Graphical Abstract Figure
Graphical Abstract Figure
Close modal

Abstract

The heat transfer and hydraulic performance of a flat evaporator, pump-assisted capillary loop cooler is evaluated for a 1cm2 heat source. The cooler consists of a copper manifold that houses a compensation chamber that feeds liquid to a sintered, flat evaporator wick below via a micro-tube array. Liquid evaporates from the copper wick as it is attached to the heater through a copper base plate. The custom cooler design offers separate flow routes for liquid and vapor phases during steady operation and thereby maintaining the pressure balance of the flow loop. The cooler performance is evaluated using de-ionized water as the coolant with an inlet volumetric flowrate of 322ml/min. The cooler achieves a steady convective heat transfer coefficient of >95kW/m2K with <2kPa pressure drop, tested up to a maximum heater temperature of 175 °C. An electronic valve installed on the cooler outlet controls the compensation chamber pressure and extends peak heat transfer performance. This control scheme has been experimentally verified to extend the range of peak heat transfer from [356,>537] to [356,>610]W/cm2 within the same temperature range. Such a cooler shows promise for systems of variable thermal load where system pressure is a key consideration.

1 Introduction

Thermal management of electronic devices has become critically important to address the increased power density of next-generation power semiconductor devices and integrated circuits [13]. With the end of Dennard scaling, future semiconductor device performance gains will partially rely on increased power levels and larger package footprints. Semiconductor industry fabrication yield and cost concerns are leading to heterogeneous chip architectures, such as multi-chip modules (MCMs) [4], to ensure continued performance scalability and reliability. Notably, implementing such next-generation MCMs will necessitate advanced thermal management strategies to dissipate high heat fluxes at the semiconductor die-level while accommodating the larger package area [57].

Among available thermal management techniques, two-phase cooling approaches, such as flow boiling in microchannel heat sinks, exhibit distinct advantages over their single-phase counterparts by leveraging the latent heat absorbed during the phase change of the coolant. This leads to higher heat transfer coefficients with reduced temperature gradients [8]. However, these benefits are primarily realized in pumped two-phase cooling systems only when operating at high exit vapor qualities at which they are prone to flow instabilities [9,10]. Flow instabilities may include the Ledinegg instability [11], pressure drop oscillations [12], or the parallel channel instability [13], and can lead to premature dry out or flow reversal. Alternatively, passive two-phase cooling systems, such as capillary pumped loops (CPL) [14,15], loop heat pipes (LHP) [16,17], and vapor chamber heat spreaders [18,19], utilize capillary pumping to supply liquid to a porous evaporator wick from which high heat fluxes can be dissipated by evaporation or boiling. Here, by using a porous evaporator to separate the liquid supply from the vapor exhaust pathways, these passive two-phase systems inherently mostly avoid the aforementioned two-phase instabilities associated with conventional pumped two-phase systems [1113], thereby offering high-exit-vapor-quality, low-thermal-resistance operation.

Conventional passive two-phase cooling loops (CPLs and LHPs) comprise an evaporator, a thermally regulated reservoir, and a condenser, all interconnected by fluid lines. Capillary pumping must continuously replenish fluid evaporated from the porous wick with liquid from the reservoir during steady operation [15,17]. However, such complete reliance on the passive capillary pumping action of the wick introduces a limit on the maximum heat flux dissipation, namely, a capillary limit at which the loop pressure drop exceeds the capillary pressure in the evaporator, causing fluid circulation to stop. The integration of a separate mechanical pump into these passive two-phase loop systems is a means to overcome the capillary limit and thereby increases the cooling performance of the system. In the pioneering work of Ku and Kroliczek [20], a pump was positioned upstream in the liquid line to aid in pumping of the working liquid to multiple porous evaporators operating in parallel. Such hybrid two-phase loop systems, that is loops having some form of mechanical pumping action alongside the capillary pumping of the evaporator wick, are generally referred to as pump-assisted capillary loops (PACL) and have been the topic of numerous recent research studies that are discussed in the literature review below [2133]. These systems are attractive because the mechanical pumping of liquid is only necessary to supplement the capillary action at high evaporator heat loads, and thus, there is a much lower pumping power required when compared to pumped single-phase cooling systems that require mechanical pumping to deliver all of the liquid. Additionally, due to their inherent two-phase nature, pump-assisted capillary loops offer better temperature uniformity and consequently lower thermal resistance than the single-phase systems, at lesser risk of flow instabilities than pumped two-phase systems.

Researchers have studied both flat and cylindrical evaporator configurations for use in PACL systems. In a cylindrical evaporator, fluid enters through a hollow liquid core at the center of the wick, subsequently permeating radially outward through the porous network of the wick before evaporating with vapor passing into outlet channels around the outer surface of the wick. For example, while investigating a PACL system with a cylindrical evaporator, Setyawan et al. [21] showed that by turning on an assisting diaphragm pump just prior to the dry out, the capillary limit was substantially increased. The loop was limited to an operating power of 140W in a passive capillary mode, but using pump assistance the system could dissipate 200W, at the expense of only 0.3W of pumping power. For many applications including electronics cooling, a cylinder-to-flat saddle [34] is needed to attach a cylindrical evaporator to a flat heated surface in order to increase the thermal contact area. Although such interfaces are made of conductive materials such as aluminum or copper (Cu), they increase the thermal resistance, temperature non-uniformity, and mass of the system. Thus, flat evaporators offer easy installation onto electronics packages and also favor a uniform temperature distribution over the thermal interface between the heated surface and the evaporator surface.

Jiang et al. [22] experimentally illustrated several startup modes of their pump-assisted capillary loop system having a flat evaporator design and custom impeller pump. They later explained the effect of the working fluid charging process on the system performance [23]. Yang et al. [25,26] also reported the heat transfer characteristics of three different startup modes for the porous (sintered nickel powder), flat evaporator of a pump-assisted capillary loop. It was found that increasing the liquid/vapor pressure difference at a fixed input power can increase the heat transfer coefficient. Crepinsek and Park [27,28] experimentally evaluated the behavior of a PACL system having a flat evaporator connected to a liquid compensation chamber through vertical porous posts. The authors investigated the effect of various operational variables such as input heat load, system pressure, and liquid flowrate, to name a few. Notably, the heat removal performance of the PACL system was evaluated with multiple evaporators placed in series and parallel configurations. Lee and Park [29] analyzed a PACL system with a flat evaporator using a thermal-hydraulic network model, wherein three distinct boiling modes were identified based on the pressure relation between the liquid chamber, vapor chamber, and evaporator wick base. In follow-on experiments [30], they used experimentally obtained capillary pumping head of the evaporator wick as a control variable for proportional-integral control to tune the capillary-fed boiling conditions of the evaporator wick. The feedback control approach could tune the pump power based on the heat load on the evaporator, resulting in a reduction in the pumping power by 48% and consequently, expanded the range of capillary-driven thin-film evaporation by 285%. The measured heat dissipation limit was 227.2W/cm2 at a thermal resistance of 0.19Kcm2/W for their system at the maximum pump-assisted flowrate of 7.5g/s. Ferreira et al. [31] numerically predicted the flooding and dry out limits, as well as proposed an operational regime map using stability analysis, for a PACL system with a 3D-printed evaporator. Their operational regime map highlights that the capillary dry out limit can be extended substantially (nearly twofold) with the active participation of a mechanical pump. Interestingly, for non-volumetric (e.g., centrifugal) pumps, the positioning of the mechanical pump with respect to the fluid reservoir also plays a crucial role in determining the system robustness and the presence of flow instabilities [32,33].

The literature reviewed above highlights the promising capability of using pump assistance to increase the heat dissipation of conventional passive capillary pumped two-phase loops well beyond the capillary limit. In this work, we design and experimentally evaluate a PACL system with a custom flat evaporator design that is able to dissipate heat fluxes >600W/cm2 without approaching the dry out limit, using de-ionized (DI) water as the working fluid. The evaporator design and function are detailed in Sec. 2. The experimental setup and procedures are described in Sec. 4. Heat loss modeling and data reduction are discussed in Sec. 4. Heat transfer and hydraulic results are presented in Sec. 5 and discussed in Sec. 6. This includes the demonstration of a control strategy to extend cooler performance using an electronic valve (e-valve). Finally, the findings are concluded and areas for future work are identified in Sec. 7.

2 Evaporator Design

For the current PACL system, the flat evaporator comprises a compensation chamber, a porous wick, and microtubes bridging the gap between the porous wick and the compensation chamber. The construction is shown in the schematic diagram in Fig. 1, which illustrates a cross-sectional view of the evaporator.

Fig. 1
Schematic representation of the cross-sectional view of a flat evaporator for a pump-assisted capillary loop with microtubes that feed liquid from the compensation chamber to the porous base wick during steady operation. The liquid and vapor pathways within the evaporator test section have been indicated with arrows in the shaded and white regions, respectively.
Fig. 1
Schematic representation of the cross-sectional view of a flat evaporator for a pump-assisted capillary loop with microtubes that feed liquid from the compensation chamber to the porous base wick during steady operation. The liquid and vapor pathways within the evaporator test section have been indicated with arrows in the shaded and white regions, respectively.
Close modal

The compensation chamber, housing the liquid inlet and outlet, acts as a reservoir and bypass route (from left to right) for the excess liquid that is not drawn to the evaporating surface during steady operation. During operation, subcooled single-phase liquid entering into the compensation chamber is pumped across the opening to the microtubes, based on the heat load, to the base wick where evaporation/boiling occurs. Generally, in an entirely passive evaporator, liquid is drawn to the base wick via the capillary action of porous posts [19]. However, in a hybrid system, replacing such porous posts with microtubes through which liquid can be mechanically pumped, reduces the capillary pumping burden (i.e., capillary pumping only needs to overcome the pressure drop in the base wick, not the posts). The liquid supplied from the compensation chamber is uniformly distributed over the base wick evaporator via an n×n square array of microtubes covering the entire base wick area. The feeding tubes have a height, ttube (protruding height), and diameter, dtube, and are separated by a pitch, s. At a given heat input to the base, evaporation or capillary-fed boiling generates vapor, which travels outward between the tubes before exiting the test section via vapor exhaust lines.

The key geometric features of the PACL evaporator are sized using model-based estimates of the pressure drop due to liquid flow through the feeding tubes and in the base wick layer, ΔPbase, such that the capillary pressure of the wick, Pwick, is not exceeded when operating at heat fluxes on the order of 100’s of W/cm2.
Pwick=ΔPbase(ttube,dtube,s)
(1)
Details of this reduced-order pressure drop modeling approach and evaporator sizing exercise are described in the previous works of Sudhakar et al. [19,35] and Soto de la Torre [36]. The modeling studies suggested that increasing the density of the tube array will increase the maximum power of the cooler given the reduction in effective wicking length. Based on this analysis, an evaporator design with a 22×22 array of 0.25mm outer diameter microtubes distributed over a sintered Cu base wick having a footprint area of 12×12mm2 was selected as a maximum tube density array due to manufacturing constraints. The salient geometric feature sizes of the PACL evaporator design are compiled in Table 1. The design and fabrication of an evaporator test section following these specifications are introduced in detail in the following.
Table 1

Evaporator geometry

ComponentParameterValueUnit
Compensation chamberWidth13mm
Length38mm
Height2mm
MicrotubesHeight, ttube1mm
Diameter, dtube0.25mm
Wall thickness0.05mm
Spacing, s0.5mm
Array size22×22
Base wickThickness, twick0.2mm
Length, levap12mm
Width12mm
Particle size74 - 104μm
Porosity0.6
Cu base plateArea50×50mm2
Thickness1mm
HeaterArea10 × 10mm2
ComponentParameterValueUnit
Compensation chamberWidth13mm
Length38mm
Height2mm
MicrotubesHeight, ttube1mm
Diameter, dtube0.25mm
Wall thickness0.05mm
Spacing, s0.5mm
Array size22×22
Base wickThickness, twick0.2mm
Length, levap12mm
Width12mm
Particle size74 - 104μm
Porosity0.6
Cu base plateArea50×50mm2
Thickness1mm
HeaterArea10 × 10mm2

An exploded view of the evaporator test section computer-aided design (CAD) model is shown in Fig. 2(a), with a cut-section view of the assembled test section in Fig. 2(b). The test section consists of a stack-up of five major components from top to bottom: (i) a transparent acrylic cover, (ii) a Cu manifold, (iii) a polyetheretherketone (PEEK) manifold support structure, (iv) a Cu base with the wick sintered on top, and (v) a PEEK bottom carrier plate. These components are assembled using bolts placed through the holes around the periphery. The test section has a modular design to enable the testing of different base wicks, as well as the use of different Cu manifolds.

Fig. 2
(a) Exploded view of the test section (excluding bolts) with the main components indicated, (b) a cross-sectional view of the test section assembly CAD model with liquid and vapor lines indicated, and (c) zoomed view of the manifold and base wick subassembly highlighting the inner liquid and vapor pathways
Fig. 2
(a) Exploded view of the test section (excluding bolts) with the main components indicated, (b) a cross-sectional view of the test section assembly CAD model with liquid and vapor lines indicated, and (c) zoomed view of the manifold and base wick subassembly highlighting the inner liquid and vapor pathways
Close modal

The bottom surface of the acrylic transparent cover seals liquid within the compensation chamber by compressing a gasket against the top of the Cu manifold. Pipe fittings are face-sealed against the top of the cover to make fluid connections to the test section. One pair of fittings aligned along the length of the Cu manifold acts as the liquid inlet and outlet as indicated by the labels in Fig. 2(b), while the other pair acts as parallel vapor outlets.

The Cu manifold forms the compensation chamber on the top side, connecting to the outlet and an array of 22×22 microtubes protruding out from the bottom. These microtubes are evenly distributed over a 12×12mm2 central area of the manifold and have an outer diameter (dtube) of 0.25mm, a wall thickness of 50μm, and a protruding height (ttube) of 1 mm. The center-to-center distance, or pitch s, between all 572 microtubes is 0.5 mm (note that the four corner tubes are omitted as they would extend outside of the evaporator wick which has rounded corners). Again, the distribution of the microtubes ensures that the evaporation/boiling area is evenly fed with liquid. The Cu manifold is fabricated by computer numerical control micromachining (Sunlight-Tech Inc., Mokena, IL).

The bottom edge of the Cu manifold is sealed at an internal step of the PEEK support structure using silicone sealant. Apart from housing the manifold on the top side, the support structure is also designed to align and seat the Cu base into a recess on the bottom side. The tolerances of this recess are carefully designed to ensure that the bottom ends of the Cu microtubes are flush with the top surface of the sintered wick, in order to avoid bypass of liquid directly into the vapor outflow region, which would short-circuit the evaporator functionality. The Cu base plate is a square, 1 mm-thick Cu plate and accommodates a square, Cu powder base wick on the top face having a side length (levap) of 12 mm and a corner radius of 1.1 mm (see Fig. 3(a)). The base wick is sintered from Cu particles of size ranging between 74μm and 104μm by a commercial vendor (Celsia Inc., Harbeson, DE) (refer to Fig. 3(b) for the scanning electron microscope (SEM) image of the wick). The 0.2 mm thickness of the base wick is chosen to match that of a two-layer vapor chamber base wick that offered a low thermal resistance under capillary-fed boiling conditions; refer to our previous works [18,35]. Likewise, following our prior work [37], the footprint area of the wick is sized slightly larger than the heater footprint area to take advantage of heat spreading in the Cu base plate between the wick and heat source. Specifically, the bottom side of the Cu base plate mounts against a PEEK carrier plate, having a central opening and wire feedthrough to allow mounting of a 10×10mm2 heater to the backside of the Cu base plate. The commercial film heater (MesoscribeTM) [38], having an embedded K-type thermocouple, is printed directly on the center of the backside of the base Cu plate (i.e., opposite to the sintered wick) with high-temperature solder for the electrical wire connections.

Fig. 3
(a) Top view of the Cu base wick prepared by Cu particle sintering and (b) SEM image showing the Cu-nanoparticle size in the sintered wick
Fig. 3
(a) Top view of the Cu base wick prepared by Cu particle sintering and (b) SEM image showing the Cu-nanoparticle size in the sintered wick
Close modal

Figure 2(b) shows the cross-sectional view of the physical evaporator assembly (without fasteners) with highlighted liquid (cyan) and vapor (red) pathways. The bypass line for the excess liquid extends from the left to the right of the section view as shown using the arrow directions. The water pumped from the compensation chamber to the base flows through the microtubes (downward arrows) which is shown in detail in the inset view in Fig. 2(c). The flow from each microtube feeds a wick area surrounding the tube via the capillary pumping. The vapor generated by evaporation/boiling travels outward from the base wick between the micro-tube array and is exhausted through separate vapor lines that release into a condenser reservoir.

3 Experimental Method

The experimental setup and procedure are described in this section in addition to data reduction and uncertainty quantification.

3.1 Experimental Setup.

A schematic of the experimental flow loop is depicted in Fig. 4. A geared pump (Micropump EagleDrive) is used to drive liquid water through the loop at a fixed volumetric flowrate. The pump is regulated using feedback control with an inline piston flowmeter (Max Machinery, Healdsburg, CA). The subcooled liquid then passes through a heat exchanger, with the secondary coolant temperature regulated using a chiller (Julabo A40), to provide a constant inlet liquid temperature to the test section. The test section has three fluid outlets leading to a reservoir. One outlet is from the test section compensation chamber provides a simple liquid bypass. This bypass line has an electronically controlled valve (Hanby m-series) and mass flowmeter (Bronkhost mini CORI-FLOW) inline before connecting to the reservoir. The remaining two outlets are are inline with the wick for liquid/vapor extraction. These outlets have valves to regulate startup conditions for the test. The fluid reservoir has a built-in coil connected to another chiller (Julabo A40) to condense vapor. The fluid reservoir is open to the environment at atmospheric pressure. The fluid temperature values at the test section inlet and outlets are measured using calibrated K-type thermocouples. The pressure at the test section inlet is measured using a gauge pressure transducer (Omega PX409). The absolute pressure at the open reservoir outlet is measured using a digital differential pressure transducer (Omega DPG108) to ensure there is no pressure buildup in the reservoir.

Fig. 4
Experimental flow loop for the pump-assisted capillary cooler
Fig. 4
Experimental flow loop for the pump-assisted capillary cooler
Close modal

3.2 Operating Principles.

The evaporative cooling operation of the test section is shown in Fig. 5 as a function of fluid outlet temperature and input heat flux. At startup without any heating, liquid is pumped through the system thus fully immersing the wick and flooding all of the outlet pathways. For a low input heat flux, the wick is fully flooded and vapor generated in the wick may condense before exiting the test section. As input heat flux increases, the wick becomes partially flooded with an increase in vapor generation and a two-phase mixture of liquid and vapor exits the test section. At higher heat flux, more of the supplied liquid evaporates, and the fluid outlet temperature plateaus at 100 °C, with the wick being in a partially flooded condition. These observations are visually confirmed at the test section outlet as shown in the inset photographs.

Fig. 5
Evaporative cooling mechanism of the PACL cooler
Fig. 5
Evaporative cooling mechanism of the PACL cooler
Close modal

Despite the assistance of the pump, the PACL cooler is still subject to dry out as input heat flux increases. To overcome this limitation and extend the performance of the cooler, an electronic valve is added to the manifold outlet as shown in Fig. 4. The valve may be used to adjust the resistance of the manifold outlet to bias fluid toward the wick, (refer to Fig. 6). Consider a compensation chamber design where 50% of the input liquid is directed to the wick and 50% is allowed to bypass the test section (shown by equal arrow sizes in Fig. 6). During steady-state evaporative operation, the wick draws as much liquid as needed to replace evaporated fluid. As heat flux increases, vapor generation will also increase, leading to a buildup of pressure in the test section. This causes a reduction in the fluid supply to the wick, resulting in more liquid bypassing the test section. In Fig. 6, we have shown a representative diagram of the aforementioned situation when 40 % of the incoming liquid is supplied to the wick and the remaining amount is diverted via the bypass line (note the different arrow sizes). Further increase in the heat flux would eventually lead to the dry out of the wick impacting cooling performance. The bypass valve can be used here to increase the pressure in the compensation chamber, biasing liquid supply toward the wick and delaying the dry out of the wick. Control of the valve setting can be decided based on operational information such as the heater temperature (and its fluctuations), wick flowrate, test section pressure drop, and other parameters of interest. As the fluid supply to the wick is increased, the maximum heat flux of the PACL cooler can be effectively extended. A series of experiments are outlined next to measure the impact of such valve modulation on the cooler thermal performance.

Fig. 6
Valve control mechanism for PACL cooler. Arrow size (representative) is proportional to mass flowrate, ratio represents liquid supplied to the wick versus bypass valve
Fig. 6
Valve control mechanism for PACL cooler. Arrow size (representative) is proportional to mass flowrate, ratio represents liquid supplied to the wick versus bypass valve
Close modal

3.3 Experimental Procedure.

At startup, the pump is set to provide an inlet volumetric flowrate of 322ml/min. The liquid/vapor line valves are then closed and the e-valve digitally is set to 100% open to confirm the total flowrate using the flowmeter on the bypass line. The heat exchanger chiller is then set to regulate the test section inlet liquid temperature to 75 °C, the reservoir chiller is set to 20 °C to support vapor condensation, and the system is allowed time to reach the steady-state. Once the system fluid temperatures have reached the steady-state, the vapor valves are opened allowing liquid to be drawn by the wick, evaporate, and exit through the liquid/vapor lines to the reservoir. This is confirmed by the measured reduction in the flowrate through the bypass line using the flowmeter readings.

For a given experiment, the e-valve is digitally set to a specific position, either 100%, 60%, or 30% open. Sensor data are collected at 1 Hz using a National Instruments data acquisition system throughout the entirety of the test. Power is then supplied to the heater in increments using a power supply (BK Precision XLN10014) to collect steady-state data at each power level. This process includes setting the power supply voltage, allowing the system to reach the steady-state, and averaging the last 30 s of data for a steady-state measurement. The system is considered to be at steady-state conditions when a change in temperature of <2% is observed over a span of 2 min. The test is stopped when the heater temperature reaches 175°C as this is near the heater temperature limit.

4 Heat Loss Modeling and Data Reduction

4.1 Heat Loss Modeling.

To understand the heat loss to the environment during the experiments, a three-dimensional steady-state finite element (FE) heat conduction analysis is performed using commercial FE software [39]. The governing equations assuming the Einstein summation convention are
Qtot=xi(ki,jTxj)onΩfori,j=1,2,3(ki,jTxj)ni=qaonΓa,hi(TTα)ni=qconΓc(ki,jTxj)ni=0onΓn
(2)
where the total power, Qtot, is a function of the thermal conductivity, k, and temperature, T, on the domain Ω. This is subject to an applied heat flux, qa, at the heater surface, Γa, as well as a convective heat flux, qc, which is a function of the convective heat transfer coefficient, hamb, and ambient temperature, Tα, on the exterior surfaces of the model, Γc. The remaining boundaries, Γn, are adiabatic and restrict heat flux within the domain.

To determine the heat loss due to convection through the structure, the experimental conditions are adapted in the simulation. A heat transfer coefficient of 15W/m2K with an ambient temperature of 20°C is used to represent the lab environment. The initial temperature of the model is set to To=75C. Given the maximum operational temperature of the heater is 175 °C, a series of simulations are conducted by slowly ramping up the input power in the model until a maximum temperature of 175 °C is reached at a heat input of 2.75 W. The simulation boundary conditions and temperature profile at 2.75 W of input power are given in Fig. 7.

Fig. 7
One-half FE symmetry model of the test section with heat conduction simulation parameters (top) and numerical results at ΔT=100∘C temperature limit
Fig. 7
One-half FE symmetry model of the test section with heat conduction simulation parameters (top) and numerical results at ΔT=100∘C temperature limit
Close modal
Based on this data, a linear correlation is built to describe the temperature-dependent heat loss as follows:
Qloss=Cfit(ThTo),whereCfit=2.75W100C
(3)

4.2 Data Reduction.

The total input power, Qtot, is calculated by the product of the heater voltage, Vh, and current, Ih, as
Qtot=Vh×Ih
(4)
The input heat flux to the test section is calculated as the difference between the total input power, Qtot, the heat loss through conduction, Qloss, over the area (10×10mm2) of the resistive heater, Ah.
The effective heat transfer coefficient, h, is calculated as a function of the input heat flux, q, and the temperature difference between the heater temperature, Th, and test section fluid outlet temperature, Tf, which records the temperature of fluid after passing by the heater, where
h=q/(ThTf)
(5)
and
q=1Ah(QtotQloss)
(6)
The pressure drop across the test section, ΔP, is taken as the gauge inlet pressure measurement, Pin, given that the test section outlet is open to the atmosphere. The volumetric liquid flowrate to the wick, V˙wick, is calculated as the difference between the pump flowrate, V˙pump, and bypass flowrate, V˙bypass.
V˙wick=V˙pumpV˙bypass
(7)
The heat transferred to the single-phase flow of working liquid through the manifold bypass can be calculated using the following expression as a function of the liquid mass flowrate, m˙bypass, specific heat capacity, Cp, and the sensible temperature rise of the fluid from compensation chamber inlet to outlet.
Qsingle,bypass=m˙bypassCp(ToutTin)
(8)
The heat transferred to the single-phase liquid flow exiting the cooler through the vapor outlet is given by the following expression that characterizes the sensible temperature rise of the liquid between the inlet and vapor outlet line.
Qsingle,cooler=m˙wickCp(TfTin)
(9)
The two-phase heat transfer is calculated as the difference between the heater power and conduction, single-phase bypass, and single-phase cooler powers, as given by the following equation:
Qtwophase=QtotQlossQsingle,bypassQsingle,cooler
(10)
The locations of the thermocouples are presented in Fig. 4.

4.3 Uncertainty Analysis.

The accuracy of the experimental measurements is given in Table 2. These values are used to calculate the uncertainty of parameters calculated using experimental data as described in Ref. [40]. This reveals up to a 1% uncertainty in heat flux, q, <2% uncertainty in heat transfer coefficient, h, <2% uncertainty in the wick volumetric flowrate, V˙wick, in the boiling regime. Error bars are omitted in plots in the following sections for clarity.

Table 2

Experimental measurement accuracy

ParameterInstrumentAccuracy
ThK-type thermocouple±0.5C
TinRTD±0.002C
TfT-type thermocouple±0.1C
PinGauge transducer±0.004kPa
V˙pumpPiston flowmeter±0.02%
V˙bypassCoriolis flowmeter±0.2%
ParameterInstrumentAccuracy
ThK-type thermocouple±0.5C
TinRTD±0.002C
TfT-type thermocouple±0.1C
PinGauge transducer±0.004kPa
V˙pumpPiston flowmeter±0.02%
V˙bypassCoriolis flowmeter±0.2%

5 Results

Experimental results are presented in this section using a fixed liquid volumetric flowrate of 322ml/min. This includes data from three separate trials with the e-valve position set to either 100%, 60%, or 30% open.

5.1 Heat Transfer Performance.

The experimentally obtained boiling curves from all three e-valve position experiments are shown in Fig. 8. When the e-valve is 100% open, a peak heat flux of 537W/cm2 is measured. As the e-valve is partially closed in the following experiments, the peak heat flux increases to 574W/cm2 and 584W/cm2, for the 60% and 30% e-valve opening experiments, respectively. In all three cases, the cooler doesn’t reach the critical heat flux (CHF) or the dryout condition resulting in temperature runaway, but rather, the test is terminated when the steady-state heater temperature reaches 175°C. Less than 1% of the input power is lost to the ambient through conductive and convective losses based on the simulation model, discussed earlier in Sec. 4.

Fig. 8
Boiling curve for pump-assisted capillary cooler with DI water for three e-valve position experiments
Fig. 8
Boiling curve for pump-assisted capillary cooler with DI water for three e-valve position experiments
Close modal

The experimentally obtained heat transfer coefficient as a function of heat flux is shown in Fig. 9. When the e-valve is 100% open, the cooler achieves a maximum heat transfer coefficient of 92,370W/m2K starting at 356W/cm2. The heat transfer coefficient is then steady until it starts to reduce at 537W/cm2 to 86,000W/m2K. When the e-valve is 60% open, a maximum heat transfer coefficient of 95,620W/m2K is observed starting at a heat flux of 408W/cm2. From there, the heat transfer coefficient slowly decreases to 91,700W/m2K at 574W/cm2. For the 30% open e-valve experiment, a maximum heat transfer coefficient of 94,850W/m2K is achieved starting at 511W/cm2 heat flux. The heat transfer coefficient then slowly decreases to 92,670W/m2K at 584W/cm2. In all three cases, the heat transfer coefficient remains relatively constant after reaching a peak heat transfer value, with minor declines as heat flux further increases.

Fig. 9
Heat transfer coefficient as a function of input heat flux for three e-valve position experiments
Fig. 9
Heat transfer coefficient as a function of input heat flux for three e-valve position experiments
Close modal

5.2 Hydraulic Performance.

Pressure drop across the test section as a function of input heat flux is presented in Fig. 10. For the 100% open e-valve position experiment the pressure drop remained relatively constant below 0.18kPa, up to an input heat flux of 356W/cm2. Above this heat flux, there is a jump in the pressure drop with further increases in heat flux, leading to a peak pressure drop of 1.5kPa at 537W/cm2. This coincides with visual confirmation of vapor in the liquid/vapor lines and an increase in oscillations in recorded data as the pressure drop increases. Similar trends are observed at the additional e-valve positions up to a maximum pressure drop of 1.57kPa and 2.10kPa for the 60% and 30% e-valve open experiments, respectively.

Fig. 10
Test section pressure drop as a function of input heat flux for three e-valve position experiments
Fig. 10
Test section pressure drop as a function of input heat flux for three e-valve position experiments
Close modal

6 Discussion

The proposed capillary cooler demonstrated relatively high cooling performance with a relatively low pressure drop, <2kPa, across the test section. Pumped two-phase coolers with similar thermal performance, such as in Ref. [41], scale pressure less favorably with an increase in power. One way to compare the thermo-hydraulic performance is to measure the coefficient of performance (COP) for each cooler, COP=Q/(ΔPV˙). The capillary cooler shows 5× higher COP compared to the pumped cooler at maximum power. This benefit increases to a 25× higher COP at 380 W of input power, the power preceding vapor oscillation in the capillary cooler. This increase can be attributed to the evaporative cooling operation, which only draws as much fluid as needed and decouples liquid and vapor flow to keep pressure drop low. The pressure oscillations in the capillary cooler at higher power may be reduced with further structural optimization to retain low pressure throughout the operational range of the capillary cooler. This is left as a topic of future work.

To demonstrate the repeatability of the experimental results, a series of additional experiments are performed using a 100% open e-valve position. The heat flux versus temperature rise using data from six separate experiments is presented in Fig. 11. These experiments are performed on separate days with various input heat flux conditions. The data can be fit with a third-order polynomial to reveal an R2 value of 0.9948, indicating repeatable performance for the pump-assisted capillary cooler.

Fig. 11
Heat flux versus temperature rise for pump-assisted capillary cooler utilizing data from six separate experiments all with 100% open e-valve positions to show test repeatability
Fig. 11
Heat flux versus temperature rise for pump-assisted capillary cooler utilizing data from six separate experiments all with 100% open e-valve positions to show test repeatability
Close modal

A selection of the experimental data using all three e-valve positions is compiled into Fig. 12 to support the interpretation of the relative trends. The cooler maintains steady linear performance in all metrics until the test section outlet reaches Tf 100°C (marked by the vertical lines in Fig. 12), where increased vapor generation is noted. This is visually confirmed after 300W/cm2 for all experiments (refer to Fig. 13). As shown in Fig. 13, a complete transition from the liquid flow with small vapor bubbles to vapor flow with small entrained liquid droplets is observed at the vapor outlet lines as the heat flux approaches 300W/cm2.

Fig. 12
Compiled experimental results including vapor temperature, liquid pressure drop, wick volumetric flowrate, and heat transfer coefficient for three e-valve position experiments. Notably, the relative positioning of the vertical lines marks the heat flux when the vapor outlet is fully saturated.
Fig. 12
Compiled experimental results including vapor temperature, liquid pressure drop, wick volumetric flowrate, and heat transfer coefficient for three e-valve position experiments. Notably, the relative positioning of the vertical lines marks the heat flux when the vapor outlet is fully saturated.
Close modal
Fig. 13
Visualization of vapor flow. Liquid flow with small vapor bubbles <300W (left) and vapor flow with small liquid drops >300W (right).
Fig. 13
Visualization of vapor flow. Liquid flow with small vapor bubbles <300W (left) and vapor flow with small liquid drops >300W (right).
Close modal

As expected, the heat transfer coefficient, h, attains a maximum value and remains relatively constant with further increases in heat flux given that vapor is visually confirmed at the test section outlet. This heat flux, coincides with two additional effects, the first being a rise in the liquid line pressure drop and the second being a decrease in the volumetric flowrate supplied to the wick. The combination of these effects suggests higher vapor generation at high heat loads, engendered by increased evaporation at the wick surface, leading to a buildup in vapor pressure and consequently, inhibiting liquid supply to the wick. As the volumetric flow reduces, the critical heat flux of the cooler would eventually be reached if the liquid supply to the wick is not maintained. However, given that the 100% open e-valve experiment properly functions without reaching CHF, even when only 100ml/min of liquid is supplied to the wick, it can be inferred that there is a significant untapped increase in power dissipation capability when the e-valve is 30% open, because the wick flowrate remains above 200ml/min at the higher input power.

One way to extend the optimal operational range of the cooler is to employ a control scheme, where the bypass e-valve is adjusted to traverse our performance curves. To demonstrate this process, an additional experiment is performed and results are presented in Fig. 14. For this experiment, the bypass e-valve is left 100% open at startup such that peak heat transfer performance is achieved at the lowest possible heat flux of 356W/cm2. As the flowrate of liquid drawn to the wick reduces with further power increase, the bypass e-valve is then partially closed to increase liquid supply to the wick and extend its performance. Specifically, the e-valve position is throttled to 60% open at an input heat flux of 537W/cm2 and once again to 30% open at an input heat flux of 568W/cm2. As expected, the cooler then follows the independent performance curve at each respective e-valve position. This experiment was continued to a maximum input heat flux of 610W/cm2 and the test was concluded due to the heater temperature limit prior to ever reaching CHF. This strategy effectively extended the peak performance range of the cooler from 356–537 W/cm2 to 356–610 W/cm2 within the experimental temperature limit. An energy balance analysis is conducted to better understand the performance of the cooler when activating the bypass valve. The conduction heat loss, Qloss, is calculated using Eq. (3), based on the simulation discussed in Sec. 4. The single-phase heat transfer to the liquid in the bypass line, Qsingle,bypass, is determined with Eq. (8) and that to the single- phase liquid passing through the cooler wick, Qsingle,cooler, with Eq. (9), both utilizing sensor data. When the wick is fully flooded at 95 W of input power, a predicted heat transfer of 95.9 W is calculated with 94 W attributed to liquid in the cooler and <1W each from conduction and liquid in the bypass line. This calculation is within the 2% uncertainty bound at the corresponding heater temperature, thus supporting the single-phase heat transfer contributions obtained in this analysis.

Fig. 14
Experimental results using an e-valve control experiment compared to the prior three experiments
Fig. 14
Experimental results using an e-valve control experiment compared to the prior three experiments
Close modal

The heat transfer in the two-phase regime for various input powers is shown in Fig. 15. The two-phase contribution, Qtwophase, (black shaded regions in Fig. 15) is calculated using Eq. (10). The single-phase cooler power (dark gray shaded regions in Fig. 15) in this regime accounts for the energy required to raise the liquid temperature at the evaporator surface from the inlet temperature to the saturation temperature. With increasing heater power up to 540 W, the wick flowrate decreases from 186ml/min to 129ml/min. This results in a decreased single-phase contribution in the cooler from 284W to 186W, while the two-phase contribution increases from 39W to 290W. By throttling the valve from 100% to 60% at a heater power of 540W, the flowrate to the wick increases, thus slightly increasing the single-phase contribution to 235W and slightly decreasing the two-phase contribution to 261W. With further throttling to 30% e-valve opening at heat fluxes higher than 570W, the single-phase contribution further increases, with the reduction of two-phase cooling contributions. Notably, for all the heat fluxes, the combined contribution of the single-phase and two-phase cooling overrides the contributions from the bypass line, as evident from Fig. 15.

Fig. 15
Energy balance for two-phase cooling (conduction loss is limited to 2.75 W for the maximum input power)
Fig. 15
Energy balance for two-phase cooling (conduction loss is limited to 2.75 W for the maximum input power)
Close modal

7 Conclusion

In this work, we designed and experimentally evaluated a pump-assisted capillary loop system for high-heat flux applications. A flat plate cooler was specified with a compensation chamber and micro-tube array to supply liquid to an evaporator wick. Several experiments were conducted to show consistent performance up to an input heat flux of 610W/cm2 with a relatively low cooler pressure drop of 2 kPa. Input heat flux was limited by the experimental facility; therefore, experiments were stopped when the heater reached a maximum temperature of 175°C prior to the wick drying out. Exploring the heat flux limits of this cooler design, the reliability of the wick and micro-tube array, and the use of alternative coolants is left as future work.

The cooler performance seems limited by a buildup of vapor pressure in the test section, leading to some reduction in liquid supply through the micro-tube array and accompanied by a minor decrease in the heat transfer coefficient. Notably, this challenge can be tackled by adjusting the pressure in the compensation chamber by partially closing the liquid bypass e-valve. This e-valve control strategy was experimentally demonstrated to extend the input heat flux range of peak performance with manual adjustments. This strategy may be automated with the inclusion of sensor-based feedback control. As an alternative strategy to explore in future work, pressure buildup may be minimized through additional structural design of the cooler and flow path.

Conflict of Interest

There are no conflicts of interest.

Data Availability Statement

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

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