The finite difference method (FDM) is applied in the present paper to solve the unsteady NHS equations for incompressible fluids. ADI and SLOR methods are served for the vorticity equation and the Poisson equation for...The finite difference method (FDM) is applied in the present paper to solve the unsteady NHS equations for incompressible fluids. ADI and SLOR methods are served for the vorticity equation and the Poisson equation for ψ respectively. The upwind scheme is used for the convective terms. The moving boundary conditions are specially treated, and the effects of outlet conditions on the flow field are abo examined. Numerical results obtained show that the spoiler's oscillation induces forming, growing and shedding of the vortices. The shedding frequency of vortices is equal to that of the spoiler's oscillation. The forced unsteady separated flows under the present investigation depend mainly on the reduced frequency. At low reduced frequency, the vortices shed from the spoiler interact weakly with each other, and move downstream at an almost uniform speed of 038 V∞. At high reduced frequency, the interaction between the adjacent vortices strengthens. They close up to and rotate around each other, and eventually, merge into one vortex.展开更多
In order to solve unsteady incompressible Navier–Stokes(N–S) equations, a new stabilized finite element method,called the viscous-splitting least square FEM, is proposed. In the model, the N–S equations are split i...In order to solve unsteady incompressible Navier–Stokes(N–S) equations, a new stabilized finite element method,called the viscous-splitting least square FEM, is proposed. In the model, the N–S equations are split into diffusive and convective parts in each time step. The diffusive part is discretized by the backward difference method in time and discretized by the standard Galerkin method in space. The convective part is a first-order nonlinear equation.After the linearization of the nonlinear part by Newton’s method, the convective part is also discretized by the backward difference method in time and discretized by least square scheme in space. C0-type element can be used for interpolation of the velocity and pressure in the present model. Driven cavity flow and flow past a circular cylinder are conducted to validate the present model. Numerical results agree with previous numerical results, and the model has high accuracy and can be used to simulate problems with complex geometry.展开更多
In this paper, we make an initial value investigation of the unsteady flow of incompressible viscous fluid between two rigid non-conducting rotating parallel plates bounded by a porous medium under the influence of a ...In this paper, we make an initial value investigation of the unsteady flow of incompressible viscous fluid between two rigid non-conducting rotating parallel plates bounded by a porous medium under the influence of a uniform magnetic field of strength H0 inclined at an angle of inclination α with normal to the boundaries taking hall current into account. The perturbations are created by a constant pressure gradient along the plates in addition to the non-torsional oscillations of the upper plate while the lower plate is at rest. The flow in the porous medium is governed by the Brinkman’s equations. The exact solution of the velocity in the porous medium consists of steady state and transient state. The time required for the transient state to decay is evaluated in detail and the ultimate quasi-steady state solution has been derived analytically. Its behaviour is computationally discussed with reference to the various governing parameters. The shear stresses on the boundaries are also obtained analytically and their behaviour is computationally discussed.展开更多
A second-order mixing difference scheme with a limiting factor is deduced with the reconstruction gradient method and applied to discretizing the Navier-Stokes equation in an unstructured grid.The transform of nonorth...A second-order mixing difference scheme with a limiting factor is deduced with the reconstruction gradient method and applied to discretizing the Navier-Stokes equation in an unstructured grid.The transform of nonorthogonal diffusion items generated by the scheme in discrete equations is provided.The Delaunay triangulation method is improved to generate the unstructured grid.The computing program based on the SIMPLE algorithm in an unstructured grid is compiled and used to solve the discrete equations of two types of incompressible viscous flow.The numerical simulation results of the laminar flow driven by lid in cavity and flow behind a cylinder are compared with the theoretical solution and experimental data respectively.In the former case,a good agreement is achieved in the main velocity and drag coefficient curve.In the latter case,the numerical structure and development of vortex under several Reynolds numbers match well with that of the experiment.It is indicated that the factor difference scheme is of higher accuracy,and feasible to be applied to Navier-Stokes equation.展开更多
Some typical unsteady problems that are mainly dominated by shock waves,vortices, or both of them have been numerically simulated in the present study. The time history of unsteady flows is time-accurately computed an...Some typical unsteady problems that are mainly dominated by shock waves,vortices, or both of them have been numerically simulated in the present study. The time history of unsteady flows is time-accurately computed and analyzed. The main factors influencing the unsteady flow features are disc-ussed. Furthermore, the key points for achieving time-accurate and cost-effective numerical simulations are systematically summarized. The whole dissertation is divided into three parts: the first, the numerical simulation of unsteady compressible inviscid flows; the second, the numerical simulation of unsteady incompressible viscous flows; and the last, studies on unsteady flow numerical simulation methods. The main contributions of this dissertation consist of : (1) The construction methods of total variation diminishing (TVD)schemes are analyzed in general, and a symmetric TVD scheme is developed in special: (2) The time-varying transonic flow fields and their influence on force features for a transonicperiodically pitching airfoil are successfully studied; (3) Using the same approach as before, theunsteady flow structures of a moving shock interacting with a vortex and with a vortex pair areinvestigated; (4) The numerical simulation of the near wake complex vortex formation for acircular cylinder oscillating in arbitrary directions in a free stream has ben conducted throughouta wide range of oscillation parameters. Many experimentally investigated phenomena areduplicated and even renewed numerically. A parameter map in the amplitude-frequency plane,showing restons of vortex shedding formation, is given. The influences of oscillation parametersand Reynolds numbers on the force characters and on the time-varying flow structures areexplained; (5) The force characters and vortex structures in the near wake of the pitching ortranslating air foils oscillating around a high incidence angle are successfully predicted bynumerically solving the Navier-Stokes equations; (6) Some key points for achieving timeaccurate and cost- effective numerical simulation of unsteady complex flows are initiallyreviewed. Some main work of all above also can be found in some our papers shown inreferences.展开更多
叶栅通道内包含复杂非定常流动特征的涡系结构,二维直叶栅的尾迹涡系中粘性、尺寸效应十分明显,进行数值模拟时计算量较大,因此对分离涡产生与脱落过程的准确、清晰的捕捉要求有更高效率的数值解法。应用隐式格式、全场统一时间步长和Ba...叶栅通道内包含复杂非定常流动特征的涡系结构,二维直叶栅的尾迹涡系中粘性、尺寸效应十分明显,进行数值模拟时计算量较大,因此对分离涡产生与脱落过程的准确、清晰的捕捉要求有更高效率的数值解法。应用隐式格式、全场统一时间步长和Baldw in-Lom ax紊流模型求解二维N av ier-Stokes方程,对二维直叶栅流场非定常涡系进行了数值模拟分析,在大攻角、不同进口马赫数的2种工况下,通过对比分析不同时刻叶栅流场的熵和压力瞬态图,捕捉到分离涡产生与脱落过程,并合理地反映了紊流流动特征。通过计算结果看出,所采用的非定常粘性流动数值模拟方法有效,计算效率较高,能够较好地捕捉复杂的尾迹非定常涡系,较为清晰地反映叶栅流场涡系的形成、发展和消失过程,为进一步研究孤立转子和多叶排环境下的非定常流动效应提供了初步的基础。展开更多
基金The project is supported by the National Nature Science Foundation of China(NNSFC)
文摘The finite difference method (FDM) is applied in the present paper to solve the unsteady NHS equations for incompressible fluids. ADI and SLOR methods are served for the vorticity equation and the Poisson equation for ψ respectively. The upwind scheme is used for the convective terms. The moving boundary conditions are specially treated, and the effects of outlet conditions on the flow field are abo examined. Numerical results obtained show that the spoiler's oscillation induces forming, growing and shedding of the vortices. The shedding frequency of vortices is equal to that of the spoiler's oscillation. The forced unsteady separated flows under the present investigation depend mainly on the reduced frequency. At low reduced frequency, the vortices shed from the spoiler interact weakly with each other, and move downstream at an almost uniform speed of 038 V∞. At high reduced frequency, the interaction between the adjacent vortices strengthens. They close up to and rotate around each other, and eventually, merge into one vortex.
基金financially supported by the National Natural Science Foundation of China(Grant No.51349011)the Foundation of Si’chuan Educational Committee(Grant No.17ZB0452)+1 种基金the Innovation Team Project of Si’chuan Educational Committee(Grant No.18TD0019)the Longshan Academic Talent Research Support Program of the Southwest of Science and Technology(Grant Nos.18LZX715 and 18LZX410)
文摘In order to solve unsteady incompressible Navier–Stokes(N–S) equations, a new stabilized finite element method,called the viscous-splitting least square FEM, is proposed. In the model, the N–S equations are split into diffusive and convective parts in each time step. The diffusive part is discretized by the backward difference method in time and discretized by the standard Galerkin method in space. The convective part is a first-order nonlinear equation.After the linearization of the nonlinear part by Newton’s method, the convective part is also discretized by the backward difference method in time and discretized by least square scheme in space. C0-type element can be used for interpolation of the velocity and pressure in the present model. Driven cavity flow and flow past a circular cylinder are conducted to validate the present model. Numerical results agree with previous numerical results, and the model has high accuracy and can be used to simulate problems with complex geometry.
文摘In this paper, we make an initial value investigation of the unsteady flow of incompressible viscous fluid between two rigid non-conducting rotating parallel plates bounded by a porous medium under the influence of a uniform magnetic field of strength H0 inclined at an angle of inclination α with normal to the boundaries taking hall current into account. The perturbations are created by a constant pressure gradient along the plates in addition to the non-torsional oscillations of the upper plate while the lower plate is at rest. The flow in the porous medium is governed by the Brinkman’s equations. The exact solution of the velocity in the porous medium consists of steady state and transient state. The time required for the transient state to decay is evaluated in detail and the ultimate quasi-steady state solution has been derived analytically. Its behaviour is computationally discussed with reference to the various governing parameters. The shear stresses on the boundaries are also obtained analytically and their behaviour is computationally discussed.
基金Supported by National Natural Science Foundation of China (No. 10632050)
文摘A second-order mixing difference scheme with a limiting factor is deduced with the reconstruction gradient method and applied to discretizing the Navier-Stokes equation in an unstructured grid.The transform of nonorthogonal diffusion items generated by the scheme in discrete equations is provided.The Delaunay triangulation method is improved to generate the unstructured grid.The computing program based on the SIMPLE algorithm in an unstructured grid is compiled and used to solve the discrete equations of two types of incompressible viscous flow.The numerical simulation results of the laminar flow driven by lid in cavity and flow behind a cylinder are compared with the theoretical solution and experimental data respectively.In the former case,a good agreement is achieved in the main velocity and drag coefficient curve.In the latter case,the numerical structure and development of vortex under several Reynolds numbers match well with that of the experiment.It is indicated that the factor difference scheme is of higher accuracy,and feasible to be applied to Navier-Stokes equation.
文摘Some typical unsteady problems that are mainly dominated by shock waves,vortices, or both of them have been numerically simulated in the present study. The time history of unsteady flows is time-accurately computed and analyzed. The main factors influencing the unsteady flow features are disc-ussed. Furthermore, the key points for achieving time-accurate and cost-effective numerical simulations are systematically summarized. The whole dissertation is divided into three parts: the first, the numerical simulation of unsteady compressible inviscid flows; the second, the numerical simulation of unsteady incompressible viscous flows; and the last, studies on unsteady flow numerical simulation methods. The main contributions of this dissertation consist of : (1) The construction methods of total variation diminishing (TVD)schemes are analyzed in general, and a symmetric TVD scheme is developed in special: (2) The time-varying transonic flow fields and their influence on force features for a transonicperiodically pitching airfoil are successfully studied; (3) Using the same approach as before, theunsteady flow structures of a moving shock interacting with a vortex and with a vortex pair areinvestigated; (4) The numerical simulation of the near wake complex vortex formation for acircular cylinder oscillating in arbitrary directions in a free stream has ben conducted throughouta wide range of oscillation parameters. Many experimentally investigated phenomena areduplicated and even renewed numerically. A parameter map in the amplitude-frequency plane,showing restons of vortex shedding formation, is given. The influences of oscillation parametersand Reynolds numbers on the force characters and on the time-varying flow structures areexplained; (5) The force characters and vortex structures in the near wake of the pitching ortranslating air foils oscillating around a high incidence angle are successfully predicted bynumerically solving the Navier-Stokes equations; (6) Some key points for achieving timeaccurate and cost- effective numerical simulation of unsteady complex flows are initiallyreviewed. Some main work of all above also can be found in some our papers shown inreferences.
文摘叶栅通道内包含复杂非定常流动特征的涡系结构,二维直叶栅的尾迹涡系中粘性、尺寸效应十分明显,进行数值模拟时计算量较大,因此对分离涡产生与脱落过程的准确、清晰的捕捉要求有更高效率的数值解法。应用隐式格式、全场统一时间步长和Baldw in-Lom ax紊流模型求解二维N av ier-Stokes方程,对二维直叶栅流场非定常涡系进行了数值模拟分析,在大攻角、不同进口马赫数的2种工况下,通过对比分析不同时刻叶栅流场的熵和压力瞬态图,捕捉到分离涡产生与脱落过程,并合理地反映了紊流流动特征。通过计算结果看出,所采用的非定常粘性流动数值模拟方法有效,计算效率较高,能够较好地捕捉复杂的尾迹非定常涡系,较为清晰地反映叶栅流场涡系的形成、发展和消失过程,为进一步研究孤立转子和多叶排环境下的非定常流动效应提供了初步的基础。
