Before anything is built, we, as engineers, try our best to investigate whether it will work. Is our idea any good? We ask those with experience, we consult textbooks, we model, and we simulate. For those of us who require significant de-risking before investing in hardware, we spend a lot of time with that last option.  

An awful lot of modern engineering simulations are a type of Finite-Something (Element, Volume, Difference, take your pick). These techniques grant us insight into our design so that we may better understand its behavior and adjust accordingly. The better our simulation, the better our insight. At some point, the problem space becomes too challenging.

How constraints shape engineering solutions

Consequently, we are forced to address at least one of the following constraints. 

  1. Size. Reduce the size of the simulation domain to focus on a smaller piece of the problem. 
  2. Resolution. Choose to ignore small features by increasing the coarseness of the mesh grid. 
  3. Accuracy. Increase tolerances on temperature, pressure, and velocity calculations and accept a less accurate physical model. 
  4. Speed. Allow the simulation to take longer. The ability of the engineer to iterate is reduced. 
  5. Compute. Increase the computational hardware (CPU, GPU) available to the simulation so that a more favourable combination of size, resolution, accuracy and speed can be achieved. 

These constraints were the motivation to find a new way. ToffeeX partnered with Imperial College London to pioneer a physics-driven design framework that insulates engineers from these five constraints.

Funded by the National Aerospace Technology Exploitation Programme, the Multiscale Optimisation for Aerospace Cold-plates (MOfAC) project focused on a typical cold plate whose internal structure is comprised only of pillars.

It models that structure and the thermo-fluid as individual unit cells. This means that as our problem size grows, we are not bound by typical constraints. At no point is CFD solved on anything larger than a unit cube!

Why multiscale modeling?

Multiscale modeling offers a computationally efficient solution to the challenges posed by traditional CFD simulations. This approach models complex systems by solving a series of decoupled smaller systems or blocks, which are then assembled to replicate the full system’s behavior accurately. The decoupling enables highly distributed computing techniques, significantly reducing computational costs in terms of both time and resources.

By breaking down the problem into manageable components, multiscale modeling for CFD optimization overcomes the limitations of solving the entire system at once.

The dramatic reduction in computational expense not only maintains accuracy but also enables extensive design optimization, allowing engineers to explore a wider range of iterations and apply cutting-edge, physics-driven generative design techniques more broadly.  

Designing, piece by piece

The project demonstrated that optimization algorithms could be driven from the physical data generated by multiscale simulations. By designing the small scale to contain a parameter, the simulations can then be controlled by an external optimization algorithm. In MOfAC, our small scale contained a simple pillar whose radius was the design parameter. (Figure 1.)

Algorithmically Assembled Heat Exchanger from Unit Cell Database
Figure 1: The example heat exchanger shown is built from multiple unit cells. CFD is only solved on the unit cell geometry, while the heat exchanger is assembled by algorithmically interrogating the unit cell database. 

Multiscale simulations do not have the same issues as CFD when the problem grows. The flow is only calculated on the unit cell, and once that calculation is done, the result can be reused elsewhere in the domain, meaning that fewer and fewer calculations are required! The exciting part is that these calculations are also massively parallelizable. This reduces the time it takes to understand the flow field and therefore reduces the time-to-design. This means that no matter how large the problem gets, it can still be solved quickly while maintaining a high resolution.  

Figure 2: A result from a large multiscale simulation showing the calculated flow path and the thermal trails from each pillar. The images are cross-sections from where each dot is the center of a pillar. 

Where next for multiscale modeling? 

We are now exploring how to bring these design techniques to market. We are excitedly perusing applications in hydrogen fuel cells where it can be applied to interstitial cooling layers and expanded to optimize the distribution of hydrogen and oxygen with the goal of improving power output of each module.  

 The advancements in multiscale modeling for CFD optimization are reshaping how engineers approach complex simulations. By addressing traditional CFD constraints and leveraging the power of physics-driven design, this technique opens new possibilities for rapid, efficient, and scalable optimization.

The success of the MOfAC project has demonstrated the potential for transformative applications where precise thermal and fluid control can drive significant performance gains. As we continue to refine and deploy these methods, we are poised to unlock new frontiers in engineering design, making ambitious ideas a reality faster and more effectively than ever before.