Control of spatio-temporal pattern formation governed by geometrical models of interface evolution

Numerous natural phenomena are characterized by spatio-temporal dynamics which give rise to time evolving spatial patterns. Although studies that address the problem of modelling these complex dynamics exist, a model based control approach for such systems is still a challenging task. The work in this thesis is concerned with the development of control methods for such spatio-temporal systems, where interface growth is represented using a geometric evolution law. In particular, the focus is set on the control of dendritic crystal growth and wind-aided wildfire sprea

Modeling strategies for multiple scenarios and fast simulations in large systems: applications to fire safety and energy engineering

The use of computational modeling has become very popular and important in many engineering and physical fields, as it is considered a fast and inexpensive technique to support and often substitute experimental analysis. In fact system design and analysis can be carried out through computational studies instead of experiments, that are typically demanding in terms of cost and technical resources; sometimes the systems characteristics and the technical problems make the experiments impossible to perform and the use of computational tools is the only feasible option. Demand of resources for realistic simulation is increasing due to the interest in studying complex and large systems. In these framework smart modeling approaches and model reduction techniques play a crucial role for making complex and large system suitable for simulations. Moreover, it should be considered that often more than one simulation is requested in order to perform an analysis. For instance, if a heuristic method is applied to the optimization of a component, the model has to be run a certain number of times. The same problem arises when a certain level of uncertainty affect the system parameters; in this case also many simulation are required for obtaining the desired information. This is the reason why the use of technique that allows to obtain compact model is an interesting topic nowadays. In this PhD thesis different reduction approaches and strategies have been used in order to analyze three energetic systems involving large domain and long time, one for each reduction approach categories. In all the topic considered, a smart model has been adopted and, when data were available, tested using experimental data. All the model are characterized by large domain and the time involved in the analysis are high in all the cases, therefore a method for compact model achievement is used in all the cases. The considered topics are: • Groundwater temperature perturbations due to geothermal heat pump installations, analyzed trough a multi-level model. • District heating networks (DHN), studied from both the fluid-dynamic and thermal point of view and applied to one of the larger network in Europe, the Turin district heating system (DHS), trough a Proper Orthogonal Decomposition - Radial Basis Function model. • Forest fire propagation simulation carried out using a Proper Orthogonal Decomposition projection model

On the critical conditions for pool-fire puffing

Pool fires are known to undergo a bifurcation to a globally unstable puffing state driven by baroclinic and buoyant vorticity production. Although the supercritical puffing regime away from the bifurcation has been studied extensively in the literature, no detailed account has been given of the critical conditions for its onset, that being the purpose of the present paper. For the relevant canonical case of round liquid pools without swirl, aside from the inherent thermochemical and transport parameters associated with the fuel, pool-fire puffing is governed by a single dimensionless number, the Rayleigh number, which scales with the cube of the pool diameter. Consequently, for a fixed fuel and under fixed ambient conditions, there is a critical fuel pool diameter, associated with a critical value of the Rayleigh number, above which the flame starts puffing. A global linear stability analysis that accounts for the axisymmetry of the prevailing instability mode is developed here to describe the bifurcation. The mathematical formulation employs the limit of infinitely fast reaction, with account taken of the nonunity Lewis number and vaporization characteristics of typical liquid fuels. Predictions of critical puffing conditions, including critical diameters and puffing frequencies, are provided for methanol and for heptane pool fires, and the results are compared with results of new small-scale experiments under controlled laboratory conditions, reported here, yielding reasonably good agreement

Improving the understanding of fundamental mechanisms that influence ignition and burning behavior of porous wildland fuel beds

The phenomenon of a fire occurring in nature comes with a very high level of complexity. One central obstacle is the range of scales in such fires. In order to understand wildfires, research has to be conducted across these scales in order to study the mechanisms which drive wildfire behavior. The hazard related to such fires is ever more increasing as the living space of communities continues to increase and infringe with the wildland at the wildland-urban interface. In order to do so, a strong understanding on the possible wildfire behavior that may occur is critical. An array of factors impact wildfire behavior, which are generally categorized into three groups: (1) fuel (type, moisture content, loading, structure, continuity); (2) environmental (wind, temperature, relative humidity, precipitation); and (3) topography (slope, aspect). The complexity and coupling of factors impacting various scales of wildfire behavior has been the focus of much experimental and numerical work over the past decades. More recently, the need to quantify wildland fuel flammability and use the knowledge in mitigating risks, for example by categorizing vegetation according to their flammability has been recognized. Fuel flammability is an integral part of understanding wildfire behavior, since it can provide a quantification of the ignition and burning behavior of wildland fuel beds. Determining flammability parameters for vegetative fuels is however not a straight forward task and a rigorous standardized methodology has yet to be established. It is the intent of this work to aid in the path of finding a most suitable methodology to test vegetative fuel flammability. This is achieved by elucidating the fundamental heat and mass transfer mechanisms that drive ignition and burning behavior of porous wildland fuel beds. The work presented herein is a continuation of vegetative fuel flammability research using bench-scale calorimetry (the FM Global Fire Propagation Apparatus). This apparatus allows a high level of control of critical parameters. Experimental studies investigate how varying external heat flux (radiative), ventilation conditions (forced airflow rate, oxygen concentration, and temperature), and moisture content affect the ignition and burning behavior of wildland fuel. Two distinct ignition regimes were observed for radiative heating with forced convection cooling: (1) convection/radiation for low heating rates; and (2) radiation only for high heating rates. The threshold for the given convection conditions was near 45 kW.m-2. For forced convection, ignition behavior is dominated by convection cooling in comparison to dilution; ignition times were constant when the oxygen flow rate was varied (constant flow magnitude). Analysis of a radiative Biot number including heat losses (convection and radiation) indicated that the pine needles tested behaved thermally thin for the given heating rates (up to 60 kW.m-2). A simplified onedimensional, multi-phase heat transfer model for porous media is validated with experimental results (in-depth temperature measurements, critical heat flux and ignition time). The model performance was adequate for two species only, when the convective Froude number is less than 1.0 (only one packing ratio was tested). Increasing air flow rates resulted in higher heat of combustion due to increased pyrolysis rates. In the given experiments (ventilation controlled environment) combustion efficiency decreased with increasing O2 flow rates. Flaming combustion of pine needles in such environments resulted in four times greater CO generation rates compared to post flaming smoldering combustion. A link was made to live fuel flammability that is important for understanding the occurrence of extreme fire conditions such as crowning and to test if live fuel flammability contributes to the occurrence of a typical fire season. Significant seasonal variations were observed for the ignition and burning behavior of conditioned live pine needles. Variation and peak flammability due to ignition time and heat release rate can be associated to the growing season (physical properties and chemical composition of the needles). Seasonal trends were masked when unconditioned needles were tested as the release of water dominated effects. For wet fuel, ignition time increases linearly with fuel moisture content (FMC, R2 = 0.93). The peak heat release rate decreased non-linearly with FMC (R2 = 0.77). It was determined that above a threshold of 60% FMC (d.w.), seasonal variation in the heat release rate can be neglected. A novel live fuel flammability assessment to evaluate the seasonality of ignition and burning behavior is proposed. For the given case (NJ Pine Barrens, USA), the flammability assessment indicated that the live fuel is most flammable in August. Such assessment can provide a framework for a live fuel flammability classification system that is based on rigorous experimentation in well controlled fire environments

High-Resolution Numerical Simulations of Buoyancy-Driven Flows

Buoyancy-driven flows are commonly found in both nature and engineering, including volcanic plumes, underwater hydrothermal vents, and industrial burners. The study of these flows using computational simulations is, however, made challenging by the large separation of physical scales inherent in these flows, and also by the presence of additional complex phenomena such as combustion. In this thesis, we outline advances in computational modeling of buoyancy-driven flows, as well as describe physical insights obtained from the simulations. First, we discuss the complexities involved in the simulation of these flows, including the challenges imposed by large scale separations and the need to assign physically accurate boundary conditions. After presenting preliminary two-dimensional simulations, we discuss an alternative formulation of the equations of motion involving a low-Mach number approximation. This, along with the use of a fully adaptive grid, allows for high fidelity computations that bridge the large scale separations found in many real-world buoyancy-driven flows. High-resolution simulations of a one-meter diameter helium plume are performed with an emphasis on the physical resolution required to accurately predict dynamics and statistics up to second-order. The highest resolution simulation is then analyzed in an attempt to improve sub-grid scale models for large eddy simulations. Finally, the fundamental puffing instability present in buoyant jets is examined through a series of simulations for a variety of inlet geometries over a range of operating conditions. We present a new, universal scaling law that is able to predict the dominant frequency of pulsation for an arbitrarily shaped buoyant jet. The new scaling law collapses data from the present simulations as well as all available experimental data from three decades of research. Ultimately, the work contained in this thesis represents a substantial step forward in our ability to computationally model and understand buoyancy-driven flows.</p

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

A Strategy for a Global Observing System for Verification of National Greenhouse Gas Emissions

Abstract and PDF report are also available on the MIT Joint Program on the Science and Policy of Global Change website (http://globalchange.mit.edu/).With the risks of climate change becoming increasingly evident, there is growing discussion regarding international treaties and national regulations to lower greenhouse gas (GHG) emissions. Enforcement of such agreements is likely to depend formally upon national and sectoral emission reporting procedures (sometimes referred to as “bottom-up” methods). However, for these procedures to be credible and effective, it is essential that these reports or claims be independently verified. In particular, any disagreements between these “bottom-up” emission estimates, and independent emission estimates inferred from global GHG measurements (so-called “top-down” methods) need to be resolved. Because emissions control legislation is national or regional in nature, not global, it is also essential that “top-down” emission estimates be determined at these same geographic scales. This report lays out a strategy for quantifying and reducing uncertainties in greenhouse gas emissions, based on a comprehensive synthesis of global observations of various types with models of the global cycles of carbon dioxide and other greenhouse gases that include both the natural and human influences on these cycles. The overall goal is to establish a global observing and estimation system that incorporates all relevant available knowledge (physical, biogeochemical, technological and economic) in order to verify greenhouse gas emissions, as a key component of any global GHG treaty.Lockheed Martin Corporation and the MIT Joint Program on the Science and Policy of Global Change, which is funded by a consortium of government, industry and foundation sponsors

The 2nd International Conference on Mathematical Modelling in Applied Sciences, ICMMAS’19, Belgorod, Russia, August 20-24, 2019 : book of abstracts

The proposed Scientific Program of the conference is including plenary lectures, contributed oral talks, poster sessions and listeners. Five suggested special sessions / mini-symposium are also considered by the scientific committe