Development of a reduced model of formation reactions in Zr-Al nanolaminates

Abstract

A computational model of anaerobic reactions in metallic multilayered systems with an equimolar composition of zirconium and aluminum is developed. The reduced reaction formalism of M. Salloum and O. M. Knio, Combust. Flame 157(2): 288–295 (2010) is adopted. Attention is focused on quantifying intermixing rates based on experimental measurements of uniform ignition as well as measurements of self-propagating front velocities. Estimates of atomic diffusivity are first obtained based on a regression analysis. A more elaborate Bayesian inference formalism is then applied in order to assess the impact of uncertainties in the measurements, potential discrepancies between predictions and observations, as well as the sensitivity of predictions to inferred parameters. Intermixing rates are correlated in terms of a composite Arrhenius law, which exhibits a discontinuity around the Al melting temperature. Analysis of the predictions indicates that Arrhenius parameters inferred for the low-temperature branch lie within a tight range, whereas the parameters of the high-temperature branch are characterized by higher uncertainty. The latter is affected by scatter in the experimental measurements, and the limited range of bilayers where observations are available. For both branches, the predictions exhibit higher sensitivity to the activation energy than the pre-exponent, whose posteriors are highly correlated.

Design analysis for optimal calibration of diffusivity in reactive multilayers

“…The predictions reveal that the peak of the distribution shifts towards lower velocities as λ increases. This is consistent with previous experimental, analytical and computational results [1,20,29,69], which indicate that the front velocity decreases with bilayer thickness, as long as the latter is sufficiently larger than the thickness of the premixed layer. The spread in the distributions, as quantified by the standard deviation, σ, is also observed to decrease with λ.…”

“…The four-dimensional polynomial basis of the resulting surrogate was found to be of the order: 3, 2, 2 and 2 along ξ 1 , ξ 2 , ξ 3 and ξ 4 respectively. The reaction time t r has been observed to increases monotonically toward T r when T r falls in the range of temperatures extending from ignition threshold to the melting point of Al, and t r also exhibits a smooth dependence on diffusivity parameters [1]. We thus expect the PC expansion of t r to converge rapidly, and a low-order expansion would be sufficient.…”

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Calibration of the uncertain Arrhenius diffusion parameters for quantifying mixing rates in Zr-Al nanolaminate foils was performed in a Bayesian setting [1]. The parameters were inferred in a low temperature regime characterized by homogeneous ignition and a high temperature regime characterized by self-propagating reactions in the multilayers.

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Sensitivity-Driven Adaptive Construction of Reduced-space Surrogates

“…Availability of a surrogate model typically enables efficient computation of Sobol' indices [11][12][13][14][15]. This has enabled performing global sensitivity analysis on a wide range of applications including in ocean modeling [16,17], geosciences [18][19][20], and chemical kinetics [21][22][23] to name a few.…”

Uncertainty quantification in non-equilibrium molecular dynamics simulations of thermal transport

“…Essentially, it is a truncated expansion with polynomial basis functions that converges in a least-squares sense. For an accurate PC representation, the output should vary smoothly with respect to the uncertain inputs [24] and must be L-2 integrable:…”