FluTO: Graded multi-scale topology optimization of large contact area fluid-flow devices using neural networks

University of Wisconsin-Madison

Given a fluid topology optimization problem, an appropriate microstructure is selected, and its size and orientation are optimized to produce a graded multi-scale design.

Abstract

Fluid-flow devices with low dissipation, but large contact area, are of importance in many applications. A well-known strategy to design such devices is multi-scale topology optimization (MTO), where optimal microstructures are designed within each cell of a discretized domain.

Unfortunately, MTO is computationally very expensive since one must perform homogenization of the evolving microstructures, during each step of the optimization process. Furthermore, methods to impose a desired contact area have not been pursued in MTO.

Here, we propose a graded multiscale topology optimization for minimizing the dissipation in fluid-flow devices, subject to a desired contact area. Several pre-selected, but size-parameterized and orientable microstructures are chosen; their constitutive tensors and contact areas are pre-computed at a finite number of sizes. Then, during optimization, a simple interpolation is used to significantly reduce the computation while retaining many of the benefits of MTO.

The algorithm allows for continuous switching between microstructures during optimization, but prevents mixing through penalization. The optimization is performed using a neural network (NN), capitalizing on the advantages of NN as described in the FluTO framework section below.

FluTO Framework

Contact area vs Pressure drop: Maximizing the fluid–solid contact area is critical in many applications including bio-sensors for detecting tumor cells, microfluidic devices for cell sorting, optofluidic reactions, micro-channel heat sinks, and other microfluidic devices involving heat transfer and mass transportation/mixing mechanisms. Therefore, in these optimization problems a total contact area constraint is more critical, changing the type of microstructures one must choose. The tradeoff between contact area and pressure drop is illustrated below.

Contact area vs Pressure drop

Offline homogenization: To reduce the computational cost due to concurrent homogenization, we assume that a set of microstuctures have been pre-selected. Then offline homogenization is performed for each microstructure at discrete sizes. Finally, interpolating polynomials are constructed from these size samples.

Offline homogenization and interpolation of permeability components

Design representation and optimization framework: The design variables (type, size and orientation of microstructures) are represented using a neural-network, whose advantages include:

(1) it implicitly guarantees the partition of unity, i.e., ensures that the net volume fraction of microstructures in each cell is unity,

(2) the number of design variables is only weakly dependent on the number of pre-selected microstructures,

(3) it supports automatic differentiation, and

(4) one can perform topology optimization at a coarser scale, and then extract a high-resolution design via a post-processing step without requiring additional projection methods.

Since neural networks are designed to minimize an unconstrained loss function, we convert the constrained minimization problem into a loss function minimization by employing the augmented Lagrangian scheme.

Optimization loop of the proposed framework

Results

Dependency on number of microstructures: The current framework can achieve better designs with larger number of candidate microstructures, and it is computationally insensitive to the number of candidates.

Designs with 1, 3, 5 and 8 microstructures respectively

High resolution design: The proposed framework utilizes a neural network to globally represent the design fields (microstructure type, orientation, and size), enabling the generation of high-resolution topologies without expensive computation.

Extraction of high resolution design through resampling

Citation

@article{padhy2023fluto,

title={FluTO: Graded multi-scale topology optimization of large contact area fluid-flow devices using neural networks},

author={Padhy, Rahul Kumar and Chandrasekhar, Aaditya and Suresh, Krishnan},

journal={Engineering with Computers},

pages={1--17},

year={2023},

publisher={Springer}

}