Investigating the potential for using a simple water reaction turbine for power production from low head hydro resources

In this analysis the simple reaction water turbine known as Barker’s Mill is revisited. The major geometrical and operational parameters have been identified and, using principles of conservation of mass, momentum and energy, the governing equations have been developed for the ideal case of there being no frictional losses. The solutions of the resulting equations are offered in a non-dimensional form. It is shown that the maximum torque produced by the machine is developed when the turbine is stationary. At this point the net output power is zero. As the load torque is decreased the turbine rotates and power is produced. Furthermore, because of a centrifugal pumping effect, the mass flow rate of water through the turbine increases during acceleration. Further decrease in the load torque is accompanied by increases of speed, output power, water mass flow rate and efficiency. It is shown that when the load torque is reduced towards half the value of the torque at the stationary condition, water mass flow rate, rotational speed and output power tend towards infinity. Under this condition the efficiency of the machine approaches unity. The non-dimensional characteristics of the idealized turbine are used to investigate the general characteristics of the machine and to explore its application for production of power from water reservoirs with low heads. Theoretical analysis of a simple reaction turbine is presented including consideration of the fluid frictional losses for a practical situation. A practical turbine will never run away towards infinite speed and the maximum power and efficiency of such a turbine will depend on the fluid frictional losses. Here a new factor is defined, representing the overall fluid frictional losses within the turbine. Finally this paper presents briefly the experimental performance results for two simple reaction water turbine prototypes. The two turbine prototypes under investigation have rotor diameters Ø0.24 m and Ø0.12 m respectively. The two turbine models were tested under supply heads ranging from 1 m to 4 m. The simple reaction water turbine can operate under very low hydro-static head with high energy conversion efficiency. This type of turbine exhibits prominent self-pumping ability at high rotational speeds. Under low head to achieve high rotational speeds the turbine diameter should be very small and this limits the volumetric capacity and hence the power generation capacity of such a turbine. Consequently the practical applications of this turbine would be limited to micro-hydro power generation. The split pipe design of the reaction turbine tested is easy to manufacture and it has been shown to have overall energy conversion efficiency of approximately 50% even under low heads

Isolated Horizon, Killing Horizon and Event Horizon

We consider space-times which in addition to admitting an isolated horizon also admit Killing horizons with or without an event horizon. We show that an isolated horizon is a Killing horizon provided either (1) it admits a stationary neighbourhood or (2) it admits a neighbourhood with two independent, commuting Killing vectors. A Killing horizon is always an isolated horizon. For the case when an event horizon is definable, all conceivable relative locations of isolated horizon and event horizons are possible. Corresponding conditions are given.Comment: 14 pages, Latex, no figures. Some arguments tightened. To appear in Class. Quant. Gra

Genericness of inflation in isotropic loop quantum cosmology

Non-perturbative corrections from loop quantum cosmology (LQC) to the scalar matter sector is already known to imply inflation. We prove that the LQC modified scalar field generates exponential inflation in the small scale factor regime, for all positive definite potentials, independent of initial conditions and independent of ambiguity parameters. For positive semi-definite potentials it is always possible to choose, without fine tuning, a value of one of the ambiguity parameters such that exponential inflation results, provided zeros of the potential are approached at most as a power law in the scale factor. In conjunction with generic occurrence of bounce at small volumes, particle horizon is absent thus eliminating the horizon problem of the standard Big Bang model.Comment: 4 pages, revtex4, one figure. Only e-print archive numbers correctedi in the second version. Reference added in the 3rd version. Final version to appear in Phys. Rev. Lett. Explanations improve

On obtaining classical mechanics from quantum mechanics

Constructing a classical mechanical system associated with a given quantum mechanical one, entails construction of a classical phase space and a corresponding Hamiltonian function from the available quantum structures and a notion of coarser observations. The Hilbert space of any quantum mechanical system naturally has the structure of an infinite dimensional symplectic manifold (`quantum phase space'). There is also a systematic, quotienting procedure which imparts a bundle structure to the quantum phase space and extracts a classical phase space as the base space. This works straight forwardly when the Hilbert space carries weakly continuous representation of the Heisenberg group and recovers the linear classical phase space $\mathbb{R}^{\mathrm{2N}}$. We report on how the procedure also allows extraction of non-linear classical phase spaces and illustrate it for Hilbert spaces being finite dimensional (spin-j systems), infinite dimensional but separable (particle on a circle) and infinite dimensional but non-separable (Polymer quantization). To construct a corresponding classical dynamics, one needs to choose a suitable section and identify an effective Hamiltonian. The effective dynamics mirrors the quantum dynamics provided the section satisfies conditions of semiclassicality and tangentiality.Comment: revtex4, 24 pages, no figures. In the version 2 certain technical errors in section I-B are corrected, the part on WKB (and section II-B) is removed, discussion of dynamics and semiclassicality is extended and references are added. Accepted for publication on Classical and Quantum Gravit

A Symmetric Generalization of Linear B\"acklund Transformation associated with the Hirota Bilinear Difference Equation

The Hirota bilinear difference equation is generalized to discrete space of arbitrary dimension. Solutions to the nonlinear difference equations can be obtained via B\"acklund transformation of the corresponding linear problems.Comment: Latex, 12 pages, 1 figur

Vertex Operators for Deformed Virasoro Algebra

Vertex operators for the deformed Virasoro algebra are defined, their bosonic representation is constructed and difference equation for the simplest vertex operators is described.Comment: stylistic errors correcte

Reflectionless analytic difference operators I. algebraic framework

We introduce and study a class of analytic difference operators admitting reflectionless eigenfunctions. Our construction of the class is patterned after the Inverse Scattering Transform for the reflectionless self-adjoint Schr\"odinger and Jacobi operators corresponding to KdV and Toda lattice solitons

Classical Many-particle Clusters in Two Dimensions

We report on a study of a classical, finite system of confined particles in two dimensions with a two-body repulsive interaction. We first develop a simple analytical method to obtain equilibrium configurations and energies for few particles. When the confinement is harmonic, we prove that the first transition from a single shell occurs when the number of particles changes from five to six. The shell structure in the case of an arbitrary number of particles is shown to be independent of the strength of the interaction but dependent only on its functional form. It is also independent of the magnetic field strength when included. We further study the effect of the functional form of the confinement potential on the shell structure. Finally we report some interesting results when a three-body interaction is included, albeit in a particular model.Comment: Minor corrections, a few references added. To appear in J. Phys: Condensed Matte

Isospectral flow in Loop Algebras and Quasiperiodic Solutions of the Sine-Gordon Equation

The sine-Gordon equation is considered in the hamiltonian framework provided by the Adler-Kostant-Symes theorem. The phase space, a finite dimensional coadjoint orbit in the dual space \grg^* of a loop algebra \grg, is parametrized by a finite dimensional symplectic vector space $W$ embedded into \grg^* by a moment map. Real quasiperiodic solutions are computed in terms of theta functions using a Liouville generating function which generates a canonical transformation to linear coordinates on the Jacobi variety of a suitable hyperelliptic curve.Comment: 12 pg

A Construction of Solutions to Reflection Equations for Interaction-Round-a-Face Models

We present a procedure in which known solutions to reflection equations for interaction-round-a-face lattice models are used to construct new solutions. The procedure is particularly well-suited to models which have a known fusion hierarchy and which are based on graphs containing a node of valency $1$. Among such models are the Andrews-Baxter-Forrester models, for which we construct reflection equation solutions for fixed and free boundary conditions.Comment: 9 pages, LaTe