Stochastic response reduction on offshore wind turbines due to flaps including soil effects

Soil Dynamics and Earthquake Engineering 114 (2018) 174–185

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Stochastic response reduction on offshore wind turbines due to flaps including soil effects

T

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Shilpa Thakur, K.A. Abhinav, Nilanjan Saha

Department of Ocean Engineering, Indian Institute of Technology Madras, Chennai 600036, India

A R T I C LE I N FO

A B S T R A C T

Keywords: Offshore wind turbine Soil-structure interaction Non-linear dynamical analysis Blade slotted flaps Probabilistic analysis

This work attempts to investigate the load mitigation effects on foundations of NREL 5-MW offshore wind turbine (OWT) supported on fixed structures using blade trailing edge flaps. The analysis is subjected to turbulent wind and irregular wave loads. The offshore wind turbine is simulated for five met-ocean conditions for Indian scenario, covering operational to the parked region of turbine. Sea states being stochastic, the responses are obtained using average of Monte Carlo simulations. The blade element momentum theory is used to obtain the aerodynamic loads by modelling in a multi-body framework while the hydrodynamic and geotechnical analysis are performed in a finite element framework. Soil-structure interaction is modelled using nonlinear Winkler spring model along the length of the pile. The trailing edge flaps are numerically implemented through a dynamic link library into the aerodynamic program. Loose sandy soils with uniform density is considered for analysis. The results bring out the importance of including blade trailing edge flaps in OWT studies with significant response reduction (2.1–16.0%) for designing pile foundations.

1. Introduction Offshore wind energy is increasingly being considered as a reliable source of clean and renewable energy. Wind turbines sited offshore are attaining popularity world-wide due to accessibility of sites, stronger and consistent winds with lesser turbulence and smaller shear than on land. In offshore deployment, due to increment in rotor size, the offshore wind turbine (OWT) blades are more flexible and subjected to vibration by wind loads along with tower interaction, which leads to structural or mechanical damage, thus increasing the downtime of the wind turbine. From this point of view, the analysis of combination of load-effects plays an important role for OWT. Almost all of the existing OWTs in European waters are supported on fixed structures [1]. These wind turbines are mostly installed in shallow water depth (20–30 m) on either monopile or the concrete gravity bases, but these technologies are not economically feasible for deep water depth (more than 45 m). Thus in order to maintain strength and stiffness requirements, space frame (tripods) and lattice frame (jacket) sub-structures will be required. Foundations represent a sizeable component in the capital expenditure for an offshore wind farm [2]. Therefore, minimizing the offshore foundation (both the platform and pile support) cost becomes imperative. In this paper, a small structural change in the blade section is

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proposed by which significant reductions may be achieved in the substructural loading. The present change is done by the introduction of slotted flaps (or aerodynamic active device that change with wind speeds) in the aerofoil section of blades. While the effects of the change may not be that predominant in offshore rigid construction, however in loose soils (of sandy nature), this can be an effective measure in mitigating loads wherein the deflection component becomes large due to parametric/flutter type excitations. In this paper, the NREL 5 MW benchmark offshore wind turbine [3] (having a NACA 64-618 airfoil section) is considered to be supported on three types of widely used fixed platforms – monopile, tripod and jacket sub-structures; which are all assumed to be located in loose sandy soils. Existing literature related to load mitigation models of wind turbine through aerodynamic changes can be broadly classified into two categories: as some that focus on structural changes (turbine blade's trailing edge flaps); and others that include advanced control techniques (through pitching of blades and restricting rotatory motion of drivetrain) to mitigate the loads. In offshore structural analysis, the effect of soil structure interaction (SSI) can become a guiding factor for design [4,5]. Being an interdisciplinary topic, the geotechnical analysis of OWTs usually resort to describing the soil effects on turbine by heuristically assuming aerodynamic/hydrodynamic loads (wind loads as sinusoidal loads, ignoring wave loads or assuming platforms as Euler-

Corresponding author. E-mail addresses: [email protected] (S. Thakur), [email protected] (K.A. Abhinav), [email protected] (N. Saha).

https://doi.org/10.1016/j.soildyn.2018.07.004 Received 29 April 2018; Received in revised form 23 June 2018; Accepted 8 July 2018 0267-7261/ © 2018 Elsevier Ltd. All rights reserved.

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monopile, tripod of asymmetric nature and tetrapods on suction caissons [27,28]. The results showed the importance of rocking modes of vibrations in the response of OWT supported through multipod foundations. In the present study, Winkler based FEM is used to account for soilstructure interaction which has been reviewed in previous studies [29–31] and acquired by standards [32,33]. Effectiveness of this p − y method has been investigated for monopile design with the suggestion for the load-displacement curves to be modified in order to mark observed soil-pile stiffness overestimation [34,35]. Also the p − y approach is assessed experimentally for dynamic application [36]. Certain limitations of the p − y method has been discussed and suggestions has been proposed [35,37]. The effect of SSI using two different flexible foundation models ( p − y and p − y with pile group effect) on the response of an OWT with jacket foundation has also been investigated [38]. The aerodynamic code FAST [39] and the hydrodynamic program USFOS [40] are used in this work. The geotechnical effects are captured by a combination of USFOS and FAST to obtain the full system model. The TEFs are modelled using computational fluid dynamics (CFD) and appropriate changes are done in the FAST model to account for their effects. Simulations were then performed for various load cases of the wind turbine supported by fixed-bottom platforms. The load analysis helped to characterize the potential design loads and the instabilities resulting from the coupling between the OWT with flaps in the presence of combined wind and wave excitation by including SSI. Design modifications using these trailing edge flaps on turbine blades are detailed, which will reduce loads and improving turbine response thus lowering the foundation cost. The objective of this study is to examine the response of OWT with the TEFs, taking into consideration the SSI. Section 2 describes in detail, the numerical modelling of the OWT using the blade flaps, support structures and the soil model. In Section 3, the methodology adopted for the analysis is explained. Section 4 presents the results of the work and highlights the importance in lowering the foundation cost. The paper ends with Section 5 mentioning the important takeaways from this work.

Bernoulli beams). In this work, therefore a comprehensive attempt is made to examine the blades trailing edge-flaps (TEF) effect on OWT response by coupling the influence of soil along with aerodynamic loads and hydrodynamic loads. Also the load mitigation technique accomplished here is through introduction of aerodynamic active devices i.e., trailing edge blade flaps in the rotor blade. Aerodynamically active devices, showing more effectiveness with spanwise controls have gained significant research interest over the last decade as it ensures stability and reduces the fatigue experienced in the wind turbines. Several numerical investigations have been done, i.e., the modelling and optimization by including blade trailing edge flaps with the aim to reduce the cost of energy [6–8]. These investigations have shown the significance of the aerodynamic devices in power capture optimization. Smit et al. [9] has shown that through the flap deflection, the maximum power output can be increased in low fatigue wind region by proper flap sizing configuration and control. Effect of deformable TEF (DTEF) in reduction of fatigue load of OWT have shown promising results in comparison with collective pitch method [10]. Also the DTEF resulted in the improved performance of the turbine. Zhang et al. [11] also showed that through the DTEF not only there is a reduction of fluctuations in power and thrust, but also in the blade fatigue loads. Attempts have made for reduction of loads through rotor blade control schemes [12]. These schemes also reduce the loads on platforms followed by reduction in the total design cost of OWT [13]. For examples, individual pitch control alleviates the cyclic loadings on rotor by adjusting the entire blade individually, resulting in response delay whereas activating smart rotor control devices alters the aerodynamics of the blades with comparatively less power requirement [14,15]. For this study, since the focus is on understanding response effects due to aerodynamic active device, the widely preferred control approach based on proportional integral derivative (PID) method is chosen. None of these works have focussed on understanding the effects on fixed OWT response with the additional appendage effects. Most of these works have ignored the effects of soil assuming the soil to be stiff [16,17] or the stiffness curves (lateral and longitudinal ones) are modelled by static springs (independent of loads) [18] or by extending the tower into the soil to a fixity level [19,20]. In the past, it was shown that the dynamic response with the inclusion that SSI greatly influenced the fatigue characteristics of the OWTs [21]. In many countries, the preferable wind farm locations are in areas of soft soil and therefore, the soil structure interaction (SSI) of pile supported OWT has gained significant importance. Bazeos et al. [22] pointed out that for soft soil the interaction between OWT platforms and soil may be the critical consideration in designing the structure. Byrne and Houlsby [23] had shown that the chances of failure also increases due to the stochastic nature of load, the direction of wave and the uncertainty associated with the same. For such OWTs, the foundation and tower structure design is greatly altered due to SSI. Therefore, there is an important requirement to mitigate the uncertain loads, thereby increasing factor of safety as they are installed in harsh locations. Experimental investigations on the influence of soil stiffness on wind turbine response were conducted by Bhattacharya & Adhikari [24]. The results were validated by means of the finite element method (FEM), considering the wind turbine as an Euler-Bernoulli beam and assuming boundary conditions by replacing soil through translational and rotational springs. The rotor-nacelle-assembly was modelled as a lumped mass. Adhikari and Bhattacharya [25] obtained an expression for fundamental frequency for a wind turbine considering soil-properties which can be used as an initial guess in design process. Bhattacharya et al. [26] examined the change in the natural frequency due to cyclic loading through g tests on a scaled Vestas V90 3 MW model. They observed that formation of strains in soil and the relative position of natural frequency with respect to exciting frequency changes under cyclic loading. The studies were extended to different foundations –

2. Numerical modelling With continual increase in rotor/blade size, the aerodynamic and structural load are also increasing. Therefore, if one can reduce the loads at the blade root through the design innovation (slotted flaps), then there would be significant savings in the tower, drive train and ultimately the foundations. For mitigating the overall response, small appendages (as trailing edge flaps) are provided in the blade profile of the OWT [41]. Flaps are devices which are affixed to the aerofoil section to increase the lift forces in the blades. The flow control active devices, i.e., trailing edge flaps (TEF), are small appurtenances that are fixed to the aerofoil section in the aero-dynamically sensitive area of the blades. The assemblage consists of a fanning arrangement in addition to the existing blade profile. The introduction of the flaps cause a change in the variation of pressure over the aerofoil due to the gap that occurs between the aerofoil section and the TEF. Due to passage of air over the top of the aerofoil, the pressure gets lowered and camber increases this effect. With this change, lift coefficient increases and therefore the boundary layer effects gets modified along with camber effects. Due to the flaps, the flow of stay remains attached at higher angle of attacks also thus delaying separation. The air velocity that is leaving the TEF increases and therefore the total lift along the entire chord increases. TEFs are usually deployed at tips to obtain highest significance. Note that the drag coefficient also changes due to the distorted span-wise lift coefficient. Fig. 1 shows the flap hinge location in accordance with NACA airfoil sections [42]. The modelling of the slotted flaps in the wind turbine along are explained in the subsequent sections. For this study, 175

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Fig. 2. Mesh design for NACA-64-618 with trailing-edge flap profile.

Fig. 3. Force vectors acting on the blade profile and Flow along slotted flaps.

on the finite volume method. Initially, the model is created along with the domain. Further, the mesh is refined taking into account the significant characteristics of mesh designing as shown in Fig. 2 with more mesh density near the airfoil-flap assembly compared to far-field. SST k − ω turbulence model is employed . Once the satisfactory convergence is obtained, the forces in normal and tangential directions are used to determine aerodynamic coefficients for an angle of attack ranging from − 5° to 20° with the average Reynolds number Re = 6 × 106 as shown in Fig. 6. Before moving for flap modelling, it is important to understand whether the blade flap effects are modelled properly for further integration into aerodynamic code. For NACA64618 airfoil profile, the experimental data with flap are not available and therefore the present numerical analysis are validated using no-flap data [43] and Fig. 4 shows the drag and inertia coefficients with respect to angle of attack. Therefore, another NACA 23012 blade profile is considered for which experimental data with flaps are available. The blade profiles are modelled to understand the optimum location of flap with respect to the airfoil trailing edge effects for the flap actuation angle (at 10°). The results are shown in Fig. 5 which ensures that there exists a good match between experimental test [42] and presently employed numerical results. So, the present numerical approach can be adopted for carrying out the computational approximations of aerodynamic characteristics of airfoil-flap assembly ( Fig. 6).

Fig. 1. Flap arrangement. Table 1 Properties of NREL 5 MW OWT [3]. Parameter

Value

Power rating Rotor orientation Rotor configuration Rotor, Hub diameter Blade length Rated rotor speed Cut-in wind speed Rated wind speed Cut-out wind speed Rated tip speed Design tip speed ratio Rotor-nacelle-assembly mass

5 MW Upwind 3 - bladed 126 m, 3 m 61.5 m 12.1 rpm 3 m/s 11.4 m/s 25 m/s 80 m/s 7.55 350,000 kg

the NREL offshore 5-MW benchmark reference wind turbine [3] is chosen and its main characteristics are reported in Table 1. 2.1. Blade profile and sections Each blade of the NREL 5 MW wind turbine is 61.5 m long and is made up of DU (Delft University) and NACA (National Advisory Committee for Aeronautics) airfoils. While the two third of the blade length is made up of DU airfoils, the NACA 64-series makes up the remaining one-third length. The blades are divided into 17 different airfoils along the length using the Cylinder, DU40, DU35, DU30, DU25, DU21, and NACA64 airfoil profiles. Further details related to airfoil geometries and their lift/drag coefficients are given in Jonkman et al. [3]. NREL 5 MW wind turbine uses NACA 64-618 airfoil section near the blade tips. The trailing edge flap is applied to this aerofoil section with 18% thickness on the outboard part of the turbine blades covering 25% of blade span, extending 20% of airfoil chord. In other words, the present focus of study is restricted to 20.5 m length from the tip of the blade which has 18% thickness. The flap deflection angle is limited to ± 5°.

2.2.1. Analytical model for flap Viterna and Janetzke [44] method is employed to obtain the same. The aerodynamic load calculation is based on the blade element momentum (BEM) theory which depends on the airfoil data, expressed through lift (Cl ) and drag (Cd ) coefficients. Any experimental data or numerical codes will usually provide this information for a limited range of α stall . But OWT calculations require these lift and drag coefficients for complete 360° angle of attack range as the turbine blades usually operates at high inflow angles. So it becomes imperative to extrapolate these limited results obtained from experiments or numerical codes. The lift and the drag coefficients are extended from the stall angle to α = 90° using an extrapolation technique – Viterna's method [44]. For obtaining values beyond 90°, those coefficients (obtained using Viterna's method) are reflected upon the α− axis in the graphs. The reflection is done with the assumption that the stalled and unstalled characteristics continue beyond the stall angle and the power (or the torque coefficient) are constant. Cd is reflected about α = 0°. The obtained Cl and Cd are given as input to the Aerodyn module [45]. The

2.2. Flap modelling and validation The numerical model is designed and analyzed using solver based 176

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Fig. 4. Comparison of numerical and experimental results for NACA 64618 airfoil section with no-flap.

Fig. 5. Comparison of numerical and experimental results for NACA 23012 airfoil section with external flap at flap angle 10°.

change in dynamic characteristics of OWT due to flap implementation is considered negligible because flap mass or stiffness is insignificant as compared to the blade mass. From the blade element profile as shown in Fig. 3, one can write the torque coefficient in terms of the lift/drag coefficients as:

B1 = Cdmax.

If the blade aspect ratio is considered to be finite, then one can write Cd max using the aspect ratio AR as

CD max = 1.11 + 0.018AR.

(1)

Cτ = Cl sin α − Cd cos α

τ = (A2 −B2) + (2A1 − B1)sin α tan α.

One can express, the lift and drag coefficients beyond stall using these above assumptions as:

(3)

Cd = B1 sin2 α + B2 cos α.

(4)

⎜

(7)

Using the assumption of constant torque with respect to wind speed, for B two distinct α 's, the Eq. (7) gives A1 as, A1 = 21 . Combining the lift and drag coefficients along with the torque equation (2) and the coefficient A1, the two coefficients A2 and B2 can be expressed as:

(2)

cos2 α ⎞ Cl = A1 sin 2α + A2 ⎛ and ⎝ sin α ⎠

(6)

Using the Cl and Cd (Eqs. (3) and (4)) and substituting in the equation for torque (2), one can write τ in terms of coefficients as

Inside the stalled region, the mathematical model that is used to obtain the correlation between the calculated and measured date is based on the condition of constant torque coefficient (or power). Even after stall it is assumed that those conditions are valid and the continuity equation is valid for stalled and un-stalled characteristics at stall angle. Torque (τ ) is expressed in terms of square of resultant velocity (Ures ) using the proportionality coefficient K τ as:

τ = Cl tan α sec α − Cd sec α.

(5)

sin α A2 = ⎜⎛Cl − Cd max sin α cos α ⎟⎞ ⎛ 2 ⎞ ⎝ ⎠ ⎝ cos α ⎠

⎟

B2 =

One is now left with finding out the coefficients A1, A2 , B1 and B2 in the above equations. If one substitutes α = 90° in Eq. (4), then the coefficient B1 is obtained as

Cd − Cd max sin2 α cos α

(8)

(9)

These above coefficient equations (8) and (9) can be used for beyond the stall angle conditions. 177

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flapwise bending moment is taken as primary input to control the flap motion in order to avoid fluctuations which may increase aerodynamic loads. Wind turbine model contains periodic terms in response arising in non-linear system. To control this, an inverse Coleman transformation is used to transfer blade variables from rotating-coordinate to fixedreference frame in order to implement proportional-integral-derivative (PID) controller. The PID controller based on the error input (e (t ) ) is employed which is expressed by controller law as

1 u (t ) = Kp ⎡e (t ) + ⎢ KI ⎣

∫0

t

e (t ) dt +

KD de (t ) ⎤ dt ⎥ ⎦

(10)

where KP , KI and KD represents the proportional coefficient, integration and derivation time constants respectively. As shown in Fig. 7, blade root flap-wise bending moments of three blades (My1, My2, My3 ) are transformed from rotating coordinate to fixed frame, thus giving the average blade root flap-wise bending moment, hub yaw-wise bending moment and hub tilt-wise bending moment (Myfw , Myyw , Mytw ). A superscript ‘ fw ’, ‘ yw ’ and ‘tw ’ denotes blade flapwise, yaw-wise and tilt-wise bending moments in fixed coordinate system. For simplicity, yaw and tilt moment are considered as independent and feedback control system is decoupled into two singleinput single-output (SISO) system. Keeping in mind the goal to reduce asymmetrical loads, reference value will always be considered as zero and thus governing equations for Myyw and Mytw are obtained as:

1 ⎡ θy (t ) = Kp ⎢ ⎜⎛0 − Myyw ⎟⎞ + KI ⎠ ⎣⎝

∫0

t

yw ⎛⎜0 − M yw ⎞⎟ dt + KD d (0 − My ) ⎤ y ⎥ dt ⎝ ⎠ ⎦

(11) Similar equation can be obtained for tilt-wise bending moment. Thus the yaw-wise and tilt-wise flap deployment angles in fixed reference frame (θy , θt ) are obtained which are further converted to rotating frame through Coleman transformation giving flap actuation angles (θ1, θ2, θ3) for the each blade as shown in Fig. 7. This feedback control approach is implemented with the aero-elastic code FAST.

Fig. 6. Lift coefficient (Cl ) and drag coefficient (Cd ) versus angle of attack (α ) curves for NACA 64-618 airfoil with flap of same profile at different actuation angles.

2.3. Implementation in the aerodynamic code 2.4. Platforms supporting OWT Currently, the reduction in the response is due to the slotted flaps is controlled using an external dynamic link library (DLL) through the Baseline type controller [46] which uses the proportional-integral-derivative (PID) algorithm. The turbine baseline controller operates the rotor at variable speed below rated condition, and limits the power above rated by collectively pitching the blades to feather, based on lowpass filtered measurements of the shaft speed. Flap controller is superimposed on turbine baseline controller which works independently. To control the flaps for load alleviation, a feedback control approach is adopted and Fig. 7 shows the overall methodology followed [14]. Blade

Offshore fixed platforms are generally supported by piles driven into the soil. Monopile, tripod and jacket support structures are amongst the widely chosen structures to support the NREL 5 MW wind turbine (see Fig. 8). All these support structures are presently modelled using Lagrangian based FE model accounting for non-linear hydrodynamic effects (through Morison's forces, Wheeler stretching and structural motions) along with geotechnical modelling (through nonlinear Winkler springs). This is done through the program USFOS [47]. Between two nodes for the platform, one beam element is assumed [47]. The geometric non-linearities is integrated using non-linear strain formulation with von-Karman approximation. It accounts for large displacements with moderate strains and also the coupling between lateral deflection and axial strain, thus representing element behaviour. For non-linear analysis, the loads increment proceeds step-wise and the load step is reversed if global instability is detected. USFOS uses the combined incremental, iterative approach. In the Newton-Raphson algorithm used by USFOS, the loads are applied in steps and iteration at each load increment is performed to obtain equilibrium. The displacement increment further calculates the strain from established relations, followed by stress, and then the internal forces are established. The iterations continue till the difference between external and internal load vectors reaches the minimum value. Each load increment contains a number of iterations for which the tangent stiffness needs to be updated through Newton-Raphson method. This whole procedure increases the computational time. Thus Newton-Raphson method is modified in order to keep the tangential stiffness constant over a number of cycles.

Fig. 7. Implementation of PID-based feedback controller approach. 178

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Fig. 8. Support structures supporting OWT (left: Monopile, center: Tripod, right: Jacket).

2.4.2. Tripod In comparison to monopiles, for deep water applications, tripods and jackets are more economical. Tripods are space-frame structures having three-legs which are supported on piles driven into the seabed. In the present work, the tripod is designed in accordance to the Offshore Code Comparison Collaboration (OC3) project [48] for a water depth of 45 m [34]. The maximum loads and moments on pile head at mudline were used for foundation pile design. Thus piles were designed to carry ultimate lateral and axial forces and moments at pile head. The properties of overall tripod support structure model is summarized in Table 3 and schematic diagram is shown in Fig. 8.

2.4.1. Monopile Monopile is the simplest structure with ease to design, fabricate and install, which can be accommodated to severe sea conditions. Due to size limitations, it is suitable for shallow waters (≤ 25 m). A monopile is a large diameter steel pipe pile, extending to a suitable penetration depth, below the mudline. A standard embedment depth with respect to the pile diameter (approximately six times) is initially considered to arrive at the final pile length [34]. The rotor-nacelle-assembly (RNA) is represented as a point mass on top of the tower. The tower is modelled using a series of step tapered beams. The cylindrical tower is attached to monopile through transition piece. The properties of overall monopile support structure model is summarized in Table 2 and schematic diagram is shown in Fig. 8. For the present study, the water depth and pile penetration depth are 20 m and 42 m, respectively.

2.4.3. Jacket Jackets are lattice frame structures with 3 or 4 legs, resting on piles, and offers a large overturning moment resistance. The Offshore Code Comparison Collaboration Continuation (OC4) jacket model [49] is

Table 2 Monopile support structure properties.

Table 3 Tripod support structure properties (Ccs: Central column section).

Properties

Values

Monopile Diameter and thickness Mass Tower base location above MSL

6 m, 0.065 m 285, 580 kg 10 m

Transition Piece Diameter and thickness Length

6.275 m, 0.065 m 15 m

Pile Diameter and thickness Penetration depth Steel density

8500 kg/m3

Modulus of elasticity

2.1 × 105 MN/m2

Tower Top diameter and thickness Base diameter and thickness

3.87 m, 0.019 m 6 m, 0.027 m

Properties Tripod Ccs diameter (constant) and thickness Ccs diameter (taper) and thickness Upper brace diameter and thickness Lower brace diameter and thickness Mud brace diameter and thickness Sleeve diameter and thickness Transition piece diameter and thickness

6 m, 0.065 m 42 m

179

Values

5.7 m, 0.05 m 3.14 m (bottom), 5.7 m (top), 0.05 m 2.475 m, 0.035 m 1.875 m, 0.025 m 1.2 m, 0.025 m 3.15 m, 0.045 m and 0.035 m (below mudjoint) 5.7 m, 0.05 m

Pile Diameter and thickness Penetration depth Steel density

3.15 m, 0.035 m 37 m

Modulus of elasticity

2.1 × 105 MN/m2

8500 kg/m3

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Table 4 Jacket foundation properties.

Table 5 Soil profile.

Properties

Values

Diameter and thickness Penetration depth Steel density

2.082 m, 0.060 m 45 m 8500 kg/m3

Modulus of elasticity

2.1 × 105 MN/m2

Properties

Internal friction angle (°) Submerged Unit weight (kN/m3 ) Relative density (ID % ) Initial subgrade modulus (MN/m3 ) Nature of soil

considered for this study at a water depth of 50 m. The foundation details are given in Table 4 and schematic diagram of jacket model is given in the Fig. 8.

Values Loose soil

Dense soil

28 10

38 10

20 29

70 30.8

Sand

Clay

2.5. Pile-soil model Piles supporting OWT can fail under axial loads through pull-out under tensile forces or punch-through under compressive forces. Unlike the case of traditional oil and gas structures, OWT foundation design is governed by lateral loading (wind and waves), rather than by the axial bearing capacity. Piles for OWT are rigid bodies and can fail due to toekick phenomenon due to movement of the soil wedge supporting the pile. In slender piles, lateral loads can cause failure by bending also. The pile-soil interaction can also be modelled through non-linear springs attached to nodes along the length of the pile. The pile foundation experiences large lateral loads, thus overall structural failure can be guided by the pile-soil model failure and therefore an important factor for the soil-structure interaction [50,51]. If these foundation models use linear springs, then there is a significant over-estimation of the system response in some cases [5]. The non-linear load displacement can therefore be modelled as set of discrete segment-wise springs or through the plastic hinge theory [52]. Offshore standards [32,33] advocate the incorporation of SSI using nonlinear springs along the pile length. The nonlinear lateral spring stiffness is calculated from the gradient of the lateral soil resistance(p) displacement(y) curve. Similarly, the stiffness in other directions is obtained from the variation of vertical displacement (z) with respect to resistance due to skin friction (t) and end-bearing (q) curves. The background of development of these curves are given in Reese and van Impe [53], Haldar et al. [54]. While the use of p − y curves for large diameter monopiles have been criticized in literature [35], design codes also suggest that they may be used after validation by numerical methods. The present work employs a finite element framework to model the soil resistance versus displacement curves. The stiffness parameter matched well with the values obtained using mobilized strength design method [55,56]. For this study, the soil component is represented by means of discrete non-linear springs (lateral, axial and end-bearing) along the length of the pile. These springs are placed at the nodes and are attached to the ground using spring-to-ground type elements. One may need to exercise caution during application of these concentrated nonlinear spring models. Though these models capture nonlinear loaddisplacement behaviour, these may be insignificant if the dynamic interaction requires continuum models (including damping as well). Moreover, if the spring stiffness is dependent on the loaded area (response dependent stiffness), then the present Winkler spring formulation may not capture the response properly. The soil parameters used in the present study are shown in Table 5. Fig. 9 shows the ensemble mean for the tower top displacement with dense and loose soil profile as mentioned in the Table 5. In order to observe the utmost blade flap effect on the wind turbine dynamic, OWT study in loose sand is considered where the effects will be more predominant [22]. Any number of nodes (aka springs) can be placed, however for obtaining a reasonable finite number the node convergence study is carried out. For this three different node spacings are considered. Fig. 10 shows the convergence study in terms of the response –

Fig. 9. Ensemble mean of tower-top displacement for dense and loose soil (cf. Table 5).

Fig. 10. Soil-spring density convergence monopile OWT with flaps at rated wind speed.

tower and pile top displacement – for three different spring spacing for monopile structure. The study signifies no remarkable variations with respect to spring convergence for other foundations. Note that plot is shown only for 30 s for clarity. Presently, the OWT response obtained for uniform (non-layered) soil profile converged with 14 layers. 3. Validation of OWT numerical model In the present study, the analysis model in USFOS [47] has been validated through comparison with SESAM Wind [57], for the jacket 180

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presence of soil. The wind loads acting at the OWT hub are obtained using FAST and subsequent coupled hydrodynamic-geotechnical analysis is performed in USFOS, with the similar wave generation capabilities of two programs.

Table 6 Comparative study of a representative maximum jacket response at the base. (BSF: Base shear force, OTM: Base Overturning moment). Load case

1 2 3 4 5

Wind speed (m/s)

6 11.4 18 24 30

SESAM wind

USFOS

BSF (MN)

OTM (MN m)

BSF (MN)

OTM (MN m)

5. Load case definition

1.20 1.49 1.40 1.25 1.52

47.12 118.38 71.34 66.45 72.30

1.22 1.51 1.42 1.26 1.54

47.16 118.44 71.69 66.91 72.36

Turbine operation is carried out for different met-ocean conditions covering wind speed in operating as well as parked condition. For each wind speed, turbulence intensity is obtained from IEC 61400-3 [59]. As waves are wind generated so they are correlated and probability based approach has been used to derive environmental load cases for OWT analysis. Wind and wave relation is calculated from joint probabilistic model represented by Johannessen et al. [60]. The sea-states embraces mainly three parameters of concern- mean wind speed, significant wave height and spectral peak period. The marginal distribution of mean wind speed is described by Weibull distribution Eq. (15)

OWT model. The ensemble average results for the maximum base shear and overturning moment, for the jacket structure are shown in Table 6 under five load cases. The results predicted by the two codes closely match each other and validates the usage of USFOS for bottom fixed OWT analysis.

U m E(Uw ) = 1 − exp ⎛−⎡ w ⎤ ⎞ ⎝ ⎣ n ⎦ ⎠

4. Load modelling

where m and n are the shape and scale parameters and Uw is the wind speed. Based on the Northern North Sea measurements shape and scale parameters are gives as m = 2 + 0.135Uw and n = 1.8 + 0.1(Uw )1.322 , respectively Johannessen et al. [60]. Further conditional mean and standard deviation for the significant wave height can be estimated by using these parameters. The significant wave height is represented by Weibull distribution and its expected value is given by the Eq. (16).

4.1. Wind loading Irregular wind is considered for the analysis. TurbSim [58] is used to generate the 3-D full field stochastic wind field. Accounting for the wind shear phenomena, wind velocity at particular elevation is computed using power law.

z ⎞ V (z ) = Vhub ⎛ ⎝ zhub ⎠ ⎜

a

⎟

(12)

Where V is the wind speed at height z, Vhub is wind speed at hub height and a is the power law exponent. The normal turbulence model (NTM) is considered for this study where turbulence intensity decreases monotonically with increasing wind speed. The frequency content of wind velocity is described through Kaimal spectrum given by Eq. (13).

SK (f ) =

4(σK )2LK / Vhub (1 + 6fLK / Vhub)5/3

(15)

1 E(Hs ) = nΓ ⎛ + 1⎞ ⎠ ⎝m

(16)

2 1 STD(Hs ) = n Γ ⎛ + 1⎞ − Γ 2 ⎛ + 1⎞ ⎠ ⎝m ⎠ ⎝m

(17)

Lognormal distribution is used to describe the peak period and the expected value for the peak period is obtained as shown in Eq. (18).

U − E (Uw ) ⎞ ⎫ ⎛ ⎞ . E (Tp) = ⎜4.883 + 2.68(Hs )0.529⎟ × ⎧1 − 0.19 ⎛ w ⎨ E (Uw ) ⎠ ⎬ ⎝ ⎭ ⎝ ⎠ ⎩ ⎜

(13)

Where f is the cyclic frequency, LK is the integral scale parameter, σK is turbulence standard deviation, Vhub is the mean wind speed and SK is power spectral density function. The aerodynamic loads acting on the blades and the hub of the OWT are computed using the blade element momentum (BEM) theory, i.e. the total aerodynamic force on the blade can be determined as the sum of the forces acting on the discrete blade elements along its span. BEM model is considered along with all 3-dimensional corrections and semiempirical Beddoes-Leishman model for the dynamic stall. 3D effects arising due to generation of vorticity at the flaps extreme is accounted in BEM theory in accordance with the Beddoes-Leishman model formulation.

⎟

(18)

Here, E(Uw ) is the expected value of wind speed and given as

E(Uw ) = 1.764 + 3.426(Hs )0.78 .

(19)

Using above relations, the sea-states values for different load cases are obtained as shown in Table 7. These load cases are representative of an eastern coast of India. For this study, the response at different metocean sea states are analyzed and observed. The velocity is chosen with the intent to cover operating as well as parked conditions. The operating condition considers different regions aerodynamic curve i.e., around cut-in speed, close to rated wind-speed, in the domain where the pitch control is acting and in the vicinity of cut-out wind speed. 6. Results and discussion

4.2. Hydrodynamic loading

6.1. Uncertainty analysis

Ocean random waves are represented through wave energy spectra which characterizes the distribution of the energy of an ocean waves with respect to frequency. For this study, JONSWAP wave spectrum given by Eq. (14), represents the irregular sea-states.

In order to carry out the dynamic analysis, an appropriate time step Table 7 Load cases for OWT analysis.

−4

ω − ω02 ⎞ ω S (ω) = αp g 2ω−5 exp ⎛⎜−1.25 ⎡ ⎤ ⎞⎟ γp exp ⎛⎜− ⎟ 2 2 ⎢ ω0 ⎦ ⎥ ⎣ ⎝ 2σ ω0 ⎠ ⎝ ⎠

(14)

Where γp is a peakedness parameter, with an average value of 3.3. Wave loads are computed using Morison's equation. Load effects arising through coupled aerodynamic - hydrodynamic analysis in FAST and hydrodynamic-geotechnical coupling in USFOS is combined to obtain response of a bottom fixed OWT under wind and wave loading, in the 181

Scenarios

Uw (m/s)

Hs (m)

Tp (s)

Intensity

Turbine state

1 2 3 4 5

6 11.4 18 24 30

2.2 3.1 4.4 5.7 7.1

9.8 10.1 10.6 11.2 11.9

0.20 0.15 0.13 0.12 0.11

operating rated, operating operating operating parked

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Fig. 11. Illustration for time-step convergence for monopile OWT with flaps at rated wind speed.

is required to be chosen. To avoid the uncertainty, time step is needed to ensure convergence. Though less time step size gives good accuracy, but results in the increased computational cost and time. The time step convergence study is carried out for the tower and pile top displacement for monopile structure as shown in the Fig. 11. Three time step values are considered for the convergence study and finally 0.05 s time step value is chosen for the analysis in the present study. Note in Fig. 11 time-series is shown for 40 s for the clear view, though analysis is done for 600 s. In this study, wave (or wind) time series are generated using different random seeds by mean of pseudo-random generator with same boundary conditions. This is done to avoid the statistical uncertainty. Monte Carlo simulations require large computational expense. Thus this necessitates a convergence study with respect to samples. Also, the JONSWAP wave spectrum is usually discretized into number of frequencies by constant area method. This introduces another epistemic uncertainty which can influence the extreme responses [61]. It is desirable to consider a convergence study with respect to frequencies used for wave-spectrum discretization for obtaining the ultimate design load. In this work, the ensemble convergence is examined based on the statistical parameters (skewness and kurtosis) plots for tower-top displacement of a monopile OWT as shown in the Fig. 12. The cumulative value (in the figure) of any statistical parameter at any seed number is given as n

Scum =

∑ i=1

Si . n

Fig. 12. Convergence for the ensemble (and also frequencies used for discretizing JONSWAP spectra) shown through response statistics (skewness and kurtosis).

OWT structures. Soil stiffness is the deciding parameter for the lateral response of the OWT structures. In the present work, loose sand profile is considered for which the tower-top displacement/rotation can be a deciding factor due to the nonlinearities [4,62]. JONSWAP spectrum is used to simulate the irregular waves while Kaimal spectrum is used for turbulent wind [63]. The analysis is carried out to determine the pile penetration depth for the respective structures in loose sand, maintaining the limiting criteria for the pile mudline rotation. The effort is made to increase life of the turbine by reducing dynamic loads through controllable flaps, maintaining the power rating. Figs. 13–15 represent the maxima rotational response of the monopile, the tripod and the jacket supporting OWT when subjected to different met-ocean conditions. The comparison with and without flaps is shown for tower-top and pile-top angular displacement (rotation about the wind-wave axis) which clearly shows the reduction due to the flaps. For irregular analyses, Monte Carlo based averaged responses are

(20)

Si is the statistical parameter corresponding to realization and n is the ensemble size for the Monte Carlo simulations. It can be noticed from the Fig. 12 that convergence is acquired within 25–30 realizations out of 100 samples. Thus ensemble averaged responses are obtained for 30 realizations based on this analysis performed. 6.2. Dynamic analysis In this study, the impact of environmental loading conditions on the response of the OWTs in soil, is investigated, with respect to sea-states. Comparative to OWT models which are considered fixed at the mudline, inclusion of soil component results in greater lateral response at rotor-nacelle assembly (RNA). This response further rise for the piled

Fig. 13. Ensemble maxima of angular displacement at tower-top and pile-top w.r.t to sea-states for monopile structure (Each wind speed refers to different load cases). 182

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wind speed, till cut-out wind speed (25 m/s) is attained. The tower top rotational displacement reduces near to the cut-out wind speed (24 m/ s), due to the wind turbine control actions that limit the aerodynamic load on the rotor. Thus, the response reduces when approaching towards the cut-out wind speed. In load case no. 5 (cf. Table 7), the turbine is shut down to avoid structural failure, turbine induces lower structural response in general. During this condition, the blades are feathering or parked which reduces the incident wind loads. The tower displacement follows the similar trend for the different support structures. It increases with respect to wind speed till rated wind speed, followed by the reduction up to cutout wind speed. Finally parked rotor condition results in moderate tower displacement. The displacement at the pile top play an important role when considering loose sand. Despite the fact, that aerodynamic loads reduces as turbine operates in parked condition, the rotation and displacement at pile top keeps on increasing in loose sand due to lower spring stiffness. For monopile and tripod, one can observe that there is a constant increase in the rotational response due to change of load-cases from 3 to 5, (i.e., effectively turning the met-ocean condition harsher). In jacket, there is an abrupt increase in the pile top rotation for load case 5, due to effect of non-linearities which cause the wind turbine to behave as an instable system in loose sand [4]. The rigidity of the jacket does not allow the proportional increase in the tower-top rotation. The ensemble values of the maxima displacement (at pile top and tower top) are reported in Table 8. Moreover, this happens as the flaps lessen the blade loads at the root resulting in reduced stresses. Also it limits the blade deflection at the tip which is important as the fouling of blades with tower causes accidental damage during operation due to prolonged usage. Along with these values, the percentage reduction in the ensemble maxima and the ensemble mean responses with respect to base shear force and the displacement (at the tower top and pile top), are given in the Table 9. The reduction can be observed at all the chosen sea-states due to flap implementation in the ranges of 2–15.7%. One may note that the maximum reduction happens when the wind speed is at rated speed when the effects of the flaps becomes predominant after which the blade pitch controller starts effective (between 11.4 m/s and 25.0 m/s). In the blade-pitch active controller region also, there is a substantial reduction in the loads and responses 7.0 − 12.2%. One may note that the flaps are effective in a small way also above cut-out wind speed (i.e., >25 m/s) in changing the boundary layer effects which results is small reduction in responses (i.e., 2.1–4.1%). Due to dynamic interaction the turbine blades loads directly effects the loads on the other turbine components. Tower top and pile top effects are the most significant as they encounters the substantial effect due to blade loading.

Fig. 14. Ensemble maxima of angular displacement at tower-top and pile-top w.r.t to sea-states for tripod structure (Each wind speed refers to different load cases).

Fig. 15. Ensemble maxima of angular displacement at tower-top and pile-top w.r.t to sea-states for jacket structure (Each wind speed refers to different load cases).

necessary as each maxima is a random quantity as the values change with each realization. Therefore, each bar-length represent the ensemble maxima across 30 realizations of the combined wind-wave stochastic processes. One can notice from the figures that the largest reduction in rotational response is obtained during load case 2 (cf. Table 7) when turbine operates at rated wind speed. The OWT model generates the maximum power output at this point, beyond which any further increment in power and rotor speed (12.1 rpm) is not possible. The blades are rotated about their longitudinal axis (i.e., pitching of blades with pitch-controller) to reduce the angle of attack as the wind speed increases, in order to maintain the optimized rated power. This results in the reduction of lateral forces at tower top with respect to

Table 8 Ensemble maxima displacement and base shear force on OWT supported with different support structures. (disp: displacement). Load cases Wind speed (m/s)

1 6

2 11.4

3 18

4 24

5 30

No flap

Flap

No flap

Flap

No flap

Flap

No flap

Flap

No flap

Flap

Monopile ↓ Tower top disp (m) Pile top disp (m) Base shear (MN)

0.408 0.027 1.129

0.383 0.026 1.062

1.088 0.062 2.008

0.916 0.053 1.693

0.753 0.051 2.200

0.668 0.047 2.003

0.804 0.058 2.651

0.738 0.055 2.482

1.069 0.081 3.873

1.035 0.078 3.741

Tripod ↓ Tower top disp (m) Pile top disp (m) Base shear (MN)

0.174 0.012 1.501

0.161 0.011 1.425

0.504 0.0203 2.497

0.421 0.017 2.115

0.290 0.022 2.794

0.255 0.021 2.527

0.262 0.027 3.396

0.241 0.026 3.190

0.264 0.033 4.045

0.249 0.032 3.914

Jacket ↓ Tower top disp (m) Pile top disp (m) Base shear (MN)

0.206 0.006 1.217

0.189 0.005 1.136

0.573 0.011 1.515

0.477 0.009 1.292

0.317 0.008 1.420

0.281 0.007 1.296

0.287 0.009 1.256

0.262 0.008 1.198

0.309 0.012 1.541

0.297 0.012 1.496

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Table 9 Percentage reduction on ensemble maxima and mean responses (loads and displacement) of OWT for different support structures due to flap implementation. Load cases Wind speed

1 6 (m/s)

2 11.4 (m/s)

3 18 (m/s)

4 24 (m/s)

5 30 (m/s)

Max

Mean

Max

Mean

Max

Mean

Max

Mean

Max

Mean

Monopile Tower top displacement (%) Pile top displacement (%) Base shear (%)

6.2 4.0 5.9

5.9 4.8 4.7

15.8 14.4 15.7

10.8 9.5 12.5

11.2 8.1 9.0

9.4 5.9 8.1

8.2 5.2 6.4

5.2 3.1 4.4

3.2 2.7 3.4

3.3 2.3 2.1

Tripod Tower top displacement (%) Pile top displacement (%) Base shear (%)

7.5 3.9 5.1

5.1 5.2 5.2

16.3 15.4 15.3

10.7 10.9 13.6

12.2 8.4 10.0

7.0 5.8 9.9

8.1 5.0 6.0

5.2 4.3 4.7

5.3 2.2 3.2

4.2 2.7 2.8

Jacket Tower top displacement (%) Pile top displacement (%) Base shear (%)

7.9 6.1 6.7

5.6 6.3 4.4

16.7 16.4 14.7

11.5 11.5 13.1

11.3 8.2 8.7

7.6 9.9 10.8

8.7 6.5 4.6

5.4 5.3 5.0

4.0 3.2 2.9

3.3 3.2 4.1

7. Conclusions

References

The present study deals with the dynamic response of an OWT under combined wind and wave loading, considering soil-structure interaction with the objective to reduce cyclic loads on the piles. Three different kind of support structures – monopile, tripod and jacket– are investigated. The rotor blades are fitted with small appendages in form of trailing edge slotted flaps which does not change the mass or natural frequencies of wind turbines. The movement of the trailing edge flaps are controlled through the feedback scheme. The flaps are modelled using Viterna's method analytically and then numerically implemented into the aero-elastic code FAST through the change in the lift/drag coefficients. Dynamic link library (DLL) is used to regulate the PID controller already available in the aerodynamic codes. Loose sandy soil of uniform density profile has been considered for which the nonlinear effects are predominant. The met-ocean states have been derived using a probabilistic approach for an eastern Indian ocean site. For validation, the flap model is validated using the experimental data available while the combined wind-wave analysis using USFOS is matched with another commercial routine SESAM Wind for a fixed base jacket structure. Lateral pile-soil analysis is carried out to determine the suitable pile penetration length. Convergence studies are carried out for determining the required spring-node density, time-step and sample size. Winkler spring models are used to model the soil-pile interaction. OWT response have been obtained for the various irregular seastates (governed by JONSWAP spectrum) which gives an idea about the response values from design consideration. The ensemble average of the stochastic responses for rotation at tower and pile head are plotted. The displacements at tower top and pile top along with the base shear of OWT are shown in tabular form. Response are presented as an ensemble average in the present study. The noticeable reduction up to 18% is observed due to implementation of trailing edge flaps, thus achieving the aim of the study. Thus flaps proves its capability in reducing the fatigue loads and lessening the cyclic load ranges on the wind turbine foundations. Thus, this paper summarizes the results of the wind turbine with controllable flaps, supported on three different fixed-bottom structures under the influence of soil.

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