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 8 shows experimental raw signals of dimensionless displacements from a point located at a distance of 4 mm from the trailing edge of the rubber plate 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. In Figure 8a) the history of the y-displacement U_y^* = U_y / D obtained in the experiment is plotted. The signal shows significant variations in the extrema: The maxima of U_y^* (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 0.05~(\pm 12 \%) of the mean value of the extrema). Minor variations are observed regarding the period in Figure 8a). Figure 8b) and 8c) show the corresponding experimental phase portrait and phase plane, respectively. The phase portrait has a quasi-ellipsoidal form. The monitoring point trajectory plotted in the phase plane describes an inversed 'C', which is typical for the first swiveling mode. The cycle-to-cycle variations in these plots are small. Therefore, the FSI phenomenon can be characterized as quasi-periodic.

Fig. 8: Experimental raw signals of dimensionless displacements from a point in the midplane of the test section located at a distance of 4 mm from the trailing edge of the rubber plate.

Figure 9 is composed of eight 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 first swiveling mode. Thus, there is only one wave node located at the clamping of the flexible structure. 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.

Unsteady PIV.png

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).

Prior to this, however, it should be pointed out that very similar figures as depicted in Fig. 9 could also be shown from the numerical predictions based on LES. Exemplary and for the sake of brevity, Fig. 10 displays the streamwise velocity component of the flow field in a x-y-plane solely at t=3T/4. As expected the LES prediction is capable to resolve small-scale flow structures in the wake region and in the shear layers. Furthermore, the figure visualizes the deformed structure showing nearly no variation in spanwise direction.

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