Numerical experiments on turbulent entrainment and mixing of scalars

Numerical experiments on the turbulent entrainment and mixing of scalars in a incompressible flow have been performed. These simulations are based on a scale decomposition of the velocity field, thus allowing the establishment from a dynamic point of view of the evolution of scalar fields under the separate action of large-scale coherent motions and small-scale fluctuations. The turbulent spectrum can be split into active and inactive flow structures. The large-scale engulfment phenomena actively prescribe the mixing velocity by amplifying inertial fluxes and by setting the area and the fluctuating geometry of the scalar interface. On the contrary, small-scale isotropic nibbling phenomena are essentially inactive in the mixing process. It is found that the inertial mechanisms initiate the process of entrainment at large scales to be finally processed by scalar diffusion at the molecular level. This last stage does not prescribe the amount of mixing but adapts itself to the conditions imposed by the coherent anisotropic motion at large scales. The present results may have strong repercussions for the theoretical approach to scalar mixing, as anticipated here by simple heuristic arguments which are shown able to reveal the rich dynamics of the process. Interesting repercussions are also envisaged for turbulence closures, in particular for large-eddy simulation approaches where only the large scales of the velocity field are resolved

A Bayesian Approach to Manifold Topology Reconstruction

In this paper, we investigate the problem of statistical reconstruction of piecewise linear manifold topology. Given a noisy, probably undersampled point cloud from a one- or two-manifold, the algorithm reconstructs an approximated most likely mesh in a Bayesian sense from which the sample might have been taken. We incorporate statistical priors on the object geometry to improve the reconstruction quality if additional knowledge about the class of original shapes is available. The priors can be formulated analytically or learned from example geometry with known manifold tessellation. The statistical objective function is approximated by a linear programming / integer programming problem, for which a globally optimal solution is found. We apply the algorithm to a set of 2D and 3D reconstruction examples, demon-strating that a statistics-based manifold reconstruction is feasible, and still yields plausible results in situations where sampling conditions are violated

Non-local control in the conduction coefficients: well posedness and convergence to the local limit

We consider a problem of optimal distribution of conductivities in a system governed by a non-local diffusion law. The problem stems from applications in optimal design and more specifically topology optimization. We propose a novel parametrization of non-local material properties. With this parametrization the non-local diffusion law in the limit of vanishing non-local interaction horizons converges to the famous and ubiquitously used generalized Laplacian with SIMP (Solid Isotropic Material with Penalization) material model. The optimal control problem for the limiting local model is typically ill-posed and does not attain its infimum without additional regularization. Surprisingly, its non-local counterpart attains its global minima in many practical situations, as we demonstrate in this work. In spite of this qualitatively different behaviour, we are able to partially characterize the relationship between the non-local and the local optimal control problems. We also complement our theoretical findings with numerical examples, which illustrate the viability of our approach to optimal design practitioners

Study of lightweighting structural design considering 3D printing constraints

One of the current challenges of the aerospace industry is the exploration of new lightweighting structures to reduce fuel consumption and limiting the environmental impact. The use of numerical methods concerning topology optimization techniques allows the obtaining of such weight reduction, also minimizing both design time and costs, and hence accelerating the design process. Nevertheless, current structural optimization leads to the apparition of complex shapes and volumes with unintuitive holes, thus needing the use of additive manufacturing constraints - minimum length scales and overhanging - to ensure manufacturability. Considering the background exposed above, the aim of this project is to study the feasibility of heuristic designs concerning lightweighting structures, materialized with additive manufacturing and considering 3D printing constraints. The design stage will be developed by means of topology optimization techniques, applied to anisotropic filtering. The methodology employed has considered all details concerning Computational Solid Mechanics (CSM) techniques used in structures optimization, as well as additive manufacturing techniques, different case studies definition and their feasibility study. More specifically, in the context of CSM, the use of Finite Element Methods (FEM) in the classical elastic problem is reviewed, as well as current topology optimization techniques, so as to implement FEM in optimization algorithms. Thus, theoretical basis in additive manufacturing techniques are reviewed, along with the mathematical formulation of length scale and overhang constraints. Lastly, the programming stage is performed by previously defining the working environment, consisting in the use of Object-Oriented Programming within the git Version Control System, and hence establishing the computational domain definition for all cases, the meshing process and the simulation setup. In the end, the present project has accomplished the main objectives, giving a positive answer to the creation of lightweighting structures and fulfillment of 3D printing constraints. Indeed, FEM combined with topology optimization techniques has led to the obtaining of optimized designs, fulfilling an objective function and a set of constraints, considering both design variables approaches, density and level set. Besides, an additional shape functional has been defined as a penalty contribution to the main cost function in order to fulfill 3D printing constraints - the anisotropic perimeter - being the evolution of the standard isotropic one, both applied to total and relative perimeters. This shape functional self-penalizes length scale constraints and keeps control in overhanging phenomena by orienting the topologies with the definition of a virtual anisotropic stiffness matrix. Results obtained show that the apparition of local features with small length scales has been avoided when including either isotropic or anisotropic perimeter as a penalty term. Furthermore, vertical tendency orientation of topologies has been generally obtained with the anisotropic cases, along with penalization of horizontal features. Overall, this project has become clearly relevant for the exploration of new lightweighting structures, achieving weight reduction with topology optimization techniques. Further exploration remains in the course of PhD professionalization, specially when considering phase-field models, high-performance computing and large-scale optimization inside the non-linear regime

Topology optimization for energy problems

The optimal design of energy systems is a challenge due to the large design space and the complexity of the tightly-coupled multi-physics phenomena involved. Standard design methods consider a reduced design space, which heavily constrains the final geometry, suppressing the emergence of design trends. On the other hand, advanced design methods are often applied to academic examples with reduced physics complexity that seldom provide guidelines for real-world applications. This dissertation offers a systematic framework for the optimal design of energy systems by coupling detailed physical analysis and topology optimization. Contributions entail both method-related and application-oriented innovations. The method-related advances stem from the modification of topology optimization approaches in order to make practical improvements to selected energy systems. We develop optimization models that respond to realistic design needs, analysis models that consider full physics complexity and design models that allow dramatic design changes, avoiding convergence to unsatisfactory local minima and retaining analysis stability. The application-oriented advances comprise the identification of novel optimized geometries that largely outperform industrial solutions. A thorough analysis of these configurations gives insights into the relationship between design and physics, revealing unexplored design trends and suggesting useful guidelines for practitioners. Three different problems along the energy chain are tackled. The first one concerns thermal storage with latent heat units. The topology of mono-scale and multi-scale conducting structures is optimized using both density-based and level-set descriptions. The system response is predicted through a transient conjugate heat transfer model that accounts for phase change and natural convection. The optimization results yield a large acceleration of charge and discharge dynamics through three-dimensional geometries, specific convective features and optimized assemblies of periodic cellular materials. The second problem regards energy distribution with district heating networks. A fully deterministic robust design model and an adjoint-based control model are proposed, both coupled to a thermal and fluid-dynamic analysis framework constructed using a graph representation of the network. The numerical results demonstrate an increased resilience of the infrastructure thanks to particular connectivity layouts and its rapidity in handling mechanical failures. Finally, energy conversion with proton exchange membrane fuel cells is considered. An analysis model is developed that considers fluid flow, chemical species transport and electrochemistry and accounts for geometry modifications through a density-based description. The optimization results consist of intricate flow field layouts that promote both the efficiency and durability of the cell

On pre-image iterations for speech enhancement

In this paper, we apply kernel PCA for speech enhancement and derive pre-image iterations for speech enhancement. Both methods make use of a Gaussian kernel. The kernel variance serves as tuning parameter that has to be adapted according to the SNR and the desired degree of de-noising. We develop a method to derive a suitable value for the kernel variance from a noise estimate to adapt pre-image iterations to arbitrary SNRs. In experiments, we compare the performance of kernel PCA and pre-image iterations in terms of objective speech quality measures and automatic speech recognition. The speech data is corrupted by white and colored noise at 0, 5, 10, and 15 dB SNR. As a benchmark, we provide results of the generalized subspace method, of spectral subtraction, and of the minimum mean-square error log-spectral amplitude estimator. In terms of the scores of the PEASS (Perceptual Evaluation Methods for Audio Source Separation) toolbox, the proposed methods achieve a similar performance as the reference methods. The speech recognition experiments show that the utterances processed by pre-image iterations achieve a consistently better word recognition accuracy than the unprocessed noisy utterances and than the utterances processed by the generalized subspace method