Liquid metal alloys(LMAs) are the potential candidates of thermal interface materials(TIMs) for electronics cooling.In the present work, buffer layers of Ag, Ti, Cu, Ni, Mo, and W were deposited on polished Cu plates ...Liquid metal alloys(LMAs) are the potential candidates of thermal interface materials(TIMs) for electronics cooling.In the present work, buffer layers of Ag, Ti, Cu, Ni, Mo, and W were deposited on polished Cu plates by DC magnetron sputtering, the contact angles of de-ionized water and diiodomethane on the buffer layers were measured by an easy drop shape analyzer and the surface free energies(SFEs) of the buffer layers were calculated by the Owens–Wendt–Kaelble equation. Samples were prepared by sandwiching the filmed Cu plates and LMAs. The thermal properties of the samples were measured by laser flash analysis method. The SFE of the buffer layer has a strong influence on the interface heat transfer, whereas the measurement temperature has no obvious effect on the thermal properties of the samples. As the SFE of the buffer layer increases, the wettability, thermal diffusivity, and thermal conductivity are enhanced, and the thermal contact resistance is decreased.展开更多
A liquid film flow over a flat plate is investigated by prescribing the unsteady interface velocity. With this prescribed surface velocity, the governing Navier–Stokes(NS) equations are transformed into a similarity ...A liquid film flow over a flat plate is investigated by prescribing the unsteady interface velocity. With this prescribed surface velocity, the governing Navier–Stokes(NS) equations are transformed into a similarity ordinary differential equation, which is solved numerically. The flow characteristics is controlled by an unsteadiness parameter S and the flow direction parameter Λ. The results show that solutions only exist for a certain range of the unsteadiness parameter, i.e., S≤1 for Λ =-1 and S≤-2.815877 for Λ = 1. In the solution domain,the dimensionless liquid film thickness β decreases with S for both the cases. The wall shear stress increases with the decrease of S for Λ =-1. However, for Λ =-1 the shear stress magnitude first decreases and then increases with the decrease of S. There are no zero crossing points for the velocity profiles for both the cases. The profiles of velocity stay either positive or negative all the time, except for the wall zero velocity. Consequently,the vertical velocity becomes a monotonic function. To maintain the prescribed velocity, mass transpiration is generally needed, but for the shrinking film case it is possible to have an impermeable wall. The results are also an exact solution to the full NS equations.展开更多
Moving particle semi-implicit （MPS） method is a fully Lagrangian particle method which can easily solve problems with violent free surface. Although it has demonstrated its advantage in ocean engineering application...Moving particle semi-implicit （MPS） method is a fully Lagrangian particle method which can easily solve problems with violent free surface. Although it has demonstrated its advantage in ocean engineering applications, it still has some defects to be improved. In this paper, MPS method is extended to the large eddy simulation （LES） by coupling with a sub-particle-scale （SPS） turbulence model. The SPS turbulence model turns into the Reynolds stress terms in the filtered momentum equation, and the Smagorinsky model is introduced to describe the Reynolds stress terms. Although MPS method has the advantage in the simulation of the free surface flow, a lot of non-free surface particles are treated as free surface particles in the original MPS model. In this paper, we use a new free surface tracing method and the key point is ＂neighbor particle＂. In this new method, the zone around each particle is divided into eight parts, and the particle will be treated as a free surface particle as long as there are no ＂neighbor particles＂ in any two parts of the zone. As the number density parameter judging method has a high efficiency for the free surface particles tracing, we combine it with the neighbor detected method. First, we select out the particles which may be mistreated with high probabilities by using the number density parameter judging method. And then we deal with these particles with the neighbor detected method. By doing this, the new mixed free surface tracing method can reduce the mistreatment problem efficiently. The serious pressure fluctuation is an obvious defect in MPS method, and therefore an area-time average technique is used in this paper to remove the pressure fluctuation with a quite good result. With these improvements, the modified MPS-LES method is applied to simulate liquid sloshing problems with large deforming free surface. Results show that the modified MPS-LES method can simulate the large deforming free surface easily. It can not only capture the large impact pressure accurately on rolling tank wall but also can generate all physical phenomena successfully. The good agreement between numerical and experimental results proves that the modified MPS-LES method is a good CFD methodology in free surface flow simulations.展开更多
This study is concerned with describing the thermodynamic equilibrium of the saturated fluid with and without a free surface area A. Discussion of the role of A as system variable of the interface phase and an estimat...This study is concerned with describing the thermodynamic equilibrium of the saturated fluid with and without a free surface area A. Discussion of the role of A as system variable of the interface phase and an estimate of the ratio of the respective free energies of systems with and without A show that the system variables given by Gibbs suffice to describe the volumetric properties of the fluid. The well-known Gibbsian expressions for the internal energies of the two-phase fluid, namely for the vapor and for the condensate (liquid or solid), only differ with respect to the phase-specific volumes and . The saturation temperature T, vapor presssure p, and chemical potential are intensive parameters, each of which has the same value everywhere within the fluid, and hence are phase-independent quantities. If one succeeds in representing as a function of and , then the internal energies can also be described by expressions that only differ from one another with respect to their dependence on and . Here it is shown that can be uniquely expressed by the volume function . Therefore, the internal energies can be represented explicitly as functions of the vapor pressure and volumes of the saturated vapor and condensate and are absolutely determined. The hitherto existing problem of applied thermodynamics, calculating the internal energy from the measurable quantities T, p, , and , is thus solved. The same method applies to the calculation of the entropy, chemical potential, and heat capacity.展开更多
A new equation for predicting surface tension is proposed based on the thermodynamic definition of surface tension and the expression of the Gibbs free energy of the system. Using the NRTL equation to represent the ex...A new equation for predicting surface tension is proposed based on the thermodynamic definition of surface tension and the expression of the Gibbs free energy of the system. Using the NRTL equation to represent the excess Gibbs free energy, a two-parameter surface tension equation is derived. The feasibility of the new equation has been tested in terms of 124 binary and 16 multicomponent systems(13-ternary and 3-quaternary) with absolute relative deviations of 0.59% and 1.55% respectively. This model is also predictive for the temperature dependence of surface tension of liquid mixtures. It is shown that, with good accuracy, this equation is simple and reliable for practical use.展开更多
Up to now, no a real full-cover liquid metal (LM) free surface flow have been successfully used in magnetic fusion devices as MHD instability and unavoidable rivulet flow. Recently, after we carried out a guidable fre...Up to now, no a real full-cover liquid metal (LM) free surface flow have been successfully used in magnetic fusion devices as MHD instability and unavoidable rivulet flow. Recently, after we carried out a guidable free curve-surface flow on theoretically and experimentally, seeking for other way to get a full-cover free surface flow is also in implementing. The superficial layer MHD effect in free surface flow is experimentally observed. After compared and analyzed the characteristic parameters of the free surface flow, the conditions of full-cover free surface flow are found. Meanwhile, the new two parameters of surface cover ratio and rivulet flow index are introduced to characterize the flowing characteristic of the full-cover free surface flow under magnetic field. According to the analysis rule, for different liquid metal, there are the different unique conditions to meet full-cover free surface flow under magnetic field. This may be a way to solve free surface flow major MHD key issue for LM PFCs.展开更多
In this study,two dimensional unsteady flows of cylinder and cylinder with additional fairing close to a free surface were numerically investigated.The governing momentum equations were solved by using the Semi Implic...In this study,two dimensional unsteady flows of cylinder and cylinder with additional fairing close to a free surface were numerically investigated.The governing momentum equations were solved by using the Semi Implicit Method for Pressure Linked Equations(SIMPLE).The Volume of Fluid(VOF)method applied to simulate a free surface.Non-uniform grid structures were used in the simulation with denser grids near the cylinder.Under the conditions of Reynolds number 150624,271123,210874 and 331373,the cylinders were simulated with different depths of invasion.It was shown that the flow characteristics were influenced by submergence depth and Reynolds numbers.When the cylinder close to the free surface,the drag coefficient,lift coefficient and Strouhal numbers will increase due to the effect of free liquid surface on vortex shedding.With additional fairing,can effectively reduce the influence of the free surface on the drag coefficient.Fairing will reduce lift coefficient at high Reynolds numbers,but increase lift coefficient when Reynolds numbers are small.Fairing can effectively reduce Strouhal numbers,thus can well suppress the vortex induced vibration.展开更多
A model for liquid-gas flow(MLGF),considering the free movement of liquid surface,was built to simulate the wastewater velocity field and gas distribution in a full-scale Caroussel oxidation ditch with surface aeratio...A model for liquid-gas flow(MLGF),considering the free movement of liquid surface,was built to simulate the wastewater velocity field and gas distribution in a full-scale Caroussel oxidation ditch with surface aeration.It was calibrated and validated by field measurement data,and the calibrated parameters and sections were selected based on both model analysis and numerical computation.The simulated velocities of MLGF were compared to that of a model for wastewater-sludge flow(MWSF).The results show that the free liquid surface considered in MLGF improves the simulated velocity results of upper layer and surface.Moreover,distribution of gas volume fraction(GVF) simulated by MLGF was compared to dissolved oxygen(DO) measured in the oxidation ditch.It is shown that DO distribution is affected by many factors besides GVF distribution.展开更多
Stability of liquid metal film flow under gradient magnetic field is investigated. Three dimensional numerical simulations on magnetohydrodynamics （MHD） effect of free surface film flow were carried out, with emphas...Stability of liquid metal film flow under gradient magnetic field is investigated. Three dimensional numerical simulations on magnetohydrodynamics （MHD） effect of free surface film flow were carried out, with emphasis on the film thickness variation and its surface stability. Three different MHD phenomena of film flow were observed in the experiment, namely, retardant, rivulet and flat film flow. From our experiment and numerical simulation it can be concluded that flat film flow is a good choice for plasma-facing components （PFCs）展开更多
Study on pinching liquid filament in literature was reviewed. The breakup of liquid filaments under surface tension is governed by incompressible, two-dimensional (2-D), Navier-Stokes Equations. Surface tension was ex...Study on pinching liquid filament in literature was reviewed. The breakup of liquid filaments under surface tension is governed by incompressible, two-dimensional (2-D), Navier-Stokes Equations. Surface tension was expressed via a CSF (continuous surface force) model that ensures robustness and accuracy. A new surface reconstruction scheme, alternative phase integration (API) scheme was proposed to solve the kinematic equation,and was compared with other three referential schemes. A general-purpose computer program has been developed for simulating transient, 2-D, incompressible fluid flows with free surface of complex topology. The transient behavior of breaking Newtonian liquid filaments under surface tension was simulated successfully using the developed program.The initial wave growth predicted using API-VOF (volume of fluid) scheme was in good agreement with Rayleigh''s linear theory and one-dimensional (l-D) long-wave theory. Both long wave theory and two-dimensional (2-D) API-VOF model on fine meshes show that as time goes on, these waves pinch off large droplets separated by smaller satellite ones that decrease in size with decreasing wavelength. Self-similar structure during the breakup was found using 1-D and 2-D models, and three breakups were predicted for a typical case. The criterion of filament breaking predicted by the 2-D model is that the wavelength is longer than the circumference of a filament. The predicted sizes of main and satellite droplets were compared with published experimental measurements.展开更多
Fluids and structures impact is one of the common phenomena in nature, and it widely exists in engineering practice,including ship hydrodynamic slamming, wave impact on offshore platforms, plunging wave on coastal str...Fluids and structures impact is one of the common phenomena in nature, and it widely exists in engineering practice,including ship hydrodynamic slamming, wave impact on offshore platforms, plunging wave on coastal structures,emergency landing of aircrafts at sea as well as impact of ultra-cold droplets and ice lumps under aviation conditions.In this paper, a two dimensional (2-D) solver for Navier-Stokes equations is developed and applied in the numerical simulation of the impact on a rigid plate by a liquid square. The computational domain is discretized by Finite Volume Method (FVM). The Volume of Fluid (VOF) technique is used to track the free surface and the PiecewiseLinear Interface Construction (PLIC) is used for reconstruction. The Continuum Surface Force (CSF) model is used to account for the surface tension. The convective term and the diffusive term are upwind and centrally differenced respectively. The Inner Doubly Iterative Efficient Algorithm for Linked Equations (IDEAL) is used to decouple the pressure and velocity. Based on the proposed techniques, collapse of water column is simulated and convergence study is performed for the validation of the numerical solver. Then the impact of a free falling liquid body is simulated, and the effect of volume and initial height of the liquid body is analyzed. In addition, the impact on a plate with a liquid layer is also simulated to study the effect of falling height on a liquid floor.展开更多
With some popular tracking methods for free surface, simulations of several typical examples are carried out under various flow field conditions. The results show that the Smoothed Particle Hydrodynamics （SPH） metho...With some popular tracking methods for free surface, simulations of several typical examples are carried out under various flow field conditions. The results show that the Smoothed Particle Hydrodynamics （SPH） method is very suitable in simulating the flow problems with a free surface. A viscous liquid droplet with an initial velocity impacting on a solid surface is simulated based on the SPH method, and the surface tension is considered by searching the free surface particles, the initial impact effect is considered by using the artificial viscosity method, boundary virtual particles and image virtual particles are introduced to deal with the boundary problem, and the boundary defect can be identified quite well. The comparisons of simulated results and experimental photographs show that the SPH method can not only exactly simulate the spreading process and the rebound process of a liquid droplet impacting on a solid surface but also accurately track the free surface particles, simulate the free-surface flow and determine the shape of the free surface due to its particle nature.展开更多
Floating zone technique is a crucible-free process for growth of high quality single crystals. Unstable thermocapillary convection is a typical phenomenon during the process under microgravity. Therefore, it is very i...Floating zone technique is a crucible-free process for growth of high quality single crystals. Unstable thermocapillary convection is a typical phenomenon during the process under microgravity. Therefore, it is very important to investigate the instability of thermocapillary convection in liquid bridges with deformable free-surface under microgravity. In this works, the Volume of Fluid(VOF) method is employed to track the free-surface movement. The results are presented as the behavior of flow structure and temperature distribution of the molten zone. The impact of Marangoni number(Ma) is also investigated on free-surface deformation as well as the instability of thermocapillary convection. The free-surface exhibits a noticeable axisymmetric(but it is non-centrosymmetric) and elliptical shape along the circumferential direction. This specific surface shape presents a typical narrow ‘neck-shaped' structure with convex at two ends of the zone and concave at the mid-plane along the axial direction. At both θ = 0° and θ = 90°, the deformation ratio ξ increases rapidly with Ma at first, and then increases slowly. Moreover, the hydrothermal wave number m and the instability of thermocapillary convection increase with Ma.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.11874191)the Natural Science Foundation of Shandong Province,China(Grant No.ZR2016FM38)
文摘Liquid metal alloys(LMAs) are the potential candidates of thermal interface materials(TIMs) for electronics cooling.In the present work, buffer layers of Ag, Ti, Cu, Ni, Mo, and W were deposited on polished Cu plates by DC magnetron sputtering, the contact angles of de-ionized water and diiodomethane on the buffer layers were measured by an easy drop shape analyzer and the surface free energies(SFEs) of the buffer layers were calculated by the Owens–Wendt–Kaelble equation. Samples were prepared by sandwiching the filmed Cu plates and LMAs. The thermal properties of the samples were measured by laser flash analysis method. The SFE of the buffer layer has a strong influence on the interface heat transfer, whereas the measurement temperature has no obvious effect on the thermal properties of the samples. As the SFE of the buffer layer increases, the wettability, thermal diffusivity, and thermal conductivity are enhanced, and the thermal contact resistance is decreased.
文摘A liquid film flow over a flat plate is investigated by prescribing the unsteady interface velocity. With this prescribed surface velocity, the governing Navier–Stokes(NS) equations are transformed into a similarity ordinary differential equation, which is solved numerically. The flow characteristics is controlled by an unsteadiness parameter S and the flow direction parameter Λ. The results show that solutions only exist for a certain range of the unsteadiness parameter, i.e., S≤1 for Λ =-1 and S≤-2.815877 for Λ = 1. In the solution domain,the dimensionless liquid film thickness β decreases with S for both the cases. The wall shear stress increases with the decrease of S for Λ =-1. However, for Λ =-1 the shear stress magnitude first decreases and then increases with the decrease of S. There are no zero crossing points for the velocity profiles for both the cases. The profiles of velocity stay either positive or negative all the time, except for the wall zero velocity. Consequently,the vertical velocity becomes a monotonic function. To maintain the prescribed velocity, mass transpiration is generally needed, but for the shrinking film case it is possible to have an impermeable wall. The results are also an exact solution to the full NS equations.
基金supported by the National Natural Science Foundation of China(Grant No.50979059)
文摘Moving particle semi-implicit （MPS） method is a fully Lagrangian particle method which can easily solve problems with violent free surface. Although it has demonstrated its advantage in ocean engineering applications, it still has some defects to be improved. In this paper, MPS method is extended to the large eddy simulation （LES） by coupling with a sub-particle-scale （SPS） turbulence model. The SPS turbulence model turns into the Reynolds stress terms in the filtered momentum equation, and the Smagorinsky model is introduced to describe the Reynolds stress terms. Although MPS method has the advantage in the simulation of the free surface flow, a lot of non-free surface particles are treated as free surface particles in the original MPS model. In this paper, we use a new free surface tracing method and the key point is ＂neighbor particle＂. In this new method, the zone around each particle is divided into eight parts, and the particle will be treated as a free surface particle as long as there are no ＂neighbor particles＂ in any two parts of the zone. As the number density parameter judging method has a high efficiency for the free surface particles tracing, we combine it with the neighbor detected method. First, we select out the particles which may be mistreated with high probabilities by using the number density parameter judging method. And then we deal with these particles with the neighbor detected method. By doing this, the new mixed free surface tracing method can reduce the mistreatment problem efficiently. The serious pressure fluctuation is an obvious defect in MPS method, and therefore an area-time average technique is used in this paper to remove the pressure fluctuation with a quite good result. With these improvements, the modified MPS-LES method is applied to simulate liquid sloshing problems with large deforming free surface. Results show that the modified MPS-LES method can simulate the large deforming free surface easily. It can not only capture the large impact pressure accurately on rolling tank wall but also can generate all physical phenomena successfully. The good agreement between numerical and experimental results proves that the modified MPS-LES method is a good CFD methodology in free surface flow simulations.
文摘This study is concerned with describing the thermodynamic equilibrium of the saturated fluid with and without a free surface area A. Discussion of the role of A as system variable of the interface phase and an estimate of the ratio of the respective free energies of systems with and without A show that the system variables given by Gibbs suffice to describe the volumetric properties of the fluid. The well-known Gibbsian expressions for the internal energies of the two-phase fluid, namely for the vapor and for the condensate (liquid or solid), only differ with respect to the phase-specific volumes and . The saturation temperature T, vapor presssure p, and chemical potential are intensive parameters, each of which has the same value everywhere within the fluid, and hence are phase-independent quantities. If one succeeds in representing as a function of and , then the internal energies can also be described by expressions that only differ from one another with respect to their dependence on and . Here it is shown that can be uniquely expressed by the volume function . Therefore, the internal energies can be represented explicitly as functions of the vapor pressure and volumes of the saturated vapor and condensate and are absolutely determined. The hitherto existing problem of applied thermodynamics, calculating the internal energy from the measurable quantities T, p, , and , is thus solved. The same method applies to the calculation of the entropy, chemical potential, and heat capacity.
基金the Scientific Research Foundation of the State Education Ministry for Returned Overseas Chinese Scholar.
文摘A new equation for predicting surface tension is proposed based on the thermodynamic definition of surface tension and the expression of the Gibbs free energy of the system. Using the NRTL equation to represent the excess Gibbs free energy, a two-parameter surface tension equation is derived. The feasibility of the new equation has been tested in terms of 124 binary and 16 multicomponent systems(13-ternary and 3-quaternary) with absolute relative deviations of 0.59% and 1.55% respectively. This model is also predictive for the temperature dependence of surface tension of liquid mixtures. It is shown that, with good accuracy, this equation is simple and reliable for practical use.
文摘Up to now, no a real full-cover liquid metal (LM) free surface flow have been successfully used in magnetic fusion devices as MHD instability and unavoidable rivulet flow. Recently, after we carried out a guidable free curve-surface flow on theoretically and experimentally, seeking for other way to get a full-cover free surface flow is also in implementing. The superficial layer MHD effect in free surface flow is experimentally observed. After compared and analyzed the characteristic parameters of the free surface flow, the conditions of full-cover free surface flow are found. Meanwhile, the new two parameters of surface cover ratio and rivulet flow index are introduced to characterize the flowing characteristic of the full-cover free surface flow under magnetic field. According to the analysis rule, for different liquid metal, there are the different unique conditions to meet full-cover free surface flow under magnetic field. This may be a way to solve free surface flow major MHD key issue for LM PFCs.
文摘In this study,two dimensional unsteady flows of cylinder and cylinder with additional fairing close to a free surface were numerically investigated.The governing momentum equations were solved by using the Semi Implicit Method for Pressure Linked Equations(SIMPLE).The Volume of Fluid(VOF)method applied to simulate a free surface.Non-uniform grid structures were used in the simulation with denser grids near the cylinder.Under the conditions of Reynolds number 150624,271123,210874 and 331373,the cylinders were simulated with different depths of invasion.It was shown that the flow characteristics were influenced by submergence depth and Reynolds numbers.When the cylinder close to the free surface,the drag coefficient,lift coefficient and Strouhal numbers will increase due to the effect of free liquid surface on vortex shedding.With additional fairing,can effectively reduce the influence of the free surface on the drag coefficient.Fairing will reduce lift coefficient at high Reynolds numbers,but increase lift coefficient when Reynolds numbers are small.Fairing can effectively reduce Strouhal numbers,thus can well suppress the vortex induced vibration.
基金Project supported by Visiting Scholar Foundation of Key Laboratory of the Resources Exploitation and Environmental Disaster Control Engineering in Southwest China (Chongqing University),Ministry of Education,China
文摘A model for liquid-gas flow(MLGF),considering the free movement of liquid surface,was built to simulate the wastewater velocity field and gas distribution in a full-scale Caroussel oxidation ditch with surface aeration.It was calibrated and validated by field measurement data,and the calibrated parameters and sections were selected based on both model analysis and numerical computation.The simulated velocities of MLGF were compared to that of a model for wastewater-sludge flow(MWSF).The results show that the free liquid surface considered in MLGF improves the simulated velocity results of upper layer and surface.Moreover,distribution of gas volume fraction(GVF) simulated by MLGF was compared to dissolved oxygen(DO) measured in the oxidation ditch.It is shown that DO distribution is affected by many factors besides GVF distribution.
基金National Natural Science Foundation of China(No.B10275019)
文摘Stability of liquid metal film flow under gradient magnetic field is investigated. Three dimensional numerical simulations on magnetohydrodynamics （MHD） effect of free surface film flow were carried out, with emphasis on the film thickness variation and its surface stability. Three different MHD phenomena of film flow were observed in the experiment, namely, retardant, rivulet and flat film flow. From our experiment and numerical simulation it can be concluded that flat film flow is a good choice for plasma-facing components （PFCs）
基金MPR Lab.,Inst.of Proc.Eng.,Chinese Academy of Sciences.
文摘Study on pinching liquid filament in literature was reviewed. The breakup of liquid filaments under surface tension is governed by incompressible, two-dimensional (2-D), Navier-Stokes Equations. Surface tension was expressed via a CSF (continuous surface force) model that ensures robustness and accuracy. A new surface reconstruction scheme, alternative phase integration (API) scheme was proposed to solve the kinematic equation,and was compared with other three referential schemes. A general-purpose computer program has been developed for simulating transient, 2-D, incompressible fluid flows with free surface of complex topology. The transient behavior of breaking Newtonian liquid filaments under surface tension was simulated successfully using the developed program.The initial wave growth predicted using API-VOF (volume of fluid) scheme was in good agreement with Rayleigh''s linear theory and one-dimensional (l-D) long-wave theory. Both long wave theory and two-dimensional (2-D) API-VOF model on fine meshes show that as time goes on, these waves pinch off large droplets separated by smaller satellite ones that decrease in size with decreasing wavelength. Self-similar structure during the breakup was found using 1-D and 2-D models, and three breakups were predicted for a typical case. The criterion of filament breaking predicted by the 2-D model is that the wavelength is longer than the circumference of a filament. The predicted sizes of main and satellite droplets were compared with published experimental measurements.
基金This study was financially supported by the Equipment Pre-Research Field Foundation(Grant Nos.61402100201,6142204180408,and 6142407180108)the National Natural Science Foundation of China(Grant Nos.51579052 and 51679045).
文摘Fluids and structures impact is one of the common phenomena in nature, and it widely exists in engineering practice,including ship hydrodynamic slamming, wave impact on offshore platforms, plunging wave on coastal structures,emergency landing of aircrafts at sea as well as impact of ultra-cold droplets and ice lumps under aviation conditions.In this paper, a two dimensional (2-D) solver for Navier-Stokes equations is developed and applied in the numerical simulation of the impact on a rigid plate by a liquid square. The computational domain is discretized by Finite Volume Method (FVM). The Volume of Fluid (VOF) technique is used to track the free surface and the PiecewiseLinear Interface Construction (PLIC) is used for reconstruction. The Continuum Surface Force (CSF) model is used to account for the surface tension. The convective term and the diffusive term are upwind and centrally differenced respectively. The Inner Doubly Iterative Efficient Algorithm for Linked Equations (IDEAL) is used to decouple the pressure and velocity. Based on the proposed techniques, collapse of water column is simulated and convergence study is performed for the validation of the numerical solver. Then the impact of a free falling liquid body is simulated, and the effect of volume and initial height of the liquid body is analyzed. In addition, the impact on a plate with a liquid layer is also simulated to study the effect of falling height on a liquid floor.
基金Project supported by the National Natural Science Foundation of China(Grant No.51079095)the Science Fund for Creative Research Groups of the National Natural Science Foundation of China(Grant No.51021004)
文摘With some popular tracking methods for free surface, simulations of several typical examples are carried out under various flow field conditions. The results show that the Smoothed Particle Hydrodynamics （SPH） method is very suitable in simulating the flow problems with a free surface. A viscous liquid droplet with an initial velocity impacting on a solid surface is simulated based on the SPH method, and the surface tension is considered by searching the free surface particles, the initial impact effect is considered by using the artificial viscosity method, boundary virtual particles and image virtual particles are introduced to deal with the boundary problem, and the boundary defect can be identified quite well. The comparisons of simulated results and experimental photographs show that the SPH method can not only exactly simulate the spreading process and the rebound process of a liquid droplet impacting on a solid surface but also accurately track the free surface particles, simulate the free-surface flow and determine the shape of the free surface due to its particle nature.
基金supported by National Natural Science Foundation of China(Grant Number 51276089)
文摘Floating zone technique is a crucible-free process for growth of high quality single crystals. Unstable thermocapillary convection is a typical phenomenon during the process under microgravity. Therefore, it is very important to investigate the instability of thermocapillary convection in liquid bridges with deformable free-surface under microgravity. In this works, the Volume of Fluid(VOF) method is employed to track the free-surface movement. The results are presented as the behavior of flow structure and temperature distribution of the molten zone. The impact of Marangoni number(Ma) is also investigated on free-surface deformation as well as the instability of thermocapillary convection. The free-surface exhibits a noticeable axisymmetric(but it is non-centrosymmetric) and elliptical shape along the circumferential direction. This specific surface shape presents a typical narrow ‘neck-shaped' structure with convex at two ends of the zone and concave at the mid-plane along the axial direction. At both θ = 0° and θ = 90°, the deformation ratio ξ increases rapidly with Ma at first, and then increases slowly. Moreover, the hydrothermal wave number m and the instability of thermocapillary convection increase with Ma.
