The fluid viscosity is known to have a significant effect on the hydrodynamic characteristics which are linked to the power conversion ability of the wave energy converter(WEC). To overcome the disadvantages of case-b...The fluid viscosity is known to have a significant effect on the hydrodynamic characteristics which are linked to the power conversion ability of the wave energy converter(WEC). To overcome the disadvantages of case-by-case study through the experiments and numerical computations employed by the former researches, the viscous effect is studied comprehensively for multiple geometries in the present paper. The viscous effect is expressed as the viscous added mass and damping solved by the free-decay method. The computational fluid dynamics(CFD) method is employed for the calculation of the motion and flow field around the floater. The diameter to draft ratio and bottom shape are considered for the geometrical evaluation on the viscous effect. The results show that a slenderer floater presents a stronger viscous effect. Through the comparisons of the floaters with four different bottom shapes, the conical bottom is recommended in terms of low viscous effect and simple geometry for manufacture. A viscous correction formula for a series of cylindrical floaters is put forward, for the first time, to help the engineering design of outer-floaters of point-absorber WECs.展开更多
The aim of the present paper is to study flow and heat transfer charac- teristics of a viscous Casson thin film flow over an unsteady stretching sheet subject to variable heat flux in the presence of slip velocity con...The aim of the present paper is to study flow and heat transfer charac- teristics of a viscous Casson thin film flow over an unsteady stretching sheet subject to variable heat flux in the presence of slip velocity condition and viscous dissipation. The governing equations are partial differential equations. They are reduced to a set of highly nonlinear ordinary differential equations by suitable similarity transformations. The re- sulting similarity equations are solved numerically with a shooting method. Comparisons with previous works are macle, and the results are found to be in excellent agreement. In the present work, the effects of the unsteadiness parameter, the Casson parameter, the Eckert number, the slip velocity parameter, and the Prandtl number on flow and heat transfer characteristics are discussed. Also, the local skin-friction coefficient and the local Nusselt number at the stretching sheet are computed and discussed.展开更多
This paper adopted a semi-analytical method based on eigenfunction matching to solve the problem of sharp resonance of cylindrical structures with a moonpool that has a restricted entrance. To eliminate the sharp reso...This paper adopted a semi-analytical method based on eigenfunction matching to solve the problem of sharp resonance of cylindrical structures with a moonpool that has a restricted entrance. To eliminate the sharp resonance and to measure the viscous effect, a quadratic dissipation is introduced by assuming an additional dissipative disk at the moonpool entrance. The fluid domain is divided into five cylindrical subdomains, and the velocity potential in each subdomain is obtained by meeting the Laplace equation as well as the boundary conditions. The free-surface elevation at the center of the moonpool, along with the pressure and velocity at the restricted entrance for first-order wave are evaluated. By choosing appropriate dissipation coefficients, the free-surface elevation calculated at the center of the moonpool is in coincidence with the measurements in model tests both at the peak period and amplitude at resonance. It is shown that the sharp resonance in the potential flow theory can be eliminated and the viscous effect can be estimated with a simple method in some provided hydrodynamic models.展开更多
Offshore structures are generally classified as small-scale structures or large-scale structures.Their wave forces are then estimated by Morison equation and diffraction/radiation theories,respectively.However,the cla...Offshore structures are generally classified as small-scale structures or large-scale structures.Their wave forces are then estimated by Morison equation and diffraction/radiation theories,respectively.However,the classification criterion is not well quantified.In the present paper,a numerical wave flume is established to simulate the wave forces acting on a fixed and vertical surface-piercing circular cylinder under linear waves.By solving Navier–Stokes equation and Euler equation with free surface involved,respectively,the viscous force and inertia force are separated accurately.The variation of viscous force and inertia force with the cylinder diameter to wave length ratio is discussed in detail.The scale intervals for significant viscous and diffraction effects are given.The error caused by neglecting viscous and diffraction forces is quantitatively analyzed.Based on these analysis,the concept of medium-scale structure is proposed and the classification criteria for small-,medium-and large-scale structures are given.In the meantime,the estimation methods of wave forces for different scales of structures are suggested.展开更多
By using Hamilton-type variation principle in non-conservation system, the nonlinear equation of wave motion of a elastic thin rod was derived according to Lagrange description of finite deformation theory. The dissip...By using Hamilton-type variation principle in non-conservation system, the nonlinear equation of wave motion of a elastic thin rod was derived according to Lagrange description of finite deformation theory. The dissipation caused due to viscous effect and the dispersion introduced by transverse inertia were taken into consideration so that steady traveling wave solution can be obtained. Using multi-scale method the nonlinear equation is reduced to a KdV-Burgers equation which corresponds with saddle-spiral heteroclinic orbit on phase plane. Its solution is called the oscillating-solitary wave or saddle-spiral shock wave. If viscous effect or transverse inertia is neglected, the equation is degraded to classical KdV or Burgers equation. The former implies a propagating solitary wave with homoclinic on phase plane, the latter means shock wave and heteroclinic orbit.展开更多
Viscous scale effects on propeller TVC were investigated by testing a series of three geosim propeller models in the large cavitation Tunnel of CSSRC without and with two different turbulence stimulators. Tests includ...Viscous scale effects on propeller TVC were investigated by testing a series of three geosim propeller models in the large cavitation Tunnel of CSSRC without and with two different turbulence stimulators. Tests included flow visualization by oil film method and cavitation observation for five different stages of development of propeller TVC: desinent, unattached, attached, developed and fully developed TVC. The main findings are: 1)there existed a size effect of the boundary-layer transition on propeller models which could be analyzed by using the critical roughness Reynolds number and a newly defined quasi-critical Reynolds number, 2)the preliminary results of the blackboardpaint used as a tripping device was encouraging, 3)the Reynolds number exponent n of TVC scaling rules was found to be dependent upon the blade surface condition, the stage of development of TVC and the thrust loading of propeller models.展开更多
The main purpose of this article is to present a mathematical model of ciliary motion in an annulus. In this analysis, the peristaltic motion of non-Newtonian Jeffrey six constant fluid is observed in an annulus with ...The main purpose of this article is to present a mathematical model of ciliary motion in an annulus. In this analysis, the peristaltic motion of non-Newtonian Jeffrey six constant fluid is observed in an annulus with ciliated tips in the presence of heat and mass transfer. The effects of viscous dissipation are also considered. The flow equations of non-Newtonian fluid for the two-dimensional tube in cylindrical coordinates are simplified using the low Reynolds number and long wave-length approximations. The main equations for Jeffrey six constant fluid are considered in cylindrical coordinates system. The resulting nonlinear problem is solved using the regular perturbation technique in terms of a variant of small dimensionless parameter α. The results of the solutions for velocity, temperature and concentration field are presented graphically. B_k is Brinkman number, ST is soret number, and SH is the Schmidth number. Outcome for the longitudinal velocity, pressure rise, pressure gradient and stream lines are represented through graphs. In the history, the viscous-dissipation effect is usually represented by the Brinkman number.展开更多
This paper presents a theoretical and numerical analysis of the magnetoelasticity of a long cylindrical superconductor model containing a central inclusion placed in a time-dependent external magnetic field with zero-...This paper presents a theoretical and numerical analysis of the magnetoelasticity of a long cylindrical superconductor model containing a central inclusion placed in a time-dependent external magnetic field with zero-field-cooled magnetization(ZFC).In order to reflect the mechanical behavior of the model more realistically,the model is defined as a material with anisotropic mechanical properties,and then the viscous flux flow effect and the flux creep effect are considered separately for the flux distribution of the model.By controlling the elastic modulus Er/E i r m,volume fraction f of composite materials,as well as the parameters affecting the flux distribution,such as the viscous flux flow velocity v1,the flux creep action coefficient K,the creep occurrence probability n,etc.,the radial stress distribution and magnetostriction characteristics of the model are analyzed in depth.In this paper,the theoretical calculation results are compared with the numerical simulation results.The results show that the distribution laws of the parametric curves plotted by the two are almost completely consistent,but there are obvious differences in the numerical values.The reason is that the superconductor conductivity is assumed to satisfy a strong nonlinear E-J relationship in the numerical simulation process,and an external magnetic field in the form of a pulse is applied;while the field-dependent critical state model is used in the theoretical calculation,and the induced current is assumed to be a critical current,so there are certain differences in the calculated values.展开更多
In order to understand the difference of ventilated supercavity in water tunnel and infinite flow field, 3-D numerical simulations are carried out to obtain the ventilated supercavity in above mentioned conditions bas...In order to understand the difference of ventilated supercavity in water tunnel and infinite flow field, 3-D numerical simulations are carried out to obtain the ventilated supercavity in above mentioned conditions based on RANS equations, using the finite volume method and SST turbulence model in the framework of the two fluid multiphase flow model. The numerical method adopted in this article for the infinite flow field and water tunnel experiments is validated by comparing results with those of empirical formulas and experimental data. On this basis the difference between water tunnel experiments and infinite flow field is studied, including the influence of the route loss and the blocking effect in the water tunnel. Finally, some suggestions are made for water tunnel experiments.展开更多
This paper is concerned with the well-posedness and large-time behavior of a two-dimensional PDE-ODE hybrid chemotaxis system describing the initiation of tumor angiogenesis. We first transform the system via a Cole-H...This paper is concerned with the well-posedness and large-time behavior of a two-dimensional PDE-ODE hybrid chemotaxis system describing the initiation of tumor angiogenesis. We first transform the system via a Cole-Hopf type transformation into a parabolic-hyperbolic system and then show that the solution to the transformed system converges to a constant equilibrium state as time tends to infinity. Finally we reverse the Cole-Hopf transformation and obtain the relevant results for the pre-transformed PDE-ODE hybrid system.In contrast to the existing related results, where continuous initial data is imposed, we are able to prove the asymptotic stability for discontinuous initial data with large oscillations. The key ingredient in our proof is the use of the so-called "effective viscous flux", which enables us to obtain the desired energy estimates and regularity. The technique of the "effective viscous flux" turns out to be a very useful tool to study chemotaxis systems with initial data having low regularity and was rarely(if not) used in the literature for chemotaxis models.展开更多
基金financially supported by the National Natural Science Foundation of China(Grant No.51761135013)the High Technology Ship Scientific Research Project from Ministry of Industry and Information Technology of the People’s Republic of China–Floating Security Platform Project(the second stage,201622)+1 种基金the Fundamental Research Fund for the Central University(Grant Nos.HEUCF180104 and HEUCFP201809)the China Scholarship Council(the International Clean Energy Talent Program,2017)
文摘The fluid viscosity is known to have a significant effect on the hydrodynamic characteristics which are linked to the power conversion ability of the wave energy converter(WEC). To overcome the disadvantages of case-by-case study through the experiments and numerical computations employed by the former researches, the viscous effect is studied comprehensively for multiple geometries in the present paper. The viscous effect is expressed as the viscous added mass and damping solved by the free-decay method. The computational fluid dynamics(CFD) method is employed for the calculation of the motion and flow field around the floater. The diameter to draft ratio and bottom shape are considered for the geometrical evaluation on the viscous effect. The results show that a slenderer floater presents a stronger viscous effect. Through the comparisons of the floaters with four different bottom shapes, the conical bottom is recommended in terms of low viscous effect and simple geometry for manufacture. A viscous correction formula for a series of cylindrical floaters is put forward, for the first time, to help the engineering design of outer-floaters of point-absorber WECs.
文摘The aim of the present paper is to study flow and heat transfer charac- teristics of a viscous Casson thin film flow over an unsteady stretching sheet subject to variable heat flux in the presence of slip velocity condition and viscous dissipation. The governing equations are partial differential equations. They are reduced to a set of highly nonlinear ordinary differential equations by suitable similarity transformations. The re- sulting similarity equations are solved numerically with a shooting method. Comparisons with previous works are macle, and the results are found to be in excellent agreement. In the present work, the effects of the unsteadiness parameter, the Casson parameter, the Eckert number, the slip velocity parameter, and the Prandtl number on flow and heat transfer characteristics are discussed. Also, the local skin-friction coefficient and the local Nusselt number at the stretching sheet are computed and discussed.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.51509048,51679044 and11572094)
文摘This paper adopted a semi-analytical method based on eigenfunction matching to solve the problem of sharp resonance of cylindrical structures with a moonpool that has a restricted entrance. To eliminate the sharp resonance and to measure the viscous effect, a quadratic dissipation is introduced by assuming an additional dissipative disk at the moonpool entrance. The fluid domain is divided into five cylindrical subdomains, and the velocity potential in each subdomain is obtained by meeting the Laplace equation as well as the boundary conditions. The free-surface elevation at the center of the moonpool, along with the pressure and velocity at the restricted entrance for first-order wave are evaluated. By choosing appropriate dissipation coefficients, the free-surface elevation calculated at the center of the moonpool is in coincidence with the measurements in model tests both at the peak period and amplitude at resonance. It is shown that the sharp resonance in the potential flow theory can be eliminated and the viscous effect can be estimated with a simple method in some provided hydrodynamic models.
基金This work was supported by the National Key R&D Program of China(Grant 2017yfc1404200)the National Natural Science Foundation of China(Grant 11572332)and the Strategic Priority Research Program of the Chinese Academy of Sciences(Grants xdb22040203 and xda22OOOOOO).
文摘Offshore structures are generally classified as small-scale structures or large-scale structures.Their wave forces are then estimated by Morison equation and diffraction/radiation theories,respectively.However,the classification criterion is not well quantified.In the present paper,a numerical wave flume is established to simulate the wave forces acting on a fixed and vertical surface-piercing circular cylinder under linear waves.By solving Navier–Stokes equation and Euler equation with free surface involved,respectively,the viscous force and inertia force are separated accurately.The variation of viscous force and inertia force with the cylinder diameter to wave length ratio is discussed in detail.The scale intervals for significant viscous and diffraction effects are given.The error caused by neglecting viscous and diffraction forces is quantitatively analyzed.Based on these analysis,the concept of medium-scale structure is proposed and the classification criteria for small-,medium-and large-scale structures are given.In the meantime,the estimation methods of wave forces for different scales of structures are suggested.
文摘By using Hamilton-type variation principle in non-conservation system, the nonlinear equation of wave motion of a elastic thin rod was derived according to Lagrange description of finite deformation theory. The dissipation caused due to viscous effect and the dispersion introduced by transverse inertia were taken into consideration so that steady traveling wave solution can be obtained. Using multi-scale method the nonlinear equation is reduced to a KdV-Burgers equation which corresponds with saddle-spiral heteroclinic orbit on phase plane. Its solution is called the oscillating-solitary wave or saddle-spiral shock wave. If viscous effect or transverse inertia is neglected, the equation is degraded to classical KdV or Burgers equation. The former implies a propagating solitary wave with homoclinic on phase plane, the latter means shock wave and heteroclinic orbit.
文摘Viscous scale effects on propeller TVC were investigated by testing a series of three geosim propeller models in the large cavitation Tunnel of CSSRC without and with two different turbulence stimulators. Tests included flow visualization by oil film method and cavitation observation for five different stages of development of propeller TVC: desinent, unattached, attached, developed and fully developed TVC. The main findings are: 1)there existed a size effect of the boundary-layer transition on propeller models which could be analyzed by using the critical roughness Reynolds number and a newly defined quasi-critical Reynolds number, 2)the preliminary results of the blackboardpaint used as a tripping device was encouraging, 3)the Reynolds number exponent n of TVC scaling rules was found to be dependent upon the blade surface condition, the stage of development of TVC and the thrust loading of propeller models.
文摘The main purpose of this article is to present a mathematical model of ciliary motion in an annulus. In this analysis, the peristaltic motion of non-Newtonian Jeffrey six constant fluid is observed in an annulus with ciliated tips in the presence of heat and mass transfer. The effects of viscous dissipation are also considered. The flow equations of non-Newtonian fluid for the two-dimensional tube in cylindrical coordinates are simplified using the low Reynolds number and long wave-length approximations. The main equations for Jeffrey six constant fluid are considered in cylindrical coordinates system. The resulting nonlinear problem is solved using the regular perturbation technique in terms of a variant of small dimensionless parameter α. The results of the solutions for velocity, temperature and concentration field are presented graphically. B_k is Brinkman number, ST is soret number, and SH is the Schmidth number. Outcome for the longitudinal velocity, pressure rise, pressure gradient and stream lines are represented through graphs. In the history, the viscous-dissipation effect is usually represented by the Brinkman number.
基金supported by the National Natural Science Foundation of China(Grant Nos.51904138 and 51076061)the Natural Science Foundation of Gansu Province(Grant No.B061709).
文摘This paper presents a theoretical and numerical analysis of the magnetoelasticity of a long cylindrical superconductor model containing a central inclusion placed in a time-dependent external magnetic field with zero-field-cooled magnetization(ZFC).In order to reflect the mechanical behavior of the model more realistically,the model is defined as a material with anisotropic mechanical properties,and then the viscous flux flow effect and the flux creep effect are considered separately for the flux distribution of the model.By controlling the elastic modulus Er/E i r m,volume fraction f of composite materials,as well as the parameters affecting the flux distribution,such as the viscous flux flow velocity v1,the flux creep action coefficient K,the creep occurrence probability n,etc.,the radial stress distribution and magnetostriction characteristics of the model are analyzed in depth.In this paper,the theoretical calculation results are compared with the numerical simulation results.The results show that the distribution laws of the parametric curves plotted by the two are almost completely consistent,but there are obvious differences in the numerical values.The reason is that the superconductor conductivity is assumed to satisfy a strong nonlinear E-J relationship in the numerical simulation process,and an external magnetic field in the form of a pulse is applied;while the field-dependent critical state model is used in the theoretical calculation,and the induced current is assumed to be a critical current,so there are certain differences in the calculated values.
基金Project supported by the Major National Natural Science Foundation of China (Grant No. 10832007)
文摘In order to understand the difference of ventilated supercavity in water tunnel and infinite flow field, 3-D numerical simulations are carried out to obtain the ventilated supercavity in above mentioned conditions based on RANS equations, using the finite volume method and SST turbulence model in the framework of the two fluid multiphase flow model. The numerical method adopted in this article for the infinite flow field and water tunnel experiments is validated by comparing results with those of empirical formulas and experimental data. On this basis the difference between water tunnel experiments and infinite flow field is studied, including the influence of the route loss and the blocking effect in the water tunnel. Finally, some suggestions are made for water tunnel experiments.
基金supported by Academy of Mathematics and Systems Science,Chinese Academy of Sciences and the Joint Laboratory of Applied Mathematics in the Hong Kong Polytechnic University where he was a postdoctoral fellow,National Natural Science Foundation of China(Grant No.11901115)Natural Science Foundation of Guangdong Province(Grant No.2019A1515010706)+4 种基金Guangdong University of Technology(Grant No.220413228)supported by the Hong Kong Research Grant Council General Research Fund(Grant No.Poly U 153031/17P)the Hong Kong Polytechnic University(Grant No.ZZHY)supported by National Natural Science Foundation of China(Grant Nos.11771150,11831003 and 11926346)Guangdong Basic and Applied Basic Research Foundation(Grant No.2020B1515310015)。
文摘This paper is concerned with the well-posedness and large-time behavior of a two-dimensional PDE-ODE hybrid chemotaxis system describing the initiation of tumor angiogenesis. We first transform the system via a Cole-Hopf type transformation into a parabolic-hyperbolic system and then show that the solution to the transformed system converges to a constant equilibrium state as time tends to infinity. Finally we reverse the Cole-Hopf transformation and obtain the relevant results for the pre-transformed PDE-ODE hybrid system.In contrast to the existing related results, where continuous initial data is imposed, we are able to prove the asymptotic stability for discontinuous initial data with large oscillations. The key ingredient in our proof is the use of the so-called "effective viscous flux", which enables us to obtain the desired energy estimates and regularity. The technique of the "effective viscous flux" turns out to be a very useful tool to study chemotaxis systems with initial data having low regularity and was rarely(if not) used in the literature for chemotaxis models.
