Sparse Narrow-Band Topology Optimization for Large-Scale Thermal-Fluid Applications

Abstract

We propose a fluid-based topology optimization methodology for convective heat-transfer problems that can manage an extensive number of design variables, enabling the fine geometric features required for the next generation of heat-exchangers design. Building on the classical Borrvall-Petersson formulation for the Stokes flow, we introduce an optimization algorithm that focuses computational effort on the fluid-solid interface, where it is most needed. To address the high cost of repeated forward and adjoint analyses and to avoid leakage through nominally solid regions, we exclude fictitious solid voxels from the analysis by imposing the no-slip boundary conditions in the vicinity of the fluid-solid interface. In contrast to the prior approaches, the fictitious solids are also excluded from the global optimization problem via reducing it to a sequence of local narrow-band subproblems with a variable design space. The contribution of our method is that large-scale optimization can be solved efficiently by continuous simplex method while reliably obtaining binary designs without additional filtering or projection. We demonstrate efficiency of the method on multiple examples, including the optimization of a two-fluid heat exchanger at $Pe=10^4$ on a $370^3$ grid comprising $5\times10^7$ design variables using only a single desktop workstation.

Figures (16)

• Figure 1: Computational domain and boundary conditions.
• Figure 2: Illustration of one iteration $\Gamma^0 \to \Gamma^1$ of the proposed narrow band optimization algorithm. (a) Classification of the current design $\Gamma_0$ according to \ref{['eq:voxel_types']}. (b) Projection onto the active set, where the local optimization subproblem is solved. (c) Solution of the optimization subproblem \ref{['eq:subprob_pert']}: yellow for removed fluid, purple for added fluid. (d) Updated active set with conserved volume. (e) Recovering of the frozen solid/fluid regions. (f) Classification of the updated design $\Gamma^1$ to proceed to the next iteration.
• Figure 3: Staggered grid DoFs arrangement: blue and red for velocity components, orange for pressure, temperature, and density. Boundary conditions are applied at green circles and stars.
• Figure 4: Excluding fully isolated solid cells and imposing the no-slip boundary conditions on the fluid-solid interface. One layer of Brinkman cells allows the interface to move inward during optimization.
• Figure 5: Minimization of the pressure drop for a fluid manifold with multiple outlets, volume constraint $V_0=0.15$.

Theorems & Definitions (4)

• Remark 1
• Remark 2
• Remark 3
• Remark 4