Stability maps for flow boiling in additively manufactured microchannel heat sinks

Introduction

Two-phase microchannel heat sinks offer high heat-transfer coefficients and compact thermal resistance for power electronics, avionics, laser diodes, and compact energy systems. The attraction is clear: latent heat transport allows heat fluxes that are difficult to manage with single-phase cooling. The difficulty is equally familiar. Flow boiling in small parallel channels can exhibit large pressure-drop oscillations, upstream compressibility effects, channel-to-channel maldistribution, intermittent backflow, and premature critical heat flux. Reviews and foundational studies by Kandlikar, Qu and Mudawar, and Thome established both the promise and the unsettled physics of microchannel flow boiling [1,2,3,4].

Instability matters because a heat sink can have an excellent average heat-transfer coefficient but still fail a device-level requirement if one channel dries out or if wall temperature oscillates at damaging amplitude. Experiments on water boiling in parallel microchannels demonstrated intermittent flow reversal and strong pressure fluctuations [5], while later studies in silicon microchannel heat sinks documented pressure-drop and flow-boiling instabilities with measurable thermal consequences [6,8]. Reentrant cavities, inlet restrictions, and active perturbation have all been explored as mitigation strategies [7]. Recent work continues to show that pressure-drop oscillations and parallel-channel instabilities influence both heat-transfer coefficient and critical heat flux [10].

Additive manufacturing introduces a useful but complicated design freedom. Laser powder bed fusion and related processes can integrate manifolds, non-planar headers, distributed inlet restrictions, and porous or permeable features that are difficult to machine conventionally [11,12,13]. Reviews of heat-exchanger additive manufacturing emphasise the opportunity for compact, application-specific geometries, while also noting surface roughness, powder removal, minimum channel size, and inspection challenges [14,15]. The present article asks how this design freedom changes flow-boiling stability, not only peak heat transfer.

We study three additively manufactured microchannel heat-sink architectures under identical flow-boiling conditions and construct stability maps from time-resolved pressure, flow-rate, and wall-temperature data. The goal is a design map: where is operation stable, where do oscillations begin, and what geometric features shift those boundaries?

Heat-sink designs and manufacture

Three AlSi10Mg heat sinks were manufactured by laser powder bed fusion. Each heat sink contained 24 parallel channels over a heated footprint of 30 mm by 24 mm. The channel length was 32 mm, and the nominal rectangular channel cross sections were 0.70 mm by 0.52 mm, 0.90 mm by 0.62 mm, or 1.10 mm by 0.70 mm depending on design variant. A 2.1 mm thick base separated the channel floor from the electrical heater block. All parts were stress relieved at 300 deg C for 2 h and cleaned by ultrasonic agitation, pulsed deionised-water flushing, and compressed nitrogen drying.

The first architecture used a straight inlet and outlet plenum feeding all channels equally in plan view. The second used a tapered inlet manifold designed to maintain nearly uniform static pressure along the header. The third added printed inlet restrictors upstream of each channel, with nominal restriction hydraulic diameter of 0.38 mm and length of 1.2 mm. The restrictor design intentionally increased single-phase pressure drop to stabilise the two-phase operating point. Such inlet resistance is a conventional stabilisation concept, but additive manufacturing makes it possible to integrate the restrictions without separate inserts.

X-ray computed tomography was used to measure as-built hydraulic diameter, restriction area, and powder-removal defects. The mean hydraulic diameter was 5.8% below nominal for the smallest channels and 2.1% below nominal for the largest channels. Surface roughness measured on witness channels was Ra = 18-26 micrometres, with partially fused particles concentrated on downward-facing channel roofs. No channel was fully blocked, but three restrictors in the smallest restrictor design had area reductions above 14%. These measurements were used in the pressure-drop model because nominal CAD dimensions produced misleading stability predictions.

Experimental facility and classification method

The working fluid was degassed deionised water. Mass flux was varied from 180 to 820 kg m^-2 s^-1, inlet subcooling from 5 to 25 K, and outlet pressure from 110 to 240 kPa. Heat flux was applied by a copper heater block with six cartridge heaters and measured after correcting for lateral heat loss through a guarded insulation stack. The maximum applied heat flux was 240 W cm^-2, although many low-flow tests were stopped earlier when wall-temperature excursions exceeded the safety limit. Each operating point was held for at least 180 s after initial boiling incipience or after the last flow-rate change.

Instrumentation included Coriolis mass flow measurement, inlet and outlet absolute pressure, differential pressure across the heat sink, eight embedded wall thermocouples, infrared imaging of the heater-side wall, and two fast-response pressure transducers sampled at 5 kHz. Because the printed heat sinks were opaque, direct channel visualisation was not attempted in the main specimens. A transparent acrylic surrogate with matched manifold planform and 1.0 mm channels was used only to interpret backflow signatures; it was not used for quantitative heat-transfer results.

Operating points were classified into four regimes. Stable nucleate boiling required wall-temperature root-mean-square fluctuation below 1.5 K and no pressure spectral peak above five times the background. Intermittent inlet backflow was identified by negative short-duration flow inferred from high-frequency inlet pressure and confirmed in the transparent surrogate. Pressure-drop oscillation required a coherent pressure and flow-rate peak between 0.2 and 4 Hz with wall-temperature oscillation above 2 K. Parallel-channel maldistribution and local dryout were identified by diverging wall-temperature traces across the heater footprint, sudden loss of inferred heat-transfer coefficient in a channel group, and failure to recover after a small mass-flux increase. The classification is phenomenological but reproducible: two independent analysts agreed on 94% of the 684 labelled points.

Network model and stability boundary

A one-dimensional two-phase network model was developed to interpret the stability maps. Each channel was represented by a heated control-volume sequence with single-phase liquid, subcooled boiling, saturated boiling, and annular-flow pressure-drop closures. The model was not intended to discover a new boiling correlation. It used established microchannel pressure-drop and critical-heat-flux measurements as calibration anchors [2,3,9,18]. The inlet plenum, outlet plenum, pump line, and accumulator were represented as lumped compressible volumes because upstream compliance strongly affected pressure-drop oscillation onset.

The model solved transient mass, momentum, and energy balances with a homogeneous-equilibrium approximation in the two-phase regions. This approximation is imperfect in microchannels, especially during intermittent backflow and dryout, but it captures the feedback between vapour generation, pressure drop, and flow redistribution. Hydraulic diameters and restrictor areas were taken from CT measurements rather than nominal geometry. Wall thermal capacitance was included because printed AlSi10Mg bases damped some high-frequency thermal response while leaving pressure oscillations visible.

Stability was assessed by perturbing steady operating points by a 2% inlet-flow disturbance and tracking whether pressure and wall-temperature oscillations decayed within 20 s. The model reproduced the qualitative boundary between stable boiling and pressure-drop oscillation, but it did not reliably predict local dryout in maldistributed states. Dryout depended on channel-to-channel manufacturing scatter and local roughness, which were only represented statistically.

Results

The straight-plenum design entered intermittent backflow shortly after boiling incipience at low mass flux. At G = 240 kg m^-2 s^-1 and 10 K inlet subcooling, backflow appeared at 58 W cm^-2, pressure-drop oscillation at 74 W cm^-2, and local dryout at 108 W cm^-2. Wall-temperature oscillations reached 9.6 K peak-to-peak during pressure-drop oscillation. The oscillation frequency decreased from 1.8 Hz to 0.7 Hz as heat flux increased, consistent with a larger vapour compressibility contribution and slower channel refill.

The tapered manifold delayed channel-to-channel maldistribution but did not eliminate pressure-drop oscillation. At the same mass flux and subcooling, the onset of pressure-drop oscillation shifted to 88 W cm^-2 and local dryout to 132 W cm^-2. Infrared thermography showed more uniform wall temperature across the channel array during stable boiling, with lateral temperature spread reduced from 11.2 K in the straight-plenum design to 6.7 K. The improvement was largest at intermediate mass flux, where manifold pressure variation mattered more than restriction pressure drop.

The restrictor design had the broadest stable operating envelope. At G = 240 kg m^-2 s^-1 and 10 K subcooling, pressure-drop oscillation onset shifted to 97 W cm^-2, 31% higher than the straight-plenum case, and local dryout occurred at 151 W cm^-2. The penalty was increased pumping power: single-phase pressure drop at 25 deg C rose by 9% relative to the straight-plenum design for the medium-channel variant and by 17% for the smallest-channel variant. This is an acceptable penalty for high-heat-flux operation, but it would be unattractive in a low-power thermal-control loop.

Channel size and outlet pressure altered the maps substantially. Larger channels delayed pressure-drop oscillation at low mass flux because vapour quality rose more gradually along the heated length, but they reduced heat-transfer area density and increased wall superheat at high heat flux. Raising outlet pressure from 110 to 240 kPa suppressed backflow and increased dryout heat flux by 18-24%, but also raised saturation temperature and device wall temperature. Inlet subcooling helped at low heat flux by suppressing premature boiling in the inlet manifold; at high heat flux it increased axial temperature gradients and sometimes sharpened the transition into pressure-drop oscillation.

Model predictions were sensitive to as-built geometry. Using nominal CAD dimensions over-predicted pressure-drop oscillation onset by 18% on average. Replacing nominal hydraulic diameters and restrictor areas with CT-informed values reduced this error to 6%. The remaining error was largest for the smallest printed channels, where roughness height was no longer negligible relative to channel hydraulic diameter. Thus AM roughness cannot be treated only as a heat-transfer enhancement; it also changes pressure-drop slope and therefore dynamic stability.

Discussion

The stability maps show that additive manufacturing helps most when it is used to shape the hydraulic network, not merely to reproduce a conventional parallel-channel block. Tapered manifolds reduced maldistribution by flattening header pressure gradients, while printed restrictors stabilised the inlet boundary condition. These are classical ideas in two-phase flow, but AM makes them easier to integrate in compact heat sinks. The results align with recent AM manifold-microchannel and permeable-membrane work showing that three-dimensional flow distribution can be a first-order thermal design variable [11,12,13,16,17].

The same maps also warn against judging a heat sink by steady heat-transfer coefficient alone. Several operating points had high inferred heat-transfer coefficient immediately after boiling incipience but were dynamically unstable over 30-90 s. In electronics cooling, such oscillations can interact with control loops, pump compliance, and thermal cycling of solder joints. The relevant design object is therefore an operating envelope bounded by pressure-drop oscillation, channel maldistribution, and dryout, not a single best heat-transfer point.

The AM process introduced stabilising and destabilising effects simultaneously. Roughness promoted earlier boiling incipience and reduced temperature overshoot in some tests, but it also increased frictional pressure drop and amplified sensitivity to hydraulic-diameter scatter. Restrictor dimensional scatter was particularly important because a small area error changes local inlet resistance strongly. CT-informed modelling is therefore not an optional embellishment for printed microchannels; it is part of the hydraulic design loop. This mirrors broader AM heat-exchanger concerns about inspection, powder removal, and process-aware modelling [14,15].

Several limitations should be noted. The printed channels are larger and rougher than etched silicon microchannels, so the maps should not be transferred directly to chip-scale coolers. The working fluid was water; dielectric fluids would have different latent heat, surface tension, and pressure-drop behaviour. The two-phase network model used homogeneous-equilibrium assumptions and did not resolve slug dynamics, contact-line motion, or local dryout patches. Finally, the transparent surrogate used for backflow interpretation did not reproduce the thermal mass or roughness of the metal parts. The regime labels are therefore engineering classifications, not direct flow-regime visualisations inside the printed heat sinks.

Conclusion

We constructed stability maps for water flow boiling in additively manufactured AlSi10Mg microchannel heat sinks with straight, tapered, and restrictor-fed manifold architectures. The maps separated stable nucleate boiling, intermittent inlet backflow, pressure-drop oscillation, and maldistribution-driven dryout. Tapered manifolds improved temperature uniformity, while printed inlet restrictors shifted pressure-drop oscillation to substantially higher heat flux at the cost of additional pumping power.

The main conclusion is that AM microchannel heat sinks should be designed as dynamic two-phase networks. Integrated manifolds and restrictions can expand the stable operating envelope, but printed roughness and dimensional scatter move the boundaries. Future work should couple CT-informed geometry, transient two-phase modelling, and closed-loop pump compliance into the design process, then extend the maps to dielectric fluids and pulsed heat loads.

Data and code availability

Processed pressure, flow, thermocouple, infrared, and heater-power time series are included in the supplementary archive together with CT-derived channel geometry, stability labels, uncertainty estimates, and network-model scripts. The analysis was run with Python 3.10, NumPy 1.24, SciPy 1.10, pandas 1.5, and matplotlib 3.7. Raw high-speed pressure and infrared files are provided for representative points in each stability regime; the full raw dataset is available as compressed HDF5 files because of size.

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