Numerical Simulation of an Oscillating Cylinder Using Large Eddy Simulation and Implicit Large Eddy Simulation

Perspective view of the flow past a fixed cylinder in a steady flow at Re = 3900 in terms of iso-surfaces of the second invariant of the velocity gradient. In (a) case 1.1, grid A: 0.6M cells, and in (b) case 1.3, grid C: 5.1M cells.

Validation for fixed cylinder at Re = 3900. In (a) the mean velocity along centerline y = 0 is shown, vertical solid lines indicate, x/D = 1.06, 1.54, 2.02, and 4. In (b) streamwise velocity profiles, and in (c) axial velocity rms fluctuations are given at x/D = 1.06, 1.54, 2.02, and 4, bottom to top. In (d), the pressure coefficient on the cylinder surface is shown, φ is the horizontal angle starting at the stagnation point. Note that for Cp there are no experimental data available.

Experimental setup used by Cetiner [5]. Published with the permission of the author.

Time sequence, with Cy on the y axis and time t on the x axis, Cetiner [5]. Published with the permission of the author.

Example of Lissajous curves emphasizing the sensitivity of these graphs to fe . (a) fe  =  100/360 Hz, and (b) fe  =  99.9/360 Hz. Experimental data provided by Cetiner [5].

Iso-surface of the second invariant of the velocity gradient together with schematic pictures for Case 2.4 at five instants during one characteristic cylinder cycle, (a) to (e), and in (f) a time series of the normalized displacement of the cylinder, xc , the drag and lift forces, Cx and Cy . In all panels is the oscillation period T =  1/fe .

Lissajous curves of the drag force (a), lift force (b), and drag force versus lift forces (c), for the grids A, B, and C. Experimental results shown in black. Legend: (solid line) experimental data, (solid line) ILES + WM on grid A, (long dashed line ILES + WM on grid B, and (short dashed line) ILES + WM on grid C.

Mean lift force versus time (a), and mean drag force versus time (b), for ILES on grid A, B, and C together with experimental results. Legend: (solid line) experimental data, (solid line) ILES + WM on grid A, (long dashed line) ILES + WM on grid B, and (short dashed line) ILES + WM on grid C.

Modulus of the fast Fourier transform (FFT) of the lift force versus normalized frequency for ILES + WM on three different grids together with experimental results. Legend: (solid line) experimental data, (solid line) ILES + WM on grid A, (long dashed line) ILES + WM on grid B, and (short dashed line) ILES+WM on grid C.

The four signals f0.5 , f1.5 , f2.5 , and f3.5 together with their total sum fΣ for ILES on grid C together with experimental results. Legend: (solid line) experimental data, and (dashed line) ILES + WM on grid C.

Lissajous curves of the drag force (a), and lift force (b), for ILES + WM, OEEVM + WM, and LDKM + WM. Legend: (solid line) experimental data, (gray dashed line) ILES + WM on grid B, (dashed line) OEEVM + WM on grid B, and (gray dashed line) LDKM + WM on grid C.

Mean lift force versus time (a), and mean drag force versus time (b). Legend: (solid line) experimental data, (gray dashed line) ILES + WM on grid B, (dashed line) OEEVM + WM on grid B, and (gray dashed line) LDKM + WM on grid C.

Modulus of the FFT of the lift force versus normalized frequency for ILES + WM, OEEVM + WM, and LDKM on grid B together with experimental results. Legend: (solid line) experimental data, (gray dashed line) ILES + WM on grid B, (dashed line) OEEVM + WM on grid B, and (gray dashed line) LDKM + WM on grid C.