Aerodynamic interference of straight and tapered cylinder pairs near the first critical wind speed

Highlights

• Aerodynamic interference of identical tall structures.

• Staggered arrangement crucial at large separations in the vicinity of the critical speed.

• Rule of thumb that “Beyond 20 diameters interference is negligible” not tenable.

Abstract

The present investigation is concerned with the phenomenon of aerodynamic interference across three cases: between two circular cylinders; a pair of 1:50 tapered cylinders; and a pair of 1:40 tapered cylinders—all in staggered arrangement. Experiments were conducted in the 1.6 ​m $\times$ 1.6 ​m wind tunnel at IIT Delhi. Our focus is on the enhanced across-wind response of the downstream cylinder near the first critical wind speed (at which the vortex shedding frequency matches the natural frequency of the structure). It is shown that the magnification in the response (with respect to that of the isolated cylinder) is a strong function of both the pitch and the orientation. It is evident from the current investigation that the magnification factors recommended in IS 4998 (Part 1: 1992, see Fig. 1 therein/2015) and Eurocode 1 (Actions on structures- General actions- Part 1–4: Wind actions, see Equation E. 11 therein) need to be revised upwards. Further, the rule of thumb, used in the design of tall structures, that beyond 15/20 diameters interference is negligible is not tenable, especially for structures of identical geometry.

Introduction

There are numerous engineering situations wherein the interaction of wind with structures is critical to their design. Some examples are chimneys of thermal power plants, high-rise buildings, and offshore structures. The situation becomes more complex when two or more such structures interfere with each other.

A lot of work has been done on the interference of bluff body wakes over the past several decades. A comprehensive review of these past works may be found in Sumner (2010), Ohya et al. (1989) and Zdravkovich (1988). The predominant geometry chosen for the bluff bodies has been cylindrical and except for a few studies, the diameters (D) of the interfering cylinders have been identical.

Fig. 1 shows a schematic view of the interference arrangement and the definitions of the pitch (P) and the incidence angle (θ). The height of the cylinders is H and the aspect ratio (H/D) is usually much larger than unity. If θ is 0° (T ​= ​0) then we get the tandem arrangement, if θ is 90° (L ​= ​0) then it is side by side configuration, while, for general θ, the term ‘staggered arrangement’ is used.

Although from a practical viewpoint the staggered configuration is the likeliest, most of the previous works concentrated on the tandem configuration or the side-by-side configuration. Since earlier studies were focused on understanding the rich variety of flow patterns generated by the interfering shear layers adjacent to the bluff bodies, the pitch ratio (P/D) was usually maintained below 7 (Gowda et al., 1993; Ruscheweyh, 1983; Sockel and Watzinger, 1998; Sumner, 2010; Zdravkovich, 1985; Zdravkovich and Pridden, 1977). Brika and Laneville (1997) considered larger separations (L/D up to 25), however, it was primarily the tandem arragement.

The motivation for the present work stems from our engagement with chimneys/windshields associated with thermal power plants. In these structures, H/D is typically between 15 and 20, while P/D may vary from 10 to 20. A typical example of the response is shown in Fig. 2 and Fig. 3 (taken from Veeravalli et al., 2014). Here, the rms across-wind bending moment (BM) at the base of the downstream chimney model is plotted for various wind speeds and incidence angles. U_∞ is the velocity outside the boundary-layer upstream of both structures and U_H is the velocity at the top of the model/chimney under test. The two interfering chimney models were identical in shape and size (the lower two-thirds height was tapered while the top one-third was straight cylindrical), and P/D was 12. From the response of the isolated chimney model (Fig. 2) the first critical speed (at which the vortex shedding frequency matches the first mode frequency of the structure) was determined to be 16 ​m/s and the peak bending moment was measured to be approximately 40 units (micro-strain).

The response for the downstream cylinder shown in Fig. 2 is for an incidence angle of 9°. It is seen the peak response of the downstream model occurs at higher U_H than the first critical speed for the isolated model. This is probably because the downstream cylinder lies in the wake of the upstream cylinder and hence experiences a slightly smaller mean velocity than U_H. From Fig. 3, it can be seen that the response is strongly dependent on the incidence angle and increases with the incidence angle up to a point (9°) and then falls quite dramatically beyond 12°. For θ equal to 9° and 10° a peculiar double-peak (indicated by the arrows) is seen. Finally, the peak magnification factor obtained from this response (2.35), at an incidence angle of 9°, was found to be approximately 30% higher than that recommended by IS 4998-1, 1992 (Figure 1 therein). As we discuss below, the magnification factors in IS 4998-1, 1992 were obtained for a constant incidence angle of 15°.

The objective here is twin-fold: First, to see whether the double-peak in the across-wind response is present for all model geometries and second, to examine whether the magnification factors reported in IS 4998-1, 1992 or in BS EN 1991-1-4, 2005, which were obtained with a fixed incidence angle of 15°, are valid if the incidence angle is allowed to vary. From the cartoon shown in Fig. 12, below, it is clear that if a fixed incidence angle of 15° is used then the downstream cylinder will move out of the wake for large P/D and hence the magnification factor could be in error. A more detailed discussion on this is given in Rajora et al. (2018). Since the motivation for the present study stems from the work on chimney models (which may have a combination of straight and tapered sections), we have chosen three different geometries for our interference studies: a) straight cylinders, b) cylinders with 1:40 taper and c) cylinders with 1:50 taper –all these cases were considered in IS 4998-1, 1992 also.

As mentioned above, most of the previous works are limited to P/D values below 10 (see for example Sumner et al., 2000; Niemann and Kasperski, 1999). The only exception we are aware of is that of Krishnaswamy et al. (1975) which is the basis for the magnification factors recommended in IS 4998-1, 1992 and the rule of thumb that interference, even for identical structures, is absent beyond P/D ​= ​20. We note that several codes (such as ACI 307-88, USA; AS 1170.2–1989, Australia; CICIND Model code 1984) were consulted when IS 4998-1, 1992 was being formulated and finalized, so presumably, the magnification factors were either absent or more benign in those codes. The recently updated code IS 4998, 2015 assumes that the interference is even less significant and ignores interference beyond P/D of 12.75 while, the magnifications recommended in BS EN 1991-1-4, 2005 (see Equation E. 11) indicate that beyond P/D of 15 interference is absent. Neither of these codes present any experimental data and we will thus be comparing our results primarily with those presented in IS 4998-1, 1992.

As is clear from the discussion above, the utility of our work is primarily in the design of tall structures (such as power-plant chimneys) for which wind loads are likely to dominate. The Reynolds numbers (Re) achievable in wind tunnel experiments with scaled down models is very much lower than those encountered in the field for the full-scale structures. However, as discussed below, this may not be a very serious issue. The Reynolds numbers for the full-scale structures, at the design/critical wind speeds, are typically greater than 1$\times$10⁷. Thus they operate in the trans-critical or post-critical range, well beyond the drag crisis. The results of the wind tunnel experiments can be scaled up provided the tests are conducted in the upper sub-critical range (i.e. 10⁴ ≤ Re ​< ​1$\times$10⁵). In both the sub-critical range and the post-critical range the drag and lift coefficients are well-behaved and nearly constant although the values are different in the two ranges (c.f. Roshko, 1961), with both coefficients taking lower values in the post-critical range. Our primary concern in this work is with the magnification/enhanced response of the downstream structure in the vicinity of the critical speed. In the post-critical range the responses of both the isolated and the downstream structure would lower than those of the corresponding structures in the sub-critical range. Thus both the numerator and the denominator, in the expression for the magnification factor (see equation (1) below), would decrease in the post-critical range yielding, we expect, a magnification factor nearly the same as that in the sub-critical range.