IntroductionAs more and more complex and sophisticated hardware and software tools are available, complex problems described by consistent mathematical models are successfully approached by numerical simulation: modelling and simulation are present at almost each level in education, research, and production. Numerical "experiments" have predictive value, and complement physical experiments. They are unique in providing valuable insights in Gedankenexperiment-class (thought experiment) investigations. This chapter presents numerical simulation results related to a structural optimization problem that arises in systems with gradients and fluxes. Although the discussion concerns the optimal electrical design of photovoltaic systems, it may be extended to a larger class of applications in electrical and mechanical engineering: diffusion and conduction problems. The first concern in simulation is the proper formulation of the physical model of the system under investigation that should lead to consistent mathematical models, or well-posed problems (in Hadamard sense) (Morega, 1998). When available, analytic solutions -even for simplified mathematical models -may outline useful insights into the physics of the processes, and may also help deciding the numerical approach to the solution to more realistic models for the systems under investigation. Homemade and third party simulation tools are equally useful as long as they are available and provide for accurate solutions. Recent technological progresses brought into attention the Spherical PhotoVoltaic Cells (SPVC), known for their capability of capturing light three-dimensionally not only from direct sunlight but also as diffuse light scattered by the clouds or reflected by the buildings. This chapter reports the structural optimization of several types of spherical photovoltaic cells (SPVC) by applying the constructal principle to the minimization of their electrical series resistance. A numerically assisted step-by-step construction of optimal, minimum series resistance SPVC ensembles, from the smallest cell (called elemental) to the largest assembly that relies on the minimization of the maximum voltage drop subject to volume (material) constraints is presented. In this completely deterministic approach the SPVC ensembles shapes and structures are the outcome of the optimization of a volume to point access problem imposed as a design request. Specific to the constructal theory, the optimal shape (geometry) and structure of both natural and engineered systems are morphed out of their functionality and resources, and of the constraints to which they are subject.
www.intechopen.comRecent Advances in Modelling and Simulation 318
Shape and structure out of a multiphysics principleThe development of the constructal principle (Bejan, 2000) relies on the analysis of natural dynamic systems with fluxes and gradients (e.g., temperature, pressure, electric potential, chemical potential, etc.) that, internally, are outside thermodynamic equilibrium. A second important aspect is...