Multi-objective genetic optimisation of additively manufactured topology-optimised heat exchangers

Introduction

Compact heat exchangers are increasingly constrained by volume, mass, pressure drop, and manufacturability rather than by heat-transfer coefficient alone. Additive manufacturing expands the design space by allowing curved manifolds, internal lattices, graded channels, and geometries that would be impractical to braze or machine [12,20]. Reviews of heat-exchanger additive manufacturing have highlighted this opportunity, but also warn that roughness, powder removal, leak tightness, inspection, and process repeatability can dominate performance [12].

Topology optimisation offers a complementary design route. Starting from foundational structural topology optimisation [2], the method has been extended to fluid flow, conjugate heat transfer, heat sinks, and two-fluid heat exchangers [3,4,5,6,7,8,9,10,11]. In principle, topology optimisation can discover flow paths and solid layouts that outperform human-drawn channels. In practice, the raw topology often contains thin members, unsupported overhangs, trapped powder, and surface features that are hard to print. A manufacturable heat exchanger therefore needs both physics optimisation and production constraints.

Multi-objective genetic algorithms are well suited to this mixed design space because the objectives conflict and the variables are partly discrete. NSGA-II remains a common reference algorithm for Pareto optimisation [1], and recent work has used genetic design and additive manufacturing to produce ultra-power-dense heat exchangers [14]. Genetic approaches have also been applied to topology-like fin design in aerospace heat exchangers [15]. The present study builds on that direction but adds explicit manufacturability variables and experimental validation.

The contribution is a workflow, not a universal optimum. We combine topology-optimised manifolds, parametric AM-compatible core modules, surrogate-assisted NSGA-II search, high-fidelity conjugate CFD, and physical testing. The aim is to quantify the trade space among heat duty, pressure drop, mass, and printability in a realistic metal AM heat exchanger.

Design problem

The target application is a compact water-to-water heat exchanger for a 12 kW electronics-cooling loop. The envelope is 110 mm x 70 mm x 42 mm, with inlet and outlet ports fixed by the surrounding package. The hot-side flow rate is 12 L min-1 at 65 deg C, and the cold-side flow rate is 10 L min-1 at 22 deg C. Maximum allowable pressure drop is 38 kPa per side, and the design must be printable in AlSi10Mg by laser powder-bed fusion without internal support removal.

The baseline design is a printed straight-channel counterflow exchanger with 1.2 mm channels and 0.55 mm walls. It is intentionally conservative: all channels are accessible to powder removal, overhangs are above 45 degrees after build orientation, and wall thickness exceeds the supplier minimum. This baseline provides a fair manufacturing reference, not the best possible conventional heat exchanger.

The optimisation design family has two layers. The distributor manifolds are generated from smoothed topology-optimised flow fields, inspired by fluid and heat-transfer topology-optimisation methods [3,6,7]. The core region uses parametric microchannel and TPMS-like modules, reflecting recent AM heat-exchanger practice with microarchitected and mathematically defined cores [16,17,18]. This hybrid approach avoids sending an arbitrary density field directly to the printer.

Four objectives are evaluated: maximise heat duty at specified inlet conditions, minimise total pumping power, minimise dry mass, and minimise manufacturability risk. Risk is a scalar penalty built from minimum channel diameter, unsupported overhang area, trapped-powder volume, wall thickness below process capability, predicted distortion, and inspection access. It is not a substitute for process qualification, but it forces the optimiser to see printing constraints during search.

Parametric geometry and constraints

Each candidate geometry is defined by 28 variables. Manifold variables include branch count, branch taper, splitter curvature, minimum bend radius, and distributor-to-core transition length. Core variables include hydraulic diameter, channel pitch, TPMS level-set offset, fin thickness, porosity gradient, and hot/cold-side phase shift. Build variables include orientation, drain-port area, sacrificial powder-removal channel placement, and minimum self-support angle.

The topology-optimised seed manifolds are generated on a coarse finite-volume grid using pressure-drop and flow-uniformity objectives. The raw density fields are skeletonised, smoothed, and converted into manufacturable splines. This conversion step is deliberately lossy. Very small branches and checkerboard-like features are removed because they would not survive printing or powder evacuation. The workflow follows the spirit of topology optimisation while acknowledging AM constraints reviewed for topology-optimised printed parts [19].

The AM constraints are based on supplier limits for AlSi10Mg powder-bed fusion: minimum enclosed channel diameter of 0.65 mm after depowdering, minimum wall thickness of 0.45 mm, self-support angle of approximately 45 degrees for long spans, and at least two drain paths for each enclosed powder volume. The optimiser is allowed to violate these limits, but violations increase manufacturability risk and can remove candidates from final fabrication.

Surface roughness is represented by an equivalent sand-grain roughness in the CFD screening model. The value depends on build orientation and channel diameter. This roughness correction is crude but important. Smooth-wall CFD systematically underpredicts pressure drop in small printed channels, as AM heat-exchanger studies repeatedly report [12,13].

Optimisation workflow

The optimisation uses NSGA-II with a population of 160 designs for 110 generations [1]. Initial populations combine Latin-hypercube samples, topology-derived manifold seeds, and perturbed baseline designs. Crossover and mutation probabilities are adapted based on Pareto-front crowding distance. Discrete variables, such as core family and build orientation, are mutated separately from continuous geometry variables.

A full CFD evaluation for every candidate would be too expensive. We therefore use a two-stage surrogate-assisted workflow. First, 1240 designs are evaluated by steady conjugate heat-transfer CFD. A gradient-boosted surrogate predicts heat duty, pressure drop, and manufacturability penalties for the evolving population. Every tenth generation, a batch of high-uncertainty or Pareto-relevant candidates is sent back to CFD, and the surrogate is retrained. This active loop keeps the search from drifting into regions where the surrogate is poorly informed.

The final Pareto front contains 96 designs re-evaluated by high-fidelity CFD with refined near-wall mesh, roughness correction, and temperature-dependent water properties. Three designs are selected for fabrication: a heat-duty-maximised design, a balanced design, and a pressure-drop-minimised design. The selection uses a knee-point criterion and manufacturability risk threshold rather than choosing the visually most complex geometry.

The workflow is intentionally more conservative than unconstrained generative design. Additive manufacturing makes complex internal channels possible, but not all complexity is useful. The optimiser is rewarded only when complexity improves the Pareto trade-off after roughness, powder removal, and minimum feature constraints are included.

Simulation model

CFD simulations solve steady incompressible conjugate heat transfer with turbulent flow where local Reynolds number exceeds 2300 and laminar flow elsewhere. The solid domain uses temperature-dependent AlSi10Mg thermal conductivity measured from printed coupons. Contact resistance is neglected because the exchanger is monolithic. The mesh contains 8-24 million cells for final candidates, with prism layers in all channels and local refinement at manifold splitters.

Boundary conditions reproduce the test loop: prescribed mass flow rates and inlet temperatures, zero-gauge pressure outlet, and adiabatic outer walls. Heat duty is computed from both hot- and cold-side enthalpy change, and simulations are accepted only when the two agree within 1.2%. Pressure drop includes inlet and outlet manifolds inside the printed envelope but excludes external fittings.

Model validation starts with the baseline straight-channel exchanger. Smooth-wall CFD underpredicts measured pressure drop by 19%, while roughness-corrected CFD reduces the error to 6%. Heat duty is predicted within 4%. This baseline calibration is then held fixed for all optimised geometries. We avoid re-tuning roughness per design because doing so would hide the manufacturability penalty of small, rough channels.

The topology-optimisation literature often reports elegant field solutions under ideal boundary conditions [4,5,6,7]. Our model instead treats topology-derived shapes as manufacturable candidates inside a constrained product envelope. This reduces theoretical optimality but makes the CFD comparison closer to what a printed heat exchanger must survive.

Pareto-front behaviour

The final Pareto front shows a clear trade-off between heat duty and pumping power. Increasing heat duty beyond about 15.5 kW requires smaller channels and higher core area density, which raises pressure drop sharply. The heat-duty-maximised design reaches 16.4 kW in CFD but exceeds the pressure-drop target by 18%. The pressure-drop-minimised design remains below 25 kPa per side but reaches only 13.7 kW. The balanced design reaches 15.2 kW with pressure drops of 34 and 32 kPa on hot and cold sides.

Mass and manufacturability introduce a second trade-off. Some high-performance designs are light because they use thin walls and high porosity, but they also have high risk scores due to long unsupported spans. Other designs are robustly printable but heavy. The useful part of the Pareto front lies between these extremes. This confirms the central premise: thermal-hydraulic optimisation and printability cannot be separated.

Topology-derived manifolds improved flow uniformity. Compared with the baseline, the balanced design reduced core inlet maldistribution from 21% to 8% coefficient of variation. This improved heat-duty utilisation even though its average channel hydraulic diameter was larger than that of the heat-duty-maximised design. Good distribution sometimes beat brute-force surface area.

TPMS-like cores performed best at high heat duty but were more sensitive to powder-removal constraints. Microchannel cores were easier to depowder and inspect but had lower compactness. Hybrid cores, with TPMS structures near high-heat-flux regions and microchannels near ports, populated much of the Pareto knee.

Fabrication and inspection

Three Pareto designs and the baseline were fabricated by laser powder-bed fusion in AlSi10Mg. Parts were built at 35 degrees from the base plane to reduce long horizontal overhangs and improve drain access. After printing, parts underwent stress relief, bead blasting on accessible external surfaces, ultrasonic cleaning, and pressure leak testing at 1.5 times the operating pressure.

Micro-CT inspection showed that the balanced and pressure-drop-minimised designs printed without blocked channels. The heat-duty-maximised design had partial powder occlusion in three channel groups with nominal hydraulic diameters below 0.72 mm. These occlusions were not catastrophic but increased measured pressure drop beyond CFD predictions. The result confirms why minimum channel diameter should be an optimisation variable and not a post-processing rule.

Surface roughness varied with build orientation. Vertical channels had arithmetic mean roughness around 13 micrometres, while downward-facing shallow overhang channels reached 31 micrometres. The roughness correction in CFD captured the trend but underpredicted the worst local losses. Future workflows should include orientation-dependent roughness maps rather than one equivalent value per design.

Dimensional inspection also found global distortion of 0.18-0.42 mm, largest near thin manifold walls. The distortion did not affect leak tightness but shifted port alignment. Designs with lower manufacturability risk had less distortion. This supports including structural and process constraints even when the primary objective is thermal performance.

Experimental thermal-hydraulic performance

Water-to-water tests were performed over flow rates from 5 to 14 L min-1 per side. At the design point, the balanced design increased heat duty by 31 +/- 4% relative to the baseline and reduced mass by 18 +/- 2%. Pressure drop increased by 11 +/- 3%, staying below the 38 kPa target. The measured effectiveness improved from 0.61 for the baseline to 0.76 for the balanced design.

The heat-duty-maximised design delivered the largest heat transfer, 38 +/- 5% above baseline, but pressure drop was 47 +/- 6% higher because of roughness and partial occlusion. This design would be attractive only if pumping power were less important than volume. The pressure-drop-minimised design reduced pumping power by 22 +/- 5% relative to baseline but sacrificed 9% heat duty. All three designs therefore occupy physically meaningful positions on the Pareto front.

CFD predicted heat duty within 5% for the balanced and pressure-drop-minimised designs. Pressure drop errors were 8% and 6%, respectively. For the heat-duty-maximised design, pressure drop error reached 24% because the simulation did not include powder occlusion. This is a manufacturability failure rather than a turbulence-model failure.

Repeated thermal cycling between 20 and 70 deg C for 200 cycles produced no leaks and no measurable change in pressure drop for the balanced design. The heat-duty-maximised design showed a 3% pressure-drop increase, likely from particle release or movement in partially occluded channels. Long-term fouling was not evaluated.

Comparison with existing AM heat exchangers

The measured performance is consistent with recent additively manufactured heat exchangers using manifold-microchannel, microarchitected, and mathematically defined cores [13,16,17]. It does not reach the ultra-power-density reported in the most aggressive genetic-algorithm AM heat-exchanger demonstrations [14], but those devices target different envelopes, materials, and heat fluxes. Our emphasis is on a repeatable workflow with explicit manufacturability accounting.

Compared with pure topology-optimised heat sinks and two-fluid heat-exchanger layouts [6,7,8,9,10,11], the present design family is more constrained but easier to fabricate. It preserves topology optimisation where it is most useful, in manifold distribution and flow routing, while using parametric cores where powder removal and inspection are critical. This hybrid strategy may be less elegant mathematically, but it is more robust experimentally.

The printed straight-channel baseline is not obsolete. It is lighter to qualify, easier to inspect, and less sensitive to powder removal. The optimised designs are justified only when volume or mass constraints make the additional design and inspection effort worthwhile. This practical comparison is often missing when AM heat exchangers are judged only by peak heat-transfer density.

Sensitivity and ablation studies

Removing manufacturability risk from the optimisation produced designs with 6-9% higher predicted heat duty but 2.4 times higher blocked-channel probability in CT-based process simulation. Removing roughness correction shifted the Pareto front toward smaller channels and caused pressure-drop underprediction above 25%. Removing topology-derived manifold seeds slowed convergence and produced more maldistributed cores, but the genetic algorithm eventually found similar lower-performance designs.

Surrogate uncertainty mattered most near the high-heat-duty end of the front. Designs in this region had narrow channels and high curvature, making CFD response more nonlinear. Active learning reduced final surrogate heat-duty error from 7.8% to 2.9% on the validation set. Without active retraining, NSGA-II exploited surrogate artefacts and proposed several nonphysical high-performance candidates.

Build orientation was not a minor variable. Fixing the orientation at the baseline build angle reduced the number of feasible Pareto designs by 31%. The optimiser used orientation changes to trade overhang risk against drain access. This reinforces design-for-AM guidance that orientation, support, and internal-channel cleanup are part of the geometry problem, not downstream manufacturing choices [19,20].

Limitations

The study uses steady single-phase water tests. Boiling, condensation, supercritical CO2, and gas-side fouling would require different models and objectives. Printed circuit heat-exchanger work shows that high-pressure and supercritical-fluid behaviour can be very sensitive to channel geometry and property variation [21]. The present water-loop results should therefore not be transferred directly to those applications.

The manufacturability risk score is empirical. It captures observed powder removal, overhang, roughness, and wall-thickness trends for one material and process supplier. Another machine, powder lot, scan strategy, or post-processing route would change the thresholds. A production workflow would require process-specific calibration and nondestructive inspection standards.

The optimisation also assumes that the topology-derived manifolds can be represented by smooth splines and that the core families are chosen before the genetic search. A more open generative representation might find better geometries, but it would also increase the risk of unprintable internal features. The conservative design family is a deliberate compromise.

Conclusion

We developed and validated a multi-objective genetic optimisation workflow for additively manufactured topology-informed heat exchangers. By combining topology-derived manifolds, parametric printable cores, surrogate-assisted NSGA-II search, manufacturability penalties, and experimental testing, the workflow identified designs that improved heat duty and mass relative to a printed straight-channel baseline while keeping pressure drop within target limits.

The main lesson is that additive manufacturing changes the optimisation problem rather than removing constraints. Small channels, high surface area, and intricate topology can improve heat transfer in simulation, but roughness, powder removal, overhangs, distortion, and inspection access decide whether the design is useful. Multi-objective optimisation is valuable because it exposes these trade-offs before fabrication.

Data and code availability

The supplementary archive contains the parametric CAD scripts, topology seed fields, NSGA-II populations, surrogate training data, CFD meshes, final STL files, build orientation reports, micro-CT measurements, flow-loop measurements, and notebooks used for Pareto analysis and uncertainty propagation.

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