Fluid-structure interaction II

Flows Around Bodies

Underlying Flow Regime 2-14

Evaluation

Unsteady results

In order to comprehend the real structure deformation and the turbulent flow field found in the present test case, experimentally and numerically obtained unsteady results are presented in this section.

A high-speed camera movie of the structure deflection illustrates the deflection of the rubber plate over several periods:

Download movie or view online at http://vimeo.com/59130975

Figure 8a shows experimental raw signals of dimensionless y-displacements from a point located at a distance of 3 mm from the trailing edge of the steel weight in the midplane of the test section. Note that only a small extract of the entire data containing several thousand cycles is shown for the sake of visibility. The signal shows only slight variations in the extrema: The maxima of Uy/D (full data set, not the extract depicted in Fig. 8) vary between 0.298 and 0.523 and the minima between -0.234 and -0.542. The standard deviations on the extrema are about $\pm 0.03~(\pm 5\%)$ of the mean value of the extrema). Minor variations are observed regarding the period in Figure 8a). Figure 8b) shows the calculated phased-averaged Ux/D and Uy/D displacements for the reference period and Fig. 8c) the corresponding phase plane, respectively. The phase-averaged result shows a sinusdosial distribution for both directions. The Ux/D displacement is phase-shifted of about 70 degrees and has a doubled frequency in comparasion to the Uy/D deflection which is set as the reference for the phase-averaging procedure. The monitoring point trajectory plotted in the phase plane describes an distored '8', which is typical for the second swiveling mode for this kind of configurations. The cycle-to-cycle variations in these plots are small. Therefore, the FSI phenomenon can be characterized as quasi-periodic.

Fig. 8: Experimental structure results for a point in the midplane of the test section located at a distance of 3 mm from the trailing edge of the rubber plate: a) Raw signals of the Uy/D displacement; b) Phase-averaged Ux/D and Uy/D-deflections; c) Phase-plane of the phase-averaged structure motion.

Figure 9 is composed of four images of the instantaneous flow field (streamwise velocity component) experimentally measured in the x-y plane located in the middle of the rubber plate. These pictures constitute a full period T of the FSI phenomenon arbitrarily chosen. As mentioned before, the rubber plate deforms in the second swiveling mode. Thus, there are two wave nodes: one is located at the clamping of the flexible structure as in the first swiveling mode; the second one is found close to the bond of the rubber and the steel weight. At the beginning of the period (t = 0) the structure is in its undeformed state. Then, it starts to deform upwards and reaches a maximal deflection at t = T / 4. Afterwards, the plate deflects downwards until its maximal deformation at t =3T/4. Finally the plate deforms back to its original undeformed state and the end of the period is reached.

As visible in Fig. 9 the flow is highly turbulent, particularly near the cylinder, the flexible structure and in the wake. The strong shear layers originating from the separated boundary layers are clearly visible. This is the region where for the sub-critical flow the transition to turbulence takes place as visible in Fig. 9. Consequently, the flow in the wake region behind the cylinder is obviously turbulent and shows cycle-to-cycle variations. That means the flow field in the next periods succeeding the interval depicted in Fig. 9 will definitely look slightly different due to the irregular chaotic character of turbulence. Therefore, in order to be able to compare these results an averaging method is needed leading to a statistically averaged representation of the flow field. Since the FSI phenomenon is quasi-periodic the phase-averaging procedure presented above is ideal for this purpose and the results obtained are presented in the next section.

Fig. 9: Experimental unsteady flow field, magnitude of the flow velocity shown by contours (x-y plane located in the middle of the rubber plate).

The rubber plate mounted behind the cylinder acts as a splitter plate (Anderson and Szewczyk, 1997). Nevertheless, quasi-periodic vortex shedding occurs. The shed vortices visualized by iso-surfaces of the velocity magnitude with a value of u = 1.1 m/s (u/u_\text{inflow} = 0.79) move downstream and start to interact with the flexible structure leading to an oscillating quasi-periodic motion. The extra steel weight at the end of the tail additionally supports the deflection by the higher inertia of the swiveling system. Fig. 10 shows two different views of a single coupled measurement (without phase-averaging) which allows a detailed analysis of the flow behavior in the wake of the structure. In these snapshots two vortex rolls with a distance of about Δx/D = 2.5 and Δy/D = 1 to each other are visible. These vortex rolls illustrate several three-dimensional flow structures, for example the contraction in the middle of the upper vortex roll. Additionally, the contours of the instantaneous spanwise velocity component are mapped onto the iso-surfaces. As obvious from these figures the wake behind the nominally two-dimensional structure is strongly three-dimensional including vortical structures with vorticity components aligned to the main flow direction. Thus for a detailed FSI simulation eddy-resolving schemes such as large-eddy simulations (Breuer et al., 2012) are required which is the topic of ongoing work.

Fig. 10: Experimental unsteady 3D flow field, structure and flow results showing a single coupled measurement at $t=\pi$ , the iso-surfaces represent the dimensionless velocity magnitude $u/u_{\text{inflow}}=0.79$ , the contours on the iso-surfaces depict the spanwise velocity component w.).

Phase-averaged results

Fig. 11: Experimental structural results: Structure contour for the reference period.

Fig. 12: Experimental phase-averaged 2D flow field, magnitude of the flow velocity shown by contours (x-y plane located in the middle of the rubber plate).

Fig. 13: Experimental phase-averaged 3D flow field, structure and flow results showing a phase-averaged coupled measurement at $t=\pi$ , the iso-surfaces represent the dimensionless velocity magnitude $u/u_{\text{inflow}}=0.79$ , the contours on the iso-surfaces depict the spanwise velocity component w.).

Data files

As explained in Section Generation of Phase-resolved Data in FSI-PfS-1a 23 reference positions were calculated with the phase-resolved post-processing algorithm. 23 phase-averaged data are enough to precisely describe the period of the FSI phenomenon.

Experimental data

The experimental data files below contains the phase-resolved flow results obtained with the PIV setup presented before. Each file has 5 columns: The 2 first ones contain the x- and y-positions of each cell center. The 3 next columns contain the x-, y-velocity and the velocity magnitude at the point.

Phase-averaged 2D flow fields:

Media:FSI-PfS-2a_exp_2Dflow_01.dat Media:FSI-PfS-2a_exp_2Dflow_02.dat Media:FSI-PfS-2a_exp_2Dflow_03.dat Media:FSI-PfS-2a_exp_2Dflow_04.dat

Media:FSI-PfS-2a_exp_2Dflow_05.dat Media:FSI-PfS-2a_exp_2Dflow_06.dat Media:FSI-PfS-2a_exp_2Dflow_07.dat Media:FSI-PfS-2a_exp_2Dflow_08.dat

Media:FSI-PfS-2a_exp_2Dflow_09.dat Media:FSI-PfS-2a_exp_2Dflow_10.dat Media:FSI-PfS-2a_exp_2Dflow_11.dat Media:FSI-PfS-2a_exp_2Dflow_12.dat

Media:FSI-PfS-2a_exp_2Dflow_13.dat Media:FSI-PfS-2a_exp_2Dflow_14.dat Media:FSI-PfS-2a_exp_2Dflow_15.dat Media:FSI-PfS-2a_exp_2Dflow_16.dat

Media:FSI-PfS-2a_exp_2Dflow_17.dat Media:FSI-PfS-2a_exp_2Dflow_18.dat Media:FSI-PfS-2a_exp_2Dflow_19.dat Media:FSI-PfS-2a_exp_2Dflow_20.dat

Media:FSI-PfS-2a_exp_2Dflow_21.dat Media:FSI-PfS-2a_exp_2Dflow_22.dat Media:FSI-PfS-2a_exp_2Dflow_23.dat

The experimental data files below contains the phase-resolved structural results obtained with the laser distance sensor presented before. Each file has 3 columns with the x-, y- and z-position of the flexible structure.

Phase-averaged structure:

Media:FSI-PfS-2a_exp_2Dstructure_01.dat Media:FSI-PfS-2a_exp_2Dstructure_02.dat Media:FSI-PfS-2a_exp_2Dstructure_03.dat Media:FSI-PfS-2a_exp_2Dstructure_04.dat

Media:FSI-PfS-2a_exp_2Dstructure_05.dat Media:FSI-PfS-2a_exp_2Dstructure_06.dat Media:FSI-PfS-2a_exp_2Dstructure_07.dat Media:FSI-PfS-2a_exp_2Dstructure_08.dat

Media:FSI-PfS-2a_exp_2Dstructure_09.dat Media:FSI-PfS-2a_exp_2Dstructure_10.dat Media:FSI-PfS-2a_exp_2Dstructure_11.dat Media:FSI-PfS-2a_exp_2Dstructure_12.dat

Media:FSI-PfS-2a_exp_2Dstructure_13.dat Media:FSI-PfS-2a_exp_2Dstructure_14.dat Media:FSI-PfS-2a_exp_2Dstructure_15.dat Media:FSI-PfS-2a_exp_2Dstructure_16.dat

Media:FSI-PfS-2a_exp_2Dstructure_17.dat Media:FSI-PfS-2a_exp_2Dstructure_18.dat Media:FSI-PfS-2a_exp_2Dstructure_19.dat Media:FSI-PfS-2a_exp_2Dstructure_20.dat

Media:FSI-PfS-2a_exp_2Dstructure_21.dat Media:FSI-PfS-2a_exp_2Dstructure_22.dat Media:FSI-PfS-2a_exp_2Dstructure_23.dat

Contributed by: Andreas Kalmbach, Guillaume De Nayer, Michael Breuer — Helmut-Schmidt Universität Hamburg