Object-oriented modeling for the transient performance simulation of solar thermal power plants using parabolic trough collectors: a review and proposal of modeling approaches for thermal energy storage

La intención de este trabajo es extender las técnicas actuales de modelización del almacenamiento térmico activo directo y activo indirecto, con dos tanques y sales fundidas como medio de almacenamiento. Con el objetivo de conseguir aumentar el conocimiento sobre su comportamiento térmico y los aspectos operacionales, los modelos desarrollados deben permitir la evaluación del sistema de almacenamiento térmico en condiciones transitorias. Así, la parte principal de este trabajo (la Parte II) se centra en la modelización y evaluación del comportamiento de los intercambiadores de calor para la tecnología de almacenamiento térmico activo indirecto, que emplea sales fundidas (60% en peso de nitrato sódico, NaNO3, y 40% en peso de nitrato potásico, KNO3) como medio de almacenamiento y aceite térmico (una mezcla de difenilo, C12H10, y oxido de difenilo, C12H10O) como fluido caloportador. Asumiendo un diseño de intercambiador de calor del tipo carcasa y tubos, el comportamiento del proceso de intercambio de calor entre el medio de almacenamiento y el fluido caloportador se analiza en detalle, considerando condiciones de operación estacionarias y transitorias bajo cargas nominales y parciales. El modelo estacionario proporciona información útil sobre el coeficiente global de transmisión de calor y los rangos de variación de pérdidas de carga para dos configuraciones de intercambiadores de calor específicas. Se demuestra que la configuración de dos intercambiadores en paralelo supera a la configuración convencional de un único intercambiador en funcionamiento. Por otro lado, la evaluación del modelo transitorio suministra paráametros típicos del proceso como la ganancia, el tiempo muerto y la constante del tiempo para el modo de carga y descarga, en condiciones nominales y parciales. Además, se ha obtenido un modelo transitorio del tanque de almacenamiento a alta temperatura razonablemente simple, el cual es muy adecuado para simulaciones del comportamiento de centrales CSP en su conjunto. En el estudio se ha demostrado que las pérdidas térmicas por convección natural en la atmosfera de gas encima de la superficie libre de las sales fundidas se pueden omitir en el modelo, causando errores despreciables. También, se pueden asumir coeficientes de convección constantes entre la superficie de las paredes del tanque y las sales fundidas. Sin embargo, la transmisión de calor por radiación entre la superficie libre de las sales fundidas y las paredes interiores del tanque, que no están en contacto con las sales, deben de ser consideradas, dada su importante influencia en las pérdidas totales. Además, debido al modelado de la trasmisión de calor por las paredes del tanque en modo transitorio y al cálculo preciso de la temperatura de la superficie exterior, la influencia que las condiciones de contorno ambientales tienen sobre las pérdidas de calor, pueden ser caracterizadas de manera mucho más adecuada que mediante métodos cuasi-estacionarios, que solo tienen en cuenta la temperatura ambiente. Finalmente, la Parte III trata de la aplicación de los modelos desarrollados para los componentes del almacenamiento térmico, a un modelo exhaustivo y completo de una central de captadores cilindro-parabólicos a nivel global. De este modo se simula, no solo el comportamiento del sistema de almacenamiento térmico activo indirecto, sino también las respuestas de la central solar térmica al completo, debido a los cambios en las condiciones de contorno ambientales. Se observa que la inercia térmica del sistema de almacenamiento activo indirecto es muy considerable, influyendo de manera notable en los rápidos cambios de carga necesarios para capturar la mayor cantidad posible de la energía solar disponible, y para alimentar el bloque de potencia con una potencia térmica constante, independientemente de la actual radiación solar. Por último pero no menos importante, los modelos presentados han sido desarrollados de manera flexible, bien estructurada y con una programación orientada a objetos, particularmente dando importancia a una implementación independiente de la plataforma de simulación, hecho que ha sido llevado a cabo utilizando el lenguaje de modelación Modelica. Este es un lenguaje de modelizado de sistemas físicos multiobjetivo, que ha sido desarrollado en un esfuerzo internacional para unificar las técnicas de simulación ya existentes y para permitir el intercambio fácil de los modelos y librerías de modelos que se desarrollen. El concepto de Modelica se basa en modelos no causales que utilizan ecuaciones diferenciales ordinarias y algebraicas.This work's intention is to extend the current state-of-the-art regarding the modeling of the active direct and the active indirect two-tank moltensalt- based thermal energy storage (TES) concept. The aim is to widen the knowledge about their thermal behavior and operational aspects. In particular, the developed models shall enable the evaluation of the storage system's transient behavior. Thus, the main part of this work (Part II) focuses on the modeling and the performance evaluation of oil-to-molten salt heat exchangers for the active indirect thermal energy storage technology, applying molten salt (60%, by weight, sodium nitrate, NaNO3, and 40%, by weight, potassium nitrate, KNO3) as storage medium and thermal oil (a mixture of diphenyl, C12H10, and diphenyl oxide, C12H10O) as heat transfer fluid. Assuming a shell-andtube heat exchanger design, the performance of the heat exchange process between the storage medium and the heat transfer fluid is discussed in detail, considering steady-state as well as transient operating conditions under nominal as well as partial loads. On the one hand, the steady-state model gives useful information about overall heat transfer coefficient and pressure drop ranges for two specific heat exchanger setups. In particular, it is shown that two separate heat exchanger trains in parallel exceed the conventional single train setup in performance. On the other hand, the evaluation of the transient performance model yields typical process parameters as process gain, dead time and time constant for charging as well as for discharging mode at representative heat exchanger loads. In addition to this, a reasonable simple transient high-temperature storage tank model is derived, which is well suited for CSP performance simulations on system level due to reasonable model simplifications. For example, it is found in this work that the convective heat losses via the tank's gas atmosphere (usually nitrogen at ambient pressure) above the molten salt surface can be neglected by only introducing negligible calculation errors. Also, the convective heat transfer coefficients between the molten salt and the wetted parts of the tank's inner steel jacket may be set to constant values. However, the important radiative heat transfer between the surface of the molten salt and the non-wetted parts of the tank's inner steel jacket must be considered, which is done assuming an ideal cylindrical geometry. Furthermore, due to the transient modeling of the storage tank walls and a detailed estimation of the exterior surface temperature, the influence of altering environmental boundary conditions can be captured more accurately than by quasi-steadystate methods that only account for the current ambient air temperature. Finally, Part III treats the application of the developed TES model components in a comprehensive model of a parabolic trough collector plant on system level, showing not only the behavior of a typical active indirect twotank TES system under transient operating conditions, but also the responses of the entire solar thermal power plant to changing environmental boundary conditions. It is shown that the thermal inertia of the active indirect TES concept is considerable and forms a major obstacle for rapid load changes that are crucial for capturing as much solar energy as possible, and to supply the power block with constant thermal power, independently of the current solar irradiance. Last but not least, the presented models have been developed in a flexible, well-structured and object-oriented way, particularly giving importance to a simulation-platform-independent implementation, which has been accomplished applying Modelica, a multi-purpose physical system modeling language, developed in an international effort in order to unify already existing similar modeling approaches, and to enable developed models and model libraries to be easily exchanged. Modelica's concept is based on non-causal models featuring true ordinary differential and algebraic equations.Programa Oficial de Doctorado en Ingeniería y Arquitectura (RD 1393/2007)Ingeniaritzako eta Arkitekturako Doktoretza Programa Ofiziala (ED 1393/2007

Error Analysis of an HDG Method for a Distributed Optimal

In this paper, we present a priori error analysis of a hybridizable discontinuous Galerkin (HDG) method for a distributed optimal control problem governed by diffusion equations. The error estimates are established based on the projection-based approach recently used to analyze these methods for the diffusion equation. We proved that for approximations of degree k on conforming meshes, the orders of convergence of the approximation to fluxes and scalar variables are k+1 when the local stabilization parameter is suitably chosen

Scale formation, properties and de-scaling in steelmaking

During continuous castings, reheating, and hot rolling, slab surfaces are exposed to atmospheres containing oxidizing gases which results in scale formation. Inefficient removal of the formed scale during reheating affects product surface quality. The effect of steel composition and operating parameters on scale formation and scale removal efficiencies were investigated. Experimental investigations were carried out using a thermogravimetric (TGA) apparatus designed to replicate the combustion gas atmosphere and temperature in actual industrial slab reheat furnaces. Report on oxidation kinetics, scale structure and properties, and descaling were conducted on laboratory cast and industrial samples. Different characterization techniques were used to analyze in-depth formed scale structure. Results on scale formation studies showed that sample chemistry, reheating parameters and sample surface condition significantly affected the development of scale structure and its properties particularly in the subsurface scale layer region. The studies showed that major alloying elements (Mn, Si,), micro alloying (Al) elements, and impurities (Cu, Ni, Cr) modified the properties of the formed scale and its kinetics mechanism. Complexity of scale formation due to alloying elements and impurities in steel and cast slab surface condition affected its efficient removal using hydraulic descaling. Samples with high alloying elements of Si and Mn were characterized by strong adhesion and complex root penetrations in the subsurface scale region which decreased descaling efficiency. Descaling hydraulic parameters and surface pretreatment that improved scale removal efficiency were suggested”--Abstract, page iv

Analysis and finite element approximations of parabolic saddle point problems with applications to optimal control

We present some results concerning boundary optimal control problems and related initial-boundary value problems. We prove the existence and uniqueness of the solution of a parabolic saddle point problem, as well as the existence and uniqueness of a penalized and an iterated penalized saddle point problem. Moreover, we derive semidiscrete error estimates for the finite element approximation of the penalized saddle point problem, and semidiscrete error estimates for the penalized and unpenalized heat equation with nonhomogeneous boundary data under minimal regularity assumptions. Finally, we use the above results for the analysis and finite element analysis of boundary optimal control problems having states constrained to parabolic partial differential equations

Structure inhomogeneities, shallow defects, and charge transport in the series of thermoelectric materials K2Bi8−xSbxSe13

The charge transport properties of the low-dimensional thermoelectric materials K2Bi8-xSbxSe13 (02Bi8-xSbxSe13 was analyzed on the basis of the classical semiconductor theory and discussed in the context of recent band calculations. The results suggest that the K2Bi8-xSbxSe13 materials possess coexisting domains with semimetallic and semiconducting characters whose ratio is influenced by the value of x and by local defects. The extent and relative distribution of these domains control the charge transport properties. Electron diffraction experiments performed on samples of K2Bi8-xSbxSe13 with x=1.6 show evidence for such domains by indicating regions with long range ordering of K+/Bi3+ atoms and regions with increased disorder. The semiconducting behavior is enhanced with increasing x (i.e., Sb/Bi ratio) in the composition through a decrease of the semimetallic fraction

A Snapshot Algorithm for Linear Feedback Flow Control Design

The control of fluid flows has many applications. For micro air vehicles, integrated flow control designs could enhance flight stability by mitigating the effect of destabilizing air flows in their low Reynolds number regimes. However, computing model based feedback control designs can be challenging due to high dimensional discretized flow models. In this work, we investigate the use of a snapshot algorithm proposed in Ref. 1 to approximate the feedback gain operator for a linear incompressible unsteady flow problem on a bounded domain. The main component of the algorithm is obtaining solution snapshots of certain linear flow problems. Numerical results for the example flow problem show convergence of the feedback gains

Analytical solution to the wave equation with discrete pressure sources: A model for the Rijke tube

Despite of having been studied for several decades the phenomena of combustion instabilities are not well understood. Pressure waves due to the combustion instabilities can become violent being detrimental for both the performance and combustor life. A good prediction of the pressure distribution inside the combustor is important in order to prevent theoccurrence of this phenomenon. In this work a technique for solving the wave equation with discrete sources (or sinks) using the Green\u27s functions was developed. One and two-dimensional approaches for cylindrical and Cartesian coordinates withconstant speed of sound were solved. Also the case of one-dimensional axially varying temperature is presented. This technique was validated with results found in the literature and experimental data showing excellent agreement. By combining the 2-D solution with constant speed of sound plus the 1-D with axially varying speed of sound this technique accounts for thecontributions of the fuel composition since the different blends of fuel produce different temperature profiles and therefore different speeds of sound. The technique is proposed to solve the 2-D pressure distribution of the Rijke tube, which can be considered as the simplest combustor configuration. The study of the pressure distribution in the Rijke tube is fundamental for the understanding of the phenomenon of combustion instabilities

Almost Block Diagonal Linear Systems: Sequential and Parallel Solution Techniques, and Applications

Almost block diagonal (ABD) linear systems arise in a variety of contexts, specifically in numerical methods for two-point boundary value problems for ordinary differential equations and in related partial differential equation problems. The stable, efficient sequential solution of ABDs has received much attention over the last fifteen years and the parallel solution more recently. We survey the fields of application with emphasis on how ABDs and bordered ABDs (BABDs) arise. We outline most known direct solution techniques, both sequential and parallel, and discuss the comparative efficiency of the parallel methods. Finally, we examine parallel iterative methods for solving BABD systems. Copyright (C) 2000 John Wiley & Sons, Ltd

Boundary control of parabolic PDE using adaptive dynamic programming

In this dissertation, novel adaptive/approximate dynamic programming (ADP) based state and output feedback control methods are presented for distributed parameter systems (DPS) which are expressed as uncertain parabolic partial differential equations (PDEs) in one and two dimensional domains. In the first step, the output feedback control design using an early lumping method is introduced after model reduction. Subsequently controllers were developed in four stages; Unlike current approaches in the literature, state and output feedback approaches were designed without utilizing model reduction for uncertain linear, coupled nonlinear and two-dimensional parabolic PDEs, respectively. In all of these techniques, the infinite horizon cost function was considered and controller design was obtained in a forward-in-time and online manner without solving the algebraic Riccati equation (ARE) or using value and policy iterations techniques. Providing the stability analysis in the original infinite dimensional domain was a major challenge. Using Lyapunov criterion, the ultimate boundedness (UB) result was demonstrated for the regulation of closed-loop system using all the techniques developed herein. Moreover, due to distributed and large scale nature of state space, pure state feedback control design for DPS has proven to be practically obsolete. Therefore, output feedback design using limited point sensors in the domain or at boundaries are introduced. In the final two papers, the developed state feedback ADP control method was extended to regulate multi-dimensional and more complicated nonlinear parabolic PDE dynamics --Abstract, page iv

Effect of Design Parameters and Intercalation Induced Stresses in Lithium Ion Batteries

Electrochemical power sources, especially lithium ion batteries have become major players in various industrial sectors, with applications ranging from low power/energy demands to high power/energy requirements. But there are some significant issues existing for lithium ion systems which include underutilization, stress-induced material damage, capacity fade, and the potential for thermal runaway. Therefore, better design, operation and control of lithium ion batteries are essential to meet the growing demands of energy storage. Physics based modeling and simulation methods provide the best and most accurate approach for addressing such issues for lithium ion battery systems. This work tries to understand and address some of these issues, by development of physics based models and efficient simulation of such models for battery design and real time control purposes. This thesis will introduce a model-based procedure for simultaneous optimization of design parameters for porous electrodes that are commonly used in lithium ion systems. The approach simultaneously optimizes the battery design variables of electrode porosities and thickness for maximization of the energy drawn for an applied current, cut-off voltage, and total time of discharge. The results show reasonable improvement in the specific energy drawn from the lithium ion battery when the design parameters are simultaneously optimized. The second part of this dissertation will develop a 2-dimensional transient numerical model used to simulate the electrochemical lithium insertion in a silicon nanowire (Si NW) electrode. The model geometry is a cylindrical Si NW electrode anchored to a copper current collector (Cu CC) substrate. The model solves for diffusion of lithium in Si NW, stress generation in the Si NW due to chemical and elastic strain, stress generation in the Cu CC due to elastic strain, and volume expansion in the Si NW and Cu CC geometries. The evolution of stress components, i.e., radial, axial and tangential stresses in different regions in the Si NW are studied in details. Lithium-ion batteries are typically modeled using porous electrode theory coupled with various transport and reaction mechanisms with an appropriate discretization or approximation for the solid phase diffusion within the electrode particle. One of the major difficulties in simulating Li-ion battery models is the need for simulating solid-phase diffusion in the second radial dimension r within the particle. It increases the complexity of the model as well as the computation time/cost to a great extent. This is particularly true for the inclusion of pressure induced diffusion inside particles experiencing volume change. Therefore, to address such issues, part of the work will involve development of efficient methods for particle/solid phase reformulation - (1) parabolic profile approach and (2) a mixed order finite difference method. These models will be used for approximating/representing solid-phase concentration variations within the active material. Efficiency in simulation of particle level models can be of great advantage when these are coupled with macro-homogenous cell sandwich level battery models