Inverse-designing a fuel injector with a neural operator
An 80-case OpenFOAM sweep of a hydrogen/air mixing nozzle trains a Fourier Neural Operator (FNO) as an instant CFD surrogate. The trained surrogate is frozen and used for gradient-based search, finding the nozzle geometry that hits a target fuel-air ratio at the outlet. The result is then checked against a real CFD rerun.
From a CFD sweep to an AI-driven search
A 2D planar nozzle mixes a hydrogen jet into a co-flowing air stream (H₂ at 8 m/s, air at 2 m/s). Sweeping the nozzle half-heightDn from 5–15 mm across 80 simulations (k‑ω SST, converged in ~7s each) gives the FNO its training data.
Once trained, the FNO replaces further CFD runs entirely. Gradient descent through the frozen surrogate searches nozzle geometry directly, converging on the diameter that hits a target exit-plane fuel fraction. That design is then rerun through real CFD to confirm the surrogate's prediction holds.
What the sweep and the search look like
Where this scales
This case is deliberately simple: one design variable, with a smooth, near-monotonic relationship between nozzle diameter and mixing outcome. For a case this size, a sweep and a lookup table would get you the same answer as the AI search did. On its own, this particular problem didn't need solving this way.
What matters is the recipe behind it. An OpenFOAM sweep trains a differentiable surrogate, and gradient descent searches that surrogate directly instead of re-running CFD for every candidate design. That recipe holds up as the design space gets harder: more design variables, objectives that trade off against each other in genuinely nonlinear, non-monotonic ways. A brute-force sweep grows exponentially with each added parameter. A differentiable surrogate still just takes a gradient step. This case study is the simplest possible demonstration of a technique built for problems too large to sweep by hand.