Thermal management model for a plug-in hybrid electric vehicle

L’elettrificazione dei veicoli diventerà sempre più preminente sia per ridurre i consumi sia per soddisfare le sempre più stringenti normative sulle emissioni. L' aggiunta di nuovi componenti, cioè motori elettrici, inverter e batteria ad alto voltaggio, permette di aumentare la massima coppia disponibile alle ruote e l’energia immagazzinata a bordo, ma aumenta anche il peso della vettura. Inoltre, questi componenti, pur avendo una efficienza molto elevata, producono una rilevante quantità di calore che deve essere opportunamente rimossa. Al fine di garantire efficienza e affidabilità dell’intero sistema veicolo, l’impianto di raffreddamento deve essere riprogettato. Lo sviluppo di un modello termico può certamente aiutare a progettare al meglio il completo sistema di gestione e controllo della temperatura, visti i molteplici aspetti da considerare. Il veicolo considerato nel presente lavoro di tesi ha un’architettura ibrida P1-P4 e comprende tre circuiti di raffreddamento tra loro separati. Il modello permette di conoscere portata, pressioni e temperature del refrigerante. In primo luogo, la parte idraulica è stata modellata, comprensiva di curva caratteristica della pompa e perdite di carico. In secondo luogo, è stata inclusa la descrizione termica. L’obiettivo principale del presente lavoro è quello di costruire un ambiente in cui successivamente sviluppare strategie di controllo di gestione termica. Gli input del modello sono principalmente parametri legati al powertrain (coppia e velocità di rotazione del motore termico ed elettrico) più i segnali di controllo (per pompe elettriche, ventilatori e compressore) mentre gli output sono la descrizione idraulica e termica del refrigerante nei tre diversi circuiti, più le temperature di batteria e motori elettrici. Il modello costruito è stato poi validato, basandosi sui dati sperimentali a disposizione

Thermal stress fields between two unequal circular holes in a ceramic medium

Thermal stresses play a significant role in a number of engineering problems ranging from the design of heat engines, nuclear plants and aircrafts to the enhancement of electronic devices and MEMS performance. In particular, the determination of stress concentrations due to thermal loadings is a main issue for the accurate design of many electronic devices, where a large number of conductive electric wires are embedded in a ceramic or Silicon matrix at a small distance from each other. In this case, the heat production due to the Joule effect may create high enough thermal stresses to cause cracking and rupture of the insulating ligament between the wires, thus reducing the performance of the device. Since cracks often initiate and propagate from the locations of stress concentration, such as holes and inclusions, then, an accurate evaluation of the stress concentration factor (SCF) in proximity of these defects is a prerequisite to assure the structural integrity of a number of ceramic components and to guarantee the proper functionality of many electronic devices. An analytic solution is presented here for thermal stresses in an infinite thermoelastic medium with two unequal circular cylindrical holes held at different temperatures, under steady-state heat flux. The most general representation for a biharmonic function in bipolar coordinates has been used. The stress field is decomposed in the sum of a particular stress field induced by the steady-state temperature distribution, which does not satisfy the conditions of vanishing tractions on the surfaces of the holes and vanishing remote stress field, and an auxiliary stress field required to satisfy these boundary conditions, which has been obtained for isothermal elasticity. The corresponding variations of the stress concentration factor, are determined in terms of the holes geometry and temperatures. Moreover, the Jk-integral vector and the M-integral are first generalized for steady state thermoelasticity and then calculated on a closed contour encircling one or both holes. Results are then presented for varying geometry of the holes

Path-independent integrals around two circular holes in a thermoelastic medium

An analytic solution obtained by using bipolar coordinates is presented for thermal stresses in an infinite thermoelastic medium with two unequal circular holes kept at different temperatures. The Jk-integral vector and M- and L- integrals are derived for steady thermoelasticity and calculated on a closed contour encircling one or both holes

Overall thermomechanical properties of layered materials for energy devices applications

This paper is concerned with the analysis of effective thermomechanical properties of multi- layered materials of interest for solid oxide fuel cells (SOFC) and lithium ions batteries fabrication. The recently developed asymptotic homogenization procedure is applied in order to express the overall thermoelastic constants of the first order equivalent continuum in terms of microfluctuations functions, and these functions are obtained by the solution of the corresponding recursive cell problems. The effects of thermal stresses on periodic multi-layered thermoelastic composite reproducing the characteristics of solid oxide fuel cells (SOFC-like) are studied assuming periodic body forces and heat sources, and the solution derived by means of the asymptotic homogenization approach is compared with the results obtained by finite elements analysis of the associate heterogeneous material

Weight Function Approach to a Crack Propagating along a Bimaterial Interface Under Arbitrar Loading in an Anisotropic Solid

The focus of this paper is the study of the dynamic steady-state propagation of interfacial cracks in anisotropic bimaterials under general, nonsymmetric loading conditions. Symmetric and skew-symmetric weight functions, defined as singular nontrivial solutions of a homogeneous traction-free crack problem, have been recently derived for a quasistatic semiinfinite crack at the interface between two dissimilar anisotropic materials. In this paper, the expressions for the weight functions are generalized to the case of a dynamic steady-state crack between two anisotropic media. A functional matrix equation, through which it is possible to evaluate the stress intensity factors and the energy release rate at the crack tip, is obtained. A general method for calculating the asymptotic coefficients of the displacement and traction fields, without any restrictions regarding the loading applied on the crack faces, is developed. The proposed approach is applied for the computing stress intensity factors and higher-order asymptotic terms corresponding to two different example loading configurations acting on the crack faces in an orthotropic bimaterial

Stroh formalism in analysis of skew-symmetric and symmetric weight functions for interfacial cracks

The focus of the article is on analysis of skew-symmetric weight matrix functions for interfacial cracks in two dimensional anisotropic solids. It is shown that the Stroh formalism proves to be an efficient approach to this challenging task. Conventionally, the weight functions, both symmetric and skew-symmetric, can be identified as a non-trivial singular solutions of the homogeneous boundary value problem for a solid with a crack. For a semi-infinite crack, the problem can be reduced to solving a matrix Wiener-Hopf functional equation. Instead, the Stroh matrix representation of displacements and tractions, combined with a Riemann-Hilbert formulation, is used to obtain an algebraic eigenvalue problem, that is solved in a closed form. The proposed general method is applied to the case of a quasi-static semi-infinite crack propagation between two dissimilar orthotropic media: explicit expressions for the weight matrix functions are evaluated and then used in the computation of complex stress intensity factor corresponding to an asymmetric load acting on the crack faces

Super band gaps and periodic approximants of generalised Fibonacci tilings

We present mathematical theory for self-similarity induced spectral gaps in the spectra of systems generated by generalised Fibonacci tilings. Our results characterise super band gaps, which are spectral gaps that exist for all sufficiently large periodic systems in a Fibonacci-generated sequence. We characterise super band gaps in terms of a growth condition on the traces of the associated transfer matrices. Our theory includes a large family of generalised Fibonacci tilings, including both precious mean and metal mean patterns. We apply our analytic results to characterise spectra in three different settings: compressional waves in a discrete mass-spring system, axial waves in structured rods and flexural waves in multi-supported beams. The theory is shown to give accurate predictions of the super band gaps, with minimal computational cost and significantly greater precision than previous estimates. It also provides a mathematical foundation for using periodic approximants (supercells) to predict the transmission gaps of quasicrystalline samples, as we verify numerically

Interfacial cracks in bi-material solids: Stroh formalism and skew-symmetric weight functions

A new general approach for deriving the weight functions for 2D interfacial cracks in anisotropic bimaterials has been developed.For perfect interface conditions, the new method avoid the use of Wiener-Hopf technique and the challenging factorization problem connected. Both symmetric and skew-symmetric weight functions can be derived by means of the new approach. Weight functions can be used for deriving singular integral formulation of interfacial cracks in anisotropic media. The proposed method can be applied for studying interfacial cracks problems in many materials:monoclinic, orthotropic, cubic, piezoelectrics, poroelastics, quasicrystals

Negative refraction in quasicrystalline multilayered metamaterials

Inspired by some recent results in elastodynamics of layered composites, we address here the problem of an antiplane elastic wave obliquely incident at the interface between a substrate and a periodic laminate with a quasicrystalline structure (generated by the Fibonacci substitution rule). The angles of refraction of the transmitted modes are computed by combining the transfer matrix method with the normal mode decomposition and evaluating the direction of the average Poynting vector. It is shown that, with respect to a periodic classical bilayer, on the one hand, beyond a certain frequency threshold, high order Fibonacci laminates can provide negative refraction for a wider range of angles of incidence, on the other, they allow negative wave refraction at lower frequencies. The outcome strongly relies on the Floquet-Bloch dynamic analysis of this class of laminates that is performed thoroughly. It is revealed that the corresponding spectra have a self-similar character linked to the specialisation of the Kohmoto’s invariant, a function of the frequency that was recently studied by the authors for periodic one-dimensional quasicrystalline-generated waveguides. This function is able to explain two types of scaling occurring in dispersion diagrams. The attained results represent an important advancement towards the realisation of multilayered quasicrystalline metamaterials with the aim to control negatively refracted elastic waves

Severe Milk-Alkali Syndrome in a Patient with Hypoparathyroidism Associated with 1,25(OH)2D, Hydrochlorothiazide and Anthranoid Laxative Consumption

Background: Milk-alkali syndrome is a life-threatening condition defined by the triad of hypercalcaemia, metabolic alkalosis and acute renal failure, and is associated with consumption of calcium and absorbable alkali. Methods: We report the case of a patient admitted to a step-down unit of a large hospital in Italy. Results: The patient was a 59-year-old woman with hypoparathyroidism and mild chronic kidney insufficiency, treated for a preceding episode of hypocalcaemia with high doses of calcitriol and calcium carbonate, who was also taking hydrochlorothiazide and unreported herbal anthranoid laxatives. The patient was admitted to hospital with severe hypercalcaemia, severe metabolic alkalosis and acute renal insufficiency. The patient was successfully treated with urgent dialysis, loop diuretics and calcitonin administration. Conclusions: This case underlines the need for caution when treating patients with impaired calcium metabolism regulation, and suggests that herbal anthranoid laxatives might act as triggers for milk-alkali syndrome.