In this paper, we develop a mathematical model of blood circulation in the liver lobule. We aim to find the pressure and flux distributions within a liver lobule. We also investigate the effects of changes in pressure that occur following a resection of part of the liver, which often leads to high pressure in the portal vein. The liver can be divided into functional units called lobules. Each lobule has a hexagonal cross-section, and we assume that its longitudinal extent is large compared with its width. We consider an infinite lattice of identical lobules and study the two-dimensional flow in the hexagonal cross-sections. We model the sinusoidal space as a porous medium, with blood entering from the portal tracts (located at each of the vertices of the cross-section of the lobule) and exiting via the centrilobular vein (located in the center of the cross-section). We first develop and solve an idealized mathematical model, treating the porous medium as rigid and isotropic and blood as a Newtonian fluid. The pressure drop across the lobule and the flux of blood through the lobule are proportional to one another. In spite of its simplicity, the model gives insight into the real pressure and velocity distribution in the lobule. We then consider three modifications of the model that are designed to make it more realistic. In the first modification, we account for the fact that the sinusoids tend to be preferentially aligned in the direction of the centrilobular vein by considering an anisotropic porous medium. In the second, we account more accurately for the true behavior of the blood by using a shear-thinning model. We show that both these modifications have a small quantitative effect on the behavior but no qualitative effect. The motivation for the final modification is to understand what happens either after a partial resection of the liver or after an implantation of a liver of small size. In these cases, the pressure is observed to rise significantly, which could cause deformation of the tissue. We show that including the effects of tissue compliance in the model means that the total blood flow increases more than linearly as the pressure rises.
The number of fully-rated converter wind turbine generators equipped with a Permanent Magnet Synchronous Generator (PMSG) has sensibly increased in the late years. The optimal utilization and controllability of a PMSG is achieved using a Pulse Width Modulation-Voltage Source Converter (PWM-VSC) that allows interfacing the electric machine with the distribution network by means of a DC link. The generator/Machine-Side Converter (MSC) controls the operation of the PMSG. This paper proposes a methodology to assess the feasibility of the steady-state working points of PMSG based wind turbines without running a set of time-consuming time-domain simulations. Three control objectives for MSC are usually considered: stator voltage control, unitary power factor control and torque control. The aim of the present paper is that of providing an analytical methodology to check the feasibility of the steady-state working points dictated by different control strategies of the MSC starting from the specific operational constraints provided by the wind power plants characteristics. The effectiveness of the proposed methodology is demonstrated comparing numerical results of a MATLAB ® implementation against dedicated time-domain simulations. Simulations results demonstrated the appropriate performance of the proposed methodology characterized by the almost negligible computational time required. Index terms: Capability chart, electric machines, power system modeling and wind power generation.
Abstract:The growing development of hybrid electric vehicles (HEVs) has seen the spread of architectures with transmission based on planetary gear train, realized thanks to two electric machines. This architecture, by continuously regulating the transmission ratio, allows the internal combustion engine (ICE) to work in optimal conditions. On the one hand, the average ICE efficiency is increased thanks to better loading situations, while, on the other hand, electrical losses are introduced due to the power circulation between the two electrical machines mentioned above. The aim of this study is then to accurately evaluate electrical losses and the average ICE efficiency in various operating conditions and over different road missions. The models used in this study are presented for both the Continuously Variable Transmission (CVT) architecture and the Discontinuously Variable Transmission (DVT) architecture. In addition, efficiency maps of the main components are shown. Finally, the simulation results are presented to point out strengths and weaknesses of the CVT architecture.
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