A numerical method for three-dimensional vortical structure of spiral vortex in wind turbine with two-dimensional velocity data at plural azimuthal angles

2016 ◽  
Author(s):  
Katsuyuki Nakayama ◽  
Lucas Dias Mizushima ◽  
Junsuke Murata ◽  
Takao Maeda
Keyword(s):  
Wind Turbine ◽  
Numerical Method ◽  
Vortical Structure ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Velocity Data ◽  
Spiral Vortex

scholarly journals A Fast Two-Dimensional Numerical Method for the Wake Simulation of a Vertical Axis Wind Turbine

Energies ◽  
2020 ◽  
Vol 14 (1) ◽  
pp. 49
Author(s):  
Zheng Yuan ◽  
Jin Jiang ◽  
Jun Zang ◽  
Qihu Sheng ◽  
Ke Sun ◽  
...  
Keyword(s):  
Velocity Distribution ◽  
Numerical Method ◽  
Three Dimensional ◽  
Particle Method ◽  
Vortex Method ◽  
Vertical Axis ◽  
Two Dimensional ◽  
Vertical Axis Wind Turbine ◽  
Wake Effect ◽  
Array Design

In the array design of the vertical axis wind turbines (VAWT), the wake effect of the upstream VAWT on the downstream VAWT needs to be considered. In order to simulate the velocity distribution of a VAWT wake rapidly, a new two-dimensional numerical method is proposed, which can make the array design easier and faster. In this new approach, the finite vortex method and vortex particle method are combined to simulate the generation and evolution of the vortex, respectively, the fast multipole method (FMM) is used to accelerate the calculation. Based on a characteristic of the VAWT wake, that is, the velocity distribution can be fitted into a power-law function, a new correction model is introduced to correct the three-dimensional effect of the VAWT wake. Finally, the simulation results can be approximated to the published experimental results in the first-order. As a new numerical method to simulate the complex VAWT wake, this paper proves the feasibility of the method and makes a preliminary validation. This method is not used to simulate the complex three-dimensional turbulent evolution but to simulate the velocity distribution quickly and relatively accurately, which meets the requirement for rapid simulation in the preliminary array design.

LIMIT CYCLES OF A DOUBLE OSCILLATOR EXCITED BY DRY FRICTION

2011 ◽  
Vol 21 (10) ◽  
pp. 3043-3046 ◽  
Author(s):  
SERGEY STEPANOV
Keyword(s):  
Fixed Points ◽  
Numerical Method ◽  
Limit Cycles ◽  
Dry Friction ◽  
Coulomb Friction ◽  
Three Dimensional ◽  
Slip Mode ◽  
Two Dimensional ◽  
Parametric Investigation ◽  
Friction Laws

A two-mass oscillator with one mass lying on the driving belt with dry Coulomb friction is considered. A numerical method for finding all limit cycles and their parametric investigation, based on the analysis of fixed points of a two-dimensional map, is suggested. As successive points for the map we chose points of friction transferred from stick mode to slip mode. These transfers are defined by two equalities and yield a two-dimensional map, in contrast to three-dimensional maps that we can construct for regularized continuous dry friction laws.

Prediction of Ice Accretion on Wind Turbine with Numerical Method

2012 ◽  
Vol 512-515 ◽  
pp. 754-757
Author(s):  
Xian Yi ◽  
Kai Chun Wang ◽  
Hong Lin Ma
Keyword(s):  
Wind Turbine ◽  
Numerical Method ◽  
Collection Efficiency ◽  
Three Dimensional ◽  
Horizontal Axis ◽  
Ice Accretion ◽  
Horizontal Axis Wind Turbine ◽  
Blade Tip ◽  
Computer Codes ◽  
Multiple Reference

A three dimensional numerical method and its computer codes, which are suitable to predict the process of horizontal axis wind turbine icing, are presented. The method is composed of the Multiple Reference Frame (MRF) method to calculate flowfield of air, an Eulerian method to compute collection efficiency and a three dimensional icing model companying with an iterative arithmetic for solving the model. Ice accretion on a 1.5 MW horizontal axis wind turbine is then computed with the numerical method, and characteristics of droplet collection efficiency and ice shape/type are obtained. The results show that ice on the hub and blade root is slight and it can be neglected comparing with ice near blade tip. From blade tip to root, ice becomes thinner and glaze ice may changes into rime ice.

Variable pitch control for vertical-axis wind turbines

2018 ◽  
Vol 42 (2) ◽  
pp. 128-135 ◽  
Author(s):  
S Horb ◽  
R Fuchs ◽  
A Immas ◽  
F Silvert ◽  
P Deglaire
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Wind Turbine ◽  
Three Dimensional ◽  
Vertical Axis ◽  
Two Dimensional ◽  
Vertical Axis Wind Turbine ◽  
Horizontal Axis Wind Turbine ◽  
Variable Pitch ◽  
Pitch Control

NENUPHAR aims at developing the next generation of large-scale floating offshore vertical-axis wind turbine. To challenge the horizontal-axis wind turbine, the variable blade pitch control appears to be a promising solution. This article focuses on blade pitch law optimization and resulting power and thrust gain depending on the operational conditions. The aerodynamics resulting from the implementation of a variable blade pitch control are studied through numerical simulations, either with a three-dimensional vortex code or with two-dimensional Navier-stokes simulations (two-dimensional computational fluid dynamics). Results showed that the three-dimensional vortex code used as quasi-two-dimensional succeeded to give aerodynamic loads in very good agreement with two-dimensional computational fluid dynamics simulation results. The three-dimensional-vortex code was then used in three-dimensional configuration, highlighting that the variable pitch can enhance the vertical-axis wind turbine power coefficient ( Cp) by more than 15% in maximum power point tracking mode and decrease it by more than 75% in power limitation mode while keeping the thrust below its rated value.

A numerical method based on three-dimensional Legendre wavelet method for two-dimensional time-fractional diffusion equation

2021 ◽  
pp. 2150008
Author(s):  
Sarkout Abdi ◽  
Aram Azizi ◽  
Mahmoud Shafiee ◽  
Jamshid Saeidian
Keyword(s):  
Numerical Method ◽  
Operational Matrix ◽  
Three Dimensional ◽  
Fractional Diffusion ◽  
Finite Domain ◽  
Two Dimensional ◽  
Linear System Of Equations ◽  
Fractional Diffusion Equations ◽  
Spatial Dimensions ◽  
Legendre Wavelet Method

In this paper, an efficient numerical method is proposed to handle two-dimensional fractional diffusion equations on a finite domain. The proposed method combines the product of Legendre wavelet bases for two spatial dimensions and a time direction. The operational matrix of the proposed method is obtained. Tikhonov regularization is employed to stabilize the system in cases where the final linear system of equations is large. The convergence analysis of the method is studied and some numerical examples are presented to investigate the efficiency and accuracy of the method.

Validation of Numerical Analysis to Estimate Airfoil Aerodynamic Characteristics at Low Reynolds Number Region

2015 ◽  
Author(s):  
Donghwi Lee ◽  
Taku Nonomura ◽  
Akira Oyama ◽  
Kozo Fujii
Keyword(s):  
Reynolds Number ◽  
Numerical Method ◽  
Low Reynolds Number ◽  
Lift Coefficient ◽  
Three Dimensional ◽  
Aerodynamic Characteristics ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Eddy Simulation ◽  
Low Reynolds

In this study, two-dimensional laminar simulation (2-D Lam), two-dimensional Reynolds Averaged Navier-Stokes simulation with the Spalart-Allmaras turbulence model (2-D RANS(SA)), and implicit three-dimensional large-eddy simulation (3-D LES) are performed for NACA0012, NACA0006, and Ishii airfoils at Rec = 3.0 × 104. The relation between a predictability of airfoil aerodynamic characteristics and a dependence of airfoil geometry shape of each numerical method is evaluated at the low Reynolds number. Although little discrepancy is observed for the lift coefficient predictability, significant differences are presented in terms of the separation and reattachment points predictability depending on the numerical methods. The 2-D Lam simulation can predict the lift coefficients as well as the separation and reattachment points qualitatively as similar to the 3-D LES results except for the high angle of attack which is accompanied by the massive separation. The 2-D RANS(SA), the weak nonlinearity and stall phenomena for the lift coefficients are observed. A good predictability of the separation point are shown, however, it cannot be estimated the reattachment points due to the trend to predict widely for the separation region. The predictabilities of each numerical method appear regardless of the airfoil shapes.

Automated Composite Fabric Layup for Wind Turbine Blades

2017 ◽  
Vol 139 (6) ◽  
Author(s):  
Siqi Zhu ◽  
Corey J. Magnussen ◽  
Emily L. Judd ◽  
Matthew C. Frank ◽  
Frank E. Peters
Keyword(s):  
Wind Turbine ◽  
Plane Deformation ◽  
Turbine Blades ◽  
Three Dimensional ◽  
3D Models ◽  
New Method ◽  
Two Dimensional ◽  
Wind Turbine Blades ◽  
Out Of Plane ◽  
Fiberglass Fabric

This work presents an automated fabric layup solution based on a new method to deform fiberglass fabric, referred to as shifting, for the layup of noncrimp fabric (NCF) plies. The shifting method is intended for fabric with tows only in 0 deg (warp) and 90 deg (weft) directions, where the fabric is sequentially constrained and then rotated through a deformation angle to approximate curvature. Shifting is conducted in a two-dimensional (2D) plane, making the process easy to control and automate, but can be applied for fabric placement in three-dimensional (3D) models, either directly or after a ply kitting process and then manually placed. Preliminary tests have been conducted to evaluate the physical plausibility of the shifting method. Layup tests show that shifting can deposit fabric accurately and repeatedly while avoiding out-of-plane deformation.

A Numerical Method to Solve the Static Problem of a Catenary Riser

2004 ◽  
Author(s):  
Lauro Massao Yamada da Silveira ◽  
Clo´vis de Arruda Martins
Keyword(s):  
Differential Equation ◽  
Boundary Layer ◽  
Numerical Method ◽  
Order Term ◽  
Three Dimensional ◽  
Static Problem ◽  
Computer Code ◽  
Bending Stiffness ◽  
Two Dimensional ◽  
Cable Model

The static configuration of a catenary riser can be obtained, with a good approximation, by a perfectly flexible cable model. However, such a model cannot deal with all the boundary conditions, as for an ideal cable there is no continuity of curvature at the touchdown point, at the top and at the points where there is change in the submerged weight. At the touchdown region, for instance, the cable model overestimates the maximum curvature. For real risers, the bending stiffness effect is relevant only at small boundary layers around the points where the cable model cannot represent well the curvature continuity. This represents a big problem in the numerical integration of the differential equation of the riser, as the leading order term is very small. One approach that can be adopted is to use firstly a perfect cable model and correct later the results with analytical expressions obtained from a boundary layer method. For a two-dimensional formulation it was already shown that this approach is very good. For a three-dimensional formulation, however, such expressions are very difficult to derive and the problem must be solved numerically. This work presents a numerical method to solve the differential equation of a catenary riser, including the bending stiffness. The results obtained are compared to analytical boundary layer solutions, for a two-dimensional case, and to a full nonlinear well-known commercial computer code.

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