AN ANALYSIS OF EXPERIMENTAL DATA AND PREDICTION METHODS FOR CRITICAL HEAT FLUXES IN MICRO-SCALE CHANNELS

Transcription

1 AN ANALYSIS OF EXPERIMENTAL DATA AND PREDICTION METHODS FOR CRITICAL HEAT FLUXES IN MICRO-SCALE CHANNELS C.B. Tibiriçá, H.O.M. Felcar, G. Ribatski Escola de Engenharia de São Carlos (EESC), University of São Paulo (USP) São Carlos, SP, Brazil Abstract Experimental results for the critical heat flux (CHF) in micro-scale channels for both multi- and single-channel configurations were obtained from the literature. The extensive database contains more than 1000 datapoints and comprises both subcooled and saturated CHF results covering 7 fluids (water, R12, R113, R134a, R123, CO 2 and Helium), mass velocities from 10.5 to 134,000 kg/m 2 s and experimental critical heat fluxes up to 276 MW/m 2. Based on a comparison against the broad experimental database taken from the literature and put together here, nine macro- and microscale CHF prediction methods for saturated and subcooled conditions were evaluated. The CHF calculation method proposed by Shah (1987) for macro- and micro-scale channels gives the best fit of the complete CHF database including saturated and subcooled conditions. In particular, the correlation proposed by Zhang et al. (2006) and the correlation by Hall and (2004) provided the most accurate predictions of saturated and subcooled critical heat fluxes, respectively. The saturated CHF model recently proposed by Revellin and Thome (2007) predicted relatively well data in multi-channel configurations. The method proposed by Revellin and Thome (2007) is also capable of predicting pressure drops for annular flows. Thus, in order to investigated its consistency, independent pressure drop data were compared against predictions by their model. The boiling data falling in the annular regime are identified using a new micro-scale flow pattern predictive method just proposed by Felcar et al. (2007), in order to utilize only test data corresponding to the annular flow model. Nomenclature D h hydraulic diameter, m m& mass velocity, kg/m 2 s L length, m q& critical heat flux, W/m 2 c T sat saturation temperature, o C p λ pressure drop, Pa fraction of data predicted to within ±30%, % ϕ mean absolute error, % ε average error, % 1 Introduction Critical heat flux (CHF), also known in the literature as burnout point, is generally related to a drastic decrease in the heat transfer coefficient. When heat is dissipated from a device which the imposed parameter is the heat flux, viz. microprocessors, fuel cells, spacecraft payloads and fuel elements in nuclear reactors, exceeding the CHF may result in an irreversible damage of the thermal-controlled device, consequently, CHF is the maximum operational heat flux that can be achieved under safe operation. Due to such a fact, this topic has attracted great attention of the academic society dealing with heat transfer and also of the industrial sector involved with the dissipation of high heat flux densities.

2 The CHF condition is observed when the liquid supply to the heated surface is blocked and the surface is covered by a layer of vapor, such that the heat is transferred from the surface to the liquid by conduction and convection through a vapor layer and, as the wall superheating increases, radiation becomes the main heat transfer mechanism. In convective boiling, the mechanisms related to the onset of CHF are related to the state of the working fluid. Distinct mechanisms are observed at subcooled and saturated conditions. The subcooled condition refers to when CHF is reached at the outlet of the test section while the thermodynamic vapor quality is lower than zero. Such scenarios are observed for high mass velocities, high degrees of subcooling at the inlet of the test section and low ratios of heated length to channel diameter. The critical heat flux under saturated condition occurs when the thermodynamic vapor quality is higher than zero at the outlet of the test section. For the saturated CHF, the liquid film dries out near the channel outlet and this is thought to be the mechanism related to the onset of CHF. At low flow rates in small-diameter tubes, this type of CHF may be prone to occur also due to the thinner liquid film thickness as suggested by Zhang et al. (2006). For subcooled CHF, the following three mechanism have been proposed by Tong and Hewitt (1972): dryout under a vapour clot at low mass velocities and high subcooling; bubble crowding promoting a vapour blanketing at high mass velocities; and evaporation of liquid film surrounding a slug bubble at low and moderate subcooling and low mass velocities. These and other theories explaining the physical mechanisms related to the achievement of critical heat flux are detailed by Maulbetsch and Griffith (1965), Kutateladze and Leont ev (1966), Weisman and Pei (1983) and Lee and (1988), suggested here as references for further reading. In this paper, the capability of nine different methods to predict subcooled and saturated CHF in micro-scale channels are evaluated by comparing them against a wide independent database including more than 1000 experimental data points. Due to the lack of a well established criterion that takes into account differences in the two-phase flow and heat transfer processes, a characteristic dimension of 3mm is adopted here to characterize the threshold from macro- to micro-scale channels as proposed by Kandlikar and Grande (2003) to characterize the transition from conventional to mini-channels. The analysis includes micro- and macro-scale methods and the recent saturated CHF model just proposed by Revellin and Thome (2007). The capability of Revellin and Thome (2007) method to predict diabatic pressure drops for annular flows was also evaluated by comparing its results against data from the literature and predicted results provided by the homogeneous model and the Müller-Steinhagen and Heck (1986) correlation for frictional pressure drops. In this comparison, the flow pattern predictive method just proposed by Felcar et al. (2007) was used in order to segregate the data as annular flow. The predictive methods are evaluated according to three criteria: the fraction of data predicted to within ±30%,λ, the mean absolute error, ϕ, and the average error, ε. The experimental database compiled here was taken from tabular values where available or by digitizing data from graphs in the literature. 2 Description of the CHF database The experimental micro-scale heat transfer database compiled here and described in Table 1 comprises datapoints under subcooled and saturated conditions. They were extracted from plots and tables presented in the literature. Except for the data of Lazareck and Black (1982) and some of the results of Lowdermilk et al. (1958) most of the studies listed in Table 1 were performed in test sections with hydraulic diameters between 240 µm and 3 mm. The database presented in Table 1 covers 6 fluids (water, R113, R134a, R123, CO 2 and Helium), and a wide range of mass velocities (10.5 to 134,000 kg/m 2 s), saturation temperatures corresponding to reduced pressures from 4.5x10-7 to , hydraulic channel diameters down to 0.2 mm, subcoolings at the inlet of the test section up to 329 o C and critical heat fluxes up to 276 MW/m 2. Tests were conducted for single and multichannel configurations. The test surfaces were heated by applying a direct current to the test section.

3 Author Lowdermilk et al. (1958) Lazareck and Black (1982) Katto and Yokoya (1984) Bowers and (1994) Vandervort et al. (1994) and Bowers (1999) Sumith et al. (2003) Yun and Kim (2003) Qu and (2004) Wojtan et al. (2006) Kosar and Peles (2007) Number. of datapoints Table 1: Micro-scale CHF database. Geometry/ number of channels/ orientation circular/17 /horizontal horizontal retangular/ 21/ horizontal horizontal retangular/ 5/ horizontal Saturated/ subcooled Fluid T sat ( o C) saturated water saturated R L (mm) D h (mm) saturated helium saturated R subcooled subcooled water water m& (kg/m 2 s) q& c (kw/m 2 ) saturated water saturated CO saturated water saturated R134a saturated R CHF prediction method Due to the fact that the CHF process in flow boiling is very complex, predictions rely heavily on empirical correlations based on dimensionless numbers. These dimensionless numbers include parameters that influence the measured CHF values, such as mass velocity, subcooling at the channel inlet, fluid properties, heated length and the diameter of the channel. Due to differences in the apparent mechanisms, correlations are normally separately proposed for CHF under subcooled and under saturated conditions. Most of these correlations were developed based on databases for water and macro-scale channels due to the fact that the majority of studies on CHF focused mainly on nuclear applications. However, during the last decade, such a scenario is changing because of the necessity to dissipate high power densities in micro-processors and power electronics and data for a wider variety of fluids and smaller diameters are now appearing in the literature. Below, the most quoted CHF prediction methods found in the literature and also some recent methods developed in order to predict CHF in micro-scale channels are described briefly. A generalized correlation of the critical heat flux (CHF) for forced convective boiling in uniformly heated single tubes based on dimensionless numbers was proposed by Katto and Ohno (1984). This is the one of the most widely used correlations and is based on a wide database and on a series of previous studies realized by the first author. In 1987, Shah proposed a new version of his previous correlation to predict CHF during upflow in uniformly heated tube under saturated and subcooled conditions. This correlation is based on data from 62 independent sources that includes 23 fluids (water, refrigerants, cryogens, chemicals, and liquid metals), tube diameters from to 37.5 mm, tube lengths from 1.3 to 940 times diameter, mass velocities from 4 to 29,051 kg/m 2 s, reduced pressures from to 0.96 and inlet quality from -4 to Mean absolute errors of 16 and 22.3% were found by Shah (1987) when comparing his predictive method and Katto and Ohno s (1984) method against his database.

4 Hall and (2000) based on 5,544 data points for water flowing in a tube developed a method to predict critical heat fluxes under subcooled conditions. Later on, Zhang et al. (2006) compared a database gathered from the literature for saturated and subcooled CHF against CHF predictive methods from the literature. Their database contains data only for water and covers hydraulic diameters from 0.33 to 6.22mm. They found that the Hall and (2000) and Shah (1987) predictive methods (both based on macro- and micro-scale data) provided the best predictions in the subcooled and saturated flow boiling regions, respectively. Here, it is important to highlight that the database used by Hall and (2000) included most of the studies used by Zhang et al. (2006), except for one study. A CHF correlation was also developed by Bowers and (1994) based on saturated R113 CHF data for two distinct heat sinks having circular channels with diameters of 2.54 and 0.510mm. Later on, Qu and (2004) obtained a correlation for saturated CHF based on the Katto and Ohno (1984) correlation (which was based on data for diameters down to 1mm), and using their own saturated data for water in a rectangular micro-channel heat sink, as well as data for R113 in a circular multi-microchannel heat sink from the previous study by Bowers and (1994). Based on their own data for R134a and R245fa in 0.5 and 0.8 mm internal diameter single microchannels and by modifying the Katto and Ohno (1984) correlation, Wojtan et al. (2006) also proposed a relation for the critical heat flux under saturated conditions. A non dimensional correlation was proposed by Zhang et al. (2006) which was based on the application of the artificial neural network to identify the dominant non dimensional number for saturated CHF. Based mainly on data for water from the literature, covering macro- and micro-scale channels, and on a dimensional analysis, Sarma et al. (2006) proposed two distinct correlations for the critical heat flux under subcooled and saturated conditions. Recently, Revellin and Thome (2007) developed a theoretical model for the prediction of the critical heat flux at saturated, stable conditions in uniformly heated, round microchannels. It is based on predicting the local dryout of the liquid film in annular flow occurring when the film thickness becomes equal to the interfacial wave height during evaporation. The model is based on the conservation of mass, momentum and energy, the Laplace Young equation and a semiempirical expression for the height of the interfacial waves. Validation was carried out by comparing the model, composed of a numerical solution of a non-linear system of five differential equations, with a database including three refrigerants (R134a, R245fa and R113) from two different laboratories. They also found that they could predict data in rectangular channels using the channel width as the characteristic dimension in their one-dimensional model. By comparing their CHF results for R236fa in a multi-microchannel heat sink against results from saturated CHF correlations from the literature, Agostini et al. (2007) ranked the Wojtan et al. (2006) method as the best followed by the CHF model of Revellin and Thome (2007) with a marginal difference between them. 4 Evaluation of the CHF prediction methods The above mentioned CHF prediction methods were evaluated by comparing them against the experimental database presented in Table 1. Table 2 depicts the statistical comparisons of the methods. Comparing prediction methods to the overall database (subcooled + saturated), the best prediction was obtained by the method proposed by Shah (1987), which ranked first according to all parameters, ε, λ and,ϕ. In the case of only saturated CHF data, the Revellin and Thome (2007) method overcame the other methods according to the three statistical parameters and, thus, was classified also as the best predicting method for saturated CHF. However, in contrary to the others saturated CHF methods, it should be mentioned that the Revellin and Thome model was evaluated without taken into account the data by Ku and (2003) and Lowdermilk et al. (1958) due to the fact that for these databases a numerical solution by using the Runge-Kutta method was not achieved. The method of Zhang et al. (2006) worked relatively well for saturated CHF. Thus, this method is suggested here to predict saturated CHF in micro-scale channels taken into account that

5 the method was compared against a broader database and has a much simpler implementation. For subcooled CHF, the method proposed by Hall and was ranked as the best. Comparisons between the general (saturated+subcooled), saturated and subcooled best predictive methods and the corresponding databases are shown in Figure 1. Based on this figures, a reasonable agreement between experimental and predicted results is observed. Table 2: Comparison of CHF prediction methods and the experimental data described in Table 1. Number of Datapoints Katto and Ohno (1984) Shah (1987) Bowers and (1994) Hall and (2000) Qu and (2004) Sarma et al. (2006) Wojtan et al. (2006) Zhang et al. (2006) Revellin and Thome (2007) * Sat+Sub ε (%) λ(%) φ(%) ε (%) * Saturated 348 λ(%) * φ(%) * ε (%) Subcooled 400 λ(%) φ(%) * Evaluated without Ku and (2003) and Lowdermilk et al. (1958) databases. q c exp [W/m 2 ] 3x Shah correlation for all data +30% -30% ε (%) = λ (%) = φ (%) = qc exp [W/m 2 ] Hall correlation for subcooled data +30% -30% q c pred [W/m 2 ] ε (%) = λ (%) = φ (%) = q c pred [W/m2] qc exp [W/m 2 ] 3x Zhang et al. (2006) correlation for for saturated data +30% -30% q c pred [W/m 2 ] ε (%) = λ (%) = φ (%) = Figure 1: Comparison of measured heat transfer coefficient with predictions. The above prediction methods were also evaluated against 300 macro-channel experimental datapoints from Pioro et al. (2002) and Katto and Yokoya (1982), with hydraulic diameter of 6.92 mm and 5.0 mm respectively. The correlation of Shah (1987) was capable to predict the macrochannel data very well, with an ε=16,8% and λ=86,3%. Although not presented here, comparisons of the predictive methods against each data set were also carried out. According to these comparisons, the method by Shah was the best predicting the data of Katto and Yokota (1982), and Bowers (1994), Pioro et al. (2002) and Sumith et al. (2003). The data of Lowdermilk

6 et al. (1958), Vandervort et al. (1994), and Wojtan et al. (2006) were also reasonably well predicted by Shah (1987) correlation (λ>70%). Additionally, it was somewhat surprising that the CHF method developed by Revellin and Thome (2007) for single channels, although including in its database some multi-channel results, worked relatively well for independent multi-channel data since interaction among distinct channels and the configuration of the heat-sink header may affect the boiling process, the two-phase flow distribution, and, consequently, the CHF level. 5 Pressure drops by the model of Revellin and Thome (2007) The saturated CHF method just proposed by Revellin and Thome (2007) is also capable of predicting pressure drops for smooth annular flows. Thus, in order to investigate its consistency, independent pressure drop data were compared against predictions by their model. It was used in such comparisons experimental results in micro-scale channels from Lazarek and Black (1982) for R113, and Tran (1998) for R134a, both for single-channel configurations, and from Qu and (2003) for water in a multi-channel configuration. Predictions by the homogeneous model and by the Müller-Steinhagen and Heck (1986) correlation for the frictional pressure drop were contrasted against those obtained by Revellin and Thome (2007). The homeogeneous model and Müller-Steinhagen and Heck (1986) correlation were selected based on the fact that Ribatski et al. (2006) have concluded that they are the most precise micro-scale pressure drop predictive methods. Such a conclusion was based on comparisons of 12 two-phase frictional pressure drop prediction methods, including both macro- and micro-scale methods, against 900 experimental micro-scale flow boiling data from independent laboratories. The boiling data falling in the annular regime are identified using a new micro-scale flow pattern predictive method just proposed by Felcar et al. (2007), in order to utilize only test data corresponding to the annular flow model. This new method is a modified version of Taitel and Dukler (1976) flow pattern model by taking into account secondary flows, wetting, and surface tension effects. Figure 2 shows comparisons of the experimental data against the predictive methods. It can be noted that both the homogenous model and the Müller-Steinhagen and Heck correlation predict 100% of data of Lazarek and Black (1982) to within ±40%. However, these methods fail into predict the data of Qu and (2003) while the model of Revellin and Thome (2007) predicts this database relatively well. The three methods underpredicted by approximately 40% the pressure drop data by Tran (1998). 6 Conclusions A comparison of the micro-scale CHF database from the literature against nine prediction methods revealed that the best predictions were obtained by Shah (1987) as general method (saturated and subcooled) and Zhang et al. (2006) for saturated conditions. In the case of the database containing only subcooled CHF data, the method of Hall and (2004) provided the most accurate predictions. Encouraging results were obtained when using the Revellin and Thome (2007) CHF method to predict saturated CHF and pressure drops. 7 Acknowledgement The authors gratefully acknowledge the support under contract numbers 05/ , 06/ , 07/ and 07/ given by FAPESP (The State of São Paulo Research Foundation, Brazil).

7 Figure 2: Comparison of the experimental pressure drop data for micro-scale channels against three prediction methods. 8 References Agostini, B., Thome, J.R., Fabbri, M., Calmi, D., Kloter, U. and Michel, B., 2007, High heat flux flow boiling in silicon multi-microchannels: Part III saturated critical heat flux of R236fa and two-phase pressure drops, Int. J. Heat Mass Transfer, in press. Bowers, M. and, I. 1994, High flux boiling in low flow rate, low pressure drop minichannel and micro-channel heat sinks, Int. J. Heat Mass Transfer, 37, Felcar, H. O. M., Ribatski, G. and Saiz Jabardo, J. M., A gas-liquid flow pattern predictive method for macro- and mini-scale round channels, A gas-liquid flow pattern predictive method for macro- and mini-scale round channels, 10th UK Heat Transfer Conference, Edinburgh, Scotland, UK, Hall, D. and, I., 2000, Critical heat flux (CHF) for water flow in tubes II Subcooled CHF correlations, Int. J. Heat Mass Transfer, 43, Kandlikar, S.G. and Grande, W.J., 2003, Evolution of microchannel flow passages thermohydraulic performance and fabrication technology, Heat Transfer Eng., 24, Katto, Y. and Ohno, H., 1984, An improved version of the generalized correlation of critical heat flux for the forced convective boiling in uniformly heated tubes, Int. J. Heat Mass Transfer, 27, Katto, Y. and Yokoya, S., 1984, Critical heat flux of liquid helium (I) in forced convective boiling, Int. Journal of Multiplhase Flow, 10, Katto, Y. and Yokoya, S., 1982, CHF of forced convection boiling in uniformly heated tubes Experimental study of HP-regime by the use of refrigerant 12, Int. Journal of Multiplhase Flow, 8, Kosar, A. and Peles, Y., 2007, Critical Heat Flux of R-123 in Silicon-Based Microchannels, Transactions of ASME, 29, Kutateladze, S.S. and Leont ev, A.I., 1966, Some applications of the asymptotic theory of the turbulent boundary layer, In: 3rd International Heat Transfer Conference, Chicago, USA, 3, 1-6.

8 Lazarek, G. M. and Black, S. H., 1982, Evaporative Heat Transfer, Pressure drop and critical heat flux in a small tube with R-113, Int. J. Heat Mass Transfer, 25, Lee, C.H. and, I., 1988, A mechanistic critical heat flux model for subcooled flow boiling based on local bulk flow conditions, Int. J. Mult. Flow, 14, Lowdermilk, W., Lanzo, C. and Siegel, L Investigation of boiling burnout and flow stability for water flowing in tubes, NACA. TN Maulbetsch, J.S. and Griffith, P., 1965, A study of system-induced instabilities in forced-convection flows with subcooled boiling, Report N. o , Department of Mechanical Engineering, Massachusetts Institute of Technology, USA., I. and Bowers, M., 1999, Ultra-high critical heat flux (CHF) for subcooled water flow boiling I CHF data and parametric effects for small diameter tubes, Int. J. Heat Mass Transfer, 42, Müller-Steinhagen, H. and Heck, K., 1986, A simple friction pressure drop correlation for twophase flow in pipes, Chem. Eng. Process, 20, Pioro, I.L., Groeneveld, D.C., Leung, L.K.H., Doerffer, S.S., Cheng, S.C., Antoshko, Yu.V., Guo, Y. and Vasic, A., 2002, Comparison of CHF measurements in horizontal and tubes cooled with R-134a, Int. J. Heat Mass Transfer, 45, Qu, W. and I., 2003, Measurement and prediction of pressure drop in two-phase microchannel heat sinks, Int. J. Heat Mass Transfer, 46, Qu, W. and, I., 2004, Measurements and correlation of critical heat flux in two-phase micro-channel heat sinks, Int. J. Heat Mass Transfer, 47, Revellin, R. and Thome, J. R., 2007, A theoretical model for the prediction of the critical heat flux, Int. J. Heat Mass Transfer, in press. Ribatski, G., Wojtan, L. and Thome, J. R., 2006, An analysis of experimental data and prediction methods for two-phase frictional pressure drop and flow boiling heat transfer in micro-scale channels, Exp. Thermal Fluid Sc., 31, Sarma, P.K., Srinivas, V., Sharma, K.V., Dharma Rao, V. and Celata, G.P., 2006, A correlation to evaluate critical heat flux in small diameter tubes under subcooled conditions of the coolant, Int. J. Heat Mass Transfer, 49, Shah, M., 1987, Improved general correlation for critical heat flux during upflow in uniformly heated tubes, Heat and Fluid Flow, 8, Sumith, B.M., Kaminaga, F. and Matsumura, K., 2003, Saturated flow boiling of water in a small diameter tube, Exp. Thermal Fluid Sc., 27, Taitel, Y., and Dukler, A. E., 1976, A model for predicting regime transitions in horizontal and near horizontal gas-liquid flow, AIChE Journal, 22, Tong, L.S. and Hewitt, G.F., 1972, Overall viewpoint of flow boiling CHF mechanism, ASME Paper 72-HT-54. Tran, T. N., 1998, Pressure drop and heat transfer study of two-phase flow in small channels, PhD Thesis, Texas Tech University. Vandervort, C., Bergles, A., and Jensen, K., 1994, An experimental study of critical heat flux in very high heat flux subcooled boiling, Int. J. Heat Mass Transfer, 37, Weisman, J. and Pei, B.S., 1983, Prediction of critical heat flux in flow boiling at low qualities, Int. J. Heat Mass Transfer, 26, Wojtan, L., Revellin, R. and Thome, J. R., 2006, Investigation of saturated critical heat flux in a single, uniformly heated microchannel, Exp. Thermal Fluid Sc., 30, Yun, R. and Kim, Y., 2003, Critical quality prediction for saturated flow boiling of CO2 in horizontal small diameter tubes, Int. J. Heat Mass Transfer, 46, Zhang, W., Hibiki, T., Mishima, K. and Mi, Y., 2006, Correlation of critical heat flux for flow boiling of water in mini-channels, Int. J. Heat Mass Transfer, 49,