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Experimental Setup

An experimental setup refers to the specific arrangement and conditions in which an experiment is conducted to investigate a hypothesis or research question. It involves manipulating independent variables, measuring dependent variables, and controlling extraneous factors.

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Control Group : A control group is a group in an experiment that does not receive the treatment or manipulation being tested. It serves as a baseline for comparison with the experimental group.

Independent Variable : The independent variable is the factor that researchers deliberately manipulate or change in an experiment to observe its effect on the dependent variable.

Dependent Variable : The dependent variable is the outcome or response that researchers measure or observe in an experiment. Its value depends on changes made to the independent variable.

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Experimental setup

When the competition between two species needs to be tested, species need to be grown together. However, the specimen distribution within the experimental units (pots) is almost as important as the number of replicates that we are using (see Experimental design ). The different species need to alternate and be evenly distributed in the experimental unit.

Once all treatments have been set up, the experimental units typically need to be randomly distributed in the available space. The reason behind distributing the experimental units randomly is to avoid the interference of any local condition on certain treatments (if they are allocated together). By doing this, all treatments will be equally affected by the conditions in the experimental area.

However, if the number of replicates is low (i.e. less than 5), it is more convenient to use a stratified random design. In a stratified random design, the replicates are first divided into groups and then distributed randomly among them. By doing this, it is ensured that the three replicates of the same treatment are not placed close to each other, and thus, spatial bias is avoided.

Experimental Setup

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To run a successful electrochemical experiment it is essential that the experimental setup is electrically correct and appropriate for the experiment planned. There are several points that should be carefully considered before the experiments are started. They include proper choice of the working, reference and auxiliary electrodes, proper selection of the solvent and supporting electrolyte, proper selection of the electroanalytical technique and its parameters, proper wiring of the electrochemical circuit, and, finally, proper setting of the parameters of the potentiostat/voltammograph used.

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Experimental Section

Electroanalytical instrumentation—how it all started: history of electrochemical instrumentation

Ciszkowska M, Stojek Z (2000) Anal Chem 72: 754A

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Bard AJ, Faulkner RF (2000) Electrochemical methods, 2nd edn. John Wiley, New York

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Stojek, Z. (2005). Experimental Setup. In: Scholz, F. (eds) Electroanalytical Methods. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04757-6_16

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I. INTRODUCTION

Ii. test case description, iii. aerodynamic forces and moments, iv. experimental method, v. numerical method, vi. experimental results, a. effects of container arrangements on wind loads, b. effects of a tarpaulin covering deck containers, vii. numerical investigations, a. numerical setup, b. discretization study, c. comparative experimental and numerical predictions, viii. conclusions, acknowledgments, author declarations, conflict of interest, author contributions, data availability, experimental and numerical investigations of effects of ship superstructures on wind-induced loads for benchmarking.

Note: This paper is part of the special topic, Recent Advances in Marine Hydrodynamics.

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Ould el Moctar , Udo Lantermann , Vladimir Shigunov , Thomas E. Schellin; Experimental and numerical investigations of effects of ship superstructures on wind-induced loads for benchmarking. Physics of Fluids 1 April 2023; 35 (4): 045124. https://doi.org/10.1063/5.0146778

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For a representative large modern containership, the effects of a deck container arrangement on the wind-induced loads were systematically investigated using physical model tests and numerical computations. Numerical simulations based on various turbulence models were performed to validate our predictions against comparative wind tunnel measurements. Not only standard two-equation turbulence models of the unsteady Reynolds-Averaged Navier–Stokes (URANS) equations solver but also the improved delayed detached eddy simulation (IDDES) and large eddy simulation (LES) turbulence models were used to determine their limits in the prediction of aerodynamic loads. Systematic discretization studies ensured adequate discretization independent predictions. With URANS, numerically predicted wind forces and moments in near-head and near-tail winds were compared favorably with the measured data. However, in oblique winds, URANS predictions deviated from measurements. In oblique winds, flow separations were pronounced; therefore, the flow was strongly transient. Consequently, a two-equation turbulence model was inappropriate. With IDDES, more accurate predictions were achieved, especially in oblique winds. With LES, although the computational effort was high, the agreement of the computed forces and moments with the measured values was superior. Flow details were also presented and discussed. The container arrangement on deck showed major effects on aerodynamic forces and moments. A tarpaulin covering the containers on deck reduced wind resistance by up to 70%.

Increased waterborne trade in recent years has led to even more new builds of large containerships. Strong winds affect the operation of these ships in many ways. Wind can substantially influence dynamics of containerships entering or leaving a port. Ship masters may decide that the wind is too strong for the ship to berth or to sail. This applies particularly to fully loaded containerships, where excessive windage may compromise the ship's maneuverability. A head wind reduces the speed of a ship and, if the master chooses to maintain speed, it increases its fuel consumption. A stern wind aids the ship and increases its speed (albeit slightly). Strong winds are also a safety-related issue since they affect ship's maneuverability when the wind pushes the ship ashore, especially if the ship is underpowered or disabled. Indeed, the provision of tugs for towing such vessels has become a serious issue, especially in restricted areas, often characterized by coastal regions of limited water depth. Furthermore, wind loads are relevant for towing operations because of forces acting on a ship's windage area, especially when the ship is fully laden. For example, the International Maritime Organization (IMO) 1 assigns towing conditions for ships at sea and, nowadays, classification societies are also increasingly called upon to support shipping companies in providing rapid and reliable technical support for towing operations. 2  

The traditional approach to study aerodynamic flows around ships employs model tests in wind tunnels. These tests are a proven tool supporting ship design. Although aerodynamic forces and moments are easy to measure, measurements of local flow details may be difficult and expensive. Computational fluid dynamics (CFD) is increasingly used to investigate aerodynamic flows in different fields, e.g., around buildings. One of the advantages of CFD over wind tunnel tests is the ability to capture complex flow details. Furthermore, numerical simulations are non-intrusive and allow full-scale predictions.

Despite these advantages, so far CFD has rarely been employed for aerodynamic analyses of ships. This is due to a combination of obstacles, e.g., pronounced flow separation in an oblique flow, unsteady flow, and complex geometry of ship superstructures. Nevertheless, recent progress in available hardware and grid generation techniques calls for reevaluating CFD techniques for the prediction of aerodynamic flows around ship superstructures.

Several researchers investigated wind loads on ships. For various kinds of ships subject to uniform steady flows of low turbulence, Blendermann 3 conducted wind tunnel measurements in model scale. Based on regression and correlation analyses, the author establishes functional relationships of aerodynamic load coefficients on wind incidence angles for different ship superstructures. Andersen 4 carried out wind tunnel measurements of a 9000 TEU containership model with various container deck load configurations, where the model was studied in wind directions ranging from head to stern winds. The author finds that in a head wind, a smooth and streamlined container configuration reduces the longitudinal force; however, a streamlined container configuration on the aft deck increases the wind-induced yaw moment compared to a fully loaded deck configuration. Highly protruding container stacks increase the longitudinal force more than empty tiers. The lateral wind force depends strongly on the wind-exposed areas and can be lowered by reducing the number of highly stacked containers.

Tracing the development of numerical approaches to estimate wind loads on ships, Haddara and Guedes Soares 5 compared the methods of Isherwood, 6 Gould, 7 Blendermann, 8 and OCIMF 9 and established a regression model, based on measurements at the incidence angles ranging from head to stern winds. The authors validated their results against measurements for a tanker model and obtained a favorable agreement for the longitudinal and lateral forces and yaw moment. Fujiwara et al. 10 also developed empirical formulas for wind loads on containerships carrying different configurations of deck containers. These formulas, accounting for the incidence angles ranging from head to stern winds, in part are compared favorably with measurements. Based on eight parameters that depend on the flow conditions and ship geometry, Ueno et al. 11 used empirical formulas to determine wind loads acting on various full-scale ships. Their associated wind loads compared generally favorably to wind tunnel measurements.

Most of the CFD methods used so far were based on solving the Reynolds-averaged Navier–Stokes (RANS) equations. For example, Wnek et al. 12 employed a steady RANS equation solver together with the two-equation shear-stress-transport (SST)- k – ε turbulence model to predict wind loads for a LNG (liquid natural gas) carrier model and compared the results with wind tunnel measurements. The numerically predicted longitudinal and lateral wind forces were, respectively, 50% and 30% too low. The yaw moment agrees fairly well with the measurements, except for the angles of incidence between 120° and 160° and between 210° and 260°, for which the numerically predicted yaw moments were 20% lower than the measured ones. Using essentially the same procedure but with a k – ε turbulence model, Chen et al. 13 computed wind loads on an inland waterway cruise ship and compared with the formulas of Fujiwara et al. , 10 Blendermann, 8 Blendermann, 14 and Isherwood. 6 Only the loads based on the Isherwood formula deviate significantly from the CFD predictions, whereas the loads based on the other formulas agree favorably.

Koop et al. 15 also used CFD techniques and an SST- k – ε turbulence model, albeit with an unsteady RANS equations solver, to compute wind loads acting on a scale model of a Floating Production Storage and Offloading Unit (FPSO) with a shuttle tanker hooked up for tandem offloading, using various deck configurations for the FPSO. For the FPSO, the longitudinal force coefficient deviates by 20% to 30% from measurements, and for the transverse flow coefficients, by 5% to 15%. For the single tanker, the longitudinal force coefficients deviate by 15% to 20%. For both ships in tandem, the numerically computed longitudinal force on the tanker was 6% less than the measured one, whereas the deviations of the numerical predictions from the measurements for the other loads spread. Using an unsteady RANS equation solver and the k – ε -SST turbulence model, Koop et al. 16 determined wind loads on several tanker and FPSO models subject to wind at various angles of incidence. Their computed results, although generally in a favorable agreement with measurements, depended strongly on the specified velocity profile at the free surface (adopted from wind tunnel measurements). The authors reported that the carpeted surface roughness inside the wind tunnel has a significant influence and should be accounted for. The computed velocities in the FPSO's wake correlate favorably with the measured velocities.

Assuming inviscid flow, Popinet et al. 17 computed full-scale wind loads acting on a research ship. A RANS equations solver is also applied. In addition, they used the large eddy simulation (LES) technique to model turbulence. The authors observed that the measured wind loads strongly depend on the relative wind direction while weakly on ship motions, ship speed, wind velocity, and sea waves. The CFD predictions agree favorably with full-scale measurements of the mean wind velocities and the associated standard deviations.

The practical relevance to reduce wind resistance of containerships became evident with the implementation of the Energy Efficiency Design Index (EEDI) as part of the commitment of IMO. 18 This led to numerous studies carried out over the last decade: Deng et al. 19 examined the effects of optimizing the superstructure and forecastle fairing, Janssen et al. 20 performed CFD simulations of wind loads to study the influence of geometric simplifications, Wang et al. 21 determined wind load coefficients for the superstructure of a containership at different wind angles, Seok and Park 22 performed numerical simulations to compare air resistance with and without a superstructure on a containership, and Deng et al. 23 investigated the effect of container configurations and forecastle fairings on wind resistance of large containerships.

Recently, Nguyen et al. 24 examined the wind loads acting on a 20 000 TEU container ship carrying deck containers to investigate the influence of the gap between container stacks on the air resistance. The authors demonstrate that the gap flow increases the stagnation pressure on the front container and decreases the pressure on the back container for each gap between container stacks and that this pressure difference contributes to the air resistance acting on the ship. The authors also report that using side covers to close the gaps between container blocks significantly reduces air resistance for apparent wind directions between 30° and 60° off bow. The standard two-equation turbulence model for the incompressible flow was used within a unsteady Reynolds-Averaged Navier–Stokes (URANS) code.

Our objectives were fourfold: first, to establish additional benchmark data for wind loads; second, to investigate the effects of a deck tarpaulin as well as deck container arrangements on wind-induced forces and moments; third, to account for aerodynamic flow details needed to reliably predict wind loads acting on a containership; and forth, to determine limits of different turbulence models in the prediction of aerodynamic loads on ship superstructures. We considered realistic loading conditions representing various configurations of deck containers on a large modern containership. We employed three turbulence models, namely, the two-equation model implemented in the RANS equations solver, the improved delayed detached eddy simulation (IDDES) method, and the large eddy simulation (LES) technique. To predict wind loads, we performed systematic numerical simulations and validated our predictions against comparative wind tunnel measurements. In addition, we performed systematic grid dependency studies to ensure that our predictions were discretization independent. We also presented and discussed associated flow details. Our numerical simulations were conducted using the software STAR-CCM+, 25 version 13.06.

Figure 1 shows the typical modern container ship we selected. The container ship is loaded in four different configurations of deck containers. The load case (i) represented the fully laden ship with 2124 containers stacked on deck; the load cases (ii) and (iii), the partially laden ship with two different configurations of containers stacked on deck; and the load case (iv), the ship with no deck containers. For all load cases, no more than five layers of containers were stacked on the deck. However, the first nine tiers on the fore ship were stacked with at most only four layers of containers. Table I lists the principal particulars of the subject container ship.

Investigated container stack arrangements [load cases (i), (ii), (iii), and (iv)] and configurations [load cases (iT), (iiT), (iiiT), and (ivT)] covered by tarpaulin.

Principal particulars of subject containership.

Four additional load cases were considered: The four configurations mentioned above were covered with the same tarpaulin to investigate the influence of the tarpaulin on the wind loads. These cases were referred to as (iT), (iiT), (iiiT), and (ivT).

Figure 2 shows a ship-bound right-handed Cartesian coordinate system x , y , and z with its origin located midships on the calm water plane. The aerodynamic forces and moments acting on the ship model refer to this coordinate system. The x -axis points toward the ship's bow; the y -axis, the starboard; and the z -axis, downwards. The incident wind angle μ specifies the relative wind direction: μ  = 0° represents a head wind, and μ  = 90°, a wind from the starboard.

Coordinate system.

Wind tunnel data were obtained in model test measurements at a scale of λ  = 200, performed by Müller and Schuckert. 26 The cross-sectional working area of the wind tunnel measured 2.0 m height by 3.0 m width, and its measurement length was 5.5 m. The tests were performed for a wind velocity of 25 m/s, and the air flow was characterized by the Reynolds number R e = 2.5923 × 10 6 ⁠ . Turbulence intensity of the wind flow was about 1.0%. A standard experimental arrangement was employed for wind force measurements: The model was suspended with a vertical rod connected to a six-component load cell to measure aerodynamic forces and moments. The model, located above a baseplate, was rotated to specify the wind angle of incidence. The distance between the model and the wind tunnel's baseplate was minimized, so that the model did not touch the baseplate if it started to vibrate. The bottom of the model was milled to a depth of 5.0 mm. This created a constant pressure distribution under the model, thereby preventing the distortion of the heel moment due to the inherent undercurrent of air beneath the model.

A brief description of the used numerical approach is based on details documented by Ferziger et al. , 27 Wendt, 28 Lomax et al. , 29 Versteeg and Malalasekera, 30 Menter, 31 Fureby et al. , 32 Kornev et al. , 33 and Shevshuk. 34  

The solution domain is subdivided into a finite number of control volumes (CVs) for which the conservation equations for mass and momentum are solved. The flow is assumed to be incompressible, isothermal, and viscous. To obtain a dedicated pressure equation, the mass equation is converted to a pressure correction equation. The SIMPLE algorithm provides an implicit coupling between pressure and velocity. At each time step, outer iterations iteratively correct pressures and velocities.

Solving the Reynolds-averaged Navier–Stokes (RANS) equations is the standard technique used to describe turbulent flows. These equations of fluid motion decompose an instantaneous quantity into its time-averaged and fluctuating quantities. The method yields approximate time-averaged solutions, i.e., forces and moments acting on a structure. Although computational times are moderate, fluctuations of the flow field cannot be always predicted accurately, because the turbulence model depends on theoretical assumptions and empirical corrections.

To simulate turbulent flows at high Reynolds numbers by numerically solving the Navier–Stokes equations requires resolving a wide range of time and length scales, all of which affect the flow field. Using the large eddy simulation (LES) model for turbulence reduces the computational effort by ignoring or modeling the smallest, computationally intensive, length scales via low-pass filtering of the Navier–Stokes equations. The LES model is often used for flows characterized by low to moderate Reynolds numbers.

For high Reynolds numbers, when turbulent structures, depending on the Reynolds number, are small, the LES model requires smaller time steps and finer grids. Higher Reynolds numbers lead to smaller characteristic lengths, thereby increasing the number of CVs necessary to identify these structures. Hybrid methods based on a combination of RANS and LES approaches have been developed for flows at high Reynolds numbers. They use the RANS model in a close proximity to the wall, so that the small turbulence vortices do not have to be dissolved. The LES method then models the detailed resolution of time-dependent larger turbulent vortex structures in the rest of the computational domain. We used a so-called segregated (zonal) model, which couples the borders of the separate regions for RANS and LES (STAR-CCM+ UG 25 ) A summary of different segregated approaches can be found in, for example, Shevshuk. 34 More details may be found in Shur et al. , 35 Strelets, 36 and Hirt and Nichols. 37  

Wind forces and moments acting on the container ship with differing arrangements of the stacked containers were measured at incident wind angles between 0° and 360° in 10° steps. The Reynolds number was kept constant at R e = 2.5923 × 10 6 ⁠ . Figure 3 plots the coefficients, Eq. (1) , of the measured forces and moments vs the wind incidence angle for all four configurations; here, all forces and moments are normalized with respect to the same projected lateral windage area A L of the fully loaded ship, Table I . For the incidence angles between 0° and 90°, the longitudinal force F X was lowest [between the loaded conditions, (i), (ii), and (iii)] for the fully loaded ship [load case (i)]. In the head wind ( μ  = 0°), this force was about 20% less than the longitudinal force of the partially loaded ship with container stacks on the deck [load cases (ii) and (iii)]. The relatively large gaps between container stacks on the deck led to an increased resistance because the numerous frontal areas of these containers were directly exposed to the wind. For the fully loaded ship, only the front surface of the foremost container stacks was subject to the wind, whereas the remaining container stacks were not exposed to the wind being situated in the wind shadow of the foremost stacks. In head wind ( μ  = 0°), the wind resistance acting on the unloaded ship was about 24% greater than for the fully loaded ship and similar to the wind resistance acting on the partially loaded ship. This is because for the unloaded ship, the entire frontal surface of the deckhouse was exposed to the wind. In an oblique bow wind, the longitudinal wind force acting on the unloaded ship decreased, and the wind resistance became less than the wind resistance acting on the partially loaded ship (while close to the wind resistance for the fully loaded ship).

Measured 26 coefficients of wind forces and moments, normalized with respect to the same projected lateral windage area in Table I .

The lateral force and heeling moment are largest for the fully loaded ship compared to the partially loaded and unloaded ship. Specifically, the maximum lateral wind force acting on the fully loaded ship was about 18% greater than the wind force acting on the partially loaded ship. This was due to the increased lateral windage area of the container stacks of the fully loaded ship.

In Fig. 4 , the projected lateral windage areas of each configuration, listed in Table II , served as the basis to compare force and moment coefficients of the differently loaded ship. The measured normalized wind-induced forces and moments in Fig. 4 are taken from Müller and Schuckert. 26 As expected, the coefficients of the forces and moments, as well as their trends, are similar to those described above.

Measured 26 coefficients of wind forces and moments, normalized with respect to projected lateral windage area for each loading condition, Table II .

Projected lateral areas of different configurations.

One of the objectives of our study was to investigate the effects of a deck tarpaulin covering all deck containers as a practical measure to reduce wind resistance. To demonstrate its effectiveness, we compared measured wind-induced load coefficients obtained for all configurations. Recall that the four load cases (i), (ii), (iii), and (iv) represented deck container configurations without the tarpaulin, and the four load cases (iT), (iiT), (iiiT), and (ivT), the corresponding configurations covered with the tarpaulin. The load cases (i) and (iT) represented the fully loaded configuration with 2124 containers stacked on the deck, and the load cases (ii), (iiT), (iii), and (iiiT), the partially loaded configurations. Load cases (iv) and (ivT) corresponded to the configurations without deck containers. Figures 5–8 plot the associated coefficients of the wind-induced forces and moments against the wind angle of incident.

Normalized with respect to A L in Table I , Eq. (1) , longitudinal forces acting on fully loaded ship without (i) and with (iT) tarpaulin and unloaded ship without (iv) and with (ivT) tarpaulin (a) and on partially loaded ship without [(ii) and (iii)] and with [(iiT) and (iiiT)] tarpaulin (b).

Normalized with respect to A L in Table I , Eq. (1) , lateral forces acting on fully loaded ship without (i) and with (iT) tarpaulin and unloaded ship without (iv) and with (ivT) tarpaulin (a) and on partially loaded ship without [(ii) and (iii)] and with [(iiT) and (iiiT)] tarpaulin (b).

Normalized with respect to A L in Table I , Eq. (1) , roll moment acting on fully loaded ship without (i) and with (iT) tarpaulin and unloaded ship without (iv) and with (ivT) tarpaulin (a) and on partially loaded ship without [(ii) and (iii)] and with [(iiT) and (iiiT)] tarpaulin (b).

Normalized with respect to A L in Table I , Eq. (1) , yaw moment acting on fully loaded ship without (i) and with (iT) tarpaulin and unloaded ship without (iv) and with (ivT) tarpaulin (a) and on partially loaded ship without [(ii) and (iii)] and with [(iiT) and (iiiT)] tarpaulin (b).

These results showed that, for all load cases, covering the containers with a tarpaulin reduced wind resistance in the head wind ( μ  = 0°) up to 60%. Specifically, for the fully loaded ship [load case (i)], this measure reduced wind resistance by about 35%, and for the partially loaded ship [load cases (ii) and (iii)], it reduced the wind resistance by about 50% and 60%, respectively. For the ship without deck containers, i.e., when the entire deck was covered with a tarpaulin, wind resistance was reduced by about 50%.

With the increasing incident wind angle, the tarpaulin reduced longitudinal wind resistance to an even greater extent. At μ  = 30°, for the fully loaded ship [load case (i)], wind resistance was reduced by 62%; for the partially loaded ship, by 72% and 73% [load cases (ii) and (iii), respectively]; and for the unloaded ship [load case (iv)], by 60%. At μ  = 50°, the effect of the tarpaulin led to a change in sign of the wind-induced longitudinal force for all four configurations, i.e., the wind now caused a forward-directed wind thrust. Figures 5–8 show that at the incident wind angles between 60° and 80°, the effect of the tarpaulin decreased the longitudinal wind-induced force significantly. This decrease was due to the streamlined shape of the covered container stacks, i.e., covering the gaps between the container stacks prevented flow separation at sharp edges of the containers.

Nevertheless, the tarpaulin partly led to a significant increase in the wind-induced lateral force, yaw moment, and heeling moment for all configurations. This increase was most noticeable at the incident wind angles of 60° and 120°, and it was greatest for the unloaded configuration [load case (ivT)]. At an oblique wind angle, the tarpaulin created a greater lift force, which increased the lateral forces and the moments about the z - and x -axes.

The method we used here solved the unsteady Reynolds-averaged Navier–Stokes (URANS) equations by discretizing the solution domain with unstructured grids consisting of predominantly hexahedral control volumes. Prism layers were attached on the ship's surfaces and on the free water surface for better resolution of the gradients in the boundary layer. The solution method coupled pressures and velocities using the SIMPLE algorithm. Spatial and temporal terms were discretized using a second-order approximation. The IDDES simulations relied on the Spalart–Allmaras turbulence model 38 All LES simulations were performed with the dynamic Smagorinsky subgrid scale model 39 We used the k – ω -SST-turbulence model, Menter, 31 in the URANS simulations.

Our URANS and IDDES simulations for the four container arrangements ( Fig. 1 ) were performed on medium grids comprising about 7.5 × 10 6 CVs. Our simulations considered air of constant density ρ = 1.18   kg / m 3 and constant dynamic viscosity μ = 1.81 × 10 5 kg/ms. The wind speed v 0 = 25 m/s. The ship's surfaces and the wind tunnel's bottom plate were assumed to be no-slip walls. We applied the same flow parameters to the URANS and IDDES simulations for all investigated cases and for all incident wind angles. Exemplarily for the load case (a), Fig. 9 presents side and top views of locally refined grid zones surrounding the ship. The finer gridding domain on the ship's portside (lee) was more extended. The Courant number (CFL) was always less than unity, and its mean value, equal to 0.025, corresponds to a time step of Δ t ≈ 5 × 10 − 6 s. First, we carried out the simulations with the URANS equations solver; the results were then used as a starting solution for simulations with the IDDES model.

Side view (i) and top view (ii) of locally refined grids surrounding the ship superstructure.

For the LES model, we used a grid consisting of 42.2 × 10 6 CVs, with a fine grid in the immediate vicinity of the hull. Compared to the URANS and IDDES grid, the cell size of the LES grid was reduced by a factor of four. The associated CFL number was always less than unity, corresponding to a time step of Δ t ≈ 2.5 × 10 − 7 s. The mean dimensionless wall spacing at the ship y + < 1 accounted for the viscous sub layer for the low Reynolds number turbulence model. The starting solution was the result obtained with the IDDES model on the medium grid. Then, the grids were refined, and the settings for the LES model were introduced.

We performed a grid study for one load case (i) using the IDDES turbulence model. For this purpose, we selected the assumed worst case, i.e., the incident wind angle of 90°. The grid generated with a refinement zone surrounding the ship was used for all incident angles.

Computed normalized (with respect to A L in TABLE I) forces and moments and related discretization errors for container arrangement (i), 90° incident angle, and R e = 2.5923 × 10 6 ⁠ .

Discretization errors of normalized (with respect to A L in Table I ) forces and moments for container arrangement (i) at incident wind angle of 90°, R e = 2.5923 × 10 6 (IDDES model).

To validate our numerical method, we performed simulations on the medium grid 2 to obtain wind loads at the incident wind angles ranging from 0° to 180° for comparison with the coefficients based on the wind tunnel measurements of Müller and Schuckert. 26 For the load case (i), we obtained these coefficients with URANS and IDDES; for the load cases (ii), (iii), and (iT), only with IDDES. In addition, we carried out additional URANS and LES simulations. Figures 11 and 12 plot longitudinal and lateral wind force coefficients C X and C Y and roll and yaw moment coefficients C MX and C MZ against incident wind angle for load cases (i) and (ii), respectively.

Measured and computed normalized (with respect to A L in Table I ) forces and moments for fully loaded container arrangement (i) using different turbulence models; R e = 2.5923 × 10 6 ⁠ .

Measured and computed normalized (with respect to A L in Table I ) forces and moments for partially loaded container arrangement (ii) using different turbulence models; R e = 2.5923 × 10 6 ⁠ .

For the load case (i), wind forces and moments obtained with URANS using the k – ω -SST turbulence model without wall functions agreed with the experimental results fairly well at the incident wind angles less than 40° and greater than 130°. However, at the incident wind angles between 40° and 130°, these URANS results deviated substantially from the experimental results. At these angles, flow separation was very pronounced. Consequently, URANS model was not able to correctly capture the unsteady flow. As expected, wind forces and moments obtained with IDDES, which relied on the Spalart–Allmaras turbulence model with the IDDES extension, were compared more favorably with the measured wind forces and moments. Moderate deviations occurred only at the incident wind angles between 50° and 70° for the longitudinal force and at the incident wind angles between 110° and 130° for the yaw moment. Thus, wind forces and moments obtained with LES were compared favorably with the experimental data. For the load case (ii), the forces and moments obtained with IDDES agreed favorably with the experimental data, while the yaw moment at the incident wind angle of 140° deviated moderately from the comparative measurements.

Pressure distribution on the lee side of the ship, obtained with URANS (a), IDDES (b), and LES (c) for container arrangement (i); R e = 2.5923 × 10 6 ⁠ .

Q -criterion iso-surfaces of vortex structures surrounding the ship, obtained with URANS (a), IDDES (b), and LES (c) for container arrangement (i); R e = 2.5923 × 10 6 ⁠ .

Horizontal velocities projected on horizontal plane (d), obtained with URANS (a), IDDES (b), and LES (c) for container arrangement (i); R e = 2.5923 × 10 6 ⁠ .

Stream lines and velocity magnitudes viewed from behind ship, obtained with URANS (a), IDDES (b), and LES (c) for container arrangement (i); R e = 2.5923 × 10 6 ⁠ .

Stream lines and velocity magnitudes viewed from above the ship, obtained with URANS (a), IDDES (b), and LES (c) for container arrangement (i); R e = 2.5923 × 10 6 ⁠ .

Time histories of normalized (with respect to A L in Table I ) longitudinal (a) and lateral (b) force, obtained with URANS, IDDES, and LES for container arrangement (i); R e = 2.5923 × 10 6 ⁠ .

The iso-surfaces of vortex structures surrounding the ship shown in Fig. 14 demonstrated that, with URANS a smoother pressure distribution was obtained than with IDDES and LES, which were significantly more irregular, see Fig. 13 . Also, with the URANS method, fewer uniform structures characterized the flow; with DES and LES, there were significantly more complex structures. The line integral convolution (LIC) representation resulted in stream lines and flow velocities presented in Fig. 15 , indicating that URANS produced a relatively uniform velocity field. With IDDES and LES, the velocity field was significantly more disturbed and included finer vortex structures. The stream lines and velocities pictured in Figs. 16 and 17 also illustrated this; i.e., URANS produced a smoother velocity field, which contained especially large vortices. With IDDES and LES, the velocity field was significantly more irregular, with increased turbulence and unsteady flow behavior. The longitudinal and lateral forces, plotted as time histories in Fig. 18 , indicate that the fluctuations about their mean values were significantly larger with IDDES and LES than with URANS. The largest longitudinal force coefficient oscillations with URANS were about ±0.001 ( ⁠ ± 2.4 % ⁠ ); with IDDES, about ±0.01 ( ⁠ ± 20.4 % ⁠ ); and with LES, about ±0.03 ( ⁠ ± 44.8 % ⁠ ). The largest lateral force oscillations with URANS were only about ±0.002 ( ⁠ ± 0.4 % ⁠ ); with IDDES, about ±0.02 ( ⁠ ± 3.6 % ⁠ ); and with LES, about ±0.06 ( ⁠ ± 9.1 % ⁠ ).

For a representative large modern containership, the effects of various deck container arrangements on wind-induced aerodynamic forces and moments were systematically investigated using physical tests and numerical computations. To determine the accuracy and limitations of today's numerical methods, systematic numerical simulations were performed employing a URANS equations solver that implemented the two-equations turbulence model, the IDDES turbulence method, and the LES technique. Systematic discretization studies ensured adequate discretization independent predictions.

With URANS, the numerically predicted wind-induced forces and moments in near-head and near-tail winds were compared favorably with the measured data. In oblique winds, computed forces and moments deviated from measurements because flow detachments and flow separations became pronounced. As a result, the flow was strongly unsteady, and the two-equation turbulence model was inappropriate. With IDDES, the agreement with the experimental measurement improved, especially in oblique winds. With LES, although the computing effort was high and, therefore, limited to a few selected cases, the agreement of computed forces and moments with measurements was superior.

Container arrangement on deck showed major effects on aerodynamic forces and moments. The absolute values of the longitudinal forces for a partial load were sometimes significantly greater (over 25%) than those for the full load. This was due to the pronounced flow separation in the gaps between the container stacks and flow separation at container edges. Furthermore, for a partially loaded ship, the frontal areas of container stacks are greater than those of a fully loaded ship.

The lateral force, relevant for maneuvering, was greater for the fully loaded case than that of the partially loaded case. Interestingly, the longitudinal force acting on the unloaded ship in a head wind (0°) was about 20% greater than that on the fully loaded ship. The influence of a tarpaulin covering the container stacks, a measure reducing the wind resistance, was investigated. For all load cases examined, this measure significantly reduced the longitudinal force in a head wind (up to 60%). The greatest effect of the tarpaulin was obtained for the partially loaded ship. However, the tarpaulin led to an increase in wind-induced lateral forces and yaw and heel moments.

The authors gratefully acknowledge the computing time granted by the Center for Computational Sciences and Simulation (CCSS) of the Universität of Duisburg-Essen and the supercomputer magnitUDE (DFG Grant Nos. INST 20876/209-1 FUGG and INST 20876/243-1 FUGG) at the Zentrum für Informations- und Mediendienste (ZIM).

The authors have no conflicts to disclose.

Ould el Moctar: Conceptualization (lead); Formal analysis (equal); Investigation (lead); Methodology (lead); Supervision (lead); Validation (equal); Visualization (equal); Writing – original draft (lead); Writing – review & editing (equal). Udo Lantermann: Investigation (equal); Methodology (equal); Validation (lead); Visualization (lead); Writing – review & editing (equal). Vladimir Shigunov: Writing – review & editing (equal). Thomas Erling Schellin: Writing – review & editing (lead).

The data that support the findings of this study are available within the article. The geometric descriptions as well as the experimental data are available upon request for researchers as a benchmark test for numerical simulations.

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What is the difference between the Method and Experimental Setup section

I am writing a Computer Science paper, however my supervisor wants me to describe the methodology in a more general form in the Method section. In the Experimental Setup section I dive into the details. My question is, what is general ?

I always assumed that the Method and Experimental Setup were one section were you describe your setup/method in detail.

• computer-science

• Quite obviously, the Method section is supposed to describe approaches / methods / techniques without implementation details . On the other hand, the Experimental Setup section is the place where those implementation details belong. –  Aleksandr Blekh Commented May 2, 2016 at 4:38

The answer to this question depends a little on the field of application.

In fields like computational sciences, this is the section where you describe a set of algorithms to be implemented. In fields like material engineering and life sciences, you describe the general procedure to be followed to solve the problem defined in the problem statement. " General " here refers to more of an overview of your implementation rather than its deeper aspects.

Experimental Setup

This is where you explain the implementation aspects in detail. You describe where and how the algorithms are applied in computation. You depict the use of instruments, apparatus, and other tangible items in material engineering and sciences.

In short, I presume your supervisor wants you to give a brief overview of your implementation in the Method section and would like you to explain it in detail in the Experimental Setup section. However, the level of detail can vary widely among the above sections.

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article heading should be "Experiment setup" or "Experimental setup"?

My advisor insists on using a heading "Experimental Setup" in his science journal articles. I always cringed a little, thinking it should be "Experiment setup" instead. Now I am writing an article and in his edits he wants me to add the -al.

To me, "experimental setup" sounds like the setup itself is experimental, but "experiment setup" sounds more like we set up an experiment. Technically, we set up an experiment, and the setup itself was not the experiment. I suppose the root of my question in this case is, is the word "experiment" supposed to be an adjective or a noun? Hopefully that explanation makes my grievance clear..

English is his 2nd language, and my first, so he won't mind me questioning it.

Does anyone have a definitive answer to that one? Thank in advance! -Curious Grad Student

• compound-adjectives

• 2 I completely agree with you on that. It reads as a setup that you are trying out. –  Avon Commented Jul 10, 2015 at 22:08

3 Answers 3

He is following convention. Try looking at other papers, this is the standard term.

If you say "Experiment Setup" you may feel better but your readers will wonder what you are trying to prove - worse they may think you have made an error.

Maybe, as a compromise, you could say "Setup of the Experiment" (?)

• I agree, this does seem to be the norm. In the long run, I will probably just go with The Boss and do it his way. Thank you! –  GradStudent Commented Jul 10, 2015 at 23:14
• It is sometimes the case that almost everybody gets it wrong. Especially when many follow like sheep and do not question. This applies to life as well as to language. –  Brian Hitchcock Commented Jul 11, 2015 at 9:35

Here's chapter subheading C from the book Quantum Mechanics by K. T. Hecht:

C   Complementary Experimental Setup

The Ngram Viewer sides with your advisor, finding the usage with -al over fifty times as popular as the usage without.

I understand your unease. It's the same one I get when I hear the words "oversight committee." Are they overseeing something or overlooking it?

• I've never seen the Ngram viewer before. What a cool tool! –  GradStudent Commented Jul 10, 2015 at 23:18

Is there a reason why 'methodology' is not a suitable alternative? That's what I would go with in this situation to avoid confusion.

Also, just a thought, are you absolutely sure that the setup itself is not experimental? Typically primary research papers will cite previously published literature that outlines the methods that were used in the research or otherwise state that the methods were developed by the authors. Often there will be a citation in addition to some specified modifications to that protocol that the authors employed in their research. Either way, if it hasn't yet been used by other researchers to reproduce data then I would say it's fair to refer to novel setups as "experimental" experiment setups.

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set-up noun [C] ( ARRANGEMENT )

Set-up noun [c] ( trick ).

(Translation of set-up from the Cambridge English–Russian Dictionary © Cambridge University Press)

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to do something in order to be allowed more time

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a) The experimental setup for studying the demultiplexing of OV beams, b) subfigure shows an example of the phase mask for generating the transmitted OAM state, c) subfigure displays the phase mask of the diffractive multichannel filter as shown on the second SLM. Experimentally obtained results of the detection of light fields with different OAM states: d) w(φ) = const, µ = 0 (correspondence of the diffraction orders in the focal plane to the OAM state is shown), e) w(φ) = exp(−i2φ), µ = −2, f) w(φ) = exp(−i1.25φ), µ = −1.25, g) w(φ) = exp(i2.5φ), µ = 2.5, h) w(φ) = exp(−iφ) + exp(iφ), µ = 0, i) w(φ) = exp(−i2φ) + exp(iφ), µ = −0.5, j) w(φ) = exp(–iφ) + exp(−i2φ), µ = −1.5, and k) w(φ) = exp(–iφ) + exp(−i2φ) + exp(i2φ), µ = −0.33. The color dashed circles show the generated correlation peaks. Reproduced with permission.[¹¹⁹] Copyright 2021, MDPI.

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