Limits of the Turbine Efficiency for Free Fluid Flow

2001 ◽  
Vol 123 (4) ◽  
pp. 311-317 ◽  
Author(s):  
Alexander N. Gorban’ ◽  
Alexander M. Gorlov ◽  
Valentin M. Silantyev
Keyword(s):  
Wind Power ◽  
Three Dimensional ◽  
Cross Flow ◽  
Free Water ◽  
Accurate Estimate ◽  
Maximum Efficiency ◽  
Free Fluid ◽  
Two Dimensional ◽  
Turbine Efficiency ◽  
Tidal Streams

An accurate estimate of the theoretical power limit of turbines in free fluid flows is important because of growing interest in the development of wind power and zero-head water power resources. The latter includes the huge kinetic energy of ocean currents, tidal streams, and rivers without dams. Knowledge of turbine efficiency limits helps to optimize design of hydro and wind power farms. An explicitly solvable new mathematical model for estimating the maximum efficiency of turbines in a free (nonducted) fluid is presented. This result can be used for hydropower turbines where construction of dams is impossible (in oceans) or undesirable (in rivers), as well as for wind power farms. The model deals with a finite two-dimensional, partially penetrable plate in an incompressible fluid. It is nearly ideal for two-dimensional propellers and less suitable for three-dimensional cross-flow Darrieus and helical turbines. The most interesting finding of our analysis is that the maximum efficiency of the plane propeller is about 30 percent for free fluids. This is in a sharp contrast to the 60 percent given by the Betz limit, commonly used now for decades. It is shown that the Betz overestimate results from neglecting the curvature of the fluid streams. We also show that the three-dimensional helical turbine is more efficient than the two-dimensional propeller, at least in water applications. Moreover, well-documented tests have shown that the helical turbine has an efficiency of 35 percent, making it preferable for use in free water currents.

Numerical Simulation of Clocking Effect on Wake Transportation and Interaction in a 1.5-Stage Axial Turbine

2010 ◽  
Author(s):  
Wei Li ◽  
Hua Ouyang ◽  
Zhao-hui Du
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Leading Edge ◽  
Navier Stokes ◽  
Maximum Efficiency ◽  
Suction Surface ◽  
Navier Stokes Equations ◽  
Pressure Surface ◽  
Turbine Efficiency ◽  
Small Influence

To give insight into the clocking effect and its influence on the wake transportation and its interaction, the unsteady three-dimensional flow through a 1.5-stage axial low pressure turbine is simulated numerically using a density-correction based, Reynolds-Averaged Navier-Stokes equations commercial CFD code. The 2nd stator clocking is applied over ten equal tangential positions. The results show that the harmonic blade number ratio is an important factor affecting the clocking effect. The clocking effect has a very small influence on the turbine efficiency in this investigation. The efficiency difference between the maximum and minimum configuration is nearly 0.1%. The maximum efficiency can be achieved when the 1st stator wake enters the 2nd stator passage near blade suction surface and its adjacent wake passes through the 2nd stator passage close to blade pressure surface. The minimum efficiency appears if the 1st stator wake impinges upon the leading edge of the 2nd stator and its adjacent wake of the 1st stator passed through the mid-channel in the 2nd stator.

Modelling the calmed region behind a spot

2005 ◽  
Vol 363 (1830) ◽  
pp. 1069-1078 ◽  
Author(s):  
S.N Brown ◽  
F.T Smith
Keyword(s):  
Boundary Layer ◽  
Theoretical Model ◽  
Slip Velocity ◽  
Three Dimensional ◽  
Cross Flow ◽  
Two Dimensional ◽  
Turbulent Spot ◽  
Mean Flow ◽  
Flow Surface ◽  
Dimensional Boundary

A theoretical model of the laminar ‘calmed region’ following a three-dimensional turbulent spot within a transitioning two-dimensional boundary layer is formulated and discussed. The flow is taken to be inviscid, and the perturbation mean flow surface streamlines calculated represent disturbances to the basic slip velocity. Available experimental evidence shows a fuller, more stable, streamwise profile in a considerable region trailing the spot, with cross-flow ‘inwash’ towards the line of symmetry. Present results are in qualitative agreement with this evidence.

On the Theory of the Wells Turbine

1984 ◽  
Vol 106 (3) ◽  
pp. 628-633 ◽  
Author(s):  
L. M. C. Gato ◽  
A. F. de O. Falca˜o
Keyword(s):  
Three Dimensional ◽  
Axial Flow ◽  
Aerodynamic Performance ◽  
Two Dimensional ◽  
Wells Turbine ◽  
Actuator Disk ◽  
Turbine Efficiency ◽  
Axial Velocity Profile ◽  
Profile Losses ◽  
Blade Shape

A theoretical investigation is presented concerning the aerodynamic performance of the Wells turbine, a self-rectifying, axial-flow turbine suitable for energy extraction from a reciprocating air flow. A two-dimensional analysis is developed, and expressions, based on potential flow, are derived for the blade shape maximizing the turbine efficiency. Three-dimensional effects and profile losses are then accounted for by means of an actuator disk theory, which shows that large radial distortions of axial velocity profile can occur, depending on blade shape, with important implications on the extent of the stall-free conditions.

An Experimental Investigation of Cross-Flow Turbine Efficiency

1994 ◽  
Vol 116 (3) ◽  
pp. 545-550 ◽  
Author(s):  
Venkappayya R. Desai ◽  
Nadim M. Aziz
Keyword(s):  
Experimental Investigation ◽  
Angle Of Attack ◽  
Cross Flow ◽  
Water Entry ◽  
Diameter Ratio ◽  
Geometric Parameters ◽  
Maximum Efficiency ◽  
Outer Diameter ◽  
Turbine Efficiency ◽  
The Cross

An experimental investigation was conducted to study the effect of some geometric parameters on the efficiency of the cross-flow turbine. Turbine models were constructed with three different numbers of blades, three different angles of water entry to the runner, and three different inner-to-outer diameter ratios. Nozzles were also constructed for the experiments to match the three different angles of water entry to the runner. A total of 27 runners were tested with the three nozzles. The results of the experiments clearly indicated that efficiency increased with increase in the number of blades. Moreover, it was determined that an increase in the angle of attack beyond 24 deg does not improve the maximum turbine efficiency. In addition, as a result of these experiments, it was determined that for a 24 deg angle of attack 0.68 was the most efficient inner-to-outer diameter ratio, whereas for higher angles of attack the maximum efficiency decreases with an increase in the diameter ratio from 0.60 to 0.75.

Performance Improvement of Cross-Flow Turbine with a Cylindrical Cavity and Guide Wall

2021 ◽  
Author(s):  
Naoto Ogawa ◽  
Mirei Goto ◽  
Shouichiro Iio ◽  
Takaya Kitahora ◽  
Young-Do Choi ◽  
...  
Keyword(s):  
Performance Improvement ◽  
Performance Test ◽  
Guide Vane ◽  
Cross Flow ◽  
Maximum Efficiency ◽  
Small Hydropower ◽  
Turbine Efficiency ◽  
Partial Load ◽  
Guide Wall ◽  
The Cross

Abstract The cross-flow turbine has been utilizing the development of small hydropower less than about 500kW in the world. The turbine cost is lower than the other turbines because of its smaller assembled parts and more straightforward structures. However, the maximum efficiency of the cross-flow turbine is lower than that of traditional turbines. Improving the turbine efficiency without increasing manufacturing costs is the best way to develop small hydropower in the future. This study is aiming to improve the turbine efficiency at the design point and partial load. The runner's outflow angle varies with turbine speed and guide vane opening in the typical cross-flow turbine. The tangential velocity component remains in the outflow in these conditions; thus, change the outflow direction along the runner's radial direction is helpful for performance improvement. The authors experimentally change the desirable outflow angle by attaching a cavity and a guide wall at the outside casing tip. The turbine performance test was conducted for various turbine speeds and guide vane opening. Next, flow visualization around the runner was performed. As a result, the effect of the cavity and the guide wall can be revealed. The outlet flow fields are different by attaching the cavity and the guide wall, especially between the partial and optimum load conditions.

scholarly journals Poly[[diaquabis[μ4-5-nitroisophthalato-κ4O1:O1:O3:O3′]bis[μ3-pyridine-4-carboxylato-κ3O:O′:N]tricobalt(II)] tetrahydrate]

2012 ◽  
Vol 68 (4) ◽  
pp. m451-m452
Author(s):  
Xia Yin ◽  
Jun Fan ◽  
Jingling Xin ◽  
Shengrun Zheng ◽  
Weiguang Zhang
Keyword(s):  
Hydrogen Bonds ◽  
Water Molecule ◽  
Three Dimensional ◽  
Free Water ◽  
Water Molecules ◽  
Two Dimensional ◽  
Lattice Water ◽  
Free Water Molecule ◽  
Carboxylate Groups ◽  
Coordinated Water

The title compound, {[Co3(C6H4NO2)2(C8H3NO6)2(H2O)2]·4H2O}n, exhibits a two-dimensional layer-like structure in which the CoIIions exhibit two kinds of coordination geometries. One nearly octahedral CoIIion with crystallographic inversion symmetry is coordinated to six carboxylate O atoms from four bridging 5-nitroisophthalate (NIPH) ligands and two isonicotinate (IN) anions, while the other type of CoIIion binds with one N atom and one carboxylate O atom from two IN anions, two carboxylate O atoms from two different NIPH anions and one ligated water molecule, displaying a distorted square-pyramidal coordination geometry. Three adjacent CoIIions are bridged by six carboxylate groups from four NIPH ligands and two IN anions to form a linear trinuclear secondary building unit (SBU). Every trinuclear SBU is linked to its nearest neighbours in theabplane, resulting in a two-dimensional layer-like structure perpendicular to thecaxis. Along thea-axis direction neighbouring molecules are connected through carboxylate and pyridyl units of the IN anions, along thebaxis through carboxylate groups of the NIPH ligands. The H atoms of one free water molecule are disordered in the crystal in a 1:1 ratio. Typical O—H...O hydrogen bonds are observed in the lattice, which include the following contacts: (a) between coordinated water molecules and carboxylate O atoms of the NIPH anions, (b) between lattice water molecules and carboxylate O atoms of the NIPH anions, and (c) between coordinated and lattice water molecules. These intermolecular hydrogen bonds connect the two-dimensional layers to form a three-dimensional supramolecular structure.

Experimental Study on Performance of Darrieus-Type Open Hydroturbine With Inlet Nozzle in Low Downstream Water Level Conditions

2011 ◽  
Author(s):  
Koutarou Hirowatari ◽  
Kai Shimokawa ◽  
Shunsuke Iwamoto ◽  
Kusuo Okuma ◽  
Satoshi Watanabe ◽  
...  
Keyword(s):  
Water Level ◽  
River Flow ◽  
Draft Tube ◽  
Cross Flow ◽  
Vertical Axis ◽  
Maximum Efficiency ◽  
Stable Operation ◽  
Lower Efficiency ◽  
Flow Type ◽  
Turbine Efficiency

A Darrieus-type open hydro turbine with inlet nozzle has been proposed for utilization of extra-low head hydropower though a ducted type is in general used, consisting of an intake, runner section and draft tube. The open turbine means the simplified one, which has no runner casing and no draft tube. By installing inlet nozzle for the open turbine, the turbine efficiency is never deteriorated in comparison with the ducted one. The role of inlet nozzle is to increase generated torque with higher efficiency on the upstream path of the Darrieus blade passing and to decrease the torque with lower efficiency on the other path by removing the runner casing as the Darrieus turbine is cross flow type. In the present paper, the more simplified open turbine, consisting of only the inlet nozzle and the quarter covered upper casing to support the runner shaft, is experimentally examined. It is found that the depth of water level, covering or uncovering the runner in downstream pond, which might be changed by flow rate in practical use due to river-flow type turbine, influences on the turbine performance. When the depth of water level is kept deeper than the runner height of vertical axis turbine, the performance is almost the same as that of the case with whole covered upper casing. With decreasing the water level shallower than the runner height, the generated power and the efficiency become deteriorated due to making the wavy motion of the water surface at first. Then the stable operation at the maximum efficiency point in normal condition cannot be obtained. The cause on the mechanism of performance deterioration is considered with visualization of fluid behavior around Darrieus blades.

Non-stationary cross-flow vortices in three-dimensional boundary-layer flows

1988 ◽  
Vol 417 (1852) ◽  
pp. 179-212 ◽  
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Cross Flow ◽  
Neutral Stability ◽  
Two Dimensional ◽  
Boundary Layer Flows ◽  
Rotating Disc ◽  
Dimensional Boundary ◽  
Flow Vortex ◽  
The Waves

The upper-branch neutral stability of three-dimensional disturbances imposed on a three-dimensional boundary-layer profile is considered and in particular we investigate non-stationary cross-flow vortices. The wave speed is taken to be small initially and with a disturbance structure analogous to that occurring in two-dimensional boundary-layer stability the linear and nonlinear eigenrelations are derived for profiles with more than one critical layer. For the flow due to a rotating disc we show that linear viscous neutral modes exist for all wave angles between 10.6° and 39.6°. As the extremes of this range are approached the flow structure evolves to another, either the viscous mode of Hall ( Proc. R. Soc. Lond . A 406, 93(1986)) or the non-stationary inviscid modes considered by Stuart in Gregory et al . ( Phil. Trans. R. Soc. Lond . A 248, 155 (1955)). In the former case, corresponding to wave angles of 39.6°, the waves become almost stationary and in the latter case, with wave angles of 10.6° the waves are travelling much faster with a disturbance structure based on the Rayleigh scalings. The analysis is extended to include O (1) wavespeeds and we show that as the wavespeed of the cross-flow vortex approaches the tree-stream value, the corresponding disturbance amplitude increases, the growth here being slower than that for two-dimensional boundary layers.

High Resolution Microscopy of Multi-Layered Biological Crystals

1982 ◽  
Vol 40 ◽  
pp. 80-83
Author(s):  
H.A. Cohen ◽  
T.W. Jeng ◽  
W. Chiu
Keyword(s):  
High Resolution ◽  
Low Dose ◽  
Three Dimensional ◽  
Data Interpretation ◽  
Two Dimensional ◽  
Biological Objects ◽  
Density Maps ◽  
Density Map ◽  
Complex Crystal ◽  
High Resolution Microscopy

This tutorial will discuss the methodology of low dose electron diffraction and imaging of crystalline biological objects, the problems of data interpretation for two-dimensional projected density maps of glucose embedded protein crystals, the factors to be considered in combining tilt data from three-dimensional crystals, and finally, the prospects of achieving a high resolution three-dimensional density map of a biological crystal. This methodology will be illustrated using two proteins under investigation in our laboratory, the T4 DNA helix destabilizing protein gp32*I and the crotoxin complex crystal.

Instrumentation For Quantitative Microscopy

1977 ◽  
Vol 35 ◽  
pp. 206-209
Author(s):  
B. Ralph ◽  
A.R. Jones
Keyword(s):  
Volume Fraction ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Automatic Data ◽  
Phase Volume Fraction ◽  
Statistical Confidence ◽  
Resultant Data ◽  
Automatic Data Collection ◽  
Third Dimension ◽  
Evolution Of Microstructure

In all fields of microscopy there is an increasing interest in the quantification of microstructure. This interest may stem from a desire to establish quality control parameters or may have a more fundamental requirement involving the derivation of parameters which partially or completely define the three dimensional nature of the microstructure. This latter categorey of study may arise from an interest in the evolution of microstructure or from a desire to generate detailed property/microstructure relationships. In the more fundamental studies some convolution of two-dimensional data into the third dimension (stereological analysis) will be necessary.In some cases the two-dimensional data may be acquired relatively easily without recourse to automatic data collection and further, it may prove possible to perform the data reduction and analysis relatively easily. In such cases the only recourse to machines may well be in establishing the statistical confidence of the resultant data. Such relatively straightforward studies tend to result from acquiring data on the whole assemblage of features making up the microstructure. In this field data mode, when parameters such as phase volume fraction, mean size etc. are sought, the main case for resorting to automation is in order to perform repetitive analyses since each analysis is relatively easily performed.

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