Reconstruction of Fractional-Order Ellipsoidal Nanofluid Turbulent Flow Fields and Particle Orientation Evolution Based on PINNs

To investigate the orientation of ellipsoidal nanoparticles in turbulence, a Physics-Informed Neural Network (PINN) framework for fractional-order problems was constructed, in which the fluid was described by a fractional-order fluid constitutive model in a periodically sinking channel. By introducing a fractional derivative into the constitutive relation, the model combines the nonlocal and memory effects of complex turbulence, making the effective rheology more accurate than classical integer-order closures. In addition, the second-order moment tensor equation derived from the Fokker-Planck equation is used to characterize the rotational diffusion behavior of ellipsoidal nanoparticles, and the variation of nanoparticle concentration in the channel is considered. The results show that the PINN based on the fractional constitutive model can predict the flow field. Based on the reconstructed flow field, the data-free neural network is used to predict the orientation and concentration distributions of nanoparticles in turbulent flow. The parameter analysis shows that as the rotating Péclet number increases, the shear effect controls rotating diffusion more strongly, resulting in ellipsoidal nanoparticles aligning more quickly and more clearly along the mainstream direction. Alignment near the wall precedes alignment at the channel center, usually accompanied by an overshoot. A smaller lateral Péclet number leads to a steep directional gradient, coupled with wall migration, resulting in higher alignment near the wall and greater dispersion at the center. In general, this study emphasizes the effectiveness of combining the fractional fluid constitutive model with PINN to solve the transport and orientation of multi-scale nanoparticles in turbulence.