Computational analysis of blade tip-to-tower clearance effects on horizontal-axis tidal current turb

Abstract

Keywords: Horizontal axis tidal current turbine; monopile support tower; computational fluid dynamics; blade tower interaction

1. Introduction

Nearly one degree of global warming has been observed and is primarily attributed to anthropogenic activity since the pre-industrial era, according to the Intergovernmental Panel on Climate Change (IPCC). Global warming is associated with the emission of greenhouse gas emissions (C02, CH4, and N2O), which result from the excessive reliance on fossil fuels

[1-4]. In response, the Paris Agreement sets a goal of limiting global warming to 2°C above pre-industrial levels this century. Achieving this target necessitates a global transition fromconventional fossil fuel-based energy systems to sustainable, renewable energy alternatives. There are numerous renewable energy resources, including biomass, wind energy, photovoltaic solar energy, solar thermal

Corresponding Author E-mail Adress: majid.baseer@insa-lyon.edu.fr *

Submitted: 11 March 2025 ; Accepted: 26 June 2025 This paper was recommended for publication in revised form by Editor-in-Chief Ahmet Selim Dalkılıç Published by Yıldız Technical University, İstanbul, Türkiye This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

electricity, low-temperature solar thermal energy, hydroelectricity, geothermal energy and marine energy [5-8]. Tidal energy is one of the renewable resources that has the greatest potential because it is very predictable and its energy density is relatively high [9]. The flows associated with tides, which are generated by lunar gravitational forces acting on the Earth’s surface, occur in a cyclic, predictable manner that can be used for the generation of renewable energy [10]. Horizontal-Axis and Vertical-Axis Tidal Current Turbines (HATCT and VATCT), oscillating hydrofoils, tidal kites, ducted turbines and tidal range systems are all examples of various energy extracting devices based on tidal currents [11, 12]. The HATCT design is the most developed design among others and approximately 76% of research activity regarding energy extraction from tidal currents is related to this design [13]. Therefore, the first generation of tidal energy systems appears to converge toward the HATCT design [14]. Several authors have observed that marine flows may significantly affect the performance of HATCT (including near- and far-wake characteristics). In particular, velocity shear conditions may have a considerable effect on turbine performance [15]. Apart from velocity shear, the effects of the wave-current interaction, bathymetry, free surface proximity and boundaries effects have been broadly investigated [16]. For example, it has been observed that the presence of wave enhances turbine performance, whereas blockage ratio effects were marginal at low TSR values but increase at higher TSR values [10, 17]. The hydrodynamic and structural performance of a turbine is heavily influenced not only by environmental flow conditions but also by the geometric configuration of turbine components. The main components of a tidal turbine are the rotor, the nacelle, and the support structure. Several authors have shown that the design of the nacelle has an insignificant effect on turbine performance [18], but the design of the support structure-in particular, the tower-can be a significant factor. The monopile tower, a widely accepted support concept across configurations, has attracted interest for first-generation tidal devices, particularly for shallow-water installations. This support has been extensively used in the wind energy sector, but its design criteria need to be re-evaluated for tidal applications due to vast differences between air and water flow conditions. Although various features of monopile-supported tidal turbines have been explored, further analysis is still needed to understand the overall impact of transferring wind turbine support structures into a marine environment. One significant effect on the turbine that can be attributed to the support structure is the ‘tower shadow effect’; the presence of the support structure locally alters the incoming flow at the rotor, and may therefore affect turbine power output [19]. The effects depend on various parameters, such as tower shape, and size, the distance between the blade tip and the tower, and struc-

tural flexibility. Generally, there appears to be some consensus that cylindrical tower sections are likely to have less impact on turbine performance than alternative cross-sectional shapes, such as square or oval [20]. and studies have found that elasticity in the tower can be related to the variability of the turbine power output [14]. Previous work analyzed the effect of tower diameter on turbine performances [21]. Accordingly, the present work analyzes the effect of blade tip-to-tower clearance on the hydrodynamic performance of HATCTs. This paper is organized into five sections. Section 1 presents the background and motivation for the study. Section 2 describes the methodology and materials, with Sections 2.1 and 2.2 giving details about the computational domain and meshing approach, respectively. Section 3 defines the performance parameters. Section 4 discusses the simulation results. Finally, Section 5 provides a summary of the key findings and conclusions.

2. Materials & methods

The full-scale St. Anthony Falls Laboratory (SAFL) Reference Model 1 (RM1) turbine, featuring a twenty-meter diameter rotor and blades shaped based on the NACA 4415 profile [22], is simulated using transient analysis for ten rotations. The simulation is conducted using a transient rotor-stator approach while varying the tip-totower clearance in the CFX package of ANSYS. CFX is a node-centered finite volume solver [23].Within a set of control volumes, the continuity and momentum equations given below as Equations (1) and (2) respectively are solved in ANSYS CFX [24]. 2t + d $ [tV] = 0 (1) 2t 2 (tU) + d $ (tU * U) = -dp + d $ x + S M (2) 2t 2 x = n 9dV + [dV] T - 3 dd $ VC (3)

Where “τ” represents the generalized form of the Cauchy stress tensor for a Newtonian fluid. “𝜌” denotes the density of the water 3 in kg/m matrix, “V” is the free-stream velocity (m /sec), and “δ” is the identity matrix.

In transient analysis, the turbine rotor is physically rotated at each time step using ANSYS CFX’s transient rotor-stator scheme, which is based on the sliding-mesh technique. The transient rotor-stator approach models the relative motion between the External Domain (ED) and Internal Domain (IRD). The external domain remains stationary, while the internal domain rotates at an angular speed of

3. Performance parameters

In this section, three performance parameters of the tidal current turbine are discussed: Where “R” is the radius of the rotor measured in meters, “ω” is the angular velocity of the rotor, expressed in radians/ second, whereas “V” is the velocity of the free stream velocity at hub height, measured in meter/second. R~ Tip Speed Ratio (TSR) = V3 (4)

Where “p” is the power available in the flow stream, “ρ” is the density of the water, and “A” is the swept area of the rotor. It is the main parameter used to evaluate the performance of the tidal current turbine. It represents the ratio of the power extracted by the turbine to the power available in the flow stream. Coefficient of performance (C P) =

T (6) 0.5tAV 32 Table 2. Parameters and its setting Coefficient of thrust (C t) =

Figure 3. (a) Hybrid mesh of the complete domain (b) Mesh of the turbine

(b) (a) Figure 4. (a) Boundaries layers on blades (b) Top view of turbine blade

Setting Transient, total time- 85.6 sec, Time step-0.14 sec Non-buoyant, rotating, SST, wall functionautomatic

No-slip wall, rotating at 0.7 rad/sec, mesh Motion option-unspecified/system coupling, Mesh deformation- region of motion specified

Subsonic, normal speed-1.5 m/sec, medium turbulence intensity-5%

General connection, transient rotor stator, mesh connection-GGI

4. Results and discussion

In this section, we investigate the impact of blade tip-to-tower clearance on the performance and stability of the St. Anthony Falls Laboratory (SAFL) Reference Model 1 (RM1) full-scale turbine, operating at a Tip Speed Ratio (TSR) of 4.87. In particular, the study investigates the effect of tip-to-tower clearance on turbine performance and the thrust force acting on the support structure, to improve understanding of the mechanisms underlying blade-tower interaction. Ten full-rotation time steps were performed for the turbine, corresponding to 90 s of physical time, with a time step of 0.1432 s. The initial layout of the turbine is presented in Figure 5. The transient analysis was conducted for approximately 600-time steps, with each time step corresponding to the rotor’s advancement through a discrete angular increment. For numerical convenience, the rotor is advanced by 6 degrees at each time step, which requires 60-time steps to cover a full 360° rotation. The parameters “C” and “d” stand for the clearance between the blade tip and the tower and the tower’s diameter, respectively. The whole number following “C” and d” represents the length of the clearance and the diameter of the tower.

It is evident that the tower significantly impacts both the coefficient of performance and thrust. Specifically, when a turbine blade aligns with the tower, the coefficient of performance is relatively low. The Cp increases smoothly as the blade rotates away from the tower and then begins to decrease again as the blade approaches the tower. These fluctuations are attributed to the tower shadow effect, which refers to the alteration of the local flow field due to the presence of the tower, resulting in localized decreases in flow velocity near the tower and thus temporarily reducing power extraction. A detailed analysis of this phenomenon is required to enable optimal turbine design and positioning, particularly to avoid significant changes in performance due to flow patterns affected by the tower wake [38-40].

Figure 7. Coefficient of performance (Cp) for 2 m, 3 m, 5 m, & 7 m blade tip-to-tower clearance having 2 m diameter tower Figure 5. Initial condition of the turbine.

Figure 6. Coefficient of performance (Cp) for complete ten rotations Figure 6 illustrates the Cp for a turbine with varying blade tip-totower clearances, while maintaining a constant tower diameter of 2 meters. The simulations span ten rotations, with a focus on the final rotation due to its relative stability.

As shown in Figure 7, variations in blade tip-to-tower clearance have a negligible influence on the mean Cp values. Specifically, clearances of 7 m and 5 m yield mean Cpvalues of 0.476 and 0.468, respectively, whereas clearances of 3 m and 2 m both yield a mean Cp of 0.472. The maximum deviation is 0.016, which corresponds to a relative change of approximately 1.69% compared to the reference value of 0.476. However, given the inherent limitations of Reynolds-Averaged Navier–Stokes (RANS)-based Computational Fluid Dynamics (CFD) simulations, such small differences fall within the range of numerical uncertainty. As such, they cannot be conclusively attributed to variations in tip-to-tower clearance. Although RANS models are computationally efficient, they provide reduced accuracy in prediction of the effects of complex turbulent flow when considering separation and recirculation regions in the flow. Therefore, the minor variations observed in the mean Cp are more likely attributable to numerical errors and model limitations as-

sociated with RANS-based simulations than to blade tip-to-tower clearance. Table 3. Fluctuations of the performance coefficient (Cp) relative to its mean value Blade tip-to-tower clearance (m) 7

Fluctuation=(max-min)/ (mean Cp) Variations in tip-to-tower clearance produce a significant effect, causing large variations in Cp about the mean, that increase in magnitude as the clearance decreases. This behavior is attributed to the increased blockage effect of the tower, pushing the rotor further into the area influenced by the tower shadow effect. This trend is consistent with the observations published in a similar experimental study [41], which examined the effect of mast closeness on rotor loads. When the relative position of a dummy mast changes, the mean load remains constant, while the coefficient of variation (COV) increases, indicating greater load fluctuations. Furthermore, it is noteworthy that the dependence of the reduction in clearance on the magnitude of fluctuation is nonlinear. As tip-totower clearance decreases to small values, the fluctuation increases sharply, as presented in Table 3.

tower varies. The thrust force on the blade is large when the blade is at positions away from the upstream region of the tower. Thus, Ct is higher at these positions. However, Ct decreases as the blade approaches the tower. This is consistent with results published in previous studies concerning different tower diameters [21]. While the mean coefficient of thrust does not appear sensitive to changes in blade tip-to-tower clearance, the deviation from the mean, used as a measure of performance stability, varies considerably. At a clearance of 2 m, the deviation from the mean is the largest, with a value of 8.45%, followed by 3 m, 5 m, and 7 m at 7.96%, 6.18%, and 5.98%, respectively, as presented in Table 4. Table 4. Variation of the coefficient of thrust (Ct) relative to its mean value Blade tip-to-tower clearance (m)

These observations show that lower tip-to-tower clearances lead to increased fluctuations in hydrodynamic forces on the turbine blades and consequently, to increased thrust fluctuations. Such unsteady forces may have implications for the structural integrity and operational reliability of the turbine.

Figure 9. Velocity contour for different blade tips to tower clearance

Figure 8. Coefficient of thrust (Ct ) for blade tip-to-tower clearances of 2 m, 3 m, 5 m, and 7 m Figure 8 illustrates the variation of the coefficient of thrust (Ct ) for different blade tip-to-tower clearances. Ct exhibits a trend similar to that of Cp as the relative angle between the turbine blade and the

Figure 9 presents the velocity contours at a radial distance of 7 m below the nacelle for varying tip-to-tower clearances. As expected, the velocities are observed to be significantly reduced upstream and downstream of the tower when compared to the overall flow field. The reduction in velocity around the tower is the so-called “tower shadow effect”, the existence of which is evident through the low-velocity region (blue/green contours) upstream of the tower. The flow along the blade, in all cases considered, displays the typical pattern of acceleration toward the trailing edge on the suction side

after initial acceleration near the leading edge. As discussed previously, the observed reduction in both the Cp and Ct is primarily associated with the blade’s periodic entry into the tower-shadow region, as reflected in the velocity field. The magnitude of the tower shadow effect increases as the tip-totower clearance decreases, whereas a larger tip-to-tower clearance corresponds to reduced interaction with the disturbed flow region around the tower. Thus, a larger tip-to-tower clearance would mitigate tower-induced flow disturbances, thereby decreasing unsteady loads and the risk of fatigue failure in the blades and supporting structure, especially under cyclic operating conditions.

Results indicate that the amplitude of thrust force fluctuations reaches approximately 98% of the mean when the tip-to-tower clearance is 2 m. With increasing tip-to-tower clearance, this fluctuation drops sharply to 18.7% at 7 m, as presented in Table 5. Table 5. Fluctuations in the thrust force acting on the tower for different blade tip-to-tower clearances. Tip-to-tower clearance (m)

The magnitude and periodicity of the thrust force on the tower are also influenced by the blade tip-to-tower clearance. This effect is more pronounced at smaller tip clearances, thus producing higher 2P oscillation amplitude in the tower thrust force signal compared to larger tip clearances, which is consistent with findings reported in previous studies on tidal turbines. The substantial reduction in fluctuation amplitude highlights the significance of tip-to-tower clearance in achieving smoother turbine loading conditions and, consequently, improved performance stability.

Figure 10. Thrust force (N) acting on the tower for blade tip-totower clearances of 7 m, 5 m, 3 m, and 2 m (Tower diameter = 2 m) Figure 10 shows the evolution of the thrust force acting on the tower over time for various tip-to-tower clearances. When the blade is directly upstream of the tower, the thrust on the tower is minimal. As the blade moves away from the upstream position, the thrust magnitude increases with angular displacement, reaches a maximum, and then decreases. This behavior is attributed to modifications in the local flow field around the tower due to blade-tower interaction. In addition, as the blade passes in front of the tower, the location of the stagnation point on the tower surface and the characteristics of flow separation are modified. Similar flow interference mechanisms have been reported in studies of wind turbines [42]. The magnitude and periodicity of the thrust force on the tower are also influenced by the blade tip-to-tower clearance. This effect is more pronounced at smaller tip clearances, producing higher 2P oscillation amplitudes in the tower thrust force signal than at larger tip clearances, which is consistent with previous studies on tidal turbines.

Figure 11. Coefficient of performance (Cp) with and without the symmetry boundary condition Figure 11 shows the Cp of the turbine over five rotations under two different boundary-condition configurations. The first configuration employs symmetry boundary conditions, with the turbine placed asymmetrically within the computational domain; the second applies a no-slip wall boundary condition on one domain boundary, with the turbine positioned asymmetrically within the domain. The above figures show that Cp does not vary significantly between the two configurations. During the 4th and 5th rotations, the variations were less than 5%. Thus, it may be concluded that the type of boundary condition used, i.e., symmetry or no-slip wall, has a negligible effect on the turbine performance predicted by the present simulations.

at clearances of 3 m, 5 m, and 7 m, it is 4.98%, 2.98%, and 1.23%, respectively. A similar trend is observed for Ct. While the mean Ct remains relatively stable, approximately 0.87 for clearances of 7 m and 5 m, and approximately 0.86 for 3 m and 2 m, the magnitude of fluctuations increases as clearance decreases. Specifically, the fluctuation reaches 8.45% at a 2 m clearance, followed by 7.96%, 6.18%, and 5.98% for clearances of 3 m, 5 m, and 7 m, respectively. Notably, this increase in fluctuations is a nonlinear phenomenon that becomes more pronounced with decreasing clearance.

Figure 12. Velocity contours for symmetry and no-slip wall boundary conditions Figure 12 further illustrates this observation by presenting velocity-contour fields for both configurations. A low-speed region downstream of the turbine is evident in both configurations (blue-green colors indicate low speed), whereas a region of increased velocity can be observed on either side of the turbine wake. The consistency of the flow fields between the two cases provides evidence that boundary-condition selection has a negligible influence on performance parameters and flow characteristics. This result aligns with established Computational Fluid Dynamics (CFD) practices. At a symmetry boundary, the normal velocity component is zero, representing a mirrored flow condition, whereas a no-slip wall enforces zero velocity at the boundary due to viscous effects. In both cases, the velocity at the boundary is zero. However, since the performance remains largely unchanged between these conditions, it can be inferred that either boundary condition is suitable for this type of simulation.

5. Conclusion

In this study, the effect of the tip-to-tower clearance on the overall performance and aerodynamic characteristics of the wind turbine is investigated. Turbine performance is evaluated using the coefficient of performance (Cp) and coefficient of thrust (Ct). Blade-tower interaction at different tip clearances is studied by analyzing the thrust force acting on the tower. Numerical simulations are performed on the full-scale SAFL RM1 turbine for ten complete rotations, employing the Reynolds-Averaged Navier-Stokes (RANS) approach in ANSYS CFX to model various tip-to-tower clearances. The results indicate that the mean Cp remains largely insensitive to variations in blade tip-to-tower clearance. Specifically, for clearances of 7 m and 5 m, the mean Cp values are 0.468 and 0.476, respectively, for clearances of 3 m and 2 m, the corresponding mean values are 0.472 and 0.470. However, the magnitude of fluctuations about the mean Cp increases significantly with decreasing blade tip-to-tower clearance. At a clearance of 2 m, the fluctuation in Cp is 12.23%;

The variation in thrust on the tower with respect to blade tip-totower clearance is also significant. Changes in the location of stagnation point and altered flow separation patterns are observed as the blade passes across the tower, resulting in fluctuations in hydrodynamic loading on the tower structure. This fluctuation becomes highly pronounced at low clearances, with fluctuations around 98% relative to the mean at 2 m, compared with 96%, 67%, and 18% at clearances of 3 m, 5 m, and 7 m, respectively. To summarize, tip-to-tower clearance has a negligible effect on the mean values of Cp and Ct, but is a major factor influencing the range of variation in performance parameters. Furthermore, the tower thrust varies substantially across different clearance settings, which could lead to increased fatigue loads on the blade and tower. As a result, tip-to-tower clearance must be carefully considered in the design of a tidal current turbine to manage unsteady loading and enhance structural reliability. Finally, the simulations indicate that applying symmetry boundary conditions has minimal influence on turbine performance or wake. However, it provides clear advantages by reducing computational cost and is therefore an efficient approach for large-scale simulations.

Copyright and permission statement All figures included in this manuscript are the authors’ original work.

Nomenclature

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