Figure 2 shows the circumferential distributions of surface pressure coefficient C_p on the upstream and downstream cylinders of biplane grid. The surface pressure coefficient is defined as following equation, which P_∞ is the atmospheric pressure and r is the density of the air.

C p = P − P ∞ ( 1 / 2 ) ρ U ∞ 2 (1)

Figure 2 also shows the pressure distribution on the crossed circular cylinders (Re = 2 ´ 10⁴) by Fox et al. [10] , the crossed circular cylinders (Re = 4000) by Yamada et al. [8] , and the single cylinder (Re = 6000) for reference. In Figure 2(a), the value of C_p in the range of approximately 130˚ ≤ θ ≤ 175˚ at z/d = 0 symmetrical plane became significantly larger. At the other measurement planes, as the measurement plane of the upstream cylinder approaches z/d = 0 symmetrical plane, the pressure on the rear side rapidly increased. The increase in pressure may be caused by the high-speed flow which penetrates into the rear of the upstream cylinder beyond the separation bubble which is on the upstream cylinder surface [8] [9] . On the other hand, as shown in Figure 2(b), the pressure distribution on the downstream cylinder are almost similar to one another,

excluding the case of y/d = 0 and y/d = 0.2 planes. In particular, in the case of y/d = 0, C_p took the maximum value at approximately θ = 45˚, and the pressure gradient is negative in the range of θ ≥ 45˚. This phenomenon suggests that there is no separation in circumferential direction on the downstream cylinder, or the separation point on the downstream cylinder moves considerably backward in the vicinity of y/d = 0 symmetrical plane.

Figure 3 shows the spanwise distribution of the base pressure coefficient C_pb behind the upstream cylinder (θ = 180˚), the spanwise distribution of the front pressure coefficient C_p0 on the downstream cylinder (θ = 0˚) and the spanwise distribution of the base pressure coefficient C_pb behind the downstream cylinder (θ = 180˚). Figure 3 also shows the results of the upstream and downstream cylinders in crossed circular cylinders (Re = 4000) by Yamada et al. [8] . As shown in Figure 3(a), the base pressure distribution had the minimum value at z/d = 0.2, and then the maximum value at z/d = 0.4. The front pressure distribution in Figure 3(b) had the maximum value at approximately y/d = 0.2 and the minimum value at approximately y/d = 0.4. After that, it rose to approach a constant value. These distributions in Figure 3(a) and Figure 3(b) are similar to those of the crossed circular cylinders (Yamada et al. [8] ). Yamada et al. reported the presence of the secondary-flow along spanwise and circumference on the surface of the upstream and downstream cylinders in the contact region by means of

oil-film methods. From this, it is suspected that there is a secondary-flow in the vicinity of the contact point between the upstream cylinder and the downstream cylinder of the biplane grid. Moreover, as shown in Figure 3(c), the value of the base pressure on the downstream cylinder had an almost constant value at every measurement position.

Figure 4 shows the relationship between the local drag coefficient C_d on the upstream and downstream cylinders and the measurement position in each span. Figure 4 also shows that of the upstream and downstream cylinders in the crossed circular cylinders (Re = 4000) by Yamada et al. [8] as well as the single cylinder (Re = 6000) for reference. The local drag coefficient C_d is defined as

C d = ∫ 0 π C p ( θ ) cos ( θ ) d θ . (2)

In the case of the upstream cylinders, the value of C_d was rapidly increasing in the range from z/d = 0 to z/d = 0.75 and then gently decreasing in the range from z/d = 0.75 to z/d = 2.0. The former is understood as the influence of the high-speed flow which penetrates behind the upstream cylinder, as mentioned in Figure 2(a). In the case of the downstream cylinder, the value of C_d decreased in the range from y/d = 0 to y/d = 0.4, the value of C_d in the region of y/d ≥ 1.0 was almost constant. The tendency of the distribution is similar to that of the crossed circular cylinders. The value of C_d is thought to be smaller in the range of 0 ≤ y/d ≤ 0.4, since there is no separation point or the separation point moves back, as mentioned in Figure 2(b). In addition, both the value of C_d on the upstream cylinder and the downstream cylinder is lower than the value of C_d on the single cylinder.

Figure 5(a) and Figure 6(a) show the path lines pattern behind the biplane grid. Figure 5(b) and Figure 6(b) show the sketch of the flow pattern, which were drawn from the path lines movie behind the biplane grid. This path lines pattern varied with a cycle of approximately 25 seconds.

As shown in Figure 5(a) and Figure 6(a), the secondary-flow was observed. In addition, the secondary-flow generates vortices which might be longitudinal vortices. In Figure 5, it was observed that two pairs of the vortices A’ and B were formed in the range of about y/d ≤ ±1.0 and z/d ≤ ±0.5 behind the downstream cylinder, and B was rather small in comparison with A’. The flow around B was entrained into the A’. At the same time, the scale of the vortex pair A in the range of 3.0 ≤ y/d ≤ 4.0 became larger. Similarly, as shown in Figure 6, the scale of vortex pair A’ was smaller, the scale of vortex pair B became larger. At the same time, the scale of vortex pair B’ in the range of −4.0 ≤ y/d ≤ −3.0 became larger. Based on the path lines movie observation, the scale of the vortex pairs (A, A’) and (B, B’) were alternately and periodically varied. The direction of the

flow which moved backward on y/d = 0 symmetrical plane on the surface of the downstream cylinder corresponds to the rotation direction of the vortices.