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HIGH ACCURATE SOLUTION OF incompressible viscous flow WITH PRIMATIVE VARIABLE

Journal of Hydrodynamics 1998年第3期10卷 62-68页

作者： Ren An-lu, Ding HongDepartment of Mechanics, Zhejiang University, Hangzhou, 310027 P.R.ChinaChen Yao-songDepartment of Mechanics, Peking University, Beijing 100871, P. R. China

This paper presents a higher order difference scheme for the computation of the incompressible viscous flows. The discretization of the two-dimensional incompressible viscous Navier-Stokes equations, in generalized curvilinear coordinates and tensor formulation, is based on a non-staggered grid. The momentum equations are integrated in time using the four-stage explicit Runge-Kutta algorithm [1] and discretized in space using the fourth-order accurate compact scheme [2]. The pressure-Poisson equation is discretized using the nine-point compact scheme. In order to satisfy the continuity constraint and ensure the smoothness of pressure field, an optimum procedure to derive a discrete pressure equation is proposed [9][3] . The method is applied to calculate the driven cavity flow on a stretched grid with the Reynolds numbers from 100 to 10000. The numerical results are in very good agreement with the results obtained by Ghia et al [7] and include the periodic solutions for high Reynolds numbers.

关键词： incompressible viscous flow compact scheme non-staggered grid

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The energy transfer mechanism of a perturbed solid-body rotation flow in a rotating pipe

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Acta Mechanica Sinica 2017年第2期33卷 274-283页

作者： Chunjuan Feng Feng Liu Zvi Rusak Shixiao Wang School of Aeronautics Northwestern Polytecrhnical University Department of Mechanical and Aerospace Engineering University of California Department of Mechanical Aerospaceand Nuclear EngineeringRensselaer Polytechnic Institute Department of Mathematics University of Auckland

Three-dimensional direct numerical simulations of a solid-body rotation superposed on a uniform axial flow entering a rotating constant-area pipe of finite length are presented. Steady in time profiles of the radial, axial, and circumferential velocities are imposed at the pipe inlet. Convective boundary conditions are imposed at the pipe outlet. The Wang and Rusak (Phys. Fluids 8:1007-1016, 1996.) axisymmetric instability mechanism is retrieved at certain operational conditions in terms of incoming flow swirl levels and the Reynolds number. However, at other operational conditions there exists a dominant, three-dimensional spiral type of instability mode that is consistent with the linear stability theory of Wang et al. (J. Fluid Mech. 797: 284-321, 2016). The growth of this mode leads to a spiral type of flow roll-up that subsequently nonlinearly saturates on a large amplitude rotating spiral wave. The energy transfer mechanism between the bulk of the flow and the perturbations is studied by the Reynolds-Orr equation. The production or loss of the perturbation kinetic energy is combined of three components: the viscous loss, the convective loss at the pipe outlet, and the gain of energy at the outlet through the work done by the pressure perturbation. The energy transfer in the nonlinear stage is shown to be a natural extension of the linear stage with a nonlinear saturated process.

关键词： Vortex instability incompressible viscous flow Cylindrical coordinates

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Solving Navier-Stokes equation by mixed interpolation method

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Journal of Southeast University(English Edition) 2006年第1期22卷 93-95页

作者：万水 Mogens Peter Nielsen 东南大学交通学院南京210096 丹麦技术大学土木工程系

The operator splitting method is used to deal with the Navier-Stokes equation, in which the physical process described by the equation is decomposed into two processes： a diffusion process and a convection process; and the finite element equation is established. The velocity field in the element is described by the shape function of the isoparametric element with nine nodes and the pressure field is described by the interpolation function of the four nodes at the vertex of the isoparametric element with nine nodes. The subroutine of the element and the integrated finite element code are generated by the Finite Element Program Generator （FEPG） successfully. The numerical simulation about the incompressible viscous liquid flowing over a cylinder is carded out. The solution agrees with the experimental results very well.

关键词： Navier-Stokes equation finite element method incompressible viscous flow mixed interpolation method

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Vibration of a Parallel Plate-Type Structure in Two-dimensional Axial flow

Vibration of a Parallel Plate-Type Structure in Two-dimensio...

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2007国际机械工程与力学会议

作者： Li LU Yiren YANG Juan ZHANG Department of Applied Mechanics and Engineering Southwest Jiaotong University

flow-induced vibrations of parallel plates in axial viscous flow were studied. viscous flow theory was applied to describe the fluid-structure interaction. The fluid was supposed to be two-dimensional. The expressions of fluid velocities were created. The pressure grads were gotten with two-dimensional Navier-Stocks equation. Semi-analytical fluid pressures of a plate-fluid-plate system, a water trough, and a three-parallel plate-type structure were obtained. The added mass coefficients, added damping and added stiffness coefficients were determined. These analytical coefficients indicate a strong dependence on gap width and water viscous coefficient. The coupling effects of flow get stronger with the gap width being smaller. Computational results reveal that the frequencies of structure in flow decrease compared with the corresponding ones in air. The frequency values decrease with the increase of fluid velocities and will keep to a positive number. This is different from the results gotten by potential flow theory, which shows that the natural frequency decreases with the increase of velocity and will decrease to zero.

关键词： Fluid pressure incompressible viscous flow Navier- Stocks equation Natural frequency Parallel plate-type structure.

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