JPResUnet: A joint probability density function translation model in partially premixed flames

Abstract

Machine learning (ML) for turbulent combustion modelling can offer high fidelity within the training regime, yet its robustness under unseen conditions remains a practical concern. Conversely, established presumed probability density function (PDF) approaches are generally robust but less accurate when the sub-grid distribution exhibits strong correlation and multi-modality. This work introduces JPResUnet (Joint PDF Residual U-net), which employs a residual U-net to translate a β -PDF into the corresponding sub-grid joint PDF in partially premixed flames. The model is trained using direct numerical simulation (DNS) of methane–air moderate or intense low-oxygen dilution (MILD) combustion, and is first evaluated through a priori assessment on out-of-sample methane–air flame data. Compared with a well-established artificial neural network (ANN) and the baseline β -PDF, JPResUnet provides improved agreement with DNS in reproducing key PDF features across filter widths and for both box and Gaussian kernels. Additional tests on an unseen, more highly diluted case indicate improved generalisation relative to the ANN, which shows a marked deterioration at the larger filter width. The approach is then deployed in large eddy simulations (LES) of a methane–air multi-regime burner (MRB) through the look-up table (LUT), considering two output PDF resolutions. The higher-resolution JPResUnet model yields improved temperature predictions relative to the conventional LUT method, illustrating the potential of PDF translation for robust LES of partially premixed reacting flows. Novelty and Significance Statement Machine learning for turbulent combustion modelling can exhibit limited robustness when applied outside the training regime. The novelty of this work lies in a PDF-to-PDF translation approach that learns a correction to the presumed joint PDF, thereby combining the robustness of an analytical distribution with data-driven refinement, and in its validation through a priori and a posteriori assessments. The model is shown to improve joint PDF prediction on out-of-sample data spanning different filter widths and kernels, as well as an unseen flame condition. Its practical impact is demonstrated via LES of a multi-regime burner, where improved temperature predictions are observed relative to the conventional tabulation method. These results support the PDF translation model as a robust ML-based LES closure.