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16_058_1 FHR reports

Evaluation of Gerris flow solver for the computation of wind coefficients Optimization of geometry preparation

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Evaluation of Gerris flow solver for the computation of wind coefficients Optimization of geometry preparation

Van Hoydonck, W.; Verwilligen, J.; López Castaño, S.; Mostaert, F.

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The Government of Flanders, Department of Mobility and Public Works, Flanders Hydraulics Research

Legal notice Flanders Hydraulics Research is of the opinion that the information and positions in this report are substantiated by the available data and knowledge at the time of writing. The positions taken in this report are those of Flanders Hydraulics Research and do not reflect necessarily the opinion of the Government of Flanders or any of its institutions. Flanders Hydraulics Research nor any person or company acting on behalf of Flanders Hydraulics Research is responsible for any loss or damage arising from the use of the information in this report. Copyright and citation The Government of Flanders, Department of Mobility and Public Works, Flanders Hydraulics Research, 2021 D/2021/3241/017 This publication should be cited as follows: sĂŶ ,ŽǇĚŽŶĐŬ͕ t͖͘ sĞƌǁŝůůŝŐĞŶ͕ :͖͘ >ſƉĞǌ ĂƐƚĂŹŽ͕ ^͖͘ DŽƐƚĂĞƌƚ͕ &͘ (2021). Evaluation of Gerris flow solver for the computation of wind coefficients: Optimization of geometry preparation. Version 2.0. FHR Reports, 16_058_1. Flanders Hydraulics Research: Antwerp Reproduction of and reference to this publication is authorised provided the source is acknowledged correctly. Document identification Customer:

Flanders Hydraulics Research

Ref.:

WL2021R16_058_1

Keywords (3‐5):

CFD, ship wind coefficients, STL geometry preprocessing, projected area computation, surface wrapping

Knowledge domains:

Harbours and waterways Manoeuvring behaviour Wind Numerical calculations

Text (p.):

Confidential:

Author(s):

Van Hoydonck, W.

Appendices (p.):

଄ Available online

Control Name Revisor(s):

Project leader:

Verwilligen, J.; López Castaño, S. Van Hoydonck, W.

Signature Getekend door:Jeroen Verwilligen (Signat Getekend op:2021-01-22 14:54:07 +01:0 Reden:Ik keur dit document goed

Getekend door:Santiago Lopez Castaño ( Getekend op:2021-02-01 14:03:15 +01:0 Reden:Ik keur dit document goed

Getekend door:Wim Van Hoydonck (Sign Getekend op:2021-01-22 14:04:48 +01:0 Reden:Ik keur dit document goed

Approval Head of division:

F‐WL‐PP10‐5 version 24 VALID AS FROM: 08/12/2020

Mostaert, F.

Getekend door:Frank Mostaert (Signature Getekend op:2021-01-22 13:56:09 +01:0 Reden:Ik keur dit document goed

Evaluation of Gerris flow solver for the computation of wind coefficients: Optimization of geometry preparation

Abstract The objective of project 16_058 is to evaluate the open‐source Gerris flow solver for the computation of ship wind coefficients. In the original project plan, it was foreseen to only execute a parameter variation and grid conver‐ gence study with Gerris. While this research was started in 2016, due to shifting priorities, it was only finalised in 2021. Not only was time spend for the validation, but time was also used to automate tasks that are executed before this type of Computational Fluid Dynamics (CFD) computations can be executed. These concern the determination of the reference areas of the vessel (to convert the resultant forces and moments to dimensionless coefficients) and the creation of manifold geometry from the simulator ship models. If done by hand, these last two tasks can require up to two days per ship model. The procedures documented in this report reduce this time to less than two hours. In the present report, the automation of the tasks to prepare geometry for CFD computations are reported. A second report will present details on the validation and use of Gerris for the determ‐ ination of wind coefficients, discuss a typographical error found in literature related to the experi‐ mental determination of wind coefficients and how this error affects the accuracy and reliability of CFD methods that use the results of this reference to validate their work. The second report will also present a critical review of past research related to the simulation of atmospheric boundary layers in FINE/Marine.

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Contents Abstract........................................................................................................ III Nomenclature ................................................................................................ VIII 1 Introduction ............................................................................................... 1.1 Computation of wind coefficients using FINE/Marine ........................................... 1.2 Wind coefficient data used in the simulator ...................................................... 1.3 Reference systems and definition of coefficients ................................................. 1.4 Problem summary.................................................................................... 1.5 Proposed solution .................................................................................... 1.5.1 Contributions of viscosity and pressure ....................................................... 1.5.2 Grid generation .................................................................................. 1.5.3 CFD Solver ........................................................................................ 1.6 Report contents ......................................................................................

1 1 2 3 5 5 5 6 6 7

2 Projected Surface Area Computation .................................................................. 2.1 Introduction........................................................................................... 2.2 Automatic approximate projected area computation............................................ 2.2.1 Introduction ...................................................................................... 2.2.2 Algorithm implementation ..................................................................... 2.2.3 Blender steps ..................................................................................... 2.3 Grid convergence study ............................................................................. 2.3.1 Simple box with analytical surface areas ...................................................... 2.3.2 Simplified Barzan hull ........................................................................... 2.3.3 Estuary vessel Tripoli ............................................................................ 2.4 Surface area extrapolation .......................................................................... 2.4.1 Test cube .......................................................................................... 2.4.2 Simplified Barzan hull ........................................................................... 2.4.3 Tripoli surface area estimation ................................................................. 2.4.4 Conclusion ........................................................................................ 2.5 Surface area computations of other ships......................................................... 2.6 Conclusions ...........................................................................................

8 8 8 8 9 10 12 13 14 15 16 17 17 18 18 19 22

3 Mesh wrapping ........................................................................................... 3.1 Introduction........................................................................................... 3.2 Available surface wrapping tools ................................................................... 3.2.1 Meshmixer........................................................................................ 3.2.2 Open Cascade CAD Processor .................................................................. 3.2.3 Blender Remesh Modifier....................................................................... 3.3 Conclusions ...........................................................................................

23 23 23 23 23 25 27

4 Summary and conclusions............................................................................... 28 References .................................................................................................... 29

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List of Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 Figure 16 Figure 17 Figure 18 Figure 19 Figure 20 Figure 21 Figure 22 Figure 23 Figure 24 Figure 25 Figure 26

Definition of the apparent wind vector 𝑈𝑎 and the relative wind angle 𝜑. .............. Relative contribution of the viscous and pressure components to the total forces and moments of a container ship in a head wind. .......................................... Wind coefficients of the Tripoli estuary vessel computed using (a) FINE/Marine with an atmospheric boundary layer and (b) Gerris with a uniform wind field. ............... CAD geometry of the DFDS JinLing car carrier as used in the simulator of Flanders Hydraulics Research (FHR). .................................................................... Dimensions of a simple box for verification of the surface area computation. .......... Convergence of surface area computation as a function of resolution for the simple box. ............................................................................................... Computing time as a function of resolution. ................................................ Dimensions of a simplified hull form of the Barzan container vessel. .................... Convergence of surface area as a function of resolution for the Barzan hull geometry. Overview of the geometry of the Tripoli estuary vessel as used in the simulator. ...... Frontal and lateral view of the Tripoli for 𝑅𝑥,𝐿 = 3200 and 𝐴𝐴 = 8, with 𝐴𝐿 = 953.60 m2 and 𝐴𝐹 = 219.94 m2 . ............................................................. Convergence of surface area as a function of resolution for the Tripoli hull geometry. Lateral and frontal view of the qmax_al_anna. ............................................. Lateral and frontal view of the qflex_mona. ................................................ Lateral and frontal view of the myzaquazo_3layers. ..................................... Lateral and frontal view of the LNG_Yamal_ARC7_299_500. .............................. Lateral and frontal view of the LNG_Conventional_300_460. ........................... Lateral and frontal view of the DFDS_JinLing_235_330. ................................. Lateral and frontal view of the Clementine. ................................................ Surface wrapping the Myzaquazo STL geometry with Autodesk’s Meshmixer. .......... Issues with the resulting solid model of the steering house of the Myzaquazo at the finest settings. ................................................................................... Remesh modifier in Voxel mode in Blender. ................................................. Blender’s Remesh modifier in Sharp mode applied to four intersecting boxes. ......... Blender’s Remesh modifier in Voxel mode applied to the Myzaquazo hull geometry. .. Blender’s Remesh modifier in Voxel mode applied to a slightly modified Myzaquazo hull geometry. ................................................................................... Surface wrapping the Myzaquazo Stereolithography (STL) geometry with Blender’s remesh modifier. ................................................................................

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3 6 7 9 13 13 14 15 15 15 16 16 20 20 20 20 21 21 21 24 25 25 26 26 27 27

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List of Tables Table 1 Table 2 Table 3 Table 4

Relative errors (%) of the lateral and frontal surface areas for the test cube. .............. Relative errors (%) of the lateral and frontal surface areas for the simplified Barzan hull. Lateral and frontal surface area values estimates for the Tripoli estuary vessel. ........... Estimates of the lateral and frontal surface areas of several simulator models. ...........

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Evaluation of Gerris flow solver for the computation of wind coefficients: Optimization of geometry preparation

Nomenclature Abbreviations CAD CFD FHR NURBS RANS STL

Computer Aided Design Computational Fluid Dynamics Flanders Hydraulics Research Non‐Uniform Rational B‐Spline Reynolds‐Averaged Navier Stokes Stereolithography

Latin symbols 𝐴 𝐴𝐹 𝐴𝐼 𝐴𝐿 𝐴𝑃 𝐶𝐾 𝐶𝑀 𝐶𝑁 𝐶𝑋 𝐶𝑋𝐴𝐹 𝐶𝑌 𝐶𝑍 𝐺 ℎ 𝐻𝑆 𝐻̄ 𝐾 𝐾′ #‰ 𝐿 𝐿𝑜𝑎 𝐿𝑝𝑝 𝑀 𝑁 𝑛 𝑁′ 𝑞 #‰ 𝑅 𝑅𝑥 𝑅𝑥,0 𝑅𝑥,𝐹 𝑅𝑥,𝐿 VIII

Surface area Frontal projected area Image area Lateral projected area Ship projected area Non‐dimensional moment around the x‐axis Non‐dimensional moment around the z‐axis Non‐dimensional moment around the y‐axis Non‐dimensional force in the x‐direction Non‐dimensional force in the x‐direction, using the frontal projected area 𝐴𝐹 Non‐dimensional force in the y‐direction Non‐dimensional force in the z‐direction Numpy array with grayscale values height, measured positive up Geometric centre of gravity of the lateral projected area, measured from the waterline Mean height of the lateral plane Moment around the x‐axis Non‐dimensional moment around the x‐axis Position of camera for rendering an orthographic projection Length over all Length between perpendiculars Moment around the z‐axis Moment around the y‐axis number of vertices Non‐dimensional moment around the y‐axis Dynamic pressure: 12 𝜌𝑈 2 Orientation of camera Horizontal resolution of image Initial horizontal resolution of image in grid convergence study Horizontal resolution of frontal image Horizontal resolution of lateral image WL2021R16_058_1

m2 m2 m2 m2 m2 − − − − − − − − m m m Nm − m m m Nm Nm − − Pa ° pixels pixels pixels pixels Final version

Evaluation of Gerris flow solver for the computation of wind coefficients: Optimization of geometry preparation

𝑅𝑦 𝑆𝑔 𝑆𝑥 𝑆𝑥,𝐹 𝑆𝑦 𝑇 𝑈𝑎 𝑈𝑠 𝑈𝑤 𝑋 𝑋′ 𝑋0 𝑌 𝑌′ 𝑌0 𝑍 Δ𝑥

Vertical resolution of frontal and lateral images Sum of grayscale values in an array Horizontal size of image Horizontal size of frontal image Vertical size of images Draft Apparent wind velocity Ship velocity Wind velocity Force in the x‐direction Non‐dimensional force in the x‐direction X‐axis of earth‐fixed axes system pointing North Force in the y‐direction Non‐dimensional force in the y‐direction Y‐axis of earth‐fixed axes system pointing East Force in the z‐direction Size of a pixel

pixels − m m m m m/s m/s m/s N − − N − − N m

Greek symbols 𝛽 𝛾 𝜌 𝜑

Drift angle: arctan −𝑣 𝑢 Angle between 𝑈𝑎 and 𝑈𝑠 Fluid (air) density Angle of relative wind, 0° is head wind

° ° kg/m3 °

Subscripts 𝐹 𝐿

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1 Introduction 1.1

Computation of wind coefficients using FINE/Marine

In the recent past, the CFD software suite FINE/Marine has been used to compute improved wind coefficients of the Tripoli estuary vessel after feedback from the skippers during real‐time simulation trials (Van Hoydonck et al., 2015b). The improved wind coefficients gave acceptable results, but a very long computing time was required (approximately one month cluster time). As a consequence, this type of computations cannot be executed on a regular basis to improve existing wind coefficients or create new wind coefficients for new simulator vessels. In another project (Van Hoydonck et al., 2016) the wind field on the leeward side of a roro ship was computed using FINE/Marine to evaluate the shelter effect of a moored vessel on the manoeuvrability of another vessel. Multiple days (both cluster time and man hours) were required to generate a suitable wind field. The origin of the long turn‐around time (discussed in more detail in the paragraphs that follow) of these computations is two‐fold: • computing times were long, and • a significant number of man‐hours was needed for the preparation of the computations. The long computing times have two principle causes: a) the inclusion of viscosity in the governing (Navier‐Stokes) equations next to the pressure and momentum equations, and b) the unsteadiness of the problem. The total force experienced by an object exposed to a relative wind field is a combin‐ ation of pressure forces (acting perpendicular to the surfaces of the object) and viscous forces (acting parallel to the surfaces of the object). To reliably compute the viscous forces, a very large number of very small cells is required close to the surface of the object1 which increases the computation time significantly. For most vessels, the superstructure consists of a set of blunt objects stacked next to and on top of each other that results in massive separation regions on the leeward side of said objects. Sharp edges make the problem unsteady: vortices are shed periodically from these parts. To get the best possible result, one should use a time‐accurate (at least second order in time) solver instead of a solver that is only first‐order accurate in time. The time‐accuracy requirement poses stricter demands on the maximum time step that can be used, with a consequence that computing times will increase further. In industrial applications, Reynolds‐Averaged Navier Stokes (RANS) solvers are most commonly used for this type of application. Apart from the momentum and pressure equations, turbulence models are required for closure of the equations. The need for a turbulence model in RANS solvers increases the problem even further, because the specific turbulence model used will have an effect on the results as well. Apart from the long computing times for this type of CFD computation, the amount of man‐hours required for the setup of the computations should not be underestimated either. For a single set of coefficients (from 𝜑 = 0° to 180°) with a 10° increment, 19 computations are required. If the CFD tool supports sliding meshes, a computational domain consisting of two separate domains (one large rectangular hexahedron and a smaller cylindrical domain in which the ship is located) can be used where the inner cylindrical domain can be rotated around the z‐axis to change the wind incid‐ ence angle without creating a new mesh. This feature was however not yet available in FINE/Marine when the coefficients of the Tripoli were initially computed, hence 19 different grids were created. 1

This can be 50% of the total number of cells used to discretize the complete domain.

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During the course of the computations, (some of) the resulting grid (or grids) may have to be altered capture the wake regions close to the ship with sufficient detail. The use of automatic adaptive grid refinement can reduce the turn around time in this case by refining the grid during the computation based on e.g. the magnitude of vorticity in the wake. Not only the step of creating the computational grid(s) may take up a significant amount of time, but also the first step, where the initial (dirty) geometry is transformed into a watertight manifold shape that has a clear distinction between inside and outside. For the determination of the wind coefficients of the Tripoli (Van Hoydonck et al., 2015b), creating a watertight geometry required multiple days of editing in Blender. At that time, Hexpress was also not capable of meshing the resulting watertight hull geometry: some simplifications had to be made near the deck at the bow and stern: the area below the railing had to be filled. This was also necessary for the initial evaluation (Van Hoydonck et al., 2015a), where the volume above the deck at the bow was filled up to the height of the railing. With the advance of time, new tools have been developed that can wrap a 3D geometry with a manifold mesh that makes the resulting geometry suitable for CFD computations, as discussed in Chapter 3.

1.2

Wind coefficient data used in the simulator

For most of the existing mathematical models of vessels currently available in the simulator at FHR, the origin of the wind coefficient data used is unknown. Some were copied from vessels with a similar shape (but different absolute dimensions), others are copied from similar vessels found in literature. For most of them, the exact origin is unknown with as a result that it is unknown if the data used is suitable in the first place2 . Some of the mathematical models contain multiple configurations where a single parameter such as the draft is changed. Also, for some container and bulk cargo ships, there are multiple configurations present where only the shape of the cargo is changed (for example an even distribution of containers over the full length of the vessel, or a more step‐wise distribution, with fewer containers near the bow). Without a large database of wind coefficients for all possible classes of ships (either computed using CFD or as a result of extensive wind tunnel measurements), it is difficult to know how wind coefficients should be changed to reflect a change in e.g. the container configuration for a specific case. It should also be noted that the effect of wind is not always very important (or, not the most important part of a simulation). The forces experienced by vessels due to the proximity of banks, the bottom of the waterway or other ships may be significantly larger in magnitude than wind effects. On the other hand, there are situations where wind may be a limiting factor in the manoeuvrability of vessels (for example, at low speed during manoeuvres in a harbour in high wind conditions). At the moment only the drag force, lateral force and yawing moment are used in the simulator: this is sufficient for a mathematical model with three degrees of freedom in the horizontal plane. For the upgrade of the simulator mathematical models to six degrees of freedom, the inclusion of the roll moment due to (lateral) wind is a logical extension. The vertical (lifting) force and the pitch moment are generally less important but could be included if the coefficients are obtained from CFD computations because their computation has no additional overhead. In the simulators at FHR, each variant of a ship has a separate load_*.xml file that contains data about the general characteristics of the ship, the wind coefficients table and related longitudinal and 2

Although it is perfectly possible to add references in comments in xml files, the load_*xml files generally do not contain such information.

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lateral windage areas, a wave table, and the type of mathematical models for bank suction and squat behaviour. For example, for the Tripoli estuary vessel, six load files are available with drafts between 2.52 m and 4.5 m. These all have the same wind coefficients, but they do have unique windage area values that correspond to the different drafts. If the draft of a vessel changes (and nothing else), the average height of the vessel that is exposed to wind changes as well. In a uniform wind field, the pressure on the superstructure will be (close to) proportional to the exposed area. When the wind field is non‐uniform, this is not the case: the distribution of pressure (and hence the coefficients derived from it) will be a function of both the reference area and a characteristic height relative to the reference height of the velocity profile. As an example, a long vessel with a limited height with the same lateral area as another shorter but higher vessel, will have a different absolute value for the pressure acting on the lateral area.

1.3

Reference systems and definition of coefficients

When a vessel moves in a still atmosphere, the superstructure is exposed to a uniform relative wind equal to its own velocity. When the vessel is not moving in the presence of wind, the vertical wind profile will be highly non‐uniform due to the viscous interaction between the moving air and the earth. For the combination of these two, when the vessel sails in the presence of wind, the total wind load consists of the wind load due to the motion of the ship in addition to the wind load due to the non‐uniform atmospheric velocity (Andersen, 2013). Hence, two sets of wind coefficients are required to compute the total load: one set determined for a uniform wind profile, and a second set determined using a suitable atmospheric profile. In most nautical simulation applications, this distinction is not made: the total relative velocity 𝑈𝑎 is computed by vector subtraction of the ships’ motion 𝑈𝑠 from the atmospheric wind 𝑈𝑤 (see Fig. 1), #‰ #‰ #‰ 𝑈 𝑎 = 𝑈 𝑤 − 𝑈 𝑠.

(1)

The relative wind angle 𝜑 can be computed3 from the drift angle 𝛽 and the three velocity components 𝑈𝑎 , 𝑈𝑤 and 𝑈𝑠 . The total wind loads are obtained by multiplying the coefficient values interpolated at the 𝜑 with the reference dynamic pressure 𝑞 and suitable reference areas and lengths. Uw

X0 Ua

β x

γ ψ

y Y0

Figure 1 – Definition of the apparent wind vector 𝑈𝑎 and the relative wind angle 𝜑.

For the current investigation, 𝜑 is set directly.

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The dimensionless wind load coefficients are defined as (Blendermann, 2013) 𝑋 , 𝑞𝐴𝐿 𝑌 𝐶𝑌 = , 𝑞𝐴𝐿 𝑍 𝐶𝑍 = , 𝑞𝐴𝐿 𝐾 , 𝐶𝐾 = 𝑞𝐴𝐿 𝐻̄ 𝑀 𝐶𝑀 = , 𝑞𝐴𝐿 𝐿𝑜𝑎 𝑁 𝐶𝑁 = , 𝑞𝐴𝐿 𝐿𝑜𝑎 𝐶𝑋 =

(2) (3) (4) (5) (6) (7)

where 𝑞 = 12 𝜌𝑈𝑎 2 is the dynamic pressure, 𝐴𝐿 the lateral projected area, 𝐿𝑜𝑎 the reference length of the lateral plane and 𝐻̄ is the mean height of the lateral plane, 𝐴 𝐻̄ = 𝐿 . 𝐿𝑜𝑎

(8)

Blendermann (2013) relates longitudinal force to the frontal projected area, 𝐶𝑋𝐴𝐹 = 𝐶𝑋

𝐴𝐿 . 𝐴𝐹

(9)

Fujiwara and Nimura (2005) and Ueno et al. (2012) use Eqs. 9, 3, 5 and 7 to derive their mathematical model of the wind loads. However, the marine literature is not entirely uniform when it comes to defining wind coefficients. For example, Andersen (2007) and Wagner (2005) use the following definitions for 𝐶𝑋 , 𝐶𝑌 , 𝐶𝑁 and 𝐶𝐾 : 𝑋 , 𝑞𝐴𝐹 𝑌 𝐶𝑌 = , 𝑞𝐴𝐿 𝐾 , 𝐶𝐾 = 𝑞𝐴𝐿 𝐻𝑆 𝑁 𝐶𝑁 = , 𝑞𝐴𝐿 𝐿𝑜𝑎 𝐶𝑋 =

(10) (11) (12) (13)

where 𝐻𝑆 is the geometric centre of gravity of the lateral projected area measured from the water‐ line (Wagner, 2005). Both 𝐻𝑆 and 𝐻̄ are reference heights, and for a rectangle with base 𝐿𝑜𝑎 and height ℎ, they are related as follows: 𝐻𝑆 =

𝐻̄ . 2

(14)

Dimensionless values computed with Eqs. 10 to 13 are preferred when experimental values are to be used for a ship that is not geometrically similar to the one for which the coefficients were de‐ termined (Andersen, 2013). To allow for a comparison of difference configurations of the same ship, 4

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coefficients that make use of reference dimensions that are independent of the reference areas 𝐴𝐿 and 𝐴𝐹 or quantities derived from these reference areas are preferred (Andersen, 2007; Andersen, 2013; Wagner, 2005): 𝑋 , 𝑞𝐿𝑝𝑝 2 𝑌 𝑌′ = , 𝑞𝐿𝑝𝑝 2 𝐾 , 𝐾′ = 𝑞𝐿𝑝𝑝 3 𝑁 𝑁′ = . 𝑞𝐿𝑝𝑝 3

𝑋′ =

1.4

(15) (16) (17) (18)

Problem summary

From the computational point of view, there is a question of efficiency that needs to be addressed so that a timely answer can be given to questions of the nautical researchers related to the adaptation of existing and creation of new wind coefficients for simulator vessels. This holds true for both the required time for preparing Computer Aided Design (CAD) models and the time to configure and execute computations. From the side of the nautical researchers at FHR, there is a desire to reduce some of the guess work that is currently involved in creating wind coefficients for new simulator vessels or adapting them based on feedback from pilots. Without knowing the magnitude of the influence of configuration changes on the wind coefficient values, it is difficult to determine if such changes even require modi‐ fications to existing wind coefficient data in the first place.

1.5 1.5.1

Proposed solution Contributions of viscosity and pressure

An analysis of the components of the resultant forces and moments from 𝜑 = 0° to 180° has shown that the contribution of the pressure to the resultant forces and moments is by far the largest (Van Hoydonck et al., 2015b). The relative contribution of viscous stresses is rather small, as can be seen in the two graphs in Fig. 2 for the case of head wind (𝜑 = 0°). For the drag, the viscous component is approximately 10% while for the other two components, it is smaller than 3%. This result (and the complete analysis presented in Van Hoydonck et al. (2015b)) suggests that it may be sufficient to use a solver that neglects the contribution of the viscosity: using an Euler solver instead of a Navier‐Stokes solver. As stated before, this can have a significant impact on the com‐ puting time as this reduces the number of cells (required for the resolution of the boundary layer) significantly. Final version

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(a)

Steady computation.

(b) Unsteady computation.

Figure 2 – Relative contribution of the viscous and pressure components to the total forces and moments for a scale model of a container ship (without containers on deck) in a head wind (Van Hoydonck et al., 2015b).

1.5.2

Grid generation

The second issue that contributes to the high turn‐around time is the pre‐processing time required to generate numerical grids. The solver should ideally be able to adapt its grid to the problem at hand in a completely automatic way, using simple logical rules.

1.5.3

CFD Solver

To the knowledge of the author, there is only one CFD solver that addresses these points: the open‐ source Gerris flow solver (discussed in more detail in section 2.5). An initial evaluation of Gerris has shown that for the Tripoli, the shape of the resultant lateral force is very similar (although somewhat higher) to the one computed using FINE/Marine (see Fig. 3), in a time frame that was almost two orders of magnitude shorter than using FINE/Marine. The latter results were computed using an atmospheric boundary layer at the inlet whereas the Gerris results were computed using a uniform wind field at the inlet, which explains the higher 𝐶𝑌 values for Gerris as compared to FINE/Marine. There is a significant difference in the longitudinal force (especially above 45 degrees) for which an explanation should be found. However, this does not mean that Gerris should be discarded if dis‐ crepancies remain, because as stated above, the velocity profile at the position of the vessel in the computational domain for the FINE/Marine result is actually unknown. Both for the Gerris results and the FINE/Marine results, the period of the 𝐶𝑋 graph is proportional to sin(4𝜑). In literature, this type of graph for 𝐶𝑋 is associated with wind tunnel tests of passenger ships (Blendermann, 2013; Fujiwara and Nimura, 2005; Ueno et al., 2012). This may mean that simplifying the containers on the deck of the CAD geometry of the Tripoli to a single block is one simplification too much; in other words, the gaps between the container bays may need to be preserved in order to get a correct graph for 𝐶𝑋 . This is also concluded by Janssen et al. (2017), where wind coefficients computed using four different geometric approximations of a container ship are compared with experimental results. They found a significant improvement in the results when the gaps between container stacks are included in the ship geometry.

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(a)

(b)

Figure 3 – Wind coefficients of the Tripoli estuary vessel computed using (a) FINE/Marine with an atmospheric boundary layer and (b) Gerris with a uniform wind field.

Although it is possible to set a non‐uniform velocity profile at the inlet in Gerris, this will not be pursued here for multiple reasons: • there is no guarantee that an arbitrary velocity profile defined at the inlet remains constant throughout the computational domain (Blocken et al., 2007; Richards and Norris, 2012); • wind tunnel tests are often performed in a uniform wind field (Blendermann, 1993); • the addition of a non‐uniform velocity profile at the inlet in Gerris means that the cell count will be enlarged to resolve the profile until it arrives at the vessel. Due to the use of square cells, Gerris has a disadvantage over a solver that uses hexahedral cells of arbitrary aspect ratio. The impact on the required computation time is significant. • it is possible to convert coefficients derived or obtained for a specific vertical velocity profile to a set of coefficients that correspond to a different wind field (Blendermann, 2013): as long as the velocity field is known for which the wind coefficients are valid, the coefficients can be converted to a different velocity field. Using a uniform velocity field to determine the wind coefficients and automatically converting them at the start of a simulation to correspond to the selected atmospheric profile seems like a good compromise.

1.6

Report contents

In this report, research is documented related to the preparation phase of a CFD computation to determine wind coefficients on a ship. Automatic computation of the reference areas from the in‐ put STL file will be discussed and a tools are documented to create a manifold geometry from the input STL file. The topics related to the fluid dynamics side of the research will be documented in a subsequent report.

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2 Projected Surface Area Computation 2.1

Introduction

This chapter describes a method to automatically compute the frontal and lateral windage areas of vessels used in the simulator at FHR. These reference areas are required to convert the output of Gerris to the coefficient forms as presented in literature (Blendermann, 2013). Due to the large number of vessels and possibly large number of configurations per vessel (e.g. with a different con‐ tainer stacking, different draft, …), the total number of area values that must be computed is very large. This calls for a method where the computation itself is automated, without requiring manual intervention from the user. Initially, focus was on developing an algorithm where a contour polygon was constructed around the part of the hull above water. Once this polygon is constructed, the area 𝐴 can be computed exactly from the positions of the vertices of the polygon: 𝑛

𝐴=∑ 𝑘=0

(𝑥𝑘+1 + 𝑥𝑘 )(𝑦𝑘+1 − 𝑦𝑘 ) , 2

(19)

where 𝑛 is the number of vertices, (𝑥𝑘 , 𝑦𝑘 ) is the k‐th vertex and (𝑥𝑘+1 , 𝑦𝑘+1 ) = (𝑥0 , 𝑦0 ): the first and last vertex are co‐located. Construction of the polygon was attempted by scaling the model in the normal direction and com‐ paring face normals of adjacent faces. If these have the opposite sign, the edge that joins the faces is located at the boundary of the shape. This works fairly well for non‐manifold geometries, but once holes are present or the mesh is manifold (i.e, an edge is shared by either one or more than two faces), detection of the boundary edges becomes difficult. Also, the 3D models generally consist of multiple disconnected parts that overlap which means that intersections between the parts must be computed as well. The algorithm described above works for simple cases, but to cover all possible corner cases, insufficient time was available for a robust implementation. This means that with the current state of the algorithm, manual intervention is required. An alternative approximate method was then devised that will be explained in the next section.

2.2 2.2.1

Automatic approximate projected area computation Introduction

By creating an Cartesian (structured) grid that overlays the ship geometry in for example the lateral or front view, the area can be estimated by determining the number of cells in the grid that are partially or fully covered by the hull geometry. An initial implementation was created in Matlab. Due to the high resolution required to capture small details, the required computing time is very high (up to 750 seconds for a grid with 1000 cells in the x‐direction for one particular case). This algorithm can only provide an estimate of the projected area and hence, one needs to ensure that the obtained value is sufficiently close to the actual projected area. If a certain ship geometry 8

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contains very small details, the computed area will fluctuate as long as the grid is coarser than the smallest geometric details. An alternative implementation of this algorithm was created in Blender (using Python) where instead of constructing an overlay grid and checking the coverage of individual grid cells, an orthographic black and white render of the hull geometry is created and the number of black pixels is counted. If the hull geometry fits the rendered image exactly, the area of an individual pixel is known and the total ship area equals the sum of the black pixels. By activating an option in Blender to use oversampling (or anti‐aliasing), pixels can be coloured grey as well based on the relative coverage of the ship geometry at the pixel location. This way, it is possible to include the influence of small details on the area computation without using a grid that is fine enough to actually resolve the details completely. For the implementation, the STL geometries of the vessel DFDS_JinLing_235_330 at a draft of 7 m (Fig. 4), a configuration of the Tripoli estuary vessel and the Barzan container ship are used.

Figure 4 – CAD geometry of the DFDS JinLing car carrier as used in the simulator of FHR.

2.2.2

Algorithm implementation

Starting from a set of user options, a command is generated with which a Python script is executed inside Blender. The user options are: • • • • • •

STL file to compute reference areas for; Draft at which to compute the reference area; horizontal resolution for the lateral view; Anti‐aliasing setting; use of nodes for rendering; base name to use for output.

For the DFDS JinLing, a typical command is displayed in Listing 1 which defines: • the Blender executable to use ("C:/Program Files/Blender Foundation/Blender/ blender.exe"); • and how it is run (--background); • that it should execute the supplied Python script ("C:/Algemene gegevens/16_058/ship_ area_computation/bpy_generate_views.py"). Final version

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Evaluation of Gerris flow solver for the computation of wind coefficients: Optimization of geometry preparation Listing 1 – DOS command to compute the surface area of the DFDS JinLing at a horizontal resolution of 3200 pixels. "C:/Program Files/Blender Foundation/Blender/blender.exe" --background^ --python "C:/Algemene gegevens/16_058/ship_area_computation/bpy_generate_views.py"^ -- 7 3200 "C:/Algemene gegevens/16_058/ship_area_computation/DFDS_JinLing_235_330.stl"^ no_nodes "C:/Algemene gegevens/16_058/ship_area_computation/DFDS_JinLing_235_330_03200px_AA8_T7"

The whitespace separated list of options after the double dash are passed to this Python script and these set: • the draft (7 m); • the horizontal size (𝑅𝑥,𝐿 ) for the lateral area computation (3200); • the input STL file ("C:/Algemene gegevens/16_058/ship_area_computation/DFDS_Jin Ling_235_330.stl") • that nodes should not be used (no_nodes); • that the basename for the output files is "C:/Algemene gegevens/16_058/ship_area_com putation/DFDS_JinLing_235_330_03200px_AA8_T7"; • the amount of anti‐aliasing samples per pixel should be set to 8. Valid values are 0, 5, 8, 11 and 16.

2.2.3

Blender steps

Using the base name for the output, a log file is opened to which useful input and output values are written for later use such as the draft, the resolution, the STL file and the filenames that contain the lateral and frontal black and white orthographic views of the vessel at the requested draft.

2.2.3.1

Importing the geometry

First a shadeless black material is created for the geometry. The STL file4 is imported and the newly created material is assigned to the ship object. Using the bounding box of the ship and its dimensions, dictionaries are constructed with geomet‐ rical data of the ship size (|𝑥|, |𝑦|, |𝑧|), its extends and the centre location (𝑥,̄ 𝑦,̄ 𝑧).̄ For the ver‐ tical extents, the supplied draft value 𝑇 is required: if the smallest z‐coordinate is less than 0, then 𝑧𝑚𝑖𝑛 = max(𝑇 , 𝑧𝑚𝑖𝑛 ), else, the (positive) draft value is used. Once the extrema of the ship are known, position and orientation for the cameras to render the lateral and frontal orthographic projections are determined where a distinction is made based on the orientation of the vessel. When the size in the x‐direction is larger than the size in the y‐direction, the following arrays are used: #‰ 𝐿𝐿 #‰ 𝑅𝐿 #‰ 𝐿𝐹 #‰ 𝑅𝐹 4

= (𝑥,̄ −|𝑥|, 𝑧)̄ ,

(20)

= (−90°, 180°, 180°) ,

(21)

= (|𝑥|, 𝑦,̄ 𝑧)̄ ,

(22)

= (−90°, 180°, −90°) ,

(23)

Blender can handle both binary and textual STL files in a transparent way.

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otherwise, the following values are used: #‰ 𝐿 𝐿 = (|𝑦|, 𝑦,̄ 𝑧)̄ , #‰ 𝑅 𝐿 = (−90°, 180°, −90°) , #‰ 𝐿 𝐹 = (𝑥,̄ |𝑦|, 𝑧)̄ , #‰ 𝑅 𝐹 = (−90°, 180°, 0°) .

(24) (25) (26) (27)

Finally, the maximum (𝑑𝑚𝑎𝑥 ) and minimum (𝑑𝑚𝑖𝑛 ) horizontal dimensions are set. 2.2.3.2

Preparing the scene for rendering

The (square) pixel size is determined from the maximum horizontal dimension and the requested horizontal image resolution: Δ𝑥 =

𝑑𝑚𝑎𝑥 . 𝑅𝑥,𝐿

(28)

The vertical resolution of the images in pixels (𝑅𝑦 ) is determined from the ship vertical size |𝑧|, 𝑅𝑦 = ⌈

|𝑧| ⌉, Δ𝑥

(29)

which may be more than the actual ship vertical size. For the frontal area computation, the horizontal resolution 𝑅𝑥,𝐹 is determined: 𝑅𝑥,𝐹 = ⌈

𝑑𝑚𝑖𝑛 ⌉, Δ𝑥

(30)

which, due to rounding, may be slightly more than the actual ship width. The vertical size of the lateral and frontal images 𝑆𝑦 is computed using the pixel size and the vertical resolution, 𝑆𝑦 = Δ𝑥𝑅𝑦 ,

(31)

while the horizontal size of the frontal images 𝑆𝑥,𝐹 follows from 𝑆𝑥,𝐹 = Δ𝑥𝑅𝑥,𝐹 .

(32)

𝑆𝑦 and 𝑆𝑥,𝐹 are in general slightly larger than |𝑧| and 𝑑𝑚𝑖𝑛 because the vertical to horizontal size ratio is not guaranteed to be an integer value. Due to the increase in vertical size, the vertical camera location must be increased slightly with Δ𝑧 = 0.5(𝑆𝑦 − |𝑧|).

(33)

It is assumed that for the frontal image, the horizontal shift of the camera is zero because the vessels are assumed symmetric with respect to the butt line (xz‐plane). Two orthographic camera objects are created: one for the lateral view and one for the frontal view. The orthographic scale (ortho_scale) is the important variable. It represents the maximum dimen‐ sion (in scene units) of the portion of the space captured by the camera. For the lateral view, this is Final version

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equal to the maximum size of the vessel, while for the frontal view, it is the maximum of the adjusted vertical size and the minimum horizontal ship size. The world (background) horizon and ambient colours are set to white. The vertical resolution of both images is 𝑅𝑦 . The horizontal resolution depends on the actual image that is generated. For the lateral view, it is the requested resolution 𝑅𝑥,𝐿 , while for the frontal view, it is 𝑅𝑥,𝐹 . Image settings are added as well: the colour mode is set to RGBA with a depth of 8 bit per channel. Compositing and the sequencer are disabled while image overwriting is enabled. Antialiasing settings are set based on what the user requested. For complex geometry with small details, a value of 8 seems to give a good balance between render speed and convergence speed (see later). 2.2.3.3

Render scene

Once the scene preparation is finished, it is rendered and the output is written to a png file. The actual filename is returned and used to load the image in memory again (as a list of pixels). Direct manipulation of the render result in memory without writing the data to disk first does not seem to work reliably in Blender 2.79. 2.2.3.4

Ship area computation

The rendered image (black and white) is converted into a numpy array 𝐺 where only each fourth pixel (due to the four channel RGBA image format) is retained, starting at the first one). This means that for every pixel, there is 1 float value (between 0 and 1) that represents its greyscale colour. The sum of this array 𝑆𝑔 is computed from the size (in pixels) of the image minus the sum of the greyscale values (here for the lateral image): 𝑆𝑔 = 𝑅𝑥 𝑅𝑦 − ∑ 𝐺.

(34)

The area covered by the image 𝐴𝐼 follows from the pixel size and the computed horizontal and vertical dimensions, 𝐴𝐼 = 𝑆𝑥 𝑆𝑦 Δ𝑥2 ,

(35)

and finally, the ship projected area 𝐴𝑃 follows as 𝐴𝑃 = 𝐴𝐼 ∗ 𝑆𝑔 /(𝑆𝑥 𝑆𝑦 ),

(36)

which can be computed directly from 𝑆𝑔 and Δ𝑥, 𝐴𝑃 = Δ𝑥2 𝑆𝑔 .

(37)

This routine is called twice, first for 𝐴𝐿 and then for 𝐴𝐹 . The computed ship area is written to the log file as well.

2.3

Grid convergence study

To ensure that the above algorithm is implemented correctly (i.e. it computes the correct area) and that it is used at a sufficient resolution, it is used to compute the frontal and lateral surface areas of simple geometries for which the surface area can be determined analytically. The influence of the antialiasing setting on the computed area will be determined as well. 12

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2.3.1

Simple box with analytical surface areas

The lateral and frontal projected surface areas of the box in Fig. 5 are 20 + 15 40 = 700 m2 , 2 15 + 20 𝐴𝐹 = 20 = 350 m2 . 2 𝐴𝐿 =

(38) (39)

An array with resolution values is generated with common ratio of approximately progression) starting at 50 and ending at 6400:

√

2 (geometric

𝑅𝑥,𝐿 = [50, 70, 100, 141, 200, 282, 400, 564, 800, 1128, 1600, 2256, 3200, 4512, 6400].

(40)

Figure 5 – Dimensions of a simple box for verification of the surface area computation.

For all values of the anti‐aliasing parameter (0, 5, 8, 11 and 16), the computed lateral and longitudinal surface areas are displayed in Fig. 6a. There is a clear difference between results obtained with anti‐ aliasing enabled, and results obtained with this feature disabled (AA = 0). The former curves (AA enabled) converge very gradually towards the analytical surface areas, whereas the results obtained with AA disabled are exact with resolutions of 800 pixels and higher. Inspection of the relative errors (Fig. 6b), the curves with AA enabled show a relative error smaller than 0.1% for resolutions starting at 3200 pixels. For relative errors smaller than 1%, a horizontal resolution of 282 is required.

(a) Absolute values.

(b)

Relative errors.

Figure 6 – Convergence of surface area computation as a function of resolution for the simple box.

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A Python run that computes the frontal and lateral surface area at 15 different resolutions takes between 71 s (AA = 0) and 82 s (AA = 16) on the author’s laptop. A breakdown of the timings is shown in Fig. 7 where for each resolution, the execution times of the Blender Python scripts are displayed as a function of the resolution. This figure also displays the slope of a quadratic equation that approximates the slope of the curves for high resolutions. This means that for high resolutions, the computing time scales with the square of the grid resolution. At (very) coarse resolutions, the computing time (≈ 0.14 s) is basically independent of the resolution: the steps to setup the scene are independent of the image resolution and dominate the total time.

Figure 7 – Computing time as a function of resolution.

For the simple geometry used here, it is clear that the anti‐aliasing settings do not improve the speed of convergence. There is also little difference between the different non‐zero anti‐aliasing settings: higher values increase the computing time slightly. The above exercise will be executed again with a simple ship geometry for which the frontal and lateral surface areas are known exactly. Afterwards, a ship geometry for which the surface area is not know exactly will be tested. For these cases, only the AA = 0 and AA = 8 settings will be tested.

2.3.2

Simplified Barzan hull

A simplified hull of the Barzan container ship has been used in CFD computations related to wind coefficient predictions (Van Zwijnsvoorde et al., 2019). For this simple geometry (see Fig. 8), the reference areas are known exactly: 𝐴𝐿 = 17 100.8 m2 and 𝐴𝐹 = 3287.46 m2 . For this case, absolute values of the lateral and frontal surface areas are shown in Fig. 9a while the relative errors of these quantities are shown in Fig. 9b. Compared to the convergence graphs of the previous geometry, the convergence now is not as smooth and quick. For the lateral area compu‐ tation, for 𝑅𝑥,𝐿 = 800, the error is smaller than 1%. For the frontal area computation, this level of error is reached with 𝑅𝑥,𝐿 = 200. For the lateral area computation, convergence is monotonic, whereas for the frontal area computation, it is oscillatory. 14

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Figure 8 – Dimensions of a simplified hull form of the Barzan container vessel.

(a) Absolute values.

(b)

Relative errors.

Figure 9 – Convergence of surface area as a function of resolution for the Barzan hull geometry.

2.3.3

Estuary vessel Tripoli

The estuary vessel the Tripoli is used as a test case of a representative geometry as used in the simu‐ lator. A modified version of this geometry has been used in a previous CFD study to determine a set of wind coefficients (Van Hoydonck et al., 2015a,b). For the current surface area computation, the actual geometry as utilised in the simulator is used –unlike the CFD computations, where the geo‐ metry was simplified significantly– which includes container stacks protruding through the bottom of the hull, see Fig. 10. The draft of the vessel is arbitrarily set to 2.5 m.

Figure 10 – Overview of the geometry of the Tripoli estuary vessel as used in the simulator.

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For this case, there is no reference area known, so only the absolute values of the frontal and lateral surface areas will be shown. As before, anti‐aliasing is used as parameter: AA=0 and AA=8 are used. The results are shown in Fig. 12. For the lateral surface area, the average of the prediction at the finest grid equals 955.8 m2 while for the frontal surface area, this average is 220.3 m2 . The lateral and frontal view of the Tripoli at a resolution of 3200 pixels with anti‐aliasing enabled is shown in Fig. 11.

Figure 11 – Frontal and lateral view of the Tripoli for 𝑅𝑥,𝐿 = 3200 and 𝐴𝐴 = 8, with 𝐴𝐿 = 953.60 m2 and 𝐴𝐹 = 219.94 m2 .

Inspection of the renderings shows that at the finest level, small gaps appear for the case with anti‐ aliasing enabled that are not visible in the case with anti‐aliasing disabled. These small details put a constraint on the minimum required grid resolution to resolve this type of features. As a con‐ sequence, it may be necessary to compute the surface areas at even finer grids. To put this argument in perspective, the STL geometry does contain features such as flags and filled polygons that are textured with transparent textures in the simulator that all increase the total sur‐ face area of the vessel. In reality, the surface areas of these features should not be used in the surface area computation. So, by increasing the resolution of the surface area computations, one can reduce the error of the estimate, but the resulting value may contain a bias because some parts of the geo‐ metry are actually transparent and should not be included in the surface area computation.

(a) Absolute values.

(b)

Zoom of Fig. 12a.

Figure 12 – Convergence of surface area as a function of resolution for the Tripoli hull geometry.

2.4

Surface area extrapolation

From the above grid convergence study, it follows that for ship geometries as used in the simulator, a fine resolution is required to capture the effect of small geometric features in the surface area computation. In this section, a sequence of successively finer grids is used to fit a function through 16

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the computed areas that can be used to improve the surface area estimation without computing extra surface area values. The following four‐parameter symmetric sigmoidal function is used to fit the data, 𝑦=𝑑+

𝑎−𝑑

𝑏,

(41)

1 + ( 𝑥𝑐 )

where 𝑎, 𝑏, 𝑐 and 𝑑 are parameters that must be determined, 𝑥 is the resolution and 𝑦 the computed surface area. In the limit of a very high resolution 𝑥, the value of 𝑦 (the ship surface area) is equal to the parameter 𝑑. This method is applied to the data generated in the previous section for the three test geometries. For the first two geometries, the error of the extrapolated surface area will be computed and compared to the relative error of the result on the finest grid.

2.4.1

Test cube

The relative errors of the parameter 𝑑 in Eq. 41 are shown in Table 1 for the lateral and frontal surface area extrapolation for all five values of the anti‐aliasing settings used before as compared to the result on the finest grid (right‐most column). The values in columns three to seven correspond to the errors obtained when the sigmoidal fit starts at the resolution indicated in the first row. When only high resolution results are used to estimate the surface areas (e.g. column seven), the relative error is significantly smaller (in some cases 6 orders smaller) than the relative error of the result on the finest grid (last column). By progressively including results at coarser resolutions in the extrapolation, the estimated surface area is further from the analytical value. One can conclude from these results that it is indeed possible to fit a function through the results to try to improve the surface area estimation without computing them at extremely fine resolu‐ tions. Table 1 – Relative errors (%) of the lateral and frontal surface areas for the test cube as a function of the anti‐aliasing value for curve fits starting at progressively finer resolutions as compared to the result on the finest grid (last column). 𝐴𝐴 𝐴𝐿 𝐴𝐹 𝐴𝐿 𝐴𝐹 𝐴𝐿 𝐴𝐹 𝐴𝐿 𝐴𝐹 𝐴𝐿 𝐴𝐹

2.4.2

0 5 8 11 16

𝑅𝑥,0 = 50

100

200

400

800

6400

−7.785 × 10−4 4.382 × 10−2 1.180 × 10−3 −9.654 × 10−3 −8.301 × 10−4 −6.018 × 10−3 −4.735 × 10−4 −1.360 × 10−2 −1.040 × 10−3 −4.464 × 10−3

−7.785 × 10−4 1.352 × 10−4 5.276 × 10−4 −8.640 × 10−3 1.370 × 10−4 −6.808 × 10−3 3.625 × 10−4 −1.339 × 10−3 3.101 × 10−4 −4.291 × 10−3

−6.712 × 10−4 −7.511 × 10−4 4.375 × 10−4 −2.101 × 10−4 −9.857 × 10−5 −1.595 × 10−4 −2.280 × 10−5 −4.775 × 10−6 −9.267 × 10−5 1.661 × 10−5

−4.014 × 10−5 7.984 × 10−5 7.100 × 10−4 −7.595 × 10−5 −1.504 × 10−4 −1.689 × 10−4 −9.788 × 10−5 −1.059 × 10−4 −1.117 × 10−4 −6.982 × 10−5

0.0 0.0 1.063 × 10−3 −1.055 × 10−7 −3.725 × 10−8 −1.248 × 10−7 −3.773 × 10−8 −1.341 × 10−7 −3.932 × 10−8 −1.275 × 10−7

0.0 0.0 −2.578 × 10−2 −3.536 × 10−2 −2.832 × 10−2 −3.910 × 10−2 −3.142 × 10−2 −4.313 × 10−2 −2.892 × 10−2 −3.942 × 10−2

Simplified Barzan hull

The same exercise is done for the simplified hull form of the Barzan container vessel. The relative errors of the parameter 𝑑 in Eq. 41 are shown in Table 2 for the lateral and frontal surface area extrapolation for the two values of the anti‐aliasing settings used before (§ 2.3.2) as compared to the result on the finest grid (right‐most column). Careful inspection of these error values reveals that the relative errors of the curve fit starting at 𝑅𝑥,0 = 100 for 𝐴𝐴 = 8 gives the smallest errors. Compared Final version

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to the results obtained with the finest grid, the errors are approximately three times smaller. This is not as good as for the test cube case discussed in the previous section, which may mean that higher resolutions are required. Table 2 – Relative errors (%) of the lateral and frontal surface areas for the simplified Barzan hull for 𝐴𝐴 = 0 and 𝐴𝐴 = 8 for curve fits starting at progressively finer resolutions as compared to the result on the finest grid. AA 𝐴𝐿 𝐴𝐹 𝐴𝐿 𝐴𝐹

2.4.3

𝑅𝑥 , 0 = 50

100

−1

0 8

200 −2

1.755 × 10 5.568 × 10−1 −2.596 × 10−1 −4.992 × 10−1

−4.146 × 10 4.876 × 10−1 2.783 × 10−2 1.521 × 10−2

400 −2

5.269 × 10 3.042 × 10−2 −6.561 × 10−2 −6.33 × 10−2

6.763 −9.824 × 101 −8.959 × 10−2 2.640 × 10−2

800

6400 −1

3.411 × 10 9.022 × 10−2 −9.175 × 10−2 −5.232 × 10−2

6.111 × 10−2 8.724 × 10−2 −9.343 × 10−2 −4.259 × 10−2

Tripoli surface area estimation

For the Tripoli estuary vessel, analytical values for the surface areas are not known, so only absolute values can be computed. Results are gathered in Table 3. Based on the increasing trends shown in Fig. 12b, one would expect the lateral area estimate to be higher than the value on the finest grid for 𝐴𝐴 = 8. Inspection of the values in Table 3 shows that this is indeed the case. The average of the ten extrapolated lateral surface area values is 956.4652 m2 , while for the frontal surface area, the average value equals 220.8162 m2 . These averaged values are closest to the extrapolated values for 𝑅𝑥 , 0 = 100 with 𝐴𝐴 = 8. Table 3 – Lateral and frontal surface area values estimates for the Tripoli estuary vessel for AA=0 and AA=8 for curve fits starting at progressively finer resolutions as compared to the result on the finest grid. AA 𝐴𝐿 /m2 𝐴𝐹 /m2 𝐴𝐿 /m2 𝐴𝐹 /m2

2.4.4

0 8

𝑅𝑥 , 0 = 50 956.777 222.454 955.645 220.732

100

200

400

800

6400

956.504 221.238 956.501 220.815

956.884 220.564 956.776 220.252

956.326 220.623 956.904 220.647

956.533 220.525 955.802 220.312

956.740 220.417 955.039 220.237

Conclusion

For the cube, it was shown that significantly more accurate results (up to 6 orders) can be obtained by using a suitable extrapolation function. However, the size of the smallest details do play a role in the extra accuracy that can be gained: for the simplified Barzan hull geometry, the improvements were at most threefold. For this geometry, the smallest errors were obtained when the function fit started at 𝑅𝑥,0 = 100, for the case with anti‐aliasing enabled (𝐴𝐴 = 8). For the Tripoli, no analytical values for the surface areas are available, so only absolute values could be compared. When computing the average of the different extrapolation results, the extrapolated results for the same parameters (𝑅𝑥,0 = 100 and 𝐴𝐴 = 8) as the Barzan case are closest to the average. One could take this as a careful recommendation to compute extrapolations using these parameters. The extrapolations that were executed here show that the results at very coarse resolutions have a detrimental effect on the accuracy of the value in the limit of a very fine resolution. 18

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2.5

Surface area computations of other ships

For a small set of ships used in the simulator at FHR, the lateral and frontal surface areas are computed with the algorithm detailed in this chapter. The coarsest resolution is set to 100, the finest to 6400 and the anti‐aliasing value equals 8. The resulting estimates of the frontal and lateral surface areas are gathered in Table 4. The lateral and frontal views of these ships with a resolution of 1600 pixels are shown in Figs. 13 to 19. For each of the computed vessels, the values as found in the load_*.xml for some drafts are shown in the last two columns as well. For most of these ships, the differences are significant (with both LNG models as exceptions). One notable example with significant differences is the Myzaquazo, where the differences in the lateral surface area between the computed value and the reference value as used in the simulator is up to 50%. This is a container vessel, and the surface areas depend a lot on the specific configuration of the containers. To ensure that the algorithm detailed in this chapter does not contain a fundamental flaw, the lateral surface areas were estimated by tracing a rough polygon around the STL model, filling the outline with triangles and computing the sum of the areas of these triangles. Only the widest gaps between the container stacks are included, and some of the smaller equipment (such as the crane) was left out, so the values estimated as such should be smaller than values in the table. The values found as such are 831 m2 , 635 m2 and 528 m2 for even draft values of 1.5 m, 2.85 m and 3.65 m. Indeed, these are smaller, but close to the computed values. Table 4 – Estimates of the lateral and frontal surface areas of several simulator models. STL file qmax_al_anna.stl qflex_mona.stl myzaquazo_3layers.stl LNG_Yamal_ARC7_299_500.stl LNG_Conventional_300_460.stl DFDS_JinLing_235_330.stl clementine.stl

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𝑇 /m

𝐴𝑙 /m2

𝐴𝑓 /m2

𝐴𝑠𝑙 /m2

𝐴𝑠𝑓 /m2

12.2 9.6 12.0 9.5 1.5 2.85 3.65 11.78 9.9 12.0 9.5 7.0 6.5

8663.92 ± 3.94 9526.66 ± 9.02 6717.49 ± 3.53 7501.22 ± 10.40 813.45 ± 1.09 632.77 ± 1.05 525.86 ± 1.33 7656.09 ± 4.08 8204.99 ± 5.68 6755.80 ± 5.02 7488.84 ± 5.56 5297.58 ± 2.71 2996.43 ± 0.87

1861.59 ± 1.41 2001.63 ± 1.89 1469.24 ± 2.19 1594.38 ± 2.04 110.793 ± 0.106 85.326 ± 0.081 76.199 ± 0.136 1710.79 ± 3.96 1805.42 ± 8.03 1408.09 ± 2.99 1524.00 ± 5.79 1224.90 ± 1.84 684.62 ± 0.32

7866.0 8727.0 7500.0 8300.0 654.8 411.8 303.8 7714.0 8207.0 6719.0 7431.5 5930.4 2615.0

1659.0 1788.0 1550.0 1650.0 84.2 63.5 54.4 1751.0 1837.0 1370.0 1480.0 1182.0 650.0

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Figure 14 – Lateral and frontal view of the qflex_mona. WL2021R16_058_1

Figure 15 – Lateral and frontal view of the myzaquazo_3layers.

Figure 16 – Lateral and frontal view of the LNG_Yamal_ARC7_299_500.

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20 Figure 13 – Lateral and frontal view of the qmax_al_anna.

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Figure 19 – Lateral and frontal view of the Clementine.

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Figure 18 – Lateral and frontal view of the DFDS_JinLing_235_330.

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2.6

Conclusions

In this chapter, an automated method is proposed to compute the reference windage areas of the ship mathematical manoeuvring models used in the simulators at FHR. These windage areas are required as input for the computation of wind loads on said ships in order to convert the resultant forces and moments into dimensionless coefficients. The method uses Blender to render a greyscale image of the front and side view of the ship. The surface areas are computed by counting the number of coloured pixels. The method is fairly effi‐ cient, being able to compute the reference areas in a manner of minutes for a range of resolutions. By fitting a four‐parameter symmetrical sigmoidal function to the reference areas computed as such, an estimate can be found for an infinite resolution. It is shown that the estimate obtained as such can be significantly more accurate than a value computed at a very fine resolution, but the improve‐ ment depends much on the presence of small details. The method shows a second‐order trend as a function of the image resolution. When determining the wind coefficients for a ship model using CFD, the resultant forces are con‐ verted to dimensionless quantities by dividing them by dynamic pressure and the reference area. There is no point in doing this if the reference area used in the simulator is not correct. Given the sometimes significant differences between the reference areas as used in the simulator and those computed in this report, it may be necessary to perform a quality check of the reference areas of all vessels as used in the simulator. Although it is demonstrated that the method gives correct results for sufficiently high resolutions, the convergence is rather slow. This is in part caused by the inexact fit of the image to the vessel dimensions: due to the use of square pixels, it is possible (and likely) that only the first dimension (ship length) exactly matches the requested number of pixels. If the fraction on the right‐hand side of Eq. 29 is a floating point number instead of an exact integer, the rounding up of this fraction results in a slightly taller image than the vessel. This then also holds for the image width of the frontal area render. With the use of non‐square pixels the rounding would not be necessary, and the results may converge faster to the correct value.

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3 Mesh wrapping 3.1

Introduction

As briefly mentioned in Chapter 2, the step of creating a watertight mesh from an initial triangular hull geometry (as used in the simulator for example) may take a significant amount of time when tackled by hand. This is caused by different requirements for the simulator and for CFD applications: the former should contain as few triangles as possible (for good rendering performance) and it is allowed to be non‐manifold. Geometry for the latter applications must be watertight to distinguish the inside from the outside. During the evaluation of StarCCM+ in project 18_030, it became clear that StarCCM+ includes a very good surface wrapper as part of its mesh preparation tools (Van Hoy‐ donck et al., 2019). A tool similar to this surface wrapper would result in a potentially significant reduction in time for the preparation of simulator ship geometries for use in CFD wind coefficient computations.

3.2 3.2.1

Available surface wrapping tools Meshmixer

Meshmixer5 is Autodesk’s free software for preparation of geometries for 3D printing. In the Edit Menu, there is a tool called Make Solid. This tool creates an internal voxel representation of the input shape to create an unambiguous solid model from the input. The result is an approximation, where the biggest drawback is the fixed size of the resulting faces of the mesh approximation. This size is governed by the size of the voxels: the smaller the dimensions of the voxels as compared to the input geometry, the more accurate the final approximation. Details smaller than a few voxels will be lost and sharp edges may be smoothed. Reducing the voxel size has a detrimental effect on the computation time. In Fig. 20a, the STL input geometry of the Myzaquazo is shown, while Figs. 20b to 20d show the resulting solid model wrapped with an increasingly more detailed mesh. A detail of the steering house is shown in Fig. 21, where it is clear that the floor and railing around the steering house are not properly captured by the tool. Given that this occurs at the finest possible settings, the controls of Meshmixer do not seem to to have enough range to execute the task at hand successfully.

3.2.2

Open Cascade CAD Processor

The commercial branch of Open Cascade markets a CAD processor tool for 3D data preparation and simplification for various applications6 that includes a shrink wrapping algorithm capable of wrap‐ ping any CAD geometry (either Non‐Uniform Rational B‐Spline (NURBS)‐based or polygonal‐based) with a watertight unstructured grid that is simulation‐ready. A trial version of the software can be downloaded, but this has not been pursued at this moment. 5 6

https://www.meshmixer.com http://www.opencascade.com/products/cad-processor/

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(a) Original STL geometry.

Surface wrapped with the default settings.

(b)

(c)

(d)

Surface wrapped with refined settings.

Surface wrapped with best (slowest) settings.

Figure 20 – Surface wrapping the Myzaquazo STL geometry with Autodesk’s Meshmixer.

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Figure 21 – Issues with the resulting solid model of the steering house of the Myzaquazo at the finest settings. The circled regions show loose geometry (right) and gaps in the model (right).

3.2.3

Blender Remesh Modifier

Starting from Blender 2.81, the Sculpt Remesher tool7 has been added as an option to the Remesh modifier, where it can be accessed as Voxel mode, see Fig. 22. As a result, there are now four modes for the Remesh modifier: • • • •

Blocks Smooth Sharp Voxel

Figure 22 – Remesh modifier in Voxel mode in Blender.

The voxel size is an absolute length with a lower limit of 0.0001 m, which is enough to capture suffi‐ cient detail of the original geometry for the purpose of CFD computations. The tool has an Adaptivity setting to increase the face sizes in areas where detail is not required such as away from sharp edges that demarcate adjacent non‐coplanar surfaces. For simple geometries consisting of overlapping or intersecting parts that are not aligned to the global axes, the Remesh modifier in Sharp mode can generate good results without increasing the cell count significantly. This is shown in Fig. 23 where four partially overlapping boxes in the same object are joined while preserving the sharp intersections between the different boxes. However, for increasingly larger and complex models, extra work is required to ensure that the model is reasonably watertight. Thin features such as railings and gaps between container stacks require a high value for the Octree depth, in the case of the Myzaquazo, a depth of at least 11 or even 12 is 7

Underneath the hood, the remesher tool uses the open‐source OpenVDB C++ library (http://www.openvdb.org) originally developed at Dreamworks Animation.

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required. At this latter depth, the resulting geometry is basically a perfect representation of the initial geometry, but without the imperfections of non‐manifold edges. This comes at a price however, because the vertex count is more than 5.772 × 106 .

(a) Input geometry.

(b) Manifold result.

Figure 23 – Blender’s Remesh modifier in Sharp mode applied to four intersecting boxes.

The requirements for the Remesh modifier in Voxel mode are not as strict: holes such as the hull bottom must be filled, but overlapping geometry is allowed, as long as the algorithm can construct a manifold mesh around the input. It does not discretize baffles (thin surfaces) as can be done in Sharp mode (see Fig. 24), so the railing at the stern should either be removed, or it should be extruded to give it some thickness (Fig. 25).

(a) Input geometry.

(b)

Manifold result with baffles removed.

Figure 24 – Blender’s Remesh modifier in Voxel mode applied to the Myzaquazo hull geometry.

For the geometry of the Myzaquazo, a first attempt at preparing the geometry to create a surface wrapped mesh took less than an hour, which is a significant reduction as compared to the required time that was needed when cleaning the Tripoli hull geometry by hand (multiple days). Fig. 26 shows the geometry of the Myzaquazo near the bow. The flags and some other loose parts were removed, but otherwise all geometry was kept. The voxel size was set to 0.02 m while the adaptivity was set to four times that value (0.08 m). With these settings, the resulting wrapped geometry is obtained in approximately one minute. Fig. 26a shows the input geometry, while the surface wrapped results is shown in edit mode in Fig. 26b. With these settings, the mast is captured accurately. The number of vertices is increased significantly (from 2672 to 1 072 518), but the resulting mesh is a perfect manifold and can be used directly in CFD applications. 26

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(a)

Modified input geometry: baffles with thickness.

(b)

Manifold result with baffles included.

Figure 25 – Blender’s Remesh modifier in Voxel mode applied to a slightly modified Myzaquazo hull geometry.

(a)

Input geometry.

(b)

Surface wrapped geometry.

Figure 26 – Surface wrapping the Myzaquazo STL geometry with Blender’s remesh modifier.

3.3

Conclusions

Using Blender’s Remesh modifier in Voxel model in the workflow to compute wind coefficients of a ship will reduce the required preparatory time significantly, which brings regular use of CFD for this type of application again closer. Although the complete geometry with all details can be captured, edge sharpness is not exactly maintained. This could be an issue when the resulting geometry is used in meshing software such as Hexpress or OpenFOAM’s snappyHexMesh. However, the intention is to use this type of model in Gerris, where the hull geometry is approximated in an octree. Sharp edges are not guaranteed to be preserved there either, this depends entirely on the number of octree subdivisions used in the computation.

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4 Summary and conclusions In this first report regarding the evaluation of the open‐source Gerris flow solver, optimisations are reported related to two preparatory steps that must be executed before actual CFD computations can be started. The first step is related to the computation of the ship frontal and lateral reference areas, while the second step concerns the conversion of the ship geometry as used in the simulators at FHR for use in CFD computations. For both steps, an STL representation of the geometry is used as input, although other polygonal formats are possible as well. The steps make use of the existing modelling and rendering capabilities available in the open‐source 3D content creation suite Blender. For the frontal and lateral surface area computations, the ship frontal and lateral views are rendered as greyscale images. The reference surface areas follow from the number of coloured pixels in the resulting renders, the total pixel count in the renders and the dimensions of the models. The method can compute the reference areas in a manner of minutes for a range of image resolutions. An extra‐ polation to an infinite resolution is implemented by fitting a four‐parameter symmetrical sigmoidal function to the computed reference areas. It is shown that the estimate obtained as such can be significantly more accurate (and quicker) than a value computed at an extremely fine resolution, but the improvement depends much on the presence of small details. For a small number of vessels as used in the simulator, the frontal and lateral surface areas at specific draft values are computed and compared with the values as recorded in the load_*xml files of the ships. For some of these, the differences are rather large between the reference areas as used in the simulator and those computed in this report. This can be caused by imperfections in the 3D models: a small error in deck height in the 3D model can result in a significant difference in the windage area. The reference areas of the models as used in the load_*xml files are also not always computed from the 3D models: some are based on general arrangement plans or information from the ship owner. Preparing a 3D geometry as used in the simulator for CFD computations is a task that requires a significant amount of time when executed by hand. The evaluation of StarCCM+ (project 18_030) showed that a significant improvement in efficiency can be obtained with the help of an automatic surface wrapping tool. Recent version of Blender link against the OpenVDB library, which makes available an efficient method to wrap an existing CAD model with a watertight shell in Blender. It is estimated that – on average – the optimisations for the steps as currently reported reduce the preparation time from up to two days to as little as two hours.

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References Andersen, I. M. V. (2007). Vindkræfter på Containerskibe. (M.Sc. thesis). Institut for Mekanik, Energi og Kon‐ struktion, Danmarks Tekniske Universitet Andersen, I. M. V. (2013). Wind loads on post‐panamax container ship. Ocean Engineering 58: 115–134. DOI: https://doi.org/10.1016/j.oceaneng.2012.10.008 Blendermann, W. (2013). Practical ship and offshore structure aerodynamics. Hamburg University of Techno‐ logy: Hamburg, Germany. ISBN: 978‐3‐89220‐669‐9 Blendermann, W. (1993). Schiffsform und Windlast‐Korrelations‐ und Regressionsanalyse von Windkanalmes‐ sungen am Modell. 533. Hamburg, Germany Blocken, B.; Stathopoulos, T.; Carmeliet, J. (2007). CFD simulation of the atmospheric boundary layer: wall function problems. Atmospheric Environment 41 (2): 238–252. DOI: https : / / doi . org / 10 . 1016 / j . atmosenv.2006.08.019 Fujiwara, T.; Nimura, T. (2005). New estimation method of wind forces acting on ships on the basis of math‐ ematical model. in: Proceedings of the Fifteenth (2005) International Offshore and Polar Engineering Confer‐ ence. Seoul, Korea, 19th–24th June 2005. The International Society of Offshore and Polar Engineers. ISBN: 1880653648. pp. 82–89 Janssen, W. D.; Blocken, B.; van Wijhe, H. J. (2017). CFD simulations of wind loads on a container ship: Valida‐ tion and impact of geometrical simplifications. Journal of Wind Engineering and Industrial Aerodynamics 166: 106–116. DOI: https://doi.org/10.1016/j.jweia.2017.03.015 Richards, P. J.; Norris, S. E. (2012). Appropriate boundary conditions for a pressure driven boundary layer. in: Brandner, P. A.; Pearce, B. W. (Eds.). Proceedings of the 18th Australasian Fluid Mechanics Conference. Launce‐ ston, Australia, 3rd–7th December 2012. Australasian Fluid Mechanics Society. ISBN: 978‐0‐646‐58373‐0. p. 4 Ueno, M.; Kitamura, F.; Sogihnara, N.; Fujiwara, T. (2012). A simple method to estimate wind loads on ships. in: The 2012 World Congress on Advances in Civil, Environmental, and Materials Research (ACEM’ 12). Seoul, Korea, 26th August 2012–30th August 2005. International Association of Structural Engineering and Mechan‐ ics. pp. 2314–2322 Van Hoydonck, W.; Delefortrie, G.; Peeters, P.; Mostaert, F. (2015a). Computation of aerodynamic coefficients of ships using FINE/Marine: initial evaluation. 3.0. WL Rapporten, 12_106. Antwerp, Belgium Van Hoydonck, W.; Delefortrie, G.; Vos, S.; Peeters, P.; Mostaert, F. (2015b). Computation of aerodynamic coefficients of ships using FINE/Marine: Wind coefficients for the Tripoli estuary container vessel at a draft of 3.5 m. 3.0. WL Rapporten, 12_106. Antwerp, Belgium Van Hoydonck, W.; Eloot, K.; Verelst, K.; Mostaert, F. (2019). Evaluation of the CFD Package StarCCM+. 2.0. WL Rapporten, 18_030. Antwerp, Belgium Van Hoydonck, W.; Vos, S.; Peeters, P.; Mostaert, F. (2016). CFD computations of the wind climate behind a roro ship. Version 3.0. FHR Reports, 15_096. Flanders Hydraulics Research: Antwerp, Belgium

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Evaluation of Gerris flow solver for the computation of wind coefficients: Optimization of geometry preparation Van Zwijnsvoorde, T.; Donatini, L.; Hoydonck, W. V.; Lataire, E. (2019). Wind modeling for large container vessels: a critical review of the calculation procedure. International Journal of Transport Development and Integration 3 (4): 369–381. DOI: 10.2495/TDI-V3-N4-369-381 Wagner, M. (2005). Wind‐Tunnel Tests with FSG NB 731/732. FORCE 2005031. FORCE Technology: Lyngby, Denmark

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DEPARTMENT MOBILITY & PUBLIC WORKS Flanders hydraulics Research Berchemlei 115, 2140 Antwerp T +32 (0)3 224 60 35 F +32 (0)3 224 60 36 waterbouwkundiglabo@vlaanderen.be www.flandershydraulicsresearch.be