Heat Transfer Engineering
ISSN: 0145-7632 (Print) 1521-0537 (Online) Journal homepage: http://www.tandfonline.com/loi/uhte20
Unified Modeling Suite for Two-Phase Flow, Convective Boiling, and Condensation in Macroand Microchannels John R. Thome & Andrea Cioncolini To cite this article: John R. Thome & Andrea Cioncolini (2016) Unified Modeling Suite for TwoPhase Flow, Convective Boiling, and Condensation in Macro- and Microchannels, Heat Transfer Engineering, 37:13-14, 1148-1157, DOI: 10.1080/01457632.2015.1112212 To link to this article: http://dx.doi.org/10.1080/01457632.2015.1112212
Accepted author version posted online: 05 Nov 2015. Published online: 22 Feb 2016. Submit your article to this journal
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Heat Transfer Engineering, 37(13–14):1148–1157, 2016 C Taylor and Francis Group, LLC Copyright ISSN: 0145-7632 print / 1521-0537 online DOI: 10.1080/01457632.2015.1112212
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Unified Modeling Suite for Two-Phase Flow, Convective Boiling, and Condensation in Macro- and Microchannels JOHN R. THOME1 and ANDREA CIONCOLINI2 1 2
Heat and Mass Transfer Laboratory, Swiss Federal Institute of Technology–EPFL, Lausanne, Switzerland School of Mechanical, Aerospace and Civil Engineering, University of Manchester, Manchester, United Kingdom
This paper focuses on the unified modeling suite for annular flow that the authors have developed and continue to develop. The annular flow suite currently includes models to predict the void fraction, the entrained liquid fraction, and the wall shear stress and pressure gradient, and a turbulence model for momentum and heat transport inside the annular liquid film. The turbulence model, in particular, allows prediction of the local average liquid film thicknesses and the local heat transfer coefficients during convective evaporation and condensation. The benefit of a unified modeling suite is that all the included prediction methods are consistently formulated and are proven to work well together, and provide a platform for continued advancement based on the other models in the suite. First the unified suite of methods is presented, illustrating in particular the most recent updates. Then results for the pressure drop and the heat transfer coefficient during convective evaporation and condensation are presented and discussed, covering both water and refrigerants flowing through circular tubes and noncircular multi-microchannel configurations for microelectronics cooling.
INTRODUCTION Annular two-phase flow is one of the most important of the two-phase flow regimes because of the large range of industrial applications in which it occurs, such as refrigeration and airconditioning systems, nuclear reactors, and chemical processing plants. Annular flow is characterized by a continuous liquid film that flows on the channel wall, surrounding a gas core loaded with entrained liquid droplets that flows in the center of the channel. Annular flow is of fundamental importance to the thermal design and simulation of microevaporators and microcondensers for compact two-phase cooling systems of high-heatflux components for the thermal management of computer chips, power electronics, laser diodes, and high-energy physics particle
Address correspondence to Dr. Andrea Cioncolini, School of Mechanical, Aerospace and Civil Engineering, University of Manchester, George Begg Building, Sackville Street, M1 3BB Manchester, United Kingdom. E-mail:
[email protected] Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/uhte.
detectors. In microevaporators, annular flow is even more conspicuous than in macrochannels, since annular flow relegates bubbly and slug flows to only the first 3–10% of the vapor quality range. In convective condensation, annular flow is established almost immediately at the inlet of the channel and persists over most of the condensation process until the condensate floods the channel. The purpose of this paper is to present the unified modeling suite for annular flow that the authors have and continue to develop, focusing in particular on the prediction of the heat transfer coefficient during convective evaporation and condensation in tubes, and the prediction of the pressure drop and the heat transfer coefficient during convective evaporation in noncircular multi-microchannels that are typical of microscale heat sinks. At present, the unified annular flow modeling suite includes methods to predict the entrained liquid fraction, the void fraction, the wall shear stress, and the frictional and total pressure gradients, and a turbulence model for momentum and heat transport inside the annular liquid film that allows one method for the prediction of the local average liquid film thickness and the local heat transfer coefficient during both convective evaporation and condensation, taking into account the
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asymmetric distribution of the liquid film along the tube perimeter in horizontal channels (Cioncolini et al. [1, 2], Cioncolini and Thome [3–6], and Mauro et al. [7]). The heat transfer methods have been adapted to noncircular (high-aspect-ratio rectangular and square) microchannels, as well as the microchannels in a multiport aluminum tube, without changing the underlying equations but just stretching the liquid film to the noncircular channel cross section. The practical advantage of a unified modeling suite is that all the included prediction methods are consistently formulated and are proven to work well together.
selt number based on the average liquid film thickness t, Prl is the liquid Prandtl number, and t+ is the dimensionless liquid film thickness expressed in wall coordinates and defined as τw t ρl V ∗ t ∗ μl + ∗ ; y = ; V = (2) t = ∗ = ∗ y μl ρl V ρl
OVERVIEW OF THE ANNULAR FLOW MODELS
where the liquid film Reynolds number Relf is defined as
In the flow boiling literature, most methods segregate the nucleate boiling and convective boiling contributions and then develop individual methods for each, and then use some form of superposition method to add them together to obtain their combined influence on the local flow boiling heat transfer coefficient. As such, Cioncolini and Thome [3] focused on convective evaporation in annular flow in the absence of wall nucleation and proposed a new algebraic turbulence model for the transport of linear momentum and heat through the annular liquid film. Algebraic models are simple turbulence models that rely on the Boussinesq assumption and consider the turbulent shear stress to be proportional to the symmetric part of the mean velocity gradient and the turbulent heat flux to be proportional to the mean temperature gradient. The constants of proportionality are flow dependent and are expressed with empirically derived algebraic relations that involve the length scale of the mean flow. In contrast with single-phase wall-bounded flow theory, normally extrapolated to two-phase flows in most existing studies, the authors assumed that the flow in the shear-driven annular liquid film is mostly affected by the interaction of the liquid film with the shearing gas-entrained droplet core flow. In other words, the liquid film was assumed to behave as a fluid-bounded flow, such as a jet or a wake, with a negligible influence of the bounding channel wall. Since the characteristic length scale of jets and wakes is normally assumed to be proportional to their width, the characteristic length scale of the liquid film was thus assumed to be proportional to its average thickness, instead of the distance from the channel wall used in single-phase wall-bounded turbulent flows. The heat transfer equation proposed by the authors for convective evaporation and condensation in annular flow reads as follows: ht = 0.0776 t + 0.90 Prl0.52 Nu = kl +
10 ≤ t ≤ 800; 0.86 ≤ Prl ≤ 6.1
where ρl and μl are the liquid density and viscosity, y∗ and V ∗ are the length and velocity wall scales, and τw is the wall shear stress. According to the authors, the dimensionless liquid film thickness is empirically predicted as follows: Rel f + , 0.0165 Rel f (3) t = max 2
Rel f = (1 − e) (1 − x)
where h is the convective evaporation or condensation heat transfer coefficient, kl is the liquid thermal conductivity, Nu is a Nusheat transfer engineering
(4)
where e is the entrained liquid fraction, x the vapor quality, G the total mass flux, and d the tube diameter. The prediction method for the average liquid film thickness in Eq. (3) expresses the conservation of mass for the annular liquid film. As described by the authors [3], this prediction method is kept mathematically simple to allow an analytical solution of the heat transfer model equations, avoiding numerical calculations that would make the model more complicated to implement in practical applications. As can be seen, Eq. (1) is formally analogous to a Dittus–Boelter like heat transfer equation, since the dimensionless liquid film thickness t+ can be interpreted as a Reynolds number for the liquid film with the velocity wall scale V ∗ as characteristic velocity and the average liquid film thickness t as the characteristic dimension. The wall shear stress τw that is required as input in Eq. (2) to calculate the velocity wall scale V ∗ is predicted according to Cioncolini et al. [2] as follows: ft p =
2 τw = 0.172 W ec−0.372 ρc Vc2 f or Bo ≥ 4
ft p =
(macr ochannels)
(5)
2 τw = 0.0196 W ec−0.372 Rel0.318 f ρc Vc2 f or Bo ≤ 4
(micr ochannels)
(6)
where ftp is the two-phase Fanning friction factor. The dropletladen core flow density ρc and average core velocity Vc are calculated neglecting the slip between the carrier gas phase and the entrained liquid droplets as follows: ρc =
(1)
Gd μl
x + e (1 − x) x ρg
+
e (1−x) ρl
; Vc =
Jg xG ; Jg = ε ρg
(7)
where Jg is the vapor superficial velocity and ε the crosssectional void fraction. The core flow Weber number Wec and vol. 37 no. 13–14 2016
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the Bond number Bo are defined as W ec =
ρc Jg2 d
σ g ρl − ρg d 2 Bo = σ
(8)
(9)
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where σ is the surface tension and g the acceleration of gravity. The entrained liquid fraction e required as input into Eqs. (4) and (7) is predicted according to Cioncolini and Thome [5] as follows: −2.209 e = 1 + 279.6 W ec−0.8395 f or
101 < W ec < 105
(10)
The void fraction ε required as input in Eq. (7) is predicted according to Cioncolini and Thome [4] as follows: ε=
h xn 1 + (h − 1) x n
0 < x < 1; 10−3 < ρg ρl−1 < 1; 0.7 < ε < 1
(11)
Figure 1 Convective boiling heat transfer coefficient vs. vapor quality for R22 data of Shin et al. [8] (heat flux: 25.0 kW/m2; saturation temperature: 285 K/12◦ C; tube diameter: 7.7 mm).
Selected results for convective evaporation and condensation in both circular and noncircular tubes and multi-microchannels are presented next.
where the parameters h and n are h = −2.129 + 3.129 (ρg ρl−1 )−0.2186 n = 0.3487 + 0.6513 (ρg ρl−1 )0.5150
RESULTS FOR CIRCULAR TUBES (12)
Using the two-phase Fanning friction factor given by either Eq. (5) or Eq. (6) together with Eq. (8) for the core Weber number, the two-phase frictional pressure gradient is calculated as follows: 2 ft p dP 4 τw = ρc Vc2 = (13) dz f r d d
Selected convective evaporation results are presented in Figures 1–4. As can be seen, the vapor quality is in the range of 0.2–0.8, which is typical of annular flow. In particular, convective boiling data for refrigerant R22 of Shin et al. [8] are compared with the predictions of the convective heat transfer model of Cioncolini and Thome [3] in Figures 1 and 2, while convective boiling data for water–steam of Kenning and Cooper [9] and model predictions are presented in Figures 3 and 4. As
For inclined flow, the gravitational pressure gradient is calculated as
dP = ρl (1 − ε) + ρg ε g sin(θ) (14) dz gr where θ is the channel inclination with respect to the horizontal (θ = 0 for horizontal flow), while the acceleration pressure gradient is calculated as follows: ⎧ ⎫ 2 2 (1 − e) (1 − x) x ⎪ ⎪ ⎪ +⎪ ⎨ ⎬ dP (1 − ε) x ρ 2 d l (15) =G 2 x ⎪ e x (1 − x) dz acc dz ⎪ ⎪ ⎪ + ⎩ ⎭ ε ρg ε ρg The unified annular flow modeling suite is currently based on a large experimental databank collected from 99 literature studies that contains 11,498 data points, and additional work is being performed to expand the underlying database and further improve the annular flow models. heat transfer engineering
Figure 2 Convective boiling heat transfer coefficient vs. vapor quality for R22 data of Shin et al. [8] (mass flux: 742 kg/m2-s; saturation temperature: 285 K/12◦ C; tube diameter: 7.7 mm).
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Figure 3 Convective boiling heat transfer coefficient vs. vapor quality for H2 O data of Kenning and Cooper [9] (mass flux: 135 kg/m2-s; saturation temperature: 417 K/144◦ C; tube diameter: 14.4 mm).
Figure 5 Convective condensation heat transfer coefficient vs. vapor quality for R236ea data of Cavallini et al. [10] (saturation temperature: 313 K/40◦ C; tube diameter: 8.0 mm).
can be noticed in Figures 1–4, the heat flux is low enough to neglect nucleate boiling and assume purely convective evaporation, so that the present heat transfer model is applicable. As can be seen, the comparison is for the most part quite satisfactory, although the water-steam data in Figure 4 are 10–15% overpredicted. Since this heat transfer model does not account for nucleate boiling, one would expect some underprediction of the data, rather than overprediction. As a 10–15% deviation is small and comparable with the measuring errors typical of boiling two-phase flow experiments, the results in Figure 4 are considered satisfactory. In particular, the authors’ convective heat transfer model predicts a dependence of the heat transfer coefficient on mass flux but not on heat flux, as typically happens with convective boiling when wall nucleation is suppressed. Selected convective condensation results are presented in
Figures 5–8. As can be seen, the vapor quality is in the range of 0.2–0.9, which is typical of annular flow. In particular, convective condensation data for refrigerants R236ea, R134a, and R22 of Cavallini et al. [10] are compared with the predictions of the convective heat transfer model of Cioncolini and Thome [3] in Figures 5–7, while convective condensation microscale data for R134a of Matkovic et al. [11] and model predictions are presented in Figure 8. As can be seen, the comparison is for the most part quite satisfactory, although the microscale R134a data in Figure 8 are underpredicted at high vapor quality. The currently ongoing improvement of the wall shear stress prediction method of Eqs. (5) and (6) with the inclusion into the underlying database of more microscale data to better resolve viscous dissipation within the liquid film is expected to improve the performance of the heat transfer model with microchannels at high
Figure 4 Convective boiling heat transfer coefficient vs. vapor quality for H2 O data of Kenning and Cooper [9] (mass flux: 304 kg/m2-s; saturation temperature: 393 K/120◦ C; tube diameter: 9.6 mm).
Figure 6 Convective condensation heat transfer coefficient vs. vapor quality for R134a data of Cavallini et al. [10] (saturation temperature: 313 K/40◦ C; tube diameter: 8.0 mm).
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Figure 7 Convective condensation heat transfer coefficient vs. vapor quality for R22 data of Cavallini et al. [10] (saturation temperature: 313 K/40◦ C; tube diameter: 8.0 mm).
mass flux and vapor quality. At present, in fact, the databank used to derive the friction model of Eqs. (5) and (6) is biased toward macrochannels.
Figure 9 Silicon multi-microchannel test section used by Costa-Patry et al. [12–14]: cut view of the evaporator channels (135 parallel channels, height: 560 μm; width: 85 μm; aspect ratio: 6.56; hydraulic diameter: 136 μm; fin thickness: 47 μm; channels length: 12.7 mm).
Based on available data, the annular flow models for the wall shear stress, the entrained liquid fraction, and the void fraction previously discussed can be extrapolated to noncircular channels using the hydraulic diameter dh (dh = 4 Aflow Pwet −1, where Aflow is the flow area and Pwet the wetted perimeter) in place of the tube diameter, as described in the cited papers. For what concerns the convective evaporation heat transfer model,
Costa-Patry et al. [12–14] proposed a simple adaptation of the Cioncolini and Thome [3] annular flow method for evaporation for circular channels to noncircular shapes, that is, high-aspectratio rectangular fins in silicon and copper in particular. VakiliFarahani et al. [15] and Szczukiewicz et al. [16] also found that this adaption works well for noncircular microchannels for an aluminum multiport tube test section and for a multimicrochannel test section with square channels of only 100 by 100 μm, respectively. These adaptions and comparisons are discussed in the following. It is worth highlighting that the data of Costa-Patry et al. [12–14], Vakili-Farahani et al. [15], and Szczukiewicz et al. [16] are independent and were not used in the development of the annular flow models. In a circular channel, the original method balances the forces in the channel to calculate a radial film thickness, while in a noncircular (rectangular, for instance) channel this film must be redistributed to the actual channel perimeter, keeping the same area proportion between the shapes and to conserve the liquid cross-sectional area proportions. To do this, the equivalent diameter deq is used, which is the diameter of an equivalent circular channel with the same cross-sectional area as the noncircular
Figure 8 Convective condensation heat transfer coefficient vs. vapor quality for R134a data of Matkovic et al. [11] (saturation temperature: 313 K/40◦ C; tube diameter: 0.96 mm).
Figure 10 Boiling two-phase flow results of Costa-Patry et al. [12, 13]: predictions vs. measurements for the pressure drop under uniform heat flux conditions (fluids: R236fa and R245fa; saturation temperature: 303 K/30◦ C).
RESULTS FOR NONCIRCULAR MICROCHANNELS
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Figure 11 Boiling two-phase flow results of Costa-Patry et al. [12, 13]: predictions vs. measurements for the heat transfer coefficient under uniform heat flux conditions (fluids: R236fa and R245fa; saturation temperature: 303 K/30◦ C).
one; a hydraulic diameter in fact has no apparent physical meaning in an annular flow with its liquid film. As a consequence of this adaptation, the average film thickness in the noncircular channel is less than the circular one since the liquid film of the equivalent diameter’s perimeter is stretched to the perimeter of the actual channel to maintain the same cross-sectional area of the liquid within the channel—essentially, since the thermal resistance across the film determines the annular flow heat transfer coefficient, this is a simple correction to implement while ignoring capillary forces in any corners. In practice, the liquid film thickness is first calculated for the equivalent circular pipe, and then the cross-sectional area Alf taken by the circular film is calculated as
π 2 Al f = (16) d − (deq − 2t)2 4 eq Since the liquid film must occupy the same area in the noncircular shape as in the circular channel, the liquid film thickness in the noncircular channel is found by dividing the liquid film cross-sectional area by the noncircular channel perimeter (t = Alf Pwet −1). The Nusselt number calculated by the method is finally transformed into a heat transfer coefficient by dividing it by this noncircular channel liquid film thickness. In contrast, for predicting two-phase frictional pressure drops in noncircular channels, the unified annular flow suite is applied using directly the hydraulic diameter in place of the circular diameter without further modification. In this case, the frictional
Figure 12 Boiling two-phase flow results of Costa-Patry et al. [14]: predictions vs. measurements for the heat transfer coefficient under nonuniform heat flux conditions (fluid: R245fa; saturation temperature: 303 K/30◦ C).
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pressure gradient is dependent on the interfacial shear between the vapor core and the annular liquid film, but not on the liquid film thickness, in Eqs. (5) and (6). Hence, both heat transfer and two-phase frictional pressure drops were adapted to noncircular flow channels without adding or changing any numerical values in the annular flow suite’s methods. In order to handle the other relevant flow regimes in microscale channels, notably isolated bubble flow and elongated bubble flow, these annular flow models have been recently combined (Costa-Patry et al. [12–14], Vakili-Farahani et al. [15], and Szczukiewicz et al. [16]) with the Lockhart and Martinelli [17] method to predict the pressure gradient in both in the isolated bubble flow regime and in the elongated bubble flow regime, and with the Cooper [18] nucleate pool boiling correlation and the Thome et al. [19] three-zone convective heat transfer model to predict the heat transfer coefficient in the isolated bubble flow regime and in the elongated bubble flow regime, respectively. The three-zone heat transfer model, in particular, treats evaporation of elongated bubbles in microchannels as a cyclic passage of a liquid slug, an evaporating elongated bubble, and a vapor slug, which is assumed to appear when the liquid film thickness near the bubble tail reaches the same value as the surface roughness of the channel. The transition from isolated bubble flow to elongated bubble flow and from elongated bubble flow to annular flow is predicted according to the microscale flow map of Ong and Thome [20]. Operatively, the microscale flow map of Ong and Thome [20] is first used to predict the flow pattern, which depending on the local flow conditions can be (1) isolated bubble flow, (2) elongated bubble flow, or (3) annular flow. If the flow pattern is isolated bubble flow, then the Lockhart and Martinelli [17] method is used to predict the pressure gradient, while the Cooper [18] nucleate pool boiling correlation is used to predict the heat transfer coefficient. If the flow pattern is elongated bubble flow, then the Lockhart and Martinelli [17] method is used to predict the pressure gradient, while the Thome et al. [19] three-zone model is used to predict the heat transfer coefficient. Finally, the authors’ annular flow models already described are used if the flow pattern is annular flow. Costa-Patry et al. [12–14] investigated two-phase flow evaporation of refrigerants R245fa and R236fa flowing in 135 highaspect-ratio silicon multi-microchannels, as shown in Figure 9. The channels were 85 μm wide, 560 μm high, aspect ratio of 6.56, hydraulic diameter of 136 μm, 12.7 mm long, and separated by 47-μm-wide fins. The multi-microchannels were electrically heated with 35 local heaters that could be operated independently, thus allowing tests to be performed with both uniform and nonuniform heating to more closely reproduce the heat load of actual microchips. Measurements carried out under uniform heat flux conditions for the pressure drop and the heat transfer coefficient are compared with the predictions of the annular flow models extended to noncircular microchannels in Figures 10 and 11. As can be seen, the agreement between measured data and predictions is quite satisfactory. Heat transfer coefficients measured under nonuniform heat flux conditions vol. 37 no. 13–14 2016
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Figure 14 Flat aluminum extruded multiport tube used by Vakili-Farahani et al. [15] (7 parallel rectangular channels, height: 1.1 mm; width: 2.1 mm; aspect ratio: 1.91; hydraulic diameter: 1.4 mm; equivalent diameter: 1.7 mm; channel length: 280 mm).
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are compared with the annular flow models predictions in Figure 12. In particular, both hot-spot and hot-row heat flux profiles have been tested, as shown in Figure 13, and implementing a heat-spreading data reduction procedure to obtain the local heat transfer coefficients. Although less accurate than with uniform heating, the annular flow models extended to noncircular microchannels predict the nonuniform heating data with a mean average error of less than 30%, which is quite good when taking into account the larger experimental uncertainty found in nonuniform heat flux situations. Vakili-Farahani et al. [15] carried out two-phase flow evaporation experiments with refrigerants R245fa and R1234ze(E) in the flat aluminum extruded multi-port tube shown in Figure 14. The multiport tube was composed of 7 parallel rectangular channels 1.1 mm wide, 2.1 mm high, aspect ratio of 1.91, equivalent diameter of 1.7 mm, and 280 mm long. The channels were fluid heated with a hot-water jacket on both sides. The system tested was a prototype cooling element for a two-phase thermosyphon electronics cooling system, which has since been commercialized by ABB for 15-MVA transformers with up to 112 kW of cooling load. Measurements of their heat transfer coefficients are compared with the predictions of the annular flow model suite extended to noncircular microchannels in Figure 15. As can be seen, the agreement between measured data and predictions is quite satisfactory; the overpredictions at higher values are thought to come from test conditions that have surpassed the onset of partial dryout; that is, the center faces of the channel walls may become dry during evaporation. Szczukiewicz et al. [16] investigated two-phase flow evaporation of refrigerants R245fa, R236fa, and R1234ze(E) flowing in 67 square-cross-section, silicon multi-microchannels, as shown in Figure 16. The channels were 100 × 100 μm size, aspect
Figure 13 Nonuniform heat flux profiles tested by Costa-Patry et al. [14]: hotspot (top), hot-row aligned with the flow (middle), and hot-row perpendicular to the flow (bottom).
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Figure 15 Boiling two-phase flow results of Vakili-Farahani et al. [15]: predictions vs. measurements for the heat transfer coefficient (fluids: R245fa and R1234ze(E); saturation temperature: 303–343 K/30–70◦ C).
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Figure 17 Boiling two-phase flow results of Szczukiewicz et al. [16]: predictions vs. measurements for the heat transfer coefficient under uniform heat flux conditions (fluids: R236fa, R245fa, and R1234ze(E); saturation temperature: 305 K/32◦ C).
in Figure 15, the underprediction in Figure 17 might be due to measuring errors. Comparing the single-channel results in Figures 1–8 with the multichannel results in Figures 11–17, it can be noticed that the present annular flow models are more accurate in single-channel configurations. This is no surprise, as multichannel configurations are more difficult to analyze due to several additional phenomena not accounted for in the annular flow models, such as axial conduction, conjugate heat transfer, uneven flow distribution, and interactions among different channels.
CONCLUSIONS
Figure 16 Silicon multi-microchannel test section used by Szczukiewicz et al. [16]: detail of the evaporator channels with inlet restrictions to stabilize the flow (67 parallel square channels, height: 100 μm; width: 100 μm; aspect ratio: 1.0; hydraulic diameter: 100 μm; fin thickness: 50 μm; channels length: 10.0 mm).
ratio of 1.0, hydraulic diameter of 100 μm, 10.0 mm long, and separated by 50-μm-wide fins. Electrical heating with uniform heat flux was used in the tests. The system tested was one layer of a future three-dimensional integrated circuit stacked architecture with interlayer cooling, and was part of the CMOSAIC–3D Stacked Architectures with Interlayer Cooling project, where the aim was to provide two-phase cooling to a high-performance, three-dimensional stacked computer chip that will eventually compress almost 1012-nm-sized functional units into a volume of 1 cm3 with a 10- to 100-fold higher connectivity than otherwise possible (Sabry et al. [21]). Measurements carried out under uniform heat flux conditions for the heat transfer coefficient are compared with the predictions of the annular flow models extended to noncircular microchannels in Figure 17. As can be seen, the agreement between measured data and predictions is quite satisfactory for R236fa and R245fa, while the R1234ze(E) data are somewhat underpredicted. Since R1234ze(E) data are correctly reproduced heat transfer engineering
The unified modeling suite for annular two-phase flow that the authors have developed and continue to develop was presented, illustrating in particular its application to noncircular microchannels. The convective heat transfer model was then compared with selected measurements for convective evaporation and condensation in tubes and with additional data obtained by the LTCM lab for refrigerant convective evaporation in noncircular multi-microchannels configurations for electronics cooling. Satisfactory agreement was found between data and predictions. This unified modeling suite provides a robust set of methods that are so far proven to work well together in a situation where the various flow parameters are interrelated and provides a basis for future additional developments.
Nomenclature Bo d e ftp g G h Jg kl
Bond number, dimensionless tube diameter, m entrained liquid fraction, dimensionless two-phase Fanning friction factor, dimensionless acceleration of gravity, m s−2 mass flux, kg m−2 s−1 heat transfer coefficient, W m−2 K−1 superficial gas velocity, m s−1 liquid thermal conductivity, W m−1 K−1
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Nu Prl Relf t t+
Nusselt number, dimensionless liquid Prandtl number, dimensionless liquid film Reynolds number, dimensionless average liquid film thickness, m dimensionless average liquid film thickness, dimensionless Vc core flow velocity, m s−1 V∗ velocity wall scale, m s−1 Wec core flow Weber number, dimensionless x vapor quality, dimensionless y∗ length wall scale, m
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Greek Symbols ε θ τw μl ρc ρg ρl σ
cross-sectional void fraction, dimensionless tube inclination with respect to the horizontal, rad wall shear stress, Pa liquid viscosity, kg m−1 s−1 core density, kg m−3 vapor density, kg m−3 liquid density, kg m−3 surface tension, kg s−2
REFERENCES [1] Cioncolini, A., Thome, J. R., and Lombardi, C., Algebraic Turbulence Modeling in Adiabatic Gas–Liquid Annular Two-Phase Flow, International Journal of Multiphase Flow, vol. 35, pp. 580–596, 2009. [2] Cioncolini, A., Thome, J. R., and Lombardi, C., Unified Macro-to-Microscale Method to Predict Two-Phase Frictional Pressure Drops of Annular Flows, International Journal of Multiphase Flow, vol. 35, pp. 1138–1148, 2009. [3] Cioncolini, A., and Thome, J. R., Algebraic Turbulence Modeling in Adiabatic and Evaporating Annular TwoPhase Flow, International Journal of Heat and Fluid Flow, vol. 32, pp. 805–817, 2011. [4] Cioncolini, A., and Thome, J. R., Void Fraction Prediction in Annular Two-Phase Flow, International Journal of Multiphase Flow, vol. 43, pp. 72–84, 2012. [5] Cioncolini, A., and Thome, J. R., Entrained Liquid Fraction Prediction in Adiabatic and Evaporating Annular TwoPhase Flow, Nuclear Engineering and Design, vol. 243, pp. 200–213, 2012. [6] Cioncolini, A., and Thome, J. R., Liquid Film Circumferential Asymmetry Prediction in Horizontal Annular TwoPhase Flow, International Journal of Multiphase Flow, vol. 51, pp. 44–54, 2013. [7] Mauro, A. W., Cioncolini, A., Thome, J. R., and Mastrullo, R., Asymmetric Annular Flow in Horizontal Circular Macro-Channels: Basic Modeling of the Liquid Film Distribution and Heat Transfer Around the Tube Perimeter in Convective Boiling, International Journal of Heat and Mass Transfer, vol. 77, pp. 897–905, 2014. heat transfer engineering
[8] Shin, J. Y., Kim, M. S., and Ro, S. T., Experimental Study on Forced Convective Boiling Heat Transfer of Pure Refrigerants and Refrigerant Mixtures in a Horizontal Tube, International Journal of Refrigeration, vol. 20, pp. 267–275, 1997. [9] Kenning, D. B. R., and Cooper, M. G., Saturated Flow Boiling of Water in Vertical Tubes, International Journal of Heat and Mass Transfer, vol. 32, pp. 445–458, 1989. [10] Cavallini, A., Censi, G., Del Col, D., Doretti, L., Longo, G. A., and Rossetto, L., Experimental Investigation on Condensation Heat Transfer and Pressure Drop on New HFC Refrigerants (R134a, R125, R32, R410a, R236ea) in a Horizontal Smooth Tube, International Journal of Refrigeration, vol. 24, pp. 73–87, 2001. [11] Matkovic, M., Cavallini, A., Del Col, D., and Rossetto, L., Experimental Study on Condensation Heat Transfer Inside a Single Circular Minichannel, International Journal of Heat and Mass Transfer, vol. 52, pp. 2311–2323, 2009. [12] Costa-Patry, E., Olivier, J., Nichita, B., Michel, B., and Thome, J. R., Two-Phase Flow of Refrigerants in 85-μmWide Multi-Microchannels, Part I: Pressure Drop, International Journal of Heat and Fluid Flow, vol. 32, pp. 451–463, 2011. [13] Costa-Patry E., Olivier, J., Michel, B., and Thome, J. R., Two-Phase Flow of Refrigerant in 85 μm-Wide MultiMicrochannels: Part II: Heat Transfer With 35 Local Heaters, International Journal of Heat and Fluid Flow, vol. 32, pp. 464–476, 2011. [14] Costa-Patry, E., Nebuloni, S., Olivier, J., and Thome, J. R., On-Chip Two-Phase Cooling With Refrigerant 85 μmWide Multi-Microchannel Evaporator Under Hot-Spot Conditions, IEEE Transactions on Components Packaging and Manufacturing Technology, vol. 2, pp. 311–320, 2012. [15] Vakili-Farahani, F., Agostini, B., and Thome, J. R., Experimental Study on Flow Boiling Heat Transfer of Multiport Tubes With R245fa and R1234ze(E), ECI 8th International Conference on Boiling and Condensation Heat Transfer, Lausanne, Switzerland, 3–7 June 2012, paper number 1480, 2012. [16] Szczukiewicz, S., Borhani, N., and Thome, J. R., FineResolution Two-Phase Flow Heat Transfer Coefficient Measurements of Refrigerants in Multi-Microchannel Evaporators, International Journal of Heat and Mass Transfer, vol. 67, pp. 913–929, 2013. [17] Lockhart, R. W., and Martinelli, R. C., Proposed Correlation of Data for Isothermal Two-Phase, Two-Component Flow in Pipes, Chemical Engineering Progress, vol. 45, pp. 39–48, 1949. [18] Cooper, M. G., Heat Flow Rates in Saturated Nucleate Pool Boiling—A Wide Ranging Examination Using Reduced Properties, Advances in Heat Transfer, vol. 16, pp. 157–239, 1984. [19] Thome, J. R., Dupont, V., and Jacobi, A. M., Heat Transfer Model for Evaporation in Microchannels. Part I: Presentavol. 37 no. 13–14 2016
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tion of the Model, International Journal of Heat and Mass Transfer, vol. 47, pp. 3387–3401, 2004. [20] Ong, C. L., and Thome, J. R., Macro-to-Microchannel Transition in Two-Phase Flow: Part I—Two Phase Flow Patterns and Film Thickness Measurements, Experimental Thermal and Fluid Science, vol. 35, pp. 37–47, 2011. [21] Sabry, M. M., Sridhar, A., Atienza, D., Temiz, Y., Leblebici, Y., Szczukiewicz, S., Borhani, N., Thome, J. R., Brunschwiler, T., and Michel, B., Towards ThermallyAware Design of 3D MPSoCs With Inter-Tier Cooling, In Design, Automation and Test in Europe, Grenoble, France, 14–18 March 2011. John R. Thome has been since 1998 a professor of heat and mass transfer at the Swiss Federal Institute of Technology in Lausanne (EPFL), Switzerland, where he is director of the Laboratory of Heat and Mass Transfer (LTCM) in the Faculty of Engineering Science and Technology (STI). His primary interests of research are two-phase flow and heat transfer, covering boiling and condensation of internal flows, external flows, enhanced surfaces, and microchannels. He received his Ph.D. at Oxford University, England, in
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1978 and was formerly a professor at Michigan State University. He is the author of several books: Enhanced Boiling Heat Transfer (1990), Convective Boiling and Condensation (1994), and Wolverine Engineering Databook III (2004). He received the ASME Heat Transfer Division’s Best Paper Award in 1998 for a three-part paper on flow boiling heat transfer published in the Journal of Heat Transfer.
Andrea Cioncolini is an assistant professor/lecturer at the School of Mechanical, Aerospace and Civil Engineering of the University of Manchester, UK. His research interests are single- and two-phase flow thermal fluid dynamics, both macro- and microscale, boiling and condensation, and fluid systems transient analysis. He received his Laurea degree and Ph.D. in nuclear engineering at the Polytechnic University of Milan, Italy. He joined the University of Manchester after 6 years as a postdoc researcher at the Laboratory of Heat and Mass Transfer (LTCM) at the Swiss Federal Institute of Technology in Lausanne, Switzerland (EPFL), and after 2 years as a senior engineer/scientist at Westinghouse Electric Company, Science and Technology Department in Pittsburgh, PA.
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