There are two types of square lattice structures to control various industrial flow fields, biplane grid and woven screen. In particular, the square biplane grid which consists of many cylinders arrayed at right angles is often used to make turbulence. The turbulent characteristics downstream from the biplane grid have been examined in detail  . In addition, the heat transfer promotion may be expected in a new heat exchanger. Accordingly, it is important to reveal the flow characteristics around circular cylinders forming a biplane grid. Shiozaki et al. investigated drag coefficient and velocity distribution behind biplane grids and woven screens at a range of low Reynolds number (Re = 1 - 300) by numerical simulation  . Moreover, much research about grid turbulence has been performed     , and the drag of woven screens which is similar to biplane grids has been studied  . However, the flow phenomenon around the circular cylinder forming a square lattice structure is not directly revealed. It is reported from the previous results of the crossed circular cylinders that the flow over the separation area on the upstream cylinder penetrates the vicinity of the contact point between upstream and downstream cylinders   . Accordingly, it is supposed that the three-dimensional flow, which is similar to the crossed circular cylinders, is made in the cross region of cylinder members forming the biplane grid. However, the flow structure around square biplane grid is hardly known. Therefore, the aim of this study is to clarify the three-dimensional flow field around the circular cylinder members forming the square biplane grid by means of the measurement of surface pressure, the estimation of local drag coefficients and the flow visualization.
2. Experimental Apparatus and Methods
Figure 1 shows the coordinate system and nomenclature. The biplane grid, composed of circular cylinders with diameters of 10 mm, was used for the pressure measurement and flow visualization. The spacing ratio of the cylinders in each row is L/d = 4, where L is distance between adjacent cylinders and d is diameter of circular cylinder.
The wind tunnel with a cross section of 200 mm ´ 200 mm was used for the measurement of the surface pressure on the cylinders. The biplane grid was placed in the position of 100 mm from the wind tunnel outlet. The pressure tapping hole with a diameter of 0.3 mm was drilled in each central cylinder surface of the upstream cylinder array and the downstream cylinder array, and the surface pressure was measured by rotating the circular cylinder in intervals of 5˚ from 0˚ to 180˚. The Reynolds number was Re = U∞∙d/ν = 6000, where U∞ is free stream velocity approaching the biplane grid, and ν is kinematic viscosity of the air. The turbulence intensity is 0.6% for the free stream velocity. In order to
Figure 1. Coordinate system and nomenclature. (a) Biplane grid model; (b) Side view of Biplane grid.
measure the surface pressure on the cylinders, a minute differential pressure transducer was used. The sampling frequency was 1000 Hz, and the number of sampling was 10,000 points. The uncertainty of the pressure coefficient Cp was estimated to be approximately 5.5%.
Flow visualization was carried out in a water tunnel which has a cross-section of 400 mm × 400 mm. To take a picture of path lines, nylon particles with an average particle diameter of 50 mm and a specific gravity of 1.03 were mixed into the water flow. The experimental Reynolds number was kept to 200 for flow visualization. The measurement plane was x/d = 2.0.
3. Experimental Results and Discussions
3.1. Surface Pressure Distribution
Figure 2 shows the circumferential distributions of surface pressure coefficient Cp 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.
Figure 2 also shows the pressure distribution on the crossed circular cylinders (Re = 2 ´ 104) by Fox et al.  , the crossed circular cylinders (Re = 4000) by Yamada et al.  , and the single cylinder (Re = 6000) for reference. In Figure 2(a), the value of Cp 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   . On the other hand, as shown in Figure 2(b), the pressure distribution on the downstream cylinder are almost similar to one another,
Figure 2. Surface pressure distributions. (a) At each z/d position along z-axis of upstream cylinder; (b) At each y/d position along y-axis of downstream cylinder.
excluding the case of y/d = 0 and y/d = 0.2 planes. In particular, in the case of y/d = 0, Cp 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 Cpb behind the upstream cylinder (θ = 180˚), the spanwise distribution of the front pressure coefficient Cp0 on the downstream cylinder (θ = 0˚) and the spanwise distribution of the base pressure coefficient Cpb 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.  . 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.  ). 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
Figure 3. Spanwise pressure coefficient. (a) Upstream cylinder (θ = 180˚); (b) Downstream cylinder (θ = 0˚); (c) Downstream cylinder (θ = 180˚).
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.
3.2. Estimation of Local Drag Coefficient
Figure 4 shows the relationship between the local drag coefficient Cd 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.  as well as the single cylinder (Re = 6000) for reference. The local drag coefficient Cd is defined as
In the case of the upstream cylinders, the value of Cd 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 Cd decreased in the range from y/d = 0 to y/d = 0.4, the value of Cd 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 Cd 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 Cd on the upstream cylinder and the downstream cylinder is lower than the value of Cd on the single cylinder.
Figure 4. Local pressure drag coefficient.
3.3. Flow Visualization
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
Figure 5. Flow visualization behind biplane grid (Vortices A, A’ became larger). (a) Path lines pattern; (b) Sketch of flow pattern.
Figure 6. Flow visualization behind biplane grid (Vortices B, B’ became larger). (a) Path lines pattern; (b) Sketch of flow pattern.
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.
The characteristics of the three-dimensional flow field around the circular cylinder members forming the square biplane grid were investigated by the measurement of surface pressure, the estimation of the local drag coefficient and the flow visualization of path lines. As a result, it was found that the drag coefficient of circular cylinders forming a biplane grid was much reduced compared to that of the single cylinder. A drag reduction would be caused by the secondary-flow.
x, y, z: Cartesian coordinate system
d: Diameter of circular cylinder
L: Distance between adjacent cylinders
θ: Circumference degree of circular cylinder
U∞: Free stream velocity approaching biplane grid
P: Surface pressure on circular cylinder
P∞: Atmospheric pressure
ν: Kinematic viscosity
r: Density of air
Re: Experimental Reynolds number
Cp: Surface pressure coefficient
Cp0: Front pressure coefficient
Cpb; Base pressure coefficient
Cd: Local pressure drag coefficient