2766. Moffat, R. J., 1988, Describing the Uncertainties in Experimental Results, Exp. Thermal and Fluid Science., Vol. 1, pp. 3 17. Ribatski, G., 2014, Estudo da ebuliçao convectiva no interior de canais de dimensoes reduzidas, Tese (Livre Docência), Universidade de São Paulo, USP, São Carlos-Brazil. Saitoh, S., Daiguji, H. and Hihara, E., 2007, Correlation for boiling heat transfer of R134a in a horizontal tubes including effect of tube diameter, Int. J. Heat Mass Transfer, Vol. 50, pp. 5215-5225. Sempértegui-Tapia, D.F. and Ribatski, G., 2013, An analysis of experimental data and predictions methods for heat transfer coefficient during convenctive boiling in non-circular miscro-scale channels Proceedings of the 8th International Conference on Multiphase Flow, Jeju, Korea. Thome, J.R., Dupont, V. and Jacobi, A.M., 2004, Heat transfer model for evaporation in microchannels. Part I: Presentation of the model, Int. J. Heat and Mass Transfer, Vol. 47, pp. 3375-3385. Tibiriçá, C.B., 2011, Estudo teórico experimental da transferência de calor e do fluxo crítico de calor durante a ebulição convectiva no interior de microcanais, Tese (Doutorado), Universidade de São Paulo, USP, São Carlos- Brazil. Tibiriçá, C.B. and Ribatski, G., 2013. Flow boiling in micro-scale channels Synthesized literature review. International Journal of Refrigeration, Vol. 36, pp. 301-324. Zhang, W., Hibiki, T., Mishima, K., 2004, Correlation for flow boiling heat transfer in mini-channels. Int. J. Heat and Mass Transfer, Vol. 47, pp. 5749-5763. 7. RESPONSIBILITY NOTICE The authors are the only responsible for the printed material included in this paper.