10.4. Design spiral process and loads' analysis
The conventional SSt design process starts with the compilation of the so-called “design basis” document, which details turbine parameters (loads, dimensions, project lifetime, PSFs, etc.), environmental site-specific conditions, and guidance on the choice of reference standards. Based on these specifications and on an initial conceptual layout, a preliminary design is achieved, which verifies simple structural checks (modal performance and ULS criteria, as discussed in the folowing sections). These first few steps in the design spiral process (see Fig. 10.13) heavily rely on the experience of the engineering team. Then, the spiral process itself tends to guide the choices based on the structural and functional requirements that must be met by the SSt. At every successive turn of the spiral, a more focused and detailed analysis cycle is accompanied by: modifications to the geometry, new and additional loads analyses, and refined limit state assessments. After each cycle, more design criteria are satisfied and the tower layout converges toward a finalized geometry. Computer-aided design/manufacturing (CAD/CAM) models can help in this process because they allow for parametric storing and updating of the data, and for an efficient exchange of geometry, material, and infrastructure information. In parallel to this process, the interaction among the designers of all OWT components should be encouraged to arrive at a fully integrated design and to verify that choices in one of the parts do not penalize load states in another.
As any other component of an OWT, the tower must be designed to sustain the loads it will encounter throughout the lifetime of the system with a sufficient safety margin and based on a target value for the structural reliability. The tower response must thus be analyzed under all possible scenarios representative of load situations encountered in real life and based on the L2 exposure level. The loading scenarios must include operational and parked conditions. Operational DLCs include normal operation and power production as well as start-up, shutdown, and fault cases. DLCs are constructed from a combination of relevant design situations and external conditions. To this end, the DLCs are normally provided by the design and certification standards to be used in conjunction with site-specific data. When combined with that data, standards such as Refs [1,11,15,23] describe the appropriate profiles, spectra, and parameters for factors such as wind, wave, current, and ice, which must be considered in the loads analyses. The DLCs account for a minimum number of combinations of design situations and external conditions such as:
• normal operation and normal environmental conditions,
• normal operation and extreme environmental conditions,
• fault situations and appropriate external conditions, and
• transportation, installation, maintenance and appropriate external conditions.
Table 10.3, for example, summarizes the DLCs and environment scenarios prescribed by Ref. [1].
In general, tower loads are determined via numerical aero-hydro-servo-elastic (AHSE) simulations carried out via dedicated computer-aided engineering (CAE) tools. These tools simultaneously model aerodynamics, hydrodynamics, structural dynamics, and control system dynamics within each DLC of interest.
Simplified calculations may be used in the very first phases of design, but the complexity of offshore systems outright bans any attempt at completing the system design without integrated approaches. During the initial design iterations, however, the designer's experience may help in the selection of a few key CAE simulations and (design driving) DLCs to rapidly narrow down the pool of candidate tower layouts. The total number of simulations for a more complete loads' analysis reaches the few thousands. This is because various combinations of wind speed and wave/current/ice conditions must be examined, and more realizations are necessary to reach statistical significance within turbulent wind regimes and stochastic wave simulations. Therefore, the full suite of loads' simulations is normally carried out on just one or two select final configurations. Within the LRFD design, the loads' analysis results are then used to verify ULS, FLS, and service limit states (SLS).
Fatigue loads have historically been validated by testing performed during type certification. ULS loads, on the other hand, cannot be easily verified with field measurements and are therefore left to numerical calculations. Experience with previous models and verifications against multiple approaches and codes will increase confidence in the results and reduce project risk.
As the design spiral converges toward the final tower layout, the number of DLCs is progressively increased and more attention is paid to the component details. While the design of an isolated tower is relatively simple, the presence of a turbine generator and SbS still in the design loop, actually renders the process more complicated than one would initially anticipate. At the end of the design process, the CVA will need to approve of the design calculations and reports, which must demonstrate compliance with the codes, standards, and CVA's internal review protocols. Through this third- party verification, the risks are further reduced.
While the process described above is fairly complex, critical identification and understanding of the relative role of each loading source, and of the main structural and performance requirements, will help the engineer complete the design work successively. The following sections discuss principal loading sources and dynamic criteria that must be satisfied to initialize the tower design.
Table 10.3
Main DLCs and loading scenarios
| DLC | Design situation | Wind conditions | Sea conditions | Other conditions | Type of analysis | ||
| Waves | Currents | Water | |||||
| 1.1–1.6 | Power production | NTMa, ETM, ECD, EWS | NSS, SSS, SWH | NCM | MSL, NWLR | (COD, UNI) & (COD, MUL) & MIS | ULS & FLS |
| 2.1–2.4 | Power production plus faults | NTM, EOG | NSS | NCM | MSL, NWLR | (COD, UNI)—control system fault/grid loss | ULS & FLS |
| 3.1–3.3 | Start-up | NWP, EOG, EDC | NSS | NCM | MSL, NWLR | (COD, UNI) | ULS & FLS |
| 4.1–4.2 | Normal shut down | NWP, EOG | NSS | NCM | MSL, NWLR | (COD, UNI) | FLS & ULS |
| 5.1 | Emergency shut down | NTM | NSS | NCM | MSL | (COD, UNI) | ULS |
| 6.1–6.4 | Parked/idling | EWM, RWM, NTM | ESS, RWH, EWH, NSS | ECM | EWLR | (MIS, MUL) & (COD, MUL)—grid loss/extreme yaw misalignment | ULS & FLS |
| 7.1–7.2 | Parked/idling plus faults | EWM, RWM, NTM | ESS, RWH, EWH, NSS | ECM | NWLR | (MIS, MUL) & (COD, MUL) | ULS & FLS |
| 8.1–8.3 | Transport/installation/maintenance | EWM, RWM, NTM | ESS, RWH, EWH, NSS | ECM | NWLR | (COD, UNI) & (COD, MUL)—grid loss | ULS & FLS |
| E1–E5 | Power production | NTM | loads from temperature fluctuations, arch effect, moving ice floe, fast ice | NWLR | – | ULS & FLS | |
| E6–E7 | Parked/idling | EWM, NTM | Hummocked ice and ice ridges, moving ice flo | NWLR | – | ULS & FLS | |
From IEC 61400–3 Wind Turbines – Part 3: Design Requirements for Offshore Wind Turbines, 2009.
10.4.1. Sources of loading
The tower, as previously mentioned, has the fundamental role of transferring loads to the SbS, or the foundation. From a civil engineering perspective, tower loads can be categorized into permanent actions (dead loads) and live loads. Dead loads are the gravitational loads associated with the self-weight of the structure, and the weights of the tower internals (see Section 10.6.1), as well as appurtenances connected to the deck (transformers, cranes, etc.) and monopile (eg, cathodic protection, platforms, boat landings, etc.). It has to be well understood that due to the vibrational and deflection characteristics of the OWT, even these so-called dead loads have very important dynamic effects, as for example the PeD effect associated with the displacement of the RNA center of mass (CM).
Live loads include:
• aerodynamic loads from the RNA, ie, forces and moments originating at the rotor and routed through the drive train and bedplate,
• drag loads from direct action of the wind on the tower, and potential vortex shedding loads,
• inertial loads associated with the vibrational modes of the system (eg, due to accelerations of the RNA mass) excited by the turbulent and sheared wind environment, by the inertial and aerostructural properties of the rotating rotor, and by the oscillations of the SbS (especially in cases of floating SbSs and seismic DLCs),
• loads derived from installation methods (hoisting, upending, etc.) and maintenance actions (including potential aircraft landing),
• hydrodynamic loads on the monopile portion: wave, current, and ice loads,
• seismic loads,
• loads derived from the actions on the SbS and reactions at the tower base,
• loads from impacts (eg, from boat landing operations, crane operations, aircraft landing), and
• loads from actuation of operation and control devices (yaw, pitch, brake, torque control mechanisms).
In Fig. 10.14, the approximate location of the application points of loads from RNA and hydrodynamics is shown together with the main coordinate system adopted by this chapter (as well as by the main standards of reference).
Only rough approximations of the above loads can be hand-calculated. For instance, in order to calculate the direct wind action on the tower, thus the associated shear and bending moments, one may use basic aerodynamics principles. Through consultations of the standards, wind shear values (eg, Ref. [1]) and dynamic amplification factors (DAFs) (or gust factors from Refs [61–64]) may be obtained to calculate and integrate the drag force along the tower span. The determination of most of the other load components, however, demands a more rigorous CAE tool and coupled numerical simulations.
Whereas only a detailed loads' analysis can quantify the coupled effects of all load sources, a few general considerations can be made. The primary loading source for the tower proper comes from the aerodynamic loads induced by the rotor. Nonetheless, gravitational and inertial loads associated with the RNA mass should not be overlooked when calculating the stability and buckling resistance of the tower. This is especially true for ULS loads. In general, fatigue loading tends to dominate the design of the flanges and welds, while the tower shell may be driven by modal and buckling-strength requirements. Moreover, depending on the water depth and the size of the OWT, the hydrodynamics may play a very important role in FLS. For shallow-water sites, tower DELs are dominated by aerodynamics. As water depths increase, hydrodynamic loads become progressively more important. Due to the aerodynamic damping behavior (discussed below), if wind and waves are misaligned or if the machine is idling (or parked), the DELs from wave action may increase substantially. Therefore, it is important to have a good understanding of the expected OWT availability and account for its positive or negative feedback on the FLS of the entire system.
10.4.1.1. Turbine loads (RNA loads)
From a steady-state point of view, RNA loads reduce to three forces and three moments along the main coordinate axes; they are generated by the rotor aerodynamics under asymmetric conditions due to wind shear and rotor orientation (eg, non-zero yaw and tilt angles). Further periodic loads are generated by structural imbalance, tower shadow effects, and turbulence sampling as discussed below in Section 10.4.1.2. In addition to the normal operational loads, transients, such as shutdowns, and blade/rotor/yaw faults can give rise to important ULS loads for the tower and cannot be underestimated. Other important load contributions derive from the gyroscopic effects when the turbine yaws with rotor spinning.
The thrust is the largest responsible for the bending moment distribution along the tower. If the turbine is a downwind turbine, the additional effect of the gravitational load due to a downwind offset of the RNA center of mass (CM) from the tower centerline may significantly increase the tower utilization. In an upwind turbine, the RNA mass contribution to the bending moment is minimal and any upwind offset of the RNA CM can be conservatively ignored, besides, the P–Δ effect would tend to reduce this effect anyway.
From an FLS standpoint, the aerodynamic loads tend to dominate the design, with the exception of cases in deep-water sites where hydrodynamics excitation and low damping situations (see Section 10.4.1.2) can also be important.
RNA loads can, at first approximation, be calculated pseudo-statically, considering a rigid tower, but DAFs should be used to start off the tower design. Thrust can increase by a factor of 1.5 or more due to inertial and gust effects. Short of high-fidelity computational fluid dynamics (CFD) simulations, rotor loads can be calculated via either beam element momentum theory (BEMT), generalized dynamic wake (GDW), or free wake vortex methods (FWVM) [65]. BEMT is fairly efficient and generally accurate, but tends to miss effects associated with the dynamic variations of the inflow and with the time-dependent evolution of the rotor wake. These effects are better captured by the GDW theory, which solves the linearized, inviscid equations of motion [66,67]. A higher-fidelity option, the FWVM methods, can track the vorticity in the rotor wake and the bound vorticity at the blade lifting lines (or surfaces depending on the level of fidelity). By using the Biot-Savart law, the flow field of interest, and the induced velocity at the rotor, can be resolved. Any of the solution methods will need to account for unsteady aerodynamics and dynamic-stall effects that can be present especially under skewed flow conditions (eg, with yaw errors > 0 degree). Among other features to model are tower flow-damming (or shadowing) effects, blade root and tip losses, and fully turbulent, 3D inflow-field, possibly accounting for wake effects within a park array. For a review of aerodynamics theory and requirements for turbine aeroelastic codes, see Ref. [67].
Dedicated turbine AHSE tools normally let the user choose the aerodynamics module options and the aerodynamic solver. They can account for the motion of the blades due to elastic and rigid motions of the hub, as well as yawed flow situations in fairly accurate fashion, returning good estimates of the loads.
10.4.1.2. 1P–nP forcing, resonance avoidance, and modal requirements
From what is stated above, major loads for a turbine tower derive from the aerodynamics and inertial actions of the RNA. Rotor aerodynamics is complicated by turbulence and unsteady phenomena, which result in effects that cannot be modeled via a quasistatic approach. Additionally, turbulence and wind shear sampling by the rotating blades produce significant periodic excitations at a frequency equal to n times the rotor rotational frequency, or nP (as well as higher harmonics), where n is the number of rotor blades. Moreover, the tower itself affects the flow field (tower shadow or damming effect), which, when sampled by the rotor, further yields an nP forcing. Finally, rotor imbalances (both aerodynamics and structural, also quantified by the standards [3,23]) give rise to 1P excitations.
For modern OWTs, the natural frequencies of the SSt and blades, and the main rotor excitation frequencies are in a comparable range. This leads to a potential coupling in the vibrational modes among the various components.
At a crude level of approximation, an OWT can be regarded as a series of damped harmonic oscillators (see also Fig. 10.31 for the one-degree-of-freedom oscillator). It can be easily shown that the equation of motion for the generic j-th modal degree of freedom (DOF) can be written as:
[10.1]
where for the j-th eigenmode, xj describes the DOF variable; mj is the generalized modal mass; ω0,j is the eigenfrequency; Fj is the generalized dynamic forcing function; and ξj is the damping ratio.
Coincidence of structural eigenfrequencies with wind turbine dynamic forcing, known as resonance condition, can lead to large amplitude stresses and increased damage rates. Simplistically, this is illustrated by the DAF trend visible in Fig. 10.15, where the DAF is the ratio of the maximum amplitude of the dynamic response to the static response, ie,
[10.2]
where ωj is the forcing frequency associated with the j-th mode of vibration.
For the above reason, the wind turbine rotor blades and SSt are designed to avoid resonance potential. In particular, the current practice is to design the wind turbine SSt such that the tower fundamental resonance frequency does not coincide with either the rotor (1P) or blade passing (nP) frequencies. Depending on the placement of the natural frequency with respect to the operational 1P and nP ranges, the SSt is defined as stiff–stiff, soft–stiff, or soft–soft (see Fig. 10.16). The stiff–stiff option may lead to extensive use of structural steel, and it is generally avoided for pure cost reasons. The soft–soft configuration may be very advantageous from an economical standpoint, but system frequencies may be dangerously close to the wave spectrum band with high-energy content. Thus far, the soft–stiff approach, where the support first bending eigenfrequency is placed between the 1P and nP ranges, has been the preferred choice. In any case, this approach has significant consequences for the structural design of OWTs, and may very well be the first driver for the total mass of towers, piles (as in the case of monopiles (MPs)), and SbSs.
Obviously, for floating systems, an additional set of resonance conditions associated with the rigid body sea-keeping modes of the floating platform must be assessed.
It is therefore not surprising that the first natural frequency of the SSt (hereafter, f0) plays a critical role within the overall system dynamics, and it is the first and foremost structural parameter to be assessed in tower design. During the front-end engineering design (FEED) (ie, when within the inner arms of the spiral of Fig. 10.13), f0 shall be accurately calculated via modal analysis in 3D finite element analysis (FEA) commercial software. In the preliminary phases of design, however, approximated expressions can be used, as for example Eq. [10.3]:
[10.3]
Eq. [10.3], shown in Ref. [68], is strictly valid for an untapered and rigidly cantilevered tower, and shows dependency on: L, the tower length, or SSt length; mtwr and mRNA, the tower mass or SSt mass, and RNA mass; E, the Young's modulus; Jxx, the cross-sectional area moment of inertia. Extensions of Eq. [10.3] have also been offered in the literature, such as Eq. [10.4] from Ref. [69]:
[10.4]
where the stiffness (γK) and mass (γM) correction factors must be calculated as a function of the structure stiffness, applied load, and soil-pile (foundation) stiffness (see Ref. [69] for details).
Energy-based methods, such as the Rayleigh–Ritz method, can be effectively used to arrive at a good approximation of the first modeshape and eigenvalue of the SSt. Using a Rayleigh–Ritz approach, and a trigonometric (or modal) representation of the tower node displacements (y(z, t)), f0 may also be written as:
[10.5]
where the integrals are written as functions of the span coordinate z, but can also be easily discretized for numerical quadrature. In Eq. [10.5], ϕj(t) is the j-th modal coefficient, or periodic function of time; ρ(z)A is the distributed mass; y is the lateral deflection of the tower along its span described by a linear combination of functions satisfying the boundary conditions (for instance known mode-shapes for a similarly constrained configuration); and the prime symbols denote derivatives with respect to z. By including the effect of the SSI stiffness (assuming krot, klat the equivalent rotational and lateral elastic constants respectively) the same method yields:
[10.6]
As can be seen from the above equations, the RNA mass and hub height are two main parameters affecting f0. While the RNA mass may be more difficult to change even in a fully integrated OWT design approach, the hub height can be manipulated to fine-tune the tower response, often more efficiently than changes in shell diameter and thickness.
The problem of resonance avoidance is nonetheless complicated by the limited accuracy in the predicted forcing amplitudes and system resonant frequencies. On the one hand, rotor aerodynamic load amplitudes depend on stochastic inflow characteristics. On the other hand, the resonant frequencies are also a function of the soil and foundation physical properties, which can only be known with a certain level of uncertainty. Soil–structure interaction characteristics are also time-dependent (eg, due to scouring effects). Scouring and reduction in foundation integrity over time are especially problematic; by reducing f0, these effects may push the system resonance to the low frequencies, at which much of the broadband wave and gust energy is contained, or align it more closely with the 1P band.
To an extreme, actual f0 can be up to 10–20% off the calculated ones because of miscalculated soil effects. It is crucial to account for this possibility and to verify the actual turbine performance in the commissioning phase. The design standards, for example, offer specific guidance toward resonance avoidance. Ref. [29] recommends avoiding operating in a frequency interval defined as the tower (SSt) eigenfrequency ±10%, whereas Ref. [15] recommends a minimum distance of 5% from the fundamental system eigenfrequency. Adopting an extra 10% margin on top of what the standards suggest is a good strategy for the first steps in the design spiral. During commissioning, the control system and operating regimes could be altered to reach acceptable parameters in case the resulting modal performance is not as expected. Alternatively, costly retrofits to the tower configuration, including the addition of dampers, could be envisaged.
An example of the response of a wind system with f0 inside and outside the 1P frequency band is given in Fig. 10.17, which shows the power spectral density (PSD) of the mudline overturning moment (OTM) for a typical 5-MW OWT. The graph is representative of the undesirable shift in f0 that may occur due to either unexpected soil conditions, degradation, or installation issues. It can be observed how the SSt response is dangerously amplified with direct consequences on fatigue loads.
Figure 10.17 Typical power spectral density response for the SSt FA bending moment at mudline during operational conditions for a 5-MW turbine. The two lines correspond to an SSt with f0 outside (without resonance) and inside the 1P frequency band. From T. Fischer, W. de Vries, Final Report Task 4.1-Deliverable d 4.1.5-(wp4: Offshore Foundations and Support Structures), Upwind Project 4.1, Universit at Stuttgart, Allmandring 5B, 70569 Suttgart, Germany, 2011 Contract No.:019945 (SES6).
Besides the frequency content of the structural response, the other key factor in the resulting loads is the system damping. If sufficient damping can be guaranteed, say via adoption of tuned mass dampers (TMDs) or active mass dampers (AMDs), proximity to resonance conditions may no longer be a limiting factor. The damping is usually given for each principal (j-th) mode of vibration in terms of cj, or more often in terms of either δj or ξj with respect to the cc,j damping ratio, see Eqs. [10.7] and [10.8].
[10.7]
[10.8]
Damping derives from, in order of contribution entity, aerodynamic effects, structural features (materials and additional dampers), soil, and hydrodynamics. Aerodynamic damping is primarily related to the aerodynamics of the rotor under a fore-aft (FA) oscillation of the tower top. As the tower head moves upwind, the relative wind speed increases, thus the blade airfoils' angles of attack increase, generally leading to an increase in lift, drag, and resulting thrust force. The opposite occurs when the tower head moves downwind. Additionally, the drag on the tower also participates in a similar fashion to increase damping, but this effect is generally small, as the effective wind speed change is insignificant, and the main effect is through the mentioned lift/thrust mechanism with changes in the rotating blade angle of attacks (AOAs).
Because of the foregoing, tower side-to-side oscillations have little or no damping, as nearly no aerodynamic damping exists. Furthermore, under idling or parked conditions, aerodynamic damping is minimal as well. This is particularly important for those loading scenarios where waves and wind present a substantial misalignment and wave forcing may be falling onto the natural frequencies of the system. In sites with large misalignments between wind and waves, the side-to-side bending moment can become a design driver in FLS.
Structural damping is primarily due to internal friction in the materials of the SSt. Most of the energy dissipation occurs at the joints, and in particular at grouted connections.
Soil damping mostly originates from ground deformation due to the action of the structure piling.
Additionally, an adequate control system, for example, acting on generator torque and blade pitch, may further decrease vibrational amplitudes in towers and SSt. For floating turbines, tower/SSt damping along roll, pitch, and yaw may be an absolute necessity to achieve with dedicated collective and cyclic pitch of the rotor blades.
Different control strategies, as for example via either the so-called “rotational speed window” (or frequency skipping) that acts on generator torque, or via tower feedback control and independent pitch control (IPC), acting on blade pitch, have been proposed (see for instance Ref. [70] for an excellent review on the subject). These strategies work well under operational conditions. As discussed above, for deeper waters where hydrodynamics may dominate the FLS loading state, idling cases with severe sea states can be design drivers. In those cases, standard torque and pitch controllers are ineffective. A “soft-cutout strategy” may be employed, however, which de facto extends the cutout wind speed and derates the turbine, thus reducing idling time spent in high wind/wave conditions. These strategies are very promising and may also bring forth larger energy capture, but need to be carefully devised. Alternatively, one could incorporate a TMD into the SSt design from the beginning (see also Section 10.6.1).
Aeroelastic tools directly account for aero-hydrodynamics and TMD damping; soil and structural (internal) damping can be input by the user. It is usually good norm not to overestimate the damping. Recent studies have shown that for 3.6-MW wind turbines a logarithmic decrement of some 12% is achievable [71].
10.4.1.3. Direct action from the wind
Direct wind loading on the tower is due to aerodynamic drag on the structural shells. The wind profile can be taken as in Eq. [10.9], where the αs is given by the standards (eg, Ref. [1]).
[10.9]
For a typical tubular tower, Eq. [10.10] can be used to calculate the pseudostatic loads on the tower due to wind action on its cylindrical or conical segments.
[10.10]
fa is the force per unit length due to wind aerodynamic drag, with ρa the air density, Dsh the outer diameter (OD) of the tower, U the wind velocity, and Cd the drag coefficient (≃ 0.6–0.7); all are potentially functions of height MSL. By integration along the span of the tower, including the thrust of the RNA, one can attain the total shear and bending moment along the tower segments. Normally the thrust of the rotor under operational DLCs is the prime responsible for the bending stresses in the tower, and for FLS verification the direct wind drag is less important; yet, parked cases under ULS conditions can give rise to important drag loads that cannot be underestimated, especially for high hub heights and smaller rotors.
The gust factor in Eq. [10.10] accounts for the effect on wind actions from the non-simultaneous occurrence of peak wind pressures on the structure surface together with the effect of the vibrations of the structure due to turbulence. Various methods to calculate Gf are offered by the standards (eg, Refs [61–64]), and more recent treatments with a focus on wind turbine towers can be found in the literature [65,72]. In Ref. [63], structures are defined as dynamically sensitive (or flexible) if their first natural frequency is f0 < 1 Hz (more detailed criteria can be found in Ref. [62], Parts 1–4). When this criterion is met, Gf can be significantly larger than 1.
Besides ULS cases, turbulent wind actions can be important in the vortex-induced vibrations, which can be observed when the rotor is either not operating or altogether absent during installation and maintenance. The frequency of vortex shedding is tied to the Strouhal number and a critical wind speed can be calculated as:
[10.11]
where Dsh can be taken as the tower-top OD. St, the Strouhal number, varies around 0.15–0.20 depending on the tower taper ratio. It should be verified that critical wind speeds are within the operational regime, where the effect of the spinning rotor would tend to disrupt the mechanism of vortex formation behind the tower. Note that the cross-wind oscillations are insidious due to the reduced damping offered by the rotor, but again they are unlikely in normal operation conditions. During installation and/or maintenance, the tower has higher natural frequencies and the probability of cross-wind resonance excitation at low and mid-wind speeds should be determined.
10.4.1.4. Hydrodynamic and ice loads in the case of a MP tower
The effects of wave and current kinematics on the loading of a monopile tower can be calculated via the Morison equation for slender members:
[10.12]
where fw is the force per unit length due to wave and current kinematics; ρw is the sea water density; Dsh is the tower OD; Uw is the wave and current velocity (vector sum); and Cd and Cm are the drag coefficient and the added mass coefficient, respectively.
Following [1], two components of sea current velocity shall be taken into account:
• wind-generated, near surface currents, and
• subsurface currents generated by tidal motion, storm surges, and atmospheric pressure variations.
The subsurface current velocity can follow a power–law profile as a function of water depth. For near-surface currents, it is common to assume a linear distribution of water speed with depth, with surface speed proportional to the hourly wind speed at 10 m MSL, and with effects vanishing below 20 m depths. Wave and current velocities should be summed vectorially to render Uw, which may be augmented to also contain the structure deflection velocity. The wave particle kinematic velocity can be calculated via Airy and Wheeler stretching theories [28,73].
The coefficients Cd and Cm should account for the presence of marine growth, and depend on Reynolds and Keulegan–Carpenter numbers, thus on the specific DLC under consideration (see also Ref. [28]).
Corrections to the Morison equation have been proposed for diffraction effects (eg, the MacCamy-Fuchs correction [74]), and for wave non-linearities. Additionally, one should verify the probability of breaking wave occurrence (normally when Hw/dw > 0.78) and associated slamming loads on the SSts; Ref. [11] prescribes a simplified equation to account for these additional loads. Clearance (for example an air-gap of approximately 1.5 m) between the wave crest and the components unable to withstand these loads should be envisioned.
Other concentrated loads may derive from the presence of secondary steel structures, such as boat landings, and J-tubes, which may attract more wave loads. These loads are normally of lesser entity, yet the welded connections to the principal steel can be a source of crack nucleation and corrosion. Efforts should be undertaken to verify that cracks are not able to propagate in the main load-bearing structure.
Beside direct hydrodynamic loads, an MP tower may need to withstand sea-ice loading. In waters with winter climates, ice loading may be severe, and several situations are to be investigated as, for example [1]:
• horizontal loads due to temperature fluctuations in fast-ice covers,
Figure 10.18 Example of an ice-cone installed at the base of the towers at the Nysted wind farm, Denmark.
• horizontal loads from moving ice floes, and
• pressure from hummocked ice and ice ridges.
A particularly important aspect to assess is the possibility of dynamic locking of the ice-breaking frequency to the wind turbine eigenfrequencies with consequences on both FLS and ULS. Specific CAE tools exist to investigate various types of ice loading configurations, and the standards provide good guidance (eg, Refs [75,11]), but Arctic engineering experience should be sought after during preliminary design in order to avoid reliability risks and expensive retrofits at later stages. A typical feature used with monopiles is the so-called ice-cone (see also Fig. 10.18), which induces bending stresses in the ice sheets that can then more easily break off, thereby reducing pressure on the SSt.
Other aspects to consider are those associated with seabed movements, including sand waves, shoals, and scouring. These effects can result in consequences to soil–structure interaction, removal or vertical and lateral support to the monopile and change of dynamic properties of the entire SSt. If these aspects are expected to be significant, the foundation design may need to consider them via embedment length modifications and possible scour protection.
10.4.1.5. Gravitational, inertial, and impact loads
Inertial and gravitational loads are both static and dynamic loads resulting from vibration, rotation, gravity, and seismic accelerations. The self-weight of the OWT is simply given by the mass schedule of the various components. For the design of the tower, the RNA mass must be known fairly accurately. Ref. [3] assumes γf ≃ 1.1 on gravitational load (to compare to 1.35 for aerodynamic loads) to account for uncertainties in the as-built masses. For transportation and erection cases, γf ≃ 1.25. Other inertial forces, when calculated separately (ie, not via AHSE coupled approaches), should also be factored (∼1.2 or 1.35 for normal and extreme DLCs, respectively, following Ref. [3]). For FLS and SLS, unity load factors may be assumed.
An earthquake analysis is normally not required for areas where the ground acceleration is less than 0.05 g. However, for certain sites, seismic activity may be combined with increased environmental loading (large wave amplitudes up to tsunami-type waves) and that should be investigated as an additional DLC, or it should be ensured that the basic load envelope from the standards' DLCs encompasses these loading scenarios.
Seismic loads may be assessed in accordance with Refs [3,23,63,64,76]. The analysis of the dynamic response to an earthquake can be performed via AHSE simulations with a given time history of the ground acceleration. Response spectrum analysis can also be used (see for example Refs [63,64,76]). The standards provide a way to combine seismic loads with other environmental and turbine state loads under normal conditions (eg, Refs [3,23]): the ground acceleration shall be evaluated with a 475-year return period, and the larger of either the average operational loads over the OWT lifetime, or the loads associated with an emergency shutdown should be superimposed to the seismic loads. For seismic loads, the PSF is taken as γf = 1. Recent studies [71,77,78] demonstrate the importance of seismic loads for the larger hub heights and tower-top masses.
Impacts from crane operations, aircraft landings, and accidental boat collisions should all be investigated. The most likely events among the above-mentioned ones are boat collisions. Dedicated boat-landing fenders are designed to plastically deform under impact, but other sections of the SSt shall withstand general impacts, without exceeding yield strength. Ref. [3] prescribes a calculation method for the horizontal load (Fsi) from boat impact:
[10.13]
where msi is the displacement mass of impact vessel; vsi is the vessel impact speed; csi is the stiffness of the impacting part of the vessel; and asi is the added mass coefficient during collision (1.4–1.6 sideway impact, 1.1 bow or stern collision).
Finally, loads from faults and emergency stop events can create dangerous impulses and shock load spectra on the entire OWT, and can culminate in very large deflections and loads. As discussed in Section 10.4, they need to be investigated following the prescriptions in the standards.
10.4.2. Aero-hydro-servo-elastic simulations
Whereas analytical relationships and approximate equations that make use of pseudo static approaches can be used for the preliminary design of OWT towers, more extensive loads' simulations are inevitable in their final design and optimization. The reason for this necessity is multifold. On the one hand, the complex structural dynamics of rotating machinery and stochastically varying environmental loads make simplified approaches too coarse. One might risk overconservatism (hence large costs) by accompanying larger safety factors to simple equations, or, more dangerously, might miss important dynamic coupling phenomena. As already stated, in fact, excitation frequencies and major component eigenfrequencies are in close proximity, thereby raising the possibility of dynamic coupling among vibrational modes of different parts of the OWT. Moreover, aeroelastic non-linearities and significant transient loads from start-ups, shutdowns, and fault events are difficult to model via pseudostatic approaches and their analytical treatment is normally out of reach. For all these reasons, the design of OWT towers and other components must be performed in integrated fashion, where fully coupled loads' simulations can be undertaken. A large variety of CAE tools exist, with various levels of detail applied to the modeling of the different components. Rotor aerodynamics, hydrodynamics, control dynamics, soil and foundation dynamics, as well as structural dynamics can all be accounted for via a combination of multibody formulations, modal reduced systems, and finite element frameworks (an example of such a framework is given in Fig. 10.19).
Figure 10.20 Example of time-series outputs from CAE tool loads' analysis simulations of a 5-MW turbine on the OC4 jacket. From top to bottom, time series of: wave elevation; generated power and blade root flapwise bending moment; OTM (fore-aft) moment at the base of the tower and at the mudline; axial force magnitude for two pile heads, one located upwind and one downwind.
Example of time-series plots from fully coupled tools are shown in Figs. 10.20 and 10.21.
Engineers should always question their models' results, and it is important to have a knowledge of the efforts undertaken for the verification and validation of the various tools before accepting their outputs. Given the lack of maturity of the offshore wind industry, validation data are still in their infancy. Moreover, validation is challenging because of difficulties associated with quality control of the measured data at sea, difficulty in selecting more standard load cases from a real-life, long-term measurement campaign, and testing costs. Code-to-code comparisons offer a great way to substantiate the validity of new codes, when compared to more established and extensively validated tools. Examples of these efforts are the offshore code comparison collaboration (OC3) and OC4 projects [79–81] (see also Fig. 10.22). In general, it is important to have the CVA on board to vet and approve the use of the CAE tools of choice.
The output of AHSE loads' simulations is then post-processed to verify ULS and FLS limit states, where the structural integrity is checked following guidance from codes and standards.
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