Towards Rapid Prototyping of Spray Injectors: A Regime-Agnostic Neural Operator Surrogate for Gas-Liquid Interface Evolution

Abstract

Spray atomisation rapidly creates large liquid-gas interfacial areas and is central to many industrial processes. However, predicting spray behaviour and surface area remains difficult: experiments cannot access all spray regions, while CFD becomes prohibitively expensive as finer structures develop. Data driven surrogates can learn interface evolution, enabling rapid design space exploration, operating condition ranking, and ultimately spray control. We investigate how state representation, neural architecture, and physics-informed regularisation affect long horizon autoregressive forecasting of spray interfaces, particularly conservation. Our principal model is a boundary-conditioned Fourier Neural Operator (FNO) that predicts the evolution of the signed distance function (SDF) from the liquid-gas interface. It is trained on 2D sharp interface Volume-of-Fluid CFD simulations spanning several atomisation regimes. The SDF-FNO retains interface fidelity better than an FNO trained directly on volume fraction, but is outperformed by a U-Net. Objective function ablation shows that a liquid inventory penalty improves conservation at a modest cost to local interface accuracy. We also introduce a physics-informed extension combining an open-domain target-increment liquid balance penalty, a narrowband Eikonal regulariser that preserves signed distance geometry, and a phase-boundedness penalty. Although this model trains stably, it leaves forecast error, interface overlap, and inventory behaviour essentially unchanged relative to the data driven baseline. Finally, we demonstrate the surrogate by ranking injection conditions according to interfacial area generated per unit gas injection power across the operating envelope of a fixed geometry.