A Complex Frequency Domain Model of Wind Turbine Structures

1995 ◽  
Vol 117 (4) ◽  
pp. 311-317 ◽  
Author(s):  
P. So̸rensen ◽  
G. C. Larsen ◽  
C. J. Christensen
Keyword(s):  
Wind Turbine ◽  
Frequency Domain ◽  
Time Domain ◽  
Domain Model ◽  
Horizontal Axis ◽  
Complex Frequency ◽  
Horizontal Axis Wind Turbine ◽  
The Time Domain

The present paper describes a frequency domain model of the structure of an operating horizontal axis wind turbine with three or more blades. The frequency domain model is implemented along with an analogous time domain model in a PC code. This PC code is used to verify the frequency domain model comparing loads on the structure calculated with the frequency domain model both to loads calculated with the time domain model and to measured loads.

Comparison of Time and Frequency Domain Simulations of an Offshore Floating Wind Turbine

2011 ◽  
Author(s):  
Maxime Philippe ◽  
Aure´lien Babarit ◽  
Pierre Ferrant
Keyword(s):  
Wind Turbine ◽  
Frequency Domain ◽  
Time Domain ◽  
Degrees Of Freedom ◽  
Domain Model ◽  
Floating Platform ◽  
Floating Wind Turbine ◽  
Non Linear ◽  
Offshore Floating Wind Turbine ◽  
The Time Domain

Time domain simulations of an offshore floating wind turbine have been performed. Hydrodynamic impulse responses of the floating platform are calculated with linear hydrodynamic simulation tool ACHIL3D. A user defined module for the wind turbine design code FAST has been developed to calculate hydrodynamic and mooring loads on the structure. Resolution of the movements of the system is done with FAST. Simulation results in time domain are compared with frequency domain results. In the frequency domain model, the whole system is linearized. In the time domain model, the wind turbine model is not linearized. A good agreement between time and frequency domain calculations is observed, even for the pitch motion. Furthermore we observe a non linearity in the response of sway, roll and yaw degrees of freedom around 0.3 rad.s-1. The effect of viscous damping on the movements of the floating wind turbine system has been studied with the time domain model, and a non linear hydrostatic and Froude-Krylov load model has been developed. Effects of these non linear terms are shown.

Analysis of Unsteady Flows Past Horizontal Axis Wind Turbine Airfoils Based on Harmonic Balance Compressible Navier-Stokes Equations With Low-Speed Preconditioning

2011 ◽  
Author(s):  
M. Sergio Campobasso ◽  
Mohammad H. Baba-Ahmadi
Keyword(s):  
Wind Turbine ◽  
Time Domain ◽  
Harmonic Balance ◽  
Stokes Equations ◽  
Unsteady Aerodynamics ◽  
Horizontal Axis ◽  
Navier Stokes ◽  
Horizontal Axis Wind Turbine ◽  
Low Speed ◽  
Computational Performance

This paper presents the numerical models underlying the implementation of a novel harmonic balance compressible Navier-Stokes solver with low-speed preconditioning for wind turbine unsteady aerodynamics. The numerical integration of the harmonic balance equations is based on a multigrid iteration, and, for the first time, a numerical instability associated with the use of such an explicit approach in this context is discussed and resolved. The harmonic balance solver with low-speed preconditioning is well suited for the analyses of several unsteady periodic low-speed flows, such as those encountered in horizontal axis wind turbines. The computational performance and the accuracy of the technology being developed are assessed by computing the flow field past two sections of a wind turbine blade in yawed wind with both the time- and frequency-domain solvers. Results highlight that the harmonic balance solver can compute these periodic flows more than 10 times faster than its time-domain counterpart, and with an accuracy comparable to that of the time-domain solver.

Simulating High Mode Vortex Induced Vibration of Riser in Linear Sheared Current Using an Empirical Time Domain Model

2020 ◽  
Author(s):  
Sang Woo Kim ◽  
Svein Sævik ◽  
Jie Wu
Keyword(s):  
Frequency Domain ◽  
Vortex Shedding ◽  
Time Domain ◽  
Structural Model ◽  
Cross Flow ◽  
Domain Model ◽  
Vortex Induced Vibrations ◽  
The One ◽  
The Time Domain ◽  
Empirical Coefficients

Abstract This paper addresses the performance evaluation of an empirical time domain Vortex Induced Vibrations (VIV) model which has been developed for several years at NTNU. Unlike the frequency domain which is the existing VIV analysis method, the time domain model introduces new vortex shedding force terms to the well known Morison equation. The extra load terms are based on the relative velocity, a synchronization model and additional empirical coefficients that describe the hydrodynamic forces due to cross-flow (CF) and In-line (IL) vortex shedding. These hydrodynamic coefficients have been tuned to fit experimental data and by considering the results from the one of existing frequency domain VIV programs, VIVANA, which is widely used for industrial design. The feature of the time domain model is that it enables to include the structural non-linearity, such as variable tension, and time-varying flow. The robustness of the new model’s features has been validated by comparing the test results in previous researches. However, the riser used in experiments has a relatively small length/diameter (L/D) ratio. It implies that there is a need for more validation to make it applicable to real riser design. In this study, the time domain VIV model is applied to perform correlation studies against the Hanøytangen experiment data for the case of linear sheared current at a large L/D ratio. The main comparison has been made with respect to the maximum fatigue damage and dominating frequency for each test condition. The results show the time domain model showed reasonable accuracy with respect to the experimental and VIVANA. The discrepancy with regard to experiment results needs to be further studied with a non-linear structural model.

scholarly journals Analysis of Unsteady Flows Past Horizontal Axis Wind Turbine Airfoils Based on Harmonic Balance Compressible Navier-Stokes Equations With Low-Speed Preconditioning

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
M. Sergio Campobasso ◽  
Mohammad H. Baba-Ahmadi
Keyword(s):  
Wind Turbine ◽  
Time Domain ◽  
Harmonic Balance ◽  
Stokes Equations ◽  
Unsteady Aerodynamics ◽  
Horizontal Axis ◽  
Navier Stokes ◽  
Horizontal Axis Wind Turbine ◽  
Low Speed ◽  
Computational Performance

This paper presents the numerical models underlying the implementation of a novel harmonic balance compressible Navier-Stokes solver with low-speed preconditioning for wind turbine unsteady aerodynamics. The numerical integration of the harmonic balance equations is based on a multigrid iteration, and, for the first time, a numerical instability associated with the use of such an explicit approach in this context is discussed and resolved. The harmonic balance solver with low-speed preconditioning is well suited for the analyses of several unsteady periodic low-speed flows, such as those encountered in horizontal axis wind turbines. The computational performance and the accuracy of the technology being developed are assessed by computing the flow field past two sections of a wind turbine blade in yawed wind with both the time-and frequency-domain solvers. Results highlight that the harmonic balance solver can compute these periodic flows more than 10 times faster than its time-domain counterpart, and with an accuracy comparable to that of the time-domain solver.

Simulating Riser VIV in Current and Waves Using an Empirical Time Domain Model

2017 ◽  
Author(s):  
Mats J. Thorsen ◽  
Svein Sævik
Keyword(s):  
Frequency Domain ◽  
Vortex Shedding ◽  
Time Domain ◽  
Theoretical Background ◽  
Domain Model ◽  
Wave Period ◽  
Time Variability ◽  
Analysis Tool ◽  
Load Model ◽  
The Time Domain

The theoretical background of an empirical model for time domain simulation of VIV is reviewed. This model allows the surrounding flow to be time varying, which is in contrast to the traditional frequency domain tools. The hydrodynamic load model consists of Morison’s equation plus an additional term representing the oscillating effect of vortex shedding. The magnitude of the vortex shedding force is given by a dimensionless coefficient, and this force is assumed to act perpendicular to the relative velocity between the cylinder and the fluid. The time variability of the vortex shedding force is described by a synchronization model, which captures how the instantaneous frequency reacts to cylinder motion. The parameters in the time domain load model are calibrated against a commonly used frequency domain VIV analysis tool, VIVANA. To do this, a finite element model of a vertical tensioned riser is established, and the structure is exposed to a linearly sheared flow. Key results such as cross-flow displacements along the riser, frequency content, r.m.s. of bending stresses and mean in-line displacements are compared, and it is shown that the frequency and time domain methods are close to equivalent in this simple case with stationary flow. Finally, the time domain model is utilized to study VIV of a riser subjected to regular waves. The characteristics of wave induced VIV are discussed in light of the simulation results. It is seen that VIV is excited in the zone close to the surface, and the energy is transported downwards as traveling waves. The vibrations typically build up as the horizontal water particle velocity is high, and die out as the velocity decreases. The effect of varying the wave amplitude and period is investigated, and it is found that the dominating frequency, mode and r.m.s. stresses increase together with the wave height. The effect of the wave period is however more complicated. For example, reducing the wave period increases the dominating mode but decreases the displacements. Hence the stress may increase or decrease, depending on which of these effects are strongest.

scholarly journals Transient Response Estimation of an Offshore Wind Turbine Support System

Energies ◽  
2019 ◽  
Vol 12 (5) ◽  
pp. 891 ◽  
Author(s):  
Fushun Liu ◽  
Xingguo Li ◽  
Zhe Tian ◽  
Jianhua Zhang ◽  
Bin Wang
Keyword(s):  
Wind Turbine ◽  
Frequency Domain ◽  
Transient Response ◽  
Time Domain ◽  
Initial Conditions ◽  
Offshore Wind ◽  
Offshore Wind Turbines ◽  
Domain Method ◽  
The Time Domain ◽  
External Loads

To obtain reliable estimations of the dynamic responses of high-rising marine structures such as offshore wind turbines with obvious nonzero initial conditions, traditional frequency-domain methods cannot be employed because they provide only steady-state results. A novel frequency-domain transient response estimation method for offshore wind turbines is presented in this paper. This method builds upon a recent, significant theoretical development, which found that expressions of external loads in the frequency domain can be obtained by discretizing their eigenvalues and corresponding complex coefficients rather than directly by discrete Fourier transform (DFT) analysis, which makes it possible to deal with nonzero conditions in the frequency domain. One engineering advantage of this approach is its computational efficiency, as the motion equations of the system can be solved in the frequency domain. In order to demonstrate this approach, a case of a monopile-supported wind turbine with nonzero initial conditions was investigated. The numerical results indicate that the approach matches well with the time-domain method, except for a small, earlier portion of the estimated responses. A second case study of a sophisticated, jacket support wind turbine, involving practical issues such as complex external loads and computation efficiency, is also discussed, and comparisons of the results with the time-domain method and traditional frequency-domain method using the commercial software ANSYS are included here.

Turbulent Unsteady Flow Analysis of Horizontal Axis Wind Turbine Airfoil Aerodynamics Based on the Harmonic Balance Reynolds-Averaged Navier-Stokes Equations

2014 ◽  
Author(s):  
M. Sergio Campobasso ◽  
Fabio Gigante ◽  
Jernej Drofelnik
Keyword(s):  
Wind Turbine ◽  
Time Domain ◽  
Harmonic Balance ◽  
Stokes Equations ◽  
Transport Model ◽  
Flow Analysis ◽  
Horizontal Axis ◽  
Navier Stokes ◽  
Horizontal Axis Wind Turbine ◽  
Reynolds Averaged Navier Stokes

Several horizontal axis wind turbine unsteady flows, such as that associated with the yawed wind regime, are predominantly periodic. Harmonic balance Reynolds-averaged Navier-Stokes solvers can be used to accurately analyze such flows substantially faster than what their time-domain counterparts can do. The paper presents the mathematical and numerical features of a new turbulent harmonic balance Navier-Stokes solver using Menter’s shear stress transport model for the turbulence closure. The effectiveness of the developed technology is demonstrated by using two-dimensional harmonic balance flow simulations to determine the periodic aerodynamic loads acting on a blade section of a 164 m-diameter wind turbine rotor in yawed wind. Presented results highlight that the turbulent harmonic balance solver can compute the sectional hysteresis force cycles more than 10 times faster than its time-domain counterpart, and with an accuracy comparable to that of the time-domain solver.

Float-Off Operation of a Land-Built COT on Dual Transportation Barges: Time- vs. Frequency-Domain Analysis

2005 ◽  
Author(s):  
Chan K. Yang ◽  
D. H. Lee ◽  
M. H. Kim ◽  
B. N. Park ◽  
Y. T. Yang ◽  
...  
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Domain Analysis ◽  
Frequency Domain Analysis ◽  
Domain Model ◽  
Mooring Line ◽  
Load Prediction ◽  
Floating Bodies ◽  
Realistic Situation ◽  
The Time Domain

In this paper, the float-off operation of a land-built crude oil tank (COT) loaded out and towed on launching dual-submersible barges is numerically simulated by a time-domain vessel-mooring-riser coupled dynamic analysis program with multiple floating bodies. The study is particularly focused on the maximum load prediction on connectors and the minimum gap prediction between barges and the COT. In case of simpler modeling, the time-domain simulation results are compared with frequency-domain results. Then, the time-domain model is run for more realistic situation with hawsers and mooring line. In hydrodynamic analysis, the interactions among the 3 floating bodies are fully taken into consideration. In the frequency-domain analysis, the connectors between barges are modeled by equivalent translational and rotational springs, the stiffness of which is estimated using Euler’s beam theory. In order to assess the possible occurrence of contact between COT and barges, the relative motions between barges and the COT at several points of interest were investigated.

scholarly journals A Frequency Domain Method for the Generation of Partially Coherent Normal Stationary Time Domain Signals

1993 ◽  
Vol 1 (1) ◽  
pp. 45-53 ◽  
Author(s):  
David O. Smallwood ◽  
Thomas L. Paez
Keyword(s):  
Density Matrix ◽  
Spectral Density ◽  
Frequency Domain ◽  
Time Domain ◽  
Frequency Domain Method ◽  
Complex Frequency ◽  
Arbitrary Length ◽  
Partially Coherent ◽  
Spectral Density Matrix ◽  
The Time Domain

A procedure for generating vectors of time domain signals that are partially coherent in a prescribed manner is described. The procedure starts with the spectral density matrix,[Gxx(f)], that relates pairs of elements of the vector random process{X(t)},−∞<t<∞. The spectral density matrix is decomposed into the form[Gxx(f)]=[U(f)][S(f)][U(f)]'where[U(f)]is a matrix of complex frequency response functions, and[S(f)]is a diagonal matrix of real functions that can vary with frequency. The factors of the spectral density matrix,[U(f)]and[S(f)], are then used to generate a frame of random data in the frequency domain. The data is transformed into the time domain using an inverse FFT to generate a frame of data in the time domain. Successive frames of data are then windowed, overlapped, and added to form a vector of normal stationary sampled time histories,{X(t)}, of arbitrary length.

scholarly journals Simulation and time-frequency analysis of the longitudinal train dynamics coupled with a nonlinear friction draft gear

2020 ◽  
Vol 9 (1) ◽  
pp. 124-144
Author(s):  
Caglar Uyulan ◽  
Ersen Arslan
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Controller Design ◽  
Response Characteristic ◽  
Domain Model ◽  
Step Response ◽  
Time Frequency ◽  
Draft Gear ◽  
Train Dynamics ◽  
The Time Domain

AbstractTrain safety and operational efficiency can be improved by investigating the dynamics of the train under varying conditions. Longitudinal train dynamics (LTD) simulations performed for such purposes, usually by utilising a nonlinear time-domain model. This paper covers two modes of LTD results corresponding to the time domain and frequency domain analysis. Time-domain solutions are essential to evaluate the full response used for parameter optimisation and controller design studies while frequency domain solutions can provide significant but straightforward clues regarding system dynamics. An advanced draft gear model, which works under a four-stage process is constructed considering all structural components, geometric relationships, friction modelling and dynamic characteristics such as hysteresis, stiffening, state transition, locked unloading, softening. Then, this model is parametrically reduced and implemented into an LTD simulation. The simulation in the time domain is conducted assuming a locomotive connected with a nine wagon via “ode3” fixed-step solver. The transfer function among the first wagon acceleration (output) and the locomotive force (input) estimated through system identification methodology. Then, the identification results interpreted by investigating step-response characteristic and best response giving parameter set is selected. Next, the modal and spectral analysis performed to reveal the behaviour of the in-train forces and the effects of vibration. This paper discusses a reliable methodology for the longitudinal dynamic analysis of the multi-bodied train in time and frequency domain and clarifies in-train vibration behaviour under the existence of sophisticated draft gear.

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