# On the Digital Twin of The Ocean Cleanup Systems—Part I: Calibration of the Drag Coefficients of a Netted Screen in OrcaFlex Using CFD and Full-Scale Experiments

^{*}

## Abstract

**:**

## 1. Introduction

`System 002`, also known as “Jenny”, was deployed in the GPGP for a testing campaign. It replaced

`System 001`, which consisted of a 600 m-long passive floating barrier with a 3 m-deep skirt, designed to take advantage of natural oceanic forces, such as currents and winds, to passively capture plastic waste. As opposed to

`System 001`, Jenny was designed to be a 800 m towed (i.e., active propulsion) floating structure composed of a containment boom and a permeable net-like skirt generally inspired by the fishing industry. As a matter of fact, the centuries of existence of fishing and aquaculture have set the ground for the development of most ocean applications involving net-like devices. In essence, the existing knowledge is directly extrapolated onto new technologies along with some additional fine-tuning. In this context, the netting, considered as a basic element of most fishing gears, has been subjected to numerous investigations. Specially, the studies on the hydrodynamic characteristics of the netting highlight the necessity of optimizing them for efficiency purposes.

`System 002`will be followed by a scale-up phase to a fleet of 2 km-long cleanup systems (

`System 03`). It is expected that a larger system will not only increase fuel consumption (implicitly the CO${}_{2}$ emission), but also decrease the system’s maneuverability such as changing heading and speed. Consequently, this decreases the capacity to sweep through previously identified plastic hot spots, meaning that the efficiency is potentially reduced. Therefore, the project KPIs, the system performance, and the whole offshore operation will have as a backbone the comprehension of the hydrodynamic behavior of the cleanup systems.

`System 002`is depicted above water in Figure 1a and underwater in Figure 1b. At first glance, the cleanup system in operation resembles a fishing net during trawling, but a closer examination reveals the following differences:

- The cleanup system catches plastic at the sea surface. Trawling is mostly performed close to the sea bed or at mid-water depth. That means that the netting, ropes, and floaters of the cleanup system are exposed to cyclic wave-induced forces for longer time periods than fishing rigs. In turn, that leads to increased wear and tear, as has been verified during the
`System 002`test campaign. - The cleanup system netting of
`System 002`has a mesh size of 10 mm to catch also mesoplastics, which are plastics with sizes between 0.5 cm and 5 cm. The netting used in the trawling has normally a mesh size larger than 10 mm. That means that the drag force on a 800 m-long system (`System 002`) or 2 km-long system (`System 03`) is considerably larger than from trawling. As a consequence, understanding this force and the variables influencing it is particularly important for the cleanup application. - The wingspan of
`System 002`adopts a “U-shape” during operation, and the netting draft is 3 m. That means that the bottom of the system is completely open, allowing fish to easily escape. Additionally, in the retention zone’s bottom, there are openings to allow marine life to escape. This emphasizes that the purpose is to capture plastics, not fish. Therefore, since the netting configuration is different from fishing nets, it is valuable to understand how this new application of netting performs in water, how it interacts with marine life, and how the offshore operation around it must be efficient to make it work. All these points were thoroughly studied and monitored within The Ocean Cleanup, and the present work is part of it. - An important difference between catching plastic and fishing is how dispersed the plastic is at the ocean’s surface, in comparison to a dense school of fish. There is a large amount of plastic floating in the GPGP, but it circulates on a massive area of the North Pacific Ocean. That means that the area density of the catch that the cleanup system encounters is much lower than in the fishing case. As a consequence, the cleanup system needs to sweep a much larger area to match a fish catch with a plastic catch. Additionally, The Ocean Cleanup objective is to get rid of 90% of the floating plastic in the GPGP by 2040, but it is not the objective of the fisheries to deplete fish to that level. Therefore, the energy invested in cleaning is larger than in fishing, making the efficiency and the hydrodynamic performance of the cleanup system even more relevant.

`System 002`Digital Twin. The validation was based on data directly measured during our GPGP offshore operations with

`System 002`. The method can be summarized as a three-stage validation process, where the following three numerical models were involved:

**OrcaFlex**is used for the dynamic analysis of offshore marine systems, including floating structures, moorings, and risers. We used it for simulating the behavior of our complex ocean cleanup system under different environmental conditions such as waves, currents, and winds. It provides a comprehensive set of features for modeling the geometric structures of the system and its dynamic response, as well as that of the lines to tow the system. It is based on Morison’s equation [30] and potential flow to model the forces on a structure generated by the fluid flow, such as the forces on a mooring line due to waves. It takes into account the inertia and drag forces of the fluid, as well as the added mass of the structure.**AquaSim**[31,32] is used to predict the behavior of aquatic ecosystems and the impacts of environmental stressors. It uses numerical methods to solve the flow around fishing farms and the resulting loads. It is a Finite-Element Analysis (FEA) program, which allows further details on the physics of interest. On the one hand, AS is ideal to increase the level of accuracy of the drag calculation on the cleanup system. On the other hand, the twine-by-twine calculation increases the computational time, specially in irregular waves. Since AS includes a formula to account for the shielding effects, it is seen, from the perspective of the present work, as an initial approximation to that effect.**Basilisk**[33,34,35] is a Direct Numerical Simulation (DNS) solver, which offers an accurate insight into the flow around the twines, especially if they are in tandem at low $\theta $. For this purpose, we highlight the cross-sectional flow features impacting the drag coefficient around individual twines to trigger the shielding effect due to the various angles of attack of the net.

## 2. Materials

#### 2.1. GPGP Measured Data

`System 002`GPGP campaign, from August 2021 until December 2022, and more recently, during the GPGP campaigns of systems larger than

`System 002`.

- The mean tension was calculated for periods of 3 h, for each of the towing lines. The sum of the mean values for each towline provides the combined towline tension, which is the variable to be validated in the present work.
- The error associated with the combined towline tension was calculated. Taking the mean tension for a specific time period introduces an error because the true mean value, for a specific metocean condition, can be anywhere between the extreme values of the dynamic response. Therefore, the difference between the calculated mean and the maximum tension for the 3 h period was taken as the associated error.
- The RLM has a high accuracy, typically between 0.5% and 2.0% of the measured load. The associated error described in the previous point is typically higher than the error associated with each instant measurement.

- A Doppler Velocity Logger (DVL) supplies the ${u}_{\mathrm{stw}}$ of the vessel, which is registered on a computer on board the vessel.
- The Speed Over Ground (SOG) of the vessel combined with the sea surface current velocity estimation, from the X-band radar of the vessel.

- The DVL on the vessels has an accuracy of 1.5%.
- Since two sources of data are considered to calculate the average value, an error of half the difference between the two measured values is introduced.
- Finally, the maximum between the previous two errors is taken as the speed-through-water-associated error.

#### 2.2. OrcaFlex

`System 002`. Morison’s equation for the calculation of the wave loads on fixed vertical cylinders involves two force components: the fluid acceleration as the fluid inertia force and the fluid velocity as the drag force. It reads:

#### 2.3. AquaSim

#### 2.4. Basilisk

- Continuity equation:$$\nabla \xb7{\mathit{u}}^{*}=0,\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\mathrm{over}\phantom{\rule{4.pt}{0ex}}\Omega .$$
- Combined momentum equations:$$\left(\frac{\partial {\mathit{u}}^{*}}{\partial {t}^{*}}+{\mathit{u}}^{*}\xb7\nabla {\mathit{u}}^{*}\right)=-\nabla {p}^{*}+\frac{1}{{\mathcal{R}e}_{t}^{*}}{\nabla}^{2}{\mathit{u}}^{*}-{\mathit{\lambda}}^{*}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\mathrm{over}\phantom{\rule{4.pt}{0ex}}\Omega ,$$$$\begin{array}{c}\hfill ({\rho}_{r}^{*}-1){V}_{b}^{*}\left(\frac{d{\mathit{v}}_{b}^{*}}{dt}-\mathcal{F}{r}^{*}{\displaystyle \frac{\mathit{g}}{g}}\right)-{\int}_{B\left(t\right)}{\mathit{\lambda}}^{*}d{\mathit{x}}^{*}=\mathit{0},\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\mathrm{over}\phantom{\rule{4.pt}{0ex}}B\left(t\right),\end{array}$$$$\begin{array}{c}\hfill {\mathit{I}}_{b}^{*}\frac{d{\mathit{\omega}}^{*}}{d{t}^{*}}+{\mathit{\omega}}^{*}\times {\mathit{I}}_{b}^{*}\xb7{\mathit{\omega}}^{*}+\sum _{j}{\left({\mathit{F}}_{\mathrm{c}}\right)}_{j}^{*}\times {\mathit{R}}_{j}^{*}+{\int}_{B\left(t\right)}({\mathit{\lambda}}^{*}\times {\mathit{r}}^{*})\xb7d{\mathit{x}}^{*}=\mathit{0},\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\mathrm{over}\phantom{\rule{4.pt}{0ex}}B\left(t\right),\end{array}$$$${\mathit{u}}^{*}-({\mathit{v}}_{b}^{*}+{\mathit{\omega}}^{*}\times {\mathit{r}}^{*})=\mathit{0},\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{3.33333pt}{0ex}}\mathrm{over}\phantom{\rule{4.pt}{0ex}}B\left(t\right),$$

## 3. Method

#### 3.1. Overview of the Method

- The variable to validate is the combined towline tension, defined as the sum of the tensions in each towline, for various speeds through water ${\mathit{u}}_{\mathrm{stw}}$. The span is the distance between the wing’s extremities as depicted in Figure 8. The figure also shows the System Length ($SL$), towlines, wings, and Retention Zone (RZ). The System Ratio ($S{R}^{*}$) is defined as the ratio between the span and the system length ($S{R}^{*}=span/SL$).Three span values are considered as shown in Table 1 for
`System 002`’s length equal to 800 m: - The OF model validation was performed in three cycles:
**First cycle**: Simulation based on the initial estimation of the OF axial drag coefficient ${C}_{D,\mathrm{OF},\phantom{\rule{4.pt}{0ex}}\mathrm{a}}^{*}$. This step is detailed in Section 3.2.**Second cycle**: Triggered by discrepancies between the model and the GPGP data, especially for a narrow span, we used the AS model of a 1 m × 1 m piece of the system’s net at multiple $\theta $. Then, the difference between the drag forces on a 1 m × 1 m section of the net from OrcaFlex and AquaSim was calculated and written as:$$\begin{array}{c}\hfill \Delta {\mathit{f}}_{D}={\mathit{f}}_{D,\mathrm{OF}}-{\mathit{f}}_{D,\mathrm{AS}}\end{array}$$Then, the Root Mean Square (RMS) of the set of differences for a group of $\theta $, corresponding to a certain span, can be calculated:$$\begin{array}{c}\hfill RMS=\sqrt{\frac{1}{{N}_{\theta}^{*}}{\displaystyle \sum _{j=1}^{{N}_{\theta}^{*}}}{|\Delta {\mathit{f}}_{D}|}_{j}^{2}}\end{array}$$**Third cycle**: Triggered by the necessity to verify the AS results, using a CFD model, a two dimensional piece of the net was simulated for various $\theta $ to quantify the effect of the vortex shedding on the twines in tandem on the average drag coefficient. This gives a piecewise definition of the average drag coefficients of the net. They are given as a function of ${u}_{\mathrm{stw}}$ and $\theta $ and used in the AS drag force Equation (28), replacing the AS drag coefficients. Then, the same optimization (Equations (20) and (21)) can be carried out one more time.

#### 3.2. OrcaFlex Drag Force Calculation

- Due to the way the net is modeled, since potential flow and one-way coupling were considered, there was no option to directly include or capture what is called the shielding effect between the twines of a submerged net. In contrast, the drag calculation in the software AquaSim and Basilisk does include this effect.
- Due to the way the net was modeled, it was not possible to calculate the drag twine-by-twine and actually differentiate between horizontal and vertical twines. In contrast, the drag calculation in the software AquaSim does include this option.
- The effect of the underwater cross-section shape of the net has on the drag force was not included in the model. Both OF normal drag coefficients were considered equal. That is, ${C}_{Dx,\mathrm{OF}}^{*}={C}_{Dy,\mathrm{OF}}^{*}={C}_{D,\mathrm{OF},n}^{*}={C}_{D,n}^{*}$. This effect can be included by considering the torsion of the drag equivalent line, but that considerably increases the computation time.

#### 3.3. AquaSim Drag Force Calculation

#### 3.4. Comparing GPGP Data with Simulation Results

`System 002`simulations in head sea and nominal span. The wave factor is the ratio between the towline force in waves and the towline force in no waves. They are presented in Table 2 for various ${u}_{\mathrm{stw}}$ and various sea states. From this table, it can be deduced that the wave factors decrease with increasing ${u}_{\mathrm{stw}}$, and they increase with increasing sea state. Since

`System 002`normally operates at ${u}_{\mathrm{stw}}\in [0.75:1.0]$ m/s, it makes sense to focus on that velocity range during the validation procedure. It also makes sense to validate for year-average conditions, that means for annual p50 conditions. Then, a wave factor of 1.15 (reading from the p50 row and 0.75 m/s column) can be used to multiply the combined towline tension estimated by OrcaFlex. That leads to a valid and conservative comparison between the simulation and real-world data.

#### 3.5. Problem Setup for CFD Model

#### 3.5.1. Space Convergence on Flow Past a Circular Cylinder

#### 3.5.2. Convergence on the Drag Coefficient of Multiple Twines in Tandem at Various Angles of Attack

## 4. Results

#### 4.1. First Validation Cycle

`System 002`. ${\mathit{u}}_{\mathrm{stw}}$ was varied from 0.25 m/s to 1.0m/s in no-wave conditions and with a simulation time $t=2500$ s to reach a steady span.

- The axial drag coefficient ${C}_{D,\mathrm{OF},a}^{*}$ led to a DT estimation larger than the measured data in the narrow span. Specifically, the average deviation between the 15% increase area and real-world data was about 276%. The main phenomenon that was not captured by OF in this case was the shielding effect (cf. Section 2.3 for an explanation on this effect).
- The axial drag coefficient ${C}_{D,\mathrm{OF},a}$ produced a 15% area that was close to the GPGP data points for the nominal span. Nevertheless, the majority of the data points were still outside of the area, and the computed mean deviation was about −3% (minus sign meaning an underestimation of the ground truth). The expectation was that the second and third validation cycle curves will comply even better with the validation criteria. The reason behind this expectation is that ${C}_{D,\mathrm{OF},a}$ was not optimized for the angles of attack to the flow and the twine-by-twine calculation had not been included yet.
- The axial drag coefficient ${C}_{D,\mathrm{OF},a}$ produced a 15% area that was close to the GPGP data points for a wide span. Even some data points were inside the area, and the calculated mean deviation was just 1%. That means that the OF model might be considered as validated at this cycle for a wide span. Nevertheless, the expectation was that the 2nd and 3rd validation cycle curves would comply with the validation criteria in a more-conservative manner, following the same reasoning as for the nominal span.

#### 4.2. Second Validation Cycle

#### 4.2.1. Optimization Cases

#### 4.2.2. Findings Based on Second validation Cycle Results

- The optimized ${C}_{D,\mathrm{OF},a}^{*}$ for a narrow span was definitely more accurate than the first cycle value. That demonstrated the influence of the shielding effect on the drag coefficients. Nevertheless, the 15% increase area was still below the data around ${\mathit{u}}_{\mathrm{stw}}=1.0$ m/s and ${\mathit{u}}_{\mathrm{stw}}=1.1$ m/s. This means that the DT was slightly underestimating for narrow span. The mean deviation in this case was −10%.
- The optimized ${C}_{D,\mathrm{OF},a}^{*}$ also produced a more-accurate and more-conservative nominal span curve, in comparison with the first cycle, since all data points between ${u}_{\mathrm{stw}}=0.75$ m/s and 1.0 m/s were inside the 15% increase area or below the curve. Having points below the curve might mean that the second cycle curve was slightly overestimating the towline tension for nominal span. Indeed, the mean deviation was about 14%.
- The optimized ${C}_{D,\mathrm{OF},a}^{*}$ led to the majority of the data points falling inside the 15% increase area. The mean deviation was computed as 6%. Then, the DT can be considered as validated and sufficiently overestimating for a wide span. This also means that the AS calculation was enough to calibrate the OF axial drag coefficient ${C}_{D,\mathrm{OF},a}^{*}$ and to obtain a proper estimation of the towline tension in a wide span.

#### 4.3. Third Validation Cycle

- The optimized ${C}_{D,\mathrm{OF},a}^{*}$ for a narrow span produced more-accurate results than the first cycle. The results were also more conservative than the second cycle ones. Nevertheless, the curve in no waves was above all points. This means that the DT was overestimating, specifically by a mean deviation of 97%. This overestimation might be due to a missing phenomenon or effect related to the flexibility of the net and the shape it adopts under water. In spite of the overestimation and from an engineering perspective, the 3rd cycle curve was preferred over the 2nd cycle curve. A better option, again from an engineering perspective and to obtain more-accurate results, is to average both curves. That averaged result is plotted in Figure 19d. In terms of validation, it can be said that the DT had not been validated yet for the narrow span. The validation for narrow span depends on future studies. Nevertheless, the validation effort brought the 276% deviation of the 1st cycle to about a −10% deviation after the 2nd cycle and to about 97% after the 3rd cycle. If the averaging option was applied, the combined deviation was about 43%.
- The optimized ${C}_{D,\mathrm{OF},a}^{*}$ produced a more-accurate nominal span curve than for the second cycle, since almost all GPGP data points were inside the 15% increase area curve. The mean deviation in this case was just 7%. This also means that the DT was validated for a nominal span.
- The optimized ${C}_{D,\mathrm{OF},a}$ led to the majority of the GPGP data points falling inside the 15% increase area, and the mean deviation was calculated to be 8%. Then, the DT at the third cycle can be considered as validated for a wide span. Since the wide span curve was considered as validated already on the second cycle, this result also means that the CFD calculation verified the AS calculation for a wide span.

#### 4.4. Calibrated Drag Coefficients for `System 002`

`System 002`’s net and for ${u}_{\mathrm{stw}}>0.5$ m/s.

#### 4.5. Boundaries for the Application of the Results

`System 002`and the present study, highlighting the inputs, results, project phase, and sector of application. Some of these findings can be readily utilized for new netting systems (colored in orange) when opting for OrcaFlex as the software to build the DT. These encompass the optimization methodology and the software’s constraints and potential opportunities. In contrast, the remaining portion of the results (colored in green) requires modification, recalculation, or re-modeling to align with the requirements of the new netting system.

`System 03`). Second, the present study considered three discrete system ratios, but in reality, the validation needs to be performed for a larger range of $S{R}^{*}$.

## 5. Discussion and Conclusions

#### 5.1. Objective-Related Conclusions

- The accuracy of the DT on the towline tension estimation of the ocean cleanup
`System 002`in wide span ($S{R}^{*}\sim 0.8$) was improved from having several GPGP data outside of the 15% increase area. Moreover, the DT for the wide span was validated against the GPGP data, with sufficient overestimation (respectively, 6% and 8% mean deviations), at the 2nd and 3rd validation cycles. - The accuracy of the DT estimation of the towline tension of the cleanup
`System 002`in the nominal span ($S{R}^{*}\sim 0.6$) was improved from from having most of the GPGP data outside of the 15% increase area. Moreover, the OF model (i.e., the DT) for the nominal span was validated against the GPGP data at the third validation cycle, with a mean deviation of 7%. - The accuracy of the DT on the towline tension estimation of the ocean cleanup
`System 002`in the narrow span ($S{R}^{*}\sim $ 0.02) was improved. An initial deviation of 276% with respect to the GPGP data was reduced in the 2nd cycle to −10% and in the 3rd cycle to 97%. In spite of the OF model for the narrow span having not been validated yet and that more GPGP data points are required for a more-robust validation, a combined deviation of 43% can be considered for engineering and design purposes, once the average of the 2nd and 3rd cycle curves is taken. - The results obtained for
`System 002`can be either directly applied to`System 03`and future systems, if the netting and system ratio inputs are the same, or easily reevaluated, recalculated, and remodeled in case the inputs are different (cf. Figure 21). Therefore, considering the same input,`System 03`DT can be also considered as validated for wide and nominal spans. - The previous conclusions have important implications for The Ocean Cleanup development. First, the DT of
`System 002`and`System 03`, provided that the latter has the same net and SR characteristics of the former, can be used to improve the efficiency of the operations. As an example, the towing configuration can be dynamically optimized through a trip, to sail with a large span when the plastic area density is high (plastic hot-spots) and in a short span in low-density areas. The under-designing and over-designing of the cleanup system were minimized, further reducing capital expenditure, but also operational expenditure by limiting the case of under-designed systems experiencing failures during operation. The maneuverability of the system can also be improved. As an example, the effect of optimizing the netting sizes can be accurately estimated. That will also improve efficiency since the system will reach and be swept through plastic hot-spots faster. Ultimately, all these improvements will bring the KPIs to values that are below the projected targets.

#### 5.2. Wide-Ranging Conclusions

- The quantification of the shielding effect is considerably different if it is performed with the AS calculation or with the CFD model. On top of that, neither the Basilisk model nor AS produce a towline tension curve that accurately fits the GPGP data for a narrow span. Therefore, both calculation methods should be investigated to find the source of the difference.
- Through the validation cycles, it was demonstrated that the semi-empirical formula of Naumov et al. [11] can be used to obtain drag coefficients that produce sufficiently accurate towline tension estimations when the net being towed experiences a flow that is close to perpendicular along most of its length. In terms of $\theta $, 50% or more of the angles found along the length are distributed between 45° and 90°. The same applies for the AS calculation and the CFD-derived drag coefficients. Furthermore, additional (future) GPGP data for a narrow span need to be included to strengthen the validation.
- Through the validation cycles, it was demonstrated that the AS drag calculation was consistent with the CFD drag calculation until approximately $\theta \sim {24}^{\xb0}$. Below that angle, which is close to parallel flow, AS seemed to underestimate the real drag and the CFD model seemed to overestimate it. Therefore, a more in-depth investigation of AS Equation (8) and of the CFD model to identify missing physical phenomena is required. In that way, the root causes of the respective deviations can be identified.
- As clearly depicted in the schematic of Figure 21, it is possible to adapt and apply the results of the present study to different systems, utilized in sectors ranging from river plastic cleaning to oceanography, through to trawling, aquaculture, oil spill response, and marine ecology. In particular, the optimization method of the OrcaFlex drag coefficient can be directly applied to any of these applications, as well as the lessons on the limitations and opportunities of the software. That should allow running OrcaFlex simulations that produce accurate estimations on motions, loads, maneuverability, operability, survivability, and steering strategies, among others. This can be combined with the modeled data on the catch itself (plastic, fish, plankton, oil, etc.) to obtain accurate estimations on catch rates. Then, considering the invested energy or input, this would lead to efficiency estimations. Ultimately, this allows developing optimization actions to improve the efficiency of the system.Additionally, the present study can also be utilized by other applications or sectors as a guideline to develop the following activities:
- To understand the hydrodynamic drag force experienced by submerged nets and the previous research related to it.
- To validate a model using the materials, knowledge, and method presented in this study.

## 6. Directions of Further Research

#### 6.1. Multi-Scale Numerical Approach

#### 6.2. How to Hydrodynamically Choose a Net for Our KPIs?

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Above-water and underwater footage of

`System 002`. Port-side vessel. Starboard-side vessel. Port-side tow bar and towing bridle, connected to a towing line. Starboard-side tow bar and towing bridle, connected to a towing line. Port-side wingspan. Starboard-side wingspan. Retention opening. Retention zone. Extraction pick-up line. (

**a**) Aerial view of

`System 002`towed by two vessels. (

**b**) Underwater view of the retention zone made of nets.

**Figure 3.**Example comparison between ${u}_{\mathrm{stw}}$ from DVL and ${u}_{\mathrm{stw}}$ calculated with SOG-sea current.

**Figure 6.**A twine in the wake of a leading twine. Illustration with dimensionless vorticity field from 2D direct numerical simulation.

**Figure 11.**(

**a**) Top view of Jenny’s wing modeled as collections of successive plane nets. (

**b**) The 2D cross-sectional sketch of a plane net modeled as circular cylinders.

**Figure 13.**Illustration of the drag coefficient and the numerical parameters related to its computation. (

**a**) Instantaneous drag coefficient at ${\mathcal{R}e}_{t}^{*}=1000$ for various smallest grid sizes. (

**b**) Instantaneous drag coefficient at ${\mathcal{R}e}_{t}^{*}=1600$ for various smallest grid sizes. (

**c**) Instantaneous number of cells for ${\delta}^{*-1}=128$ as a function of c at ${\mathcal{R}e}_{t}^{*}=1000$. (

**d**) Instantaneous number of cells for ${\delta}^{*-1}=128$ as a function of c at ${\mathcal{R}e}_{t}^{*}=1600$. (

**e**) Instantaneous drag coefficient for ${\delta}^{*-1}=128$ as a function of ${c}^{*}$ at ${\mathcal{R}e}_{t}^{*}=1000$. (

**f**) Instantaneous drag coefficient for ${\delta}^{*-1}=128$ as a function of ${c}^{*}$ at ${\mathcal{R}e}_{t}^{*}=1600$.

**Figure 14.**Close-up illustration of the shielding effect mechanism for $\theta ={8}^{\xb0}$ at ${\mathcal{R}e}_{t}^{*}=1000$. Blue and red, respectively, indicate negative and positive values of the vorticity fields.

**Figure 15.**Illustration of the flow structure using the velocity field ${u}_{x}$ as a function of $\theta $ at ${\mathcal{R}e}_{t}^{*}=1000$ and ${t}^{*}=90$. Blue and red, respectively, indicate low and high values of ${u}_{x}^{*}$.

**Figure 16.**Influence of the number of twines ${N}_{t}^{*}$ on the instantaneous total drag coefficient for various low angles of attack $\theta $ at ${\mathcal{R}e}_{t}^{*}=800$.

**Figure 17.**Dependence of the drag coefficient on the angle of attack. The median of the fluctuations is shown with the standard deviation.

**Figure 18.**Dependence of the lift coefficient on the angle of attack. Median of the fluctuations is shown with standard deviation.

**Figure 19.**Dependence of the combined towline tension on the ${\mathit{u}}_{\mathrm{stw}}$. Superscripts 16, 480, and 630 indicate the span in meters. The colored areas are the 15% increase in the mean load. GPGP data selected from August 2021 to August 2022. The error bar estimation is explained in Section 2.1.

**Figure 22.**Interdependence of the twine diameter, the mesh size, the solidity, and the drag coefficient of a net. Adapted from the work of Cheng et al. [13]. (

**a**) Dependence of the solidity $S{n}^{*}$ on the twine diameter and the mesh size. (

**b**) Dependence of the drag coefficient on the solidity for nylon nets at $\theta ={90}^{\xb0}$. (I) Tang et al. [59], (II) Gansel et al. [60], (III) Tsukrov et al. [61].

Span Type | Span (m) | System Ratio | System Status |
---|---|---|---|

Narrow | ≈16 | 0.02 | Towing behind one vessel |

Nominal | ≈480 | 0.6 | Optimal performance in operation |

Wide | ≈630 | 0.8 | Maximize plastic catch |

**Table 2.**Wave factors for several ${\mathit{u}}_{\mathrm{stw}}$ and several sea states.

^{(†)}Annual non-exceeding probability in the GPGP considered location.

Sea State | ${\mathit{u}}_{\mathbf{stw}}$ (m/s) | ||||||
---|---|---|---|---|---|---|---|

a.n.e.p. ^{(†)} | ${\mathit{H}}_{\mathit{s}}$ (m) | ${\mathit{T}}_{\mathit{p}}$ (s) | 0.1 | 0.25 | 0.5 | 0.75 | 1.0 |

p25 | 1.7 | 10.8 | 3.83 | 1.74 | 1.19 | 1.09 | 1.11 |

p50 | 2.3 | 11.9 | 4.72 | 2.02 | 1.30 | 1.15 | 1.13 |

p75 | 3.0 | 11.9 | 6.77 | 2.62 | 1.54 | 1.28 | 1.19 |

p90 | 4.1 | 13.1 | 9.56 | 3.37 | 1.81 | 1.41 | 1.26 |

Optimization Case | Span Type | Angles |
---|---|---|

1 | Narrow | ${0}^{\xb0}\le \theta \le {2}^{\xb0}$ |

2 | Nominal | ${30}^{\xb0}\le \theta \le {90}^{\xb0}$ |

3 | Wide | ${45}^{\xb0}\le \theta \le {90}^{\xb0}$ |

**Table 4.**Mesh cross flow drag coefficients (${C}_{D,\mathrm{mem}}^{{*}^{\prime}}$) for the 2nd and 3rd validation cycles.

$\mathit{\theta}$ (${}^{\xb0}$) | 2nd Cycle | 3rd Cycle |
---|---|---|

90 | 1.5999 | 1.5967 |

45 | 1.5999 | 1.5589 |

30 | 1.5999 | 1.3822 |

20 | 1.5589 | 1.2649 |

10 | 0.5639 | 0.8492 |

5 | 0.2005 | 0.6076 |

3 | 0.0933 | 0.5253 |

2 | 0.0508 | 0.4849 |

1 | 0.0180 | 0.4732 |

0 | 0.0 | 0.4614 |

**Table 5.**Recommended axial drag coefficients (${C}_{D,\mathrm{OF},a}^{*}$) for OrcaFlex

`System 002`model.

Span Type | 1st Cycle | 2nd Cycle | 3rd Cycle | 3rd Cycle—Averaged |
---|---|---|---|---|

Narrow | 0.208 | 0.010 | 0.082 | 0.046 |

Nominal | 0.208 | 0.332 | 0.285 | 0.285 |

Wide | 0.208 | 0.301 | 0.324 | 0.324 |

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## Share and Cite

**MDPI and ACS Style**

Gonzalez Jimenez, M.A.; Rakotonirina, A.D.; Sainte-Rose, B.; Cox, D.J.
On the Digital Twin of The Ocean Cleanup Systems—Part I: Calibration of the Drag Coefficients of a Netted Screen in OrcaFlex Using CFD and Full-Scale Experiments. *J. Mar. Sci. Eng.* **2023**, *11*, 1943.
https://doi.org/10.3390/jmse11101943

**AMA Style**

Gonzalez Jimenez MA, Rakotonirina AD, Sainte-Rose B, Cox DJ.
On the Digital Twin of The Ocean Cleanup Systems—Part I: Calibration of the Drag Coefficients of a Netted Screen in OrcaFlex Using CFD and Full-Scale Experiments. *Journal of Marine Science and Engineering*. 2023; 11(10):1943.
https://doi.org/10.3390/jmse11101943

**Chicago/Turabian Style**

Gonzalez Jimenez, Martin Alejandro, Andriarimina Daniel Rakotonirina, Bruno Sainte-Rose, and David James Cox.
2023. "On the Digital Twin of The Ocean Cleanup Systems—Part I: Calibration of the Drag Coefficients of a Netted Screen in OrcaFlex Using CFD and Full-Scale Experiments" *Journal of Marine Science and Engineering* 11, no. 10: 1943.
https://doi.org/10.3390/jmse11101943