Numerical modelling of heat transfer and experimental validation in Powder-Bed Fusion with the Virtual Domain Approximation

Among metal additive manufacturing technologies, powder-bed fusion features very thin layers and rapid solidification rates, leading to long build jobs and a highly localized process. Many efforts are being devoted to accelerate simulation times for practical industrial applications. The new approach suggested here, the virtual domain approximation, is a physics-based rationale for spatial reduction of the domain in the thermal finite-element analysis at the part scale. Computational experiments address, among others, validation against a large physical experiment of 17.5 $\mathrm{[cm^3]}$ of deposited volume in 647 layers. For fast and automatic parameter estimation at such level of complexity, a high-performance computing framework is employed. It couples FEMPAR-AM, a specialized parallel finite-element software, with Dakota, for the parametric exploration. Compared to previous state-of-the-art, this formulation provides higher accuracy at the same computational cost. This sets the path to a fully virtualized model, considering an upwards-moving domain covering the last printed layers

A "poor man's" approach to topology optimization of natural convection problems

Topology optimization of natural convection problems is computationally expensive, due to the large number of degrees of freedom (DOFs) in the model and its two-way coupled nature. Herein, a method is presented to reduce the computational effort by use of a reduced-order model governed by simplified physics. The proposed method models the fluid flow using a potential flow model, which introduces an additional fluid property. This material property currently requires tuning of the model by comparison to numerical Navier-Stokes based solutions. Topology optimization based on the reduced-order model is shown to provide qualitatively similar designs, as those obtained using a full Navier-Stokes based model. The number of DOFs is reduced by 50% in two dimensions and the computational complexity is evaluated to be approximately 12.5% of the full model. We further compare to optimized designs obtained utilizing Newton's convection law.Comment: Preprint version. Please refer to final version in Structural Multidisciplinary Optimization https://doi.org/10.1007/s00158-019-02215-

Multivariate calibration of a water and energy balance model in the spectral domain

The objective of this paper is to explore the possibility of using multiple variables in the calibration of hydrologic models in the spectral domain. A simple water and energy balance model was used, combined with observations of the energy balance and the soil moisture profile. The correlation functions of the model outputs and the observations for the different variables have been calculated after the removal of the diurnal cycle of the energy balance variables. These were transformed to the frequency domain to obtain spectral density functions, which were combined in the calibration algorithm. It has been found that it is best to use the square root of the spectral densities in the parameter estimation. Under these conditions, spectral calibration performs almost equally as well as time domain calibration using least squares differences between observed and simulated time series. Incorporation of the spectral coefficients of the cross-correlation functions did not improve the results of the calibration. Calibration on the correlation functions in the time domain led to worse model performance. When the meteorological forcing and model calibration data are not overlapping in time, spectral calibration has been shown to lead to an acceptable model performance. Overall, the results in this paper suggest that, in case of data scarcity, multivariate spectral calibration can be an attractive tool to estimate model parameters

A variational Bayesian method for inverse problems with impulsive noise

We propose a novel numerical method for solving inverse problems subject to impulsive noises which possibly contain a large number of outliers. The approach is of Bayesian type, and it exploits a heavy-tailed t distribution for data noise to achieve robustness with respect to outliers. A hierarchical model with all hyper-parameters automatically determined from the given data is described. An algorithm of variational type by minimizing the Kullback-Leibler divergence between the true posteriori distribution and a separable approximation is developed. The numerical method is illustrated on several one- and two-dimensional linear and nonlinear inverse problems arising from heat conduction, including estimating boundary temperature, heat flux and heat transfer coefficient. The results show its robustness to outliers and the fast and steady convergence of the algorithm.Comment: 20 pages, to appear in J. Comput. Phy

Loss terms in free-piston Stirling engine models

Various models for free piston Stirling engines are reviewed. Initial models were developed primarily for design purposes and to predict operating parameters, especially efficiency. More recently, however, such models have been used to predict engine stability. Free piston Stirling engines have no kinematic constraints and stability may not only be sensitive to the load, but also to various nonlinear loss and spring constraints. The present understanding is reviewed of various loss mechanisms for free piston Stirling engines and how they have been incorporated into engine models is discussed

Operational snow modeling: Addressing the challenges of an energy balance model for National Weather Service forecasts

Prediction of snowmelt has become a critical issue in much of the western United States given the increasing demand for water supply, changing snow cover patterns, and the subsequent requirement of optimal reservoir operation. The increasing importance of hydrologic predictions necessitates that traditional forecasting systems be re-evaluated periodically to assure continued evolution of the operational systems given scientific advancements in hydrology. The National Weather Service (NWS) SNOW17, a conceptually based model used for operational prediction of snowmelt, has been relatively unchanged for decades. In this study, the Snow-Atmosphere-Soil Transfer (SAST) model, which employs the energy balance method, is evaluated against the SNOW17 for the simulation of seasonal snowpack (both accumulation and melt) and basin discharge. We investigate model performance over a 13-year period using data from two basins within the Reynolds Creek Experimental Watershed located in southwestern Idaho. Both models are coupled to the NWS runoff model [SACramento Soil Moisture Accounting model (SACSMA)] to simulate basin streamflow. Results indicate that while in many years simulated snowpack and streamflow are similar between the two modeling systems, the SAST more often overestimates SWE during the spring due to a lack of mid-winter melt in the model. The SAST also had more rapid spring melt rates than the SNOW17, leading to larger errors in the timing and amount of discharge on average. In general, the simpler SNOW17 performed consistently well, and in several years, better than, the SAST model. Input requirements and related uncertainties, and to a lesser extent calibration, are likely to be primary factors affecting the implementation of an energy balance model in operational streamflow prediction. © 2008 Elsevier B.V. All rights reserved

Thermal dosimetry for bladder hyperthermia treatment. An overview.

The urinary bladder is a fluid-filled organ. This makes, on the one hand, the internal surface of the bladder wall relatively easy to heat and ensures in most cases a relatively homogeneous temperature distribution; on the other hand the variable volume, organ motion, and moving fluid cause artefacts for most non-invasive thermometry methods, and require additional efforts in planning accurate thermal treatment of bladder cancer. We give an overview of the thermometry methods currently used and investigated for hyperthermia treatments of bladder cancer, and discuss their advantages and disadvantages within the context of the specific disease (muscle-invasive or non-muscle-invasive bladder cancer) and the heating technique used. The role of treatment simulation to determine the thermal dose delivered is also discussed. Generally speaking, invasive measurement methods are more accurate than non-invasive methods, but provide more limited spatial information; therefore, a combination of both is desirable, preferably supplemented by simulations. Current efforts at research and clinical centres continue to improve non-invasive thermometry methods and the reliability of treatment planning and control software. Due to the challenges in measuring temperature across the non-stationary bladder wall and surrounding tissues, more research is needed to increase our knowledge about the penetration depth and typical heating pattern of the various hyperthermia devices, in order to further improve treatments. The ability to better determine the delivered thermal dose will enable clinicians to investigate the optimal treatment parameters, and consequentially, to give better controlled, thus even more reliable and effective, thermal treatments

Residual Minimizing Model Interpolation for Parameterized Nonlinear Dynamical Systems

We present a method for approximating the solution of a parameterized, nonlinear dynamical system using an affine combination of solutions computed at other points in the input parameter space. The coefficients of the affine combination are computed with a nonlinear least squares procedure that minimizes the residual of the governing equations. The approximation properties of this residual minimizing scheme are comparable to existing reduced basis and POD-Galerkin model reduction methods, but its implementation requires only independent evaluations of the nonlinear forcing function. It is particularly appropriate when one wishes to approximate the states at a few points in time without time marching from the initial conditions. We prove some interesting characteristics of the scheme including an interpolatory property, and we present heuristics for mitigating the effects of the ill-conditioning and reducing the overall cost of the method. We apply the method to representative numerical examples from kinetics - a three state system with one parameter controlling the stiffness - and conductive heat transfer - a nonlinear parabolic PDE with a random field model for the thermal conductivity.Comment: 28 pages, 8 figures, 2 table