Drag Reduction and Secondary-Flow Occurrence by Square Biplane Grid

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.


Introduction
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 [1].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 [2].Moreover, much research about grid turbulence has been per-  [6], and the drag of woven screens which is similar to biplane grids has been studied [7].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 [8] [9].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.

Surface Pressure Distribution
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 ρ is the density of the air.
( ) 2   1 2 Figure 2 also shows the pressure distribution on the crossed circular cylinders (Re = 2 × 10 4 ) 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 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

Estimation of Local Drag Coefficient
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 1 Figure 1 .z
Figure1shows 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 2 (Figure 2 .
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.

Figure 4
Figure4shows the relationship between the local drag coefficient C d on the upstream and downstream cylinders and the measurement position in each span.

Figure 4
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 ( ) ( ) π 0

Figure 2 (
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.