Three-dimensional particulate volume fraction reconstruction in the fluid based on the Lambert–Beer physics information neural network

The measurement of particle volume fraction in flow fields is of great significance in scientific research and engineering applications. As one of the particle detection techniques, the light extinction method is widely used in measuring nano-particles volume fraction in flow fields due to its simplicity and non-contact nature. In particular, in complex reactive flow fields like combustion reactions, the volume fraction of soot particulate and other particles can be accurately measured and reconstructed via the light extinction method that based on the Beer–Lambert law. This is crucial for exploring combustion phenomena, understanding their internal mechanisms, and reducing pollutant emissions. However, due to the enormous computational burden, current algebra reconstruction techniques struggle to achieve high-precision three-dimensional (3D) reconstruction of particles. Therefore, this paper originally proposes a 3D reconstruction algorithm based on the Beer–Lambert law physical information neural networks (LB-PINNs). By incorporating physical information as constraints into the particle reconstruction process, it is possible to achieve high-precision 3D reconstruction of particles in complex flow field environments with low computational cost. Meanwhile, to address the trade-off issues of reconstruction accuracy and smooth noise resistance in previous reconstruction algorithms, i.e., Tikhonov regularization, this paper employs dynamically adjusted regularization parameters in the LB-PINN algorithm. This approach ensures smooth noise-resistant processing while maintaining reconstruction accuracy, significantly reducing computation time and resource consumption. According to the experimental results, LB-PINNs demonstrate superior performance compared to previous reconstruction algorithms when reconstructing the soot volume fraction in complex reacting flow fields, i.e., combustion flame scenarios.