Thomsen, Jonas Bjerg

English

This report covers a simple investigation of mean drift forces found by use of the boundary element method code NEMOH. The results from NEMOH are compared to analytical results from literature and to numerical values found from the commercial software package WADAM by DNV-GL.The work was conducted under the project "Mooring Solutions for Large Wave Energy Converters", during "Work Package 4: Full Dynamic Analysis". The validation compares results from a simple sphere and from a vertical cylinder.This report covers a simple investigation of mean drift forces found by use of the boundary element method code NEMOH. The results from NEMOH are compared to analytical results from literature and to numerical values found from the commercial software package WADAM by DNV-GL.The work was conducted under the project ”Mooring Solutions for Large Wave Energy Converters”, during", Work Package 4: Full Dynamic Analysis". The validation compares results from a simple sphere and from a vertical cylinder

    Aalborg UniversitetValidation of Mean Drift Forces Computed with the BEM Code NEMOHThomsen, Jonas BjergPublication date:2017Document VersionPublisher's PDF, also known as Version of recordLink to publication from Aalborg UniversityCitation for published version (APA):Thomsen, J. B. (2017). Validation of Mean Drift Forces Computed with the BEM Code NEMOH. Department ofCivil Engineering, Aalborg University. DCE Technical reports No. 215General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.            ? Users may download and print one copy of any publication from the public portal for the purpose of private study or research.            ? 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You may freely distribute the URL identifying the publication in the public portal ?Take down policyIf you believe that this document breaches copyright please contact us at vbn@aub.aau.dk providing details, and we will remove access tothe work immediately and investigate your claim.Downloaded from vbn.aau.dk on: December 25, 2020ISSN 1901-726X DCE Technical Report No. 215             Validation of Mean Drift Forces Computed with the BEM Code NEMOH   Jonas Bjerg Thomsen  DCE Technical Report No. 215      Validation of Mean Drift Forces Computed  with the BEM Code NEMOH    by   Jonas Bjerg Thomsen June 2017          © Aalborg University         Aalborg University Department of Civil Engineering Wave Energy Research Group      Scientific Publications at the Department of Civil Engineering  Technical Reports are published for timely dissemination of research results and scientific work carried out at the Department of Civil Engineering (DCE) at Aalborg University. This medium allows publication of more detailed explanations and results than typically allowed in scientific journals.  Technical Memoranda are produced to enable the preliminary dissemination of scientific work by the personnel of the DCE where such release is deemed to be appropriate. Documents of this kind may be incomplete or temporary versions of papers—or part of continuing work. This should be kept in mind when references are given to publications of this kind.  Contract Reports are produced to report scientific work carried out under contract. Publications of this kind contain confidential matter and are reserved for the sponsors and the DCE. Therefore, Contract Reports are generally not available for public circulation.  Lecture Notes contain material produced by the lecturers at the DCE for educational purposes. This may be scientific notes, lecture books, example problems or manuals for laboratory work, or computer programs developed at the DCE.  Theses are monograms or collections of papers published to report the scientific work carried out at the DCE to obtain a degree as either PhD or Doctor of Technology. The thesis is publicly available after the defence of the degree.  Latest News is published to enable rapid communication of information about scientific work carried out at the DCE. This includes the status of research projects, developments in the laboratories, information about collaborative work and recent research results.  Published 2017 by Aalborg University Department of Civil Engineering Thomas Manns Vej 23 DK-9220 Aalborg Ø, Denmark  Printed in Aalborg at Aalborg University  ISSN 1901-726X DCE Technical Report No. 215 PrefaceThis report covers a simple investigation of mean drift forces found by use of the boundaryelement method code NEMOH. The results from NEMOH are compared to analyticalresults from literature and to numerical values found from the commercial software packageWADAM by DNV-GL.The work was conducted under the project Mooring Solutions for Large Wave EnergyConverters, during "Work Package 4: Full Dynamic Analysis". The validation comparesresults from a simple sphere and from a vertical cylinder.Aalborg University, June 9, 2017vContentsPreface vContents 11 Introduction 32 Calculation of Mean Drift Forces 53 Investigation of Spherical Shape 74 Investigation of Vertical Cylinder 95 Conclusion 11Bibliography 1311 | IntroductionWhen considering wave loads on oshore structures, the total load is often divided intothree separate contributions: a load oscillating at the frequency of the incoming wave anddenoted the wave frequency (WF) load, a second order low frequency (LF) load and amean load, also of second order, cf. Fig 1.1.      Low frequency component High frequency component Time Steady component Force Fig. 1.1. Denition of rst order wave frequency (WF) load, second order low frequency (LF)load and the mean load contribution. Adapted from API (2005)In many applications, only the rst order WF load is considered, which is a directoutput of many commercial software packages such as WAMIT (Lee and Newman, 2013)and WADAM (DNV, 2013), or of open source codes such as NEMOH (Babarit andDelhommeau, 2015). All of these takes advantage of the boundary element method (BEM),with its linear wave potential theory. In design of mooring systems, the second orderloads are of considerable inuence, and need to be included in the calculations. Dierentmethods are available for estimation of the second order response, including use of fullquadratic transfer functions (QTFs) which can be calculated directly by e.g. WAMIT,but at present, not by NEMOH and WADAM. In many cases, however, the Newmanapproximation is used, implying that only the mean drift forces are required to calculatethe second order response. These mean drift forces can be calculated from rst orderquantities, using dierent methods such as the far-eld or near-eld formulations, and,therefore, from the direct output of rst order BEM codes.The present report tends to validate the calculation of drift force coecients usingoutput from the boundary element method code NEMOH (Babarit and Delhommeau,2015) and the MATLAB routine available at ECN (2016). The report is structured withan initiating chapter which shortly describes the method, followed by a chapter whichcompares numerical (NEMOH ) results of a oating sphere with analytical results availablein literature. The nal chapter compares results from NEMOH and the commercialsoftware WADAM for a vertical cylinder.32 | Calculation of Mean Drift ForcesIn calculation of mean drift forces, it is possible to use only the rst order quantities, whichputs less demands on the analysis tool. Codes such as NEMOH and WADAM, are fullycapable of calculating the rst order quantities but are currently not capable of includingsecond order eects. This chapter briey deals with the method used for calculation ofthe drift force coecients. For more detailed description of the theory, cf. e.g. Mauro(1960), Newman (1967), Pinkster (1980), Kim (1999) and Lee and Newman (2005).Dierent methods are available for estimation of the horizontal drift forces. Twomethods that are often encountered are: The momentum conservation formulation (Far-eld formulation) The pressure integration formulation (Near-eld formulation)The present report deals only with the far-eld formulation. A disadvantage of thefar-eld formulation is that it is restricted to calculate only the horizontal components ofthe drift force, but in many applications, this is sucient.Similar to the rst order wave excitation force, the second order drift force is composedby a radiation and diraction contribution. The drift force can be determined from eq.(2.1).(Fdrift,xFdrift,y)= − 2πρaω(cos βsin β)Im(H̃ (β, ω))− 8πρk (k0h)2h((kh)2 − (k0h)2 + k0h) ∫ π2−pi2Re(H̃(θ, ω)) Im(H̃(θ, ω))(cos θsin θ)dθ (2.1)Where,Fdrift,x Drift force in the x-axisFdrift,y Drift force in the y-axisρ Fluid densitya Incoming wave amplitudeω Wave angular frequencyβ Incoming wave angleH̃ (β, ω) The complex Kochin functionk Wave length at given water depthk0 Deep water wave lengthh Water depthThe Kochin functions are combined by a contribution from radiation and diractionand the total Kochin function can be found from equation (2.2) as the complex sum(Folley, 2016; Babarit and Delhommeau, 2015). The output of e.g. NEMOH is theseparate diraction and radiation Kochin functions.56 2. Calculation of Mean Drift ForcesH̃ (β, ω) =aH̃D (β, ω) eiπ2 +6∑j=1aX̃j (ω) H̃R (β, ω) e−iπ2 iω (2.2)Where,H̃D (β, ω) The Kochin function for the diraction potentialH̃R (β, ω) The Kochin function for the radiation potentialX̃j (ω) The motion Response Amplitude Operators (RAO)For use in many types of calculations, the drift force is normalized according the theincoming wave amplitude, a.Drift Force Coecient from WADAMThe theory behind the WADAM code will not be treated in this report and must be foundin e.g. DNV (2013), but it is worth to notice that the code is capable of using either thefar-eld or near-eld formulation. When using the far-eld formulation, however, the codeonly consider the three horizontal degrees of freedom (DoFs), hence only surge, sway andyaw. The eects of heave, roll and pitch are, therefore, not considered.3 | Investigation of Spherical ShapeThe rst geometric shape which is considered is a oating sphere as illustrated in Fig. 3.1.The body is located in deep water conditions, and when presenting the results later inthis chapter, the drift forces are normalized according to wave amplitude and buoy radius,hence, listing any geometric parameters is without any importance.Fig. 3.1. Illustration of investigated sphere.Since the BEM does not consider the geometry above the SWL, the investigated shapeis actually a hemisphere, with a panel mesh as illustrated in Fig. 3.2. Several authorssuch as Pinkster (1980) and Mauro (1960), have described the drift forces on a oatinghemisphere, and this chapter will compare the numerical results from NEMOH, with theanalytical solution from Pinkster (1980).78 3. Investigation of Spherical ShapeFig. 3.2. Panel mesh used in NEMOH.When plotting the results from NEMOH against the analytical solution in Fig. 3.3a great agreement is observed. The drift force is seen to increase with ka (where k =wave number and a = wave amplitude) until reaching a maximum value, before it startsto decrease until it converges towards a certain value. For a spherical shape like this, therotational DoFs do not aect the drift forces, while the peak in Fig. 3.3 arises from thevertical heave motions. If e.g. the heave DoF was restrained in the NEMOH analysis, thepeak would not be present.In cases with very short and steep waves, there would be almost complete reection.According to Faltinsen (1993), the drift force on a body with circular waterplane area,can be estimated by equation (3.1), assuming short and fully reected waves.Fd,x =23ρga2r cosβ (3.1)This value is plotted in Fig. 3.3 (≈ 0.67), which corresponds to the value at which thecalculated drift force in NEMOH converges towards.Fig. 3.3. Comparison between numerical and analytical drift force on a sphere, and withindication of the drift force on a sphere with full wave reection.Considering the agreement between analytical results, the drift force coecientcalculated by NEMOH is considered valid for a simple shape like a sphere.4 | Investigation of VerticalCylinderThe second case that is considered in this report, consist of a vertical cylinder locatedin deep water depth, cf. Fig. 4.1. In this chapter, the results found from NEMOH arecompared to results from the WADAM package.Fig. 4.1. Illustration of the investigated cylinder.The geometrical properties of the cylinder are as listed below.Dimension Notation ValueDiameter D 10 mHeight H 20 mDraught d 10 mWater depth h ∞The wetted surface of the model was analysed in both WADAM and NEMOH, withthe mesh illustrated in Fig. 4.2.910 4. Investigation of Vertical CylinderFig. 4.2. Panel mesh used in NEMOH and WADAM.In calculation of the drift forces in the WADAM model, the far-eld formulation wasused as this is the method that was used in NEMOH. This means that only the horizontalDoFs (surge, sway and yaw) were considered in WADAM. Comparing the results from thetwo models, the eect of this is clearly seen.In general, Fig. 4.3 present a good agreement between the two models. An analysiswas performed in NEMOH, considering the same DoFs as in WADAM and insignicantdierence is seen between the two methods. The eects of using six DoFs in NEMOH areobtained from the gure, and present some inuence from the inclusion of pitch and heavemotions.Fig. 4.3. Comparison between WADAM results and NEMOH drift force, where the latter hasbeen analysed with all DoFs and with restrain on the pitch DoF.For very short waves, full reection can be assumed and equation (3.1) can be used tond the analytical drift force. As presented in Fig. 4.3, it is seen that both WADAM andNEMOH converge towards this value for the highest wave frequencies.In general, the comparison proves good agreement between the commercial WADAMsoftware package and NEMOH, and helps justify the use of the model and the codeavailable at ECN (2016).5 | ConclusionThis report has investigated the drift forces calculated by the open source BEM codeNEMOH and the corresponding code available at ECN (2016). The investigation covereda comparison with analytical results and results from the commercial software packageWADAM by DNV (2013).The report compared the results for a simple spherical shape and compared it toanalytical results. Good agreement was found between the two, and similar was seen forthe results from a cylinder, which was compared toWADAM. This gives a simple validationof the drift force coecients from NEMOH and help justify the use of the code for morecomplex structures. The study was limited to simple shapes as these are relatively easyto analyse analytically, while more complex structures need more advanced calculations.Before the use of the coecients in a detailed analysis of a complex oating structure itis, therefore, recommended to validate the results against e.g. experimental data or moresophisticated models. This is out of scope of this report, but must be considered in laterwork.11BibliographyAPI (2005). Design and analysis of station keeping systems for oating structures, API-RP-2SK. American Petroleum Institute.Babarit, A. and Delhommeau, G. (2015). Theoretical and numerical aspects of theopen source bem solver nemoh. In 11th European Wave and Tidal Energy Conference(EWTEC2015).DNV (2013). Sesam user manual. wadam: Wave analysis by diraction and morisontheory. Høvik, Norway.ECN (2016). Nemoh. http://lheea.ec-nantes.fr/doku.php/emo/nemoh/start.Faltinsen, O. (1993). Sea loads on ships and oshore structures, volume 1. Cambridgeuniversity press.Folley, M. (2016). Numerical Modelling of Wave Energy Converters: State-of-the-ArtTechniques for Single Devices and Arrays. Academic Press.Kim, Y. (1999). Computation of higher-order hydrodynamic forces on ships and oshorestructures in waves. PhD thesis, Massachusetts Institute of Technology.Lee, C. and Newman, J. (2013). Wamit user manual, version 7.0. WAMIT, Inc., ChestnutHill, MA.Lee, C.-H. and Newman, J. (2005). Computation of wave eects using the panel method.WIT Transactions on State-of-the-art in Science and Engineering, 18.Mauro, H. (1960). The drift of a body oating on waves. Journal of Ship Research, 4:15.Newman, J. t. (1967). The drift force and moment on ships in waves. J. Ship Res.,11(1):5160.Pinkster, J. A. (1980). Low frequency second order wave exciting forces on oatingstructures.13 ISSN 1901-726X DCE Technical Report No. 215 

Validation of Mean Drift Forces Computed with the BEM Code NEMOH

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Validation of Mean Drift Forces Computed with the BEM Code NEMOH

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