The velocity field in meandering compound channels with overhank flow is highly three dimensional. To date, its features have been investigated experimentally and little research has been undertaken to investigate the...The velocity field in meandering compound channels with overhank flow is highly three dimensional. To date, its features have been investigated experimentally and little research has been undertaken to investigate the feasibility of reproducing these velocity fields with computer models. If computer modeling were to prove successful in this context, it could become a useful prediction technique and research tool to enhance our understanding of natural river dynamics. A 3-D k-E turbulence hydrodynamic model in curvilinear coordinates is established to simulate the overhank flow. The bodyfitted coordinate is adopted in the horizontal plane, the part grid is adopted in the vertical direction, and the wall-function method is employed to simulate the bed resistance. The model is applied to the simulation of the meandering channel with straight flood plain banks, and the main velocities and secondary velocities for both the longitudinal and cross sections are presented. Comparison and analysis show that the results of simulation are fit to reflect the results of experiment. These results show the application value of the model to 3D overhank flow.展开更多
This paper seeks to develop an efficient multigrid algorithm for solving the Burgers problem with the use of non-orthogonal structured curvilinear grids in L-shaped geometry.For this,the differential equations were di...This paper seeks to develop an efficient multigrid algorithm for solving the Burgers problem with the use of non-orthogonal structured curvilinear grids in L-shaped geometry.For this,the differential equations were discretized by Finite Volume Method(FVM)with second-order approximation scheme and deferred correction.Moreover,the algebraic method and the differential method were used to generate the non-orthogonal structured curvilinear grids.Furthermore,the influence of some parameters of geometric multigrid method,as well as lexicographical Gauss–Seidel(Lex-GS),η-line Gauss–Seidel(η-line-GS),Modified Strongly Implicit(MSI)and modified incomplete LU decomposition(MILU)solvers on the Central Processing Unit(CPU)time was investigated.Therefore,several parameters of multigrid method and solvers were tested for the problem,with the use of nonorthogonal structured curvilinear grids and multigrid method,resulting in an algorithm with the combination that achieved the best results and CPU time.The geometric multigrid method with Full Approximation Scheme(FAS),V-cycle and standard coarsening ratio for this problem were utilized.This article shows how to calculate the coordinates transformation metrics in the coarser grids.Results show that the MSI and MILU solvers are the most efficient.Moreover,theMSI solver is faster thanMILU for both grids generators;and the solutions are more accurate for the Burgers problem with grids generated using elliptic equations.展开更多
This paper discusses the relationship between natural coordinates in fluid mechanics and orthogonal curvilinear coordinates. Since orthogonal curvilinear coordinates have some excellent mathematical properties, natura...This paper discusses the relationship between natural coordinates in fluid mechanics and orthogonal curvilinear coordinates. Since orthogonal curvilinear coordinates have some excellent mathematical properties, natural coordinates can be applied more widely if they can be transformed to orthogonal curvilinear coordinates. Frenet formulas which describe the differential properties of natural coordinates were compared with the derivative formulas of orthogonal curvilinear coordinates to show that natural coordinates are not generally orthogonal curvilinear coordinates. A method was introduced to transform natural coordinormal planes of the natural coordinates about the streamlines. The transformation is true as long as the natural coordinates satisfy several equations. Vorticity decomposition in the natural coordinates is used to show that these conditional equations are satisfied only if the streamlines are perpendicular to the vortexlines on every given point in the flow field. These equations apply in both planar flows and axisymmetric flows without a circumferential velocity component, but do not apply in some 3-D flows such as Beltrami flow.展开更多
A 3-D numerical model for calculating flow in non-curvilinear coordinates was established in this article. The flow was simulated by solving the full Reynolds-averaged Navier-Stokes equations with the RNG κ-ε turbul...A 3-D numerical model for calculating flow in non-curvilinear coordinates was established in this article. The flow was simulated by solving the full Reynolds-averaged Navier-Stokes equations with the RNG κ-ε turbulence model. In the horizontal x-y-plane, a boundary-fitted curvilinear co-ordinate system was adopted, while in the vertical direction, a σ co-ordinate transformation was used to represent the free surface and bed topography. The water level was determined by solving the 2-D Poisson equation derived from 2-D depth averaged momentum equations. The finite-volume method was used to discretize the equations and the SIMPLEC algorithm was applied to acquire the coupling of velocity and pressure. This model was applied to simulate the meandering channels and natural rivers, and the water levels and the velocities for all sections were given. By contrasting and analyzing, the agreement with measurements is generally good. The feasibility studies of simulating flow of the natural fiver have been conducted to demonstrate its applicability to hydraulic engineering research.展开更多
Through analyzing the motion characteristics of bird-like flapping flight, it is considered that the wing angular acceleration is equal to zero at the point of maximum angular speed. Thus, the flapping flight is equiv...Through analyzing the motion characteristics of bird-like flapping flight, it is considered that the wing angular acceleration is equal to zero at the point of maximum angular speed. Thus, the flapping flight is equivalent to a uniform rotating motion which can be analyzed by using the stream surface theory of turbomachinery during a micro period of time. In this article, the N-S equations of the motion are expanded in a non-orthogonal curvilinear coordinate system, and simplified on stream surfaces of the flapping flight model. By using stream function me- thod, the three-dimensional unsteady flow equations are simplified as a two-order partial differential equation with variable coefficients eventually and the equation＇s iterative solving method on S1 and $2 stream surfaces of the flapping flight model is presented. Through expanding the relatively steady equations of flapping flight at an arbitrary time point of a stroke on meridional plane of the flapping flight model, it can use a relatively steady mo- tion to approximate the real flapping flight at that time point, and analyze the flow stability influenced by the wing＇s flexibility. It can be seen that the wing flexibility is related to the higher pressurization capacity and the flow stability, and the pressurization capacity of flexible wing is proportional to the angular speed, angular distor- tion rate and radius square.展开更多
文摘The velocity field in meandering compound channels with overhank flow is highly three dimensional. To date, its features have been investigated experimentally and little research has been undertaken to investigate the feasibility of reproducing these velocity fields with computer models. If computer modeling were to prove successful in this context, it could become a useful prediction technique and research tool to enhance our understanding of natural river dynamics. A 3-D k-E turbulence hydrodynamic model in curvilinear coordinates is established to simulate the overhank flow. The bodyfitted coordinate is adopted in the horizontal plane, the part grid is adopted in the vertical direction, and the wall-function method is employed to simulate the bed resistance. The model is applied to the simulation of the meandering channel with straight flood plain banks, and the main velocities and secondary velocities for both the longitudinal and cross sections are presented. Comparison and analysis show that the results of simulation are fit to reflect the results of experiment. These results show the application value of the model to 3D overhank flow.
文摘This paper seeks to develop an efficient multigrid algorithm for solving the Burgers problem with the use of non-orthogonal structured curvilinear grids in L-shaped geometry.For this,the differential equations were discretized by Finite Volume Method(FVM)with second-order approximation scheme and deferred correction.Moreover,the algebraic method and the differential method were used to generate the non-orthogonal structured curvilinear grids.Furthermore,the influence of some parameters of geometric multigrid method,as well as lexicographical Gauss–Seidel(Lex-GS),η-line Gauss–Seidel(η-line-GS),Modified Strongly Implicit(MSI)and modified incomplete LU decomposition(MILU)solvers on the Central Processing Unit(CPU)time was investigated.Therefore,several parameters of multigrid method and solvers were tested for the problem,with the use of nonorthogonal structured curvilinear grids and multigrid method,resulting in an algorithm with the combination that achieved the best results and CPU time.The geometric multigrid method with Full Approximation Scheme(FAS),V-cycle and standard coarsening ratio for this problem were utilized.This article shows how to calculate the coordinates transformation metrics in the coarser grids.Results show that the MSI and MILU solvers are the most efficient.Moreover,theMSI solver is faster thanMILU for both grids generators;and the solutions are more accurate for the Burgers problem with grids generated using elliptic equations.
文摘This paper discusses the relationship between natural coordinates in fluid mechanics and orthogonal curvilinear coordinates. Since orthogonal curvilinear coordinates have some excellent mathematical properties, natural coordinates can be applied more widely if they can be transformed to orthogonal curvilinear coordinates. Frenet formulas which describe the differential properties of natural coordinates were compared with the derivative formulas of orthogonal curvilinear coordinates to show that natural coordinates are not generally orthogonal curvilinear coordinates. A method was introduced to transform natural coordinormal planes of the natural coordinates about the streamlines. The transformation is true as long as the natural coordinates satisfy several equations. Vorticity decomposition in the natural coordinates is used to show that these conditional equations are satisfied only if the streamlines are perpendicular to the vortexlines on every given point in the flow field. These equations apply in both planar flows and axisymmetric flows without a circumferential velocity component, but do not apply in some 3-D flows such as Beltrami flow.
基金the National Basic Research Program of China (973 Program, Grant No. 2006CB403302)the National Natural Science Foundation of China (Grant No.50779006)the Natural Science Foundation of LiaoningProvince (Grant No. 20062170)
文摘A 3-D numerical model for calculating flow in non-curvilinear coordinates was established in this article. The flow was simulated by solving the full Reynolds-averaged Navier-Stokes equations with the RNG κ-ε turbulence model. In the horizontal x-y-plane, a boundary-fitted curvilinear co-ordinate system was adopted, while in the vertical direction, a σ co-ordinate transformation was used to represent the free surface and bed topography. The water level was determined by solving the 2-D Poisson equation derived from 2-D depth averaged momentum equations. The finite-volume method was used to discretize the equations and the SIMPLEC algorithm was applied to acquire the coupling of velocity and pressure. This model was applied to simulate the meandering channels and natural rivers, and the water levels and the velocities for all sections were given. By contrasting and analyzing, the agreement with measurements is generally good. The feasibility studies of simulating flow of the natural fiver have been conducted to demonstrate its applicability to hydraulic engineering research.
文摘Through analyzing the motion characteristics of bird-like flapping flight, it is considered that the wing angular acceleration is equal to zero at the point of maximum angular speed. Thus, the flapping flight is equivalent to a uniform rotating motion which can be analyzed by using the stream surface theory of turbomachinery during a micro period of time. In this article, the N-S equations of the motion are expanded in a non-orthogonal curvilinear coordinate system, and simplified on stream surfaces of the flapping flight model. By using stream function me- thod, the three-dimensional unsteady flow equations are simplified as a two-order partial differential equation with variable coefficients eventually and the equation＇s iterative solving method on S1 and $2 stream surfaces of the flapping flight model is presented. Through expanding the relatively steady equations of flapping flight at an arbitrary time point of a stroke on meridional plane of the flapping flight model, it can use a relatively steady mo- tion to approximate the real flapping flight at that time point, and analyze the flow stability influenced by the wing＇s flexibility. It can be seen that the wing flexibility is related to the higher pressurization capacity and the flow stability, and the pressurization capacity of flexible wing is proportional to the angular speed, angular distor- tion rate and radius square.
