## Abstract

The dynamic response of a jacket-supported offshore wind turbine under coupled wind, wave, and current fields during Hurricane Sandy is the subject of this study. To illustrate the detailed procedure related to the response evaluation of a 5-MW offshore wind turbine with a jacket support structure, we consider a single site where the water depth is 50 m. Loads are computed using two simulation tools, fast and abaqus, with partial coupling. Aerodynamic loads on the turbine rotor are first evaluated using a wind turbine model in fast with a fixed base; then, these rotor aerodynamic loads are applied as point loads at the top of a model of a tower that is supported by a jacket structure in abaqus. On the basis of stochastic simulations, we discuss the applicability of the abaqus jacket modeling and describe the characteristics and comparisons of the aerodynamic and hydrodynamic effects on loads on the jacket members. Details related to the structural model and soil–pile interaction model employed in the analyses are also discussed.

## 1 Introduction

In the United States, potential offshore wind plant sites were identified along the Atlantic seaboard and in the Gulf of Mexico. At such sites, it is imperative that we consider load cases for and define external conditions associated with hurricanes and severe winter storms for which wind turbines may need to be designed.

For turbine loads assessment, it is important that the coupled influences of the changing wind, wave, and current fields are simulated throughout the evolution of the hurricanes. We employ a coupled model—specifically, the University of Miami Coupled Model (UMCM) [1–4]—that integrates atmospheric, wave, and ocean components to produce needed wind, wave, and current data. The wind data are used to generate appropriate vertical wind profiles and full wind velocity fields including turbulence; the current field over the water column is obtained by interpolated discrete output current data; and short-crested irregular second-order waves are simulated using output directional wave spectra from the coupled model. In a companion paper [5], we presented a detailed procedure for the simulation of turbulent wind fields and coupled wave kinematics based on the UMCM output.

In this article, we focus on carrying out a dynamic time-domain analysis of a jacket space-frame platform-supported offshore wind turbine (OWT) sited in 50 m of water in the mid-Atlantic region so as to estimate loads during Hurricane Sandy. We discuss in detail how the simulated hurricane wind, wave, and current output data are used in turbine loads studies. A framework is presented that explains how these environmental inputs can be included in turbine loads studies during a hurricane; this can aid in future efforts aimed at developing offshore wind turbine design criteria and load cases related to hurricanes.

We wish to note, as described in our companion paper [5], that the key contribution and novelty of the presented work lie in the fact that the generation of coupled inputs from wind, waves, and currents for an evolving real historical storm (Hurricane Sandy, sometimes referred to Superstorm Sandy) is a significant computational challenge, and this study represents the only attempt, as far as we know, at representing such hurricane-induced loads, albeit with many assumptions, on a jacket-supported offshore wind turbine. Our primary focus is on description of changing input conditions in an evolving tropical cyclone and how these can influence an offshore wind turbine’s loads.

## 2 Problem Description

For evaluating the response of an OWT during the evolution of Hurricane Sandy (2012), as part of a larger study, we originally considered ten mid-Atlantic sites identified for potential wind energy development. In the present work, only one of those sites is studied in detail. In our analyses, various water depths ranging from 20 m to 50 m resulted at the ten originally selected sites. Because a monopile support structure becomes progressively uneconomical as the water depth increases beyond 25–30 m [6], other types of support structures such as jackets or tripods might be better candidates at those water depths. To illustrate the detailed procedure employed in response evaluations of an offshore wind turbine with a jacket support structure, we consider a single site, i.e., Site No. 1, where the water depth is 50 m (see Fig. 1).

### 2.1 Uncoupled Analysis.

An uncoupled modeling scheme is used to analyze the response of an offshore wind turbine with a jacket support structure as illustrated in Fig. 2. While in a coupled modeling approach, aerodynamic and hydrodynamic load effects are evaluated in a single computation step or an integrated software tool, an admittedly less refined uncoupled modeling approach uses two separate software tools or computational steps to evaluate the aerodynamic and hydrodynamic load effects. The rotor aerodynamic forces are first evaluated in fast, using a wind turbine model, assumed fixed rigidly at the base. Aerodynamic loads evaluated at the nacelle (top of the tower) are then applied as point loads in abaqus [7] to a structural model of the tower and jacket support structure, which is also subjected to hydrodynamic forces resulting from waves and currents. Unlike monopile-type support structures that have rotational symmetry due to their cylindrical sections, the orientation of a jacket support structure beneath the rotor and tower affects the overall response of the wind turbine system due to lack of rotational symmetry. Hence, as shown in Fig. 3, a combination of three separate considerations should be made to evaluate the response of the wind turbine with a jacket support structure during a hurricane. These three considerations include:

support structure orientation,

*θ*_{1}(defined with respect to the wind direction);wind and wave misalignment,

*θ*_{2}; andyaw misalignment,

*θ*_{3}.

To simplify the analyses in this study, we assume that the support structure orientation, *θ*_{1}, and the yaw misalignment, *θ*_{3}, are each equal to zero. Thus, only the wind-wave misalignment is assumed to vary during the evolution or passage of the hurricane in our analyses. As mentioned earlier, we present response evaluations of 1 h, beginning at 00:00 UTC on October 28, 2012 (the start of the UMCM simulations). These response computations are repeated every 10 h, beginning 10 h after the start of the simulations and ending 60 h after the start. The response computations are only for the selected site (i.e., Site No. 1), as shown in Fig. 1.

A detailed study of the changing wind, wave, and current field parameters during a 60 h period beginning at 00:00 UTC on Oct. 28, 2012 (0 h) was recently presented in a companion study [5]. We wish to note that establishing and ascribing temporal correlation between environmental conditions and response is not so straightforward to assess. As discussed in the cited study [5], the mean wind profile is updated once in the last hour of every 10 h from the WRF (Weather Research and Forecasting) simulations; this provides the time-varying wind shear that influences the evolving mean wind field during the hurricane. Atmospheric turbulence is also simulated using similarly obtained time-varying hourly friction velocity values from the WRF simulations. From these and with stated assumptions on coherence, the full three-dimensional wind field is generated for the load simulations. For the waves, the complexity arises from the fact that only spectra, not time series, are available from the UMCM output. From these spectra, every 10 h, directional second-order waves need to be simulated in the time domain. From these various outputs, not all of which are physical as most wind and wave inputs are hybrid physical-stochastic constructs, it is not meaningful to study correlation at a fine temporal scale. It is for this reason that only average statistics are studied, and focus is on the 1 h period at a point in time 50 h after the simulation is begun when the storm is at most intense.

## 3 Turbine Model

All the investigations in this study are for a 5-MW offshore wind turbine with a jacket support structure. This is the same system used in the Offshore Code Comparison Collaboration Continuation (OC4) project (Phase I). The rotor-nacelle assembly (RNA) of the OWT is that of the NREL 5-MW baseline turbine [8]. The jacket support structure has four legs, four levels of X-braces, and mudbraces. This support structure has been described in detail by Vorpahl et al. [9].

### 3.1 OC4 Jacket Support Structure.

The jacket support structure for the NREL 5-MW turbine is based on a reference design developed as part of the European Union’s UpWind project [10]. This UpWind jacket is designed for a site with a water depth of 50 m. The jacket consists of four legs, four levels of X-braces, and mudbraces. The top and bottom widths of the jacket are 8 m and 12 m, respectively. A rigid concrete block with a weight of 660 tons and dimensions of 9.6 m (length) × 9.6 m (width) × 4 m (height) is positioned at the top of the jacket and serves as the transition piece (TP) or platform that connects the jacket with the tower of the baseline wind turbine. The geometric configuration and dimensions of the members of the OC4 jacket support structure are presented in Fig. 4. The jacket is made up of a medium-grade structural steel with a Young’s modulus of 210 GPa. The density is assumed to be 8,500 kg/m^{3}, which accounts for paint, bolts, welds, and all other additional masses.

The abaqus model used in this study consists of a tower-top mass, a tower, a transition piece, and the jacket structure. All the separate parts in the model are connected via kinematic coupling constraints in abaqus. The RNA including the hub is modeled as a nodal mass without rotary inertia and the transition piece between the baseline turbine and the jacket structure is modeled as a rigid body, where the 660 tons dead load of this transition piece is modeled as a rectangular body with dimensions of 9.6 m (length) × 9.6 m (width) × 4 m (height). Because the purpose of this study is not to evaluate localized stress concentration at member joints or local buckling of members, all the jacket members are modeled using Euler-Bernoulli beam elements.

In this study, member forces and reaction forces at a total of 13 locations (referred to as “sensor locations”) are evaluated. Figure 5 provides detailed information on these sensor locations. The structural response of the braces and legs is evaluated with respect to the member (local) coordinate system; for axial forces, positive values imply tensile forces, while negative values imply compressive forces.

### 3.2 Verification of the abaqus Model.

We first compare the structural mass in the model with that in the study by Popko et al. [11]. This is presented in Table 1. Structural mass includes the jacket, transition piece, tower, and RNA. In general, a very good agreement is observed when our model is compared with that in the study by Popko et al. [11].

An eigenvalue analysis is performed to obtain natural frequencies, based on our abaqus model, which are then compared with the natural frequencies evaluated with an ansys model used by Song et al. [12]. The natural frequencies for the abaqus and ansys models are presented in Table 2. Generally, values from the two models are in a good agreement with each other. Small discrepancies are expected, as the two models include a different number of degrees-of-freedom and somewhat dissimilar structural modeling assumptions.

### 3.3 Modeling Soil–Pile Interaction.

Because the interaction between the soil and the embedded pile changes the dynamic characteristics of the wind turbine, this interaction effect is considered in our abaqus model of the jacket support structure. In our model, this interaction is represented by a *p*-*y* curve model specified in the American Petroleum Institute (API) RP2A guidelines [13]. The *p*-*y* curve method for designing offshore pile foundations has been utilized by the offshore oil and gas industry for decades and is based largely on work performed in the early 1970s [14,15].

The method approximates the stiffness of the soil–pile system by a number of discrete nonlinear soil springs arranged along the length of the pile. These springs act independently of one another and therefore do not affect the displacement of neighboring springs. The lateral resistance of the pile is represented by *p*-*y* curves, where “*p*” represents the lateral resistance and “*y*” represents the lateral displacement of the pile. The soil profile assumed for the design of the OC4 jacket [10] is used to evaluate the lateral soil stiffness characteristics and is presented in Table 3.

Figures 6(a) and 6(b) present characteristic shapes of the *p*-*y* curves for sand and clay, respectively. In our abaqus model, the lateral stiffness of the soil is modeled using a nonlinear spring element, SPRING1. Table 4 presents the effect of soil–structure interaction (SSI) on the eigenfrequencies of the model; consideration of SSI effects leads to noticeable reduction in the system natural frequencies.

## 4 Hydrodynamic Loads and Associated Response on Jacket Members

*f*, as follows:

*f*

_{D}and Δ

*f*

_{M}are the drag and inertia forces per unit length, respectively,

*C*

_{D}is the drag coefficient taken as 1.0, and

*C*

_{M}is the inertia coefficient taken as 2.0. Also, in Eq. (1),

*u*

_{r}and $u\u02d9r$, respectively, are the “relative” velocity and acceleration (accounting for the motion of the water particles as well as the structure),

*ρ*

_{w}is the density of water, and

*D*is the diameter of the jacket member. In the case of linear Gaussian waves, the inertia force in Morison’s equation is a Gaussian process as it is a linear function of the water particle acceleration, which is also a Gaussian process; the drag force, however, is a non-Gaussian process as it is a nonlinear function of the water particle velocity.

We are interested in the response of the jacket support structure at various locations—primarily, at the braces and legs. The two response measures that we consider here are as follows: the axial force in brace, BRA-W-L4 and the axial force in leg, LEG-SW-L4. Please refer to Fig. 5 that serves to identify these response variables and their locations on the jacket platform. Response statistics discussed next are for hydrodynamic loading alone and apply to a single hour during Hurricane Sandy for the wind turbine at the selected site.

Table 5 summarizes response statistics considering hydrodynamic drag and inertia loads separately as well as in a combined (total) effect. Based on an estimate of the number of upcrossings of the mean of the response process, one can compute a theoretical peak factor for response 1 h extremes, assuming the process were Gaussian [16]. As presented in Table 5 for the axial force in the brace considered, the response due to inertia forces has skewness close to zero, kurtosis close to 3, and peak factor close to the corresponding Gaussian peak factor—all of these findings are in line with expected Gaussian characteristics of the response due to inertial load effects alone. Similar observations can be made as well for statistics of the axial force in a leg, under inertia loads, as presented in Tables 6. In contrast, the response due to drag forces has a significantly higher kurtosis and a peak factor much greater than the corresponding Gaussian peak factor—therefore, the response due to drag forces is clearly strongly non-Gaussian.

Tables 5 and 6 are presented not to suggest that these findings are “representative” in any generalized manner. Indeed, we present these extreme response values at our selected site, during the hurricane, merely to convey the magnitude of the loads, not to suggest statistical results that are by any means “converged” or satisfactory to draw general conclusions from. There is a significant computational effort involved in simulating a multiday tropical cyclone event data archival needs to store wind and wave inputs even for any possible offshore turbine site; this makes it prohibitive to compute full field short-term wind, wave, and current time series globally. We acknowledge that there is significant uncertainty associated with input fields and thus with turbine extreme response statistics if one considers site-to-site variability as well. Because we had defined the precise location of the offshore turbine in question, our results on extreme response are restricted to the selected location and no generalization is implied.

Agarwal and Manuel [17] studied the relative importance of drag and inertia forces to the tower base bending moment of an offshore wind turbine supported by a monopile, which was a cylinder of 6 m diameter installed in 20 m of water. It was found in that study that the response due to hydrodynamic loading was dominated by inertia forces and that the response was close to a Gaussian process. However, the OC4 reference jacket support structure used in the present study is composed of brace members of 1.0 m diameter and leg members of 1.2 m diameter, which are much small-sized sections than the monopile studied by Agarwal and Manuel [17]. Thus, the relative contribution of drag to inertia forces toward the total response is greatly increased in our study. From Tables 5 and 6, it is clear that inertia and drag force effects are of comparable importance for all the response variables studied. The ratios of the maximum response due to drag loads alone to the maximum response due to inertia loads alone are about 1.23 and 1.00, respectively, for the brace axial force and the leg axial force; the corresponding ratios for the response standard deviation are about 0.91 and 0.92, respectively.

We note from the preceding results that although the drag and inertia contributions to the different response variables are comparable, the response due to the combined or total hydrodynamic load effects, accounting for drag and inertia, depends on the location. For example, for the axial force evaluated in a brace, the computed response extreme peak factor is quite close to the peak factor theoretically estimated based on the assumption of a Gaussian response process. This implies that the 1 h maximum values of this response variable during Hurricane Sandy can be estimated based on Gaussian response assumptions. In contrast, the computed response extreme peak factor for the axial force in a leg is significantly higher than the corresponding Gaussian peak factor; this implies that maximum response values estimated based on Gaussian assumptions can be significantly different from the actual response maxima computed from the hour-long simulations.

## 5 Effect of Hurricane-Induced Currents

In the case of a monopile-supported offshore wind turbine, because the contribution of drag loads to the total hydrodynamic loads is insignificant as was shown by Agarwal and Manuel [17], we might expect that the contribution of wave currents to the total response would also be negligible. In the present study, we have seen that drag load effects for the OC4 jacket support structure are of comparable importance to the inertia load effects. Since the drag load effects include contributions from ocean currents, we are interested in learning to what extent these currents influence the total response. For Hurricane Sandy, available depth-dependent ocean current velocities from HYCOM (HYbrid Coordinate Ocean Model [18]) are vectorially combined with the wave particle velocities before computing drag forces. Figure 7 shows the variation with time of the ocean current velocities, evaluated by postprocessing HYCOM output at the selected site, following the UMCM simulation of Hurricane Sandy over 70 h. Inertial currents, in the northern hemisphere, cause streamlines to curve to the right. Their dominant direction in a hurricane is influenced by a balance of Coriolis and inertial effects. Current velocity profiles can be very different during tropical cyclones; in Hurricane Sandy, around 40 h after the start of the simulation—i.e., 40 h after 00:00 UTC on Oct. 28, 2012—there is a noticeable change in the current direction over the depth, consistent with findings during other hurricanes. For example, as reported by Spencer et al. [19] for Hurricane Isaac based on data from moorings, current directions and magnitudes over the depth can be highly variable before the storm. As Hurricane Isaac approached, the topmost flows changed significantly, while stronger near-bottom currents were observed after passage of the hurricane. Some of these trends are similar to what was seen during Hurricane Sandy. Figure 8 shows how the ocean current velocity components, *u*_{cx} and *u*_{cy}, influence the axial force in a brace, BRA-W-L4; inclusion of the ocean currents increases the maximum axial force in the brace by about $19%$ (from 1255 kN to 1499 kN).

## 6 Hydrodynamic Versus Aerodynamic Loads

In this section, we evaluate the relative importance of hydrodynamic loads versus aerodynamic loads toward different jacket response measures.

Figure 9 shows maximum mudline reaction forces and moments evaluated from 1 h simulations (carried out every 10 h) over a period from 10 to 60 h into the UMCM simulation of Hurricane Sandy. As seen in this figure, the contribution of wind loads to the various mudline reaction forces and moments is insignificant. It is only for the vertical reaction force, *F*_{z}, at the mudline that the wind loads are relatively more important but, even there, when wind and wave load effects are combined, the very largest *F*_{z} value (which occurs at 50 h) suggests that the total effect on the 1 h maximum *F*_{z} resulting from wind and waves together is almost the same as that due to waves alone.

## 7 Conclusions

In-depth studies of the response, during Hurricane Sandy, of a 5-MW offshore wind turbine with a jacket support structure have been presented. To evaluate the response of offshore wind turbines during the evolution of this hurricane, only one site (with a 50 m water depth) out of ten potential mid-Atlantic offshore wind plant sites was selected. The track and intensity of Hurricane Sandy were numerically simulated by a fully coupled atmospheric-wave-ocean model, UMCM.

An uncoupled modeling scheme was used to analyze the response of the selected offshore wind turbine with a jacket support structure. While in a coupled modeling approach, aerodynamic and hydrodynamic load effects can be evaluated simultaneously, an uncoupled modeling approach requires separate computational steps to evaluate the aerodynamic loads and the hydrodynamic loads. The aerodynamic load effects on the turbine rotor were first evaluated using a wind turbine model in fast with a fixed base; rotor aerodynamic loads were then applied as point loads at the top of a model of the tower that was supported by a jacket structure in abaqus. Before evaluating the response of the offshore wind turbine with the jacket support during Hurricane Sandy, the uncoupled model was verified. Because interaction between the soil and an embedded pile can change the dynamic characteristics of the wind turbine, this interaction effect was included in an abaqus model of the jacket support structure.

First, we evaluated the nature of the hydrodynamic loads experienced by jacket structural members. The small section size of jacket members makes the drag load effect comparable to the inertia load effect; it also increases the nonlinearity of the total hydrodynamic load effect. Consequently, this high nonlinearity of the response process leads to significant differences between actual response maxima versus Gaussian-based maxima.

We also evaluated the effect of ocean currents on the overall turbine response. Because drag load effects for the selected OC4 jacket platform are of comparable importance to inertia load effects and because drag loads directly account for contributions from ocean currents, we found that the influence of ocean currents on the total response was nonnegligible. This was confirmed by studying maximum axial forces in a diagonal brace member of the jacket structure.

The relative importance of hydrodynamic and aerodynamic loads was also investigated. It was found that the contribution of wind load effects to the total mudline reaction forces is not significant.

There are several acknowledged limitations of this work. For one, only a single site was selected for analysis where a hypothetical jacket platform-supported offshore wind turbine is sited. Second, only uncoupled load and response simulations were carried out and several simplifications were made. Nevertheless, to the best of our knowledge, not a single other study has been carried out where a historical hurricane’s track and physics were simulated and coupled wind, wave, and current input fields ingested into a hypothetical bottom-supported offshore wind turbine. Full-field tropical cyclone simulation with atmosphere-ocean mesoscale physics requires multiple nests and downscaling of computational domains and subdomains to ultimately yield wind, wave, and current fields at turbine scales of interest—temporally and spatially—to allow turbine response simulations. The needed inputs are generated—using WRF, UMWM and HYCOM—over an entire 60 h period corresponding to the evolution and passage of Hurricane Sandy in the Atlantic Ocean, with genesis in the Gulf of Mexico. While this study is indeed not comprehensive, it still offers interesting insights that can serve to aid other researchers interested in assessing turbine loads and control strategies in hurricane design load cases.

## Acknowledgment

The authors are pleased to acknowledge the financial support received from the U.S. Department of Energy via Grant No. DE-FOA-0000415. They also wish to acknowledge assistance received from project collaborators including Dr. Shuyi Chen, Dr. Mark Donelan, and Dr. Milan Curcic from the University of Miami’s Rosenstiel School of Marine and Atmospheric Science and Dr. Paul S. Veers, Dr. Caleb Phillips, and Mr. John Michalakes (currently at NOAA) of the National Renewable Energy Laboratory.

## Conflict of Interest

There are no conflicts of interest.

## Data Availability Statement

No data, models, or code were generated or used for this paper.