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a flat plate installed perpendicular to the wind direction; when the side ratio is large to infinity, the rectangular structure is a flat plate installed parallel to the wind direction.

The drag force of a rectangular structure is strongly related to flow pattern around the rectangular structure:

1. In the case of B/D < 0.6, separation flow is completely separated. The separated shear layers from both upstream edges flow down without reattaching to the side surfaces and roll up alternately in the wake to construct Karman vortex streets. In this region, the distance between the rolling up position of the separated flow and the downstream surface of the structure becomes shorter with increment of B/D and the base pressure on the downstream surface decreases remarkably. As a result, the drag force increases with increment of B/D. At about B/D = 0.6, the rolling up position becomes nearest to the downstream surface of the structure to be a peak value of the drag force in variety of B/D.

2. In the case of 0.6 < B/D < 2.8, the approaching flow is also completely separated. In this region, the separated flow interferes with the downstream corners of the structure to increase the distance between the rolling up position and the downstream surface of the body and increases the pressure on the downstream surface (which is called pressure recovery). As a result, the drag force decreases with increment of B/D. At the same time, the interval of vortex occurrence increases with increment of B/D and Strouhal number decreases as shown in Figure 13.3.

3. In the case of B/D > 2.8, the separation flow steadily reattaches to the side surface and separates again at a further downstream position than the reattachment position on the side surface to construct the Karman vortex streets in the wake of the body. The separation flow periodically reattaches to the surfaces and constructs vortex as on the surfaces. This region is called the complete reattachment region of separation flow.

13.2.2.2 Drag Reduction Method

13.2.2.2.1 Corner Shape Effect

The drag force of the rectangular cross-section structure can be reduced by making corners round or by cutting corners. Figure 13.4 shows one example for the reduction of the drag force of a square structure [4]. The horizontal axis indicates the ratio of radius of rounded corner to side length and the vertical axis indicates the drag force coefficient. Type 2 is the square structure with a rounded corner at upstream corners, Type 3 has four rounded corners, and Type 4 has a rounded corner at downstream corners. The drag force of Type 2 decreases with increase in the radius of the rounded corner. The drag force of Type 4 takes a little larger value than the value of a square structure without rounded corners. Type 3 takes the value between Type 2 and Type 4. Referring to the results, it is clear that it is very important to reduce the drag force to make upstream corners round or of cutting shape. On the other hand, making downstream corners round has no effect in the reduction of drag force.

13.2.2.2.2 Roughness Effect

Figure 13.5 shows the drag force of a circular cross-section structure to Reynolds number [5]. Reynolds number (Re) is defined as the ratio of inertial force to viscous force of fluid:

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