Neural Network Based Deep Learning Method for Multi-Dimensional Neutron Diffusion Problems with Novel Treatment to Boundary

In this paper, the artificial neural networks (ANN) based deep learning (DL) techniques were developed to solve the neutron diffusion problems for the continuous neutron flux distribution without domain discretization in advance. Due to its mesh-free property, the DL solution can easily be extended to complicated geometries. Two specific realizations of DL methods with different boundary treatments are developed and compared for accuracy and efficiency, including the boundary independent method (BIM) and boundary dependent method (BDM). The performance comparison on analytic benchmark indicates BDM being the preferred DL method. Novel constructions of trial function are proposed to generalize the application of BDM. For a more in-depth understanding of the BDM on diffusion problems, the influence of important hyper-parameters is further investigated. Numerical results indicate that the accuracy of BDM can reach hundreds of times higher than that of BIM on diffusion problems. This work can provide a new perspective for applying the DL method to nuclear reactor calculations.

Smoothed Particle Hydrodynamics Simulation of Orthogonal Cutting with Enhanced Thermal Modeling

Smoothed Particle Hydrodynamics (SPH) is a mesh-free numerical method that can simulate metal cutting problems efficiently. The thermal modeling of such processes with SPH, nevertheless, is not straightforward. The difficulty is rooted in the computationally demanding procedures regarding convergence properties and boundary treatments, both known as SPH Grand Challenges. This paper, therefore, intends to rectify these issues in SPH cutting models by proposing two improvements: (1) Implementing a higher-order Laplacian formulation to solve the heat equation more accurately. (2) Introducing a more realistic thermal boundary condition using a robust surface detection algorithm. We employ the proposed framework to simulate an orthogonal cutting process and validate the numerical results against the available experimental measurements.

Direct Numerical Simulations of Turbulent Channel Flow With Polymer Additives

ABSTRACTDirect numerical simulations have been applied to simulate flows with polymer additives. FENE-P (finite-extensible-nonlinear-elastic-Peterlin) dumbbell model solving for the conformation tensor is adopted to investigate the influence of the polymer on the flowfield. Boundary treatments of the conformation tensor on the flowfield are examined first, where boundary condition based on the linear extrapolation scheme provides more accurate results with second-order accurate error norms. Further simulations of the turbulent channel flow at different Weissenberg numbers are also conducted to investigate the influence on drag reduction. Drag reduction increases in tandem with the increase of Weissenberg number and the increase saturates at Weτ~200, where the drag reduction is close to the maximum drag reduction (MDR) limit. At the regime of y+ > 5, the viscous layer thickens with the increase of the Weissenberg number showing a departure from the traditional log-law profile, and the velocity profiles approach the MDR line at high Weissenberg number. The Reynolds stress decreases in tandem with the increase of Weτ, whereas the levels of laminar stress and polymer stress act adversely. However, as the Weissenberg number increases, the proportion of the laminar stress in the total stress increases, and this contributes to the drag reduction of the polymer flow.