Numerical Analysis on a Dual-Loop Waste Heat Recovery System Coupled with an ORC for Vehicle Applications

The internal combustion (IC) engines exploits only about 30% of the chemical energy ejected through combustion, whereas the remaining part is rejected by means of cooling system and exhausted gas. Nowadays, a major global concern is finding sustainable solutions for better fuel economy which in turn results in a decrease of carbon dioxide (CO2) emissions. The Waste Heat Recovery (WHR) is one of the most promising techniques to increase the overall efficiency of a vehicle system, allowing the recovery of the heat rejected by the exhaust and cooling systems. In this context, Organic Rankine Cycles (ORCs) are widely recognized as a potential technology to exploit the heat rejected by engines to produce electricity. The aim of the present paper is to investigate a WHR system, designed to collect both coolant and exhausted gas heats, coupled with an ORC cycle for vehicle applications. In particular, a coolant heat exchanger (CLT) allows the heat exchange between the water coolant and the ORC working fluid, whereas the exhausted gas heat is recovered by using a secondary circuit with diathermic oil. By using an in-house numerical model, a wide range of working conditions and ORC design parameters are investigated. In particular, the analyses are focused on the regenerator location inside the ORC circuits. Five organic fluids, working in both subcritical and supercritical conditions, have been selected in order to detect the most suitable configuration in terms of energy and exergy efficiencies.

Application of Volterra Equations to Solve Unit Commitment Problem of Optimised Energy Storage and Generation

Development of reliable methods for optimised energy storage and generation is one of the most imminent challenges in modern power systems. In this paper an adaptive approach to load leveling problem using novel dynamic models based on the Volterra integral equations of the first kind with piecewise continuous kernels. These integral equations efficiently solve such inverse problem taking into account both the time dependent efficiencies and the availability of generation/storage of each energy storage technology. In this analysis a direct numerical method is employed to find the least-cost dispatch of available storages. The proposed collocation type numerical method has second order accuracy and enjoys self-regularization properties, which is associated with confidence levels of system demand. This adaptive approach is suitable for energy storage optimisation in real time. The efficiency of the proposed methodology is demonstrated on the Single Electricity Market of Republic of Ireland and Northern Ireland.

Combustion Noise

Combustion noise is becoming increasingly important as a major noise source in aeroengines and ground based gas turbines. This is partially because advances in design have reduced the other noise sources, and partially because next generation combustion modes burn more unsteadily, resulting in increased external noise from the combustion. This review reports recent progress made in understanding combustion noise by theoretical, numerical and experimental investigations. We first discuss the fundamentals of the sound emission from a combustion region. Then the noise of open turbulent flames is summarized. We subsequently address the effects of confinement on combustion noise. In this case not only is the sound generated by the combustion influenced by its transmission through the boundaries of the combustion chamber, there is also the possibility of a significant additional source, the so-called ‘indirect’ combustion noise. This involves hot spots (entropy fluctuations) or vorticity perturbations produced by temporal variations in combustion, which generate pressure waves (sound) as they accelerate through any restriction at the exit of the combustor. We describe the general characteristics of direct and indirect noise. To gain further insight into the physical phenomena of direct and indirect sound, we investigate a simple configuration consisting of a cylindrical or annular combustor with a low Mach number flow in which a flame zone burns unsteadily. Using a low Mach number approximation, algebraic exact solutions are developed so that the parameters controlling the generation of acoustic, entropic and vortical waves can be investigated. The validity of the low Mach number approximation is then verified by solving the linearized Euler equations numerically for a wide range of inlet Mach numbers, stagnation temperature ratios, frequency and mode number of heat release fluctuations. The effects of these parameters on the magnitude of the waves produced by the unsteady combustion are investigated. In particular the magnitude of the indirect and direct noise generated in a model combustor with a choked outlet is analyzed for a wide range of frequencies, inlet Mach numbers and stagnation temperature ratios. Finally, we summarize some of the unsolved questions that need to be the focus of future research

Temperature fields in a channel partially filled with a porous material under local thermal non-equilibrium condition-an exact solution

This work examines analytically the forced convection in a channel partially filled with a porous material and subjected to constant wall heat flux. The Darcy–Brinkman–Forchheimer model is used to represent the fluid transport through the porous material. The local thermal non-equilibrium, two-equation model is further employed as the solid and fluid heat transport equations. Two fundamental models (models A and B) represent the thermal boundary conditions at the interface between the porous medium and the clear region. The governing equations of the problem are manipulated, and for each interface model, exact solutions, for the solid and fluid temperature fields, are developed. These solutions incorporate the porous material thickness, Biot number, fluid to solid thermal conductivity ratio and Darcy number as parameters. The results can be readily used to validate numerical simulations. They are, further, applicable to the analysis of enhanced heat transfer, using porous materials, in heat exchangers.

Heating the Early Universe : Numerical Methods and Their Analysis

During the epoch when the first collapsed structures formed (6<z<50) our Universe went through an extended period of changes. Some of the radiation from the first stars and accreting black holes in those structures escaped and changed the state of the Intergalactic Medium (IGM). The era of this global phase change in which the state of the IGM was transformed from cold and neutral to warm and ionized, is called the Epoch of Reionization.In this thesis we focus on numerical methods to calculate the effects of this escaping radiation. We start by considering the performance of the cosmological radiative transfer code C2-Ray. We find that although this code efficiently and accurately solves for the changes in the ionized fractions, it can yield inaccurate results for the temperature changes. We introduce two new elements to improve the code. The first element, an adaptive time step algorithm, quickly determines an optimal time step by only considering the computational cells relevant for this determination. The second element, asynchronous evolution, allows different cells to evolve with different time steps. An important constituent of methods to calculate the effects of ionizing radiation is the transport of photons through the computational domain or ``ray-tracing''. We devise a novel ray tracing method called PYRAMID which uses a new geometry - the pyramidal geometry. This geometry shares properties with both the standard Cartesian and spherical geometries. This makes it on the one hand easy to use in conjunction with a Cartesian grid and on the other hand ideally suited to trace radiation from a radially emitting source. A time-dependent photoionization calculation not only requires tracing the path of photons but also solving the coupled set of photoionization and thermal equations. Several different solvers for these equations are in use in cosmological radiative transfer codes. We conduct a detailed and quantitative comparison of four different standard solvers in which we evaluate how their accuracy depends on the choice of the time step. This comparison shows that their performance can be characterized by two simple parameters and that the C2-Ray generally performs best.

Numerical Simulation Of Ultrasonic Wave Propagation In Elastically Anisotropic Media

The ultrasonic non-destructive testing of components may encounter considerable difficulties to interpret some inspections results mainly in anisotropic crystalline structures. A numerical method for the simulation of elastic wave propagation in homogeneous elastically anisotropic media, based on the general finite element approach, is used to help this interpretation. The successful modeling of elastic field associated with NDE is based on the generation of a realistic pulsed ultrasonic wave, which is launched from a piezoelectric transducer into the material under inspection. The values of elastic constants are great interest information that provide the application of equations analytical models, until small and medium complexity problems through programs of numerical analysis as finite elements and/or boundary elements. The aim of this work is the comparison between the results of numerical solution of an ultrasonic wave, which is obtained from transient excitation pulse that can be specified by either force or displacement variation across the aperture of the transducer, and the results obtained from a experiment that was realized in an aluminum block in the IEN Ultrasonic Laboratory. The wave propagation can be simulated using all the characteristics of the material used in the experiment evaluation associated to boundary conditions and from these results, the comparison can be made.

On (p, q) − equations with concave terms

We consider a (p, q)− equation (1 < q < p, p ≥ 2) with a parametric concave term and a (p − 1)− linear perturbation. We show that the problem have five nontrivial smooth solutions: four of constant sign and the fifth nodal. When q = 2 (i.e., (p, 2) equation) we show that the problem has six nontrivial smooth solutions, but we do not specify the sign of the sixth solution. Our approach uses variational methods, together with truncation and comparison techniques and Morse theory.

Eigenfunctions and fundamental solutions of the fractional Laplace and Dirac operators: the Riemann-Liouville case

In this paper we study eigenfunctions and fundamental solutions for the three parameter fractional Laplace operator $\Delta_+^{(\alpha,\beta,\gamma)}:= D_{x_0^+}^{1+\alpha} +D_{y_0^+}^{1+\beta} +D_{z_0^+}^{1+\gamma},$ where $(\alpha, \beta, \gamma) \in \,]0,1]^3$, and the fractional derivatives $D_{x_0^+}^{1+\alpha}$, $D_{y_0^+}^{1+\beta}$, $D_{z_0^+}^{1+\gamma}$ are in the Riemann-Liouville sense. Applying operational techniques via two-dimensional Laplace transform we describe a complete family of eigenfunctions and fundamental solutions of the operator $\Delta_+^{(\alpha,\beta,\gamma)}$ in classes of functions admitting a summable fractional derivative. Making use of the Mittag-Leffler function, a symbolic operational form of the solutions is presented. From the obtained family of fundamental solutions we deduce a family of fundamental solutions of the fractional Dirac operator, which factorizes the fractional Laplace operator. We apply also the method of separation of variables to obtain eigenfunctions and fundamental solutions.

DIRECT NUMERICAL SIMULATION OF INCOMPRESSIBLE MULTIPHASE FLOW WITH PHASE CHANGE

Phase change problems arise in many practical applications such as air-conditioning and refrigeration, thermal energy storage systems and thermal management of electronic devices. The physical phenomenon in such applications are complex and are often difficult to be studied in detail with the help of only experimental techniques. The efforts to improve computational techniques for analyzing two-phase flow problems with phase change are therefore gaining momentum. The development of numerical methods for multiphase flow has been motivated generally by the need to account more accurately for (a) large topological changes such as phase breakup and merging, (b) sharp representation of the interface and its discontinuous properties and (c) accurate and mass conserving motion of the interface. In addition to these considerations, numerical simulation of multiphase flow with phase change introduces additional challenges related to discontinuities in the velocity and the temperature fields. Moreover, the velocity field is no longer divergence free. For phase change problems, the focus of developmental efforts has thus been on numerically attaining a proper conservation of energy across the interface in addition to the accurate treatment of fluxes of mass and momentum conservation as well as the associated interface advection. Among the initial efforts related to the simulation of bubble growth in film boiling applications the work in \cite{Welch1995} was based on the interface tracking method using a moving unstructured mesh. That study considered moderate interfacial deformations. A similar problem was subsequently studied using moving, boundary fitted grids \cite{Son1997}, again for regimes of relatively small topological changes. A hybrid interface tracking method with a moving interface grid overlapping a static Eulerian grid was developed \cite{Juric1998} for the computation of a range of phase change problems including, three-dimensional film boiling \cite{esmaeeli2004computations}, multimode two-dimensional pool boiling \cite{Esmaeeli2004} and film boiling on horizontal cylinders \cite{Esmaeeli2004a}. The handling of interface merging and pinch off however remains a challenge with methods that explicitly track the interface. As large topological changes are crucial for phase change problems, attention has turned in recent years to front capturing methods utilizing implicit interfaces that are more effective in treating complex interface deformations. The VOF (Volume of Fluid) method was adopted in \cite{Welch2000} to simulate the one-dimensional Stefan problem and the two-dimensional film boiling problem. The approach employed a specific model for mass transfer across the interface involving a mass source term within cells containing the interface. This VOF based approach was further coupled with the level set method in \cite{Son1998}, employing a smeared-out Heaviside function to avoid the numerical instability related to the source term. The coupled level set, volume of fluid method and the diffused interface approach was used for film boiling with water and R134a at the near critical pressure condition \cite{Tomar2005}. The effect of superheat and saturation pressure on the frequency of bubble formation were analyzed with this approach. The work in \cite{Gibou2007} used the ghost fluid and the level set methods for phase change simulations. A similar approach was adopted in \cite{Son2008} to study various boiling problems including three-dimensional film boiling on a horizontal cylinder, nucleate boiling in microcavity \cite{lee2010numerical} and flow boiling in a finned microchannel \cite{lee2012direct}. The work in \cite{tanguy2007level} also used the ghost fluid method and proposed an improved algorithm based on enforcing continuity and divergence-free condition for the extended velocity field. The work in \cite{sato2013sharp} employed a multiphase model based on volume fraction with interface sharpening scheme and derived a phase change model based on local interface area and mass flux. Among the front capturing methods, sharp interface methods have been found to be particularly effective both for implementing sharp jumps and for resolving the interfacial velocity field. However, sharp velocity jumps render the solution susceptible to erroneous oscillations in pressure and also lead to spurious interface velocities. To implement phase change, the work in \cite{Hardt2008} employed point mass source terms derived from a physical basis for the evaporating mass flux. To avoid numerical instability, the authors smeared the mass source by solving a pseudo time-step diffusion equation. This measure however led to mass conservation issues due to non-symmetric integration over the distributed mass source region. The problem of spurious pressure oscillations related to point mass sources was also investigated by \cite{Schlottke2008}. Although their method is based on the VOF, the large pressure peaks associated with sharp mass source was observed to be similar to that for the interface tracking method. Such spurious fluctuation in pressure are essentially undesirable because the effect is globally transmitted in incompressible flow. Hence, the pressure field formation due to phase change need to be implemented with greater accuracy than is reported in current literature. The accuracy of interface advection in the presence of interfacial mass flux (mass flux conservation) has been discussed in \cite{tanguy2007level,tanguy2014benchmarks}. The authors found that the method of extending one phase velocity to entire domain suggested by Nguyen et al. in \cite{nguyen2001boundary} suffers from a lack of mass flux conservation when the density difference is high. To improve the solution, the authors impose a divergence-free condition for the extended velocity field by solving a constant coefficient Poisson equation. The approach has shown good results with enclosed bubble or droplet but is not general for more complex flow and requires additional solution of the linear system of equations. In current thesis, an improved approach that addresses both the numerical oscillation of pressure and the spurious interface velocity field is presented by featuring (i) continuous velocity and density fields within a thin interfacial region and (ii) temporal velocity correction steps to avoid unphysical pressure source term. Also I propose a general (iii) mass flux projection correction for improved mass flux conservation. The pressure and the temperature gradient jump condition are treated sharply. A series of one-dimensional and two-dimensional problems are solved to verify the performance of the new algorithm. Two-dimensional and cylindrical film boiling problems are also demonstrated and show good qualitative agreement with the experimental observations and heat transfer correlations. Finally, a study on Taylor bubble flow with heat transfer and phase change in a small vertical tube in axisymmetric coordinates is carried out using the new multiphase, phase change method.