Establishment of Numerical Wave Flume Based on the Second-Order Wave-Maker Theory
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摘要
With growing computational power, the first-order wave-maker theory has become well established and is widely used for numerical wave flumes. However, existing numerical models based on the first-order wave-maker theory lose accuracy as nonlinear effects become prominent. Because spurious harmonic waves and primary waves have different propagation velocities, waves simulated by using the first-order wave-maker theory have an unstable wave profile. In this paper, a numerical wave flume with a piston-type wave-maker based on the second-order wave-maker theory has been established. Dynamic mesh technique was developed. The boundary treatment for irregular wave simulation was specially dealt with. Comparisons of the free-surface elevations using the first-order and second-order wave-maker theory prove that second-order wave-maker theory can generate stable wave profiles in both the spatial and time domains. Harmonic analysis and spectral analysis were used to prove the superiority of the second-order wave-maker theory from other two aspects. To simulate irregular waves, the numerical flume was improved to solve the problem of the water depth variation due to low-frequency motion of the wave board. In summary, the new numerical flume using the second-order wave-maker theory can guarantee the accuracy of waves by adding an extra motion of the wave board. The boundary treatment method can provide a reference for the improvement of nonlinear numerical flume.
With growing computational power, the first-order wave-maker theory has become well established and is widely used for numerical wave flumes. However, existing numerical models based on the first-order wave-maker theory lose accuracy as nonlinear effects become prominent. Because spurious harmonic waves and primary waves have different propagation velocities, waves simulated by using the first-order wave-maker theory have an unstable wave profile. In this paper, a numerical wave flume with a piston-type wave-maker based on the second-order wave-maker theory has been established. Dynamic mesh technique was developed. The boundary treatment for irregular wave simulation was specially dealt with. Comparisons of the free-surface elevations using the first-order and second-order wave-maker theory prove that second-order wave-maker theory can generate stable wave profiles in both the spatial and time domains. Harmonic analysis and spectral analysis were used to prove the superiority of the second-order wave-maker theory from other two aspects. To simulate irregular waves, the numerical flume was improved to solve the problem of the water depth variation due to low-frequency motion of the wave board. In summary, the new numerical flume using the second-order wave-maker theory can guarantee the accuracy of waves by adding an extra motion of the wave board. The boundary treatment method can provide a reference for the improvement of nonlinear numerical flume.
With growing computational power, the first-order wave-maker theory has become well established and is widely used for numerical wave flumes. However, existing numerical models based on the first-order wave-maker theory lose accuracy as nonlinear effects become prominent. Because spurious harmonic waves and primary waves have different propagation velocities, waves simulated by using the first-order wave-maker theory have an unstable wave profile. In this paper, a numerical wave flume with a piston-type wave-maker based on the second-order wave-maker theory has been established. Dynamic mesh technique was developed. The boundary treatment for irregular wave simulation was specially dealt with. Comparisons of the free-surface elevations using the first-order and second-order wave-maker theory prove that second-order wave-maker theory can generate stable wave profiles in both the spatial and time domains. Harmonic analysis and spectral analysis were used to prove the superiority of the second-order wave-maker theory from other two aspects. To simulate irregular waves, the numerical flume was improved to solve the problem of the water depth variation due to low-frequency motion of the wave board. In summary, the new numerical flume using the second-order wave-maker theory can guarantee the accuracy of waves by adding an extra motion of the wave board. The boundary treatment method can provide a reference for the improvement of nonlinear numerical flume.
引文
Agamloh,E.B.,Wallace,A.K.and von Jouanne,A.,2008.Application of fluid-structure interaction simulation of an ocean wave energy extraction device,Renewable Energy,33(4),748-757.
Altomare,C.,Domínguez,J.M.,Crespo,A.J.C.,González-Cao,J.,Suzuki,T.,Gómez-Gesteira,M.and Troch,P.,2017.Long-crested wave generation and absorption for SPH-based DualSPHysics model,Coastal Engineering,127,37-54.
Anbarsooz,M.,Passandideh-Fard,M.and Moghiman,M.,2013.Fully nonlinear viscous wave generation in numerical wave tanks,Ocean Engineering,59,73-85.
Berberovi?,E.,van Hinsberg,N.P.,Jakirli?,S.,Roisman,I.V.and Tropea,C.,2009.Drop impact onto a liquid layer of finite thickness:dynamics of the cavity evolution,Physical Review E,79(3),036306.
Farahani,R.J.,Dalrymple,R.A.,Hérault,A.and Bilotta,G.,2014.Three-dimensional SPH modeling of a Bar/Rip channel system,Journal of Waterway,Port,Coastal,and Ocean Engineering,140(1),82-99.
Finnegan,W.and Goggins,J.,2012.Numerical simulation of linear water waves and wave-structure interaction,Ocean Engineering,43,23-31.
Fontanet,P.,1961.Théorie de la génération de la houle cylindrique par un batteur plan(2e ordre d'approximation),La Houille Blanche,(1),3-31.(in French)
Higuera,P.,Losada,I.J.and Lara,J.L.,2015.Three-dimensional numerical wave generation with moving boundaries,Coastal Engineering,101,35-47.
Lara,J.L.,Ruju,A.and Losada,I.J.,2011.Reynolds averaged NavierStokes modelling of long waves induced by a transient wave group on a beach,Proceedings of the Royal Society A:Mathematical,Physical and Engineering Sciences,467(2129),1215-1242.
Liang,X.F.,Yang,J.M.,Li,J.,Xiao,L.F.and Li,X.,2010.Numerical simulation of irregular wave-simulating irregular wave train,Journal of Hydrodynamics,Series B,22(4),537-545.
Madsen,O.S.,1971.On the generation of long waves,Journal of Geophysical Research,76(36),8672-8683.
Prasad,D.,Zullah,M.A.,Ahmed,M.R.and Lee,Y.H.,2010.Effect of front guide nozzle shape on the flow characteristics in an augmentation channel of a direct drive turbine for wave power generation,Science in China Series E:Technological Sciences,53(1),46-51.
Prasad,D.D.,Ahmed,M.R.and Lee,Y.H.,2014.Flow and performance characteristics of a direct drive turbine for wave power generation,Ocean Engineering,81,39-49.
Prasad,D.D.,Ahmed,M.R.,Lee,Y.H.and Sharma,R.N.,2017.Validation of a piston type wave-maker using numerical wave tank,Ocean Engineering,131,57-67.
Sch?ffer,H.A.,1996.Second-order wavemaker theory for irregular waves,Ocean Engineering,23(1),47-88.
Sch?ffer,H.A.and Steenberg,C.M.,2003.Second-order wavemaker theory for multidirectional waves,Ocean Engineering,30(10),1203-1231.
Spinneken,J.and Swan,C.,2009a.Second-order wave maker theory using force-feedback control.Part I:A new theory for regular wave generation,Ocean Engineering,36(8),539-548.
Spinneken,J.and Swan,C.,2009b.Second-order wave maker theory using force-feedback control.Part II:An experimental verification of regular wave generation,Ocean Engineering,36(8),549-555.
Sriram,V.,Sannasiraj,S.A.and Sundar,V.,2006.Simulation of 2-Dnonlinear waves using finite element method with cubic spline approximation,Journal of Fluids and Structures,22(5),663-681.
Wen,H.J.,Ren,B.,Dong,P.and Wang,Y.X.,2016.A SPH numerical wave basin for modeling wave-structure interactions,Applied Ocean Research,59,366-377.
Wood,D.J.,Pedersen,G.K.and Jensen,A.,2003.Modelling of run up of steep non-breaking waves,Ocean Engineering,30(5),625-644.
Zullah,M.A.,Prasad,D.,Ahmed,M.R.and Lee,Y.H.,2010.Performance analysis of a wave energy converter using numerical simulation technique,Science in China Series E:Technological Sciences,53(1),13-18.
Altomare,C.,Domínguez,J.M.,Crespo,A.J.C.,González-Cao,J.,Suzuki,T.,Gómez-Gesteira,M.and Troch,P.,2017.Long-crested wave generation and absorption for SPH-based DualSPHysics model,Coastal Engineering,127,37-54.
Anbarsooz,M.,Passandideh-Fard,M.and Moghiman,M.,2013.Fully nonlinear viscous wave generation in numerical wave tanks,Ocean Engineering,59,73-85.
Berberovi?,E.,van Hinsberg,N.P.,Jakirli?,S.,Roisman,I.V.and Tropea,C.,2009.Drop impact onto a liquid layer of finite thickness:dynamics of the cavity evolution,Physical Review E,79(3),036306.
Farahani,R.J.,Dalrymple,R.A.,Hérault,A.and Bilotta,G.,2014.Three-dimensional SPH modeling of a Bar/Rip channel system,Journal of Waterway,Port,Coastal,and Ocean Engineering,140(1),82-99.
Finnegan,W.and Goggins,J.,2012.Numerical simulation of linear water waves and wave-structure interaction,Ocean Engineering,43,23-31.
Fontanet,P.,1961.Théorie de la génération de la houle cylindrique par un batteur plan(2e ordre d'approximation),La Houille Blanche,(1),3-31.(in French)
Higuera,P.,Losada,I.J.and Lara,J.L.,2015.Three-dimensional numerical wave generation with moving boundaries,Coastal Engineering,101,35-47.
Lara,J.L.,Ruju,A.and Losada,I.J.,2011.Reynolds averaged NavierStokes modelling of long waves induced by a transient wave group on a beach,Proceedings of the Royal Society A:Mathematical,Physical and Engineering Sciences,467(2129),1215-1242.
Liang,X.F.,Yang,J.M.,Li,J.,Xiao,L.F.and Li,X.,2010.Numerical simulation of irregular wave-simulating irregular wave train,Journal of Hydrodynamics,Series B,22(4),537-545.
Madsen,O.S.,1971.On the generation of long waves,Journal of Geophysical Research,76(36),8672-8683.
Prasad,D.,Zullah,M.A.,Ahmed,M.R.and Lee,Y.H.,2010.Effect of front guide nozzle shape on the flow characteristics in an augmentation channel of a direct drive turbine for wave power generation,Science in China Series E:Technological Sciences,53(1),46-51.
Prasad,D.D.,Ahmed,M.R.and Lee,Y.H.,2014.Flow and performance characteristics of a direct drive turbine for wave power generation,Ocean Engineering,81,39-49.
Prasad,D.D.,Ahmed,M.R.,Lee,Y.H.and Sharma,R.N.,2017.Validation of a piston type wave-maker using numerical wave tank,Ocean Engineering,131,57-67.
Sch?ffer,H.A.,1996.Second-order wavemaker theory for irregular waves,Ocean Engineering,23(1),47-88.
Sch?ffer,H.A.and Steenberg,C.M.,2003.Second-order wavemaker theory for multidirectional waves,Ocean Engineering,30(10),1203-1231.
Spinneken,J.and Swan,C.,2009a.Second-order wave maker theory using force-feedback control.Part I:A new theory for regular wave generation,Ocean Engineering,36(8),539-548.
Spinneken,J.and Swan,C.,2009b.Second-order wave maker theory using force-feedback control.Part II:An experimental verification of regular wave generation,Ocean Engineering,36(8),549-555.
Sriram,V.,Sannasiraj,S.A.and Sundar,V.,2006.Simulation of 2-Dnonlinear waves using finite element method with cubic spline approximation,Journal of Fluids and Structures,22(5),663-681.
Wen,H.J.,Ren,B.,Dong,P.and Wang,Y.X.,2016.A SPH numerical wave basin for modeling wave-structure interactions,Applied Ocean Research,59,366-377.
Wood,D.J.,Pedersen,G.K.and Jensen,A.,2003.Modelling of run up of steep non-breaking waves,Ocean Engineering,30(5),625-644.
Zullah,M.A.,Prasad,D.,Ahmed,M.R.and Lee,Y.H.,2010.Performance analysis of a wave energy converter using numerical simulation technique,Science in China Series E:Technological Sciences,53(1),13-18.