# Effect of Roughness of Mussels on Cylinder Forces from a Realistic Shape Modelling

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

^{−3}over an average sample of 300 permanent mooring systems from oil and gas industry. This assessment steered operators towards a strengthening of safety factors, which can involve solutions such as mooring lines redundancy or thicker mooring lines. However, reducing mooring system CAPEX leads to avoid redundancy, to lighten mooring lines components, to shorten their length and to use high-performance nonstandard materials such as synthetic ropes. The nascent floating offshore wind industry then faces a challenge: reducing mooring system CAPEX without increasing the risk of high consequences in case of failure. According to Fontaine et al.’s review of “past failures, pre-emptive replacements and reported degradations” (Figure 7 in [5]), over 74 analyzed failures, it became clear that fatigue is one of the main issues. Based on the same observations, the JIP led by Carbon Trust identified four major innovation needs for mooring systems ([6], p.48), among them the “Understanding of fatigue mechanisms in floating wind mooring systems”. According to Braithwaite and McEvoy, offshore fish farms experienced failures due to the presence of biofouling [7]. The loading of these underwater beam components is usually modeled through the Morison quasi-static equation [8] where drag and inertia coefficients comprise as much as possible the complex hydrodynamic interactions between water and the cable. Macro-fouling, called marine growth in the following, has been shown to change drastically the value of these coefficients and thus the loading [9,10,11] and the structural reliability [12,13,14]. Three effects have been shown to drive the loading changes [10]: the change of the diameter, of the mass and of the roughness by both changing the quasi-static and the dynamic loading [15].

## 2. Hard Marine Growth Reproduction and Experimental Setup

#### 2.1. Realistic Shape of Colonization by Mussels

^{®}(Figure 1c) developed during the ULTIR project [25]. In these best conditions (luminosity, turbidity, distance to the target), the accuracy reaches 0.7 cm. This chain is the main anchoring material for the buoy equipment of the SEMREV site, operated by Ecole Centrale de Nantes, where adult mussels were observed. The same type of pictures was obtained 10 km away, on the test platform UN@SEA ee (called UN-SEA-SMS previously) [3] of Université de Nantes, two years after its installation in June 2017. The organization of each specimen and the roughness were measured. Figure 1 illustrates the organization of the specimen. On Figure 1a, the red frame represents a pattern of size 20 cm × 20 cm that was shown to be representative of an elementary representative organization of the specimens on the covered surface. Figure 1b represents the top view of mussels by an elliptical shape whose major axis inclination with respect to x axis is reported in Table 1. Note that for simplifying the presentation, mussels are aligned horizontally and vertically in Figure 1b that is not the case due to the important difference between the size of vertical and horizontal axes (see position X and Y in Table 1). For simplifying future modeling and bench-marking, the major axis is approximated by 8 values: 0°, +/− 30°, +/− 45°, +/− 60° and 90°. Similar absolute value of the inclination is plotted with the same color. Table 1 gives the position of the centers and the inclination for each of the 16 specimens in the patch. It is shown that the organization is not totally random and that similar angles are observed: it comes from the fact that an optimal organization of mussels should optimize the access to food, that is, phytoplankton obtained by filtering the sea water.

_{e}, where k is the dimension of the studied roughness and D

_{e}the equivalent diameter. In the literature, several definitions of the roughness exist [10,31]. Decurey et al. [3] give a definition of D

_{e}in line with on-site measurements. In Ameryoun et al. [17], they used a stochastic modeling of marine growth and hydrodynamic parameters to define the roughness as the ratio of the apparent height of the surface roughness (mussel length from the wider section to the external extremity, k) on the equivalent diameter of the studied configuration. Indeed, a mussel cover may be composed of several highly compact superimposed layers. As such, layers below the external one represent a thickness of closed surfaces where no fluid dynamics is permitted, with no entrapped water volume. This closed volume corresponds therefore to the difference between the whole thickness (from the internal diameter to the extremity, th) and the surface roughness (k). Figure 3 represents the different parameters for the calculation of the equivalent diameter.

_{e}= D

_{i}+ 2 (th − k).

_{e}. Applying the same principle on the external layer, the part below the wider section of the mussel is considered closed. Consequently, only the mussel height upon the wider section is considered to define the roughness k, representing the surface irregularities impacting the flow boundary layer. Several lines were inspected and Figure 4 provides the distribution of the roughness that were measured between 1.5 and 3 cm [30].

- − to analyze the effect of a realistic roughness on the loading and to compare with other tests in the literature,
- − to highlight whether the realistic size of mussels significantly impacts the loading.

#### 2.2. Realistic Hydrodynamic Configurations

_{e}and Keulegan-Carpenter KC numbers have been shown to drive the evolution of drag forces and inertia coefficient of Morison equations with the water particle velocity. Their definition in the presence of marine growth [11] is presented in Equations (2) and (3):

^{4}< R

_{e}< 3.10

^{5}and 4 < KC < 12. The range of KC allows to detect the strong non-linearities of drag and inertia forces with particle velocity.

## 3. Experimental Setup

#### 3.1. Ifremer Flume Tank, Assembly and Instrumentation

_{x}and its frequency f. The axis coordinate system (x, y, z) is chosen so that the Ox axis is in the same direction as the current. The Oz axis is across the width of the basin and the Oy axis is vertical and oriented upwards, see Figure 7 left.

_{x;y;z}= 150 daN, fixed at each extremity of the cylinder, allow the measurement of the forces applied on the cylinder. The location of these load cells is identified by their own axis systems as shown in the Figure 7 (right). The two cylindrical load cells measure the forces applied on the cylinder only; half of the total load for each cell. The noise of the measurement is negligible. The data treatment from Morison equation requires a sinusoidal loading [33]. That explains the presence of residuals.

#### 3.2. Post-Processing of Results

- − C
_{D}for the drag coefficient in steady flow (also written C_{DS}in standards) - − C
_{d}for the drag coefficient in oscillating motion (also written C_{D}in standards) - − C
_{m}for the inertia coefficient in oscillating motion (also written C_{M}in standards).

_{e}, KC and U

_{r}). All the raw data can be found on the data share platform SEANOE [34,35].

- − Current only
- − Oscillating motion
- − Current and oscillating motion

## 4. Results and Discussion

#### 4.1. Current Only Tests

_{D}≈ 200N.

_{e}. Moreover, by comparing C1 and C2, the small change of the roughness increases the drag force of around 8% for velocities between 0.5 and 1.5 m/s.

_{D}, denoted C

_{DS}in some standards, the Strouhal number ${S}_{t}=\frac{{f}_{\nu}{D}_{e}}{U}$ (with ${f}_{\nu}$ the vortex shedding frequency) and the r.m.s. values of the lift with Reynolds number (Figure 9).

_{D}(R

_{e}) curve clearly coincides with the results presented in the literature. In the subcritical Reynolds number regime, a nearly constant value for C

_{D}of about 0.9 is found. For increasing Reynolds numbers, hence by approaching the critical flow state or lower transition that starts at R

_{e}≈ 2.1 × 10

^{5}, this value gradually decreases. The minimum value of the drag coefficient of C

_{D}≈ 0.28 at R

_{e}≈ 2 × 10

^{5}marks the transition from the critical Reynolds number regime to the upper transition. This phenomenon is well known [36,37] and confirms the accuracy of the experimental set-up and of the measurements.

^{−1}) studied. It was observed for the smallest relative roughness between 5 × 10

^{−4}and 2 × 10

^{−2}[38]. The results show that C

_{D}increases with the size of the roughness, reaching a nearly constant value of about 1.05 for C1 and 1.15 for C2. Note that API and DNV standards gathered studies from 1971 to 1986 and recommend values of 1.11 for the relative roughness of C1 (e = 0.09). However, standards do not report the results of the PhD of Theophanatos [18] (p. 96), where a discussion about similar values of e is available. In this study, cylinders fully covered by a relative roughness close to C1 were tested (e = 0.085) from a single layer of mussels of size 0.27 mm with a value of C

_{D}of 1.2, close to the value obtained by pyramids and gravels. However, the areal density of the peaks was not given. For C1 and C2, they are the following (Table 2):

- − Areal density for C1 = 2969 specimens/m
^{2}. - − Areal density for C2 = 1374.5 specimens/m
^{2}.

_{D}varies from 1.15 to 1.2 for percentages of cover of 75% and 100%, respectively. The results of the present study suggest 1.05 instead 1.11 (standards) or 1.2 (Theophanatos), which leads to a reduction of respectively 5% and 13% of the drag force.

_{D}= f(e) curves with a drag coefficient larger than 1.14 for the range of relative roughness 2 × 10

^{−6}–4.5 × 10

^{−2}. The results of this paper show that standards could suggest a value of 1.15 for larger relative roughness up to e = 0.14.

_{e}≈ 2 × 10

^{5}in the subcritical state. For larger Reynolds numbers inside this flow regime, a steep decrease of the r.m.s. values is observed. For both rough cases, the fluctuations are very low with: Cl′ ≪ 0.05.

_{e}< 2 × 10

^{5}). The vortices are shed into the wake with different frequencies. The Fourier transform of the lift forces shows (Figure 10) that the amplitude peaks of the vortex shedding frequencies are much higher for the smooth configuration with values of 25 N for 2 ≤ R

_{e}/10

^{5}≤ 2.5 when it reaches only 2 N for the two rough configurations.

#### 4.2. Oscillating Motions

_{d}(left), denoted by C

_{D}in some standards, and the inertia coefficient C

_{m}, denoted by C

_{M}in some standards, as a function of the Keulegan-Carpenter number KC. Several points are plotted per KC because several tests have been carried out at the same motion amplitude Ax but with different frequencies.

_{m}with KC for KC < 15 [16,40,41]. The results show a constant difference between the inertia coefficient of 0.3 between the two rough cylinders with a higher value for the higher relative roughness (C2). The C

_{m}of the smooth cylinder is slightly lower than the rough cases. To our knowledge, only the studies of Nath [42] reported values of C

_{m}for e = 0.1 with artificial roughness represented by cones. The values reported are significantly higher: 2.8 and 2.5 for KC = 5 and 12, respectively, where our test results give 1.4 and 1 for C1. However, again, the areal density of peaks is not reported in the paper. A realistic shape for mussels appears to drastically change the inertia coefficient.

_{d}≈ 2.5 for KC > 6 for the rough cases and C

_{d}≈ 0.5 for KC ≤ 16 for the smooth cylinder. The behavior of the rough cylinders is mainly governed by the flow and not by their motions, contrary to the smooth cylinder for which its behavior is mainly governed by its motions. Again, only the studies of Nath were carried out with a relative roughness close to ours (C1): they are compared with other studies in [18] (Figure 9.9). Again, the values reported are significantly higher: 3.2 and 2.7 for KC = 5 and 12, respectively, with large scatters where our tests give 1.7 and 2.3 for C1. The effect of roughness is shown to be significant, especially for low KC (≈3) where C

_{d}≈ 1.3 for C1 and 2.1 for C2, leading to a 62% increase of drag forces.

#### 4.3. Current and Oscillating Motions

_{D}, the oscillating drag coefficient C

_{d}and the inertia coefficient C

_{m}. These coefficients are at first presented configuration by configuration as a function of U

_{r}in Figure 12. It is first observed that mean and oscillating drag are very close for both roughness cases. The mean drag coefficients are two times higher for the rough cases than for the smooth one. These results confirm that the behavior of the rough cylinders is mainly governed by the flow and not by their motions, contrary to the smooth cylinder for which its behavior is mainly governed by its motions. Inertia coefficients for the rough cases present less dispersion than for the smooth cylinder and show a value for C2 25% higher than for C1 for U

_{r}< 10.

_{m}tends to be similar for each configuration. The higher the frequency (small U

_{r}), the lower the coefficient. Moreover, the motion amplitude has no impact on the evolution of the inertia coefficient. Regarding drag coefficients C

_{d}and C

_{D}, their behaviors are totally the opposite. The value of C

_{d}increases with the reduced velocity U

_{r}. Moreover, for a fixed frequency (or U

_{r}fixed) the amplitude parameter has a high impact and the value of the coefficient increases when the amplitude A

_{m}decreases. The exact opposite phenomenon occurs concerning the mean drag coefficient C

_{D}, with the value of the coefficient decreasing when the amplitude Am increases.

## 5. Discussion and Conclusions

_{d}≈ 1.3 for C1 and 2.1 for C2, leading to a 62% increase of drag forces. The results show a constant difference between the inertia coefficient of 0.3 between the two rough cylinders with a higher value for the higher relative roughness (C2). The vortices are shed into the wake with different frequencies and different amplitudes, the amplitude peaks of the vortex shedding frequencies are much higher for the smooth configuration than the rough configuration with a difference of about 90%. The r.m.s. values are always lower for the rough circular cylinders. A difference of about 10% between cases on the drag coefficient is observed for R

_{e}< 2 × 10

^{5}. For the oscillating cases, the inertia coefficients for the rough cases present less dispersion than for the smooth cylinder. For U

_{r}< 10, the mean drag coefficients are two times higher for the rough cases than for the smooth one. In this case, a strong dependency on the amplitude of the drag coefficients at fixed frequency for the rough cases has been highlighted, while they are stable in static. This shows that the commonly used approach of C

_{d}= ψ(KC). C

_{D}(R

_{e}) is not legitimate. Moreover, while Morison’s linearization for static drag force is justified, it means that it is not for oscillating cases, the KC defined only with the amplitude is not representative of the flow variety, this number should also depend on the frequency. These results highlight the fact that the behavior of the rough cylinders is mainly governed by the flow and not by their motions, contrary to the smooth cylinder for which its behavior is mainly governed by its motions. Moreover, the results have been compared with similar studies carried out for high relative roughness (0.1); significant differences have been observed due to the fact that the shape of the rough cylinders is not well described in these studies: key information about the organization and the areal density of peaks are usually not given.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Typical underwater picture with the organization of the specimen; (

**b**) corresponding elliptical shape with major and minor axis: purple (0°), green (+/− 30°), black (+/− 45°), blue (+/− 60°) and red (90°); (

**c**) using the aksi3D

^{®}system (tested at IFREMER).

**Figure 2.**(

**a**) Definition of the roughness for a given size of the shell S (numbers in cm); (

**b**) typical extraction of the roughness from image processing.

**Figure 5.**Mussels’ roughness shape for C1 on top and C2 at the bottom. On the right, mussels distribution around the cylinder with the C2 shape.

**Figure 6.**On the left, from the top to the bottom, cases S, C1 and C2. On the right, C2 roughness mounted on the cylinder.

**Figure 7.**Presentation of the global set-up with the 6-axis hexapod (

**left**), the smooth cylinder (

**top center**) and one of the rough cylinder (

**bottom center**) and axis coordinate system (x, y, z) used in tests (

**left**). In black, the main system. The Ox axis is common to all systems and corresponds to the main flow direction. In red, the axes of the load cells (

**right**and

**left**).

**Figure 9.**Distribution of the three main hydrodynamic parameters as function of the Reynolds number from direct force measurements for the three test cases: S, C1 and C2.

**Figure 10.**Lift forces Fourier transform as function of the Reynolds number for the three test cases: S, C1 and C2.

**Figure 12.**Evolution of C

_{m}, C

_{d}and C

_{D}vs. KC for the S (

**top**), C1 (

**middle**) and C2 (

**bottom**) cases.

N° Position/Angle | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

X | 8 | 25 | 41 | 58 | 8 | 24 | 43 | 59 | 8 | 26 | 42 | 58 | 8 | 25 | 41 | 58 |

Y | 59 | 58 | 58 | 59 | 42 | 42 | 42 | 41 | 26 | 25 | 26 | 23 | 9 | 8 | 9 | 8 |

Inclination of major axis/axis x | +45° | −30° | +30° | −45° | +45° | +45° | +90° | 0° | +45° | +90° | 0° | +90° | 0° | −30° | +30° | +60° |

Configurations | D_{i} [mm] | D_{ext} [mm] | k [mm] | th [mm] | D_{e} [mm] | e = k/D_{e} | Mass System [daN] | Areal Density for nb. Specimens/m^{2} |
---|---|---|---|---|---|---|---|---|

S | 160 | 160 | 0 | 0 | 160 | 0 | 47 | - |

C1 | 160 | 260 | 20 | 50 | 220 | 0.091 | 105 | 2969 |

C2 | 160 | 280 | 30 | 60 | 220 | 0.136 | 110 | 1374.5 |

Configurations | KC | U_{r} | Re/10^{5} |
---|---|---|---|

S | 3.9–15.7 | 4.1–39.1 | 0.4–2.7 |

C1 | 2.5–11.4 | 3–56.8 | 0.55–3.8 |

C2 | 2.5–11.4 | 3–56.8 | 0.55–3.8 |

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## Share and Cite

**MDPI and ACS Style**

Marty, A.; Schoefs, F.; Soulard, T.; Berhault, C.; Facq, J.-V.; Gaurier, B.; Germain, G.
Effect of Roughness of Mussels on Cylinder Forces from a Realistic Shape Modelling. *J. Mar. Sci. Eng.* **2021**, *9*, 598.
https://doi.org/10.3390/jmse9060598

**AMA Style**

Marty A, Schoefs F, Soulard T, Berhault C, Facq J-V, Gaurier B, Germain G.
Effect of Roughness of Mussels on Cylinder Forces from a Realistic Shape Modelling. *Journal of Marine Science and Engineering*. 2021; 9(6):598.
https://doi.org/10.3390/jmse9060598

**Chicago/Turabian Style**

Marty, Antoine, Franck Schoefs, Thomas Soulard, Christian Berhault, Jean-Valery Facq, Benoît Gaurier, and Gregory Germain.
2021. "Effect of Roughness of Mussels on Cylinder Forces from a Realistic Shape Modelling" *Journal of Marine Science and Engineering* 9, no. 6: 598.
https://doi.org/10.3390/jmse9060598