Lucas Lestandi

Two-dimensional (2D) flow inside a lid driven cavity (LDC) is shown to display multi-modal behavior in a consistent manner following the first Hopf bifurcation with varying Reynolds numbers (Re), depending upon the chosen spatial and temporal discretization scheme. Direct numerical simulation (DNS) following impulsive start, is used to show spatio-temporal growth and its nonlinear saturation of disturbance growth. Despite the fact that researchers have produced different value of Reynolds number when first Hopf bifurcation occurs (Recr1), DNS fundamentally differs from classical bifurcation studies involving global instability study of an equilibrium flow due to adopted nonlinear approach and not restricting the analysis to temporal instability only. The accuracy attribute of the DNS adopted here has been shown conclusively earlier via demonstration of a weak transient polygonal core vortex surrounded by relatively stronger gyrating vortices, which appear as a constellation after the disappearance of the transient, in [26]. Investigated LDC flow is characterized by multiple time scales at any Re, which are weak function of Re in selective intervals, punctuated by multiple bifurcations. The present investigation achieves two primary goals. First, it proposes to reconcile that Recr1 obtained by different numerical approaches can be shown to be in same range, provided the equilibrium flow obtained is of good quality, untainted by excessive diffusion. Secondly, we also show that for increasing Re following the first Hopf bifurcation, the flow during the limit cycle suffers a secondary instability, thus, requiring computation of the flow field over a longer time period. The first goal is met by exciting the flow field with a pulsating vortex inside the LDC for a very high accuracy scheme, we are able to show the universal nature of the primary bifurcation for Re in the range between 8020 and 8025. The flow at higher Re displays significantly increased spectral peaks, including broad-band spectrum and the understanding of all these have been aided by phase space portraits.

In order to enable the industrialization of additive manufacturing, it is necessary to develop process simulation models that can rapidly predict part quality. Although multi-physics simulations have shown success at predicting residual stress, distortion, microstructure and mechanical properties of additively manufactured parts, they are generally too computationally expensive to be directly used in applications, such as optimization, controls, or digital twinning. In this study, a critical evaluation is made of how data-driven surrogate models can be used to model the residual stress of parts fabricated by Laser Powder-Bed Fusion. Residual stress data is generated by using an inherent-strain based process simulation for two families of part geometries. Three different models using varying levels of sophistication are compared: a multilayer perceptron (MLP), a convolutional neural network (CNN) based on the U-Net architecture, and an interpolation-based method based on mapping geometries onto a reference. All three methods were found to be sufficient for part design, providing mechanical predictions for a CPU time below 0.2 s, representing a runtime speed-up of at least 3900x. Neural network-based models are significantly more expensive to train compared to using interpolation. However, the generality of models based on the U-Net architecture is attractive for applications in optimization.