^{1}

^{1}

^{1}

In this paper, the characteristics of the three-dimensional flow field around the circular cylinder members forming a square biplane grid were experimentally investigated by using a wind tunnel and a water tunnel. In the wind tunnel testing, the span wise and circumference pressure distributions of surface on the circular cylinder were measured on the center mesh members formed by biplane grid in detail. Local drag coefficient was calculated from the surface pressure distributions. In addition, the flow visualization was performed in the water tunnel. As a result, it was suggested that the flow penetrating the contact region produced secondary-flow behind the biplane grid. Accordingly, the drag reduction would be caused by the presence of the secondary-flow.

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 [

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

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 C_{p} 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.

_{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)

^{4}) by Fox et al. [_{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 [

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.

_{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˚).

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

_{d} on the upstream and downstream cylinders and the measurement position in each span. _{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 _{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 _{d} on the upstream cylinder and the downstream cylinder is lower than the value of C_{d} on the single cylinder.

As shown in

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.

Tachimoto, Y., Iwamoto, M. and Yamada, H. (2018) Drag Reduction and Secondary-Flow Occurrence by Square Biplane Grid. Open Journal of Fluid Dynamics, 8, 78-85. https://doi.org/10.4236/ojfd.2018.81007

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

C_{p}: Surface pressure coefficient

C_{p0}: Front pressure coefficient

C_{pb}; Base pressure coefficient

C_{d}: Local pressure drag coefficient