The article studies the homogenization of a stationary Navier-Stokes fluid in porous medium with thin film under Dirichlet boundary condition.At the end of the article,＂Darcy＇s law＂is rigorously derived from this m...The article studies the homogenization of a stationary Navier-Stokes fluid in porous medium with thin film under Dirichlet boundary condition.At the end of the article,＂Darcy＇s law＂is rigorously derived from this model as the parameter ε tends to zero,which is independent of the coordinates towards the thickness.展开更多
In this paper,we consider solving the topology optimization for steady-state incompressibleNavier-Stokes problems via a new topology optimization method called parameterized level set method,which can maintain a relat...In this paper,we consider solving the topology optimization for steady-state incompressibleNavier-Stokes problems via a new topology optimization method called parameterized level set method,which can maintain a relatively smooth level set function with a local optimality condition.The objective of topology optimization is tond an optimal conguration of theuid and solid materials that minimizes power dissipation under a prescribeduid volume fraction constraint.An articial friction force is added to the Navier-Stokes equations to apply the no-slip boundary condition.Although a great deal of work has been carried out for topology optimization ofuidow in recent years,there are few researches on the topology optimization ofuidow with physical body forces.To simulate theuidow in reality,the constant body force(e.g.,gravity)is considered in this paper.Several 2D numerical examples are presented to discuss the relationships between the proposed method with Reynolds number and initial design,and demonstrate the feasibility and superiority of the proposed method in dealing with unstructuredmesh problems.Three 3D numerical examples demonstrate the proposedmethod is feasible in three-dimensional.展开更多
This paper is devoted to estimates on weighted L^(q)-norms of the nonstationary 3D Navier-Stokes flow in an exterior domain.By multiplying the Navier-Stokes equation with a well selected vector field,an integral equat...This paper is devoted to estimates on weighted L^(q)-norms of the nonstationary 3D Navier-Stokes flow in an exterior domain.By multiplying the Navier-Stokes equation with a well selected vector field,an integral equation is derived,from which,w etablish the eight etmate‖|x|^(α)u(t)‖q≤(1+t^(α/2+ε))t^−3/2(1-1/q),t>0, where 0<α≤1 and 3/2<q<∞,or 1<α<2 and 3/3-α<q<∞,0<ε<1 is arbitrary,and μ_(0)∈L_(σ)^(3)(Ω),|x|^(α)u(0)∈L^(1)(Ω) with ‖μ_(0)‖_(3) sufficiently small.With the aid of the representation of the flow,we also prove that if in addition μ_(0)∈D_(a)^(1-1/b,b) for some 6/5≤α<3/2 and 1<b<2 with 3/a+2/b=4,then the ptimal estimate ‖|x|^(α)u(t)‖q≤C(1+t^(α/2))t^(-3/2(1-1/q)),t>0 holds,where α>0 and 1<q<∞.Compared with the literature,here no extra restriction is laid on the range of the exponents α and q.展开更多
The existence of a global attractor is established for generalized Navier-Stokes equations incorporating damping term within the periodic domainΩ=[−π,π]^(n).Initially,we show the existence and uniqueness of strong ...The existence of a global attractor is established for generalized Navier-Stokes equations incorporating damping term within the periodic domainΩ=[−π,π]^(n).Initially,we show the existence and uniqueness of strong solutions.Subsequently,we verify the continuity of the associated semigroup when max{2n+1/n-1,5n+2/3n-2} < β <3n+2/n-2.Finally,we establish the existence of both H^(α)-global attractor and H^(2α)-global attractor.展开更多
We present the existence/non-existence criteria for large-amplitude boundary layer solutions to the inflow problem of the one-dimensional(1D)full compressible NavierStokes equations on a half line R_+.Instead of the c...We present the existence/non-existence criteria for large-amplitude boundary layer solutions to the inflow problem of the one-dimensional(1D)full compressible NavierStokes equations on a half line R_+.Instead of the classical center manifold approach for the existence of small-amplitude boundary layer solutions in the previous results,the delicate global phase plane analysis,based on the qualitative theory of ODEs,is utilized to obtain the sufficient and necessary conditions for the existence/non-existence of large boundary layer solutions to the half-space inflow problem when the right end state belongs to the supersonic,transonic,and subsonic regions,respectively,which completely answers the existence/nonexistence of boundary layer solutions to the half-space inflow problem of 1D full compressible Navier-Stokes equations.展开更多
We study the time-decay properties of weighted norms of solutions to the Stokes equations and the Navier-Stokes equations in the half-space Rn+(n 2).Three kinds of the weighted Lp-Lr estimates are established for the ...We study the time-decay properties of weighted norms of solutions to the Stokes equations and the Navier-Stokes equations in the half-space Rn+(n 2).Three kinds of the weighted Lp-Lr estimates are established for the Stokes semigroup generated by the Stokes operator in the half-space R+n(n 2).As an application of the weighted estimates of the Stokes semigroup,a class of local and global strong solutions in weighted Lp(R+n)are constructed,following the approach given by Kato.展开更多
The preconditioning method is used to solve the low Mach number flow. The space discritisation scheme is the Roe scheme and the DES turbulence model is used. Then, the low Mach number turbulence flow around the NACA00...The preconditioning method is used to solve the low Mach number flow. The space discritisation scheme is the Roe scheme and the DES turbulence model is used. Then, the low Mach number turbulence flow around the NACA0012 airfoil is used to verify the efficiency of the proposed method. Two cases of the low Mach number flows around the multi-element airfoil and the circular cylinder are also used to test the proposed method. Numerical results show that the methods combined the preconditioning method and compressible Navier-Stokes equations are efficient to solve low Mach number flows.展开更多
A robust unsteady rotor flowfield solver CLORNS code is established to predict the complex unsteady aerodynamic characteristics of rotor flowfield. In order to handle the difficult problem about grid generation around...A robust unsteady rotor flowfield solver CLORNS code is established to predict the complex unsteady aerodynamic characteristics of rotor flowfield. In order to handle the difficult problem about grid generation around rotor with complex aerodynamic shape in this CFD code,a parameterized grid generated method is established, and the moving-embedded grids are constructed by several proposed universal methods. In this work, the unsteady Reynolds-Averaged Navier-Stokes（RANS） equations with Spalart-Allmaras are selected as the governing equations to predict the unsteady flowfield of helicopter rotor. The discretization of convective fluxes is accomplished by employing the second-order central difference scheme, third-order MUSCL-Roe scheme, and fifth-order WENO-Roe scheme. Aimed at simulating the unsteady aerodynamic characteristics of helicopter rotor, the dual-time scheme with implicit LU-SGS scheme is employed to accomplish the temporal discretization. In order to improve the computational efficiency of holecells and donor elements searching of the moving-embedded grid technology, the ‘‘disturbance diffraction method＂ and ‘‘minimum distance scheme of donor elements method＂ are established in this work. To improve the computational efficiency, Message Passing Interface（MPI） parallel method based on subdivision of grid, local preconditioning method and Full Approximation Storage（FAS） multi-grid method are combined in this code. By comparison of the numerical results simulated by CLORNS code with test data, it is illustrated that the present code could simulate the aerodynamic loads and aerodynamic noise characteristics of helicopter rotor accurately.展开更多
In this paper, the nonreflecting boundary conditions based upon fundamental ideas of the linear analysis are developed for gas dynamic equations, and the modified boundary conditions for Navier-Stokes equations are pr...In this paper, the nonreflecting boundary conditions based upon fundamental ideas of the linear analysis are developed for gas dynamic equations, and the modified boundary conditions for Navier-Stokes equations are proposed as a substitute of the nonreflecting boundary conditions inside boundary layers near rigid walls. These derived boundary conditions are then applied to calculations both for the Euler equations and the Navier-Stokes equations to determine if they can produce acceptable results for the subsonic flows in channels. The numerical results obtained by an implicit second-order upwind difference scheme show the effective- ness and generality of the boundary conditions. Furthermore, the formulae and the analysis performed here may be extended to three dimensional problems.展开更多
A numerical approach based on the solution of the Reynolds-averaged Navier-Stokes(RANS) equations using the shear-stress transport(SST) turbulence model has been employed to investigate the hydrodynamic performance an...A numerical approach based on the solution of the Reynolds-averaged Navier-Stokes(RANS) equations using the shear-stress transport(SST) turbulence model has been employed to investigate the hydrodynamic performance and flow of tunnel thrusters.The flow passages between adjacent blades are discretized with prismatic cells so that the boundary layer flow is resolved down to the viscous sub-layer.The hydrodynamic performances predicted by the quasi-steady approach agree well with the experimental data for three impellers covering a range of blade area and pitch.Through analysis of the flow field,the reason why the hub of impeller also contributes to thrust which can amount to 40%—60% of the impeller thrust,and the mechanism of the impeller inducing an axial force on the hull are elucidated.展开更多
In order to account for the effect of particle existence on gas-particle turbulence flow in large-eddy simulation (LES),a new gas-particle turbulent kinetic energy subgrid-scale (SGS) turbulence model is established,a...In order to account for the effect of particle existence on gas-particle turbulence flow in large-eddy simulation (LES),a new gas-particle turbulent kinetic energy subgrid-scale (SGS) turbulence model is established,and the effect of particle wake is also considered in gas turbulent kinetic energy SGS turbulence model.Simulation of gas-particle turbulence flow in backward-facing step is carried out by LES using present model and by unified second-order moment (USM) model.The prediction statistical results including mean velocity and fluctuation velocity by LES using present model are in reasonable agreement with the experimental results.It is shown that present model is with higher calculating accuracy than USM model,which indicates that the turbulent kinetic energy SGS turbulence model is suitable.展开更多
基金National NaturalScience Foundation of China(10171113 and 10471156)Natural Science Foundation of Guangdong(4009793)
文摘The article studies the homogenization of a stationary Navier-Stokes fluid in porous medium with thin film under Dirichlet boundary condition.At the end of the article,＂Darcy＇s law＂is rigorously derived from this model as the parameter ε tends to zero,which is independent of the coordinates towards the thickness.
基金supported by the National Natural Science Foundation of China (Grant No.12072114)the National Key Research and Development Plan (Grant No.2020YFB1709401)the Guangdong Provincial Key Laboratory of Modern Civil Engineering Technology (2021B1212040003).
文摘In this paper,we consider solving the topology optimization for steady-state incompressibleNavier-Stokes problems via a new topology optimization method called parameterized level set method,which can maintain a relatively smooth level set function with a local optimality condition.The objective of topology optimization is tond an optimal conguration of theuid and solid materials that minimizes power dissipation under a prescribeduid volume fraction constraint.An articial friction force is added to the Navier-Stokes equations to apply the no-slip boundary condition.Although a great deal of work has been carried out for topology optimization ofuidow in recent years,there are few researches on the topology optimization ofuidow with physical body forces.To simulate theuidow in reality,the constant body force(e.g.,gravity)is considered in this paper.Several 2D numerical examples are presented to discuss the relationships between the proposed method with Reynolds number and initial design,and demonstrate the feasibility and superiority of the proposed method in dealing with unstructuredmesh problems.Three 3D numerical examples demonstrate the proposedmethod is feasible in three-dimensional.
文摘This paper is devoted to estimates on weighted L^(q)-norms of the nonstationary 3D Navier-Stokes flow in an exterior domain.By multiplying the Navier-Stokes equation with a well selected vector field,an integral equation is derived,from which,w etablish the eight etmate‖|x|^(α)u(t)‖q≤(1+t^(α/2+ε))t^−3/2(1-1/q),t>0, where 0<α≤1 and 3/2<q<∞,or 1<α<2 and 3/3-α<q<∞,0<ε<1 is arbitrary,and μ_(0)∈L_(σ)^(3)(Ω),|x|^(α)u(0)∈L^(1)(Ω) with ‖μ_(0)‖_(3) sufficiently small.With the aid of the representation of the flow,we also prove that if in addition μ_(0)∈D_(a)^(1-1/b,b) for some 6/5≤α<3/2 and 1<b<2 with 3/a+2/b=4,then the ptimal estimate ‖|x|^(α)u(t)‖q≤C(1+t^(α/2))t^(-3/2(1-1/q)),t>0 holds,where α>0 and 1<q<∞.Compared with the literature,here no extra restriction is laid on the range of the exponents α and q.
文摘The existence of a global attractor is established for generalized Navier-Stokes equations incorporating damping term within the periodic domainΩ=[−π,π]^(n).Initially,we show the existence and uniqueness of strong solutions.Subsequently,we verify the continuity of the associated semigroup when max{2n+1/n-1,5n+2/3n-2} < β <3n+2/n-2.Finally,we establish the existence of both H^(α)-global attractor and H^(2α)-global attractor.
基金partially supported by the NSFC(12171459,12288201,12090014,12421001)CAS Project for Young Scientists in Basic Research(YSBR-031)。
文摘We present the existence/non-existence criteria for large-amplitude boundary layer solutions to the inflow problem of the one-dimensional(1D)full compressible NavierStokes equations on a half line R_+.Instead of the classical center manifold approach for the existence of small-amplitude boundary layer solutions in the previous results,the delicate global phase plane analysis,based on the qualitative theory of ODEs,is utilized to obtain the sufficient and necessary conditions for the existence/non-existence of large boundary layer solutions to the half-space inflow problem when the right end state belongs to the supersonic,transonic,and subsonic regions,respectively,which completely answers the existence/nonexistence of boundary layer solutions to the half-space inflow problem of 1D full compressible Navier-Stokes equations.
基金supported in part by National Basic Research Program of China(Grant No.2006CB805902)Knowledge Innovation Funds of Chinese Academy of Sciences(Grant No.KJCX3-SYW-S03)+1 种基金supported in part by Scientific Research Plan Projects of Shaanxi Education(Grant No.09JK770)China Postdoctoral Science Foundation(Grant No.20090461305)
文摘We study the time-decay properties of weighted norms of solutions to the Stokes equations and the Navier-Stokes equations in the half-space Rn+(n 2).Three kinds of the weighted Lp-Lr estimates are established for the Stokes semigroup generated by the Stokes operator in the half-space R+n(n 2).As an application of the weighted estimates of the Stokes semigroup,a class of local and global strong solutions in weighted Lp(R+n)are constructed,following the approach given by Kato.
文摘The preconditioning method is used to solve the low Mach number flow. The space discritisation scheme is the Roe scheme and the DES turbulence model is used. Then, the low Mach number turbulence flow around the NACA0012 airfoil is used to verify the efficiency of the proposed method. Two cases of the low Mach number flows around the multi-element airfoil and the circular cylinder are also used to test the proposed method. Numerical results show that the methods combined the preconditioning method and compressible Navier-Stokes equations are efficient to solve low Mach number flows.
基金co-supported by the National Natural Science Foundation of China (Nos. 11272150, 10872094 and 10602024)
文摘A robust unsteady rotor flowfield solver CLORNS code is established to predict the complex unsteady aerodynamic characteristics of rotor flowfield. In order to handle the difficult problem about grid generation around rotor with complex aerodynamic shape in this CFD code,a parameterized grid generated method is established, and the moving-embedded grids are constructed by several proposed universal methods. In this work, the unsteady Reynolds-Averaged Navier-Stokes（RANS） equations with Spalart-Allmaras are selected as the governing equations to predict the unsteady flowfield of helicopter rotor. The discretization of convective fluxes is accomplished by employing the second-order central difference scheme, third-order MUSCL-Roe scheme, and fifth-order WENO-Roe scheme. Aimed at simulating the unsteady aerodynamic characteristics of helicopter rotor, the dual-time scheme with implicit LU-SGS scheme is employed to accomplish the temporal discretization. In order to improve the computational efficiency of holecells and donor elements searching of the moving-embedded grid technology, the ‘‘disturbance diffraction method＂ and ‘‘minimum distance scheme of donor elements method＂ are established in this work. To improve the computational efficiency, Message Passing Interface（MPI） parallel method based on subdivision of grid, local preconditioning method and Full Approximation Storage（FAS） multi-grid method are combined in this code. By comparison of the numerical results simulated by CLORNS code with test data, it is illustrated that the present code could simulate the aerodynamic loads and aerodynamic noise characteristics of helicopter rotor accurately.
文摘In this paper, the nonreflecting boundary conditions based upon fundamental ideas of the linear analysis are developed for gas dynamic equations, and the modified boundary conditions for Navier-Stokes equations are proposed as a substitute of the nonreflecting boundary conditions inside boundary layers near rigid walls. These derived boundary conditions are then applied to calculations both for the Euler equations and the Navier-Stokes equations to determine if they can produce acceptable results for the subsonic flows in channels. The numerical results obtained by an implicit second-order upwind difference scheme show the effective- ness and generality of the boundary conditions. Furthermore, the formulae and the analysis performed here may be extended to three dimensional problems.
文摘A numerical approach based on the solution of the Reynolds-averaged Navier-Stokes(RANS) equations using the shear-stress transport(SST) turbulence model has been employed to investigate the hydrodynamic performance and flow of tunnel thrusters.The flow passages between adjacent blades are discretized with prismatic cells so that the boundary layer flow is resolved down to the viscous sub-layer.The hydrodynamic performances predicted by the quasi-steady approach agree well with the experimental data for three impellers covering a range of blade area and pitch.Through analysis of the flow field,the reason why the hub of impeller also contributes to thrust which can amount to 40%—60% of the impeller thrust,and the mechanism of the impeller inducing an axial force on the hull are elucidated.
基金the National Natural Science Foundation of China (Nos.50736006 and 51066006)the Aero-Science Fund (No.2009ZB56004)the Jiangxi Provincial Natural Science Foundation (Nos.2009GZC0100 and 2008GZW0016)
文摘In order to account for the effect of particle existence on gas-particle turbulence flow in large-eddy simulation (LES),a new gas-particle turbulent kinetic energy subgrid-scale (SGS) turbulence model is established,and the effect of particle wake is also considered in gas turbulent kinetic energy SGS turbulence model.Simulation of gas-particle turbulence flow in backward-facing step is carried out by LES using present model and by unified second-order moment (USM) model.The prediction statistical results including mean velocity and fluctuation velocity by LES using present model are in reasonable agreement with the experimental results.It is shown that present model is with higher calculating accuracy than USM model,which indicates that the turbulent kinetic energy SGS turbulence model is suitable.
