The flow control at low Reynolds numbers is one of the most promising technologies in the field of aerodynamics,and it is also an important source of the innovation for novel aircraft.In this study,a new way of nonlin...The flow control at low Reynolds numbers is one of the most promising technologies in the field of aerodynamics,and it is also an important source of the innovation for novel aircraft.In this study,a new way of nonlinear flow control by interaction between two flexible flaps is proposed,and their flow control mechanism is studied employing the self-constructed immersed boundary-lattice Boltzmann-finite element method(IB-LB-FEM).The effects of the difference in material properties and flap length between the two flexible flaps on the nonlinear flow control of the airfoil are discussed.It is suggested that the relationship between the deformation of the two flexible flaps and the evolution of the vortex under the fluid-structure interaction(FSI).It is shown that the upstream flexible flap plays a key role in the flow control of the two flexible flaps.The FSI effect of the upstream flexible flap will change the unsteady flow behind it and affect the deformation of the downstream flexible flap.Two flexible flaps with different material properties and different lengths will change their own FSI characteristics by the induced vortex,effectively suppressing the flow separation on the airfoil’s upper surface.The interaction of two flexible flaps plays an extremely important role in improving the autonomy and adjustability of flow control.The numerical results will provide a theoretical basis and technical guidance for the development and application of a new flap passive control technology.展开更多
This study experimentally analyzes the nonlinear flow characteristics and channelization of fluid through rough-walled fractures during the shear process using a shear-flow-visualization apparatus.A series of fluid fl...This study experimentally analyzes the nonlinear flow characteristics and channelization of fluid through rough-walled fractures during the shear process using a shear-flow-visualization apparatus.A series of fluid flow and visualization tests is performed on four transparent fracture specimens with various shear displacements of 1 mm,3 mm,5 mm,7 mm and 10 mm under a normal stress of 0.5 MPa.Four granite fractures with different roughnesses are selected and quantified using variogram fractal dimensions.The obtained results show that the critical Reynolds number tends to increase with increasing shear displacement but decrease with increasing roughness of fracture surface.The flow paths are more tortuous at the beginning of shear because of the wide distribution of small contact spots.As the shear displacement continues to increase,preferential flow paths are more distinctly observed due to the decrease in the number of contact spots caused by shear dilation;yet the area of single contacts in-creases.Based on the experimental results,an empirical mathematical equation is proposed to quantify the critical Reynolds number using the contact area ratio and fractal dimension.展开更多
A nonlinear flow reservoir mathematical model was established based on the flow characteristic of low-permeability reservoir.The well-grid equations were deduced and the dimensionless permeability coefficient was intr...A nonlinear flow reservoir mathematical model was established based on the flow characteristic of low-permeability reservoir.The well-grid equations were deduced and the dimensionless permeability coefficient was introduced to describe the permeability variation of nonlinear flow.The nonlinear flow numerical simulation program was compiled based on black-oil model.A quarter of five-spot well unit was simulated to study the effect of nonlinear flow on the exploitation of low-permeability reservoir.The comprehensive comparison and analysis of the simulation results of Darcy flow,quasi-linear flow and nonlinear flow were provided.The dimensionless permeability coefficient distribution was gained to describe the nonlinear flow degree.The result shows that compared with the results of Darcy flow,when considering nonlinear flow,the oil production is low,and production decline is rapid.The fluid flow in reservoir consumes more driving energy,which reduces the water flooding efficiency.Darcy flow model overstates the reservoir flow capability,and quasi-linear flow model overstates the reservoir flow resistance.The flow ability of the formation near the well and artificial fracture is strong while the flow ability of the formation far away from the main streamline is weak.The nonlinear flow area is much larger than that of quasi-linear flow during the fluid flow in low-permeability reservoir.The water propelling speed of nonlinear flow is greatly slower than that of Darcy flow in the vertical direction of artificial fracture,and the nonlinear flow should be taken into account in the well pattern arrangement of low-permeability reservoir.展开更多
It was derived that micro-scale amount level of average pore radius of clay changed from 0.01 to 0.1 micron by an equivalent concept of flow in porous media. There is good agreement between the derived results and tes...It was derived that micro-scale amount level of average pore radius of clay changed from 0.01 to 0.1 micron by an equivalent concept of flow in porous media. There is good agreement between the derived results and test ones. Results of experiments show that flow in micro-scale pore of saturated clays follows law of nonlinear flow. Theoretical analyses demonstrate that an interaction of solid-liquid interfaces varies inversely with permeability or porous radius. The interaction is an important reason why nonlinear flow in saturated clays occurs. An exact mathematical model was presented for nonlinear flow in micro-scale pore of saturated clays. Dimension and physical meanings of parameters of it are definite. A new law of nonlinear flow in saturated clays was established. It can describe characteristics of flow curve of the whole process of the nonlinear flow from low hydraulic gradient to high one. Darcy law is a special case of the new law. A math- ematical model was presented for consolidation of nonlinear flow in radius direction in saturated clays with constant rate based on the new law of nonlinear flow. Equations of average mass conservation and moving boundary, and formula of excess pore pressure distribution and average degree of consolidation for nonlinear flow in saturated clay were derived by using an idea of viscous boundary layer, a method of steady state in stead of transient state and a method of integral of an equation. Laws of excess pore pressure distribution and changes of average degree of consolidation with time were obtained. Re- sults show that velocity of moving boundary decreases because of the nonlinear flow in saturated clay. The results can provide geology engineering and geotechnical engineering of saturated clay with new scientific bases. Calculations of average degree of consolidation of the Darcy flow are a special case of that of the nonlinear flow.展开更多
A mathematical model of two-phase fluid nonlinear flow in the direction of normal of ellipse through low-permeability porous media was established according to a nonlinear flow law expressed in a continuous function w...A mathematical model of two-phase fluid nonlinear flow in the direction of normal of ellipse through low-permeability porous media was established according to a nonlinear flow law expressed in a continuous function with three parameters, a mass conservation law and a concept of turbulent ellipses. A solution to the model was obtained by using a finite difference method and an extrapolation method. Formulas of calculating development index not only before but also after water breaks through an oil well in the condition of two-phase fluid nonlinear flow in the media were derived. An example was discussed. Water saturation distribution was presented. The moving law of drainage front was found. Laws of change of pressure difference with time were recognized. Results show that there is much difference of water saturation distribution between nonlinear flow and linear flow; that drainage front by water moves faster, water breaks through sooner and the index gets worse because of the nonlinear flow; and that dimensionless pressure difference gets larger at the same dimensionless time and difficulty of oil development becomes bigger by the nonlinear flow. Thus, it is necessary that influence of nonlinear flow on development indexes of the oil fields be taken into account. The results provide water-flooding development of the oilfields with scientific basis.展开更多
By studying a fully nonlinear flow deforming conformal metrics on a compact and connected manifold, we prove the long time existence and the exponential convergence of the solutions of the flow for any initial metric ...By studying a fully nonlinear flow deforming conformal metrics on a compact and connected manifold, we prove the long time existence and the exponential convergence of the solutions of the flow for any initial metric g0 with the Schouten tensor Ag0 ∈ Γk.展开更多
The nonlinear flow properties of Newtonian fluids through crossed fractures are estimated by considering the influences of length,aperture,and surface roughness of fractures.A total of 252 computational runs are perfo...The nonlinear flow properties of Newtonian fluids through crossed fractures are estimated by considering the influences of length,aperture,and surface roughness of fractures.A total of 252 computational runs are performed by creating 36 computational domains,in which the Navier-Stokes equations are solved.The results show that the nonlinear relationship between flow rate and hydraulic gradient follows Forchheimer’s law–based equation.When the hydraulic gradient is small(i.e.,10^(−6)),the streamlines are parallel to the fracture walls,indicating a linear streamline distribution.When the hydraulic gradient is large(i.e.,10^(0)),the streamlines are disturbed by a certain number of eddies,indicating a nonlinear streamline distribution.The patterns of eddy distributions depend on the length,aperture,and surface roughness of fractures.With the increment of hydraulic gradient from 10^(−6) to 10^(0),the ratio of flow rate to hydraulic gradient holds constants and then decreases slightly and finally decreases robustly.The fluid flow experiences a linear flow regime,a weakly nonlinear regime,and a strongly nonlinear regime,respectively.The critical hydraulic gradient ranges from 3.27×10^(−5) to 5.82×10^(−2) when fracture length=20–100mmandmechanical aperture=1–5mm.The joint roughness coefficient plays a negligible role in the variations in critical hydraulic gradient compared with fracture length and/or mechanical aperture.The critical hydraulic gradient decreases with increasing mechanical aperture,following power-law relationships.The parameters in the functions are associated with fracture length.展开更多
Nonlinear flow behavior of fluids through three-dimensional(3D)discrete fracture networks(DFNs)considering effects of fracture number,surface roughness and fracture aperture was experimentally and numerically investig...Nonlinear flow behavior of fluids through three-dimensional(3D)discrete fracture networks(DFNs)considering effects of fracture number,surface roughness and fracture aperture was experimentally and numerically investigated.Three physical models of DFNs were 3D-printed and then computed tomography(CT)-scanned to obtain the specific geometry of fractures.The validity of numerically simulating the fluid flow through DFNs was verified via comparison with flow tests on the 3D-printed models.A parametric study was then implemented to establish quantitative relations between the coefficients/parameters in Forchheimer’s law and geometrical parameters.The results showed that the 3D-printing technique can well reproduce the geometry of single fractures with less precision when preparing complex fracture networks,numerical modeling precision of which can be improved via CT-scanning as evidenced by the well fitted results between fluid flow tests and numerical simulations using CT-scanned digital models.Streamlines in DFNs become increasingly tortuous as the fracture number and roughness increase,resulting in stronger inertial effects and greater curvatures of hydraulic pressure-low rate relations,which can be well characterized by the Forchheimer’s law.The critical hydraulic gradient for the onset of nonlinear flow decreases with the increasing aperture,fracture number and roughness,following a power function.The increases in fracture aperture and number provide more paths for fluid flow,increasing both the viscous and inertial permeabilities.The value of the inertial permeability is approximately four orders of magnitude greater than the viscous permeability,following a power function with an exponent a of 3,and a proportional coefficient b mathematically correlated with the geometrical parameters.展开更多
The models of the nonlinear radial flow for the infinite and finite reservoirs including a quadratic gradient term were presented. The exact solution was given in real space for flow equation including quadratic gradi...The models of the nonlinear radial flow for the infinite and finite reservoirs including a quadratic gradient term were presented. The exact solution was given in real space for flow equation including quadratic gradiet term for both constant-rate and constant pressure production cases in an infinite system by using generalized Weber transform. Analytical solutions for flow equation including quadratic gradient term were also obtained by using the Hankel transform for a finite circular reservoir case. Both closed and constant pressure outer boundary conditions are considered. Moreover, both constant rate and constant pressure inner boundary conditions are considered. The difference between the nonlinear pressure solution and linear pressure solution is analyzed. The difference may be reached about 8% in the long time. The effect of the quadratic gradient term in the large time well test is considered.展开更多
This article studies the nonlinear evolution of disturbance waves in supersonic nonparallel boundary layer flows by using nonlinear parabolic stability equations （NPSE）. An accurate numerical method is developed to ...This article studies the nonlinear evolution of disturbance waves in supersonic nonparallel boundary layer flows by using nonlinear parabolic stability equations （NPSE）. An accurate numerical method is developed to solve the equations and march the NPSE in a stable manner. Through computation,are obtained the curves of amplitude and disturbance shape function of harmonic waves. Especially are demonstrated the physical characteristics of nonlinear stability of various harmonic waves,including instantaneous stream wise vortices,spanwise vortices and Λ structure etc,and are used to study and analyze the mechanism of the transition process. The calculated results have evidenced the effectiveness of the proposed NPSE method to research the nonlinear stability of the supersonic boundary layers.展开更多
This paper gives an overview on nonlinear porous flow in low permeability porous media, reveals the microscopic mechanisms of flows, and clarifies properties of porous flow fluids. It shows that, deviating from Darcy...This paper gives an overview on nonlinear porous flow in low permeability porous media, reveals the microscopic mechanisms of flows, and clarifies properties of porous flow fluids. It shows that, deviating from Darcy＇s linear law, the porous flow characteristics obey a nonlinear law in a low-permeability porous medium, and the viscosity of the porous flow fluid and the permeability values of water and oil are not constants. Based on these characters, a new porous flow model, which can better describe low permeability reservoir~ is established. This model can describe various patterns of porous flow, as Darcy＇s linear law does. All the parameters involved in the model, having definite physical meanings, can be obtained directly from the experiments.展开更多
Based on the energy flow theory of nonlinear dynamical system,the stabilities,bifurcations,possible periodical/chaotic motions of nonlinear water-lubricated bearing-shaft coupled systems are investigated in this paper...Based on the energy flow theory of nonlinear dynamical system,the stabilities,bifurcations,possible periodical/chaotic motions of nonlinear water-lubricated bearing-shaft coupled systems are investigated in this paper.It is revealed that the energy flow characteristics around the equlibrium point of system behaving in the three types with different friction-para-mters.(a)Energy flow matrix has two negative and one positive energy flow factors,constructing an attractive local zero-energy flow surface,in which free vibrations by initial disturbances show damped modulated oscillations with the system tending its equlibrium state,while forced vibrations by external forces show stable oscillations,(b)Energy flow matrix has one negative and two positive energy flow factors,spaning a divergence local zero-energy flow surface,so that the both free and forced vibrations are divergence oscillations with the system being unstable,(c)Energy flow matrix has a zero-energy flow factor and two opposite factors,which constructes a local zero-energy flow surface dividing the local phase space into stable,unstable and central subspace,and the simulation shows friction self-induced unstable vibrations for both free and forced cases.For a set of friction parameters,the system behaves a periodical oscillation,where the bearing motion tends zero and the shaft motion reaches a stable limit circle in phase space with the instant energy flow tending a constant and the time averaged one tending zero.Numerical simulations have not found any possible chaotic motions of the system.It is discovered that the damping matrices of cases(a),(b)and(c)respectively have positive,negative and zero diagonal elements,resulting in the different dynamic behavour of system,which gives a giderline to design the water-lubricated bearing unit with expected performance by adjusting the friction parameters for applications.展开更多
Geometrical nonlinearity of the soft soil and the deviation of water flow in the soft clay from Darcy's law have been well recognized in practice. However, the theory of consolidation, which can account for both t...Geometrical nonlinearity of the soft soil and the deviation of water flow in the soft clay from Darcy's law have been well recognized in practice. However, the theory of consolidation, which can account for both the geometrical nonlinearity and the non-Darcian flow, has not been reported so far. In this contribution, a model for the consolidation of soft clay which can allow for these two factors simultaneously is proposed. Utilizing the finite difference method, the numerical model for this problem is developed. With the numerical model, the effects of the geometrical nonlinearity and the non-Darcian flow on the consolidation of the soft soil are investigated. The results show that when the self-weight stress is calculated by the same method, the rate of the non-Darcian consolidation for the large-strain case is larger than that for the small-strain case, but the difference between them is limited. However, the difference between the consolidation rates caused by the non-Darcian and Darcian flows is significant. Therefore, when the geometrical nonlinearity of the soft clay is considered in calculating the consolidation settlement, due to the complexity of the large-strain assumption, the small-strain assumption can be used to replace it if the self-weight stress for the small-strain assumption is calculated by considering its sedimentation. However, due to the aforementioned large difference between the consolidation rates with consideration of the non-Darcian flow in soft clay or not, it is better to consider the non-Darcian flow law for both the small and large stain assumptions.展开更多
Analysis of rotorcraft dynamics requires solution of the rotor induced flow field.Often,the appropriate model to be used for induced flow is nonlinear potential flow theory（which is the basis of vortex-lattice method...Analysis of rotorcraft dynamics requires solution of the rotor induced flow field.Often,the appropriate model to be used for induced flow is nonlinear potential flow theory（which is the basis of vortex-lattice methods）.These nonlinear potential flow equations sometimes must be solved in real time––such as for real-time flight simulation,when observers are needed for controllers,or in preliminary design computations.In this paper,the major effects of nonlinearities on induced flow are studied for lifting rotors in low-speed flight and hover.The approach is to use a nonlinear statespace model of the induced flow based on a Galerkin treatment of the potential flow equations.展开更多
By using the conservation laws and the method of variational principle, an improved Arnol′d′s second nonlinear stability theorem for the two-dimensional multilayer quasi-geostrophic model in periodic channel is obta...By using the conservation laws and the method of variational principle, an improved Arnol′d′s second nonlinear stability theorem for the two-dimensional multilayer quasi-geostrophic model in periodic channel is obtained.展开更多
Based on the non-Darcian flow law described by exponent m and threshold gradient i 1 under a low hydraulic gradient and the classical nonlinear relationships e-lgσ′ and e-lgk v (Mesri and Rokhsar, 1974), the governi...Based on the non-Darcian flow law described by exponent m and threshold gradient i 1 under a low hydraulic gradient and the classical nonlinear relationships e-lgσ′ and e-lgk v (Mesri and Rokhsar, 1974), the governing equation of 1D nonlinear consolidation was modified by considering both uniform distribution of self-weight stress and linear increment of self-weight stress. The numerical solutions for the governing equation were derived by the finite difference method (FDM). Moreover, the solutions were verified by comparing the numerical results with those by analytical method under a specific case. Finally, consolidation behavior under different parameters was investigated, and the results show that the rate of 1D nonlinear consolidation will slow down when the non-Darcian flow law is considered. The consolidation rate with linear increment of self-weight stress is faster than that with uniform distribution one. Compared to Darcy's flow law, the influence of parameters describing non-linearity of soft soil on consolidation behavior with non-Darcian flow has no significant change.展开更多
Nonlinear stability criteria for quasi-geostrophic zonally symmetric flow are improved by establishing an optimal Poincard inequality. The inequality is derived by a variational calculation considering the additional ...Nonlinear stability criteria for quasi-geostrophic zonally symmetric flow are improved by establishing an optimal Poincard inequality. The inequality is derived by a variational calculation considering the additional invariant of zonal momentum. When applied to the Eady model in a periodic channel with finite zonal length, the improved nonlinear stability criterion is identical to the linear normal-mode stability criterion provided the channel meridional width is no greater than 0.8605... times its channel length （which is the geophysically relevant case）.展开更多
The equation of motion of sandwich beam with pyramidal lattice core in the supersonic flow considering geometric nonlinearity is formulated using Hamilton＇s principle. The piston theory is used to evaluate aerodynami...The equation of motion of sandwich beam with pyramidal lattice core in the supersonic flow considering geometric nonlinearity is formulated using Hamilton＇s principle. The piston theory is used to evaluate aerodynamic pressure. The structural aeroelastic properties are analyzed using frequency- and time-domain methods, and some interesting phenomena are observed. It is noted that the flutter of sandwich beam occurs under the coupling effect of low order modes. The critical flutter aerodynamic pressure of the sandwich beam is higher than that of the isotropic beam with the same weight, length and width. The influence of inclination angle of core truss on flutter characteristic is analyzed.展开更多
An attempt has been made to apply Arnold type nonlinear stability criteria to the diagnostic study of the persistence (stability) or breakdown (instability) of the atmospheric flows. In the case of the blocking high, ...An attempt has been made to apply Arnold type nonlinear stability criteria to the diagnostic study of the persistence (stability) or breakdown (instability) of the atmospheric flows. In the case of the blocking high, the cut-off low and the zonal flow, the relationships of the geostrophic stream function versus the potential vorticity of the observed atmosphere are analyzed, which indicates that Arnold second type nonlinear stability theorem is more relevant to the observed atmosphere than the first one. For both the stable and unstable zonal flows, Arnold second type nonlinear stability criteria are applied to the diagnosis. The primary results show that our analyses correspond well to the evolution of the atmospheric motions. The synoptically stable zonal flows satisfy Arnol′d second type nonlinear stability criteria; while the synoptically unstable ones violate the nonlinear stability criteria.展开更多
This work systematically simulates the external mass transfer from/to a spherical drop and solid particle suspended in a nonlinear uniaxial extensional creeping flow.The mass transfer problem is governed by three dime...This work systematically simulates the external mass transfer from/to a spherical drop and solid particle suspended in a nonlinear uniaxial extensional creeping flow.The mass transfer problem is governed by three dimensionless parameters:the viscosity ratio(λ),the Peclet number(Pe),and the nonlinear intensity of the flow(E).The existing mass transfer theory,valid for very large Peclet numbers only,is expanded,by numerical simulations,to include a much larger range of Peclet numbers(1≤Pe≤105).The simulation results show that the dimensionless mass transfer rate,expressed as the Sherwood number(5 h),agrees well with the theoretical results at the convection-dominated regime(Pe>103).Only when E>5/4,the simulated Sh for a solid sphere in the nonlinear uniaxial extensional flow is larger than theoretical results because the theory neglects the effect of the vortex formed outside the particle on the rate of mass transfer.Empirical correlations are proposed to predict the influence of the dimensionless governing parameters(λ,Pe,E)on the Sherwood number(Sh).The maximum deviations of all empirical correlations are less than 15%when compared to the numerical simulated results.展开更多
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.92371201,52192633,11872293,and 92152301)the Natural Science Basic Research Program of Shaanxi(Grant Nos.2024JC-YBQN-0008,and 2022JC-03)+1 种基金Shaanxi Key Research and Development Program(Grant No.2022ZDLGY02-07)the Joint Natural Science Foundation of China with Guangdong Province for TianHe-II Supercomputer Resources,and the Research Start-up Foundation of Xi’an University of Science and Technology for the High-Level Talent.
文摘The flow control at low Reynolds numbers is one of the most promising technologies in the field of aerodynamics,and it is also an important source of the innovation for novel aircraft.In this study,a new way of nonlinear flow control by interaction between two flexible flaps is proposed,and their flow control mechanism is studied employing the self-constructed immersed boundary-lattice Boltzmann-finite element method(IB-LB-FEM).The effects of the difference in material properties and flap length between the two flexible flaps on the nonlinear flow control of the airfoil are discussed.It is suggested that the relationship between the deformation of the two flexible flaps and the evolution of the vortex under the fluid-structure interaction(FSI).It is shown that the upstream flexible flap plays a key role in the flow control of the two flexible flaps.The FSI effect of the upstream flexible flap will change the unsteady flow behind it and affect the deformation of the downstream flexible flap.Two flexible flaps with different material properties and different lengths will change their own FSI characteristics by the induced vortex,effectively suppressing the flow separation on the airfoil’s upper surface.The interaction of two flexible flaps plays an extremely important role in improving the autonomy and adjustability of flow control.The numerical results will provide a theoretical basis and technical guidance for the development and application of a new flap passive control technology.
基金This study has been partially funded by National Key Research and Development Program of China(Grant No.2020YFA0711800)the National Natural Science Foundation of China(Grant No.51979272)the Natural Science Foundation of Shandong Province,China(Grant No.ZR2021QE069).
文摘This study experimentally analyzes the nonlinear flow characteristics and channelization of fluid through rough-walled fractures during the shear process using a shear-flow-visualization apparatus.A series of fluid flow and visualization tests is performed on four transparent fracture specimens with various shear displacements of 1 mm,3 mm,5 mm,7 mm and 10 mm under a normal stress of 0.5 MPa.Four granite fractures with different roughnesses are selected and quantified using variogram fractal dimensions.The obtained results show that the critical Reynolds number tends to increase with increasing shear displacement but decrease with increasing roughness of fracture surface.The flow paths are more tortuous at the beginning of shear because of the wide distribution of small contact spots.As the shear displacement continues to increase,preferential flow paths are more distinctly observed due to the decrease in the number of contact spots caused by shear dilation;yet the area of single contacts in-creases.Based on the experimental results,an empirical mathematical equation is proposed to quantify the critical Reynolds number using the contact area ratio and fractal dimension.
基金Project(10672187) supported by the National Natural Science Foundation of ChinaProject(2008ZX05000-013-02) supported by the National Science and Technology Major Program of China
文摘A nonlinear flow reservoir mathematical model was established based on the flow characteristic of low-permeability reservoir.The well-grid equations were deduced and the dimensionless permeability coefficient was introduced to describe the permeability variation of nonlinear flow.The nonlinear flow numerical simulation program was compiled based on black-oil model.A quarter of five-spot well unit was simulated to study the effect of nonlinear flow on the exploitation of low-permeability reservoir.The comprehensive comparison and analysis of the simulation results of Darcy flow,quasi-linear flow and nonlinear flow were provided.The dimensionless permeability coefficient distribution was gained to describe the nonlinear flow degree.The result shows that compared with the results of Darcy flow,when considering nonlinear flow,the oil production is low,and production decline is rapid.The fluid flow in reservoir consumes more driving energy,which reduces the water flooding efficiency.Darcy flow model overstates the reservoir flow capability,and quasi-linear flow model overstates the reservoir flow resistance.The flow ability of the formation near the well and artificial fracture is strong while the flow ability of the formation far away from the main streamline is weak.The nonlinear flow area is much larger than that of quasi-linear flow during the fluid flow in low-permeability reservoir.The water propelling speed of nonlinear flow is greatly slower than that of Darcy flow in the vertical direction of artificial fracture,and the nonlinear flow should be taken into account in the well pattern arrangement of low-permeability reservoir.
基金Project supported by the National Natural Science Foundation of China (Nos.40202036,40572163,50579042)the Youth Science Foundation of Siehuan Province of China (No.05ZQ026-043)+1 种基金the Science Foundation of State Key Laboratory of Geohazard Prevention and Geoenvironment Protection(No.GZ2004-05)the Postdoctoral Science Foundation of China (No.35)
文摘It was derived that micro-scale amount level of average pore radius of clay changed from 0.01 to 0.1 micron by an equivalent concept of flow in porous media. There is good agreement between the derived results and test ones. Results of experiments show that flow in micro-scale pore of saturated clays follows law of nonlinear flow. Theoretical analyses demonstrate that an interaction of solid-liquid interfaces varies inversely with permeability or porous radius. The interaction is an important reason why nonlinear flow in saturated clays occurs. An exact mathematical model was presented for nonlinear flow in micro-scale pore of saturated clays. Dimension and physical meanings of parameters of it are definite. A new law of nonlinear flow in saturated clays was established. It can describe characteristics of flow curve of the whole process of the nonlinear flow from low hydraulic gradient to high one. Darcy law is a special case of the new law. A math- ematical model was presented for consolidation of nonlinear flow in radius direction in saturated clays with constant rate based on the new law of nonlinear flow. Equations of average mass conservation and moving boundary, and formula of excess pore pressure distribution and average degree of consolidation for nonlinear flow in saturated clay were derived by using an idea of viscous boundary layer, a method of steady state in stead of transient state and a method of integral of an equation. Laws of excess pore pressure distribution and changes of average degree of consolidation with time were obtained. Re- sults show that velocity of moving boundary decreases because of the nonlinear flow in saturated clay. The results can provide geology engineering and geotechnical engineering of saturated clay with new scientific bases. Calculations of average degree of consolidation of the Darcy flow are a special case of that of the nonlinear flow.
文摘A mathematical model of two-phase fluid nonlinear flow in the direction of normal of ellipse through low-permeability porous media was established according to a nonlinear flow law expressed in a continuous function with three parameters, a mass conservation law and a concept of turbulent ellipses. A solution to the model was obtained by using a finite difference method and an extrapolation method. Formulas of calculating development index not only before but also after water breaks through an oil well in the condition of two-phase fluid nonlinear flow in the media were derived. An example was discussed. Water saturation distribution was presented. The moving law of drainage front was found. Laws of change of pressure difference with time were recognized. Results show that there is much difference of water saturation distribution between nonlinear flow and linear flow; that drainage front by water moves faster, water breaks through sooner and the index gets worse because of the nonlinear flow; and that dimensionless pressure difference gets larger at the same dimensionless time and difficulty of oil development becomes bigger by the nonlinear flow. Thus, it is necessary that influence of nonlinear flow on development indexes of the oil fields be taken into account. The results provide water-flooding development of the oilfields with scientific basis.
基金Research supported by NSFC (10771189 and 10831008)
文摘By studying a fully nonlinear flow deforming conformal metrics on a compact and connected manifold, we prove the long time existence and the exponential convergence of the solutions of the flow for any initial metric g0 with the Schouten tensor Ag0 ∈ Γk.
基金funded by National Key Research and Development Program of China,China (Grant No.2020YFA0711800)Natural Science Foundation of China,China (Grant Nos.51979272 and 51879150)+1 种基金Natural Science Foundation of Jiangsu Province,China (Grant No.BK20211584)Xuzhou Science and Technology Planning Project,China (Grant No.KC21004).
文摘The nonlinear flow properties of Newtonian fluids through crossed fractures are estimated by considering the influences of length,aperture,and surface roughness of fractures.A total of 252 computational runs are performed by creating 36 computational domains,in which the Navier-Stokes equations are solved.The results show that the nonlinear relationship between flow rate and hydraulic gradient follows Forchheimer’s law–based equation.When the hydraulic gradient is small(i.e.,10^(−6)),the streamlines are parallel to the fracture walls,indicating a linear streamline distribution.When the hydraulic gradient is large(i.e.,10^(0)),the streamlines are disturbed by a certain number of eddies,indicating a nonlinear streamline distribution.The patterns of eddy distributions depend on the length,aperture,and surface roughness of fractures.With the increment of hydraulic gradient from 10^(−6) to 10^(0),the ratio of flow rate to hydraulic gradient holds constants and then decreases slightly and finally decreases robustly.The fluid flow experiences a linear flow regime,a weakly nonlinear regime,and a strongly nonlinear regime,respectively.The critical hydraulic gradient ranges from 3.27×10^(−5) to 5.82×10^(−2) when fracture length=20–100mmandmechanical aperture=1–5mm.The joint roughness coefficient plays a negligible role in the variations in critical hydraulic gradient compared with fracture length and/or mechanical aperture.The critical hydraulic gradient decreases with increasing mechanical aperture,following power-law relationships.The parameters in the functions are associated with fracture length.
基金the Natural Science Foundation of Zhejiang Province(Grant No.LR19E090001)the Natural Science Foundation of China(Grant Nos.42077252,42011530122,and 51979272).
文摘Nonlinear flow behavior of fluids through three-dimensional(3D)discrete fracture networks(DFNs)considering effects of fracture number,surface roughness and fracture aperture was experimentally and numerically investigated.Three physical models of DFNs were 3D-printed and then computed tomography(CT)-scanned to obtain the specific geometry of fractures.The validity of numerically simulating the fluid flow through DFNs was verified via comparison with flow tests on the 3D-printed models.A parametric study was then implemented to establish quantitative relations between the coefficients/parameters in Forchheimer’s law and geometrical parameters.The results showed that the 3D-printing technique can well reproduce the geometry of single fractures with less precision when preparing complex fracture networks,numerical modeling precision of which can be improved via CT-scanning as evidenced by the well fitted results between fluid flow tests and numerical simulations using CT-scanned digital models.Streamlines in DFNs become increasingly tortuous as the fracture number and roughness increase,resulting in stronger inertial effects and greater curvatures of hydraulic pressure-low rate relations,which can be well characterized by the Forchheimer’s law.The critical hydraulic gradient for the onset of nonlinear flow decreases with the increasing aperture,fracture number and roughness,following a power function.The increases in fracture aperture and number provide more paths for fluid flow,increasing both the viscous and inertial permeabilities.The value of the inertial permeability is approximately four orders of magnitude greater than the viscous permeability,following a power function with an exponent a of 3,and a proportional coefficient b mathematically correlated with the geometrical parameters.
文摘The models of the nonlinear radial flow for the infinite and finite reservoirs including a quadratic gradient term were presented. The exact solution was given in real space for flow equation including quadratic gradiet term for both constant-rate and constant pressure production cases in an infinite system by using generalized Weber transform. Analytical solutions for flow equation including quadratic gradient term were also obtained by using the Hankel transform for a finite circular reservoir case. Both closed and constant pressure outer boundary conditions are considered. Moreover, both constant rate and constant pressure inner boundary conditions are considered. The difference between the nonlinear pressure solution and linear pressure solution is analyzed. The difference may be reached about 8% in the long time. The effect of the quadratic gradient term in the large time well test is considered.
基金National Natural Science Foundation of China (10772082)Doctoral Foundation of Ministry of Education of China (20070287005)
文摘This article studies the nonlinear evolution of disturbance waves in supersonic nonparallel boundary layer flows by using nonlinear parabolic stability equations （NPSE）. An accurate numerical method is developed to solve the equations and march the NPSE in a stable manner. Through computation,are obtained the curves of amplitude and disturbance shape function of harmonic waves. Especially are demonstrated the physical characteristics of nonlinear stability of various harmonic waves,including instantaneous stream wise vortices,spanwise vortices and Λ structure etc,and are used to study and analyze the mechanism of the transition process. The calculated results have evidenced the effectiveness of the proposed NPSE method to research the nonlinear stability of the supersonic boundary layers.
文摘This paper gives an overview on nonlinear porous flow in low permeability porous media, reveals the microscopic mechanisms of flows, and clarifies properties of porous flow fluids. It shows that, deviating from Darcy＇s linear law, the porous flow characteristics obey a nonlinear law in a low-permeability porous medium, and the viscosity of the porous flow fluid and the permeability values of water and oil are not constants. Based on these characters, a new porous flow model, which can better describe low permeability reservoir~ is established. This model can describe various patterns of porous flow, as Darcy＇s linear law does. All the parameters involved in the model, having definite physical meanings, can be obtained directly from the experiments.
基金We gratefully acknowledge NSFC(51509194)CSC for providing finacial support eanabling Li Qin and Hongling Qin to visit the University of Southampton to engage the related research.
文摘Based on the energy flow theory of nonlinear dynamical system,the stabilities,bifurcations,possible periodical/chaotic motions of nonlinear water-lubricated bearing-shaft coupled systems are investigated in this paper.It is revealed that the energy flow characteristics around the equlibrium point of system behaving in the three types with different friction-para-mters.(a)Energy flow matrix has two negative and one positive energy flow factors,constructing an attractive local zero-energy flow surface,in which free vibrations by initial disturbances show damped modulated oscillations with the system tending its equlibrium state,while forced vibrations by external forces show stable oscillations,(b)Energy flow matrix has one negative and two positive energy flow factors,spaning a divergence local zero-energy flow surface,so that the both free and forced vibrations are divergence oscillations with the system being unstable,(c)Energy flow matrix has a zero-energy flow factor and two opposite factors,which constructes a local zero-energy flow surface dividing the local phase space into stable,unstable and central subspace,and the simulation shows friction self-induced unstable vibrations for both free and forced cases.For a set of friction parameters,the system behaves a periodical oscillation,where the bearing motion tends zero and the shaft motion reaches a stable limit circle in phase space with the instant energy flow tending a constant and the time averaged one tending zero.Numerical simulations have not found any possible chaotic motions of the system.It is discovered that the damping matrices of cases(a),(b)and(c)respectively have positive,negative and zero diagonal elements,resulting in the different dynamic behavour of system,which gives a giderline to design the water-lubricated bearing unit with expected performance by adjusting the friction parameters for applications.
基金Projects(51109092,11272137)supported by the National Natural Science Foundation of ChinaProjects(2013M530237,2014T70479)supported by China Postdoctoral Science FoundationProject(SJLX15-0498)supported by Jiangsu Provincial Graduate Students Research and Innovation Program,China
文摘Geometrical nonlinearity of the soft soil and the deviation of water flow in the soft clay from Darcy's law have been well recognized in practice. However, the theory of consolidation, which can account for both the geometrical nonlinearity and the non-Darcian flow, has not been reported so far. In this contribution, a model for the consolidation of soft clay which can allow for these two factors simultaneously is proposed. Utilizing the finite difference method, the numerical model for this problem is developed. With the numerical model, the effects of the geometrical nonlinearity and the non-Darcian flow on the consolidation of the soft soil are investigated. The results show that when the self-weight stress is calculated by the same method, the rate of the non-Darcian consolidation for the large-strain case is larger than that for the small-strain case, but the difference between them is limited. However, the difference between the consolidation rates caused by the non-Darcian and Darcian flows is significant. Therefore, when the geometrical nonlinearity of the soft clay is considered in calculating the consolidation settlement, due to the complexity of the large-strain assumption, the small-strain assumption can be used to replace it if the self-weight stress for the small-strain assumption is calculated by considering its sedimentation. However, due to the aforementioned large difference between the consolidation rates with consideration of the non-Darcian flow in soft clay or not, it is better to consider the non-Darcian flow law for both the small and large stain assumptions.
基金co-supported by the National Natural Science Foundation of China(No.51375104)the Heilongjiang Province Funds for Distinguished Young Scientists(No.JC201405)+1 种基金the China Postdoctoral Science Foundation(No.2015M581433)the Postdoctoral Science Foundation of Heilongjiang Province(No.LBH-Z15038)
文摘Analysis of rotorcraft dynamics requires solution of the rotor induced flow field.Often,the appropriate model to be used for induced flow is nonlinear potential flow theory（which is the basis of vortex-lattice methods）.These nonlinear potential flow equations sometimes must be solved in real time––such as for real-time flight simulation,when observers are needed for controllers,or in preliminary design computations.In this paper,the major effects of nonlinearities on induced flow are studied for lifting rotors in low-speed flight and hover.The approach is to use a nonlinear statespace model of the induced flow based on a Galerkin treatment of the potential flow equations.
文摘By using the conservation laws and the method of variational principle, an improved Arnol′d′s second nonlinear stability theorem for the two-dimensional multilayer quasi-geostrophic model in periodic channel is obtained.
基金Project supported by the National Natural Science Foundation of China (No. 51109092)the National Science Foundation for Post-doctoral Scientists of China (No. 2013M530237)the Jiangsu University Foundation for Advanced Talents (No. 12JDG098), China
文摘Based on the non-Darcian flow law described by exponent m and threshold gradient i 1 under a low hydraulic gradient and the classical nonlinear relationships e-lgσ′ and e-lgk v (Mesri and Rokhsar, 1974), the governing equation of 1D nonlinear consolidation was modified by considering both uniform distribution of self-weight stress and linear increment of self-weight stress. The numerical solutions for the governing equation were derived by the finite difference method (FDM). Moreover, the solutions were verified by comparing the numerical results with those by analytical method under a specific case. Finally, consolidation behavior under different parameters was investigated, and the results show that the rate of 1D nonlinear consolidation will slow down when the non-Darcian flow law is considered. The consolidation rate with linear increment of self-weight stress is faster than that with uniform distribution one. Compared to Darcy's flow law, the influence of parameters describing non-linearity of soft soil on consolidation behavior with non-Darcian flow has no significant change.
文摘Nonlinear stability criteria for quasi-geostrophic zonally symmetric flow are improved by establishing an optimal Poincard inequality. The inequality is derived by a variational calculation considering the additional invariant of zonal momentum. When applied to the Eady model in a periodic channel with finite zonal length, the improved nonlinear stability criterion is identical to the linear normal-mode stability criterion provided the channel meridional width is no greater than 0.8605... times its channel length （which is the geophysically relevant case）.
基金Project supported by the National Natural Science Foundation of China(Nos.11572007 and 11172084)
文摘The equation of motion of sandwich beam with pyramidal lattice core in the supersonic flow considering geometric nonlinearity is formulated using Hamilton＇s principle. The piston theory is used to evaluate aerodynamic pressure. The structural aeroelastic properties are analyzed using frequency- and time-domain methods, and some interesting phenomena are observed. It is noted that the flutter of sandwich beam occurs under the coupling effect of low order modes. The critical flutter aerodynamic pressure of the sandwich beam is higher than that of the isotropic beam with the same weight, length and width. The influence of inclination angle of core truss on flutter characteristic is analyzed.
文摘An attempt has been made to apply Arnold type nonlinear stability criteria to the diagnostic study of the persistence (stability) or breakdown (instability) of the atmospheric flows. In the case of the blocking high, the cut-off low and the zonal flow, the relationships of the geostrophic stream function versus the potential vorticity of the observed atmosphere are analyzed, which indicates that Arnold second type nonlinear stability theorem is more relevant to the observed atmosphere than the first one. For both the stable and unstable zonal flows, Arnold second type nonlinear stability criteria are applied to the diagnosis. The primary results show that our analyses correspond well to the evolution of the atmospheric motions. The synoptically stable zonal flows satisfy Arnol′d second type nonlinear stability criteria; while the synoptically unstable ones violate the nonlinear stability criteria.
基金support and helpful insight.This work was supported by the National Key Research and Development Program(2021YFC2902502)the National Natu-ral Science Foundation of China(21938009,91934301,22078320)+5 种基金the Major Scientific and Technological Innovation Projects in Shan-dong Province(2019JZZY010302)the Shandong Key Research and Development Program(International Cooperation Office)(2019GHZ018)the Shandong Province Postdoctoral Innovative Talents Support Plan(SDBX2020018)the External Cooperation Program of BIC,Chinese Academy of Sciences(122111KYSB20190032)Chemistry and Chemical Engineering Guangdong Laboratory(1922006)GHfund B(202107021062).
文摘This work systematically simulates the external mass transfer from/to a spherical drop and solid particle suspended in a nonlinear uniaxial extensional creeping flow.The mass transfer problem is governed by three dimensionless parameters:the viscosity ratio(λ),the Peclet number(Pe),and the nonlinear intensity of the flow(E).The existing mass transfer theory,valid for very large Peclet numbers only,is expanded,by numerical simulations,to include a much larger range of Peclet numbers(1≤Pe≤105).The simulation results show that the dimensionless mass transfer rate,expressed as the Sherwood number(5 h),agrees well with the theoretical results at the convection-dominated regime(Pe>103).Only when E>5/4,the simulated Sh for a solid sphere in the nonlinear uniaxial extensional flow is larger than theoretical results because the theory neglects the effect of the vortex formed outside the particle on the rate of mass transfer.Empirical correlations are proposed to predict the influence of the dimensionless governing parameters(λ,Pe,E)on the Sherwood number(Sh).The maximum deviations of all empirical correlations are less than 15%when compared to the numerical simulated results.
