Modelling two-phase flow and transport effects of multi-component fuels

Three novel multicomponent fuel spray droplet evaporation models are developed by employing the theory of continuous thermodynamics(CT) with the aim of applying them in the design and analysis of various energy conversion devices such as, aircraft jet engines, liquid-fuel rocket engines, diesel engines, and industrial furnaces. The CT methodology seeks to represent complex mixtures - for example,aviation kerosene or JP8 that typically comprise blends of a large number of chemical compounds by using probability distribution functions (PDFs). The components of JP8, which is constituted by the homologous series of paraffin, naphthene, and aromatic hydrocarbons; are each represented by the Pearson-Shultz type three-parameter gamma PDF, where the three (shape, scale, and origin) parameters characterise changes in the mixture composition. The phase transition of the liquid droplet due to evaporation is modelled using both low-pressure (LP) and high-pressure (HP) vapour-liquid equilibrium (VLE) models employing various mixing and combining rules by applying a general cubic equation of state (CEOS). Interestingly enough, the phase transition of the liquid fuel into vapour mixture is characterised by a change in the PDF scale parameter alone. Once the description of the fuel mixture is complete, the traditional species and energy transport equations both for the liquid and vapour phases respectively, are re-written using the composition PDF moments under Lagrangian and Eulerian frameworks. In order to solve the governing equations for the three droplet evaporation models, which characteristically involve phase change and a moving interface, a novel fully Adaptive Method Of Lines using B-Spline Collocation (AMOLBSC) is developed. The models are tested at various pressures, temperatures and convective conditions, including at a lean, premixed, prevaporised (LPP) combustor operating condition. In general, the computational results at an ambient pressure close to atmospheric showed good to excellent agreement against available experimental data in the literature. However, for ambient conditions with elevated-high pressures and temperatures only models that employ the HP formulation gave reliable results. In particular, when the liquid is at or near its critical pressure and temperature it is characterised by faster vaporisation and shorter droplet lifetime, including some evidence of liquid mass diffusion. The liquid model that incorporates the effects of liquid core circulation using semiempirical approximation and adaptive mesh refinement (AMR) technique is the most accurate and computationally efficient, although further work is required to establish its ranges of applicability.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

A Metalearning Approach for Physics-Informed Neural Networks (PINNs): Application to Parameterized PDEs

Physics-informed neural networks (PINNs) as a means of discretizing partial differential equations (PDEs) are garnering much attention in the Computational Science and Engineering (CS&E) world. At least two challenges exist for PINNs at present: an understanding of accuracy and convergence characteristics with respect to tunable parameters and identification of optimization strategies that make PINNs as efficient as other computational science tools. The cost of PINNs training remains a major challenge of Physics-informed Machine Learning (PiML) - and, in fact, machine learning (ML) in general. This paper is meant to move towards addressing the latter through the study of PINNs on new tasks, for which parameterized PDEs provides a good testbed application as tasks can be easily defined in this context. Following the ML world, we introduce metalearning of PINNs with application to parameterized PDEs. By introducing metalearning and transfer learning concepts, we can greatly accelerate the PINNs optimization process. We present a survey of model-agnostic metalearning, and then discuss our model-aware metalearning applied to PINNs as well as implementation considerations and algorithmic complexity. We then test our approach on various canonical forward parameterized PDEs that have been presented in the emerging PINNs literature

Multifidelity Modeling for Physics-Informed Neural Networks (PINNs)

Multifidelity simulation methodologies are often used in an attempt to judiciously combine low-fidelity and high-fidelity simulation results in an accuracy-increasing, cost-saving way. Candidates for this approach are simulation methodologies for which there are fidelity differences connected with significant computational cost differences. Physics-informed Neural Networks (PINNs) are candidates for these types of approaches due to the significant difference in training times required when different fidelities (expressed in terms of architecture width and depth as well as optimization criteria) are employed. In this paper, we propose a particular multifidelity approach applied to PINNs that exploits low-rank structure. We demonstrate that width, depth, and optimization criteria can be used as parameters related to model fidelity, and show numerical justification of cost differences in training due to fidelity parameter choices. We test our multifidelity scheme on various canonical forward PDE models that have been presented in the emerging PINNs literature

Computational Engineering

This Workshop treated a variety of finite element methods and applications in computational engineering and expanded their mathematical foundation in engineering analysis. Among the 53 participants were mathematicians and engineers with focus on mixed and nonstandard finite element schemes and their applications

Fractional Calculus and the Future of Science

Newton foresaw the limitations of geometry’s description of planetary behavior and developed fluxions (differentials) as the new language for celestial mechanics and as the way to implement his laws of mechanics. Two hundred years later Mandelbrot introduced the notion of fractals into the scientific lexicon of geometry, dynamics, and statistics and in so doing suggested ways to see beyond the limitations of Newton’s laws. Mandelbrot’s mathematical essays suggest how fractals may lead to the understanding of turbulence, viscoelasticity, and ultimately to end of dominance of the Newton’s macroscopic world view.Fractional Calculus and the Future of Science examines the nexus of these two game-changing contributions to our scientific understanding of the world. It addresses how non-integer differential equations replace Newton’s laws to describe the many guises of complexity, most of which lay beyond Newton’s experience, and many had even eluded Mandelbrot’s powerful intuition. The book’s authors look behind the mathematics and examine what must be true about a phenomenon’s behavior to justify the replacement of an integer-order with a noninteger-order (fractional) derivative. This window into the future of specific science disciplines using the fractional calculus lens suggests how what is seen entails a difference in scientific thinking and understanding