Design and optimization of turbo-expanders for organic rankine cycles

In a world focused on the need to produce energy for a growing population, while reducing atmospheric emissions of carbon dioxide, organic Rankine cycles represent a solution to fulfil this goal. This study focuses on the design and optimization of axial-flow turbines for organic Rankine cycles. From the turbine designer point of view, most of this fluids exhibit some peculiar characteristics, such as small enthalpy drop, low speed of sound, large expansion ratio. A computational model for the prediction of axial-flow turbine performance is developed and validated against experimental data. The model allows to calculate turbine performance within a range of accuracy of ±3%. The design procedure is coupled with an optimization process, performed using a genetic algorithm where the turbine total-to-static efficiency represents the objective function. The computational model is integrated in a wider analysis of thermodynamic cycle units, by providing the turbine optimal design. First, the calculation routine is applied in the context of the Draugen offshore platform, where three heat recovery systems are compared. The turbine performance is investigated for three competing bottoming cycles: organic Rankine cycle (operating cyclopentane), steam Rankine cycle and air bottoming cycle. Findings indicate the air turbine as the most efficient solution (total-to-static efficiency = 0.89), while the cyclopentane turbine results as the most flexible and compact technology (2.45 ton/MW and 0.63 m3/MW). Furthermore, the study shows that, for organic and steam Rankine cycles, the optimal design configurations for the expanders do not coincide with those of the thermodynamic cycles. This suggests the possibility to obtain a more accurate analysis by including the computational model in the simulations of the thermodynamic cycles. Afterwards, the performance analysis is carried out by comparing three organic fluids: cyclopentane, MDM and R245fa. Results suggest MDM as the most effective fluid from the turbine performance viewpoint (total-to-total efficiency = 0.89). On the other hand, cyclopentane guarantees a greater net power output of the organic Rankine cycle (P = 5.35 MW), while R245fa represents the most compact solution (1.63 ton/MW and 0.20 m3/MW). Finally, the influence of the composition of an isopentane/isobutane mixture on both the thermodynamic cycle performance and the expander isentropic efficiency is investigated. Findings show how the mixture composition affects the turbine efficiency and so the cycle performance. Moreover, the analysis demonstrates that the use of binary mixtures leads to an enhancement of the thermodynamic cycle performance.

Calculation of the eigenfunctions of the two-group neutron diffusion equation and application to modal decomposition of BWR instabilities

In this thesis, numerical methods aiming at determining the eigenfunctions, their adjoint and the corresponding eigenvalues of the two-group neutron diffusion equations representing any heterogeneous system are investigated. First, the classical power iteration method is modified so that the calculation of modes higher than the fundamental mode is possible. Thereafter, the Explicitly-Restarted Arnoldi method, belonging to the class of Krylov subspace methods, is touched upon. Although the modified power iteration method is a computationally-expensive algorithm, its main advantage is its robustness, i.e. the method always converges to the desired eigenfunctions without any need from the user to set up any parameter in the algorithm. On the other hand, the Arnoldi method, which requires some parameters to be defined by the user, is a very efficient method for calculating eigenfunctions of large sparse system of equations with a minimum computational effort. These methods are thereafter used for off-line analysis of the stability of Boiling Water Reactors. Since several oscillation modes are usually excited (global and regional oscillations) when unstable conditions are encountered, the characterization of the stability of the reactor using for instance the Decay Ratio as a stability indicator might be difficult if the contribution from each of the modes are not separated from each other. Such a modal decomposition is applied to a stability test performed at the Swedish Ringhals-1 unit in September 2002, after the use of the Arnoldi method for pre-calculating the different eigenmodes of the neutron flux throughout the reactor. The modal decomposition clearly demonstrates the excitation of both the global and regional oscillations. Furthermore, such oscillations are found to be intermittent with a time-varying phase shift between the first and second azimuthal modes.

Comparative study of the different models for the calculation of BLEVEs overpressure effects

The BLEVE, acronym for Boiling Liquid Expanding Vapour Explosion, is one of the most dangerous accidents that can occur in pressure vessels. It can be defined as an explosion resulting from the failure of a vessel containing a pressure liquefied gas stored at a temperature significantly above its boiling point at atmospheric pressure. This phenomenon frequently appears when a vessel is engulfed by a fire: the heat causes the internal pressure to raise and the mechanical proprieties of the wall to decrease, with the consequent rupture of the tank and the instantaneous release of its whole content. After the breakage, the vapour outflows and expands and the liquid phase starts boiling due to the pressure drop. The formation and propagation of a distructive schock wave may occur, together with the ejection of fragments, the generation of a fireball if the stored fluid is flammable and immediately ignited or the atmospheric dispersion of a toxic cloud if the fluid contained inside the vessel is toxic. Despite the presence of many studies on the BLEVE mechanism, the exact causes and conditions of its occurrence are still elusive. In order to better understand this phenomenon, in the present study first of all the concept and definition of BLEVE are investigated. A historical analysis of the major events that have occurred over the past 60 years is described. A research of the principal causes of this event, including the analysis of the substances most frequently involved, is presented too. Afterwards a description of the main effects of BLEVEs is reported, focusing especially on the overpressure. Though the major aim of the present thesis is to contribute, with a comparative analysis, to the validation of the main models present in the literature for the calculation and prediction of the overpressure caused by BLEVEs. In line with this purpose, after a short overview of the available approaches, their ability to reproduce the trend of the overpressure is investigated. The overpressure calculated with the different models is compared with values deriving from events happened in the past and ad-hoc experiments, focusing the attention especially on medium and large scale phenomena. The ability of the models to consider different filling levels of the reservoir and different substances is analyzed too. The results of these calculations are extensively discussed. Finally some conclusive remarks are reported.