Assessing epistemic uncertainties is considered as a milestone for improving numerical predictions of a dynamical system. In hydrodynamics, uncertainties in input parameters translate into uncertainties in simulated water levels through the shallow water equations. We investigate the ability of generalized polynomial chaos (gPC) surrogate to evaluate the probabilistic features of water level simulated by a 1-D hydraulic model (MASCARET) with the same accuracy as a classical Monte Carlo method but at a reduced computational cost. This study highlights that the water level probability density function and covariance matrix are better estimated with the polynomial surrogate model than with a Monte Carlo approach on the forward model given a limited budget of MASCARET evaluations. The gPC-surrogate performance is first assessed on an idealized channel with uniform geometry and then applied on the more realistic case of the Garonne River (France) for which a global sensitivity analysis using sparse least-angle regression was performed to reduce the size of the stochastic problem. For both cases, Galerkin projection approximation coupled to Gaussian quadrature that involves a limited number of forward model evaluations is compared with least-square regression for computing the coefficients when the surrogate is parameterized with respect to the local friction coefficient and the upstream discharge. The results showed that a gPC-surrogate with total polynomial degree equal to 6 requiring 49 forward model evaluations is sufficient to represent the water level distribution (in the sense of the \(\ell _2\) norm), the probability density function and the water level covariance matrix for further use in the framework of data assimilation. In locations where the flow dynamics is more complex due to bathymetry, a higher polynomial degree is needed to retrieve the water level distribution. The use of a surrogate is thus a promising strategy for uncertainty quantification studies in open-channel flows and should be extended to unsteady flows. It also paves the way toward cost-effective ensemble-based data assimilation for flood forecasting and water resource management. 相似文献
A major challenge in recycling of silicon powder from kerf loss slurry waste is the complete removal of metal particles. The traditional acid leaching method is costly and not green. In this paper, a novel approach to recover high-purity Si from the kerf loss slurry waste of solar grade silicon was investigated. The metal impurities were removed with superconducting high gradient magnetic separation technology. The effects of process parameters such as magnetic flux density, slurry density, and slurry flow velocity on the removal efficiency were investigated, and the parameters were optimized. In one lot of control experiments, the silicon content was increased from 90.91 to 95.83%, iron content reduced from 3.24 to 0.57%, and aluminum content from 2.44 to 1.51% under the optimum conditions of magnetic flux density of 4.0 T, slurry density of 20 g/L, and slurry flow velocity of 500 mL/min. The result indicates that the superconducting high gradient magnetic separation technology is a feasible purifying method, and the magnetic separation concentrate could be used as an intermediate product for high-purity Si powder.
In a proton exchange membrane electrolyzer cell (PEMEC), liquid/gas diffusion layer (LGDL) is expected to transport electrons, heat, and reactants/products to and from the catalyst layer with minimum voltage, current, thermal, interfacial, and fluidic losses. In addition, carbon materials, which are typically used in PEM fuel cells (PEMFCs), are unsuitable in PEMECs due to the high ohmic potential and highly oxidative environment of the oxygen electrode. In this study, a set of titanium gas diffusion layers with different thicknesses and porosities are designed and examined coupled with the development of a robust titanium bipolar plate. It has been found that the performance of electrolyzer improves along with a decrease in thickness or porosity of the anode LGDL of titanium woven meshes. The ohmic resistance of anode LGDL and contact resistance between anode LGDL and the anode catalyst play dominant roles in electrolyzer performance, and better performance can be obtained by reducing ohmic resistance. Thin titanium LGDLs with straight-through pores and optimal pore morphologies are recommended for the future developments of low-cost LGDLs with minimum ohmic/transport losses. 相似文献