**5. Conclusions**

328 Computational Simulations and Applications

lines perturbation and tube motion. The times delay model approximates how quickly flow along the monitoring points shown in Figure 1 is affected by any intervening tube motion. In models such as that of Lever and Weaver (Lever & Weaver, 1981), it is assumed the flow inside the tube bundle is divided into wake and channel flows. The wake flow appears as large recirculation zones located between tubes in the spaces running transverse to the flow (zones 1 and 2 in Figure 6a). Spaces between tubes aligned with the flow direction allow the flow to proceed relatively freely along lanes (or channels as depicted in Figure 6a). The outer

Streamlines in the channel regions are assumed not to between intervening recirculation zones. Therefore the mass flow at each gap between tubes remains constant. In the present

Figure 6 shows the streamlines prevalent at three instances during one period (of time *T*) of tube motion in the lift direction. At time 0 s (Figure 6a) there exists a significant recirculation zone between tubes 2 and 1 (zone 1), while at time 1/3T (Figure 6b), when the tube has just passed it peak downward position, fluid streamlines are redirected from the channel 2 to the channel 1. Conversely when the tube, at 2/3 T (Figure 6c), is nearing its peak upward position, streamlines are diverted from channel 1 to channel 2. The migration of flow back and forth between channels 1 and 2 through zones 1 and 2 is not entirely periodic as other

(a) (b)

(c)

Fig. 6. Flow visualization showing flow conditions proceeding moving tube at period

intervals of 0T, 1/3T and 2/3T. (*P/d*=1.33, *Ur*=50, *T*= 3.33s).

*1* and *2*.

edges of the lanes attach and separate from neighbouring tubes on the basis of

study the flow patterns are examined in light of these approximations.

asymmetries exist in the overall flow structure.

In this study the use of CFD to generate force coefficients in the unsteady flow models for FEI of Chen (Chen, 1991) and Tanaka and Takahara (Tanaka & Takahara, 1981) has been undertaken. The unsteady CFD simulations, with appropriate care taken for mesh and time step resolution, yield results that enable force coefficients to be well predicted. With comprehensive studies that cover a range of pitch-to-diameter ratios and reduced velocities, a series of FEI stability curves can be generated. The curves generated in this work based on CFD derived data follow the trends of that available in the literature, and reveal expected trends such as increasing critical reduced velocity with increasing *P/d* ratio. The results thus far indicate the CFD based approach for computing stability maps for family of arrays (in this case in-line) is very promising. The use of CFD data also has the added benefit of providing considerable detail on the flow behaviour in the array, and thus enables extracting information that could be used in models such as those of Weaver and Lever (Lever & Weaver, 1981). Along this vein simulations are planned using a larger array in order to isolate the region of interest around the oscillating tube from the downstream vortex shedding. This would allow a more careful investigation of the movement of the stagnation regions on the attachment side, and the degree of mass flow redirected, as a function of pitch-to-diameter ratio and reduced velocity.
