Estimation of numerical uncertainty in computational fluid dynamics simulations of a passively controlled wave energy converter

Weizhi Wang, Minghao Wu, Johannes Palm, Claes Gunnar Eskilsson

Research output: Contribution to journalJournal articleResearchpeer-review

8 Citations (Scopus)

Abstract

The wave loads and the resulting motions of floating wave energy converters are traditionally computed using linear radiation–diffraction methods. Yet for certain cases such as survival conditions, phase control and wave energy converters operating in the resonance region, more complete mathematical models such as computational fluid dynamics are preferred and over the last 5 years, computational fluid dynamics has become more frequently used in the wave energy field. However, rigorous estimation of numerical errors, convergence rates and uncertainties associated with computational fluid dynamics simulations have largely been overlooked in the wave energy sector. In this article, we apply formal verification and validation techniques to computational fluid dynamics simulations of a passively controlled point absorber.
The phase control causes the motion response to be highly nonlinear even for almost linear incident waves. First, we show that the computational fluid dynamics simulations have acceptable agreement to experimental data. We then present a verification and validation study focusing on the solution verification covering spatial and temporal discretization, iterative and domain modelling errors. It is shown that the dominating source of errors is, as expected, the spatial discretization, but temporal and iterative errors cannot be neglected. Using hexahedral cells with low aspect ratio and 30 cells per wave height, we obtain results with less than 5% uncertainty in motion response (except for surge) and restraining forces for the buoy without phase control. The amplified nonlinear response due to phase control caused a large increase in numerical uncertainty, illustrating the difficulty to obtain reliable solutions for highly nonlinear responses, and that much denser meshes are required for such cases.
Original languageEnglish
JournalInstitution of Mechanical Engineers. Proceedings. Part M: Journal of Engineering for the Maritime Environment
Volume232
Issue number1
Pages (from-to)71–84
ISSN1475-0902
DOIs
Publication statusPublished - 2018

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Computational fluid dynamics
Phase control
Computer simulation
Uncertainty
Aspect ratio
Mathematical models

Keywords

  • Wave energy converter
  • Passive control
  • Computational fluid dynamics modelling
  • Numerical uncertainty
  • Verification and validation

Cite this

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title = "Estimation of numerical uncertainty in computational fluid dynamics simulations of a passively controlled wave energy converter",
abstract = "The wave loads and the resulting motions of floating wave energy converters are traditionally computed using linear radiation–diffraction methods. Yet for certain cases such as survival conditions, phase control and wave energy converters operating in the resonance region, more complete mathematical models such as computational fluid dynamics are preferred and over the last 5 years, computational fluid dynamics has become more frequently used in the wave energy field. However, rigorous estimation of numerical errors, convergence rates and uncertainties associated with computational fluid dynamics simulations have largely been overlooked in the wave energy sector. In this article, we apply formal verification and validation techniques to computational fluid dynamics simulations of a passively controlled point absorber.The phase control causes the motion response to be highly nonlinear even for almost linear incident waves. First, we show that the computational fluid dynamics simulations have acceptable agreement to experimental data. We then present a verification and validation study focusing on the solution verification covering spatial and temporal discretization, iterative and domain modelling errors. It is shown that the dominating source of errors is, as expected, the spatial discretization, but temporal and iterative errors cannot be neglected. Using hexahedral cells with low aspect ratio and 30 cells per wave height, we obtain results with less than 5{\%} uncertainty in motion response (except for surge) and restraining forces for the buoy without phase control. The amplified nonlinear response due to phase control caused a large increase in numerical uncertainty, illustrating the difficulty to obtain reliable solutions for highly nonlinear responses, and that much denser meshes are required for such cases.",
keywords = "Wave energy converter, Passive control, Computational fluid dynamics modelling, Numerical uncertainty, Verification and validation, Wave energy converter, Passive control, Computational fluid dynamics modelling, Numerical uncertainty, Verification and validation",
author = "Weizhi Wang and Minghao Wu and Johannes Palm and Eskilsson, {Claes Gunnar}",
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Estimation of numerical uncertainty in computational fluid dynamics simulations of a passively controlled wave energy converter. / Wang, Weizhi; Wu, Minghao; Palm, Johannes; Eskilsson, Claes Gunnar.

In: Institution of Mechanical Engineers. Proceedings. Part M: Journal of Engineering for the Maritime Environment, Vol. 232, No. 1, 2018, p. 71–84.

Research output: Contribution to journalJournal articleResearchpeer-review

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T1 - Estimation of numerical uncertainty in computational fluid dynamics simulations of a passively controlled wave energy converter

AU - Wang, Weizhi

AU - Wu, Minghao

AU - Palm, Johannes

AU - Eskilsson, Claes Gunnar

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N2 - The wave loads and the resulting motions of floating wave energy converters are traditionally computed using linear radiation–diffraction methods. Yet for certain cases such as survival conditions, phase control and wave energy converters operating in the resonance region, more complete mathematical models such as computational fluid dynamics are preferred and over the last 5 years, computational fluid dynamics has become more frequently used in the wave energy field. However, rigorous estimation of numerical errors, convergence rates and uncertainties associated with computational fluid dynamics simulations have largely been overlooked in the wave energy sector. In this article, we apply formal verification and validation techniques to computational fluid dynamics simulations of a passively controlled point absorber.The phase control causes the motion response to be highly nonlinear even for almost linear incident waves. First, we show that the computational fluid dynamics simulations have acceptable agreement to experimental data. We then present a verification and validation study focusing on the solution verification covering spatial and temporal discretization, iterative and domain modelling errors. It is shown that the dominating source of errors is, as expected, the spatial discretization, but temporal and iterative errors cannot be neglected. Using hexahedral cells with low aspect ratio and 30 cells per wave height, we obtain results with less than 5% uncertainty in motion response (except for surge) and restraining forces for the buoy without phase control. The amplified nonlinear response due to phase control caused a large increase in numerical uncertainty, illustrating the difficulty to obtain reliable solutions for highly nonlinear responses, and that much denser meshes are required for such cases.

AB - The wave loads and the resulting motions of floating wave energy converters are traditionally computed using linear radiation–diffraction methods. Yet for certain cases such as survival conditions, phase control and wave energy converters operating in the resonance region, more complete mathematical models such as computational fluid dynamics are preferred and over the last 5 years, computational fluid dynamics has become more frequently used in the wave energy field. However, rigorous estimation of numerical errors, convergence rates and uncertainties associated with computational fluid dynamics simulations have largely been overlooked in the wave energy sector. In this article, we apply formal verification and validation techniques to computational fluid dynamics simulations of a passively controlled point absorber.The phase control causes the motion response to be highly nonlinear even for almost linear incident waves. First, we show that the computational fluid dynamics simulations have acceptable agreement to experimental data. We then present a verification and validation study focusing on the solution verification covering spatial and temporal discretization, iterative and domain modelling errors. It is shown that the dominating source of errors is, as expected, the spatial discretization, but temporal and iterative errors cannot be neglected. Using hexahedral cells with low aspect ratio and 30 cells per wave height, we obtain results with less than 5% uncertainty in motion response (except for surge) and restraining forces for the buoy without phase control. The amplified nonlinear response due to phase control caused a large increase in numerical uncertainty, illustrating the difficulty to obtain reliable solutions for highly nonlinear responses, and that much denser meshes are required for such cases.

KW - Wave energy converter

KW - Passive control

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KW - Numerical uncertainty

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KW - Passive control

KW - Computational fluid dynamics modelling

KW - Numerical uncertainty

KW - Verification and validation

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M3 - Journal article

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SP - 71

EP - 84

JO - Proceedings of the Institution of Mechanical Engineers, Part M: Journal of Engineering for the Maritime Environment

JF - Proceedings of the Institution of Mechanical Engineers, Part M: Journal of Engineering for the Maritime Environment

SN - 1475-0902

IS - 1

ER -