Analysis of Renewable Energy Devices
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Analysis refers to the application of scientific and engineering principles and processes to reveal the properties of a system.
Renewable energy devices may operate in complex internal and external conditions, and engineering analysis is a key element of the design process. Because of the sophisticated physics associated with specific renewable energy devices, simplified analysis is often not adequate for a full understanding of the system behavior. With the advent of information and digital technologies, analysis at various fidelity levels can be achieved using simulation tools. To reduce the computational costs and to validate the accuracy of simulation tools, significant efforts have been invested from both industry and academia.
Hydrodynamic analysis of monopile-type wind turbines using the ME can be found in Veldkamp and Van Der Tempel (2005), Shirzadeh et al. (2013), and Jiang (2018). For monopile foundations supporting 10-megawatt (MW) wind turbines, the diameter can reach 10 m (Velarde 2016), and the ME is not necessarily applicable for short waves. For jacket-type wind turbines, the tubular members have relatively small diameters. For example, the maximum leg diameters of traditional jackets supporting 5-MW wind turbines generally do not exceed 2 m (Chen et al. 2016; Dong et al. 2011). Thus, the hydrodynamic loads are drag-dominated for extreme waves, and the ME is well-suited for the analysis. Shi et al. (2013a, b) performed dynamic loads analysis of jacket-type wind turbines extensively and applied the ME during the hydrodynamic analysis. The ME has also been considered in the hydrodynamic analysis of floating platforms including spar buoy (Jonkman 2007; Jiang et al. 2013b), tension leg platform (Bachynski and Moan 2012), as well as mooring systems (Kvittem et al. 2012).
The panel method is a frequency-domain approach applicable to weakly nonlinear hydrodynamic problems. If there is highly nonlinear interaction between waves and floating bodies, analytical approaches (Faltinsen et al. 2004), the time-domain boundary element approaches (Schløer et al. 2016; Salehyar et al. 2017), or computational fluid dynamics methods (Li and Yu 2012) can be used. Chella et al. (2012) presented an overview of the wave impact forces on OWT substructures. Saletti (2018) studied the bottom slamming phenomenon for a combined wind and wave energy converter.
Aerodynamic and Aeroelastic Analysis
For renewable energy devices that are exposed to wind loads, analysis of wind effect is indispensable. Wind turbines are particularly designed to harness the kinetic energy from the wind, and modern wind turbine blades are long and slender. For horizontal-axis wind turbines (HAWTs), the longest blade announced approaches 90 m for an 8-MW wind turbine (LM Wind Power 2018). Such flexible blades may experience large deformation under the combined effect of wind excitations, centrifugal forces, gravitational forces, and control actions. Aerodynamic analysis helps to understand the behavior of the airflow and the forces acting on the blades and the performance of the wind turbine. The classical blade element moment (BEM) was initially proposed by Glauert (1983) and modified for wind turbine analysis. The basic assumption of the BEM theory is that the force of a blade element is solely responsible for the change of axial momentum of the air which passes through the annulus swept by the elements, and there is no radial interaction between the flows through contiguous annuli (Burton et al. 2011). BEM can be used to calculate the steady loads, the thrust, and the power of HAWTs. A simple BEM algorithm to find the axial and tangential induction factors is presented in Hansen (2008). A BEM algorithm with improved convergence rate is presented in Ning (2014). The classical BEM needs to be corrected by Prandtl’s tip loss factor and Glauert correction to get reasonably good results, as compared to the measurements. Due to unsteadiness of the wind seen by the rotor, the classical BEM cannot realistically capture the aeroelastic behavior of wind turbines, and the unsteady BEM method should be considered. The unsteady BEM, albeit still efficient, considers the time behavior of loads and power by the dynamic wake model and the dynamic change of angle of attack by the dynamic stall model (Hansen 2008). Further, physical phenomena like wake meandering can also be incorporated as engineering corrections to BEM (Larsen et al. 2013).
The BEM theory considers uniform pressure distribution across a rotor plane. Unlike BEM, the generalized dynamic wake (GDW) method, also known as the acceleration potential method, allows for a more general distribution of pressure across a rotor plane and includes inherent modeling of the dynamic wake effect, tip losses, and skewed wake aerodynamics (Moriarty and Hansen 2005). However, the GDW method was developed for lightly loaded rotors at high wind speeds, and the induced velocities are small relative to the mean inflow velocity. Detailed descriptions of the GDW theory can be found in Pitt and Peters (1980) and Suzuki (2000).
Over the past decades, computational fluid dynamics (CFD) has been widely used in aerodynamic analysis of rotors, and actuator disc and actuator line methods are special types of CFD methods (Hansen and Aagaard Madsen 2011). Krogstad and Eriksen (2013) presented a summary of different computational methods that were applied to predict the performance and wake development of a tested model wind turbine. De Vaal et al. (2014) used the actuator disc model to study the effect of surge motion of a floating wind turbine on rotor thrust and induced velocity. Wen et al. (2018) applied the free vortex method to study the power coefficient overshoot of a floating wind turbine in surge oscillations.
Aeroelastic analysis refers to the type of analysis that deals with the interaction between the inertial, elastic, and aerodynamic forces when the structure is exposed to a fluid flow. For commercial wind turbines, stall-induced vibrations and classical flutter are two categories of instabilities that have been observed for stall- and pitch-regulated wind turbines, respectively. Hansen (2003, 2007) presented a state-of-the-art review on aeroelastic stability analysis of wind turbines.
Integrated Dynamic Analysis
Global motions and structural responses are two main aspects of concern. The global motions refer to the horizontal displacement and rotation of structural members or bodies. For floating wind turbines, rigid body motions of the floating platforms under dynamic loading can provide insights into system dynamics. Nielsen et al. (2006) conducted dynamic response analysis of the floating wind turbine concept HYWIND under wind, wave, and current conditions and compared the simulated and experimental decay tests of tower pitch angle. Pereya et al. (2018) analyzed the nacelle acceleration and platform pitch motion of the TetraSpar floating wind turbine. Such global motion responses, albeit not stated explicitly, can form design constraints for drivetrain components. Kurniawan et al. (2012) performed modeling and global motion analysis of a pitching wave energy converter and discussed dynamics of such a system with different hydraulic components. Muliawan et al. (2013b) conducted dynamic response analysis of a combined wind-wave energy converter and uncovered positive synergy between the two floating bodies by global motion analysis. Shi et al. (2016) developed an ice load force module for an aero-hydro-servo-elastic program and identified important response characteristics of a monopile-type wind turbine under combined ice and wave loads. From an integrated dynamic analysis, structural responses are available. To ensure structural integrity of renewable energy devices, the structural responses need be checked against possible failure modes including fatigue and ultimate limit states. Dong et al. (2011) checked the long-term fatigue damage of tubular joints of a jacket-type OWT (see Fig. 1 right) after performing integrated dynamic analysis. Jiang et al. (2015) analyzed the short-term fatigue damage of mooring lines of a floating wind turbine during shutdown. Wei et al. (2014) calculated the structural capacity of jacket support structure of an OWT under extreme wind and wave loading.
Analysis of Mechanical Components
Hydraulic components including valves, pumps, accumulators, pipelines, and motors are also mechanical components that have been suggested for use in wave energy converters and wind turbines. Analysis of hydraulic systems often involves mathematical modeling and numerical simulations. Henderson (2006) presented both numerical simulation and laboratory tests of the hydraulic system employed in the Pelamis wave energy converter. Yang et al. (2010) investigated the wear damage in the piston ring and cylinder bore of a heaving-buoy wave energy converter. Numerical simulations of hydraulic transmission of wind turbines can be found in the works of Jiang et al. (2014b), Yang et al. (2015), Buhagiar et al. (2016), and Buhagiar and Sant (2017).
Code Verification and Validation
A multitude of design codes have been developed and extensively used for analysis of renewable energy devices. In general, many design codes adopt simplified physical representations of actual systems with reduced degrees of freedom but account for most prominent system features. Before being put into use, a new code should be verified against other state-of-the-art codes with adequate model fidelity levels or validated against experimental results. Larsen et al. (2013) showed good comparison between HAWC2 and the CFD code EllipSys3D for aerodynamic forces on a blade. Extensive benchmark work usually involves international collaboration among various academic and industrial partners. Passon et al. (2007) introduced the first international investigation and verification of aeroelastic codes for OWTs. Modeling capabilities of offshore environment, structural modeling, and rotor aerodynamics were compared among nine design codes for four different support structures. Later, code-to-code verifications were conducted of other types of foundations with an increased number of participants and additional load cases; see Jonkman et al. (2008), Popko et al. (2012), and Vorpahl et al. (2014).
Experiments at model scale or full-scale testing are other effective means of code verification. Discrepancies in results between model testing and numerical codes are not uncommon, especially for renewable energy devices that have both aerodynamic and hydrodynamic excitations, because similarity between inertia and viscous forces of the models cannot be achieved simultaneously. Li and Calisal (2010) developed numerical codes using a discrete vortex method for vertical axis tidal current turbines and verified the two- and three-dimensional codes with experiments. Preliminary verification of a wave energy converter design tool with experimental wave tank results is presented in Ruehl et al. (2014). Coulling et al. (2013) verified a numerical model constructed in the design code FAST (Jonkman and Buhl 2005) with 1/50th-scale model test data for a semisubmersible floating wind turbine system. Luan et al. (2018) compared the simulated sectional responses of a semisubmersible using a nonlinear finite element code SIMO-Riflex with the 1/30th-scale model test results.
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