Related papers: The complementary Betz Theory
When an elastic object is dragged through a viscous fluid tangent to a rigid boundary, it experiences a lift force perpendicular to its direction of motion. An analogous lift mechanism occurs when a rigid symmetric object translates…
Vogt's theorem, concerning boundary angles of a convex arc with monotonic curvature (spiral arc), is taken as a starting point to establish basic properties of spirals. The theorem is expanded by removing requirements of convexity and…
The Curzon-Ahlborn efficiency has long served as the definite upper bound for the thermal efficiency at maximum output power, and has thus shaped the development of finite-time thermodynamics. In this paper, we repeal the ruling consensus…
The blade element momentum (BEM) theory introduced by Lock et al. and formulated in its modern form by Glauert provides a framework to model the aerodynamic interaction between a turbine and a fluid flow. This theory is used either to…
In ZM theory the direction of time has a non-zero projection onto space and this projection corresponds to the local velocity relative to the observer. Classical trajectories can be obtained by following the local direction of time. The…
In this paper, we review a few known facts on the coordinate Bethe ansatz. We present a detailed construction of the Bethe ansatz vector $\psi$ and energy $\Lambda$, which satisfy $V \psi = \Lambda \psi$, where $V$ is the the transfer…
We introduce a rotation invariant short distance cut-off in the theory of an ideal fluid in three space dimensions, by requiring momenta to take values in a sphere. This leads to an algebra of functions in position space is non-commutative.…
The concepts of weighted reciprocal of temperature and weighted thermal flux are proposed for a heat engine operating between two heat baths and outputting mechanical work. With the aid of these two concepts, the generalized thermodynamic…
In this paper, we revive a special, less-common, variational principle in analytical mechanics (Hertz' principle of least curvature) to develop a novel variational analogue of Euler's equations for the dynamics of an ideal fluid. The new…
When a real fluid is expelled quickly from a tube, it forms a jet separated from the surrounding fluid by a thin, turbulent layer. On the other hand, when the same fluid is sucked into the tube, it comes in from all directions, forming a…
If the work per cycle of a quantum heat engine is averaged over an appropriate prior distribution for an external parameter $a$, the work becomes optimal at Curzon-Ahlborn efficiency. More general priors of the form $\Pi(a) \propto…
As the most fundamental empirical law, Zipf's law has been studied from many aspects. But its meaning is still an open problem. Some models have been constructed to explain Zipf's law. In the letter, a new concept named nonsymmetric entropy…
In this work we develop a new classical perturbation theory for water which incorporates the transition to tetrahedral symmetry in both the dispersion and hydrogen bonding contributions to the free energy. This transition is calculated…
An analytical wind turbine wake model is proposed to predict the wind velocity distribution for all distances downwind of a wind turbine, including the near-wake. This wake model augments the Jensen model and subsequent derivations thereof,…
Noether's theorem is widely regarded as one of the most elegant results in theoretical physics. The article presents two simple examples that can be used to demonstrate the basic idea behind Noether's theorem, by deriving a relation between…
Airborne wind energy systems aim to generate renewable energy by means of the aerodynamic lift produced by a wing tethered to the ground and controlled to fly crosswind paths. The problem of maximizing the average power developed by the…
This paper describes a particularly didactic and transparent derivation of basic properties of the Lorentz group. The generators for rotations and boosts along an arbitrary direction, as well as their commutation relations, are written as…
This chapter provides an introduction to the modeling and control of power generation from wind turbine systems. In modeling, the focus is on the electrical components: electrical machine (e.g. permanent-magnet synchronous generators),…
Thermodynamics is usually developed starting from entropy and the maximum entropy principle. We investigate here to what extent one can replace entropy with relative entropy which has several advantages, for example in the context of local…
Cross-flow, or vertical-axis, turbines are a promising technology for capturing kinetic energy in wind or flowing water and their inherently unsteady fluid mechanics present unique opportunities for control optimization of individual rotors…