The effects of milling parameters on the surface quality,microstructures and mechanical properties of machined parts with ultrafine grained(UFG)gradient microstructures are investigated.The effects of the cutting spee...The effects of milling parameters on the surface quality,microstructures and mechanical properties of machined parts with ultrafine grained(UFG)gradient microstructures are investigated.The effects of the cutting speed,feed per tooth,cutting tool geometry and cooling strategy are demonstrated.It has been found that the surface quality of machined grooves can be improved by increasing the cutting speed.However,cryogenic cooling with CO_2 exhibits no significant improvement of surface quality.Microstructure and hardness investigations revealed similar microstructure and hardness variations near the machined groove walls for both utilized tool geometries.Therefore,cryogenic cooling can decrease more far-ranging hardness reductions due to high process temperatures,especially in the UFG regions of the machined parts,whilst it cannot prevent the drop in hardness directly at the groove walls.展开更多
Numerous laboratory experiments and field cases show that even very small amount of oil in injected water can cause severe injectivity damage. Although injectivity decline caused by oil droplets has been studied exper...Numerous laboratory experiments and field cases show that even very small amount of oil in injected water can cause severe injectivity damage. Although injectivity decline caused by oil droplets has been studied experimentally, there is still lack of an easy-to-use and widely accepted model to predict the decline behavior. In this work, we developed an analytical model to predict the time-dependent progress of the water permeability reduction in linear flow by analyzing experimental data obtained from linear core flooding. The model considers mass transfer of the oil phase from the produced water to the rock due capture effects by dispersion, advection and adsorption inside the rock. As the captured oil saturation increases, permeability reduces following the relative permeability drainage relationship. The reduction stabilizes when the oil saturation comes to an equilibrium value controlled by oil droplet size and injection velocity. The model is calibrated using published experimental data from prolonged core floods with oil- contaminated waste water. Theoretical runs of the model replicate all the effects known from experimental observations. Resulting from the model is a distributed change of permeability vs. time and distance from the point of injection that can be converted to the overall injectivity damage.展开更多
On the backdrop of dwindling conventional reserves,unconventional reservoirs have emerged as a pivotal chapter in resource extraction.Despite their challenges,such as low permeability,complex fluid storage,and flow me...On the backdrop of dwindling conventional reserves,unconventional reservoirs have emerged as a pivotal chapter in resource extraction.Despite their challenges,such as low permeability,complex fluid storage,and flow mechanisms,hydraulic fracturing technology has underpinned the development of unconventional reservoirs.Consequently,this has brought about a shift in the sequence of flow regimes,e.g.,the transient radial flow regime has been largely shortened by the lengthy transient linear flow regime due to the low permeability of unconventional reservoirs.Moreover,straight-line analysis(SLA),the simplest technique in rate transient analysis(RTA),is a fundamental and potent tool for swiftly extracting reservoir and hydraulic fracture information,estimating oil and gas reserves,and furnishing crucial initial data for subsequent historical matching processes.However,there is currently a dearth of review papers pertaining to a necessary guide of applying SLA in various transient linear flow(TLF)regimes and different unconventional reservoirs.Hence,this paper commences by elucidating the classification of TLF regimes,commonly used methods for recognizing flow regimes,and the diverse SLA methods used for different TLF regimes.Subsequently,it delves into a discussion of different modification techniques for variable rate/flowing pressure,gas phase,complex reservoir characteristics in unconventional reservoirs,and dynamic drainage area concepts etc.Furthermore,the application of SLA in specific domains,namely core analysis and the flowback period,is described.It culminates by surveying the advancements through an integration of novel technologies to enhance estimation accuracy.The paper also highlights certain drawbacks of current SLA technology and proposes new research directions.Ultimately,this paper would serve as an indispensable resource,offering foundational knowledge for the application of SLA in TLF to promote the production of global unconventional resources in a cost-effective and environmentally sustainable fashion in the face of a climate-resilient world.展开更多
Rate-transient analysis(RTA)has been widely applied to extract estimates of reservoir/hydraulic fracture properties.However,the majority of RTA techniques can lead to misdiagnosis of reservoir/fracture information whe...Rate-transient analysis(RTA)has been widely applied to extract estimates of reservoir/hydraulic fracture properties.However,the majority of RTA techniques can lead to misdiagnosis of reservoir/fracture information when the reservoir exhibits reservoir heterogeneity and multiphase flow simultaneously.This work proposes a practical-yet-rigorous method to decouple the effects of reservoir heterogeneity and multiphase flow during TLF,and improve the evaluation of reservoir/fracture properties.A new,general,semi-analytical model is proposed that explicitly accounts for multiphase flow,fractalbased reservoir heterogeneity,anomalous diffusion,and pressure-dependent fluid properties.This is achieved by introducing a new Boltzmann-type transformation,the exponent of which includes reservoir heterogeneity and anomalous diffusion.In order to decouple the effects of reservoir heterogeneity and multiphase flow during TLF,the modified Boltzmann variable allows the conversion of three partial differential equations(PDE's)(i.e.,oil,gas and water diffusion equations)into ordinary differential equations(ODE's)that are easily solved using the Runge-Kutta(RK)method.A modified time-power-law plot is also proposed to estimate the reservoir and fracture properties,recognizing that the classical square-root-of-time-plot is no longer valid when various reservoir complexities are exhibited simultaneously.Using the slope of the straight line on the modified time-power-law plot,the linear flow parameter can be estimated with more confidence.Moreover,because of the new Boltzmann-type transformation,reservoir and fracture properties can be derived more efficiently without the need for defining complex pseudo-variable transformations.Using the new semi-analytical model,the effects of multiphase flow,reservoir heterogeneity and anomalous diffusion on rate-decline behavior are evaluated.For the case of approximately constant flowing pressure,multiphase flow impacts initial oil rate,which is a function of oil relative permeability and well flowing pressure.However,multiphase flow has a minor effect on the oil production decline exponent.Reservoir heterogeneity/anomalous diffusion affect both the initial oil production rate and production decline exponent.The production decline exponent constant is a function of reservoir heterogeneity/anomalous diffusion only.The practical significance of this work is the advancement of RTA techniques to allow for more complex reservoir scenarios,leading to more accurate production forecasting and better-informed capital planning.展开更多
This paper uses the Oseen transformation to solve the differential equations governing motion of the vertical linear gradient flow distribution close to a wall surface. The Navier-Stokes equations are used to consider...This paper uses the Oseen transformation to solve the differential equations governing motion of the vertical linear gradient flow distribution close to a wall surface. The Navier-Stokes equations are used to consider the inertia term along the flow direction. A novel contour integral method is used to solve the complex Airy function. The boundary conditions of linear gradient flow distribution for finite problems are determined. The vorticity function, the pressure function, and the turbulent velocity profiles are provided, and the stability of particle trajectories is studied. An Lx-function form of the third derivative circulation is used to to simplify the solution. Theoretical results are compared with the experimental measurements with satisfactory agreement.展开更多
Considering that the fluid is inviscid and incompressible and the flow is irrotational in a fixed frame of reference and using the multiple scale analysis method, we derive a nonlinear Schrodinger equation(NLSE) descr...Considering that the fluid is inviscid and incompressible and the flow is irrotational in a fixed frame of reference and using the multiple scale analysis method, we derive a nonlinear Schrodinger equation(NLSE) describing the evolution dynamics of gravity-capillary wavetrains in arbitrary constant depth. The gravity-capillary waves(GCWs) are influenced by a linear shear flow(LSF) which consists of a uniform flow and a shear flow with constant vorticity. The modulational instability(MI) of GCWs with the LSF is analyzed using the NLSE. The MI is effectively modified by the LSF. In infinite depth, there are four asymptotes which are the boundaries between MI and modulational stability(MS) in the instability diagram. In addition, the dimensionless free surface elevation as a function of time for different dimensionless water depth,surface tension, uniform flow and vorticity is exhibited. It is found that the decay of free surface elevation and the steepness of free surface amplitude change over time, which are greatly affected by the water depth, surface tension, uniform flow and vorticity.展开更多
The main goal of this paper is to study the following combinatorial problem : given a finite set E = (e1, e2, ...,em} and a subset family a - [S1,S2, ... ,Sk} of E , does there exist a tree T with the edge set E such ...The main goal of this paper is to study the following combinatorial problem : given a finite set E = (e1, e2, ...,em} and a subset family a - [S1,S2, ... ,Sk} of E , does there exist a tree T with the edge set E such that each induced subgraph T[Si] of Si is precisely a path (1≤i≤k) ?展开更多
New approximate analytical solutions for steady flow in parallel-plates channels filled with porous materials governed by non-linear Brinkman-Forchheimer extended Darcy model for three different physical situations ar...New approximate analytical solutions for steady flow in parallel-plates channels filled with porous materials governed by non-linear Brinkman-Forchheimer extended Darcy model for three different physical situations are presented. These results are compared with those obtained from an implicit finite-difference solution of the corresponding time dependent flow problem. It is seen that the time dependent flow solutions yield the almost same steady state values as obtained by using the new approximate analytical展开更多
Assume that a fluid is inviscid, incompressible, and irrotational. A nonlinear Schr?dinger equation(NLSE) describing the evolution of gravity waves in finite water depth is derived using the multiple-scale analysis me...Assume that a fluid is inviscid, incompressible, and irrotational. A nonlinear Schr?dinger equation(NLSE) describing the evolution of gravity waves in finite water depth is derived using the multiple-scale analysis method. The gravity waves are influenced by a linear shear flow, which is composed of a uniform flow and a shear flow with constant vorticity. The modulational instability(MI) of the NLSE is analyzed, and the region of the MI for gravity waves(the necessary condition for existence of freak waves) is identified. In this work, the uniform background flows along or against wave propagation are referred to as down-flow and up-flow, respectively. Uniform up-flow enhances the MI, whereas uniform down-flow reduces it. Positive vorticity enhances the MI, while negative vorticity reduces it. Hence, the influence of positive(negative)vorticity on MI can be balanced out by that of uniform down(up) flow. Furthermore, the Peregrine breather solution of the NLSE is applied to freak waves. Uniform up-flow increases the steepness of the free surface elevation, while uniform down-flow decreases it. Positive vorticity increases the steepness of the free surface elevation, whereas negative vorticity decreases it.展开更多
Numerical simulations on focused wave propagation are carried out by using three types of numerical models,including the linear potential flow,the nonlinear potential flow and the viscous fluid flow models.The wave-wa...Numerical simulations on focused wave propagation are carried out by using three types of numerical models,including the linear potential flow,the nonlinear potential flow and the viscous fluid flow models.The wave-wave interaction of the focused wave group with different frequency bands and input wave amplitudes is examined,by which the influence of free surface nonlinearity and fluid viscosity on the related phenomenon of focused wave is investigated.The significant influence of free surface nonlinearity on the characteristics of focused wave can be observed,including the increased focused wave crest,delayed focused time and downstream shift of focused position with the increase of input amplitude.It can plot the evident difference between the results of the nonlinear potential flow and linear potential flow models.However,only a little discrepancy between the nonlinear potential flow and viscous fluid flow models can be observed,implying the insignificant effect of fluid viscosity on focused wave behavior.Therefore,the nonlinear potential flow model is recommended for simulating the non-breaking focused wave problem in this study.展开更多
In this paper, a transportation problem with an objective function as the sum of a linear and fractional function is considered. The linear function represents the total transportation cost incurred when the goods are...In this paper, a transportation problem with an objective function as the sum of a linear and fractional function is considered. The linear function represents the total transportation cost incurred when the goods are shipped from various sources to the destinations and the fractional function gives the ratio of sales tax to the total public expenditure. Our objective is to determine the transportation schedule which minimizes the sum of total transportation cost and ratio of total sales tax paid to the total public expenditure. Sometimes, situations arise where either reserve stocks have to be kept at the supply points, for emergencies or there may be extra demand in the markets. In such situations, the total flow needs to be controlled or enhanced. In this paper, a special class of transportation problems is studied where in the total transportation flow is restricted to a known specified level. A related transportation problem is formulated and it is shown that to each basic feasible solution which is called corner feasible solution to related transportation problem, there is a corresponding feasible solution to this restricted flow problem. The optimal solution to restricted flow problem may be obtained from the optimal solution to related transportation problem. An algorithm is presented to solve a capacitated linear plus linear fractional transportation problem with restricted flow. The algorithm is supported by a real life example of a manufacturing company.展开更多
The identification of vortex,vortex,sound and heat motions and the interactions among them are discussed by means of velocity vector split and perturbation method in this paper.Especially the shear.flow is considered...The identification of vortex,vortex,sound and heat motions and the interactions among them are discussed by means of velocity vector split and perturbation method in this paper.Especially the shear.flow is considered.All the obtained weakly non-linear equarions have clear physics concept. Basing on the analysis.the interaction between first order sound and vortex.and the creation of the secnd order vortex are studied and some.experiment phenomena of airfoil.flow control by sound are explained.展开更多
A multilayer flow is a stratified fluid composed of a finite number of layers with densities homogeneous within one layer but different from each other. It is an intermediate system between the single-layer barotropic...A multilayer flow is a stratified fluid composed of a finite number of layers with densities homogeneous within one layer but different from each other. It is an intermediate system between the single-layer barotropic model and the continuously stratified baroclinic model. Since this system can simulate the baroclinic effect simply, it is widely used to study the large-scale dynamic process in atmosphere and ocean. The present paper is concerned with the linear stability of the multilayer quasi-geostrophic flow, and the associated linear stability criteria are established. Firstly, the nonlinear model is turned into the form of a Hamiltonian system, and a basic flow is defined. But it cannot be an extreme point of the Hamiltonian function since the system is an infinite-dimensional one. Therefore, it is necessary to reconstruct a new Hamiltonian function so that the basic flow becomes an extreme point of it. Secondly, the linearized equations of disturbances in the multilayer quasi-geostrophic flow are derived by introducing infinitesimal disturbances superposed on the basic flows. Finally, the properties of the linearized system are discussed, and the linear stability criteria in the sense of Liapunov are derived under two different conditions with respect to certain norms.展开更多
It is well known that plane creeping Couette flow of UCM and Oldroy-B fluids are linearly stable. However, for Burges fluid, which includes UCM and Oldroyd-B fluids as special cases, unstable modes are detected in the...It is well known that plane creeping Couette flow of UCM and Oldroy-B fluids are linearly stable. However, for Burges fluid, which includes UCM and Oldroyd-B fluids as special cases, unstable modes are detected in the present work. The wave speed, critical parameters and perturbation mode are studied for neutral waves. Energy analysis shows that the sustaining of perturbation energy in Poiseuille flow and Couette flow is completely different. At low Reynolds number limit, analytical solutions are obtained for simpli- fied perturbation equations. The essential difference between Burgers fluid and Oldroyd-B fluid is revealed to be the fact that neutral mode exists only in the former.展开更多
Based on the hydrodynamic stability theory of distorted laminar flow and the kind of distortion profiles on the mean velocity in parallel shear flow given in paper [1], this paper investigates the linear stability beh...Based on the hydrodynamic stability theory of distorted laminar flow and the kind of distortion profiles on the mean velocity in parallel shear flow given in paper [1], this paper investigates the linear stability behaviour of parallel shear flow, presents unstable results of plane Couette flow and pipe Poiseuille flow to two-dimensional or axisymmetric disturbances for the first time, and obtains neutral curves of these two motions under certain definition.展开更多
Linearized equations of fluid dynamics of cell two phase flow for one dimensional case are proposed. Based on the equations, an analytic solution is derived, in which the frequency of wave is observed. The frequency f...Linearized equations of fluid dynamics of cell two phase flow for one dimensional case are proposed. Based on the equations, an analytic solution is derived, in which the frequency of wave is observed. The frequency formula consists of all important parameters of the fluid dynamics. In our observation, the group velocity and phase velocity of the motion of wave propagation are explicitly exhibited as well.展开更多
A method of linear momentum approximation is proposed that deals with weak nonlinear problems in an approximate manner. A motion of nonlinear nature is obtained in the system by assuming the motion to be in the form o...A method of linear momentum approximation is proposed that deals with weak nonlinear problems in an approximate manner. A motion of nonlinear nature is obtained in the system by assuming the motion to be in the form of linear momentum flow in the corresponding space introduced, followed by the transformation from the specified into a physical space. Significant results have been thereby derived in examining the effects of baroclinic Ekman momentum flow upon Eady-type baroclinic waves and frontogenesis. Also, this technique can be applied to investigate the dynamic characteristics of the weak nonlinear boundary layer including topography, stratification and non-Ekmantype friction for gaining further insight into the influence on the boundary layer inner parameters of terrain, baroclinicity and inhomogeneous process so that the classic theory is revised.展开更多
Recognition method of traffic flow change point was put forward based on traffic flow theory and the statistical change point analysis of multiple linear regressions. The method was calibrated and tested with the fiel...Recognition method of traffic flow change point was put forward based on traffic flow theory and the statistical change point analysis of multiple linear regressions. The method was calibrated and tested with the field data of Liantong Road of Zibo city to verify the validity and the feasibility of the theory. The results show that change point method of multiple linear regression can make out the rule of quantitative changes in traffic flow more accurately than ordinary methods. So, the change point method can be applied to traffic information management system more effectively.展开更多
The explicit solution to Cauchy problem for linearized system of two-dimensional isentropic flow with axisymmetrical initial data in gas dynamics is given.
基金supported by the German Research Foundation(DFG)the DFG for funding the subproject B3 and C5 of the Collaborative Research Center 666 "Integral sheet metal design with higher order bifurcations-Development,Production,Evaluation″
文摘The effects of milling parameters on the surface quality,microstructures and mechanical properties of machined parts with ultrafine grained(UFG)gradient microstructures are investigated.The effects of the cutting speed,feed per tooth,cutting tool geometry and cooling strategy are demonstrated.It has been found that the surface quality of machined grooves can be improved by increasing the cutting speed.However,cryogenic cooling with CO_2 exhibits no significant improvement of surface quality.Microstructure and hardness investigations revealed similar microstructure and hardness variations near the machined groove walls for both utilized tool geometries.Therefore,cryogenic cooling can decrease more far-ranging hardness reductions due to high process temperatures,especially in the UFG regions of the machined parts,whilst it cannot prevent the drop in hardness directly at the groove walls.
基金part of a research program, Downhole Water Sink Technology Initiative (DWSTI) ―a Joint Industry Project (JIP) at LSU
文摘Numerous laboratory experiments and field cases show that even very small amount of oil in injected water can cause severe injectivity damage. Although injectivity decline caused by oil droplets has been studied experimentally, there is still lack of an easy-to-use and widely accepted model to predict the decline behavior. In this work, we developed an analytical model to predict the time-dependent progress of the water permeability reduction in linear flow by analyzing experimental data obtained from linear core flooding. The model considers mass transfer of the oil phase from the produced water to the rock due capture effects by dispersion, advection and adsorption inside the rock. As the captured oil saturation increases, permeability reduces following the relative permeability drainage relationship. The reduction stabilizes when the oil saturation comes to an equilibrium value controlled by oil droplet size and injection velocity. The model is calibrated using published experimental data from prolonged core floods with oil- contaminated waste water. Theoretical runs of the model replicate all the effects known from experimental observations. Resulting from the model is a distributed change of permeability vs. time and distance from the point of injection that can be converted to the overall injectivity damage.
基金support from the China Scholarship Council(CSC)the University of Calgary.
文摘On the backdrop of dwindling conventional reserves,unconventional reservoirs have emerged as a pivotal chapter in resource extraction.Despite their challenges,such as low permeability,complex fluid storage,and flow mechanisms,hydraulic fracturing technology has underpinned the development of unconventional reservoirs.Consequently,this has brought about a shift in the sequence of flow regimes,e.g.,the transient radial flow regime has been largely shortened by the lengthy transient linear flow regime due to the low permeability of unconventional reservoirs.Moreover,straight-line analysis(SLA),the simplest technique in rate transient analysis(RTA),is a fundamental and potent tool for swiftly extracting reservoir and hydraulic fracture information,estimating oil and gas reserves,and furnishing crucial initial data for subsequent historical matching processes.However,there is currently a dearth of review papers pertaining to a necessary guide of applying SLA in various transient linear flow(TLF)regimes and different unconventional reservoirs.Hence,this paper commences by elucidating the classification of TLF regimes,commonly used methods for recognizing flow regimes,and the diverse SLA methods used for different TLF regimes.Subsequently,it delves into a discussion of different modification techniques for variable rate/flowing pressure,gas phase,complex reservoir characteristics in unconventional reservoirs,and dynamic drainage area concepts etc.Furthermore,the application of SLA in specific domains,namely core analysis and the flowback period,is described.It culminates by surveying the advancements through an integration of novel technologies to enhance estimation accuracy.The paper also highlights certain drawbacks of current SLA technology and proposes new research directions.Ultimately,this paper would serve as an indispensable resource,offering foundational knowledge for the application of SLA in TLF to promote the production of global unconventional resources in a cost-effective and environmentally sustainable fashion in the face of a climate-resilient world.
基金The authors would like to acknowledge financial support provided by National Natural Science Foundation of China(No.52074338)We are also grateful to the support of the National Key R&D Program of China(No.2019YFA0708700)+1 种基金National Key Basic Research Program of China(20CX06071A)Bin Yuan would like to thank for the support of Shandong Mountain Tai Scholar Program.Chris Clarkson would like to acknowledge funding support from an NSERC Alliance grant(ALLRP 548652-19)for research related to the topic of this paper.
文摘Rate-transient analysis(RTA)has been widely applied to extract estimates of reservoir/hydraulic fracture properties.However,the majority of RTA techniques can lead to misdiagnosis of reservoir/fracture information when the reservoir exhibits reservoir heterogeneity and multiphase flow simultaneously.This work proposes a practical-yet-rigorous method to decouple the effects of reservoir heterogeneity and multiphase flow during TLF,and improve the evaluation of reservoir/fracture properties.A new,general,semi-analytical model is proposed that explicitly accounts for multiphase flow,fractalbased reservoir heterogeneity,anomalous diffusion,and pressure-dependent fluid properties.This is achieved by introducing a new Boltzmann-type transformation,the exponent of which includes reservoir heterogeneity and anomalous diffusion.In order to decouple the effects of reservoir heterogeneity and multiphase flow during TLF,the modified Boltzmann variable allows the conversion of three partial differential equations(PDE's)(i.e.,oil,gas and water diffusion equations)into ordinary differential equations(ODE's)that are easily solved using the Runge-Kutta(RK)method.A modified time-power-law plot is also proposed to estimate the reservoir and fracture properties,recognizing that the classical square-root-of-time-plot is no longer valid when various reservoir complexities are exhibited simultaneously.Using the slope of the straight line on the modified time-power-law plot,the linear flow parameter can be estimated with more confidence.Moreover,because of the new Boltzmann-type transformation,reservoir and fracture properties can be derived more efficiently without the need for defining complex pseudo-variable transformations.Using the new semi-analytical model,the effects of multiphase flow,reservoir heterogeneity and anomalous diffusion on rate-decline behavior are evaluated.For the case of approximately constant flowing pressure,multiphase flow impacts initial oil rate,which is a function of oil relative permeability and well flowing pressure.However,multiphase flow has a minor effect on the oil production decline exponent.Reservoir heterogeneity/anomalous diffusion affect both the initial oil production rate and production decline exponent.The production decline exponent constant is a function of reservoir heterogeneity/anomalous diffusion only.The practical significance of this work is the advancement of RTA techniques to allow for more complex reservoir scenarios,leading to more accurate production forecasting and better-informed capital planning.
基金Project supported by the National Natural Science foundation of China(No.51079095)the Science Fund for Creative Research Groups of the National Natural Science Foundation of China(No.51021004)
文摘This paper uses the Oseen transformation to solve the differential equations governing motion of the vertical linear gradient flow distribution close to a wall surface. The Navier-Stokes equations are used to consider the inertia term along the flow direction. A novel contour integral method is used to solve the complex Airy function. The boundary conditions of linear gradient flow distribution for finite problems are determined. The vorticity function, the pressure function, and the turbulent velocity profiles are provided, and the stability of particle trajectories is studied. An Lx-function form of the third derivative circulation is used to to simplify the solution. Theoretical results are compared with the experimental measurements with satisfactory agreement.
基金Project supported by the National Natural Science Foundation of China(Grant No.41830533)the National Key Research and Development Program of China(Grant Nos.2016YFC1401404 and 2017YFA0604102).
文摘Considering that the fluid is inviscid and incompressible and the flow is irrotational in a fixed frame of reference and using the multiple scale analysis method, we derive a nonlinear Schrodinger equation(NLSE) describing the evolution dynamics of gravity-capillary wavetrains in arbitrary constant depth. The gravity-capillary waves(GCWs) are influenced by a linear shear flow(LSF) which consists of a uniform flow and a shear flow with constant vorticity. The modulational instability(MI) of GCWs with the LSF is analyzed using the NLSE. The MI is effectively modified by the LSF. In infinite depth, there are four asymptotes which are the boundaries between MI and modulational stability(MS) in the instability diagram. In addition, the dimensionless free surface elevation as a function of time for different dimensionless water depth,surface tension, uniform flow and vorticity is exhibited. It is found that the decay of free surface elevation and the steepness of free surface amplitude change over time, which are greatly affected by the water depth, surface tension, uniform flow and vorticity.
基金Supported by the National Natural Science Foundation of China
文摘The main goal of this paper is to study the following combinatorial problem : given a finite set E = (e1, e2, ...,em} and a subset family a - [S1,S2, ... ,Sk} of E , does there exist a tree T with the edge set E such that each induced subgraph T[Si] of Si is precisely a path (1≤i≤k) ?
文摘New approximate analytical solutions for steady flow in parallel-plates channels filled with porous materials governed by non-linear Brinkman-Forchheimer extended Darcy model for three different physical situations are presented. These results are compared with those obtained from an implicit finite-difference solution of the corresponding time dependent flow problem. It is seen that the time dependent flow solutions yield the almost same steady state values as obtained by using the new approximate analytical
基金Project supported by the National Key Research and Development Program of China(Grant Nos.2016YFC1401404 and 2017YFA0604102)the National Natural Science Foundation of China(Grant No.41830533)
文摘Assume that a fluid is inviscid, incompressible, and irrotational. A nonlinear Schr?dinger equation(NLSE) describing the evolution of gravity waves in finite water depth is derived using the multiple-scale analysis method. The gravity waves are influenced by a linear shear flow, which is composed of a uniform flow and a shear flow with constant vorticity. The modulational instability(MI) of the NLSE is analyzed, and the region of the MI for gravity waves(the necessary condition for existence of freak waves) is identified. In this work, the uniform background flows along or against wave propagation are referred to as down-flow and up-flow, respectively. Uniform up-flow enhances the MI, whereas uniform down-flow reduces it. Positive vorticity enhances the MI, while negative vorticity reduces it. Hence, the influence of positive(negative)vorticity on MI can be balanced out by that of uniform down(up) flow. Furthermore, the Peregrine breather solution of the NLSE is applied to freak waves. Uniform up-flow increases the steepness of the free surface elevation, while uniform down-flow decreases it. Positive vorticity increases the steepness of the free surface elevation, whereas negative vorticity decreases it.
基金the National Natural Science Foundation of China(Grant Nos.51909027 and 51679035),the Project of Educational Commission of Liaoning Province(Grant No.L201601),the High-Level Innovation and Entrepreneurship Team of Liaoning Province(Grant No.XLYC1908027),the Fundamental Research Funds for the Central Universities(Grant No.DUT2017TB05).
文摘Numerical simulations on focused wave propagation are carried out by using three types of numerical models,including the linear potential flow,the nonlinear potential flow and the viscous fluid flow models.The wave-wave interaction of the focused wave group with different frequency bands and input wave amplitudes is examined,by which the influence of free surface nonlinearity and fluid viscosity on the related phenomenon of focused wave is investigated.The significant influence of free surface nonlinearity on the characteristics of focused wave can be observed,including the increased focused wave crest,delayed focused time and downstream shift of focused position with the increase of input amplitude.It can plot the evident difference between the results of the nonlinear potential flow and linear potential flow models.However,only a little discrepancy between the nonlinear potential flow and viscous fluid flow models can be observed,implying the insignificant effect of fluid viscosity on focused wave behavior.Therefore,the nonlinear potential flow model is recommended for simulating the non-breaking focused wave problem in this study.
文摘In this paper, a transportation problem with an objective function as the sum of a linear and fractional function is considered. The linear function represents the total transportation cost incurred when the goods are shipped from various sources to the destinations and the fractional function gives the ratio of sales tax to the total public expenditure. Our objective is to determine the transportation schedule which minimizes the sum of total transportation cost and ratio of total sales tax paid to the total public expenditure. Sometimes, situations arise where either reserve stocks have to be kept at the supply points, for emergencies or there may be extra demand in the markets. In such situations, the total flow needs to be controlled or enhanced. In this paper, a special class of transportation problems is studied where in the total transportation flow is restricted to a known specified level. A related transportation problem is formulated and it is shown that to each basic feasible solution which is called corner feasible solution to related transportation problem, there is a corresponding feasible solution to this restricted flow problem. The optimal solution to restricted flow problem may be obtained from the optimal solution to related transportation problem. An algorithm is presented to solve a capacitated linear plus linear fractional transportation problem with restricted flow. The algorithm is supported by a real life example of a manufacturing company.
文摘The identification of vortex,vortex,sound and heat motions and the interactions among them are discussed by means of velocity vector split and perturbation method in this paper.Especially the shear.flow is considered.All the obtained weakly non-linear equarions have clear physics concept. Basing on the analysis.the interaction between first order sound and vortex.and the creation of the secnd order vortex are studied and some.experiment phenomena of airfoil.flow control by sound are explained.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.41575026,41275113,and 41475021)
文摘A multilayer flow is a stratified fluid composed of a finite number of layers with densities homogeneous within one layer but different from each other. It is an intermediate system between the single-layer barotropic model and the continuously stratified baroclinic model. Since this system can simulate the baroclinic effect simply, it is widely used to study the large-scale dynamic process in atmosphere and ocean. The present paper is concerned with the linear stability of the multilayer quasi-geostrophic flow, and the associated linear stability criteria are established. Firstly, the nonlinear model is turned into the form of a Hamiltonian system, and a basic flow is defined. But it cannot be an extreme point of the Hamiltonian function since the system is an infinite-dimensional one. Therefore, it is necessary to reconstruct a new Hamiltonian function so that the basic flow becomes an extreme point of it. Secondly, the linearized equations of disturbances in the multilayer quasi-geostrophic flow are derived by introducing infinitesimal disturbances superposed on the basic flows. Finally, the properties of the linearized system are discussed, and the linear stability criteria in the sense of Liapunov are derived under two different conditions with respect to certain norms.
基金supported by the National Natural Science Foundation of China (11172152)
文摘It is well known that plane creeping Couette flow of UCM and Oldroy-B fluids are linearly stable. However, for Burges fluid, which includes UCM and Oldroyd-B fluids as special cases, unstable modes are detected in the present work. The wave speed, critical parameters and perturbation mode are studied for neutral waves. Energy analysis shows that the sustaining of perturbation energy in Poiseuille flow and Couette flow is completely different. At low Reynolds number limit, analytical solutions are obtained for simpli- fied perturbation equations. The essential difference between Burgers fluid and Oldroyd-B fluid is revealed to be the fact that neutral mode exists only in the former.
文摘Based on the hydrodynamic stability theory of distorted laminar flow and the kind of distortion profiles on the mean velocity in parallel shear flow given in paper [1], this paper investigates the linear stability behaviour of parallel shear flow, presents unstable results of plane Couette flow and pipe Poiseuille flow to two-dimensional or axisymmetric disturbances for the first time, and obtains neutral curves of these two motions under certain definition.
基金Supported by the National Natural Science Foundation of China(10672022)
文摘Linearized equations of fluid dynamics of cell two phase flow for one dimensional case are proposed. Based on the equations, an analytic solution is derived, in which the frequency of wave is observed. The frequency formula consists of all important parameters of the fluid dynamics. In our observation, the group velocity and phase velocity of the motion of wave propagation are explicitly exhibited as well.
文摘A method of linear momentum approximation is proposed that deals with weak nonlinear problems in an approximate manner. A motion of nonlinear nature is obtained in the system by assuming the motion to be in the form of linear momentum flow in the corresponding space introduced, followed by the transformation from the specified into a physical space. Significant results have been thereby derived in examining the effects of baroclinic Ekman momentum flow upon Eady-type baroclinic waves and frontogenesis. Also, this technique can be applied to investigate the dynamic characteristics of the weak nonlinear boundary layer including topography, stratification and non-Ekmantype friction for gaining further insight into the influence on the boundary layer inner parameters of terrain, baroclinicity and inhomogeneous process so that the classic theory is revised.
基金National Natural Science Foundations of China(No. 61074140,No. 60974094)Young Teacher Development Support Project of Shandong University of Technology,China
文摘Recognition method of traffic flow change point was put forward based on traffic flow theory and the statistical change point analysis of multiple linear regressions. The method was calibrated and tested with the field data of Liantong Road of Zibo city to verify the validity and the feasibility of the theory. The results show that change point method of multiple linear regression can make out the rule of quantitative changes in traffic flow more accurately than ordinary methods. So, the change point method can be applied to traffic information management system more effectively.
文摘The explicit solution to Cauchy problem for linearized system of two-dimensional isentropic flow with axisymmetrical initial data in gas dynamics is given.
