*3.1. Motionless Blade Simulation with One Barnacle*

To compare the numerical model results to experimental data, the pressure field around the barnacles is taken at every fluid cell centre (along the blade surface) in the studied area at fixed time points chosen after the flow stabilisation. On Figure 6 is presented the opposite of the pressure coefficient *Cp* given by <sup>−</sup>*Cp* <sup>=</sup> *<sup>p</sup>* <sup>−</sup> *<sup>p</sup>*<sup>∞</sup> −*q* , with *q* = 0.5*ρU*<sup>2</sup> <sup>∞</sup> = 1191.71 Pa. *X*∗ is the scaled position as *X*∗ = (*x*/*c*, *y*/*c*, *z*/*c*)=(*x*∗, *y*∗, *z*∗), where *x*, *y* and *z* are, respectively, the stream-wise, the span-wise and the vertical directions. Nevertheless, with the LES model, results are not averaged, which explains slight asymmetries on pressure fields (Figure 6). The blade curvature is suppressed by projecting all the cells in a plane parallel to the blade mean angle. The mesh is refined around the complex geometries and the shape of the barnacle appears in the field extraction process.

The effects of the numerical conic barnacle are very similar to the experimental ones (Figure 6) (experimental pressure fields are available in [13]) : in all cases, the barnacle is preceded by an over-pressure followed by a strong depression at the top of it. The flow change extends further downstream (3 radii) than upstream (2 radii). On the sides, the impact is felt up to 4 radii. Even with a numerical model, the perfect symmetry of the results is not guaranteed because the turbulence of the fluid creates slight variations in the flow that impact the distribution of the fluid pressure near the wall. The orders of magnitude of the *Cp* coefficient are the same as those measured experimentally. The main value in the field is 5.2% higher in the numerical results. The effect of the angle of attack on the pressure field is consistent with measurements: the higher the angle, the smaller the biofouling effect. The pressure field is almost unchanged for an angle of attack of 15°.

**Figure 6.** Opposite of the pressure coefficient (−*Cp*) around barnacle for an angle of attack of 5° (**a**), 10° (**b**), 14° (**c**) and 15° (**d**) on the blade surface. Results are from LES simulation.

To represent better the scales of the pressure variation and compare the models, the evolution of the opposite of *Cp* along the chord is plotted in Figure 7. The two models present different behaviours downstream of the barnacle. The k-*ω* SST model is better for the lowest angle of attack (5°), with the pressure increasing progressively along the chord as in the experimental data until it reaches its final value at the trailing edge. In contrast, the Smagorinsky model overestimates the pressure field which tends to decrease behind the barnacle. However, both turbulence models allow a good reproduction of the pressure drop in the fouling area.

With the 10° angle, the two turbulence models are closer in terms of mean value. However, the k-*ω* SST model better represents the overpressure in front of the barnacle. Downstream, both models underestimate the pressure along the blade.

The modelling is less accurate for 15°. Indeed, both turbulence models underestimate the impact of the barnacle on the flow. An additional computation is then performed to study the behaviour of the model in this critical range of values (Figure 8). At 14°, the simulated impact is more coherent with the measurements but some discrepancies are observed. We deduced that the experiment is highly sensitive to the angle of attack in the range between 14° and 15°. Small variations in the experiment or the 3D geometry can also interfere with results.

**Figure 7.** Opposite Pressure coefficient evolution (−*Cp*) according to the dimensionless x position (*x*∗) along the chord-wise position on the centre-line for an angle of attack of 5° (**a**) and 10° (**b**). Numerical results with k-*ω* SST (blue line) and Smagoginsky (red line) are presented for the fouled blade. Experimental values for clean and fouled blades are shown in green and black squares, respectively, from [13] data.

**Figure 8.** Opposite Pressure coefficient (−*Cp*) evolution according to the dimensionless *x* position (*x*∗) along the chord-wise position on the centre-line for an angle of attack of 15° (**a**) and 14° (**b**). Numerical results with k-*ω* SST (blue line) and Smagorinsky (red line) are presented for the fouled blade. Experimental values for clean and fouled blades are shown in green and black squares, respectively, (with an angle of attack of 15°) from [13] data.

Numerical simulation ensures a full *Cp* profile along the blade without having to invest in additional probes (Figure 9). For example, the small decrease in pressure before the overpressure (0.56 < *x*∗ < 0.57) was not captured by the probes during the experimental session. This phenomenon only appears for low angles (up to 10°). Normal (*Cn* <sup>=</sup> *<sup>n</sup> q* , where *<sup>n</sup>* is the forces normal to the blade per unit of span) and drag (*Cd* <sup>=</sup> *<sup>d</sup> q* , where *d* is the pressure drag forces of the blade per unit of span) coefficients are computed (Figure 10). As shown in experimental data, the barnacle has no significant impact on *Cn*. The coefficient grows until it reaches the aerodynamic stall around 13° before decreasing with the angle. The drag coefficient is more impacted by the barnacle with an exponential increase for a mean angle greater than 10°. The barnacle causes an increase in this coefficient for low mean angles. However, when the angle continues to increase, the dynamic stall becomes more important and the effect of the barnacle fades. The numerical model reproduces this tendency. For the angle of attack of 15°, the pressure variations caused by the barnacle are

almost zero. The simulation then shows results close to those expected for a clean blade. The experimental data still show an impact for this angle but the numerical results at 14° overestimate these variations. Thus, the model seems very sensitive to the angle of attack parameter.

**Figure 9.** −*Cp* evolution against the dimensionless x-position profile (including the lower face) at a fixed time point for numerical modelling with fouling (blue line) and experimental mean values for a clean blade (green squares) and a fouled blade (black squares) for an angle of attack of 5° from [13] data.

**Figure 10.** Normal (**Left**) and drag (**Right**) coefficients measurements against the mean angle for clean (black squares) and fouled (green crosses) blades from [13] data. Numerical results for fouled blades are represented by red lozenges.

The main difference between the two turbulence models is their ability to compute the wake. Figure 11 shows that the LES successfully separates the vortex releases from each other. The RANS model, which averages the physical quantities, only identifies the general shape of the wake. The intensity of the vortexes is also lower, indicating a higher numerical dissipation. Thus, the LES is chosen over the RANS for its better ability to represent the wake.

**Figure 11.** Magnitude of the vorticity around and behind the blade for the LES Smagorinsky (**a**) and the RANS k-*ω* SST turbulence model (**b**).

Figure 12 compares the time evolution of the wake of the clean part of the blade with the one in the plane of the barnacle with an angle of attack of 5°. In both cases, the first vortex is identical (T = 0.4 s) but, while the clean case starts to stabilise quickly with vortex releases alternating between the lower and upper surface, the barnacle case does not show vortexes of high vorticity intensity (>300 s<sup>−</sup>1) during the first time steps. Once the wake is stabilised, the biofouling blade releases vortexes that propagate "upwards" in a regular manner. The clean blade, on the other hand, shows a turbulence structure similar to Von Karman vortex streets.

**Figure 12.** Magnitude of vorticity around and behind the blade at T = 0.04 s, T = 0.13 s, T = 0.26 s, and T = 1.14 s for cases without (**a**) and with (**b**) a barnacle.

Finally, the wake thickness is an interesting physical quantity to analyse: Figure 13 shows, as expected, that for the case without a barnacle as well as for the case with a barnacle, the wake thickness increases with the distance behind the blade. However, the behaviour of this increase is not the same in both cases. In the clean case, the increase is slower and follows a parabolic trend, while the case with the barnacle shows a faster and linear increase. Off the finer part of the mesh shown in Figure 3 which extends 4 chords downstream of the blade, the mesh is too coarse and diffuses the vortexes too quickly to follow the evolution of the wake thickness. It would be interesting to know if, further downstream, the wake thickness of the case without a barnacle eventually catches up with the one of the case with a barnacle.

**Figure 13.** Dimensionless wake thickness as a function of dimensionless position in the wake without (red diamonds) and with (black squares) a barnacle for angles of attack of 5° (**left**) and 15° (**right**).

#### *3.2. Full Rotor Simulation Simulation*

3.2.1. Impact of Biofouling on Tidal Turbine Performances

The time evolution of the power and drag coefficients (*Cpower* and *Cd*) for the complete rotor are shown in Figures 14 and 15. The realistic addition of the sessile species, according to [13], does not change the general behaviour of the turbine. However, a decrease in *Cpower* by 1.6% is observed. It is explained by an early dynamic stall and the formation of re-circulation loops on the upper surface. However, under the chosen conditions, the barnacles do not seem to create any additional boundary layer stall, which transitions by itself relatively close to the leading edge This can be explained by the particular position of the barnacles: the individuals naturally fix themselves in a zone that is already less energetic, where it is easier to settle. This small drop of *Cpower* may also be related to the small area colonised. If the blade was more fouled, with larger or more numerous species, the result might be more significant. In any case, the difference of the pressure coefficient is not sufficient to conclude to a performance loss.

**Figure 14.** Time evolution of the corrected power coefficient (*C*∗ *power*). Measurements for a clean turbine are in black while numerical results for clean and fouled turbines are in blue and red, respectively.

**Figure 15.** Same legend as for Figure 14 but for the corrected drag coefficient (*C*∗ *d* ).

The drag coefficient increases by 7.5% (Figure 15). It is significantly less than for the motionless blade case simulation that reached a rising of 800% for low angles of attack. This result can be explained by two points. Barnacles do not take part in the dynamic stall, contrary to the motionless blade case where the barnacle is located at 60% of the chord. Then, the barnacles are not evenly distributed on the blade and remain relatively far from each other. 3D effects also play a role in the process: the vortexes generated by the more upstream barnacles are not directly sent into the wake as in 2D but continue to follow the blade on a different plane from the barnacle.

#### 3.2.2. Impact of Biofouling on Tidal Turbine Wake

The chosen configuration does not allow us to see any significant impact of the colonisation on the wake of the tidal turbine. The fluid–structure interactions generated by the barnacles are small and are therefore quickly diffused and dissipated. The isovalues of the Q criteria show no significant differences in the wake or near wall. Nevertheless, a probe is placed downstream (1 diameter) of the turbine at the tip of the blade position (0.7, 0.35, 0) to study pressure, velocity and vorticity variations. The signals are relatively close for the clean and fouled cases. The amplitude of vorticity magnitude variation is lower in the biofouled case than in the clean one. The curve is also less smooth: showing that small vortexes regularly pass in the wake. A Discrete Fourier Transform (DFT) analysis of the vorticity signal is performed over 1.2 s with a time step of 0.005 s (240 samples) (Figure 16). The sample is one second long on the same time period for both cases. Both signals show a main harmonic around 2 Hz that corresponds to the tip vortex releases of the turbine. The intensity of the main harmonic (H1) is lower in the biofouled case than in the clean case. The first three harmonics are also slightly shifted (0.1 Hz) towards the high frequencies and less intense than in the clean case. In general, biofouling leads to an energetic decrease in the vortexes generated by the colonised surfaces.

A zoomed view of the blades allows us to understand how barnacles act on fluid to generate these vortexes (Figure 17). These figures confirm the fact that barnacles are behind the boundary layer transition. Nevertheless, in the case of a single barnacle, the vortexes generated by the fouling are directly sent downstream whereas in presence of a second barnacle in the same plan, the vortexes remain blocked between the two barnacles. The recirculation loop acts as a new surface over which the fluid flows. This shows that a single barnacle can have more effect on the wake than a couple in the same plane.

**Figure 17.** Zoomed view of two sections of one blade of the tidal turbine in the X–Z plan. The left refers to (1) and the right section refers to (2) on Figure 5.

#### **4. Discussion and Conclusions**

The three-dimensional study of explicit roughness raises difficult issues. The authors are aware that, despite the good results for the total forces, the pressure profiles shown in Figures 7–9, denote a non-physical behaviour (especially at the leading edge) even when averaged over time. This issue could perhaps be fixed using a finer mesh around the blade in the uniform straight flow. A mesh convergence study should therefore be carried out to overcome the issue.

For the full rotor, the authors were strongly constrained by the computational facilities. The mesh convergence was ensured by a preliminary study [23]. The numerical stability for the converged mesh requires very small time steps reaching (10−<sup>12</sup> s). Thus, the simulations could only achieve three rotations in the clean case and two for the biofouled case. This produces drag and power coefficients which converge to a constant value, which allows us to conclude that the simulation is valid concerning the forces. However, the simulation time is too short to study a realistic behaviour of the wake, especially for the biofouled case. The DFT gives interesting results but should be performed on a longer time period.

The Reynolds number is also constant for the motionless blade and the full rotor simulations (around 1.6 × <sup>10</sup>5). A full scale turbine could have a higher *Re* in a realistic configuration. The increase in the *Re* would correspond to an increase in flow velocity relative to the blade profiles. However, experimental data from the motionless blade tends to show that the sooner the stall occurs, the less impact the biofouling has. The tests presented here may overestimate the actual losses due to biofouling.

This paper presents a numerical analysis of the impact of biofouling on turbines performances. Two turbulence models are compared to know which is the more suitable here. *k* − *ω SST* is better at predicting forces on the blade in the motionless blade cases (Figures 7 and 8) but the Smagorinsky model was used for the full rotor because of its capacity to compute the wake with accuracy (Figure 11).

Conclusions on the impact of biofouling on tidal turbines performances are close to the experimental results: for the motionless blade case, the barnacle does not impact the normal forces but highly increases the drag, especially for low mean angles. This phenomenon decreases when the angle continues to rise because of the natural stall of the profile that occurs upstream of the barnacle (Figures 6–8). No significant differences are noted between the conical and realistic barnacle structures. It is therefore recommended to work with the simplest model. A dynamic simulation of a full scale rotor is also performed with a realistic colonisation. Barnacles tend to be placed on the second part of the chord where the hydrodynamic stall creates a less energetic zone. This has the effect of greatly reducing their impact on the performance of the tidal turbine, which only loses less than 1% of its efficiency. The impact of the biofouling on the tidal turbine performance is clearly reduced in the full rotor case (Figures 14 and 15). First of all, the realistic position of barnacles (mostly in the second part of the chord) plays an important role on this result. Then, the fouled surface remains relatively low compared to the blade's surfaces. Lastly, the turbulence is quite different in the full rotor case; the blades generate big vortexes that propagate and possibly impact with the others. This increase in turbulence may be one of the reasons for the drop in the impact of the biofouling in realistic configurations. However, regardless of their position, biofouling generates drag (Figures 10 and 15). In the wake, the vortexes created by the biofouled structures are less energetic and diffuse more quickly (Figures 13 and 16). This phenomenon could even be advantageous for tidal farms where it is important that the downstream tidal turbines suffer little disturbance from the upstream tidal turbines in order to avoid rapid fatigue of the installations and a significant loss of production. However, it is important to remember that, although this is a realistic layout, there are as many configurations as there are geographical areas and therefore as many sessile species. Erect *Hydrozoans* that are not robust could have far greater effects than those highlighted here. More extensive colonisation could also change our results. Other implantation scenarios should now be explored. A characterisation and parametrisation of the biofouling will be considered to estimate the impact of the biofouling at different scale and development phases.

**Author Contributions:** Conceptualization, I.R. and A.-C.B.; methodology, I.R. and A.-C.B.; software, I.R.; investigation, I.R., A.-C.B.; writing—original draft preparation, I.R.; writing—review and editing, I.R., A.-C.B. and J.-C.D.; supervision, A.-C.B and J.-C.D.; funding acquisition, A.-C.B. and J.-C.D. All authors have read and agreed to the published version of the manuscript.

**Funding:** The research was supported by the "Région Normandie" through a PhD grant (no grant number) and by the "Université de Caen Normandie" (no grant number).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The authors will provide OpenFoam files and result data on request.

**Acknowledgments:** I. Robin was supported by the "Région Normandie" through a PhD grant and by the "Université de Caen Normandie". A.-C. Bennis was funded by "Université de Caen Normandie". The authors are grateful to the CRIANN for the calculation facilities and technical support. Thank you Patrice Robin for the English reviewing. The authors are grateful to the CRIANN for the calculation facilities and technical support. We thank Patrice Robin for his English revision.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.
