Density-based topology optimization strategy for optimal design of uniform flow manifolds

TL;DR

This work tackles the challenge of achieving uniform flow distribution across multi-channel manifolds by introducing a scalable density-based topology optimization framework that enforces flow uniformity via a single ensemble constraint. Implemented in the open-source SU2 suite and integrated through FlowForge, the method is benchmarked against VOA and ICA on planar z-type manifolds and then extended to 3D cylindrical and radial manifolds. Results show VOA struggles with uniformity, while ICA and the proposed Flow Uniformity based Approach (FUA) achieve near-uniform distributions, with FUA offering substantial computational savings due to its ensemble constraint. The 3D demonstrations establish robustness and scalability, highlighting the method’s potential for complex energy systems where uniform distribution is critical, and suggesting future work in turbulence, heat transfer, and hybrid optimization strategies.

Abstract

Uniform flow distribution across parallel channels directly impacts the performance and efficiency of many fluid and energy systems. However, designing efficient flow manifolds that ensure uniform flow distribution remains a challenge. This issue is even more pronounced in the design of multichannel three-dimensional manifolds. Hence, this study presents a scalable topology optimization framework for the systematic design of multi-channel flow manifolds. The proposed method extends the conventional density-based topology optimization formulation by introducing a flow maldistribution coefficient as an explicit constraint. This novel approach was implemented using the incompressible Navier-Stokes flow solver available in the open-source CFD suite SU2. The performance of the proposed method was benchmarked against two established topology optimization strategies using an exemplary planar z-type flow manifold, wherein both the inlet and outlet manifoldswere designed simultaneously. The results demonstrate that the proposed method achieves flow uniformity comparable to that obtained by established approaches while significantly reducing the associated computational cost. Furthermore, when applied to large-scale three-dimensional problems, the proposed method produces feasible designs that achieve uniform flow distribution and exhibit innovative geometrical features. Thus advocating for the robustness and scalability of the proposed method.

Figures (19)

• Figure 1: Geometric illustration of the planar z-type flow manifold case. The light blue regions indicate the design domains subject to optimization, while the dark gray regions represent fluid domains not participating in the optimization process.
• Figure 2: Comparison of adjoint gradients (AD) against finite-difference gradients (FD) obtained for the planar z-type flow manifold case.
• Figure 3: Optimization history objective function ${\mathcal{J}}/{\mathcal{J}_o}$ (top) and maximum normalized constraint violation$g_{i}$ (bottom).
• Figure 4: Comparison of the baseline design and optimal designs obtained through different optimization strategies for the planar z-type flow manifold.
• Figure 5: Comparison of normalized mass flow rate variation across the channels for optimum designs obtained through different strategies, alongside the baseline design.