We study stockpiling problems under uncertain economic and physical factors, and investigate the valuation and optimisation of storage systems where the availability and spot price of the underlying are both subject to stochasticity. Following a Real Options valuation approach, we first study financial derivatives linked to Asian options. A comprehensive set of boundary conditions is compiled, and an alternative (and novel) similarity reduction for fixed-strike Asian options is derived. Hybrid semi-Lagrangian methods for numerically solving the related partial differential equations (PDEs) are implemented, and we assess the accuracy of the valuations thus obtained with respect to results from classical finite-difference valuation methods and with respect to high precision calculations for valuing Asian options with spectral expansion theory techniques. Next we derive a PDE model for valuing the storage of electricity from a wind farm, with an attached back-up battery, that operates by trading electricity in a volatile market in order to meet a contracted fixed rate of energy generation; this system comprises two diffusive-type (stochastic) variables, namely the energy production and the electricity spot price, and two time-like (deterministic) variables, specifically the battery state and time itself. An efficient and novel semi-Lagrangian alternating-direction implicit (SLADI) methodology for numerically solving advection-diffusion problems is developed: here a semi-Lagrangian approach for hyperbolic problems of advection is combined with an alternating-direction implicit method for parabolic problems involving diffusion. Efficiency is obtained by solving (just) tridiagonal systems of equations at every time step. The results are compared to more standard semi-Lagrangian Crank-Nicolson (SLCN) and semi-Lagrangian fully implicit (SLFI) methods. Once he have established our PDE model for a storage-upgraded wind farm, a system that depends heavily on the highly stochastic nature of wind and the volatile market where electricity is sold, we derive a Hamilton-Jacobi-Bellman (HJB) equation for optimally controlling charging and discharging rates of the battery in time, and we assess a series of operation regimes. The solution of the related PDE models is approached numerically using our SLADI methodology to efficiently treat this mixed advection and diffusion problem in four dimensions. Extensive numerical experimentation confirms our SLADI methodology to be robust and yields highly accurate solutions and efficient computations, we also explore effects from correlation between stochastic electricity generation and random prices of electricity as well as effects from a seasonal electricity spot price. Ultimately, the objective of approximating optimal storage policies for a system under uncertain economic and physical factors is accomplished. Finally we examine the steady-state solution of a stochastic storage problem under uncertain electricity market prices and fixed demand. We use a HJB formulation for optimally controlling charging and discharging rates of the storage device with respect to the electricity spot price. A projected successive over-relaxation coupled with the semi-Lagrangian method is implemented, and we explore the use of boundary-fitted coordinates techniques.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1979. / Bibliography: leaves 58-59. / by Boris A. Kupershmidt. / Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1979.

Heat-release in CI engines occurs in the presence of concentration and temperature gradients. Recognizing the need for a validation of chemical kinetic models in transport-affected systems, this study employs non-premixed systems to better understand complex couplings between low/high temperature oxidation kinetics and diffusive transport. This dissertation is divided into two sections. In the first section, a two-stage Lagrangian model compares model prediction of ignition delay time and experimental data from the KAUST ignition quality tester, and ignition data for liquid sprays in constant volume combustion chambers. The TSL employed in this study utilizes detailed chemical kinetics while also simulating basic mixing processes. The TSL model was found to be efficient in simulating IQT in long ignition delay time fuels; it was also effective in CVCC experiments with high injection pressures, where physical processes contributed little to ignition delay time. In section two, an atmospheric pressure counterflow burner was developed and fully validated. The counterflow burner was employed to examine the effects of molecular structure on low/high temperature reactivity of various fuels in transport-affected systems. These effects were investigated through measurement of conditions of extinction and ignition of various fuel/oxidizer mixtures. Data generated were used to validate various chemical kinetic models in diffusion flames. Where necessary, suggestions were made for improving these models. For hot flames studies, tested fuels included C3-C4 alcohols and six FACE gasoline fuels. Results for alcohols indicated that the substituted alcohols were less reactive than the normal alcohols. The ignition temperature of FACE gasoline was found to be nearly identical, while there was a slight difference in their extinction limits. Predictions by Sarathy et al. (2014) alcohol combustion model, and by the gasoline surrogate model (Sarathy et al., 2015), agreed with the experimental data. For cool diffusion flames studies, tested fuels included butane isomers, naphtha, gasolines and their surrogates. Results revealed that the addition of ozone successfully established cool flames in the fuels at low and moderate strain rates. Numerical simulations were performed to replicate the extinction limits of the cool flames of butane isomers. The model captured experimental trends for both fuels; but over-predicted their extinction limits.

In a field of environmental protection there is a very important question about the options to determine impact of different pollution sources on air quality in areas more or less distant from those sources. For those predictions we can use physical or computer modelling. In this paper a computer model (Lagrangian Dispersion Model, or LDM) of air pollution propagation is developed and described. The LDM was created in order to work within the CLMM - Charles University Large-Eddy Microscale Model. In this paper we discuss theory of those models as well as technical solutions used to develop the LDM. The model is validated and subsequently applied on several cases with different degree of geometry complexity. Powered by TCPDF (www.tcpdf.org)

This thesis investigated the heat transfer of internally oil cooled rotors in permanent magnet electric machines which are, among other things, used in hybrid vehicles or zero emission vehicles. The magnets become sensitive and can be demagnetized at high working temperatures, hence the need of cooling. The scope of this work included CFD simulations in STAR-CCM+. Three different 3D multiphase models simulating the oil propagation in the rotor were performed. A Lagrangian multiphase model combined with a fluid film model was the most suitable model for simulating the spray of the oil and the film thickness along the inner rotor wall. It was noticed that periodic boundaries caused problems for the fluid film model, therefore a complete geometry was preferred over a truncated model. The 3D solutions provided thicker film thicknesses than the analytical solutions from the fluid film thickness theory. The maximum analytical thickness was of the same order of magnitude as the surface average film thickness provided by the multiphase models. This thickness was assumed to be constant when used as the base for the fluid region in the 2D one-phase models.The study showed that aluminum was the most suitable rotor material due to its high conductive capacity, which provided a more even distribution of the temperature in the solid and hence resulted in lower overall temperatures. The cooling power increased linearly with the volumetric flow rate, however the heat transfer coefficient decreased for the higher flow rates. A volumetric flow rate of 10dl/min was recommended. A 2D model was compared to a preliminary experiment and showed that these were not correlated. The conclusion was that more experiments and simulations are needed in order to confirm the validity of the 2D model.

The work is focused on experimental study and modelling of spacer grid influence on single- and two-phase flow. In the experimental study a mock-up of a realistic fuel bundle with five spacer grids of thin plate spring construction was investigated. A special pressure measuring technique was used to measure pressure distribution inside the spacer. Five pressure taps were drilled in one of the rods, which could exchange position with other rods, in this way providing a large degree of freedom. Laser Doppler Velocimetry was used to measure mean local axial velocity and its fluctuating component upstream and downstream of the spacer in several subchannels with differing spacer part. The experimental study revealed an interesting behaviour. Subchannels from the interior part of the bundle display a different effect on the flow downstream of the spacer compared to subchannels close to the box wall, even if the spacer part is the same. This behaviour is not reflected in modern correlations. The modelling part, first, consisted in comparing the present experimental data to Computational Fluid Dynamics calculations. It was shown that stand-alone subchannel models could predict the local velocity, but are unreliable in prediction of turbulence enhancement due to spacer. The second part of the modelling consisted in developing a deposition model for increase due to spacer. In this study Lagrangian Particle Tracking (LPT) coupled to Discrete Random Walk (DRW) technique was used to model droplet movements through turbulent flow. The LPT technique has an advantage to model the influence of turbulence structure effect on droplet deposition, in this way presenting a generalized model in view of spacer geometry change. The verification of the applicability of LPT DRW method to model deposition in annular flow at Boiling Water Reactor conditions proved that the method is unreliable in its present state. The model calculations compare reasonably well to air-water deposition data, but display a wrong trend if the fluids have a different density ratio than air-water.

Les extensions bifluides des méthodes Lattice Boltzmann à frontière libre utilisent généralement des pseudopotentiels microscopiques pour modéliser l'interface. Nous avons choisi d'orienter nos recherches vers une méthode Lattice Boltzmann à capture d'interface où la fraction massique d'un des deux fluides, inconnue, est transportée. De nombreux travaux ont montré les difficultés des méthodes Lattice Boltzmann à traiter des systèmes bifluides, et ce d'autant plus que le ratio de densité est important. Nous expliquerons l'origine de ces problèmes en mettant en évidence le manque de diffusion numérique pour capturer précisément les discontinuités de contact. Pour régler cet obstacle, nous proposerons une formulation Arbitrary Lagrangian Eulerian (ALE) des méthodes Lattice Boltzmann. Cela permet de séparer le traitement des ondes matérielles de celui des ondes de pression. Une fois l'étape ALE terminée, une phase de projection ramène les variables sur la grille eulérienne de calcul initiale. Nous expliquons comment obtenir une procédure de projection ayant une précision d'ordre 2 et une interface fine et dépourvue d'oscillations. Il sera montré que la fraction massique satisfait un principe du maximum discret et qu'elle reste donc entre 0 et 1. Les simulations numériques sont en accord avec la théorie. Même si notre méthode n'est pour le moment utilisée que pour simuler des écoulements de fluides non visqueux (Equations d'Euler), nous sommes convaincus qu'elle pourra être étendue à des simulations d'écoulements bifluides visqueux. / Two-fluid extensions of Lattice Boltzmann methods with free boundaries usually consider ``microscopic'' pseudopotential interface models. In this paper, we rather propose an interface-capturing Lattice Boltzmann approach where the mass fraction variable is considered as an unknown and is advected. Several works have reported the difficulties of LBM methods to deal with such two-fluid systems especially for high-density ratio configurations. This is due to the mixing nature of LBM, as with Flux vector splitting approaches for Finite Volume methods. We here give another explanation of the lack of numerical diffusion of Lattice Boltzmann approaches to accurately capture contact discontinuities. To fix the problem, we propose an arbitrary Lagrangian-Eulerian (ALE) formulation of Lattice-Boltzmann methods. In the Lagrangian limit, it allows for a proper separated treatment of pressure waves and advection phenomenon. After the ALE solution, a remapping (advection) procedure is necessary to project the variables onto the Eulerian Lattice-Boltzmann grid.We explain how to derive this remapping procedure in order to get second-order accuracy and achieve sharp stable oscillation-free interfaces. It has been shown that mass fractions variables satisfy a local discrete maximum principle and thus stay in the range $[0,1]$. The theory is supported by numerical computations of rising bubbles (without taking into account surface tension at this current state of development).Even if our methods are currently used for inviscid flows (Euler equations) by projecting the discrete distributions onto equilibrium ones at each time step, we believe that it is possible to extend the framework formulation for multifluid viscous problems. This will be at the aim of a next work.

This (Diplom-) thesis deals with the particle trajectories of an incompressible and ideal fluid flow in 𝑛 ≥ 2 dimensions. It presents a complete and detailed proof of the surprising fact that the trajectories of a smooth solution of the incompressible Euler equations are locally analytic in time. In following the approach of P. Serfati, a complex ordinary differential equation (ODE) is investigated which can be seen as a complex extension of a partial differential equation, which is solved by the trajectories. The right hand side of this ODE is in fact given by a singular integral operator which coincides with the pressure gradient along the trajectories. Eventually, we may apply the Cauchy-Lipschitz existence theorem involving holomorphic maps between complex Banach spaces in order to get a unique solution for the above mentioned ODE. This solution is real-analytic in time and coincides with the particle trajectories.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第18444号 / 理博第4004号 / 新制||理||1577(附属図書館) / 31322 / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)教授 加藤 毅, 教授 堤 誉志雄, 教授 小野 薫 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

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