Wendt, Fabian F. (National Wind Technology Center, National Renewable Energy Laboratory) | Robertson, Amy N. (National Wind Technology Center, National Renewable Energy Laboratory) | Jonkman, Jason M. (National Wind Technology Center, National Renewable Energy Laboratory)
During the Offshore Code Comparison Collaboration, Continued, with Correlation (OC5) project, which focused on the validation of numerical methods through comparison against tank test data, the authors created a numerical FAST model of the 1:50-scale DeepCwind semisubmersible system that was tested at the Maritime Research Institute Netherlands ocean basin in 2013. The OC5 project revealed a general underprediction of loads and motions by the participating numerical models. This paper discusses several model calibration studies that were conducted to identify potential model parameter adjustments that help to improve the agreement between the numerical simulations and the experimental test data. These calibration studies cover wind-field-specific parameters (coherence, turbulence), and hydrodynamic and aerodynamic modeling approaches, as well as rotor model (blade-pitch and blade-mass imbalances) and tower model (structural tower damping coefficient) adjustments. These calibration studies were conducted based on relatively simple calibration load cases (wave only/wind only). The agreement between the final FAST model and experimental measurements is then assessed based on more complex combined wind and wave validation cases. The analysis presented in this paper does not claim to be an exhaustive parameter identification study but is aimed at describing the qualitative impact of different model parameters on the system response. This work should help to provide guidance for future systematic parameter identification and uncertainty quantification efforts.
Chen, Ling (University of Chinese Academy of Sciences, Beijing) | Zhou, Jifu (Chinese Academy of Sciences, Beijing) | Wang, Xu (Chinese Academy of Sciences, Beijing) | Wang, Zhan (Chinese Academy of Sciences, Beijing)
A new type of bottom-fixed structure, the so-called high-rise pile cap foundation, has been proposed and used to support offshore wind turbines in the Donghai Bridge Wind Farm, China. Engineers are unaware of the wave load mechanisms for this new structure. Using the Navier–Stokes equations and volume of fluid technique, a fully nonlinear numerical wave tank is established to investigate free surface wave loads and moments for the new structure. The interaction between the cap and piles are discussed in detail. In the case of fully nonlinear waves, the maximum horizontal wave load on all the piles with the cap can increase by 30% compared with those without the cap, and the maximum horizontal wave load on a single pile is nearly doubled. The horizontal wave load on the cap with the piles can increase by about 15%, while the vertical wave load decreases slightly. The conventional Morison formula and diffraction theory generally underestimate the wave loads on the piles and the cap as well.
Tsunamis cause tremendous damages and loss of life at many coastal areas around the world. The main purpose of this study is to investigate propagation of tsunami in order to validate tsunami run-up and inundation and assess ocean environment at shallow water region. We used Smoothed Particle Hydrodynamics based on Shallow Water Equation (SWE-SPH) to reproduce the previous tsunami event. The results were compared with water elevations at the survey locations. Moreover, we applied to compute wave propagation and velocity filed around offshore structures such as a wind farm.
Tsunamis cause tremendous damages and loss of life at many coastal areas around the world. Tsunamis with destruction at spreading areas should be accurately predicted to establish evacuation routes and to find out safety locations at inundation areas. Tsunami inundation process at flooding area and tsunami behaviors become a key factor to protect coastal areas and to reduce number of victims. In particular, it is difficult to estimate wave deformation and its propagation at shallow water region caused by shoring due to bottom topography and coastline.
In general, wave propagation at shallow water region can be represented by Sallow Water Equations (SWE) and its computation is lower cost comparing with that of full-3D model. In Grid Based Method, to obtain reliable results dynamically, adaptive structured (Liang, 2009; George, 2010) or unstructured grid systems (LeVeque, 2007) were employed. However, the Grid Based Method needs to generate grids at complicated domains, and then it is difficult to compute water elevation and wave propagation at focused areas. On the other hand, in Particle Based Method, Rodriguez-Paz and Bonet (2005) introduced a shallow water formulation based on SPH method (Monaghan (1994)) with variable smoothing length, which treats the continuum as a Hamiltonian system of particles. And also, de Leffe et al. (2010) employed Riemann approach proposed by Vila (1999) to realize more robustness for computations. Moreover, R. Vacondio et al. (2012a) applied open boundaries conditions using SWE-SPH for shallow water flow to simulate flood inundations due to tsunami attacking.
The actuator line method (ALM) introduces an actuator-line to represent a wind turbine by adding a body force term in the momentum equation. As ALM simplifies the process of mesh refinement and moving mesh, it can get much higher efficiency for wind turbine wake simulation. In this paper, ALM is implemented to investigate the NREL 5-MW wind turbine wakes by using OpenFOAM. The results of the power and the thrust of NREL 5-MW wind turbine can get a good agreement with the results of benchmarkes. According to the analysis of wind turbine wakes in details, ALM can predict wind turbine wakes accurately.
The effect of wind turbine wakes always makes the whole wind farm production turning decline (Gaumond et al, 2013). Generally speaking, it is significant for the wind farm control strategies, but the wind turbine wakes are so complicated and difficult to simulate. At present, the Blade-Element\ Momentum (BEM) theory (Betz, 1920; Glauert, 1935) and computational fluid dynamics (CFD) method are frequently adopted to the load simulations (Tran et al, 2012) and performance calculations (Sanderse et al, 2011) of wind turbines. The BEM model is simple and fast, but it needs to introduce some corrections to get higher accurate results, such as dynamic stall, tip loss, added mass of rotors, et al. However, CFD method is very expansive for CPU time and can get highly accuracate results without these corrections. Even so, many researches concentrated on wind turbine wake simulation with CFD (Liu YC et al, 2017).
Then, ALM was introduced by Shen and Sørensen (2002). It adds a body force term in a three dimensional Navier-Stokes solver, body forces are distributed radially along the blades. The body force is the load on the blade calculated by tabulated airfoil data and local angles of attack. With this concept, the dynamics of the wake and the tip vortices can be studied fastly and completely. Troldborg (2008) pointed out that ALM can be used to reproduce the vortex accurately and only use simple structured grids. In addition, it is effective to calculate the loading on the blade (Shen et al, 2012). However, most models by using ALM do not consider elastic blades and the motion of each element is rigid body rotation. Hang Meng et al (2018) combined the ALM and a finite difference structural model, and named it as elastic actuator line (EAL). Nevertheless, that is the first step to propose the concept of EAL and it still exists some limitations which need to do further study.
Due to large variability of the offshore environment, the load analysis of an offshore wind turbine is a complex task. It is normally performed in the time domain, by running stochastic simulations. This is usually very time consuming due to the necessity of having long time series in order to obtain results with little bias, or to sample events with a low probability of happening. An alternative is to perform the analysis in the frequency domain. The drawback is that this method is only valid for linear systems, which makes it rather inaccurate for fatigue damage results. Also, there are well-known inaccuracies when estimating fatigue damage from a response spectrum. This paper investigates a novel approach based on probability evolution methods, which can obtain accurate results for linear, as well as non-linear systems. The method is not very well known, and a drawback is that it can be numerically challenging, especially for high-dimensional problems. The benefits of the method are that it evaluates all possible states of the wind turbine without generating a long signal in the time domain. We show how this can be used to efficiently evaluate fatigue damage.
This paper presents a probability density evolution method in the time domain for a simplified wind turbine model with one mode. The cell mapping approach discretizes the two-dimensional phase space (Hsu, 1987). The method is evaluated using both deterministic and random loads and compared to time domain simulations. Different sizes in the discretization of the mesh and in the area of state space covered are investigated, to determine when the method converges towards the final solution. The algorithm has been programmed in Python with the Numba Just-In-Time compiler to help speed up the calculations. How to implement a simple stochastic load model by the cell-mapping method is discussed. The result is a joint response probability density that contains information about the extrema of the structure motion, and how often these occur. This allows for calculating Markov transition probabilities between minima and maxima from the response density, which then makes it possible to estimate fatigue damage. Determining the response probability density is done by many short time-domain integrations, instead of one or more long simulations. The main novelty introduced and demonstrated here is that as soon as one has calculated the cell mapping, one can easily obtain the peak transition matrix and use this to obtain fatigue damage estimates.
In this paper we show how a new idea for how to calculate the derivatives of extrapolated 50-year return values, used in extreme load safety criteria, can be used to estimate the uncertainty in these return values resulting from uncertainty in the simulations and in the load extrapolation procedure itself. The method yields uncertainty estimates with a high degree of accuracy. Additionally, to highlight one of the subtler uncertainties involved in this setting, we also make a small study of how changing the block size used in the extraction of maxima from load time series affects the 50-year return value.
Finding ways to reduce the cost of offshore wind turbine support structures is one of the main objectives of current research on this topic. One of the main challenges involved in cost reduction of structures is the balance between measures that reduce the resistance to loading (like e.g. lighter designs) and the safety requirements. A primary reason for the difficulty posed by this balance is the large amount of uncertainties in the analysis. On the load side there are a lot of uncertainties coming from various sources such as measurements, local variations within windfarms and simplified modeling of the environment. In the structure there are uncertainties such as those related to the production of components and to simplified structural models. The usual solution to this issue is to make designs that are very conservative, scaling preliminary designs as dictated by analysis by large safety factors. Hence, increased knowledge about uncertainty could potentially enable designers to be less conservative and make more economical choices.
Extreme load, or Ultimate Limit State (ULS), criteria present a particular challenge for uncertainty analysis due to the way these are evaluated. Chiefly, this is because of the requirement (Det Norske Veritas, 2014) that extreme loads should be the 50-year return values calculated from the loads obtained by simulations. While this is a standard procedure in the design of wind turbines, it is not trivial. It entails fitting the short term maximum loads to extreme value distributions and then extrapolating from these distributions to the 50-year return value. A considerable amount of work has gone into the study of various aspects of the load extrapolation procedure for wind turbines. A comparison of three different approaches, including a process model, was made by Cheng (2002). A study of the effect of turbulence level on the predicted extreme load was performed by Moriarty et al. (2002). A report discussing, among other things, several aspects of extreme load extrapolation, including selection of threshold values, the statistical uncertainty of the fits, details of both short term and long term statistics and possibilities for model simplification was made by Moriarty et al. (2004). Further studies and discussion of various standard and alternative methods for short term fitting and long term extrapolation methods, as well as details of uncertainty, can be found in, e.g., Saranyasoontorn and Manuel (2006), Ragan and Manuel (2007), Agarwal and Manuel (2007), Fogle et al. (2008), Toft and Sørensen (2009), Agarwal and Manuel (2010) and Dimitrov (2016).
In most of free vortex wake models (FVWMs), the induced velocity is computed by Biot-Savart law. But the details of velocity calculation are still incomplete in their self-integrated loss of adjacent segment's influence. Curved filament correction has already been studied to recover the FVWM in helicopter problems. In this work, an extended FVWM with the correction is developed intended to improve aerodynamic predictions of wind turbines. Numerical simulations are performed on ring vortices and practical modeling of flow state of both fixed and floating wind turbines. It has been shown that the newly-designed technique may generate higher fidelity.
Among multiple modeling methods in aerodynamics of wind turbines, vortex lattice method (VLM) with straight line segmentation have been commonly used. The trailing filaments generated by the blades are assumed to convect freely with material lines of concentrated vorticity in potential flow. Such force free motion is governed by the vortex transportation equation. The governing equation is a partial differential equation which can be solved by various numerical approximation with high-order accuracy in both time and space domain.
It has been studied that for the straight-line segmentation, the approximation of induced velocity is relatively accurate with respect to corresponding theoretical result with the exclusion of self-induced velocity. It means that the collocation points lie in nowhere in vicinity to the discrete vortex segments (Gupta and Leishman, 2005). When it comes to the case that collocation points are extremely close to the discrete segments, the self-induced velocities tend to be infinite. The solutions for this singularity can be eliminated by “cutoff’ process (Bhagwat and Leishman, 2001) and vortex core models (Leishman,2006). These solutions are initially introduced by core regularization to eliminate singularity of the collocation points or simply fulfill the physical mechanism. However, techniques with these processes are incomplete because they fail to add up the total induced velocity.
Evaluation of the fatigue limit state (FLS) for offshore wind turbine foundations is normally based on deterministic design approaches, where partial safety factors are used to account for load and resistance uncertainties. In this paper, the propagation of uncertainties related to structural, environmental and fatigue damage model parameters is evaluated by performing Monte Carlo fatigue simulations of a reference Gravity Based Foundation (GBF) supporting a 5 MW offshore wind turbine. A linear model for concrete fatigue damage is formulated based on the S-N approach, and fatigue structural reliability is evaluated using the FORM technique. Results indicate that the uncertainty related to wind turbulence intensity has the highest influence on fatigue loads during power production. Adopting a probabilistic damage model for concrete also increases the fatigue damage standard deviation by 60% and 85% for structures in water and in air, respectively. In addition, the assumption on Miner’s rule uncertainty has a large influence on the structural reliability. A reduction of this uncertainty from Δcov=0.40 to Δcov=0.30 could increase the annual reliability index by 22%.
In the detailed design of offshore wind turbine (OWT) foundations, the structure has to be evaluated for fatigue to ensure that the structure withstands environmental loads throughout its intended design life (typically 25 years). Current design standards are based on deterministic approaches, where partial safety factors are used to account for uncertainties in loads and resistance models. This approach, however, can either be over conservative or unsafe. It has been shown that target reliability level for OWTs can be lowered compared to other fixed offshore structures due to lower risks and consequences related to failure (Marquez-Dominguez & Sorensen, 2012). Moreover, uncertainties related to environmental inputs, which affect reliability assessments, are site-specific. To achieve more robust and cost-effective solutions, relevant sources of uncertainties have to be accounted for when performing reliability analyses and calibration of safety factors.
Aggarwal, Ankit (Norwegian University of Science and Technology) | Chella, Mayilvahanan Alagan (Norwegian University of Science and Technology) | Bihs, Hans (Norwegian University of Science and Technology) | Pákzodi, Csaba (SINTEF Ocean) | Berthelsen, Petter Andreas (SINTEF Ocean) | Arntsen, Øivind A. (Norwegian University of Science and Technology)
Offshore structures are exposed to irregular sea states consisting of breaking and nonbreaking waves. They perpetually experience extreme wave loads after installation in the open ocean. Thus, the study of steep waves is an important factor in the design of offshore structures. In the present study, a numerical investigation is performed to study steep irregular waves in deep water. The irregular waves are generated using the Torsethaugen spectrum, which is a double-peaked spectrum defined for a locally fully developed sea and which takes both the sea and swell waves into account. Thus, the generated waves can be very steep. The numerical investigation of such steep waves is quite challenging because of their high wave steepness and wave–wave interaction. The present investigation is performed using the open-source computational fluid dynamics (CFD) model. The wave generation and propagation of steep irregular waves in the numerical model are validated by comparing the numerical wave spectrum with the experimental input wave spectrum. The numerical results are in good agreement with experimental results. The changes in the spectral wave density during the wave propagation are studied. Further, the double-hinged flap wavemaker is also tested and validated by comparing the numerical and experimental free-surface elevations over time. The time and the frequency domain analysis is also performed to investigate the changes in the free-surface horizontal velocity. Complex flow features during the wave propagation are well captured by the CFD model.
Offshore wind turbines are exposed to extreme irregular sea states. Extreme waves exert extreme hydrodynamic loads on substructures. Thus, the study of such irregular waves is very important in the design of offshore wind turbines. Several experimental and field investigations have been performed in the past to study extreme waves. Such spectra exhibit two peaks, because of the presence of swell and wind waves. Ochi and Hubble (1976) carried out a statistical analysis of 800 measured wave spectra in the North Atlantic Ocean. They derived a six-parameter double-peaked spectrum that is composed of two parts: the first primarily includes the low-frequency wave components and the second contains the high-frequency wave components. Each part of the wave spectrum is represented by three parameters. The six-parameter spectrum represents almost all stages of the sea conditions associated with a storm. Guedes Soares and Nolasco (1992) analyzed wave data from the North Atlantic and the North Sea and proposed a four-parameter double-peaked spectrum. This double-peaked spectrum was formulated by superimposing individual spectral components of the JONSWAP-type single-peaked spectrum.
Dragt, R. C. (Netherlands Institute for Applied Scientific Research (TNO)) | Allaix, D. L. (Netherlands Institute for Applied Scientific Research (TNO), Eindhoven University of Technology) | Maljaars, J. (Keppel Verolme BV) | Tuitman, J. T. (Keppel Verolme BV) | Salman, Y. | Otheguy, M.
Fatigue is one of the main design drivers for offshore wind substructures. Using Fracture Mechanics methods, load sequence effects such as crack growth retardation due to large load peaks can be included in the fatigue damage estimation. Due to the sequence dependency, a method is required that represents the sequences of loads in the design or maintenance procedures.
This paper presents a methodology to deal with this challenge. First, a framework is presented for coupling between the design load cases and the Fracture Mechanics methods, resulting into the requirements for loads and load sequences. Second, a 2-stage Markov Chain Monte Carlo model is presented which is able to create realistic loading sequences based on measurement data. The method is elaborated for fluctuating wind loads.
One of the main design drivers for Offshore Wind Turbine (OWT) substructures is fatigue. Current standards (e.g.; DNVGL, 2016; IEC, 2009) specify a wide range of operational conditions, such as normal operation, parked condition and fault conditions, and the environmental conditions (combinations of wind, wave and current conditions) that are to be included in the fatigue assessment. Every single combination is used as input for a time domain simulation, which results in a stress history at given (hot)spots in the structure. Prescribed Stress Concentration Factors (SCF) are used to account for structural details. Standards prescribe that a 1-hour period is simulated (by either simulating 6 times a 10-minute realization or a 1-hour realization) per load combination. The total analysis requires several thousands of individual 1-hour long time-domain simulations, each typically containing several thousands of stress cycles.
The stress history is used to estimate the fatigue damage in a structural detail during its intended lifetime. Fatigue damage is referred to as the utilization of the total fatigue capacity of a structural detail expressed in terms of life. For every stress history, the number of occurring cycles for each stress range are counted using the Rainflow Counting method. The appropriate SN-curve is selected from the design standard and used to determine the number of cycles to failure for each stress range. The damage contribution per range of stress cycles is defined as the ratio between the occurring number of cycles and the number of cycles per stress range. The damage contributions of all stress cycles are summed in agreement with the damage accumulation rule of Palmgren-Miner in order to arrive at the total fatigue damage. The result is multiplied by a Design Fatigue Factor (DFF) in order to arrive at a certain probability of failure, which amongst others accounts for difficulties encountered during inspection or repair of a specific detail and for the risk of structural failure (DNVGL, 2016). The final result is the estimated design fatigue damage for this particular hotspot, for a particular environmental and operational condition.