Numerical Study Of Viscous Flow Research Articles

Numerical study of viscous flow in a rotating rectangular channel

A numerical study of the incompressible viscous flow in rotating channel with rectangular cross-section is presented in this paper. The incompressible parabolized Navier-Stokes equations are solved by a finite difference technique for various Reynolds and Rossby numbers in the laminar regime. At weak rotating rate, a pair of stable vortex secondary flow appears in the transverse planes of the channel and the flow can be developed fully in the channel. In the regime of the middle rotating rate, there are several unstable vortexes in the secondary flow and the fully developed flow in the channel can not be obtained. At a more rapid rotating rate, the stable secondary flow and fully developed flow appear again. At lower Reynolds numbers, a pair of stable vortex secondary flow and fully developed flow appear in the channel even if the rotating rate is rapid. To determine the critical condition of the stability of the flow in the rotating channel, the eigenvalues of the Jacobian matrix of the linearized Navier-Stokes equation are predicted.

Flow Field and Pressure Drop of Filters with Rectangular Fibers

A numerical study of viscous flow in a fibrous filter modeled as a staggered array of rectangular or cylindrical fibers arranged perpendicular to the flow direction was conducted to determine the fiber drag. The calculated dimensionless drag values for the case of the cylindrical fibers were found to be in excellent agreement with the analytical results of Kuwabara (1959). The effect of the fluid inertia on the flow around a cylindrical or rectangular fiber was found to be negligible for Reynolds number values < 0.2. Further, the dimensionless drag on rectangular fibers with aspect ratios > 1 was found to be a strong function of the filter solid-volume fraction, which correlated well with the Kuwabara results for the case of cylindrical fibers.

Numerical study of viscous flow in rotating rectangular ducts

A numerical study of the laminar flow of an incompressible viscous fluid in rotating ducts of rectangular cross-section is conducted. The full time-dependent nonlinear equations of motion are solved by finite-difference techniques for moderate to relatively rapid rotation rates where both the convective and viscous terms play an important role. At weak to moderate rotation rates, a double-vortex secondary flow appears in the transverse planes of the duct whose structure is relatively independent of the aspect ratio of the duct. For Rossby numbers Ro c 100 this secondary flow is shown to lead to substantial distortions of the axial velocity profiles. For more rapid rotations (Ro c l), the Secondary flow (in a duct with an aspect ratio of two) is shown to split into an asymmetric configuration of four counter-rotating vortices similar to that which appears in curved ducts. It is demonstrated mathematically that this effect could result from a disparity in the symmetry of the convective and Coriolis terms in the equations of motion. If the rotation rates are increased further, the secondary flow restabilizes to a slightly asymmetric double-vortex configuration and the axial velocity wumes a Taylor-Proudman configuration in the interior of the duct. Comparisons with existing experimental results are quite favourable.

Numerical study of viscous flow in a cavity

Numerical solutions have been obtained for the steady two-dimensional flow of a viscous incompressible fluid in rectangular cavities by solving various implicit finite-difference approximations of the Navier-Stokes equations. The sets of implicit difference equations were solved using a recently introduced iterative numerical scheme called the strongly implicit procedure. The strongly implicit procedure was found to be an effective and economical numerical scheme for obtaining iterative solutions for sets of linear finite-difference equations. Various qualitative and quantitative comparisons have been made to determine the effects of Reynolds number and grid size on four different finite-difference forms of the governing equations. The results show that one difference scheme was particularly accurate for Reynolds numbers and grid sizes which satisfy the Thom and Apelt stability restriction. Streamline plots for Reynolds numbers of 100 and 1000 are shown. The behavior of the vortex center and secondary vortices with increasing Reynolds number is exhibited. The growth of the secondary vortices with increasing cavity depth is also shown.