Heat Transfer Mechanisms During Flow Boiling in

Heat Transfer Mechanisms During Flow Boiling in Microchannels

Satish G. Kandlikar e-mail: [email protected] Thermal Analysis and Microfluidics Laboratory, Department of Mechanical Engineering, Rochester Institute of Technology, Rochester, NY 14623

The forces due to surface tension and momentum change during evaporation, in conjunction with the forces due to viscous shear and inertia, govern the two-phase flow patterns and the heat transfer characteristics during flow boiling in microchannels. These forces are analyzed in this paper, and two new nondimensional groups, K1 and K2 , relevant to flow boiling phenomenon are derived. These groups are able to represent some of the key flow boiling characteristics, including the CHF. In addition, a mechanistic description of the flow boiling phenomenon is presented. The small hydraulic dimensions of microchannel flow passages present a large frictional pressure drop in single-phase and two-phase flows. The small hydraulic diameter also leads to low Reynolds numbers, in the range 100–1000, or even lower for smaller diameter channels. Such low Reynolds numbers are rarely employed during flow boiling in conventional channels. In these low Reynolds number flows, nucleate boiling systematically emerges as the dominant mode of heat transfer. The high degree of wall superheat required to initiate nucleation in microchannels leads to rapid evaporation and flow instabilities, often resulting in flow reversal in multiple parallel channel configuration. Aided by strong evaporation rates, the bubbles nucleating on the wall grow rapidly and fill the entire channel. The contact line between the bubble base and the channel wall surface now becomes the entire perimeter at both ends of the vapor slug. Evaporation occurs at the moving contact line of the expanding vapor slug as well as over the channel wall covered with a thin evaporating film surrounding the vapor core. The usual nucleate boiling heat transfer mechanisms, including liquid film evaporation and transient heat conduction in the liquid adjacent to the contact line region, play an important role. The liquid film under the large vapor slug evaporates completely at downstream locations thus presenting a dryout condition periodically with the passage of each large vapor slug. The experimental data and high speed visual observations confirm some of the key features presented in this paper. 关DOI: 10.1115/1.1643090兴 Keywords: Boiling, Bubble Growth, Heat Transfer, Interface, Microscale

Introduction It has been well recognized that the flow boiling heat transfer consists of a nucleate boiling component and a convective boiling component, e.g., Schrock and Grossman 关1兴. The convective boiling component results from the convective effects, whereas the nucleate boiling component results from the nucleating bubbles and their subsequent growth and departure at the heated surface. The nucleate boiling and the convective boiling mechanisms cannot be distinguished precisely, as they are closely interrelated. The nucleation, growth and subsequent departure of bubbles from a heated wall constitute the major stages of a bubble ebullition cycle in pool boiling. The heat transfer mechanisms associated with pool boiling include: transient conduction, film vaporization, microconvection, contact line heat transfer, and to a lesser degree, the vaporization condensation, and Marangoni convection. The bubble dynamics under flow boiling conditions are affected in such a way as to shift toward smaller nucleation cavity sizes and smaller departure bubble diameters. In this paper, the forces governing the liquid vapor interface in microchannels during flow boiling are analyzed and two new dimensionless groups are identified. The role of nucleate boiling is re-examined and the heat transfer mechanisms are discussed. The high-speed flow visualization conducted by the author and his co-workers and the experimental heat transfer data from literature are used in arriving at the mechanistic description of the flow boiling phenomena in microchannels. In this paper, the channel classification proposed by Kandlikar Contributed by the Heat Transfer Division for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received by the Heat Transfer Division February 20, 2003; revision received September 24, 2003. Associate Editor: M. K. Jensen.

8 Õ Vol. 126, FEBRUARY 2004

and Grande 关2兴 is used. This classification should be used as a mere guide indicating the size range, rather than rigid demarcations based on specific criteria. In reality, the effects will depend on fluid properties and their variation with pressure changes. Undoubtedly, the actual flow conditions, such as single phase liquid or gas flow, or flow boiling or flow condensation, will present different classification criteria. The classification by Kandlikar and Grande is based on rarefaction effects for common gases around 1 atmospheric pressure. At smaller dimensions below about 10 ␮m, molecular effects begin to be important, again subject to specific operating conditions. Molecular nanochannels are still very large compared to the molecular dimensions, but the intermolecular forces begin to play an important role especially in the near wall region. In two-phase applications, recently Kawaji and Chung 关3兴 reported significant departure for their 100 ␮m microchannels from the linear relationship between volumetric quality versus void fraction proposed by Ali et al. 关4兴 for narrow channels. Conventional channels: ⬎3 mm Minichannels: 3 mm⭓Dh⬎200 ␮ m Microchannels: 200 ␮ m⭓Dh⬎10 ␮ m Transitional Channels: 10 ␮ m⭓Dh⬎0.1 ␮ m 共100 nanometer, nm, or 1000 Å兲 Transitional Microchannels: 10 ␮ m⭓Dh⬎1 ␮ m Transitional Nanochannels: 1 ␮ m⭓Dh⬎0.1 ␮ m Molecular Nanochannels: 0.1 ␮ m⭓Dh

Review of Available Non-Dimensional Groups Related to Two-Phase Flow and Interfacial Phenomena Before deriving the relevant new non-dimensional groups in microchannels, the existing groups commonly applied in the two-

Copyright © 2004 by ASME

Transactions of the ASME

Table 1 Non-dimensional Groups relevant to two-phase flow studies in microchannels Non-dimensional number Martinelli parameter, X dp dp X2⫽ dz F dz F

冉冏冏冊冒冉冏冏冊 L

G

Convection Number, Co Co⫽ 关 (1⫺x)/x 兴 0.9关 ␳ G / ␳ L 兴 0.5 Boiling number, Bo q Bo⫽ G hfg Bond number, Bo g共 ␳ L⫺ ␳ G 兲D 2 Bo⫽ ␴ Eo¨tvo¨s Number, Eo g共 ␳ L⫺ ␳ G 兲L 2 Eo⫽ ␴ Capillary number, Ca ␮V Ca⫽ ␴ Ohnesorge Number, Z ␮ Z⫽ 共␳ L ␴兲1/2 Weber Number, We L G2 We⫽ ␳ ␴ Jakob Number, Ja ␳ L c p,L ⌬T Ja⫽ ␳ hfg V

Significance

Relevance to Microchannels

Groups based on Empirical Considerations Because of its success in predicting pressure drop in Represents the Ratio of frictional pressure drops with compact evaporator geometries, it is expected to be a useful liquid and gas flow. It has been employed successfully parameter in microchannels as well. in two-phase pressure drop models in simple as well as complex geometries Co is a modified Martinelli parameter, introduced by Its direct usage beyond flow boiling correlation may be Shah 关5兴 in correlating flow boiling data limited. Since it combines two important flow parameters, q and G, Heat flux is non-dimensionalized with mass flux and it will be used in empirical treatment of flow boiling. latent heat. It is not based on any fundamental considerations. Groups based on Fundamental Considerations Since the effect of gravitational force is expected to be Bo represents the ratio of buoyancy force to surface small, Bo is not expected to play an important role in tension force. Used in droplet atomization and spray microchannels. applications. Eo¨tvo¨s number is similar to the Bond number, except that the characteristic dimension L could be D h or any other physically relevant parameter.

Similar to Bo, Eo is not expected to be important in microchannels except at very low flow velocities and vapor fractions.

Ca represents the ratio of viscous to surface tension forces. It is useful in analyzing the bubble removal process.

Ca is expected to play a critical role as both the surface tension and the viscous forces are important in microchannel flows.

Z represents the ratio of the viscous force to the square root of the product of the inertia and the surface tension forces. It is used in analyzing liquid droplets and droplet atomization processes. We represents the ratio of the inertia to the surface tension forces. For flow in channels, D h is used in place of L.

The combination of the three forces into one masks the individual effects of each force. Although Z may come out as an important variable, it may not be suitable in the early stages of microchannel research. We I useful in studying the relative effects of surface tension and inertia forces on flow patterns in microchannels.

Ja represents the ratio of the sensible heat for a given volume of liquid to heat or cool through ⌬T in reaching its saturation temperature, to the latent heat required in evaporating the same volume of vapor.

Ja may be used as an important parameter in studying the effects of liquid superheat prior to initiation of nucleation in microchannels. It may also be useful in studying the subcooled boiling conditions.

phase and flow boiling applications are reviewed in this section. Non-dimensional groups are useful in arriving at key basic relations among system variables that are valid for different fluids under different operating conditions. Some of these groups have been derived empirically, often on the basis of experimental data. Fundamental considerations of the governing forces and their mutual interactions lead to non-dimensional groups that provide important insight into the physical phenomena. A listing of both types of non-dimensional groups, based on empirical considerations and on theoretical analysis of forces, is given in Table 1. A brief description of their significance along with their relevance to flow boiling in microchannels is also included in the table. The non-dimensional groups based on empirical considerations have been proposed in literature on the basis of extensive data analysis. Their extension to other systems requires rigorous validation, often requiring modifications of constants or exponents. Convection number and boiling number fall under this category. Although the Martinelli parameter is derived from fundamental considerations of the gas and the liquid phase friction pressure gradients, it is used extensively as an empirical group in correlating experimental results on pressure drop, void fraction, and is some cases, heat transfer as well. It can be seen from Table 1 that among the groups derived from fundamental considerations, Capillary number, Ca, and Weber number, We, are important in microchannel two-phase flows. They represent the ratios of viscous and surface tension forces, and inertia and surface tension forces respectively. The ratio of inertia to viscous forces, represented by Reynolds number, Re, is extensively used in single phase flows; it is also expected to have an important role in two-phase flows, as the single-phase heat transfer and pressure drop characteristics are often found to be useful in predicting the two-phase flow behavior. The Bond number represents the ratio of the gravitational to surface tension forces on a droplet or a bubble. Departure bubble Journal of Heat Transfer

diameter is sometimes used as the characteristic dimension in the definition of the Bond number in pool boiling. Since the gravitational forces are expected to be small compared to the surface tension and viscous forces, usefulness of Bond number in microchannel application is limited. Additionally, there are a number of non-dimensional groups used in literature for correlating different boiling phenomena. For example, Stephan and Abdelsalam 关6兴 utilized eight dimensionless groups in developing a comprehensive correlation for saturated pool boiling heat transfer. Similarly, Kutateladze 关7兴 combined the critical heat flux with other parameters through dimensional analysis to obtain a non-dimensional group. However, only those non-dimensional groups that are derived from some basic considerations are reviewed here. Forces Acting on a Liquid-Vapor Interface Due to Evaporation Momentum Change, Inertia and Surface Tension. The non-dimensional groups employed so far in literature for analyzing the flow patterns during flow boiling have been similar to those employed in the adiabatic two-phase flow applications. The Jakob number is used in analyzing the bubble growth phenomenon. The Weber number has been recently introduced in flow pattern maps for microchannels and minichannels. The effect of heat flux appears only in the Boiling number, which is used in heat transfer correlations along with the density ratio; the Boiling number has not been used in flow pattern maps. Heat flux has a significant effect on the two-phase structure during flow boiling. A higher heat flux results in a more rapid bubble growth leading to quickly filling the channel with a vapor slug. The forces generated due to rapid evaporation become significant for microchannels, as the growing bubbles interact with the channel walls. Further discussion on this aspect is presented in the following sections. As a nucleating bubble grows, the difference in the densities of FEBRUARY 2004, Vol. 126 Õ 9

Similarly, the force per unit length due to the surface tension force is given by F S⬘ ⫽ ␴ cos ␪

(3)

where ␪ is the appropriate contact angle, advancing or receding, depending on the direction of the motion of the liquid into or away from the interface respectively. The net gravitational force 共due to buoyancy兲 may be represented in a similar manner as F g⬘ ⫽ 共 ␳ L ⫺ ␳ G 兲 gD 2

Fig. 1 Forces acting on a vapor bubble growing on a heater surface in a liquid pool, only half of a symmetric bubble shown

the two phases causes the vapor phase to leave at a much higher velocity than the corresponding liquid velocity toward the receding and evaporating interface. The resulting change in momentum due to evaporation introduces a force on the interface. The magnitude of this force is highest near the heater surface due to a higher evaporation rate in the contact line region between the bubble base and the heater surface as illustrated in Fig. 1. For the case of saturated flow boiling, the heat flux at the wall results in an evaporation mass flux of q/h f g . The resulting momentum change introduces a force on the liquid interface that can be expressed as described below per unit characteristic dimension, either based on the bubble diameter as shown in Fig. 1, or based on the channel diameter as shown in Fig. 2. This force was first introduced by Kandlikar 关8兴 in developing a CHF model based on the force balance at the contact line at the base of a bubble on the heater surface. Thus force per unit length due to momentum change caused by evaporation at the interface is given by F ⬘M ⫽

冉冊

q qD q 1 ⫽ h fg h fg ␳G hfg

2

D ␳G

(1)

where D is the characteristic dimension. The other forces acting on the interface are due to the inertia of the flow and the surface tension in the contact line region. The forces per unit length are given by the respective equations below. The stress resulting from the inertia forces is given by ␳ V 2 . The resulting force per unit length due to the inertia is then given by F I⬘ ⫽ ␳ L V 2 D⫽

G 2D ␳L

(2)

(4)

The gravitational force is generally quite small compared to the forces due to inertia and the momentum change during flow boiling in microchannels. The viscous forces are not considered here, although they are important in determining the flow stability in microchannels. Their effect is represented through the Capillary number and the Reynolds number. New Non-Dimensional Groups Relevant to Flow Boiling in Microchannels. The relative magnitudes of the forces due to evaporation momentum, inertia, and surface tension, introduced in Eqs. 共1–3兲, influence the two-phase structure during flow boiling. The ratios of these forces, taken two at a time, yield the relevant non-dimensional groups in flow boiling. New Non-Dimensional Group K1. This group represents the ratio of the evaporation momentum force, Eq. 共1兲, and the inertia force, Eq. 共2兲. It is given by

冉冊

q 2D h fg ␳G q K1⫽ ⫽ G 2D Gh f g ␳L

冉冊

2

␳L ␳G

(5)

The non-dimensional group K1 includes the Boiling number and the liquid to vapor density ratio. The Boiling number alone does not represent the true effect of the evaporation momentum, and its coupling with the density ratio is important in representing the evaporation momentum force. A higher value of K1 indicates that the evaporation momentum forces are dominant and are likely to alter the interface movement. As an example, consider the bubble growth shown in Fig. 3 inside a 200 ␮m square microchannel, Steinke and Kandlikar, 关9兴. Each frame in Fig. 3 is 8 ms apart. The bubble grows rapidly aided by the evaporation at the liquid-vapor interface. The high evaporation rate causes the interface to move rapidly downstream. The upstream interface also experiences the force due to evaporation momentum and the increased pressure inside the bubble, causing it to move against the flow direction in one of the channels as shown. The flow reversal occurs at high heat fluxes and has been observed in 1 mm square minichannels as well by Kandlikar et al. 关10兴 and Kandlikar 关11兴. Further discussion on the actual values of K1 employed in microchannels and minichannels is presented in later sections. New Non-Dimensional Group K2. This new group represents the ratio of the evaporation momentum force, Eq. 共1兲, and the surface tension force, Eq. 共3兲. It is given by

冉冊

q 2D h fg ␳G q K2⫽ ⫽ ␴ hfg

Fig. 2 Forces acting on a liquid-vapor interface that covers the entire channel cross section


冉冊

2

D ␳ G␴

(6)

The contact angle is not included in the above ratio. The actual force balance in a given situation may involve more complex dependence on contact angles and surface orientation. However, it should be recognized that the contact angles play an important role in bubble dynamics and contact line movement and need to be included in a comprehensive analysis. The non-dimensional group K2 governs the movement of the interface at the contact Transactions of the ASME

Fig. 4 Variation of K2,CHF with diameter for flow boiling CHF data of Vandervort et al. †12‡ for different values of G in kgÕm2 s

Fig. 3 Rapid bubble growth causing reversed flow in a parallel microchannel. Water flow is from left to right, single channel shown, t Ä„a… 0 ms, „b… 8 ms, „c… 16 ms, „d… 24 ms, „e… 32 ms, „f… 40 ms, „g… 48 ms, and „h… 56 ms, Steinke and Kandlikar †9‡.

line. The high evaporation momentum force causes the interface to overcome the retaining surface tension force. This group was effectively used by Kandlikar 关8兴 in developing a model for CHF in pool boiling. The characteristic dimension D was replaced with the departure bubble diameter. The resulting expression for the CHF in pool boiling from a smooth planar surface oriented at an angle of ␸ with the horizontal was obtained as 1/2 q CHF⫽h f g ␳ G

冉

1⫹cos ␪ 16

冊冋

2 ␲ ⫹ 共 1⫹cos ␪ 兲 cos ␾ ␲ 4

册

1/2

⫻ 关 ␴ g 共 ␳ L ⫺ ␳ G 兲兴 1/4

(7)

Alternatively, the value of K2 at CHF for the case of pool boiling may be written as K2,CHF⫽

冉冊冉冋册 q CHF hfg

⫻

2

D 1⫹cos ␪ ⫽ ␳ G␴ 16

g共 ␳ L⫺ ␳ G 兲 ␴

冊冋 2

2 ␲ ⫹ 共 1⫹cos ␪ 兲 cos ␾ ␲ 4

册

1/2

D

(8)

The characteristic dimension D is simply half of the critical wavelength, 共alternatively, it may be taken as the departing bubble diameter兲, given by D⫽2 ␲

冋

␴ g共 ␳ L⫺ ␳ G 兲

册

冉

1⫹cos ␪ 16

冊冋 2

Ranges of Non-Dimensionless Parameters Employed in Microchannel and Minichannel Flow Boiling Experiments in Literature. A large body of experimental data is available for flow boiling in conventional sized channels. There are only a handful

2 ␲ ⫹ 共 1⫹cos ␪ 兲 cos ␾ ␲ 4

(9)

册

(10)

In other words, the non-dimensional number K2 has a unique value for CHF in pool boiling and depends on the contact angle and the orientation angle of the heater with respect to the horizontal. This group is expected to be important in CHF analysis during flow boiling in microchannels and minichannels as well. The experimental CHF data of Vandervort et al. 关12兴 during flow boiling is plotted with K2,CHF as a function of the hydraulic Journal of Heat Transfer

Importance of Weber Number and Capillary Number in Microchannel Flow Boiling. The Weber number, We, and the Capillary number, Ca, should prove to be useful in determining the transition boundaries between different flow patterns. We and Ca are believed to influence the CHF phenomenon as well. These groups are commonly employed in analyzing the gas-liquid adiabatic flows. They may prove to be useful in refining the mass flux 0.75 and viscous effects on CHF in the K2,CHF K1,CHF group shown in Fig. 5. Further work on this can be undertaken after reliable experimental data become available for CHF in microchannels with a wide variety of fluids.

1/2

Thus, K2,CHF for pool boiling is given by K2,CHF⫽2 ␲

diameter for three different mass fluxes. The result is shown in Fig. 4. The value of K2,CHF for each mass flux set is seen to be quite constant, considering the scatter present in the original data. This is quite remarkable, and further, as expected, a dependence of the respective K2,CHF values on the mass flux is seen since K2,CHF does not include the inertia related forces. Further CHF modeling needs to include the mass flux effect. Incidentally, K2,CHF is seen to increase with mass flux as one would expect. 0.75 As a first attempt, applying a mass flux correction factor K1,CHF to K2,CHF nearly collapses the data of Vandervort et al. 关12兴 for different mass fluxes on a single horizontal line. Figure 5 shows the resulting plot. Considering the scatter in the CHF data due to measurement uncertainties, the agreement is very encouraging. However, further experimental data need to be included in the comparison, and additional property effects 共including contact angles兲 need to be considered while developing a CHF model for flow boiling in microchannels.

0.75 Fig. 5 Variation of K2,CHF K1,CHF with diameter for flow boiling CHF data of Vandervort et al. †12‡ for different values of G in kgÕm2 s

FEBRUARY 2004, Vol. 126 Õ 11

Fig. 6 Ranges of the new non-dimensional parameter K1 employed in various experimental investigations

of reliable experimental data sets available for minichannels and microchannels, e.g., 关9兴 and 关13–21兴, although more are emerging in literature as the interest continues to grow in this field. It is interesting to look at the ranges of dimensionless parameters employed in these experiments as a function of hydraulic diameter. Figures 6 –10 show the ranges of non-dimensional parameters employed in several investigations. The ranges of K1 over the channel hydraulic diameters employed in literature are shown in Fig. 6. The 6 and 15-mm diameter data for R-11 by Chawla 关13兴 covers a wide range of K1 . Looking into the experimental data sets, it is seen that the higher end values of K1 correspond to the nucleate boiling dominant region, while the lower end values of K1 indicate the convective boiling dominant region. The large diameter data sets cover a wide range, whereas it is seen that most

Fig. 7 Ranges of the new non-dimensional parameter K2 employed in various experimental investigations

Fig. 8 Ranges of Weber Number, We, employed in various experimental investigations

Fig. 10 Ranges of Reynolds Number, Re, employed in various experimental investigations

of the minichannel and microchannel data sets fall toward the higher end of K1 values. Especially the data set of Yen et al. 关14兴 is seen to fall at the very high end. Higher values of K1 are indicative of a relatively higher heat flux for a given mass flux value, and also of the increased importance of the evaporation momentum force. Figure 7 shows a similar plot for K2 plotted against D h . The maximum value of K2 共not shown in the plot as no data are available兲 is indicative of the CHF location. There are very few studies available on CHF in Minichannels, and practically none for the microchannels. This is an area where further research is warranted. Figure 8 shows the range of We in the data sets analyzed here. No appreciable differences are noted, and the data sets do not show any shift in the We range indicative of any change in the experimental conditions for smaller hydraulic diameter channels. Although We does not appear to be a significant parameter in this plot, it may be representative of the inertia effects that are important in modeling the CHF in flow boiling. The Capillary number is expected to be important in the microchannel flows as both the viscous and the surface tension forces are expected to be important. Figure 9 shows the variation of Ca range with hydraulic diameter for representative data sets. It can be seen that there is a systematic shift toward higher values of Ca for smaller channel diameters. This indicates that the viscous forces become more important than the surface tension forces under flow boiling conditions in microchannels. This is somewhat of an unexpected result, as one would believe the dominance of the surface tension forces at smaller channel dimensions. Finally, Fig. 10 shows the range of all liquid flow Reynolds numbers employed in the data sets. As the channel diameter is decreased, a clear shift toward lower Reynolds number is seen. This points to the increased importance of the viscous forces in microchannels. Combining this observation with the discussion on the Capillary number in the above paragraph, it can be concluded that the viscous forces are extremely important in microchannel flows. The effect of lower Re on flow boiling heat transfer modeling will be discussed in the section on heat transfer coefficient prediction.

Influence of Channel Hydraulic Diameter on Flow Boiling Heat Transfer Mechanisms Flow Patterns. Flow boiling in a channel is studied from the subcooled liquid entry at the inlet to a liquid-vapor mixture flow at the channel outlet. As the liquid flows through a microchannel, nucleation occurs over cavities that fall within a certain size range under a given set of flow conditions. Assuming that cavities of all sizes are present on the heater surface, the wall superheat necessary for nucleation may be expressed from the equations developed by Hsu and Graham 关22兴 and Sato and Matsumura 关23兴:

Fig. 9 Ranges of Capillary Number, Ca, employed in various experimental investigations


⌬T sat,ONB⫽

冋冑

4 ␴ T satv f g h 1⫹ kh f g

1⫹

kh f g ⌬T sub 2 ␴ T satv f g h

册

(11)


Fig. 11 Wall superheat required to initiate nucleation in a channel with hydraulic diameter D h for saturated liquid conditions

For a conservative estimate, ⌬T sub⫽0 is taken in estimating the local superheat at the onset of nucleate boiling. Since the single phase liquid flow is in the laminar region, the Nusselt number is given by Nu⫽

hD h ⫽C k

(12)

where C is a constant dependent on the channel geometry and the wall thermal boundary condition. Combining Eqs. 共11兲 and 共12兲 with zero subcooling, we get, ⌬T sat,ONB⫽

8 ␴ T satv f g C D hh f g

(13)

Taking the case of a constant wall temperature boundary condition, representative of microchannels in a large copper block, the variation of ⌬T sat with D h is plotted in Fig. 11 for water at a saturation temperature of 100°C and for R-134a at 30°C. For channels larger than 1 mm, the wall superheat is quite small, but as the channel size becomes smaller, larger superheat values are required to initiate nucleation. For water in a 200 ␮m channel, a wall superheat of 2°C is required before nucleation can begin. The actual nucleation wall superheat may increase due to the absence of cavities of all sizes, while it may reduce due to 共a兲 the presence of dissolved gases in the liquid, Kandlikar et al., 关24兴, 共b兲 corners in the channel cross section, and 共c兲 pressure fluctuations. From the above discussion, for channels smaller than 50 ␮m, the wall superheat may become quite large, in excess of 10°C with water, and above 2 – 3°C for refrigerants. Flow boiling in channels smaller than 10 ␮m will pose significant challenges. The buildup of wall superheat presents another issue that is discussed in the following paragraph. Once the nucleation begins, the large wall superheat causes a sudden release of energy into the vapor bubble, which grows rapidly and occupies the entire channel. A number of investigators have considered this vapor slug as an elongated bubble. The rapid bubble growth pushes the liquid-vapor interface on both caps of the vapor slug at the upstream and the downstream ends, and leads to a reversed flow in the parallel channel case as the liquid on the upstream side is pushed back, and the other parallel channels carry the resulting excess flow. Kandlikar et al. 关10兴 observed this reversed flow in 1-mm square parallel channels, while Steinke and Kandlikar 关9兴 report a rapid flow reversal inside individual channels in a set of six parallel microchannels, D h ⫽200 ␮ m. Reversed flow was also observed by Peles et al. 关26兴. Kandlikar and Balasubramanian 关25兴 observed only a small reverse displacement of the interface in a 197 ␮m x 1054 ␮m single microchannel. Due to the relatively high inlet ‘‘stiffness’’ of the water supply loop, the single microchannel does not show as dramatic reversed flow behavior as the parallel microchannels. 共In case of parallel channels, the other channels act as the upstream sections for any given channel兲. Figure 3 by Steinke and Kandlikar 关9兴 shows a sequence of bubble formation and reversed flow 共from right to left兲 in a channel. The images are 8 ms apart and show a bubble from its nucleation stage, as it occupies the entire channel, and eventually Journal of Heat Transfer

Fig. 12 High speed flow visualization of water boiling in a 197 ␮ mÃ1054 ␮ m channel showing rapid dryout and wetting phenomena with periodic passage of liquid and vapor slugs, each successive frame is 5ms apart, Kandlikar and Balasubramanian †25‡

becomes a vapor slug that expands in both directions. The flow patterns are seen as periodic, with small nucleating bubbles growing into large bubbles that completely fill the tube and lead to rapid movement of the liquid-vapor interface along the channel. Figure 12 shows the periodic dryout and rewetting through an image sequence obtained with a flow of water in a single channel, 197 ␮ m⫻1054 ␮ m in cross-section, by Kandlikar and Balasubramanian 关25兴. Here the bubble growth is extremely rapid, and the moving interface could not be precisely imaged. However, the flow goes from all liquid flow in frames 共a兲 and 共b兲 to a thin film in frames 共c兲-共d兲-共e兲. In frames 共f兲-共l兲, the liquid film has been completely evaporated, and the channel walls are under a dryout condition. The liquid front is seen to pass through the channel in frame 共m兲, followed by all liquid flow in the last frame. The periodic wetting and rewetting phenomena were also observed by Hetsroni et al. 关27兴 for parallel microchannels of 103–129 ␮m hydraulic diameters. Other flow patterns reported by Steinke and Kandlikar 关9兴 include slug flow, annular flow, churn flow and dryout condition. A number of investigators, including Hetsroni et al. 关27兴 and Zhang et al. 关28兴 have also reported these flow patterns. The long vapor bubble occurring in a microchannel is similar to annular flow with intermittent slugs of liquid between two long vapor trains. The periodic phenomena described above is seen to be very similar to the nucleate boiling phenomena, with the exception that the entire channel acts like the area beneath a growing bubble, going through periodic drying and rewetting phases. The transient heat conduction under the approaching rewetting film and the heat transfer in the evaporating meniscus region of the liquid-vapor interfaces in the contact line region exhibit the same characteristics as the nucleate boiling phenomena. Dynamic Advancing and Receding Contact Angles. The contact angles are believed to play an important role during dryout and rewetting phenomena during flow boiling in a microchannel. These angles are important in the events leading to the CHF as FEBRUARY 2004, Vol. 126 Õ 13

Fig. 14 Comparison of the Kandlikar †1,2,35‡ correlation and Eqs. „15… and „16… for the Nucleate Boiling Dominant Region with Yen et al. †14‡ data in the laminar region, plotted with heat transfer coefficient as a function of local vapor quality x , R-134a, D h Ä190 ␮ m, ReLOÄ73, GÄ171 kgÕm2 s, q 2 Ä6.91 kWÕm

Fig. 13 Changes in contact angle at the liquid front during flow reversal sequence, water flowing in a parallel microchannel with D h Ä200 ␮ m, Steinke and Kandlikar †9‡

well. The pool boiling CHF model by Kandlikar 关8兴 incorporates these angles as seen from Eq. 共7兲. During normal bubble growth, the dynamic receding contact angle comes into play. During the rewetting process, the liquid front is advancing with its dynamic advancing contact angle. As the CHF is approached, or as the flow reversal takes place due to flow instabilities, the liquid front changes its shape from the dynamic advancing angle to the dynamic receding angle. This event was captured by Steinke and Kandlikar 关9兴 using high-speed imaging techniques and is displayed in Fig. 13 for the flow of water in a set of six parallel microchannels, each with a 200 ␮m square cross section. The events in Fig. 13 show the changes in the contact angles. The liquid front is moving forward from left to right in frames 共a兲-共d兲. In frame 共d兲, it stops moving forward. Note the dynamic advancing contact angle in this frame, which is greater than 90 deg. During frames 共d兲-共i兲, it experiences rapid evaporation at the right side of the front interface and changes to the receding contact angle value, which is less than 90 deg. The liquid slug subsequently becomes smaller, making way to the vapor core with its residual liquid film in frames 共i兲-共m兲. Eventually, the liquid film dries out completely as seen in frames 共n兲-共p兲. Additional studies on the contact angle changes at evaporating interfaces are reported by Kandlikar 关29兴. More detailed experiments are needed to further understand the precise effect of contact angles on CHF.

As the channel size becomes smaller, the Reynolds number also becomes smaller for a given mass velocity, and the flow patterns exhibit characteristics similar to a bubble ebullition cycle as discussed in the previous sections. It is therefore expected that the flow boiling correlation for the nucleate boiling dominant region should work well here. Consider the flow boiling correlation by Kandlikar 关30,31兴.

再

h T P,NBD h T P,CBD

(14)

h T P,NBD⫽0.6683Co ⫺0.2共 1⫺x 兲 0.8 f 2 共 FrLO 兲 h LO ⫹1058.0Bo 0.7共 1⫺x 兲 0.8F Fl h LO

(15)

h T P,CBD⫽1.136Co ⫺0.9共 1⫺x 兲 0.8 f 2 共 FrLO 兲 h LO ⫹667.2Bo 0.7共 1⫺x 兲 0.8F Fl h LO where FrLO is the Froude number with all flow as liquid. Since the effect of Froude number is expected to be small in microchannels, 14 Õ Vol. 126, FEBRUARY 2004

NuLO ⫽

h LO D h ⫽C, kL

(16)

where the constant C is dependent on the channel geometry and the wall thermal boundary condition. Kandlikar and Steinke 关34兴 showed that the use of Eq. 共16兲 for h LO is appropriate in Eq. 共15兲 when the all-liquid flow is in the laminar region. The use of turbulent flow correlation by Gnieliski was found to be appropriate for Re⬎3000, while for Re⬍1600, the use of laminar flow correlation yielded good agreement. In the transition region, a linear interpolation was recommended between the limiting ReLO values of 1600 and 3000. With further reduction in the Reynolds number, Re⬍300, Kandlikar and Balasubramanian 关35兴 showed that the flow boiling mechanism is nucleate boiling dominant and the use of only the nucleate boiling dominant expression in Eq. 共15兲 for h T P,NBD is appropriate in the entire range of vapor quality. Thus, Kandlikar and Balasubramanian 关35兴 recommend the following scheme: h T P ⫽h T P,NBD

Heat Transfer Coefficients during Flow Boiling in Microchannels

h T P ⫽larger of

the function f 2 (FrLO ) is taken as 1.0. The single-phase, all-liquid flow heat transfer coefficient h LO is given by appropriate correlations given by Petukhov and Popov 关32兴, and Gnielinski 关33兴, depending on the Reynolds number in the turbulent liquid flow. The values of the fluid-dependent parameter F Fl can be found in 关34兴 or 关35兴. For microchannels with the all-liquid flow in the laminar region, the corresponding all-liquid flow Nusselt number is given by

for ReLO ⬍300

(17)

Using the above scheme, a recent data set published by Yen et al. 关14兴 was tested. Figure 15 shows a comparison between the experimental data and the above correlation scheme. Here ReLO ⫽73, and only the nucleate boiling dominant part of the correlation in Eq. 共15兲 is used. At such low Reynolds numbers, the convective boiling does not become the dominant mechanism in the entire vapor quality range. In this plot, the first few points show a very high heat transfer coefficient. This is due to the sudden release of the high liquid superheat following nucleation that causes rapid bubble growth in this region as seen in Fig. 14 as well. Steinke and Kandlikar 关36兴 observed a similar behavior with their water data as shown in Fig. 15. The flow boiling mechanism is quite complex in microchannels as seen from the experimental data and flow visualization studies. Although simple models available in literature, e.g., 关37兴, present a good analysis under certain idealized conditions, phenomena such as rapid bubble growth, flow reversal, and periodic dryout introduce significantly greater complexities. Effect of parallel channels on heat transfer is another area where little experimental work is published. Transactions of the ASME

Conclusions Flow boiling in microchannels is addressed from the perspective of interfacial phenomena. The following major conclusions are derived from this study:

Fig. 15 Comparison of the Kandlikar †1,2,35‡ correlation and Eqs. „15… and „16… for the Nucleate Boiling Dominant Region with Steinke and Kandlikar 36 data in the laminar region, plotted with heat transfer coefficient as a function of local vapor quality x , water, D h Ä207 ␮ m, ReLOÄ291, GÄ157 kgÕm2 s, q Ä473 kWÕm2

Heat Transfer Mechanism during Flow Boiling in Microchannels Based on the above discussion, the heat transfer mechanisms can be summarized as follows: 1. When the wall superheat exceeds the temperature required to nucleate cavities present on the channel walls, nucleate boiling is initiated in a microchannel. Absence of nucleation sites of appropriate sizes may delay nucleation. Other factors such as sharp corners, fluid oscillations, and dissolved gases affect the nucleation behavior. The necessary wall superheat is estimated to be 2 – 10°C for channels smaller than 50–100 ␮m hydraulic diameter with R-134a and water respectively at atmospheric pressure conditions. 2. Immediately following nucleation, a sudden increase in heat transfer coefficient is experienced due to release of the accumulated superheat in the liquid prior to nucleation. This leads to rapid evaporation, sometimes accompanied by flow reversal in parallel channels. 3. The role of the convective boiling mechanism is diminished in microchannels. The nucleate boiling plays a major role as the periodic flow of liquid and vapor slugs in rapid succession continues. The wall dryout may occur during the vapor passage. The wetting and rewetting phenomena have marked similarities with the nucleate boiling ebullition cycle. The dryout period becomes longer at higher qualities and/or at higher heat fluxes. The nucleate boiling heat transfer suffers further as the liquid film completely evaporates 共dryout兲 during extended periods of vapor passage. 4. As the heat flux increases, the dry patches become larger and stay longer, eventually reaching the CHF condition. Closing Remarks. Although it is desirable to have a good mathematical description of the heat transfer mechanism during flow boiling in microchannels, the rapid changes of flow patterns, complex nature of the liquid film evaporation, transient conduction, and nucleation make it quite challenging to develop a comprehensive analytical model. Further, the conduction in the substrate, parallel channel instability issues, header-channel interactions, and flow maldistribution in parallel channels pose additional challenges. The usage of the new non-dimensional groups K1 and K2 in conjunction with the Weber number and the Capillary number is expected to provide a better tool for analyzing the experimental data and developing more representative models. The scale change in hydraulic diameter introduces a whole new set of issues in microchannels that need to be understood first from a phenomenological standpoint. Journal of Heat Transfer

1. After reviewing the non-dimensional groups employed in the two-phase applications, the forces acting on the liquid-vapor interface during flow boiling are investigated, and two new nondimensional groups K1 and K2 are derived. These groups represent the surface tension forces around the contact line region, the momentum change forces due to evaporation at the interface, and the inertia forces. 2. In a simple first-cut approach, the combination of the nondimensional groups, K2K0.75 is seen to be promising in represent1 ing the flow boiling CHF data by Vandervort et al. 关12兴. Further analysis and testing with a larger experimental data bank with a wide variety of fluids is recommended in developing a more comprehensive model for CHF. In additon, the influence of We, and Ca on the CHF needs to be studied further. 3. The nucleation criterion in flow boiling indicates that the wall superheat required for nucleation in microchannels becomes significantly large (⬎2 – 10°C) as the channel hydraulic diameter becomes smaller, about 50–100 ␮m depending on the fluid. The presence of dissolved gases in the liquid, sharp corners in the cross section geometry, and flow oscillations will reduce the required wall superheat, while the absence of cavities of appropriate sizes may increase the nucleation wall superheat. 4. Considerable similarities are observed between the flow boiling in microchannels and the nucleate boiling phenomena with the bubbles nucleating and occupying the entire channel. The process is seen to be very similar to the bubble ebullition cyle in pool boiling. 5. Heat transfer during flow boiling in microchannels is seen to be nucleate boiling dominant. 6. A description of the heat transfer mechanisms during flow boiling in microchannels is provided based on the above observations. Some of the key features, such s rapid bubble growth, flow reversal, nucleate boiling dominant heat transfer have been confirmed with high speed video pictures and experimental data. 7. Further experimental research is needed to generate more data for developing more accurate models and predictive techniques for flow boiling heat transfer and CHF in microchannels.

Nomenclature A Bo Bo C Ca Co cp d d P/dz Dh Eo F Fl

⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽

Fr F⬘ f G g h hfg Ja K1 K2 k

⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽

area, (m2 ) Bond number, Table 1 Boiling number, Table 1 a constant capillary number, Table 1 convection number, ( ␳ G / ␳ L ) 0.5((1⫺x)/x) 0.8 specific heat, 共J/kg K兲 diameter, 共m兲 pressure gradient, N/m3 hydraulic diameter, 共m兲 Eo¨tvo¨s number, Table 1 Fluid dependent parameter in Kandlikar 关1,2兴 correlation, ⫽1 for water, ⫽1.60 for R-134a Froude number, ⫽G2 /( ␳ L2gD) force per unit length, 共N/m兲 friction factor mass flux, (kg/m2 s) gravitational acceleration, (m/s2 ) heat transfer coefficient, (W/m2 K) latent heat of vaporization, 共J/kg兲 Jakob number, Table 1 new non-dimensional constant, eq. 共5兲 new non-dimensional constant, eq. 共6兲 thermal conductivity, 共W/m K兲 FEBRUARY 2004, Vol. 126 Õ 15

L,l m ˙ Nu P q Re T ⌬T V v We w X x Z

⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽

length 共m兲 mass flow rate 共kg/s兲 Nusselt number (⫽hDh /k) pressure 共Pa兲 heat flux (W/m2 ) Reynolds number (⫽GDh / ␮ ) temperature (°C) temperature difference 共K兲 velocity 共m/s兲 specific volume (m3 /kg) Weber number, Table 1 channel width 共m兲 Martinelli parameter, Table 1 vapor mass fraction Ohnesorge number, Table 1

Greek

␾ ⫽ orientation with respect to horizontal (°) ␮ ⫽ dynamic viscosity (Ns/m2 ) ␪ ⫽ contact angle (°) ␳ ⫽ density (kg/m3 ) ␴ ⫽ surface tension 共N/m兲 Subscripts CHF ⫽ critical heat flux F ⫽ friction CBD ⫽ convection dominated region G ⫽ gas or vapor g ⫽ due to gravity I ⫽ inertia L ⫽ liquid LO ⫽ all flow as liquid f g ⫽ latent quantity, difference between vapor and liquid properties M ⫽ due to momentum change NBD ⫽ nucleate boiling dominant region ONB ⫽ onset of nucleate boiling S ⫽ surface tension sat ⫽ saturation sub ⫽ subcooled T P ⫽ two-phase

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