Abstract
The 3D numerical simulation was carried out for an idealized Rankine vortex using nonlineark-εmodel (one kind of RANS model) and large eddy simulation (LES) techniques. In this 3D simulation, the vortex flow field was given to rotate with the vertical axis in a free surface rectangular domain. In order to investigate the predictability of standard (linear) and non-lineark-εmodels, the decay of a trailing vortex was simulated and compared with previous DNS data. The governing equations for mean velocities and turbulent flows were discretized with the finite volume method based on a staggered grid system. It was observed that in the growth phase as well as in stabilized phase of turbulence, the decay rate of tangential velocity by RANS model was well comparable with LES simulation as well as previous DNS data. However, in the decay phase of turbulence, RANS model showed slightly faster decay of tangential velocity due to its slower decay of turbulence compared to LES or DNS. The patterns as well as magnitudes of secondary currents predicted by RANS and LES models were well comparable to each other.
Highlights
The basic types of plane vortices can be classified into two categories: one with slower velocity at center and maximum at sides and the other with maximum at center and minimum velocity at edges
The rotary fluid motion of the first one is called the solid body rotation, since it is similar to the fluid motion filled in a rotating hollow box
Fluid motion composed of a potential vortex and solid body rotation is called Rankine vortex (Figure 1) after the fluid dynamicist Rankine
Summary
The basic types of plane vortices can be classified into two categories: one with slower velocity at center and maximum at sides and the other with maximum at center and minimum velocity at edges. If a long circular rod rotates in a fluid with constant velocity around its axis, the fluid velocity is found highest and equal to the velocity of rod at the rod’s surface (due to adhesion), and with increasing distance from the rod, the velocity is diminished in inverse proportional to the distance Such a fluid motion is called a potential vortex. For a steady circular motion without a velocity component normal to the plane of rotation, the Rankine vortex is the only possible vortex whose velocity is zero at the center as well as far away from it In addition to these basic vortices, there are other time-dependent rotary motions that have azimuthal velocity component as well as radial and axial components. Comparison is shown for the general flow features such as temporal change of vortex decay, radial distribution of tangential velocity, and water surface profile
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