Wave Scattering by Twin Surface-Piercing Plates Over A Stepped Bottom:Trapped Wave Energy and Energy Loss
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摘要
To evaluate the trapped wave energy and energy loss, the problem of wave scattering by twin fixed vertical surfacepiercing plates over a stepped bottom is numerically simulated using the open source package OpenFOAM and the associated toolbox waves2 Foam. The volume of fluid(VOF) method was employed to capture the free surface in the time domain. The validation of the present numerical model was performed by comparing with both the analytical and experimental results. The effects of the spacing between two plates and the configuration of stepped bottom on the hydrodynamic characteristics, such as reflection and transmission coefficients, viscous dissipation ratio, and relative wave height between the plates(termed as trapped wave energy), were examined. Moreover, the nonlinear effects of the incident wave height on the hydrodynamic characteristics were addressed as well. The results show that the step configuration can be tuned for efficient-performance of wave damping, and the optimum configurations of the step length B, the step height h1 and the spacing b, separately equaling λ/4, 3 h/4, and 0.05 h(λ and h are the wavelength and the water depth, respectively), are recommended for the trapping of wave energy.
To evaluate the trapped wave energy and energy loss, the problem of wave scattering by twin fixed vertical surfacepiercing plates over a stepped bottom is numerically simulated using the open source package OpenFOAM and the associated toolbox waves2 Foam. The volume of fluid(VOF) method was employed to capture the free surface in the time domain. The validation of the present numerical model was performed by comparing with both the analytical and experimental results. The effects of the spacing between two plates and the configuration of stepped bottom on the hydrodynamic characteristics, such as reflection and transmission coefficients, viscous dissipation ratio, and relative wave height between the plates(termed as trapped wave energy), were examined. Moreover, the nonlinear effects of the incident wave height on the hydrodynamic characteristics were addressed as well. The results show that the step configuration can be tuned for efficient-performance of wave damping, and the optimum configurations of the step length B, the step height h1 and the spacing b, separately equaling λ/4, 3 h/4, and 0.05 h(λ and h are the wavelength and the water depth, respectively), are recommended for the trapping of wave energy.
To evaluate the trapped wave energy and energy loss, the problem of wave scattering by twin fixed vertical surfacepiercing plates over a stepped bottom is numerically simulated using the open source package OpenFOAM and the associated toolbox waves2 Foam. The volume of fluid(VOF) method was employed to capture the free surface in the time domain. The validation of the present numerical model was performed by comparing with both the analytical and experimental results. The effects of the spacing between two plates and the configuration of stepped bottom on the hydrodynamic characteristics, such as reflection and transmission coefficients, viscous dissipation ratio, and relative wave height between the plates(termed as trapped wave energy), were examined. Moreover, the nonlinear effects of the incident wave height on the hydrodynamic characteristics were addressed as well. The results show that the step configuration can be tuned for efficient-performance of wave damping, and the optimum configurations of the step length B, the step height h1 and the spacing b, separately equaling λ/4, 3 h/4, and 0.05 h(λ and h are the wavelength and the water depth, respectively), are recommended for the trapping of wave energy.
引文
Ashlin,S.J.,Sundar,V.and Sannasiraj,S.A.,2016.Effects of bottom profile of an oscillating water column device on its hydrodynamic characteristics,Renewable Energy,96,341-353.
Deng,Z.Z.,Huang,Z.H.and Law,A.W.K.,2013.Wave power extraction by an axisymmetric oscillating-water-column converter supported by a coaxial tube-sector-shaped structure,Applied Ocean Research,42,114-123.
Deshpande,S.S.,Anumolu,L.and Trujillo,M.F.,2012.Evaluating the performance of the two-phase flow solver interFoam,Computational Science and Discovery,5(1),014016.
Elhanafi,A.,Fleming,A.,Macfarlane,G.and Leong,Z.,2016.Numerical energy balance analysis for an onshore oscillating water column-wave energy converter,Energy,116,539-557.
Goda,Y.and Suzuki,Y.,1977.Estimation of incident and reflected waves in random wave experiments,Proceedings of the 15th Coastal Engineering Conference,ASCE,New York,pp.828-845.
Howe,D.and Nader,J.R.,2017.OWC WEC integrated within a breakwater versus isolated:Experimental and numerical theoretical study,International Journal of Marine Energy,20,165-182.
Isaacson,M.,Baldwin,J.,Premasiri,S.and Yang,G.,1999.Wave interactions with double slotted barriers,Applied Ocean Research,21(2),81-91.
Jacobsen,N.G.,Fuhrman,D.R.and Freds?e,J.,2012.A wave generation toolbox for the opensource CFD library:OpenFOAM?,International Journal for Numerical Methods in Fluids,70(9),1073-1088.
Jasak,H.,1996.Error Analysis and Estimation for the Finite Volume Method With Applications to Fluid Flows,Ph.D.Thesis,Imperial College London,London.
Ju,L.H.,Zuo,Q.H.,Teng,L.and Wang,X.G.,2017.Study on wave dissipation of the structure combined by baffle and submerged breakwater,China Ocean Engineering,31(6),674-682.
Kriebel,D.L.and Bollmann,C.A.,1996.Wave transmission past vertical wave barriers,Proceedings of the 25th International Conference on Coastal Engineering,ASCE,Orlando,Florida,pp.2470-2483.
López,I.,Andreu,J.,Ceballos,S.,de Alegría,I.M.and Kortabarria,I.,2013.Review of wave energy technologies and the necessary power-equipment,Renewable and Sustainable Energy Reviews,27,413-434.
Losada,M.A.,Losada,I.J.and Roldán,A.J.,1993.Propagation of oblique incident modulated waves past rigid,vertical thin barriers,Applied Ocean Research,15(5),305-310.
Luo,Y.Y.,Nader,J.R.,Cooper,P.and Zhu,S.P.,2014.Nonlinear 2Danalysis of the efficiency of fixed oscillating water column wave energy converters,Renewable Energy,64,255-265.
Mei,C.C.and Black,J.L.,1969.Scattering of surface waves by rectangular obstacles in waters of finite depth,Journal of Fluid Mechanics,38(3),499-511.
Ning,D.Z.,Shi,J.,Teng,B.and Zhao,H.T.,2014.Numerical simulation of a land-based oscillating water column wave energy conversion device,Journal of Harbin Engineering University,35(7),789-794.(in Chinese)
Ning,D.Z.,Shi,J.,Zou,Q.P.and Teng,B.,2015.Investigation of hydrodynamic performance of an OWC(oscillating water column)wave energy device using a fully nonlinear HOBEM(higher-order boundary element method),Energy,83,177-188.
Ning,D.Z.,Wang,R.Q.,Zou,Q.P.and Teng,B.,2016.An experimental investigation of hydrodynamics of a fixed OWC Wave Energy Converter,Applied Energy,168,636-648.
Ohkusu,M.,1974.Hydrodynamic forces on multiple cylinders in waves,Proceedings of International Symposium on the Dynamics of Marine Vehicles and Structures in Waves,Institute of Mechanical Engineers,London.
Porter,R.and Evans,D.V.,1995.Complementary approximations to wave scattering by vertical barriers,Journal of Fluid Mechanics,294,155-180.
Rezanejad,K.,Bhattacharjee,J.and Soares,C.G.,2013.Stepped sea bottom effects on the efficiency of nearshore oscillating water column device,Ocean Engineering,70,25-38.
Rusche,H.,2003.Computational Fluid Dynamics of Dispersed Twophase Flows at High Phase Fractions,Ph.D.Thesis,Imperial College London,London.
Shin,D.M.and Cho,Y.,2016.Diffraction of waves past two vertical thin plates on the free surface:A comparison of theory and experiment,Ocean Engineering,124,274-286.
Srokosz,M.A.and Evans,D.V.,1979.A theory for wave-power absorption by two independently oscillating bodies,Journal of Fluid Mechanics,90(2),337-362.
Stiassnie,M.,Boguslavsky,I.and Naheer,E.,1986.Scattering and dissipation of surface wave by a bi-plate structure,Applied Ocean Research,8(1),33-37.
Vicinanza,D.,Contestabile,P.,N?rgaard,J.Q.H.and Andersen,T.L.,2014.Innovative rubble mound breakwaters for overtopping wave energy conversion,Coastal Engineering,88,154-170.
Wang,R.Q.,Ning,D.Z.,Zhang,C.W.,Zou,Q.P.and Liu,Z.,2018.Nonlinear and viscous effects on the hydrodynamic performance of a fixed OWC wave energy converter,Coastal Engineering,131,42-50.
Weller,H.G.,2002.Derivation,Modelling and Solution of the Conditionally Averaged Two-phase Flow Equations,Nabla Ltd.
Wiegel,R.L.,1960.Transmission of waves past a rigid vertical thin barrier,Journal of the Waterways and Harbors Division,86(1),1-12.
Windt,C.,Davidson,J.,Akram,B.and Ringwood,J.V.,2018.Performance assessment of the overset grid method for numerical wave tank experiments in the OpenFOAM environment,Proceedings of the ASME 2018 37th International Conference on Ocean,Offshore and Arctic Engineering,Ocean,Offshore and Arctic Engineering Division,Madrid,Spain,pp.V010T09A006.
Zheng,Y.H.,Shen,Y.M.,You,Y.G.,Wu,B.J.and Liu,R.,2006.Scattering of linear water waves by a fixed and infinitely long rectangular structure parallel to a vertical wall in oblique seas,Journal of Waterway,Port,Coastal,and Ocean Engineering,132(2),106-113.
Deng,Z.Z.,Huang,Z.H.and Law,A.W.K.,2013.Wave power extraction by an axisymmetric oscillating-water-column converter supported by a coaxial tube-sector-shaped structure,Applied Ocean Research,42,114-123.
Deshpande,S.S.,Anumolu,L.and Trujillo,M.F.,2012.Evaluating the performance of the two-phase flow solver interFoam,Computational Science and Discovery,5(1),014016.
Elhanafi,A.,Fleming,A.,Macfarlane,G.and Leong,Z.,2016.Numerical energy balance analysis for an onshore oscillating water column-wave energy converter,Energy,116,539-557.
Goda,Y.and Suzuki,Y.,1977.Estimation of incident and reflected waves in random wave experiments,Proceedings of the 15th Coastal Engineering Conference,ASCE,New York,pp.828-845.
Howe,D.and Nader,J.R.,2017.OWC WEC integrated within a breakwater versus isolated:Experimental and numerical theoretical study,International Journal of Marine Energy,20,165-182.
Isaacson,M.,Baldwin,J.,Premasiri,S.and Yang,G.,1999.Wave interactions with double slotted barriers,Applied Ocean Research,21(2),81-91.
Jacobsen,N.G.,Fuhrman,D.R.and Freds?e,J.,2012.A wave generation toolbox for the opensource CFD library:OpenFOAM?,International Journal for Numerical Methods in Fluids,70(9),1073-1088.
Jasak,H.,1996.Error Analysis and Estimation for the Finite Volume Method With Applications to Fluid Flows,Ph.D.Thesis,Imperial College London,London.
Ju,L.H.,Zuo,Q.H.,Teng,L.and Wang,X.G.,2017.Study on wave dissipation of the structure combined by baffle and submerged breakwater,China Ocean Engineering,31(6),674-682.
Kriebel,D.L.and Bollmann,C.A.,1996.Wave transmission past vertical wave barriers,Proceedings of the 25th International Conference on Coastal Engineering,ASCE,Orlando,Florida,pp.2470-2483.
López,I.,Andreu,J.,Ceballos,S.,de Alegría,I.M.and Kortabarria,I.,2013.Review of wave energy technologies and the necessary power-equipment,Renewable and Sustainable Energy Reviews,27,413-434.
Losada,M.A.,Losada,I.J.and Roldán,A.J.,1993.Propagation of oblique incident modulated waves past rigid,vertical thin barriers,Applied Ocean Research,15(5),305-310.
Luo,Y.Y.,Nader,J.R.,Cooper,P.and Zhu,S.P.,2014.Nonlinear 2Danalysis of the efficiency of fixed oscillating water column wave energy converters,Renewable Energy,64,255-265.
Mei,C.C.and Black,J.L.,1969.Scattering of surface waves by rectangular obstacles in waters of finite depth,Journal of Fluid Mechanics,38(3),499-511.
Ning,D.Z.,Shi,J.,Teng,B.and Zhao,H.T.,2014.Numerical simulation of a land-based oscillating water column wave energy conversion device,Journal of Harbin Engineering University,35(7),789-794.(in Chinese)
Ning,D.Z.,Shi,J.,Zou,Q.P.and Teng,B.,2015.Investigation of hydrodynamic performance of an OWC(oscillating water column)wave energy device using a fully nonlinear HOBEM(higher-order boundary element method),Energy,83,177-188.
Ning,D.Z.,Wang,R.Q.,Zou,Q.P.and Teng,B.,2016.An experimental investigation of hydrodynamics of a fixed OWC Wave Energy Converter,Applied Energy,168,636-648.
Ohkusu,M.,1974.Hydrodynamic forces on multiple cylinders in waves,Proceedings of International Symposium on the Dynamics of Marine Vehicles and Structures in Waves,Institute of Mechanical Engineers,London.
Porter,R.and Evans,D.V.,1995.Complementary approximations to wave scattering by vertical barriers,Journal of Fluid Mechanics,294,155-180.
Rezanejad,K.,Bhattacharjee,J.and Soares,C.G.,2013.Stepped sea bottom effects on the efficiency of nearshore oscillating water column device,Ocean Engineering,70,25-38.
Rusche,H.,2003.Computational Fluid Dynamics of Dispersed Twophase Flows at High Phase Fractions,Ph.D.Thesis,Imperial College London,London.
Shin,D.M.and Cho,Y.,2016.Diffraction of waves past two vertical thin plates on the free surface:A comparison of theory and experiment,Ocean Engineering,124,274-286.
Srokosz,M.A.and Evans,D.V.,1979.A theory for wave-power absorption by two independently oscillating bodies,Journal of Fluid Mechanics,90(2),337-362.
Stiassnie,M.,Boguslavsky,I.and Naheer,E.,1986.Scattering and dissipation of surface wave by a bi-plate structure,Applied Ocean Research,8(1),33-37.
Vicinanza,D.,Contestabile,P.,N?rgaard,J.Q.H.and Andersen,T.L.,2014.Innovative rubble mound breakwaters for overtopping wave energy conversion,Coastal Engineering,88,154-170.
Wang,R.Q.,Ning,D.Z.,Zhang,C.W.,Zou,Q.P.and Liu,Z.,2018.Nonlinear and viscous effects on the hydrodynamic performance of a fixed OWC wave energy converter,Coastal Engineering,131,42-50.
Weller,H.G.,2002.Derivation,Modelling and Solution of the Conditionally Averaged Two-phase Flow Equations,Nabla Ltd.
Wiegel,R.L.,1960.Transmission of waves past a rigid vertical thin barrier,Journal of the Waterways and Harbors Division,86(1),1-12.
Windt,C.,Davidson,J.,Akram,B.and Ringwood,J.V.,2018.Performance assessment of the overset grid method for numerical wave tank experiments in the OpenFOAM environment,Proceedings of the ASME 2018 37th International Conference on Ocean,Offshore and Arctic Engineering,Ocean,Offshore and Arctic Engineering Division,Madrid,Spain,pp.V010T09A006.
Zheng,Y.H.,Shen,Y.M.,You,Y.G.,Wu,B.J.and Liu,R.,2006.Scattering of linear water waves by a fixed and infinitely long rectangular structure parallel to a vertical wall in oblique seas,Journal of Waterway,Port,Coastal,and Ocean Engineering,132(2),106-113.