The unsteady natural convective couple stress fluid flow over a semi-infinite vertical cylinder is analyzed for the homogeneous first-order chemical reaction effect. The couple stress fluid flow model introduces the l...The unsteady natural convective couple stress fluid flow over a semi-infinite vertical cylinder is analyzed for the homogeneous first-order chemical reaction effect. The couple stress fluid flow model introduces the length dependent effect based on the material constant and dynamic viscosity. Also, it introduces the biharmonic operator in the Navier-Stokes equations, which is absent in the case of Newtonian fluids. The solution to the time-dependent non-linear and coupled governing equations is carried out with an unconditionally stable Crank-Nicolson type of numerical schemes. Numerical results for the transient flow variables, the average wall shear stress, the Nusselt number, and the Sherwood number are shown graphically for both generative and destructive reactions. The time to reach the temporal maximum increases as the reaction constant K increases. The average values of the wall shear stress and the heat transfer rate decrease as K increases, while increase with the increase in the Sherwood number.展开更多
An analysis is performed to study transient free convective boundary layer flow of a couple stress fluid over a vertical cylinder, in the absence of body couples. The solution of the time-dependent non-linear and coup...An analysis is performed to study transient free convective boundary layer flow of a couple stress fluid over a vertical cylinder, in the absence of body couples. The solution of the time-dependent non-linear and coupled governing equations is carried out with the aid of an unconditionally stable Crank-Nicolson type of numerical scheme. Numerical results for the steady-state velocity, temperature as well as the time histories of the skin-friction coefficient and Nus- selt number are presented graphically and discussed. It is seen that for all flow variables as the couple stress control parameter, Co, is amplified, the time required for reaching the temporal maximum increases but the steady-state decreases.展开更多
This paper presents a numerical study on the high-frequency wave loads and ringing response of offshore wind turbine foundations exposed to moderately steep transient water waves.Input wave groups are generated by the...This paper presents a numerical study on the high-frequency wave loads and ringing response of offshore wind turbine foundations exposed to moderately steep transient water waves.Input wave groups are generated by the technique of frequency-focusing,and the numerical simulation of focused waves is based on the NewWave model and a Fourier time-stepping procedure.The proposed model is validated by comparison with the published laboratory data.In respect of both the wave elevations and the underlying water particle kinematics,the numerical results are in excellent agreement with the experimental data.Furthermore,the local evolution of power spectra and the transfer of energy into higher frequencies can be clearly identified.Then the generalized FNV theory and Rainey’s model are applied respectively to calculate the nonlinear wave loads on a bottom-hinged vertical cylinder in focused waves.Resonant ringing response excited by the nonlinear high-frequency wave loads is found in the numerical simulation when frequency ratios(natural frequency of the structure to peak frequency of wave spectra)are equal to 3–5.Dynamic amplification factor of ringing response is also investigated for different dynamic properties(natural frequency and damping ratio)of the structure.展开更多
In this paper,the focused wave groups with different parameters and their actions on a vertical cylinder are experimentally studied. The harmonic wave characteristics of the focusing waves are analyzed by the addition...In this paper,the focused wave groups with different parameters and their actions on a vertical cylinder are experimentally studied. The harmonic wave characteristics of the focusing waves are analyzed by the addition and subtraction of the crest and trough focusing waves. The analyzed results show that higher order harmonics can be generated because of the interaction of component waves. Nonlinearity increases with the inputted wave amplitude and the frequency width increment. Further, the wave run-up around the vertical circular cylinder is experimentally studied. It increases with the wave steepness and the relative cylinder diameter increase. However, the variations of wave run-up around the circular cylinder are different. The researches provide a reference for further numerical studies.展开更多
In this paper,the interactions between extreme waves and a vertical cylinder are investigated through a 3-D two-phase flow model.The numerical model is verified and validated by experimental data.Then,two factors are ...In this paper,the interactions between extreme waves and a vertical cylinder are investigated through a 3-D two-phase flow model.The numerical model is verified and validated by experimental data.Then,two factors are considered,the global wave steepness and the frequency bandwidth of the wave groups,in the studies of the in-line wave forces and the wave run-up around a cylinder.It is found that both the in-line wave forces and the wave run-up are remarkably increased with the increase of the global wave steepness,whereas the effect of the frequency bandwidth on the in-line wave forces is relatively weak in comparison with its effect on the wave run-up.The minimum and maximum wave run-ups are located in the directions of 22.5°and 180°with respect to the direction of the incident waves,respectively.Additionally,a new empirical formula is proposed for predicting the in-line wave forces by using only the free surface elevations around the cylinder.The results of the formula agree well with the simulation results.展开更多
This paper aims to provide a better understanding of the interaction between solitary waves and vertical circular cylinders. This is achieved via process based numerical modelling using the parallel particle-in-cell b...This paper aims to provide a better understanding of the interaction between solitary waves and vertical circular cylinders. This is achieved via process based numerical modelling using the parallel particle-in-cell based incompressible flow solver PICIN. The numerical model solves the Navier-Stokes equations for free-surface flows and incorporates a Cartesian cut cell method for fluid-structure interaction. Solitary waves are generated using a piston-type wave paddle. The PICIN model is first validated using a test case that involves solitary wave scattering by a single vertical cylinder. Comparisons between the present results and experimental data show good agreement for the free surface elevations around the cylinder and the horizontal wave force on the cylinder. The model is then employed to investigate solitary wave interaction with a group of eleven vertical cylinders. The wave run-up and wave forces on the cylinders are discussed.展开更多
The hydrodynamic interaction between two vertical cylinders in water waves is investigated based on the linearized potential flow theory. One of the two cylinders is fixed at the bottom while the other is articulated ...The hydrodynamic interaction between two vertical cylinders in water waves is investigated based on the linearized potential flow theory. One of the two cylinders is fixed at the bottom while the other is articulated at the bottom and oscillates with small amplitudes in the direction of the incident wave. Both the diffracted wave and the radiation wave are studied in the present paper. A simple analytical expression for the velocity potential on the surface of each cylinder is obtained by means of Graf's addition theorem. The wave-excited forces and moments on the cylinders, the added masses and the radiation damping coefficients of the oscillating cylinder are all expressed explicitly in series form. The coefficients of the series are determined by solving algebraic equations. Several numerical examples are given to illustrate the effects of various parameters, such as the separation distance, the relative size of the cylinders, and the incident angle, on the first-order and steady second-order forces, the added masses and radiation-damping coefficients as well as the response of the oscillating cylinder.展开更多
The free surface problem bound by two cylinders is analysed based on the velocity potential theory. An analytical solution in the take domain is obtained up to the second order in the perturbation expansion. The resul...The free surface problem bound by two cylinders is analysed based on the velocity potential theory. An analytical solution in the take domain is obtained up to the second order in the perturbation expansion. The results are compared with those obtainal from the fully nonlinear theory based on a finite element formulation.It is found that the second order solutiongives a fsr better agreement with the fully nonlinear solution.展开更多
Stimulated by thermal optimization in magnetic materials process engineering,the present investigation investigates theoretically the entropy generation in mixed convection magnetohydrodynamic(MHD)flow of an electrica...Stimulated by thermal optimization in magnetic materials process engineering,the present investigation investigates theoretically the entropy generation in mixed convection magnetohydrodynamic(MHD)flow of an electrically-conducting nanofluid from a vertical cylinder.The mathematical model includes the effects of viscous dissipation,second order velocity slip and thermal slip,has been considered.The cylindrical partial differential form of the two-component non-homogenous nanofluid model has been transformed into a system of coupled ordinary differential equations by applying similarity transformations.The effects of governing parameters with no-flux nanoparticle concentration have been examined on important quantities of interest.Furthermore,the dimensionless form of the entropy generation number has also been evaluated using homotopy analysis method(HAM).The present analytical results achieve good correlation with numerical results(shooting method).Entropy is found to be an increasing function of second order velocity slip,magnetic field and curvature parameter.Temperature is elevated with increasing curvature parameter and magnetic parameter whereas it is reduced with mixed convection parameter.The flow is accelerated with curvature parameter but decelerated with magnetic parameter.Heat transfer rate(Nusselt number)is enhanced with greater mixed convection parameter,curvature parameter and first order velocity slip parameter but reduced with increasing second order velocity slip parameter.Entropy generation is also increased with magnetic parameter,second order slip velocity parameter,curvature parameter,thermophoresis parameter,buoyancy parameter and Reynolds number whereas it is suppressed with first order velocity slip parameter,Brownian motion parameter and thermal slip parameter.展开更多
In this paper, the diffraction of water waves by a vertically floating cylinder in a two-layer fluid of a finite depth is studied. Analytical expressions for the hydrodynamic loads on the vertically floating cylinder ...In this paper, the diffraction of water waves by a vertically floating cylinder in a two-layer fluid of a finite depth is studied. Analytical expressions for the hydrodynamic loads on the vertically floating cylinder are obtained by use of the method of eigenfunction expansions. The hydrodynamic loads on the vertically floating cylinder in a two-layer fluid inelude not only the surge, heave and pitch exciting forces due to the incident wave of the surface-wave mode, but also those due to the incident wave of the internal-wave mode. This is different from the case of a homogenous fluid. Some given examples show that, for a two-layer fluid system with a small density difference, the hydrodynamic loads for the surface-wave mode do not differ significantly from those due to surface waves in a single-layer fluid, but the hydrodynamic loads for the internal-wave mode are important over a wide range of frequencies. Moreover, also considered are the free surface and interface elevations generated by the diffraction wave due to the incident wave of the surface-wave and interhal-wave modes, and transfer of energy between modes.展开更多
The transition from an axisymmetric stationary flow to three-dimensional time-dependent flows is carefully studied in a vertical cylinder partially heated from the side, with the aspect ratio A = 2 and Prandtl number ...The transition from an axisymmetric stationary flow to three-dimensional time-dependent flows is carefully studied in a vertical cylinder partially heated from the side, with the aspect ratio A = 2 and Prandtl number Pτ=0.021. The flow develops from the steady toroidal pattern beyond the first instability threshold, breaks the axisymmetric state at a Rayleigh number near 2000, and transits to standing or travelling azimuthal waves. A new result is observed that a slightly unstable flow pattern of standing waves exists and will transit to stable travelling waves after a long time evolution. The onset of oscillations is associated with a supercritical Hopf bifurcation in a system with O(2) symmetry.展开更多
Under the assumption of potential flow and linear wave theory, a semi-analytic method based on eigenfunciton expansion is proposed to predict the hydrody-namic forces on an array of three bottom-mounted, surface-pierc...Under the assumption of potential flow and linear wave theory, a semi-analytic method based on eigenfunciton expansion is proposed to predict the hydrody-namic forces on an array of three bottom-mounted, surface-piercing circular cylinders. The responses of the cylinders induced by wave excitation are determined by the equa-tions of motion coupled with the solutions of the wave radiation and diffraction problems. Experiments for three-cylinder cases are then designed and performed in a wave flume to determine the accuracy of this method for regular waves.展开更多
Wave slamming is an important phenomenon due to its destructive power,and with the rapid development of offshore wind turbines,wave slamming on vertical cylinders has garnered lots of attention.However,the phenomenon ...Wave slamming is an important phenomenon due to its destructive power,and with the rapid development of offshore wind turbines,wave slamming on vertical cylinders has garnered lots of attention.However,the phenomenon of wave slamming on vertical cylinders is very complicated due to both the intrinsic complexity of breaking waves and that of slamming forces.The objective of this paper is to provide a general review of research related to this problem,including theoretical methods,experimental studies,numerical simulations,and full-scale measurements.Based on these approaches,the momentum theory/pressure impulse theory,spatial distribution characteristics of impacts to various breaking waves,wave generation methods,analysis methods for measured forces under structure response,scale effects in experiments,and in-situ measurements have been introduced and discussed.Results show that simplifications in existing models for wave impacting such as wave characteristics and structural response reduce its applicability and should be studied further both in theoretical,experimental and numerical researches.展开更多
The purpose of this paper is to find some better methods for calculating in-line forces on a vertical circular cylinder and for analysing the hydrodynamic coefficients C_D and C_M in wave-current co-existing field. In...The purpose of this paper is to find some better methods for calculating in-line forces on a vertical circular cylinder and for analysing the hydrodynamic coefficients C_D and C_M in wave-current co-existing field. In this pa- per, in order to calculate hydrodynamic forces, the authors try to find a way of applying a great number of the re- sults about C_D and C_M for wave-only field in the case of wave-current co-existing field, and the results about C_D and C_M obtained in regular waves in the ease of irregular waves. Such a way may be of significance in engineering and further research.展开更多
文摘The unsteady natural convective couple stress fluid flow over a semi-infinite vertical cylinder is analyzed for the homogeneous first-order chemical reaction effect. The couple stress fluid flow model introduces the length dependent effect based on the material constant and dynamic viscosity. Also, it introduces the biharmonic operator in the Navier-Stokes equations, which is absent in the case of Newtonian fluids. The solution to the time-dependent non-linear and coupled governing equations is carried out with an unconditionally stable Crank-Nicolson type of numerical schemes. Numerical results for the transient flow variables, the average wall shear stress, the Nusselt number, and the Sherwood number are shown graphically for both generative and destructive reactions. The time to reach the temporal maximum increases as the reaction constant K increases. The average values of the wall shear stress and the heat transfer rate decrease as K increases, while increase with the increase in the Sherwood number.
文摘An analysis is performed to study transient free convective boundary layer flow of a couple stress fluid over a vertical cylinder, in the absence of body couples. The solution of the time-dependent non-linear and coupled governing equations is carried out with the aid of an unconditionally stable Crank-Nicolson type of numerical scheme. Numerical results for the steady-state velocity, temperature as well as the time histories of the skin-friction coefficient and Nus- selt number are presented graphically and discussed. It is seen that for all flow variables as the couple stress control parameter, Co, is amplified, the time required for reaching the temporal maximum increases but the steady-state decreases.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.51879039 and 51490672)。
文摘This paper presents a numerical study on the high-frequency wave loads and ringing response of offshore wind turbine foundations exposed to moderately steep transient water waves.Input wave groups are generated by the technique of frequency-focusing,and the numerical simulation of focused waves is based on the NewWave model and a Fourier time-stepping procedure.The proposed model is validated by comparison with the published laboratory data.In respect of both the wave elevations and the underlying water particle kinematics,the numerical results are in excellent agreement with the experimental data.Furthermore,the local evolution of power spectra and the transfer of energy into higher frequencies can be clearly identified.Then the generalized FNV theory and Rainey’s model are applied respectively to calculate the nonlinear wave loads on a bottom-hinged vertical cylinder in focused waves.Resonant ringing response excited by the nonlinear high-frequency wave loads is found in the numerical simulation when frequency ratios(natural frequency of the structure to peak frequency of wave spectra)are equal to 3–5.Dynamic amplification factor of ringing response is also investigated for different dynamic properties(natural frequency and damping ratio)of the structure.
基金supported bythe National Natural Science Foundation of China (Grant Nos.50379002 and 50921001)the New Century Excellent Talents in University (Grant No.NCET-05-0282)
文摘In this paper,the focused wave groups with different parameters and their actions on a vertical cylinder are experimentally studied. The harmonic wave characteristics of the focusing waves are analyzed by the addition and subtraction of the crest and trough focusing waves. The analyzed results show that higher order harmonics can be generated because of the interaction of component waves. Nonlinearity increases with the inputted wave amplitude and the frequency width increment. Further, the wave run-up around the vertical circular cylinder is experimentally studied. It increases with the wave steepness and the relative cylinder diameter increase. However, the variations of wave run-up around the circular cylinder are different. The researches provide a reference for further numerical studies.
基金supported by the National Key Research and Development Program of China(Grant No.2017 YFC1404200)the National Nature Science Foundation of China(Grant Nos.51679031,51720105010 and 51979029)the Liaoning Revitalization Talents Program(Grant No.XLYC1807010).
文摘In this paper,the interactions between extreme waves and a vertical cylinder are investigated through a 3-D two-phase flow model.The numerical model is verified and validated by experimental data.Then,two factors are considered,the global wave steepness and the frequency bandwidth of the wave groups,in the studies of the in-line wave forces and the wave run-up around a cylinder.It is found that both the in-line wave forces and the wave run-up are remarkably increased with the increase of the global wave steepness,whereas the effect of the frequency bandwidth on the in-line wave forces is relatively weak in comparison with its effect on the wave run-up.The minimum and maximum wave run-ups are located in the directions of 22.5°and 180°with respect to the direction of the incident waves,respectively.Additionally,a new empirical formula is proposed for predicting the in-line wave forces by using only the free surface elevations around the cylinder.The results of the formula agree well with the simulation results.
基金funded by the University of Bath (Graduate school funding, sponsor code: 3451)HR Wallingford (internal research project: DDY0485).
文摘This paper aims to provide a better understanding of the interaction between solitary waves and vertical circular cylinders. This is achieved via process based numerical modelling using the parallel particle-in-cell based incompressible flow solver PICIN. The numerical model solves the Navier-Stokes equations for free-surface flows and incorporates a Cartesian cut cell method for fluid-structure interaction. Solitary waves are generated using a piston-type wave paddle. The PICIN model is first validated using a test case that involves solitary wave scattering by a single vertical cylinder. Comparisons between the present results and experimental data show good agreement for the free surface elevations around the cylinder and the horizontal wave force on the cylinder. The model is then employed to investigate solitary wave interaction with a group of eleven vertical cylinders. The wave run-up and wave forces on the cylinders are discussed.
文摘The hydrodynamic interaction between two vertical cylinders in water waves is investigated based on the linearized potential flow theory. One of the two cylinders is fixed at the bottom while the other is articulated at the bottom and oscillates with small amplitudes in the direction of the incident wave. Both the diffracted wave and the radiation wave are studied in the present paper. A simple analytical expression for the velocity potential on the surface of each cylinder is obtained by means of Graf's addition theorem. The wave-excited forces and moments on the cylinders, the added masses and the radiation damping coefficients of the oscillating cylinder are all expressed explicitly in series form. The coefficients of the series are determined by solving algebraic equations. Several numerical examples are given to illustrate the effects of various parameters, such as the separation distance, the relative size of the cylinders, and the incident angle, on the first-order and steady second-order forces, the added masses and radiation-damping coefficients as well as the response of the oscillating cylinder.
文摘The free surface problem bound by two cylinders is analysed based on the velocity potential theory. An analytical solution in the take domain is obtained up to the second order in the perturbation expansion. The results are compared with those obtainal from the fully nonlinear theory based on a finite element formulation.It is found that the second order solutiongives a fsr better agreement with the fully nonlinear solution.
文摘Stimulated by thermal optimization in magnetic materials process engineering,the present investigation investigates theoretically the entropy generation in mixed convection magnetohydrodynamic(MHD)flow of an electrically-conducting nanofluid from a vertical cylinder.The mathematical model includes the effects of viscous dissipation,second order velocity slip and thermal slip,has been considered.The cylindrical partial differential form of the two-component non-homogenous nanofluid model has been transformed into a system of coupled ordinary differential equations by applying similarity transformations.The effects of governing parameters with no-flux nanoparticle concentration have been examined on important quantities of interest.Furthermore,the dimensionless form of the entropy generation number has also been evaluated using homotopy analysis method(HAM).The present analytical results achieve good correlation with numerical results(shooting method).Entropy is found to be an increasing function of second order velocity slip,magnetic field and curvature parameter.Temperature is elevated with increasing curvature parameter and magnetic parameter whereas it is reduced with mixed convection parameter.The flow is accelerated with curvature parameter but decelerated with magnetic parameter.Heat transfer rate(Nusselt number)is enhanced with greater mixed convection parameter,curvature parameter and first order velocity slip parameter but reduced with increasing second order velocity slip parameter.Entropy generation is also increased with magnetic parameter,second order slip velocity parameter,curvature parameter,thermophoresis parameter,buoyancy parameter and Reynolds number whereas it is suppressed with first order velocity slip parameter,Brownian motion parameter and thermal slip parameter.
基金This project was financially supported by the National Natural Science Foundation of China(Grant No.10572092)the High Technology Research and Development Programof China(863Program,Grant Nos.2006AA09Z352 and 2006AA09196-6)
文摘In this paper, the diffraction of water waves by a vertically floating cylinder in a two-layer fluid of a finite depth is studied. Analytical expressions for the hydrodynamic loads on the vertically floating cylinder are obtained by use of the method of eigenfunction expansions. The hydrodynamic loads on the vertically floating cylinder in a two-layer fluid inelude not only the surge, heave and pitch exciting forces due to the incident wave of the surface-wave mode, but also those due to the incident wave of the internal-wave mode. This is different from the case of a homogenous fluid. Some given examples show that, for a two-layer fluid system with a small density difference, the hydrodynamic loads for the surface-wave mode do not differ significantly from those due to surface waves in a single-layer fluid, but the hydrodynamic loads for the internal-wave mode are important over a wide range of frequencies. Moreover, also considered are the free surface and interface elevations generated by the diffraction wave due to the incident wave of the surface-wave and interhal-wave modes, and transfer of energy between modes.
文摘The transition from an axisymmetric stationary flow to three-dimensional time-dependent flows is carefully studied in a vertical cylinder partially heated from the side, with the aspect ratio A = 2 and Prandtl number Pτ=0.021. The flow develops from the steady toroidal pattern beyond the first instability threshold, breaks the axisymmetric state at a Rayleigh number near 2000, and transits to standing or travelling azimuthal waves. A new result is observed that a slightly unstable flow pattern of standing waves exists and will transit to stable travelling waves after a long time evolution. The onset of oscillations is associated with a supercritical Hopf bifurcation in a system with O(2) symmetry.
基金supported by the National Marine Public Welfare Research Projects of China(No.201005002)The Hong Kong Polytechnic University(No.H-ZG 68)
文摘Under the assumption of potential flow and linear wave theory, a semi-analytic method based on eigenfunciton expansion is proposed to predict the hydrody-namic forces on an array of three bottom-mounted, surface-piercing circular cylinders. The responses of the cylinders induced by wave excitation are determined by the equa-tions of motion coupled with the solutions of the wave radiation and diffraction problems. Experiments for three-cylinder cases are then designed and performed in a wave flume to determine the accuracy of this method for regular waves.
基金the National Natural Science Foundation of China(Grant Nos.51720105010,51979029)the Major Scientific and Technological Project of CNOOC(KJGG2022-0202)Innovative Research Foundation of Ship General Performance(Grant No.31422119).
文摘Wave slamming is an important phenomenon due to its destructive power,and with the rapid development of offshore wind turbines,wave slamming on vertical cylinders has garnered lots of attention.However,the phenomenon of wave slamming on vertical cylinders is very complicated due to both the intrinsic complexity of breaking waves and that of slamming forces.The objective of this paper is to provide a general review of research related to this problem,including theoretical methods,experimental studies,numerical simulations,and full-scale measurements.Based on these approaches,the momentum theory/pressure impulse theory,spatial distribution characteristics of impacts to various breaking waves,wave generation methods,analysis methods for measured forces under structure response,scale effects in experiments,and in-situ measurements have been introduced and discussed.Results show that simplifications in existing models for wave impacting such as wave characteristics and structural response reduce its applicability and should be studied further both in theoretical,experimental and numerical researches.
文摘The purpose of this paper is to find some better methods for calculating in-line forces on a vertical circular cylinder and for analysing the hydrodynamic coefficients C_D and C_M in wave-current co-existing field. In this pa- per, in order to calculate hydrodynamic forces, the authors try to find a way of applying a great number of the re- sults about C_D and C_M for wave-only field in the case of wave-current co-existing field, and the results about C_D and C_M obtained in regular waves in the ease of irregular waves. Such a way may be of significance in engineering and further research.