Related papers: The complementary Betz Theory
Betz's law, purportedly, says an ideal wind harvester cannot extract more than 16/27 ($\sim$59\%) of the wind energy. As the law's derivation relies on momentum and energy conservation with incompressible flow and not the physical mechanism…
The Betz limit expresses the maximum proportion of the kinetic energy flux incident on an energy conversion device that can be extracted from an unbounded flow. The derivation of the Betz limit requires an assumption of steady flow through…
The Betz law places a fundamental limit on the amount of power that can be extracted by a wind turbine for a fixed area wind column. This manuscript extends the original Betz Law derivation to a "multi-turbine" approach.
A new theoretical approach is proposed to predict a practical upper limit to the efficiency of a very large wind farm. The new theory suggests that the efficiency of ideal turbines in an ideal very large wind farm depends primarily on a…
A novel method for calculating power output from wind turbines using Newtonian mechanics is proposed. This contrasts with current methods based on interception rates by airfoils of kinetic energy to estimate power output, governed by the…
Despite substantial growth in wind energy technology in recent decades, aerodynamic modeling of wind turbines relies on momentum models derived in the late 19th and early 20th centuries, which are well-known to break down under flow regimes…
Using the fluctuation theorem supplemented with geometric arguments, we derive universal features of the (long-time) efficiency fluctuations for thermal and isothermal machines operating under steady or periodic driving, close or far from…
The Carnot engine sets an upper limit to the efficiency of a practical heat engine. An arbitrary irreversible engine is sometimes believed to behave closely as the Curzon-Ahlborn engine. Efficiency of the latter is obtained commonly by…
An extended theoretical approach is proposed to predict the average power of wind turbines in a large finite-size wind farm. The approach is based on the two-scale momentum theory proposed recently for the modelling of ideal very large wind…
A wind turbine works with the principle of extracting energy from the wind to generate electricity. The power generated is directly proportional to the wind speed available. There are two major types of wind turbine design namely the…
We present a new outlook on the climate system thermodynamics, studying some of its macroscopic properties in terms of the 1st and 2nd laws of thermodynamics. We review and clarify the notion of efficiency of the climate system by…
The central result about fast rotating-flow structures is the Taylor-Proudman theorem (TPT) which connects various aspects of the dynamics. Taylor's geometrical proof of TPT is reproduced and extended substantially, with Lie's theory for…
Classical actuator disk theory, developed more than a century ago, provides an idealised description of turbine rotor performance. It treats a rotor as an infinitesimally-thin permeable disk and applies the governing flow equations over a…
We present direct numerical simulations of a novel concept for a micro-scale wind turbine, inspired in the mechanics of the auto-rotation of winged seeds. In this nature-inspired concept the turbine blades have two degrees of freedom: the…
A new analytical model for the generation of axisymmetric tornado-type vortices has been developed. A solution to the nonlinear equation for the stream function in an unstable stratified atmosphere is obtained and analyzed within the…
A new theoretical method is presented for future multi-scale aerodynamic optimisation of very large wind farms. The new method combines a recent two-scale coupled momentum analysis of ideal wind turbine arrays with the classical…
It has been asserted previously by the author that optimal control theory can be a valuable framework for theoretical studies about the shape that a wind instrument should have in order to satisfy some optimization criterion, inside a…
It is shown that the upper limit on the fraction of power that can be extracted from an airstream approaching a wind turbine is about 78% rather than the historical value of 59%. This higher limit is based on the assumption that the wind…
We consider the Lorenz equations, a system of three dimensional ordinary differential equations modeling atmospheric convection. These equations are chaotic and hard to study even numerically, and so a simpler "geometric model" has been…
Constructor theory seeks to express all fundamental scientific theories in terms of a dichotomy between possible and impossible physical transformations - those that can be caused to happen and those that cannot. This is a departure from…