DQM to Simulate 3D Vortex Structure of Cuboid Cavity Driven Flow

2013 ◽  
Vol 671-674 ◽  
pp. 1588-1595
Author(s):  
Shi Hua He ◽  
Li Xiang Zhang ◽  
Tian Mao Xu
Keyword(s):  
Vortex Structure ◽  
Continuity Equation ◽  
Differential Quadrature Method ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Staggered Grid ◽  
Quadrature Method ◽  
Governing Equations ◽  
Simple Strategy ◽  
Suitable Boundary Condition

The vortex structure of lid-driven flow in a cuboid cavity with one or a pair of moving lids is numerated using the differential quadrature method (DQM). According to the characteristics of cavity driven flow, the dimensionless governing equations and its boundary conditions used to describe the flow are established. Based on a non-staggered grid technology, the polynomial-based DQM is combined with the SIMPLE strategy to solve three-dimensional (3D) cavity driven flow. The suitable boundary condition for pressure correction equation on a non-staggered system is implemented and the continuity equation on the boundary is enforced to be satisfied. The 3D vortex structure distributions in a cuboid cavity are obtained for different Reynolds numbers and different driving modes. The analysis shows that the DQM is very suitable for the simulation of 3D vortex structure in a cavity.

scholarly journals Axisymmetric Consolidation of Unsaturated Soils by Differential Quadrature Method

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Wan-Huan Zhou
Keyword(s):  
Pore Water ◽  
Unsaturated Soils ◽  
Differential Quadrature Method ◽  
Vertical Direction ◽  
Differential Quadrature ◽  
Excess Pore Pressure ◽  
Foundation Engineering ◽  
Quadrature Method ◽  
Governing Equations ◽  
Excess Pore

Axisymmetric consolidation in a sand drain foundation is a common problem in foundation engineering. In unsaturated soils, the excess pore-water and pore-air pressures simultaneously change during the consolidation procedure; and the solutions are not easy to obtain. The present paper uses the differential quadrature method (DQM) for axisymmetric consolidation of unsaturated soils in a sand drain foundation. The radial seepage of sand drain foundation is considered based on the framework of Fredlund’s one-dimensional consolidation theory in unsaturated soils. With the use of Darcy’s law and Fick’s law, the polar governing equations of excess pore-air and pore-water pressures of axisymmetric consolidation are derived. By using DQM, the two governing equations are transformed into two sets of ordinary differential equations. Then the solutions of excess pore-water and pore-air pressures can be obtained by Rong-Kutta method. The DQM solution can be used to deal with the case of nonuniform initial pore-air and pore-water distributions. Finally, case studies are presented to investigate the behavior of axisymmetric consolidation of unsaturated soils. The convergence analysis and average degree of consolidation, the settlements in radial and vertical direction, and the effects of different initial excess pore pressure distributions are presented, and discussed in this paper.

scholarly journals NUMERICAL ANALYSIS OF THE NATURAL CONVECTION IN HORIZONTAL ANNULI AT LOW AND MODERATE Ra

2006 ◽  
Vol 5 (2) ◽  
pp. 58
Author(s):  
E. L. M. Padilla ◽  
R. Campregher ◽  
A. Silveira-Neto
Keyword(s):  
Natural Convection ◽  
Three Dimensional ◽  
Staggered Grid ◽  
Governing Equations ◽  
Concentric Cylinders ◽  
Wide Range ◽  
Horizontal Annuli ◽  
Rayleigh Numbers ◽  
The Heat Transfer Coefficient ◽  
Good Agreement

The natural convection at low and moderate Rayleigh numbers (Ra) incylindrical horizontal annuli with imposed temperatures in both surfaces isnumerically studied. This flow inside concentric cylinders classic configuration has a wide range of practical and technological applications, which justifies its growing studies efforts. In this work, the governing equations are discretized by the volume finite technique over a staggered grid, with second-order accuracy in space and time. The flow pattern is presented by several Rayleigh numbers, with an analysis of the heat transfer coefficient and flow properties. Furthermore, a three-dimensional field is shown at a moderate Ra number. The results showed a good agreement with the experimental data.

scholarly journals Kazantsev model in non-helical 2.5-dimensional flows

2016 ◽  
Vol 806 ◽  
pp. 627-648 ◽  
Author(s):  
K. Seshasayanan ◽  
A. Alexakis
Keyword(s):  
Turbulent Flows ◽  
Three Dimensional ◽  
Analytical Calculation ◽  
Reynolds Numbers ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Control Parameters ◽  
Governing Equations ◽  
Field Correlation ◽  
Good Agreement

We study the dynamo instability for a Kazantsev–Kraichnan flow with three velocity components that depend only on two dimensions $\boldsymbol{u}=(u(x,y,t),v(x,y,t),w(x,y,t))$ often referred to as 2.5-dimensional (2.5-D) flow. Within the Kazantsev–Kraichnan framework we derive the governing equations for the second-order magnetic field correlation function and examine the growth rate of the dynamo instability as a function of the control parameters of the system. In particular we investigate the dynamo behaviour for large magnetic Reynolds numbers $Rm$ and flows close to being two-dimensional and show that these two limiting procedures do not commute. The energy spectra of the unstable modes are derived analytically and lead to power-law behaviour that differs from the three-dimensional and two-dimensional cases. The results of our analytical calculation are compared with the results of numerical simulations of dynamos driven by prescribed fluctuating flows as well as freely evolving turbulent flows, showing good agreement.

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