Designing Heat Exchangers with Lattices

Heat exchangers convert thermal energy between fluid streams. Their performance is governed by a simple principle: maximize the surface area in contact with the fluid while minimizing the resistance to heat flow and the pressure drop through the flow path. Traditional heat exchangers --- finned tubes, plate-and-frame, shell-and-tube --- achieve this with macroscopic channels and fins arranged in regular patterns.

Lattice-based heat exchangers take a fundamentally different approach. Instead of discrete channels, the heat transfer surface is a continuous, periodic 3D structure --- a lattice --- that fills the exchanger volume. The lattice creates an intricate network of interconnected flow paths with surface-area-to-volume ratios that conventional designs cannot match. The result is heat exchangers that are 30—60% smaller and lighter than conventional designs at equivalent thermal performance.

Why Lattices Work for Heat Exchange

The effectiveness of a heat exchanger depends on three factors:

1. Surface area density. More surface area per unit volume means more heat transfer per unit size. TPMS (triply periodic minimal surface) lattices achieve surface area densities of 500—2000 m2/m3, compared to 100—300 m2/m3 for typical finned-tube designs.

2. Flow mixing. Lattice structures create tortuous flow paths that promote turbulent mixing even at low Reynolds numbers. This thins the thermal boundary layer and increases the local heat transfer coefficient. The effect is analogous to turbulator inserts in conventional tubes, but distributed throughout the entire volume.

3. Structural efficiency. TPMS lattices are self-supporting, load-bearing structures. The heat exchanger does not need a separate structural shell --- the lattice itself carries mechanical loads. This dual function reduces total mass and part count.

TPMS Lattice Types

Triply periodic minimal surfaces are mathematically defined surfaces that divide space into two interpenetrating, non-intersecting channel networks. Each network can carry a separate fluid (hot side and cold side), and the dividing surface is the heat transfer area.

Gyroid

sin(2*pi*x/p) * cos(2*pi*y/p) + sin(2*pi*y/p) * cos(2*pi*z/p) + sin(2*pi*z/p) * cos(2*pi*x/p) = t

The gyroid is the most commonly used TPMS for heat exchangers. It has zero mean curvature (minimal surface), produces two identical, mirror-image channel networks, and has excellent self-supporting properties for additive manufacturing (no overhang exceeds 42 degrees from vertical). The smooth, continuous surface minimizes stress concentrations.

Schwarz-P (Primitive)

cos(2*pi*x/p) + cos(2*pi*y/p) + cos(2*pi*z/p) = t

The Schwarz-P surface creates larger, more open channels than the gyroid. This results in lower pressure drop but also lower surface area density. It is preferred when pressure drop is the binding constraint, such as in gas-phase heat exchangers where pumping power is expensive.

Schwarz-D (Diamond)

sin(2*pi*x/p)*sin(2*pi*y/p)*sin(2*pi*z/p) + sin(2*pi*x/p)*cos(2*pi*y/p)*cos(2*pi*z/p) + cos(2*pi*x/p)*sin(2*pi*y/p)*cos(2*pi*z/p) + cos(2*pi*x/p)*cos(2*pi*y/p)*sin(2*pi*z/p) = t

The diamond surface has higher surface area density than the gyroid and creates more tortuous flow paths. This increases both heat transfer and pressure drop. It is suited for compact liquid-liquid exchangers where pumping power is cheap relative to the value of thermal performance.

Lidinoid and IWP

Less common TPMS types that offer different trade-offs between surface area, channel geometry, and manufacturability. The design space of TPMS is large, and new surface types are actively researched.

Design Parameters

Cell Size (Period, p)

The period determines the size of individual channels. Smaller periods create finer channels with higher surface area density but also higher pressure drop and more difficulty in additive manufacturing (minimum feature size constraints).

Typical ranges:

• Liquid-liquid exchangers: 2—8 mm period.
• Gas-liquid exchangers: 4—15 mm period.
• Gas-gas exchangers: 8—25 mm period.

Wall Thickness

The wall thickness of the TPMS surface controls the volume fraction (how much of the total volume is solid material) and the structural strength. Thicker walls increase strength and thermal conduction through the wall but reduce channel volume and increase pressure drop.

Typical ranges: 0.2—1.0 mm for metal AM (L-PBF in stainless steel, Inconel, or titanium).

Volume Fraction (Porosity)

The parameter t in the TPMS equation controls the volume split between the two channel networks. At t = 0, the split is 50/50 (equal volumes for hot and cold streams). Adjusting t shifts the split, making one network larger at the expense of the other. This is useful when the flow rates or heat capacities of the two streams differ significantly.

Grading

A uniform lattice has constant period and wall thickness throughout. A graded lattice varies these parameters spatially:

• Period grading: Fine cells near the inlet (where the temperature difference is largest and heat transfer is most valuable) and coarser cells near the outlet (where the temperature difference is smaller and pressure drop matters more).
• Thickness grading: Thicker walls near structural mounting points and thinner walls in the core where thermal performance is prioritized.
• Density grading: Higher volume fraction (more solid) near the hot-side inlet to handle thermal stresses and lower volume fraction in the interior for maximum flow.

Grading is where implicit CAD shines. In NeuroCAD, the TPMS function parameters are fields, not constants. The period field, thickness field, and density field can each be defined as functions of position, distance from a surface, temperature data from simulation, or any other spatial variable. The lattice naturally adapts to these varying parameters without any special geometric operations.

Multi-Scale Design Approach

A practical lattice heat exchanger design has three scales:

Macro Scale: Overall Envelope and Manifolds

The outer shell, inlet/outlet manifolds, and mounting features are designed using conventional CAD operations. The manifold geometry distributes flow uniformly into the lattice core --- poor manifold design creates flow maldistribution that negates the lattice’s thermal advantages.

Meso Scale: Lattice Core

The TPMS lattice fills the core volume. The lattice type, period, and grading are defined to meet the thermal and hydraulic performance targets. CFD (computational fluid dynamics) simulation validates the design.

Micro Scale: Surface Features

Surface roughness from the AM process (Ra 5—20 um for L-PBF) affects both heat transfer (positively --- increased turbulence) and pressure drop (negatively --- increased friction). These effects must be accounted for in simulation, typically through empirical correlations calibrated to the specific AM process and material.

Materials

Stainless Steel 316L

The workhorse material for L-PBF heat exchangers. Good corrosion resistance, well-characterized AM process parameters, and adequate thermal conductivity (15 W/mK). Suitable for most liquid-liquid applications.

Inconel 718 / 625

Nickel superalloys for high-temperature applications (up to 700 C for 718, 1000 C for 625). Essential for gas turbine recuperators, exhaust heat recovery, and chemical processing. Higher cost and more challenging AM processing than stainless steel.

Titanium Ti-6Al-4V

Excellent strength-to-weight ratio and corrosion resistance. Used in aerospace and marine heat exchangers where weight is critical. Lower thermal conductivity (6.7 W/mK) than steel, which limits performance in some configurations.

Copper Alloys

Highest thermal conductivity (up to 400 W/mK for pure copper). Ideal for electronics cooling and high-performance liquid cooling. AM processing of copper is challenging due to its high reflectivity and thermal conductivity, but recent progress with green laser L-PBF has made it viable.

AlSi10Mg

Aluminum alloy with good thermal conductivity (130 W/mK) and low cost. Suitable for automotive and consumer applications. Good AM processability but lower strength and temperature limits than steel or nickel alloys.

Design Workflow

1. Define requirements. Thermal duty (heat transfer rate), allowable pressure drop per side, maximum temperatures, fluid properties, envelope constraints.

2. Select TPMS type. Gyroid for balanced performance, Schwarz-P for low pressure drop, diamond for maximum compactness.

3. Initial sizing. Use analytical correlations (Nusselt number and friction factor correlations for TPMS lattices, available in published literature) to estimate the required lattice volume, period, and wall thickness.

4. Build the model. In implicit CAD, define the TPMS function with the chosen parameters. Intersect with the envelope geometry. Add manifolds and mounting features. Apply grading if the initial analysis suggests non-uniform conditions.

5. CFD validation. Simulate conjugate heat transfer through the lattice. Validate that thermal duty and pressure drop meet requirements. Iterate on lattice parameters as needed.

6. Structural validation. Check thermal stresses (especially at start-up and shutdown transients), pressure containment, and fatigue life. The lattice structure typically has lower stress concentrations than finned designs, but validation is still required.

7. AM preparation. Orient the part for printing (TPMS lattices are largely self-supporting, but the manifold geometry may need supports). Validate minimum feature sizes against the AM process capability. Generate the build file.

8. Test. Manufacture a prototype, measure thermal performance and pressure drop, and compare against the simulation predictions. Calibrate the simulation model for future designs.

Performance Benchmarks

Published research on TPMS heat exchangers consistently shows:

• 2—5x higher volumetric heat transfer coefficient compared to conventional plate-and-frame designs.
• 30—60% reduction in heat exchanger volume at equivalent thermal duty.
• 20—40% reduction in mass.
• Pressure drop comparable to or moderately higher than conventional designs (dependent on lattice type and period).

These numbers vary widely with the specific TPMS type, period, material, and operating conditions. The key takeaway is that the performance improvement is real and significant, not marginal.

Conclusion

Lattice-based heat exchangers represent one of the most mature applications of design-for-additive-manufacturing. The combination of TPMS mathematics, implicit CAD tools that handle lattice geometry natively, and metal AM processes that can produce these structures reliably creates a complete engineering pathway from concept to hardware. The thermal performance gains are substantial enough to justify the higher per-unit cost of additive manufacturing for applications where size, weight, or performance are critical constraints.