The extended Betz–Lanchester limit

A proposal for an extended formulation of the power coefficient of a wind turbine is presented. This new formulation is a generalization of the Betz–Lanchester expression for the power coefficient as function of the axial deceleration of the wind speed provoked by the wind turbine in operation. The extended power coefficient takes into account the benefits of the power produced and the cost associated to the production of this energy. By the simple model proposed is evidenced that the purely energetic optimum operation condition giving rise to the Betz–Lanchester limit (maximum energy produced) does not coincide with the global optimum operational condition (maximum benefit generated) if cost of energy and degradation of the wind turbine during operation is considered. The new extended power coefficient is a general parameter useful to define global optimum operation conditions for wind turbines, considering not only the energy production but also the maintenance cost and the economic cost associated to the life reduction of the machine.

Source terms for calculations of vaporizing and burning fuel sprays with non-unity Lewis numbers in gases with temperature-dependent thermal conductivities

Liquid-fueled burners are used in a number of propulsion devices ranging from internal combustion engines to gas turbines. The structure of spray flames is quite complex and involves a wide range of time and spatial scales in both premixed and non-premixed modes (Williams 1965; Luo et al. 2011). A number of spray-combustion regimes can be observed experimentally in canonical scenarios of practical relevance such as counterflow diffusion flames (Li 1997), as sketched in figure 1, and for which different microscalemodelling strategies are needed. In this study, source terms for the conservation equations are calculated for heating, vaporizing and burning sprays in the single-droplet combustion regime. The present analysis provides extended formulation for source terms, which include non-unity Lewis numbers and variable thermal conductivities.