Critical heat flux for subcooled flow boiling in micro-channel heat sinks

https://doi.org/10.1016/j.ijheatmasstransfer.2008.12.019Get rights and content

Abstract

Critical heat flux (CHF) was measured and examined with high-speed video for subcooled flow boiling in micro-channel heat sinks using HFE 7100 as working fluid. High subcooling was achieved by pre-cooling the working fluid using a secondary low-temperature refrigeration system. The high subcooling greatly reduced both bubble departure diameter and void fraction, and precluded flow pattern transitions beyond the bubbly regime. CHF was triggered by vapor blanket formation along the micro-channel walls despite the presence of abundant core liquid, which is consistent with the mechanism of Departure from Nucleate Boiling (DNB). CHF increased with increasing mass velocity and/or subcooling and decreasing hydraulic diameter for a given total mass flow rate. A pre-mature type of CHF was caused by vapor backflow into the heat sink’s inlet plenum at low mass velocities and small inlet subcoolings, and was associated with significant fluctuations in inlet and outlet pressure, as well as wall temperature. A systematic technique is developed to modify existing CHF correlations to more accurately account for features unique to micro-channel heat sinks, including rectangular cross-section, three-sided heating, and flow interaction between micro-channels. This technique is shown to be successful at correlating micro-channel heat sink data corresponding to different hydraulic diameters, mass velocities and inlet temperatures.

Introduction

Critical heat flux (CHF) is arguably the most important design limit for systems involving heat dissipation from heat-flux controlled surfaces. The occurrence of CHF is associated with a sudden, large reduction in the heat transfer coefficient, which is caused by the loss of liquid contact with the solid surface upon which evaporation or flow boiling is occurring. Depending on heat flux magnitude, thermophysical properties, and operating conditions, the loss of coolant contact can result in surface overheating, burnout, or some other form of catastrophic system failure; hence the importance designers place on accurately determining the CHF limit.

Electronics cooling is a rather recent application where CHF determination is crucial to the safe design and operation of high performance microprocessors. The transition from air-cooling to single-phase liquid cooling and, ultimately, two-phase cooling has been spurred by an unprecedented rise in chip heat flux, brought about by aggressive integration of an increasing number of electronic components in a single chip. Nowhere is this rise more alarming than in defense electronics, such as those found in directed energy laser and microwave weapons, and in radars. Current developments in these applications point to the need to dissipate as high as 1000 W/cm2 at the device level [1]. This task is complicated by the fact that only dielectric coolants are permitted in these applications. Despite their many attractive attributes, such as high dielectric strength and compatibility with most materials comprising an electronic package, these coolants possess relatively poor thermal transport properties. Therefore, every effort must be made to enhance their cooling potential in order to safely dissipate the anticipated high heat fluxes.

Recently, the authors suggested a thermal management solution for high-flux defense electronics in which the dielectric coolant HFE 7100 is pre-cooled by a secondary refrigeration cooling system before entering a micro-channel heat sink to which the electronic device is attached [2], [3]. The refrigeration system provides two key benefits. First, it reduces the temperature of the HFE 7100, which helps maintain relatively low device temperatures when dissipating very high heat fluxes. Second, the low temperature of HFE 7100 helps maintain subcooled flow boiling conditions inside the heat sink, which greatly increases CHF for a given flow rate. This system was capable of dissipating in excess of 700 W/cm2.

The present study concerns the determination of CHF for this indirect-refrigeration-cooled micro-channel configuration. Unlike most published two-phase micro-channel studies, which involve saturated boiling, the present cooling configuration involves highly subcooled flow boiling. The key difference between subcooled boiling and saturated boiling is that subcooled boiling occurs at the surface with a bulk liquid temperature below the saturated temperature. With high subcooling, boiling commences when the applied heat flux is capable of superheating liquid adjacent to the surface. Because subcooling is highest in the inlet region of the micro-channel, bubbles near the inlet quickly re-condense at the wall. As the bulk liquid temperature increases along the micro-channel, bubbles are able to grow larger and detach from the surface, mixing into the bulk flow where they undergo partial or full condensation. Condensation greatly reduces the magnitude of void fraction in subcooled compared to saturated boiling. Unlike the drastic flow pattern transitions in saturated flow (bubbly, churn, slug, annular), subcooled flow boiling is dominated by bubbly flow alone. Those differences in flow pattern have a strong bearing on both the mechanism and magnitude of CHF for subcooled versus saturated boiling.

Fig. 1 illustrates these differences in CHF mechanism. For saturated flow boiling, large increases in void fraction trigger a succession of flow regimes. The flow eventually culminates in the high void fraction annular flow pattern, where cooling is sustained by evaporation of a thin liquid film along the surface. CHF results from dryout of the liquid film as the surface is exposed directly to the vapor. While the ensuing downstream mist flow provides some cooling by droplet impact with surface, the heat transfer coefficient is drastically smaller than upstream of the dryout point. Dryout typically occurs with low inlet subcoolings, low mass velocities, and large length-to-diameter ratios, and CHF magnitude with dryout is relatively small.

With highly subcooled flow boiling, bubbly flow persists over much of the channel length, and CHF ensues when bubbles near the wall coalesce into a localized vapor blanket that causes a sharp reduction in the local heat transfer coefficient. This form of CHF is termed Departure from Nucleate Boiling (DNB) and occurs with high inlet subcoolings, high mass velocities, and small length-to-diameter ratios. The magnitude of CHF is much higher than with dryout, and the ensuing surface temperature rise is far more catastrophic.

A significant body of literature has been published that addresses subcooled flow-boiling CHF. The majority of these studies are devoted to the development of correlations from large CHF database or limited experimental data [4], [5], [6], [7], [8], [9], [10], [11]; most of these studies are focused on water data and nuclear reactor cooling. Theoretical treatments of DNB are far more limited (e.g., Refs. [12], [13], [14]).

Because most prior subcooled boiling studies concern nuclear reactor cooling, available correlations typically address high-pressure water conditions. No effort has yet been made to assess the suitability of these correlations to electronic cooling applications and dielectric coolants.

Another limitation of prior flow boiling CHF correlations is that they are derived from data for macro-channel. Despite the intense recent interest in micro-channel heat sinks for electronic cooling applications, very few studies have been published that address CHF determination [15], [16]; alas, these studies concern only saturated flow boiling CHF.

Different recommendations have been made concerning the channel size below which the channel begins to behave as a micro-channel. For the most part, recommendations have been based on hydraulic diameter. For example, Thome suggested diameters of 100–600 μm be classified as micro-channels [17].

Distinguishing between macro- and micro-channel flows cannot be based on channel size alone. As will be shown below, a channel may behave as a micro-channel for certain fluids and operating conditions and as a macro-channel for others. Clearly a more rigorous treatment is necessary to define a mechanistically based boundary between the two flow extremes.

For two-phase flow, this boundary is closely related to the ratio of bubble size to channel diameter, the larger the ratio, the more likely that the flow will behave as a micro-channel flow. Kew and Cornwell [18] used this rationale to determine the boundary between micro-channel and macro-channel flows based on a Confinement number defined asCo=σg(ρf-ρg)Dh21/2.They showed that channels become too confining when Co > 0.5, which is where macro-channel assumptions begin to fall apart. Table 1 summarizes hydraulic diameter values corresponding to Co = 0.5 for several fluids. Notice that low surface tension fluids, such the dielectric coolants FC-72 and HFE 7100, and refrigerant R134a, have lower hydraulic diameters corresponding to the transition from macro- to micro-channel flow, whereas water, with its higher surface tension, produces micro-channel flow in larger channels. However, the boundary values listed in Table 1 are quite larger than those deemed typical of micro-channel flows.

A key weakness of Eq. 1 is that it is based on the ratio of surface tension force to buoyancy, evidenced by the appearance of gravitational acceleration in the definition of the Confinement number. While this criterion is a good representation for pool boiling in, say, a confined vertical channel, it is not able to account for bubble size in a flow-boiling situation. Aside from surface tension, bubble size in flow boiling is dominated by liquid drag rather than buoyancy. In the present study, an alternative measure of the boundary between macro- and micro-channel flows is developed which incorporates the influence of liquid drag on bubble size. Equating the drag force on the bubble to the surface tension force that holds the bubble to the wall givesCDπDb2412ρfU2πDbσ.A channel tends to confine the flow when the diameter determined from Eq. 2 approaches the diameter of the channel. Therefore, the channel diameter corresponding to the transition from macro- to micro-channel flow can be determined from the relationDtranDb.For circular channels, Dtran is simply the diameter of the channel.

Two-phase micro-channel flow applications of practical interest are characterized by modest laminar Reynolds numbers, generally greater than 50. Under these conditions, the drag coefficient can be determined from [19]CD=24Retran1+3160Retran.Combining Eqs. (2), (3), (4) and substituting G = ρf U, yield the following criterion for the transitional channel dimension,Dtran=1609(σρf-3μfG)G2.

Table 2 shows calculated values of Dtran for water and HFE 7100 based on Eq. 5. Notice how these values are significantly smaller than those given in Table 1, and more representative of values deemed typical of micro-channel flow in recent experimental studies. Table 2 also shows decreasing surface tension and/or increasing mass velocity enables smaller channels to behave as macro-channels.

It is interesting to note that Eq. 5 can also be expressed as a Weber number criterion for confinementWetran=160911+1603Retran,which can be approximated asWetran=1609for high mass velocities. Eq. 7 shows Weber number plays an important role in micro-channel flows, and its effect must therefore be incorporated in any micro-channel CHF correlation. This important issue will be discussed later in this paper.

Section snippets

Test facility and micro-channel test sections

Fig. 2 shows a schematic diagram of the flow control system used in the present CHF experiments. The system consists of a primary HFE 7100 loop that contains the micro-channel test module, and a secondary vapor compression refrigeration system. The primary coolant is subcooled by rejecting heat to the refrigeration system via an intermediate heat exchanger.

HFE 7100 is an environmentally friendly non-ozone-depleting dielectric fluid with very low global warming potential. Because of its

CHF trends and flow visualization results

Several key parameters were used to characterize flow conditions and CHF. Aside from total flow rate, m˙, of the primary coolant, tests were also based on mass velocity, which is defined asG=m˙NAch,where N is the number of micro-channels in the heat sink, and Ach the cross-sectional area of each micro-channel. Two definitions are used for heat flux as shown in Fig. 4. The first is the effective heat flux, qeff, which is based on the total base area of the micro-channel heat sink. This would be

Conclusions

This study explored the critical heat flux (CHF) limit for micro-channel sinks under subcooled flow conditions using HFE 7100 as working fluid. The subcooling was achieved by pre-cooling the fluid using a low-temperature refrigeration system. Prior CHF correlations were modified to accommodate the unique features of micro-channel heat sinks, such as rectangular geometry, three-sided heating and flow interactions between micro-channels. Key conclusions from the study are as follows:

  • (1)

    High inlet

Acknowledgement

The authors are grateful for the support of the Office of Naval Research (ONR) for this study.

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