## Abstract

Offshore wind turbine blade installation using jack-up crane vessel is a challenging task. Wave- and wind-induced loads on the installation system can cause large relative motion between the blade root and the hub during the mating process. Currently, several numerical tools are used to analyze such critical global motion responses; however, the industry suffers from lack of experiments and full-scale measurements to validate the accuracy of these results. Consequently, a code-to-code comparison exercise becomes critical as it allows comparing different numerical tools for reliable prediction and verification of results. In the present article, a numerical model of the offshore wind turbine blade mating process using a jack-up crane vessel is developed in orcaflex, and a code-to-code comparison is performed against sima; both these tools are immensely used in the industry for modeling marine operations. Different comparisons are made between both the tools such as: (1) modal analyses of the jack-up vessel and the blade lifting gear, (2) time-domain analysis of the fully coupled installation vessel-crane-blade system, and (3) a comprehensive sensitivity study based on different seed numbers and simulation periods. The results of the study show a good agreement between both the tools with a deviation of less than 3% in terms of modal analysis and less than 5% variation in time-domain results. Further, the article provides modeling guidelines for the industry practitioners that heavily rely on both the tools for modeling marine operations.

## Introduction

The demand for extracting power from sustainable sources of energy is consistently increasing. Wind is a natural, reliable, and renewable source of energy that can be harnessed using wind turbines. The principle of power extraction involves converting kinetic energy present in the wind into the mechanical energy by means of blade rotation, which is then converted to useful electrical energy through generators in the nacelle. The development of offshore wind energy is witnessing even a rapid growth, given that offshore wind turbines (OWTs) are placed away from human settlements and are associated with steadier and less turbulent wind resources compared to onshore counterparts [2]. In 2021, the global installed capacity of offshore wind reached 55 GW—a 14 times increase in the capacity compared to a decade ago [3]. In addition, the current trend is large size turbines with nominal power capacity reaching as high as 15 MW with rotor diameter exceeding 230 m [4]. While the increase in the turbine size and rotor swept area increases the power production; however, this poses complex installation challenges. For instance, there is an excessive demand for larger cranes with high tonnage capacity that are capable of transporting and installing sensitive turbine components to higher lifting heights [5]. In addition, installation vessels are dynamic systems and are sensitive to environmental loads. Consequently, the installation of offshore wind farms with hundreds of turbine components takes considerable time and contributes significantly to the overall capital expenditure cost. In fact, the cost of installation of an offshore wind turbine is more than three times higher than that of an equivalent onshore wind turbine [6].

The installation procedure and the type of installation vessel utilized in a project depend on the water depth in which the wind turbine is going to be installed [2]. For small wind turbines, the tower and the blade could be assembled onshore and towed to the installation site. However, in many cases, this is not possible due to lack of deck space area on the vessel or inadequate crane capacity. A split assembly method is generally carried out that includes separated turbine components being transported to the wind turbine site location and assembled piece by piece using offshore crane vessels (Fig. 1(a)). There are different types of crane vessels that can be used; however, jack-up crane vessels are commonly used in shallow waters. The legs of the jack up crane vessels are anchored in the seabed and provides a stable platform during installation [7]. Among different turbine components, OWT blade installation is a demanding task due to two major reasons: (a) blades are sensitive structures made up of fiber composite materials and susceptible to damages that are barely visible and (b) blades are lifted at large hub heights and are required to be mated with the hub that requires significant precision [8]. This final stage is critical as it involves individual bolts of blade root connections being docked into the flange holes of the hub using sensitive guide pins (Fig. 1(b)). In case of any failure such as damages to the root connection, the cost of replacement is very high [9]. Therefore, it is crucial to reliably estimate the motions of the blade installation system during the planning of the marine operations [8].

Several works have been carried out on the dynamic analysis of OWTs subjected to operational and parked loads. However, few studies describe behavior of offshore wind turbine components during installation. A typical installation system during blade mating process consists of an offshore crane vessel, lifting arrangements, and hoisted wind turbine blade, with these subsystems subjected to stochastic environmental loads [10]. Jiang et al. [11] performed a comprehensive study of a blade root mating phase in HAWC2, where the relative motion between blade and the hub was studied for different wind and wave conditions. It was found in the study that the hydrodynamic loads on the monopile cause large tower top hub motions and contribute significantly to the overall relative motion. In addition, it was argued that the monopile structure has deficient damping characteristics that become further critical during the mating process as the aerodynamic damping from the blade is missing. Note that the tool HAWC2 [12] is primarily an aeroelastic software developed by DTU for time-domain simulation of operational or parked turbines. However, crane vessels cannot be explicitly modeled in HAWC2, and the crane tip is usually considered as fixed in such analyses, which does not represent system reality. Similar approaches are considered in Refs. [13]–[15], where HAWC2 is utilized. Verma et al. [13] conducted an impact assessment of the collision loads between blade root and hub using finite element code abaqus [16]. Though the tool is beneficial for the local structural analysis, however, the tool has not been used in the literature to study global motion responses of marine operations. Further, Ren et al. [17] developed an open source simulator for OWT blade installation using matlab/simulink. Wang and Bai [18] analyzed the aerodynamic load on the turbine blade during installation using computationally expensive computational fluid dynamics tool ansys fluent [19]. Compared to the other tools, sima [20] (using simo and riflex modules) has been used extensively for modeling marine operations. Zhao et al. [21,22] developed an in-house simo-aero [22] tool to calculate aerodynamic loads on lifted blade which was extended to simo-aero-riflex [21,23]. Note that the sima standard package cannot explicitly model aerodynamic loads on hoisted blades. Therefore, the simo-aero tool is used as an external dynamic link library (DLL) with the sima standard package [17].

Overall, it can be seen that different tools have been used to study the global motion responses during the blade root mating process. However, one common issue with all these studies is the lack of experimental data or full-scale measurements to validate these models and verify the accuracy of these results. Consequently, a code-to-code comparison exercise becomes important as it allows comparing different tools for reliable prediction and verification of results. As per the authors’ knowledge, there are currently no such comparative studies where different numerical tools have been used to compare modeling and analysis of offshore wind turbine blade installation. Therefore, the present article is the first-ever attempt to perform a code-to-code comparison for analyzing global motion responses during the blade root mating process. In addition, we choose two specific tools for comparison—orcaflex [24] and sima [20]—which are used extensively in the industry for modeling marine operations. While orcaflex is one of the highly utilized tools in the industry for modeling marine operations; however, no published literature exist where blade root mating process is modeled in orcaflex. Therefore, the present study has two specific novelties: (a) develop a fully coupled model of OWT blade mating process in orcaflex that consists of blade lifting gear and jack-up crane vessel, and (b) perform a code-to-code comparison of orcaflex results with sima; note that the results from sima will be utilized from Ref. [22]. In this article, different comparisons are made between both the tools such as: (1) modal analyses of the jack-up vessel and the blade lifting gear, (2) time-domain analysis of the fully coupled installation vessel-crane-blade system, and (3) a comprehensive sensitivity study based on different seed numbers and simulation periods.

### Scope of the Article.

The scope of this article is intrinsically related to marine operations in general. Marine operations are defined as nonroutine operations of limited time duration, which are performed during temporary phases in the marine environment [25]. The critical events that can lead to failure of the operation must be identified first [5,26]. In the case of single-blade installations, the blade mating process is identified as the critical event [1]. Figure 2 shows the response-based methodology for determining the operational limits of marine operations [1,5]. The enclosed box indicates the scope of this article. The numerical model of the critical event is developed in orcaflex, and a code-to-code comparison with existing literature is performed for verification. The four load cases selected in this study are taken from the study by Zhao et al. [22] in order to make a direct comparison. Once the global motion response results are obtained, the safety criteria is imposed based on the prospective damage that the motion could cause [1]. The blade mating process requires very high precision, and hence, the accuracy of the motion response prediction is of paramount importance. Experimental data are not available for motion response characteristics during blade installation, and it is also highly time consuming to do the same. The complex dynamics of wind turbines in a partially installed state is not yet fully understood. Building new numerical models would help us to further understand and predict the motion response accurately. Therefore, there is a pressing need for further numerical investigations and code-to-code comparisons in order to ensure that the results are as reliable and accurate as possible. Additionally, the sensitivity study is performed to identify the critical parameters affecting the dynamic response of the installation system. Upon verification, the model built in orcaflex can be used for making reliable predictions of the safe weather window for the blade mating operation in the future. During the weather window analysis, a large number of load cases will be considered and the allowable load cases will be identified based on the operational limit criteria (*OP*_{LIM}).

## Methodology

Figure 3 shows the methodology flowchart considered in this article to perform a systematic code-to-code comparison for modeling and analysis of blade root mating process between sima and orcaflex. The first crucial step is modeling an installation system in orcaflex that is comparable to sima. For this, the modeling parameters described in Ref. [22] are utilized in orcaflex. Two separate numerical models of the blade installation systems are developed: (a) a model of jack-up vessel with legs and without the crane and (b) a model of the lifting gear consisting of hook, blade, and yoke. This was considered given that the article from Ref. [22] presents the natural periods and mode shapes of these individual models and can be used to compare the modal analysis results from orcaflex.

Figure 4 shows the building blocks of the model in orcaflex. First, the vessel alone is modeled as shown in Fig. 4(a). Second, the blade and lifting gear arrangements are modeled as shown in Fig. 4(b). A sound and independent comparison of eigen value analyses results with those reported in the study by Zhao et al. [22] will ensure that the basic building blocks of the installation system in orcaflex are working similar to the sima model. After a sound comparison, a crane model is developed that consisted of pedestal, king, backstay, boom, boom wires, and crane tip. The pedestal and crane tip are rigidly connected to the vessel and blade lifting gear, respectively. In this way, a fully coupled installation vessel-crane-blade system is obtained in orcaflex that can be used for the time-domain analysis of dynamic responses (Figs. 4(c) and 4(d)). Once the free vibration characteristics have been verified, four different environmental load cases are applied for the time-domain analysis. Again, the load cases used for comparison are consistent with those considered in the sima analysis by Zhao et al. [22]. The environment is modeled using turbulent wind for wind loads and irregular waves for wave loads. The wind load is generated using TurbSim [27], which can then be imported into orcaflex. The wave loads are applied using the in-built option in orcaflex. The JONSWAP spectrum [28] has been used to generate the desired wave loads. Different global motion response results such as motion of the vessel, crane tip, and blade motions are verified by comparing results with Ref. [22]. Finally, to provide modeling guidelines, a comprehensive sensitivity of the motion response results is studied by running simulations with different seed numbers, stages, and simulation periods. A detailed description of the installation system and the modeling procedure is discussed later in this article.

### Assumptions.

The data required for building the model in orcaflex are solely obtained from the study by Zhao et al. [22]. The mass properties of each and every element are not available, and hence, missing data were assumed appropriately. In addition, the blade used in orcaflex is taken from the IEA 10 MW 198 RWT reference wind turbine [29], whereas the blade used in sima is from the DTU 10 MW reference wind turbine [30]. The IEA 10 MW blade is assumed to be equivalent to the DTU 10 MW counterpart because both blades have the same wind regime (IEC class 1A), hub height, and airfoil series (FFA -W3) [29].

### General Description of the Installation System.

This study deals with the installation of an offshore wind turbine by a typical jack-up crane vessel in the North Sea. The data required to build the model of the installation system are taken from the study by Zhao et al. [22]. Table 1 shows the vessel parameters along with site-specific data. Table 2 shows the crane, blade, and lifting gear data. The model developed in orcaflex with all parts of the system labeled is shown in Fig. 5. The coordinate system adopted for the vessel and the blade are shown in Fig. 5.

Parameters | Values |
---|---|

Hull length, breadth, and depth (m) | 132, 39, and 9 |

Displacement during transportation (m^{3}) | 2.2 × 10^{4} |

Total elevated load (t) | 1.69 × 10^{4} |

Leg length and diameter (m) | 92.4, 4.5 |

Longitudinal and transverse leg spacing (m) | 68.3 and 30.6 |

Airgap (m) | 7.2 |

Leg below hull (m) | 49 |

Penetration (m) | 2.7 |

Water depth (m) | 39.1 |

Soil type | Dense sand |

K_{x} (KN/m) | 1.35 × 10^{6} |

K_{y} (KN/m) | 1.35 × 10^{6} |

K_{z} (KN/m) | 1.47 × 10^{6} |

$K\varphi $ (KNm/deg) | 6.4 × 10^{5} |

$K\theta $ (KNm/deg) | 6.4 × 10^{5} |

$K\psi $ (KNm/deg) | 8.3 × 10^{5} |

Parameters | Values |
---|---|

Hull length, breadth, and depth (m) | 132, 39, and 9 |

Displacement during transportation (m^{3}) | 2.2 × 10^{4} |

Total elevated load (t) | 1.69 × 10^{4} |

Leg length and diameter (m) | 92.4, 4.5 |

Longitudinal and transverse leg spacing (m) | 68.3 and 30.6 |

Airgap (m) | 7.2 |

Leg below hull (m) | 49 |

Penetration (m) | 2.7 |

Water depth (m) | 39.1 |

Soil type | Dense sand |

K_{x} (KN/m) | 1.35 × 10^{6} |

K_{y} (KN/m) | 1.35 × 10^{6} |

K_{z} (KN/m) | 1.47 × 10^{6} |

$K\varphi $ (KNm/deg) | 6.4 × 10^{5} |

$K\theta $ (KNm/deg) | 6.4 × 10^{5} |

$K\psi $ (KNm/deg) | 8.3 × 10^{5} |

Parameters | Values |
---|---|

Boom length (m) | 107.6 |

Crane boom angle (deg) | 67.6 |

Number of equivalent boom wires | 2 |

Equivalent boom wire stiffness (KN/m) | 9048 |

Equivalent boom wire damping (KNs/m) | 90.5 |

Hook mass (tons) | 10 |

Yoke mass (tons) | 47 |

Blade mass (tons) | 41.67 |

Blade length (m) | 86.37 |

Blade COG (m) | 26.2 |

Installation height (m) | 119 |

Tugger line arm length (m) | 10 |

Length of crane wire (m) | 4.7 |

Length of slings (m) | 20.4 |

Parameters | Values |
---|---|

Boom length (m) | 107.6 |

Crane boom angle (deg) | 67.6 |

Number of equivalent boom wires | 2 |

Equivalent boom wire stiffness (KN/m) | 9048 |

Equivalent boom wire damping (KNs/m) | 90.5 |

Hook mass (tons) | 10 |

Yoke mass (tons) | 47 |

Blade mass (tons) | 41.67 |

Blade length (m) | 86.37 |

Blade COG (m) | 26.2 |

Installation height (m) | 119 |

Tugger line arm length (m) | 10 |

Length of crane wire (m) | 4.7 |

Length of slings (m) | 20.4 |

### Numerical Modeling of the Installation System

#### Structural Modeling.

*c*is the damping matrix,

**m**is the mass matrix,

**k**is the stiffness matrix,

*α*

_{1}is the mass proportional damping coefficient, and

*α*

_{2}is the stiffness proportional damping coefficient. The damping ratio is taken as 3% of the critical damping for large diameter structures like jack-legs and crane boom [23]. The damping ratio for lift wire and slings is taken as 1% of the

^{2}critical damping [23].

Components | orcaflex model types | sima model types |
---|---|---|

Blade | 10 MW turbine (only blade) | SIMO body |

Hook | 3D buoy | Supernode |

Yoke | 3D buoy | Supernode |

Lift wire and slings | Lines | Lines |

Tugger lines | Link–linear springs | Simple wire couplings |

Crane boom | Lines | Lines |

King, backstay, and pedestal | Lines | Lines |

Hull | 6D buoy | SIMO body |

Hull-leg connections | Rigid | Rigid |

Legs | Lines | Lines |

Components | orcaflex model types | sima model types |
---|---|---|

Blade | 10 MW turbine (only blade) | SIMO body |

Hook | 3D buoy | Supernode |

Yoke | 3D buoy | Supernode |

Lift wire and slings | Lines | Lines |

Tugger lines | Link–linear springs | Simple wire couplings |

Crane boom | Lines | Lines |

King, backstay, and pedestal | Lines | Lines |

Hull | 6D buoy | SIMO body |

Hull-leg connections | Rigid | Rigid |

Legs | Lines | Lines |

Note: Please refer to the Appendix for definitions of the software-specific terms.

#### Aerodynamic Loads.

In sima, the cross-flow principle has been used to build an external DLL file. The effects of wind turbulence, shear, and dynamic stall have also been considered in sima. The aerodynamic load in orcaflex is calculated using the same cross-∖flow principle [31]. The aerodynamic loads are calculated individually at the aerodynamic center of each element. The loads are due to the relative inflow velocity *ω* and its angle of attack *α*. The blade velocity relative to the wind velocity is calculated as the relative inflow velocity in orcaflex [31], and the steady-state lift and drag coefficients are used to calculate the aerodynamic loads. It is important to consider blade velocity in aerodynamic load calculation as it significantly affects the aerodynamic damping [23]. If the blade velocity is ignored, there will be an overestimation of the blade motion [22]. To calculate the aerodynamic load acting on the blade, all the loads on the elements are added. The blade element coordinate system is defined in Fig. 6.

*z*-axis is given by

*ρ*is the air density,

*A*is the element area,

*c*is the chord length, and

*C*

_{L},

*C*

_{D}, and

*C*

_{M}are the lift, drag, and moment coefficients, respectively. The jack-up hull is modeled as 6D buoy in orcaflex. The option to include wind loads on 6D buoys is selected to calculate the wind load on the jack-up hull. On the other hand, the hull is modeled as a SIMO body in sima. The wind load on the hull in sima is calculated using the equivalent wind area and coefficients [20].

#### Hydrodynamic Loads.

*ρ*is the density of water,

*f*is the fluid force per unit length on the body,

*C*

_{m}is the inertia coefficient for the body, Δ is the mass of the fluid displaced by the body,

*a*

_{f}is the fluid acceleration relative to earth,

*C*

_{d}is the drag coefficient for the body,

*A*is the drag area, and

*ν*

_{f}is the fluid velocity relative to the leg. The water inside the leg is considered in sima, which gives rise to an extra term due to the acceleration of water inside the leg [20].

#### Jack-Up Soil–Structure Interaction.

*F*

_{s}is the soil reaction force,

**K**is the soil stiffness vector,

*X*is the spudcan displacement, and

**C**is the damping vector of soil.

#### Mechanical Coupling.

*L*is the wire elongation,

*T*is the tension, and

*k*is the stiffness.

#### Identification of System Natural Periods.

**M**and

**K**represent the mass and restoring matrix, respectively,

**X**is the vector of modal shape, and

*ω*is the natural frequency.

#### Time-Domain Solutions.

The load cases chosen for comparison with results from sima have been presented in Table 4. The load case numbers are obtained from Ref. [22]. For the initial comparison, wind speed is set at a mean wind speed of 10 m/s with a turbulence intensity of 20.8%. The wind field is generated using TurbSim [27] and imported into orcaflex with a .bts file extension. The wind direction (*θ*_{wd}) is assumed to be 0 deg for all the load cases. The relative frequency range was set to the default values of 0.5 to 10 in orcaflex, and the maximum component frequency was set to 0.5 Hz. The total number of components was set to 200. Time-domain solutions were obtained from orcaflex for all the four load cases. The total simulation time was set to 1200 s (20 min) with a time-step of 0.01 s. Implicit time-domain solution method was used with the maximum number of iterations set to 100 and the tolerance level set to 25e − 6. The first 600 s (10 min) were removed from the calculations to avoid transient effects. The dynamic response of the blade installation system (vessel motion, crane tip motion, and blade motion) during the mating phase is calculated. Finally, various combinations of seed numbers, stages, and simulation periods have been used to perform time-domain simulations for the sensitivity study and compared with the results from sima.

Load case | Crane tip | H_{s} (m) | T_{p} (s) | θ_{wv} (deg) | U_{W} | Turbulence intensity (%) |
---|---|---|---|---|---|---|

LC1 | Fixed | – | – | – | 10 | 20.8 |

LC3 | Free | 2.4 | 8.55 | 0 | 10 | 20.8 |

LC6 | Free | 2.4 | 8.55 | 65.87 | 10 | 20.8 |

LC11 | Free | 2.4 | 5.65 | 65.87 | 10 | 20.8 |

Load case | Crane tip | H_{s} (m) | T_{p} (s) | θ_{wv} (deg) | U_{W} | Turbulence intensity (%) |
---|---|---|---|---|---|---|

LC1 | Fixed | – | – | – | 10 | 20.8 |

LC3 | Free | 2.4 | 8.55 | 0 | 10 | 20.8 |

LC6 | Free | 2.4 | 8.55 | 65.87 | 10 | 20.8 |

LC11 | Free | 2.4 | 5.65 | 65.87 | 10 | 20.8 |

## Results and Discussions

### Eigenvalue Analysis.

An eigenvalue analysis has been carried out in order to compare the model developed in orcaflex with sima. The mode shapes of the first four modes of vessel motion are shown in Fig. 9. The last two modes of vessel motion and the mode shapes of blade motion are shown in Fig. 10. The natural periods of the first six modes of vessel motion obtained from orcaflex have been compared with sima results from the study by Zhao et al. [22] in Fig. 11(a). The comparison of natural periods of the dominant blade motions are shown in Fig. 11(b). The first three modes of the blade motion are blade roll resonance, blade yaw resonance, and blade-hook double pendulum motion. The natural periods of vessel motion mostly comply well with the results from sima. The natural period of surge motion shows a deviation of around 3%, while the natural periods of other motions show negligible differences. This deviation is caused by the minor differences in the modeling of the hull where the mass moment of inertia is slightly different in the orcaflex model. There is no major difference in the natural periods of blade roll and blade yaw resonance. There is a minor deviation of around 4% in the natural period of blade-hook double pendulum motion. The main reason for this deviation can be explained by the fact that the orcaflex blade weighs 48.59 tons based on the IEA 10 MW 198 RWT reference wind turbine, while the sima blade used in the study by Zhao et al. [22] weighs 41.7 tons for DTU 10 MW turbines. However, note that the overall weight of the blade and yoke together is still maintained consistent at 88.67 tons, as reported in the article by Zhao et al. [22]. Nevertheless, the mass distribution of wind turbine blade is different in both the models and may explain a 4% difference in the natural period in one of the three blade motions. The natural periods of the two models need to be within 5% of each other in order to make a satisfactory comparison [32]. Overall, the eigenvalue analysis showed that the natural periods and mode shapes of the orcaflex model are analogous to those of the sima model. Hence, the developed orcaflex model accurately predicts the dynamic response of the installation system.

### Dynamic Response of the Installation System.

The global dynamic response of the installation system has been obtained from time-domain simulations in orcaflex. The motion of the vessel, crane tip, and blade have been calculated. Additionally, the translational motion at the blade root is analyzed using the assumption that the blade is a rigid body. Vessel motion and crane tip motion are obtained with respect to the vessel coordinate system shown in Fig. 5. The blade and the blade root motion are obtained with respect to the blade coordinate system defined in Fig. 5. The results from orcaflex have been compared with corresponding sima results from Ref. [22]

#### Motion of the Vessel.

The motion responses in the 6DOFs for the vessel have been obtained. There is no motion of the vessel in LC1 as no wave load was considered. The time-series of the vessel surge, sway, yaw and roll motion response is illustrated in Figs. 12(a), 12(b), 12(c), and 12(d), respectively. In the time-series results, the largest response is marked with dots, the second largest is marked with dashes, and smallest response is marked with a line for each motion. The time-series representation of vessel heave and pitch motion is not shown since the response is relatively very small compared to other motions. Vessel heave motion is largely restricted by the dense sand foundation. Vessel pitch motion is smaller than roll due to the larger moment of inertia in the pitch direction. Vessel surge motion is highest in LC11 followed by LC6 and then LC3. In LC3, wave direction is oriented along the *Y*-axis, and hence, surge motion is minimal. In LC6 and LC11, the wave direction is the same, but LC11 surge motion is larger due to the difference in the peak period. Similar analysis can also be applied to sway motion where it is largest in LC3 followed by LC11 and then LC6. Vessel roll and sway motion follow the same pattern. Vessel yaw motion follows the same pattern as surge motion due to the incident wave directions. The standard deviations of vessel motion response for LC3, LC6, and LC11 are shown in Figs. 13(a), 13(b), and 13(c), respectively. Figure 13(d) shows the power spectral density of vessel surge motion for LC11. In all the load cases, wave-induced motions are more significant than wind-induced motion for the vessel. Vessel motion is influenced by the incident wave direction and the peak period. It can be observed that the standard deviations are compliant with the time-series results. The amplitude of vessel motion tends to increase with a decrease in the peak period. Sway and roll motion are the highest in LC3 due to the incident wave direction of 0 deg. Surge and yaw motion are the highest in LC11 due to the wave direction as well as lower peak period compared to LC6. The general trend observed is that the standard deviations of vessel motion response obtained from orcaflex are less for all the load cases. The standard deviations of vessel motion from orcaflex show an average variation of around 8% compared to the results from sima. The vessel surge motion spectrum also corroborates the difference in the surge motion response for LC11. Previous comparative studies have found that such differences are known to arise between orcaflex and sima [32]. The differences can be attributed to several factors due to the complexity of the blade installation system. The variation in the natural period of the surge motion as mentioned earlier will affect the motion response of the system. The random seed number generated for wave load in sima is also a parameter, which leads to uncertainty as the vessel motion response is strongly dependent on it.

#### Motion at the Crane Tip.

The translational motion at the crane tip has been calculated. There is no crane tip motion in LC1 as the crane tip is assumed to be fixed. Figures 14(a), 14(b), and 14(c) show the standard deviations of the crane tip translational motion for LC3, LC6, and LC11, respectively. It is found that crane tip motion in the sway direction is dominant for all the load cases. The deformation of the boom and the boom wires contributes to crane tip motion. As shown in Fig. 5, the crane is extending along the *Y*-axis, and hence, the crane tip sway motion gets significant contribution from crane resonance. This effect can also be observed in the power spectral density for crane tip sway motion for LC11 shown in Fig. 14(d). It can be noted that the crane tip motion is the largest when the wave is incident at 0 deg (beam sea, LC3). The average difference in the standard deviations of the crane tip motion between orcaflex and sima is found to be around 15%. One possible reason for the variation could be due to the minor difference in orientation of the crane after the static analysis in orcaflex. Minor differences in the line element properties of the boom and boom wire could amplify the variation while calculating global response.

#### Motion of the Blade.

The six degrees-of-freedom rigid body motion of the blade has been obtained. Figures 15(a), 15(b), 15(c), and 15(d) show the standard deviations of the blade motion for LC1, LC3, LC6, and LC11, respectively. It is found that the blade roll motion is far greater than blade yaw motion in all the load cases. This is due to the fact that tugger lines are very effective in restricting blade yaw motion. Blade surge, heave, and pitch motions are largely dependent on the wave loads, and they are almost negligible in LC1 where there is no wave load. Blade sway motion is affected mainly by blade roll resonance, double pendulum-induced motion, and vessel surge resonance, which are evident from the power spectral density of blade sway motion shown in Fig. 15(e). The average difference in the standard deviations of blade motion between sima and orcaflex is around 12%. This is consistent with the variations observed with other motions. The factors for vessel and crane motion variations are also applicable to blade motion as they are dependent on each other. Differences could also arise from the minor changes in line properties assigned in orcaflex for slings and the lift wire. Additionally, the external DLL code used in the study by Zhao et al. [22] (simo-aero) for aerodynamic load calculation uses a dynamic stall model that is not available in orcaflex.

#### Blade Root Motion.

The blade root motion is critical for studying the blade-hub mating process, as the environmental limits for carrying out the blade mating process is affected by both the blade root motion and the hub motion [11]. The time series of blade root surge, sway, and heave motions are shown in Figs. 16(a), 16(b), and 16(c), respectively. In the time-series, the largest response is marked with dots, while the smallest response is marked with a line for each motion. Blade root surge motion is highest in LC3 because the blade *x*-axis is aligned along *y*-axis of the vessel. Since the contribution from the vessel sway motion is significant in LC3, the blade surge motion is also correspondingly larger. Similarly, the blade root sway motion is largest in LC11 due to contribution from vessel surge motion. Although the blade root heave motion is largest in LC11, the heave motion response is almost equal in all the load cases. The standard deviations of blade root motions for LC1, LC3, LC6, and LC11 are shown in Figs. 17(a), 17(b), 17(c), and 17(d), respectively. The standard deviations follow the same pattern as illustrated in the time-series results. The blade root surge and sway motions remain almost the same as that at the blade COG due to the tugger lines restricting them. However, the blade root heave motion is significantly larger than at the blade COG. The differences in the blade root heave motion is clearly visible when we look at the standard deviations. There is a variation in the results from orcaflex and sima of about 10%. Apart from the aforementioned factors, the difference in the numerical integration scheme of sima and orcaflex can also give rise to variation in the results. sima uses the Newmark – *β* integration scheme, whereas orcaflex uses the generalized – *α* integration scheme [33].

### Sensitivity Analysis.

A sensitivity study has been carried out to evaluate the effects of simulation period and the wave seed numbers on the motion response results. LC1 and LC3 have been chosen for this study to demonstrate the effects of wave and wind loads separately. Only wind loads are applied in LC1, while both wave and wind loads are applied in LC3. For LC1, three different simulation periods of 600 s (10 min), 3600 s (1 h), and 6000 s were chosen. The 10-min simulations in orcaflex were used for the initial comparative study to save computational power and to obtain results quickly for verification. This time duration is also more realistic considering the actual mating process. The 1-h simulation period matches with that of the simulation period used to obtain sima results. The 6000 s simulation period was chosen to examine the effects of running the simulation for ten stages of 10 min each. The same simulation periods are used for the sensitivity study of LC3. Additionally, ten different random wave seed numbers were chosen, and the average of those ten results was taken. For the 6000 s simulations, the time series of the response is split into ten stages, and the average of the standard deviations of the ten stages was taken. This case is particularly useful while performing operability studies. In the case of 3-h simulation period, one single stage was considered and the standard deviation of the entire time-series has been calculated. All the results are compared against the benchmark of the results from sima, which was obtained using a simulation period of 1 h in a single stage and a random wave seed number.

Figure 18 shows the sensitivity of motion response result of LC1 to different simulation periods. It can be observed that the simulation period has a significant impact on the overall motion response results. The 10-min simulations provide the lowest motion response results, which are to be expected. The 1-h simulations produce almost identical results as that of sima. The motion response results for 6000 s are higher than that of the results from sima. It implies that longer simulation periods provide conservatively high motion response results. The 3-h simulation period provides the highest estimate for motion response. However, the difference between the results for 6000 s (1 h and 40 min) and 3 h is almost negligible. A similar pattern of motion response results can be observed for LC3, which is shown in Fig. 19. The simulation periods have the same effect for LC3. The longer simulation periods associated with larger standard deviations. The average of standard deviations of the results for ten different seed numbers is found to be higher than the corresponding simulations with a single seed. It is worth noting that running ten different simulations with considerably long simulation periods is computationally very expensive. In general, it can be noted that longer simulation periods and more seed numbers provide higher estimates for the motion response. Long simulation periods are required to capture the nonlinearity in the motion response. However, these longer simulations are computationally expensive. If the level of accuracy required is less than 15% variation, then 10-min simulations would be the efficient solution. It must be noted that running one simulation of 6000 s (10 × 10 min) is computationally more efficient than running ten different simulations with different seed numbers. This is due to the fact that running ten different simulations results in ten different periods of transience that need to be cropped out of the calculation of the standard deviation. Running one long simulation with ten different stages is advantageous because it contains only one period of transience. It is also worth noting that these simulations with different stages are highly useful while performing operability studies, which requires the testing of a very large number of load cases. Hence, it is important to choose the appropriate simulation period and wave seeds in order to derive conservative estimates as well as maintaining computational efficiency.

### Reasons for Variations and Modeling Guidelines.

Future code-to-code comparisons must take these factors into consideration while modeling the system.

The bottom-up strategy must be adopted while modeling. The complex system must be split into modules.

The characteristics of each module must be studied and verified using an eigenvalue analysis.

The difference between the mass properties of each and every element must be verified before making the comparison.

When it is not possible to obtain the model of the same reference wind turbine blade, the alternatives must be carefully verified to have similar mass properties, airfoil series, wind regime, etc.

The difference in the eigenvalue analysis is caused by these differences in mass properties of the blade and jack-up legs.

The wave spectrum properties must be analyzed in detail in order to ensure there are no discrepancies.

The random wave seed generator is an inevitable source of uncertainty and it must be taken into consideration.

The difference in integration scheme between Newmark –

*β*and generalized –*α*is another unavoidable source of error.The difference in the motion response results are caused by these minor differences in natural periods of certain motions, wave spectral properties, random wave seeds, and integration schemes.

It is noted from the sensitivity analysis that running simulations with different seed numbers and/or stages provides a conservatively higher estimate for the motion response. It is computationally more efficient to run one simulation of 6000 s (10 × 10 min) with ten stages rather than running ten different simulations of 10 min each.

The time period for the simulation must be selected based on the level of accuracy required and such that the least computational effort is used.

## Conclusions

In the present article, a numerical model of the offshore wind turbine blade mating process using a jack-up crane vessel is developed in orcaflex, and a code-to-code comparison is performed against sima; both these tools are immensely used in the industry for modeling marine operations. Different comparisons are made between both the tools such as: (1) modal analyses of the jack-up vessel and the blade lifting gear, (2) time-domain analysis of the fully coupled installation vessel-crane-blade system, and (3) a comprehensive sensitivity study based on different seed numbers and simulation periods. Following are the main conclusions of the study:

Eigenvalue analysis was performed to ensure that the orcaflex model is consistent with the sima model. The difference between the natural periods of the sima and orcaflex model was found to be within 3%. Since the variation is less than 5%, the orcaflex model can provide a reasonable estimate of the dynamic response of the blade installation system.

The dynamic response results obtained from orcaflex were found to be within 5% variation compared to the results reported for sima in Ref. [22] for all the load cases. The possible reasons behind the differences in the results have been discussed in the article that includes the random wave seed number used in sima that leads to uncertainty in the wave load. It is important to make sure that wave loads generated in two software are exactly the same since wave loads contribute significantly to both the vessel and the blade motion. Nevertheless, the results from orcaflex and sima are found to be in a good agreement. Hence, the orcaflex model can act as a robust tool for making reliable predictions of the motion response of the offshore wind turbine blade installation system.

The sensitivity study demonstrates the effect that the simulation period and seed numbers have on the motion response results. Longer simulation periods ensure that conservatively higher response results are obtained. Although 10-min simulations are enough to capture the behavior of the system, it is observed that simulation periods of at least 1 h is required such that the results converge toward the sima results. Simulations as long as 3 h do not provide any significant difference in motion response results.

## Footnote

Refer to the Appendix for definitions of software-specific terms.

## Acknowledgment

The authors would like to thank Dr. Yuna Zhao for providing additional data that helped the authors to build the model in orcaflex. This work was financially supported by the Research Council of Norway granted through the Centre for Research-based Innovation of Marine Operations (SFI MOVE) at NTNU (Project Number 237929). The corresponding author acknowledges the start-up support provided by Office of the Vice President for Research and Dean of the Graduate School, University of Maine.

## Conflict of Interest

There are no conflicts of interest.

## Data Availability Statement

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

## Appendix: Definition of Terms Used in Table 3

*orcaflex 3D Buoys*—These are simplified point elements used in orcaflex with only 3 degrees-of-freedom, allowing only translations. Rotational degrees-of-freedom is not allowed, so the loads described here are based on forces with no contributions from the moment. The elements can be specified with mass and hydrodynamic data.*orcaflex 6D Buoys*—These are rigid bodies used in orcaflex with 6 degrees-of-freedom, i.e., having both translations and rotational degrees-of-freedom. Mass, moments of inertia, and forces from various effects can be modeled using 6D buoys.*SIMO Body*—These are rigid bodies used in sima with 6 degrees-of-freedom, i.e., having both translations and rotational degrees-of-freedom. Each body can be associated with mass properties and hydrodynamic data, e.g., hydrodynamic added mass and radiation damping.*Link*—Links used in orcaflex are simple springs (or spring damper system) connecting two points with the specified stiffness and damping. There are two types of links in orcaflex, namely, tethers (that can only take tension and no compression) and spring/damper (can take both tension and compression).*Wire Coupling*—Wire couplings are used in sima to model simple force–elongation relationships (like springs) between two points with specified stiffness and damping.*Lines*—Lines in orcaflex applies the line theory that follow the finite element model with nodes and segments. Mass properties of each segment are lumped into the two nodes at the end. Further, the axial and torsional properties of the lines are specified for each segment. On the other hand, lines in sima are modeled explicitly based on beam elements as described in the study by Mollestad [34] and Engseth [35].

## References

*α*Method