Session: 13-03 Heat Transfer Modeling Methods and Analysis

Submission Number: 177862

Adjoint-Based Shape Optimisation of Periodic Unit Cells for Compact Heat Transfer Devices Using Periodically Developed Flow and Conjugate Heat Transfer Models 

Efficient thermal management remains a critical challenge in advanced turbomachinery and energy systems, where compact heat exchangers and cooling components must simultaneously achieve high heat-transfer performance and low pressure losses within stringent spatial and design constraints. This work presents a shape-optimization framework for the three-dimensional design of compact heat-transfer devices composed of periodic units, including applications to gas recuperators, condensers, and cooling channels. The framework enables free-form optimization of the surface geometry within a periodic unit cell to maximize thermal performance, minimize pressure losses, or achieve tailored trade-offs, while enforcing minimal wall-thickness constraints.

The methodology is built upon a computationally efficient finite-element implementation in DOLFIN/FEniCS for solving the periodically developed flow and heat-transfer equations, along with their associated eigenvalue problems. The governing equations describe incompressible laminar or turbulent flow coupled with conjugate heat transfer between the solid structure and one or more fluid streams. Periodic boundary conditions are applied consistently to the state, adjoint, and design variables, ensuring that the optimized shape functions as a repeatable unit for large-scale assemblies, while also accounting for linear and exponential temperature gradients across the device. Minimal wall thickness is computed through the solution of an Eikonal equation, providing a distance field to possibly complex surface boundary parts.

Shape sensitivities are computed via adjoint-based automated differentiation of an augmented Lagrangian functional coupling the flow, temperature, and constraint equations, yielding exact gradients with respect to mesh deformations. These sensitivities are regularized through appropriate inner-product metrics, such as elasticity- or Laplace–Beltrami–based formulations, to produce smooth and physically meaningful geometry updates. Mesh deformation is carried out using an Arbitrary Lagrangian–Eulerian (ALE) framework within FEniCS, with Gmsh employed for remeshing as needed to preserve mesh quality.

The framework is demonstrated through the optimization of unit cells for compact gas-to-gas heat recuperators and cooling channels under laminar operating conditions. The resulting optimized surfaces are compared with designs obtained via density-based topology optimization, highlighting the advantages of the proposed approach in achieving smooth, manufacturable geometries while satisfying both thermal and hydraulic performance objectives.

Presenting Author: Geert Buckinx VITO

Presenting Author Biography: Dr. Ir. Geert Buckinx is a senior researcher at the Flemish Institute for Technological Research (VITO) in Belgium, specializing in thermal and fluid engineering. He holds a master's degree in mechanical engineering and a doctorate from KU Leuven, where he also served as a lecturer and a researcher in the Section of Applied Mechanics and Energy Conversion. His research focuses on computational fluid dynamics (CFD), heat exchangers, porous media, and numerical modeling, with a particular emphasis on optimizing compact heat transfer devices through adjoint-based shape optimization and macro-scale modeling methods. Dr. Buckinx has co-authored over 20 publications and has received several prestigious grants from the Research Foundation – Flanders (FWO) for his work in this domain.

Authors:

Geert Buckinx VITO