Topology optimization of thermal-fluid coupling problems has received widespread attention.This article proposes a novel topology optimization method for laminar two-fluid heat exchanger design.The proposed method uti...Topology optimization of thermal-fluid coupling problems has received widespread attention.This article proposes a novel topology optimization method for laminar two-fluid heat exchanger design.The proposed method utilizes an artificial density field to create two permeability interpolation functions that exhibit opposing trends,ensuring separation between the two fluid domains.Additionally,a Gaussian function is employed to construct an interpolation function for the thermal conductivity coefficient.Furthermore,a computational program has been developed on the OpenFOAM platform for the topology optimization of two-fluid heat exchangers.This program leverages parallel computing,significantly reducing the time required for the topology optimization process.To enhance computational speed and reduce the number of constraint conditions,we replaced the conventional pressure drop constraint condition in the optimization problem with a pressure inlet/outlet boundary condition.The 3D optimization results demonstrate the characteristic features of a surface structure,providing valuable guidance for designing heat exchangers that achieve high heat exchange efficiency while minimizing excessive pressure loss.At the same time,a new structure appears in large-scale topology optimization,which proves the effectiveness and stability of the topology optimization program written in this paper in large-scale calculation.展开更多
Climate change is a reality. The burning of fossil fuels from oil, natural gas and coal is responsible for much of the pollution and the increase in the planet’s average temperature, which has raised discussions on t...Climate change is a reality. The burning of fossil fuels from oil, natural gas and coal is responsible for much of the pollution and the increase in the planet’s average temperature, which has raised discussions on the subject, given the emergencies related to climate. An energy transition to clean and renewable sources is necessary and urgent, but it will not be quick. In this sense, increasing the efficiency of oil extraction from existing sources is crucial, to avoid waste and the drilling of new wells. The purpose of this work was to add diffusive and dispersive terms to the Buckley-Leverett equation in order to incorporate extra phenomena in the temporal evolution between the water-oil and oil-water transitions in the pipeline. For this, the modified Buckley-Leverett equation was discretized via essentially weighted non-oscillatory schemes, coupled with a three-stage Runge-Kutta and a fourth-order centered finite difference methods. Then, computational simulations were performed and the results showed that new features emerge in the transitions, when compared to classical simulations. For instance, the dispersive term inhibits the diffusive term, adding oscillations, which indicates that the absorption of the fluid by the porous medium occurs in a non-homogeneous manner. Therefore, based on research such as this, decisions can be made regarding the replacement of the porous medium or the insertion of new components to delay the replacement.展开更多
Computational fluid dynamics(CFD)has become a valuable tool to study the complex gas-solid hydrodynamics in the circulating fluidized bed(CFB).Based on the two fluid model(TFM)under the Eulerian-Eulerian framework and...Computational fluid dynamics(CFD)has become a valuable tool to study the complex gas-solid hydrodynamics in the circulating fluidized bed(CFB).Based on the two fluid model(TFM)under the Eulerian-Eulerian framework and the dense discrete phase model(DDPM)under the Eulerian-Lagrangian framework,this work conducts the comparative study of the gas-solid hydrodynamics in a CFB riser by these two different models.Results show that DDPM could be used to predict gas-solid hydrodynamics in the circulating fluidized bed,and there are differences between TFM and DDPM,especially in the radial distribution profiles of solid phase.Sensitivity analysis results show that the gas-solid drag model exhibits significant effects on the results for both the two models.The specularity coefficient and the restitution coefficient in the TFM,as well as the reflection coefficient and the parcel number in the DDPM,exhibit less impact on the simulated results.展开更多
The flow characteristics in a spouted-fluid bed differ from those in spouted or fluidized beds because of the injection of the spouting gas and the introduction of a fluidizing gas. The flow behavior of gas-solid phas...The flow characteristics in a spouted-fluid bed differ from those in spouted or fluidized beds because of the injection of the spouting gas and the introduction of a fluidizing gas. The flow behavior of gas-solid phases was predicted using the Eulerian-Eulerian two-fluid model （TFM） approach with kinetic theory for granular flow to obtain the flow patterns in spouted-fluid beds. The gas flux and gas incident angle have a significant influence on the porosity and particle concentration in gas-solid spouted-fluid beds. The fluidizing gas flux affects the flow behavior of particles in the fountain. In the spouted-fluid bed, the solids volume fraction is low in the spout and high in the annulus. However, the solids volume fraction is reduced near the wall.展开更多
Many new forms of Boussinesq-type equations have been developed to extend the range of applicability of the classical Boussinesq equations to deeper water in the Study of the surface waves. One approach was used by Nw...Many new forms of Boussinesq-type equations have been developed to extend the range of applicability of the classical Boussinesq equations to deeper water in the Study of the surface waves. One approach was used by Nwogu （1993. J. Wtrw. Port Coastal and Oc. Eng. 119, 618-638） to improve the linear dispersion characteristics of the classical Boussinesq equations by using the velocity at an arbitrary level as the velocity variable in derived equations and obtain a new form of Boussinesq-type equations, in which the dispersion property can be optimized by choosing the velocity variable at an adequate level. In this paper, a set of Boussinesq-type equations describing the motions of the interracial waves propagating alone the interface between two homogeneous incompressible and inviscid fluids of different densities with a free surface and a variable water depth were derived using a method similar to that used by Nwogu （1993. J. Wtrw. Port Coastal and Oc. Eng. 119, 618-638） for surface waves. The equations were expressed in terms of the displacements of free surface and density-interface, and the velocity vectors at arbitrary vertical locations in the upper layer and the lower layer （or depth-averaged velocity vector across each layer） of a two-layer fluid. As expected, the equations derived in the present work include as special cases those obtained by Nwogu （1993, J. Wtrw. Port Coastal and Oc. Eng. 119, 618-638） and Peregrine （1967, J. Fluid Mech. 27, 815-827） for surface waves when the density of the upper fluid is taken as zero.展开更多
In the present paper, we endeavor to accomplish a diagram, which demarcates the validity ranges for interfacial wave theories in a two-layer system, to meet the needs of design in ocean engineering. On the basis of th...In the present paper, we endeavor to accomplish a diagram, which demarcates the validity ranges for interfacial wave theories in a two-layer system, to meet the needs of design in ocean engineering. On the basis of the available solutions of periodic and solitary waves, we propose a guideline as principle to identify the validity regions of the interfacial wave theories in terms of wave period T, wave height H, upper layer thickness dl, and lower layer thick-ness d2, instead of only one parameter-water depth d as in the water surface wave circumstance. The diagram proposed here happens to be Le Mehaute＇s plot for free surface waves if water depth ratio r= d1/d2 approaches to infinity and the upper layer water density p1 to zero. On the contrary, the diagram for water surface waves can be used for two-layer interfacial waves if gravity acceleration g in it is replaced by the reduced gravity defined in this study under the condition of σ=（P2 - Pl）/P2 → 1.0 and r 〉 1.0. In the end, several figures of the validity ranges for various interfacial wavetheories in the two-layer fluid are given and compared with the results for surface waves.展开更多
The hydroelastic response of a circular, very large floating structure(VLFS), idealized as a floating circular elastic thin plate, is investigated for the case of time-harmonic incident waves of the surface and interf...The hydroelastic response of a circular, very large floating structure(VLFS), idealized as a floating circular elastic thin plate, is investigated for the case of time-harmonic incident waves of the surface and interfacial wave modes, of a given wave frequency, on a two-layer fluid of finite and constant depth. In linear potential-flow theory, with the aid of angular eigenfunction expansions, the diffraction potentials can be expressed by the Bessel functions. A system of simultaneous equations is derived by matching the velocity and the pressure between the open-water and the platecovered regions, while incorporating the edge conditions of the plate. Then the complex nested series are simplified by utilizing the orthogonality of the vertical eigenfunctions in the open-water region. Numerical computations are presented to investigate the effects of different physical quantities, such as the thickness of the plate, Young’s modulus, the ratios of the densities and of the layer depths, on the dispersion relations of the flexural-gravity waves for the two-layer fluid. Rapid convergence of the method is observed, but is slower at higher wave frequency. At high frequency, it is found that there is some energy transferred from the interfacial mode to the surface mode.展开更多
The derivation of Green function in a two-layer fluid model has been treated in different ways. In a two-layer fluid with the upper layer having a free surface, there exist two modes of waves propagating due to the fr...The derivation of Green function in a two-layer fluid model has been treated in different ways. In a two-layer fluid with the upper layer having a free surface, there exist two modes of waves propagating due to the free surface and the interface. This paper is concerned with the derivation of Green functions in the three dimensional case of a stationary source oscillating. The source point is located either in the upper or lower part of a two-layer fluid of finite depth. The derivation is carried out by the method of singularities. This method has an advantage in that it involves representing the potential as a sum of singularities or multipoles placed within any structures being present. Furthermore, experience shows that the systems of equations resulted from using a singularity method possess excellent convergence characteristics and only a few equations are needed to obtain accurate numerical results. Validation is done by showing that the derived two-layer Green function can be reduced to that of a single layer of finite depth or that the upper Green function coincides with that of the lower, for each case. The effect of the density on the internal waves is demonstrated. Also, it is shown how the surface and internal wave amplitudes are compared for both the wave modes. The fluid in this case is considered to be inviscid and incompressible and the flow is irrotational.展开更多
A quite general coupled variable coefficient modified KdV (VCmKdV) equation in a two-layer fluid systemis derived by means of the reductive perturbation method.Making use of the CK's direct method,some similarityr...A quite general coupled variable coefficient modified KdV (VCmKdV) equation in a two-layer fluid systemis derived by means of the reductive perturbation method.Making use of the CK's direct method,some similarityreductions of the coupled VCmKdV equation are obtained and their corresponding group explanations are discussed.Some exact solutions of the coupled equations are also presented.展开更多
RH vacuum degasser is a very important secondary refining device in the production of high quality steels. The flow field of molten steel in RH system plays a significant role in determining productivity of the equipm...RH vacuum degasser is a very important secondary refining device in the production of high quality steels. The flow field of molten steel in RH system plays a significant role in determining productivity of the equipment. The homogeneous model and VOF method were often used to predict the flow field in RH system, but these kinds of models simplified the interaction between gas bubbles and molten steel. In the present work, a numerical model of a whole RH system, including vacuum degasser, immersed legs and ladle,was built based on gas-liquid two-fluid model, and it could be used to analyze the interaction between argon bubbles and molten steel, to understand the effect of the bubble size to the flow field.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
A previous study （Song. 2004. Geophys Res Lett, 31 （15）：L15302） of the second-order solutions for random interracial waves is extended in a constant depth, two-layer fluid system with a rigid lid is extended into...A previous study （Song. 2004. Geophys Res Lett, 31 （15）：L15302） of the second-order solutions for random interracial waves is extended in a constant depth, two-layer fluid system with a rigid lid is extended into a more general case of two-layer fluid with a top free surface. The rigid boundary condition on the upper surface is replaced by the kinematical and dynamical boundary conditions of a free surface, and the equations describing the random displacements of free surface, density-interface and the associated velocity potentials in the two-layer fluid are solved to the second order using the same expansion technology as that of Song （2004. Geophys Res Lett, 31 （15）：L15302）. The results show that the interface and the surface will oscillate synchronously, and the wave fields to the first-order both at the free surface and at the density-interface are made up of a linear superposition of many waves with different amplitudes, wave numbers and frequencies. The second-order solutions describe the second-order wave-wave interactions of the surface wave components, the interface wave components and among the surface and the interface wave components. The extended solutions also include special cases obtained by Thorpe for progressive interracial waves （Thorpe. 1968a.Trans R Soc London, 263A：563～614） and standing interracial waves （Thorpe. 1968b. J Fluid Mech, 32：489-528） for the two-layer fluid with a top free surface. Moreover, the solutions reduce to those derived for random surface waves by Sharma and Dean （1979.Ocean Engineering Rep 20） if the density of the upper layer is much smaller than that of the lower layer.展开更多
Interfacial waves and wave-induced tangential stress are studied for geostrophic small amplitude waves of two-layer fluid with a top free surface and a fiat bottom. The solutions were deduced from the general form of ...Interfacial waves and wave-induced tangential stress are studied for geostrophic small amplitude waves of two-layer fluid with a top free surface and a fiat bottom. The solutions were deduced from the general form of linear fluid dynamic equations of two-layer fluid under the f-plane approximation, and wave-induced tangential stress were estimated based on the solutions obtained. As expected, the solutions derived from the present work include as special cases those obtained by Sun et al. （2004. Science in China, Ser. D, 47（12）： 1147-1154） for geostrophic small amplitude surface wave solutions and wave-induced tangential stress if the density of the upper layer is much smaller than that of the lower layer. The results show that the interface and the surface will oscillate synchronously, and the influence of the earth＇s rotation both on the surface wave solutions and the interfacial wave solutions should be considered.展开更多
Interracial waves propagating along the interface between a three-dimensional two-fluid system with a rigid upper boundary and an uneven bottom are considered. There is a light fluid layer overlying a heavier one in t...Interracial waves propagating along the interface between a three-dimensional two-fluid system with a rigid upper boundary and an uneven bottom are considered. There is a light fluid layer overlying a heavier one in the system, and a small density difference exists between the two layers. A set of higher-order Boussinesq-type equations in terms of the depth-averaged velocities accounting for stronger nonlinearity are derived. When the small parameter measuring frequency dispersion keeping up to lower-order and full nonlinearity are considered, the equations include the Choi and Camassa＇s results （1999）. The enhanced equations in terms of the depth-averaged velocities are obtained by applying the enhancement technique introduced by Madsen et al. （1991） and Schaffer and Madsen （1995a）. It is noted that the equations derived from the present study include, as special cases, those obtained by Madsen and Schaffer （1998）. By comparison with the dispersion relation of the linear Stokes waves, we found that the dispersion relation is more improved than Choi and Camassa＇s （1999） results, and the applicable scope of water depth is deeper.展开更多
By method of the Laplace transform, this arti- cle presents semi-analytical solutions for transient electro- osmotic and pressure-driven flows （EOF/PDF） of two-layer fluids between microparallel plates. The lineariz...By method of the Laplace transform, this arti- cle presents semi-analytical solutions for transient electro- osmotic and pressure-driven flows （EOF/PDF） of two-layer fluids between microparallel plates. The linearized Poisson- Boltzmann equation and the Cauchy momentum equation have been solved in this article. At the interface, the Maxwell stress is included as the boundary condition. By numerical computations of the inverse Laplace transform, the effects of dielectric constant ratio e, density ratio p, pressure ratio p, viscosity ratioμ of layer II to layer I, interface zeta potential difference △ψ, interface charge density jump Q, the ratios of maximum electro-osmotic velocity to pressure velocity , and the normalized pressure gradient B on transient veloc- ity amplitude are presented.We find the velocity amplitude becomes large with the interface zeta potential difference and becomes small with the increase of the viscosity. The ve- locity will be large with the increases of dielectric constant ratio; the density ratio almost does not influence the EOF ve- locity. Larger interface charge density jump leads to a strong jump of velocity at the interface. Additionally, the effects of the thickness of fluid layers （hi and h2） and pressure gradient on the velocity are also investigated.展开更多
Based on the two-phase model (Eulerian-Eulerian model), the three dimensional fluid flow in water and that liquid steel systems stirred by one or two multiple gas jets are simulated. In the Eulerian-Eulerian two-phase...Based on the two-phase model (Eulerian-Eulerian model), the three dimensional fluid flow in water and that liquid steel systems stirred by one or two multiple gas jets are simulated. In the Eulerian-Eulerian two-phase model, the gas and the liquid phase are considered to be two different continuous fluids interacting with each other through the finite inter-phase areas. The exchange between the phases is represented by source terms in conversation equations. Turbulence is assumed to be a property of the liquid phase. A new turbulence modification - model is introduced to consider the bubbles movement contribution to and . The dispersion of phases due to turbulence is represented by introducing a diffusion term in mass conservation equation. The mathematical simulation agrees well with the experiment results. The study results indicate that the distance of two nozzles has big effect on fluid flow behavior in the vessel. Using two gas injection nozzles at the half radii of one diameter of the bottom generates a much better mixing than with one nozzle under the condition of the same total gas flow rate.展开更多
This paper provides the exact solutions for the fully developed two layer pressure driven flows of incompressible Phan-Thien-Tanner fluids in a horizontal cylindrical pipe. Exact equations are formulated and solved fo...This paper provides the exact solutions for the fully developed two layer pressure driven flows of incompressible Phan-Thien-Tanner fluids in a horizontal cylindrical pipe. Exact equations are formulated and solved for important kinematic properties, such as, velocity profiles, normal and shear stresses, total volume fluxes through a circular cross-section and average velocities. Graphical results are provided and discussed for the different flow parameters. A comparison of Upper Convected Maxwell (UCM), Linear Phan-Thien-Tanner (LPTT) and Exponential Phan-Thien-Tanner (EPTT) shows that UCM is a low viscosity fluid as compared to LPTT, and EPTT and LPTT is lighter than EPTT.展开更多
The validity of Navier’s partial slip condition is investigated by studying the oscillatory flow in a coated channel.The two-fluid model is used to solve the unsteady viscous equations exactly.Partial slip is experie...The validity of Navier’s partial slip condition is investigated by studying the oscillatory flow in a coated channel.The two-fluid model is used to solve the unsteady viscous equations exactly.Partial slip is experienced by the core fluid.It is found that Naviers condition does not hold for an unsteady core fluid.展开更多
This paper considers interfacial waves propagating along the interface between a two-dimensional two-fluid with a flat bottom and a rigid upper boundary. There is a light fluid layer overlying a heavier one in the sys...This paper considers interfacial waves propagating along the interface between a two-dimensional two-fluid with a flat bottom and a rigid upper boundary. There is a light fluid layer overlying a heavier one in the system, and a small density difference exists between the two layers. It just focuses on the weakly non-linear small amplitude waves by introducing two small independent parameters： the nonlinearity ratio ε, represented by the ratio of amplitude to depth, and the dispersion ratio μ, represented by the square of the ratio of depth to wave length, which quantify the relative importance of nonlinearity and dispersion. It derives an extended KdV equation of the interfacial waves using the method adopted by Dullin et al in the study of the surface waves when considering the order up to O（μ^2）. As expected, the equation derived from the present work includes, as special cases, those obtained by Dullin et al for surface waves when the surface tension is neglected. The equation derived using an alternative method here is the same as the equation presented by Choi and Camassa. Also it solves the equation by borrowing the method presented by Marchant used for surface waves, and obtains its asymptotic solitary wave solutions when the weakly nonlinear and weakly dispersive terms are balanced in the extended KdV equation.展开更多
In this paper, the nonlinear dynamical behavior of two coupled pipes conveying pulsating fluid is studied. The connection between the two pipes is considered as a distributed linear spring. Based on this consideration...In this paper, the nonlinear dynamical behavior of two coupled pipes conveying pulsating fluid is studied. The connection between the two pipes is considered as a distributed linear spring. Based on this consideration, the equations of motion of the coupled two-pipe system are obtained. The two coupled nonlinear partial differential equations, discretized using the fourth- order Galerkin method, are solved by a fourth-order Runge-Kutta integration algorithm. Results show that the connection stiffness has a significant effect on the dynamical behavior of the coupled system. It is found that for some parameter values the motion types of the two pipes might be synchronous.展开更多
基金supported by the Aeronautical Science Foundation of China(Grant No.2020Z009063001)the Fundamental Research Funds for the Central Universities(Grant No.DUT22GF303).
文摘Topology optimization of thermal-fluid coupling problems has received widespread attention.This article proposes a novel topology optimization method for laminar two-fluid heat exchanger design.The proposed method utilizes an artificial density field to create two permeability interpolation functions that exhibit opposing trends,ensuring separation between the two fluid domains.Additionally,a Gaussian function is employed to construct an interpolation function for the thermal conductivity coefficient.Furthermore,a computational program has been developed on the OpenFOAM platform for the topology optimization of two-fluid heat exchangers.This program leverages parallel computing,significantly reducing the time required for the topology optimization process.To enhance computational speed and reduce the number of constraint conditions,we replaced the conventional pressure drop constraint condition in the optimization problem with a pressure inlet/outlet boundary condition.The 3D optimization results demonstrate the characteristic features of a surface structure,providing valuable guidance for designing heat exchangers that achieve high heat exchange efficiency while minimizing excessive pressure loss.At the same time,a new structure appears in large-scale topology optimization,which proves the effectiveness and stability of the topology optimization program written in this paper in large-scale calculation.
文摘Climate change is a reality. The burning of fossil fuels from oil, natural gas and coal is responsible for much of the pollution and the increase in the planet’s average temperature, which has raised discussions on the subject, given the emergencies related to climate. An energy transition to clean and renewable sources is necessary and urgent, but it will not be quick. In this sense, increasing the efficiency of oil extraction from existing sources is crucial, to avoid waste and the drilling of new wells. The purpose of this work was to add diffusive and dispersive terms to the Buckley-Leverett equation in order to incorporate extra phenomena in the temporal evolution between the water-oil and oil-water transitions in the pipeline. For this, the modified Buckley-Leverett equation was discretized via essentially weighted non-oscillatory schemes, coupled with a three-stage Runge-Kutta and a fourth-order centered finite difference methods. Then, computational simulations were performed and the results showed that new features emerge in the transitions, when compared to classical simulations. For instance, the dispersive term inhibits the diffusive term, adding oscillations, which indicates that the absorption of the fluid by the porous medium occurs in a non-homogeneous manner. Therefore, based on research such as this, decisions can be made regarding the replacement of the porous medium or the insertion of new components to delay the replacement.
基金Financial support by National Natural Foundation Fund of China(No.J1770040,Nu.J1070042)is gldtefully dcklluwledged.
文摘Computational fluid dynamics(CFD)has become a valuable tool to study the complex gas-solid hydrodynamics in the circulating fluidized bed(CFB).Based on the two fluid model(TFM)under the Eulerian-Eulerian framework and the dense discrete phase model(DDPM)under the Eulerian-Lagrangian framework,this work conducts the comparative study of the gas-solid hydrodynamics in a CFB riser by these two different models.Results show that DDPM could be used to predict gas-solid hydrodynamics in the circulating fluidized bed,and there are differences between TFM and DDPM,especially in the radial distribution profiles of solid phase.Sensitivity analysis results show that the gas-solid drag model exhibits significant effects on the results for both the two models.The specularity coefficient and the restitution coefficient in the TFM,as well as the reflection coefficient and the parcel number in the DDPM,exhibit less impact on the simulated results.
基金supported by the Natural Science Foundation of China through Grant No.21076043 and No.51206020Province in Heilongjiang's Outstanding Youth Science Foundation(JC201202)Program for New Century Excellent Talents in Heilongjiang Provincial University(1252-NCET-010)
文摘The flow characteristics in a spouted-fluid bed differ from those in spouted or fluidized beds because of the injection of the spouting gas and the introduction of a fluidizing gas. The flow behavior of gas-solid phases was predicted using the Eulerian-Eulerian two-fluid model （TFM） approach with kinetic theory for granular flow to obtain the flow patterns in spouted-fluid beds. The gas flux and gas incident angle have a significant influence on the porosity and particle concentration in gas-solid spouted-fluid beds. The fluidizing gas flux affects the flow behavior of particles in the fountain. In the spouted-fluid bed, the solids volume fraction is low in the spout and high in the annulus. However, the solids volume fraction is reduced near the wall.
文摘Many new forms of Boussinesq-type equations have been developed to extend the range of applicability of the classical Boussinesq equations to deeper water in the Study of the surface waves. One approach was used by Nwogu （1993. J. Wtrw. Port Coastal and Oc. Eng. 119, 618-638） to improve the linear dispersion characteristics of the classical Boussinesq equations by using the velocity at an arbitrary level as the velocity variable in derived equations and obtain a new form of Boussinesq-type equations, in which the dispersion property can be optimized by choosing the velocity variable at an adequate level. In this paper, a set of Boussinesq-type equations describing the motions of the interracial waves propagating alone the interface between two homogeneous incompressible and inviscid fluids of different densities with a free surface and a variable water depth were derived using a method similar to that used by Nwogu （1993. J. Wtrw. Port Coastal and Oc. Eng. 119, 618-638） for surface waves. The equations were expressed in terms of the displacements of free surface and density-interface, and the velocity vectors at arbitrary vertical locations in the upper layer and the lower layer （or depth-averaged velocity vector across each layer） of a two-layer fluid. As expected, the equations derived in the present work include as special cases those obtained by Nwogu （1993, J. Wtrw. Port Coastal and Oc. Eng. 119, 618-638） and Peregrine （1967, J. Fluid Mech. 27, 815-827） for surface waves when the density of the upper fluid is taken as zero.
基金the Knowledge Innovation Project of CAS(KJCX-YW-L02)the National 863 Project of China(2006AAO9A103-4)+1 种基金China National Oil Corporation in Beijing(CNOOC)the National Natural Science Foundation of China(10672056).
文摘In the present paper, we endeavor to accomplish a diagram, which demarcates the validity ranges for interfacial wave theories in a two-layer system, to meet the needs of design in ocean engineering. On the basis of the available solutions of periodic and solitary waves, we propose a guideline as principle to identify the validity regions of the interfacial wave theories in terms of wave period T, wave height H, upper layer thickness dl, and lower layer thick-ness d2, instead of only one parameter-water depth d as in the water surface wave circumstance. The diagram proposed here happens to be Le Mehaute＇s plot for free surface waves if water depth ratio r= d1/d2 approaches to infinity and the upper layer water density p1 to zero. On the contrary, the diagram for water surface waves can be used for two-layer interfacial waves if gravity acceleration g in it is replaced by the reduced gravity defined in this study under the condition of σ=（P2 - Pl）/P2 → 1.0 and r 〉 1.0. In the end, several figures of the validity ranges for various interfacial wavetheories in the two-layer fluid are given and compared with the results for surface waves.
基金sponsored by the National Basic Research Program of China(973 Program,Grant No.2014CB046203)the National Natural Science Foundation of China(Grant No.11072140)
文摘The hydroelastic response of a circular, very large floating structure(VLFS), idealized as a floating circular elastic thin plate, is investigated for the case of time-harmonic incident waves of the surface and interfacial wave modes, of a given wave frequency, on a two-layer fluid of finite and constant depth. In linear potential-flow theory, with the aid of angular eigenfunction expansions, the diffraction potentials can be expressed by the Bessel functions. A system of simultaneous equations is derived by matching the velocity and the pressure between the open-water and the platecovered regions, while incorporating the edge conditions of the plate. Then the complex nested series are simplified by utilizing the orthogonality of the vertical eigenfunctions in the open-water region. Numerical computations are presented to investigate the effects of different physical quantities, such as the thickness of the plate, Young’s modulus, the ratios of the densities and of the layer depths, on the dispersion relations of the flexural-gravity waves for the two-layer fluid. Rapid convergence of the method is observed, but is slower at higher wave frequency. At high frequency, it is found that there is some energy transferred from the interfacial mode to the surface mode.
基金supported by the National Natural Science Foundation of China (Grant No. 50779008)
文摘The derivation of Green function in a two-layer fluid model has been treated in different ways. In a two-layer fluid with the upper layer having a free surface, there exist two modes of waves propagating due to the free surface and the interface. This paper is concerned with the derivation of Green functions in the three dimensional case of a stationary source oscillating. The source point is located either in the upper or lower part of a two-layer fluid of finite depth. The derivation is carried out by the method of singularities. This method has an advantage in that it involves representing the potential as a sum of singularities or multipoles placed within any structures being present. Furthermore, experience shows that the systems of equations resulted from using a singularity method possess excellent convergence characteristics and only a few equations are needed to obtain accurate numerical results. Validation is done by showing that the derived two-layer Green function can be reduced to that of a single layer of finite depth or that the upper Green function coincides with that of the lower, for each case. The effect of the density on the internal waves is demonstrated. Also, it is shown how the surface and internal wave amplitudes are compared for both the wave modes. The fluid in this case is considered to be inviscid and incompressible and the flow is irrotational.
基金The project supported by National Natural Science Foundation of China under Grant Nos.10547124,10475055,and 90503006the Youth Foundation of Shanghai Jiao Tong University
文摘A quite general coupled variable coefficient modified KdV (VCmKdV) equation in a two-layer fluid systemis derived by means of the reductive perturbation method.Making use of the CK's direct method,some similarityreductions of the coupled VCmKdV equation are obtained and their corresponding group explanations are discussed.Some exact solutions of the coupled equations are also presented.
文摘RH vacuum degasser is a very important secondary refining device in the production of high quality steels. The flow field of molten steel in RH system plays a significant role in determining productivity of the equipment. The homogeneous model and VOF method were often used to predict the flow field in RH system, but these kinds of models simplified the interaction between gas bubbles and molten steel. In the present work, a numerical model of a whole RH system, including vacuum degasser, immersed legs and ladle,was built based on gas-liquid two-fluid model, and it could be used to analyze the interaction between argon bubbles and molten steel, to understand the effect of the bubble size to the flow field.
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.
基金supported by the National Science Foundation for Distinguished Young Scholars of China under contract No.40425015the Cooperative Project of Chinese Academy Sciences and the China National 0ffshore 0il Corporation("Behaviours of internal waves and their roles on the marine stuctures").
文摘A previous study （Song. 2004. Geophys Res Lett, 31 （15）：L15302） of the second-order solutions for random interracial waves is extended in a constant depth, two-layer fluid system with a rigid lid is extended into a more general case of two-layer fluid with a top free surface. The rigid boundary condition on the upper surface is replaced by the kinematical and dynamical boundary conditions of a free surface, and the equations describing the random displacements of free surface, density-interface and the associated velocity potentials in the two-layer fluid are solved to the second order using the same expansion technology as that of Song （2004. Geophys Res Lett, 31 （15）：L15302）. The results show that the interface and the surface will oscillate synchronously, and the wave fields to the first-order both at the free surface and at the density-interface are made up of a linear superposition of many waves with different amplitudes, wave numbers and frequencies. The second-order solutions describe the second-order wave-wave interactions of the surface wave components, the interface wave components and among the surface and the interface wave components. The extended solutions also include special cases obtained by Thorpe for progressive interracial waves （Thorpe. 1968a.Trans R Soc London, 263A：563～614） and standing interracial waves （Thorpe. 1968b. J Fluid Mech, 32：489-528） for the two-layer fluid with a top free surface. Moreover, the solutions reduce to those derived for random surface waves by Sharma and Dean （1979.Ocean Engineering Rep 20） if the density of the upper layer is much smaller than that of the lower layer.
基金supported by the National Science Fund for Distinguished Young Scholars of China undercontract No 40425015 the Knowledge Innovation Programs of the Chinese Academy of Sciences under contract Nos KZCX1-YW-12and KZCX2-YW-201
文摘Interfacial waves and wave-induced tangential stress are studied for geostrophic small amplitude waves of two-layer fluid with a top free surface and a fiat bottom. The solutions were deduced from the general form of linear fluid dynamic equations of two-layer fluid under the f-plane approximation, and wave-induced tangential stress were estimated based on the solutions obtained. As expected, the solutions derived from the present work include as special cases those obtained by Sun et al. （2004. Science in China, Ser. D, 47（12）： 1147-1154） for geostrophic small amplitude surface wave solutions and wave-induced tangential stress if the density of the upper layer is much smaller than that of the lower layer. The results show that the interface and the surface will oscillate synchronously, and the influence of the earth＇s rotation both on the surface wave solutions and the interfacial wave solutions should be considered.
基金Knowledge Innovation Programs of the Chinese Academy of Sciences under contract Nos KZCX2-YW-201 and KZCX1-YW-12Natural Science Fund supported by the Educational Department of Inner Mongolia under contract Nos NJzy080005,and NJ09011A Grant from Science Fund for Young Scholars of Inner Mongolia University under contract NoND0801
文摘Interracial waves propagating along the interface between a three-dimensional two-fluid system with a rigid upper boundary and an uneven bottom are considered. There is a light fluid layer overlying a heavier one in the system, and a small density difference exists between the two layers. A set of higher-order Boussinesq-type equations in terms of the depth-averaged velocities accounting for stronger nonlinearity are derived. When the small parameter measuring frequency dispersion keeping up to lower-order and full nonlinearity are considered, the equations include the Choi and Camassa＇s results （1999）. The enhanced equations in terms of the depth-averaged velocities are obtained by applying the enhancement technique introduced by Madsen et al. （1991） and Schaffer and Madsen （1995a）. It is noted that the equations derived from the present study include, as special cases, those obtained by Madsen and Schaffer （1998）. By comparison with the dispersion relation of the linear Stokes waves, we found that the dispersion relation is more improved than Choi and Camassa＇s （1999） results, and the applicable scope of water depth is deeper.
基金supported by the National Natural Science Foundation of China(11062005 and 11202092)Open Fund of State Key Laboratory of Nonlinear Mechanics,the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region(NJYT-13-A02)+4 种基金the Natural Science Foundation of Inner Mongolia(2010BS0107 and 2012MS0107)the Research Start Up Fund for Excellent Talents at Inner Mongolia University(Z20080211)the support of Natural Science Key Fund of Inner Mongolia(2009ZD01)the Postgraduate Scientific Research Innovation Project of Inner Mongoliathe Enhancing Comprehensive Strength Project of Inner Mongolia University(14020202)
文摘By method of the Laplace transform, this arti- cle presents semi-analytical solutions for transient electro- osmotic and pressure-driven flows （EOF/PDF） of two-layer fluids between microparallel plates. The linearized Poisson- Boltzmann equation and the Cauchy momentum equation have been solved in this article. At the interface, the Maxwell stress is included as the boundary condition. By numerical computations of the inverse Laplace transform, the effects of dielectric constant ratio e, density ratio p, pressure ratio p, viscosity ratioμ of layer II to layer I, interface zeta potential difference △ψ, interface charge density jump Q, the ratios of maximum electro-osmotic velocity to pressure velocity , and the normalized pressure gradient B on transient veloc- ity amplitude are presented.We find the velocity amplitude becomes large with the interface zeta potential difference and becomes small with the increase of the viscosity. The ve- locity will be large with the increases of dielectric constant ratio; the density ratio almost does not influence the EOF ve- locity. Larger interface charge density jump leads to a strong jump of velocity at the interface. Additionally, the effects of the thickness of fluid layers （hi and h2） and pressure gradient on the velocity are also investigated.
文摘Based on the two-phase model (Eulerian-Eulerian model), the three dimensional fluid flow in water and that liquid steel systems stirred by one or two multiple gas jets are simulated. In the Eulerian-Eulerian two-phase model, the gas and the liquid phase are considered to be two different continuous fluids interacting with each other through the finite inter-phase areas. The exchange between the phases is represented by source terms in conversation equations. Turbulence is assumed to be a property of the liquid phase. A new turbulence modification - model is introduced to consider the bubbles movement contribution to and . The dispersion of phases due to turbulence is represented by introducing a diffusion term in mass conservation equation. The mathematical simulation agrees well with the experiment results. The study results indicate that the distance of two nozzles has big effect on fluid flow behavior in the vessel. Using two gas injection nozzles at the half radii of one diameter of the bottom generates a much better mixing than with one nozzle under the condition of the same total gas flow rate.
文摘This paper provides the exact solutions for the fully developed two layer pressure driven flows of incompressible Phan-Thien-Tanner fluids in a horizontal cylindrical pipe. Exact equations are formulated and solved for important kinematic properties, such as, velocity profiles, normal and shear stresses, total volume fluxes through a circular cross-section and average velocities. Graphical results are provided and discussed for the different flow parameters. A comparison of Upper Convected Maxwell (UCM), Linear Phan-Thien-Tanner (LPTT) and Exponential Phan-Thien-Tanner (EPTT) shows that UCM is a low viscosity fluid as compared to LPTT, and EPTT and LPTT is lighter than EPTT.
文摘The validity of Navier’s partial slip condition is investigated by studying the oscillatory flow in a coated channel.The two-fluid model is used to solve the unsteady viscous equations exactly.Partial slip is experienced by the core fluid.It is found that Naviers condition does not hold for an unsteady core fluid.
文摘This paper considers interfacial waves propagating along the interface between a two-dimensional two-fluid with a flat bottom and a rigid upper boundary. There is a light fluid layer overlying a heavier one in the system, and a small density difference exists between the two layers. It just focuses on the weakly non-linear small amplitude waves by introducing two small independent parameters： the nonlinearity ratio ε, represented by the ratio of amplitude to depth, and the dispersion ratio μ, represented by the square of the ratio of depth to wave length, which quantify the relative importance of nonlinearity and dispersion. It derives an extended KdV equation of the interfacial waves using the method adopted by Dullin et al in the study of the surface waves when considering the order up to O（μ^2）. As expected, the equation derived from the present work includes, as special cases, those obtained by Dullin et al for surface waves when the surface tension is neglected. The equation derived using an alternative method here is the same as the equation presented by Choi and Camassa. Also it solves the equation by borrowing the method presented by Marchant used for surface waves, and obtains its asymptotic solitary wave solutions when the weakly nonlinear and weakly dispersive terms are balanced in the extended KdV equation.
基金Project supported by the National Natural Science Foundation of China(Nos.11172107 and 11172109)the Program for New Century Excellent Talents in University(No.NCET-11-0183)
文摘In this paper, the nonlinear dynamical behavior of two coupled pipes conveying pulsating fluid is studied. The connection between the two pipes is considered as a distributed linear spring. Based on this consideration, the equations of motion of the coupled two-pipe system are obtained. The two coupled nonlinear partial differential equations, discretized using the fourth- order Galerkin method, are solved by a fourth-order Runge-Kutta integration algorithm. Results show that the connection stiffness has a significant effect on the dynamical behavior of the coupled system. It is found that for some parameter values the motion types of the two pipes might be synchronous.
