1. Introduction

Okinawa is located in the southern area in Japan and is subtropical islands enclosed in the ocean. There, therefore, is a problem that corrosion of the structures progresses quickly because of high temperature, high humidity and adhesion of sea-water mist flying from sea. For instance, since the Benoki Bridge located in Kunigami village, Okinawa, was built by weatherability steel in 1981, it collapsed by remarkable corrosions in July, 2009 [1] [2] .

Author is interested in the relationship between flow structure around bridge beams and corrosion of sea-water mist. Therefore, two approaches are attempted. One is flow visualization and PIV to understand the flow structures inside bridge beams and another is numerical approach to understand the collision of sea-water mists on beams walls.

2. Experiment Setup

Figure 1 shows a 1/15 scale bridge model to investigate the flow around the

bridge beams. Table 1 shows the configuration of the bridge model. The bridge beams consist of two cavity structures. Flat plate is set below the bridge beam like as the water surface. The model and plate are made of the transparency acrylic resin to visualize the inside cavity flow. The beam model has 0.1 m in height (H), 0.4 m in width ( $W_1$ ) and 0.125 m in each cavity width ( $W_2$ ). The distance L from bridge beams to water surface is varied at that L/H = 0.5, 1, 2. Velocity U is set at 5 m/s, and then the Reynolds number Re is about 5.0 × 10⁴.

The inside flow images are captured by high-speed camera (Phantom V710, Frame rate: 3000 fps, image size: 1280 × 800 pixels). The flow is illuminated by CW Nd: YAG (Output power: 8 W, wave length: 532 nm) as laser sheet light with about 1 mm width. For seeding, smoke generated by heating the glycol solution is derived from three locations. One is at upstream of bridge beam, the others are on wall in behind of two cavities.

Whole area including the two cavities is captured to investigate the relationship between their upstream and downstream cavities. Calculated areas are cropped to two areas of A (upstream cavity) and B (downstream cavity) areas as shown in Figure 1. For PIV analysis, time-series velocity vectors for each area are obtained by recursive direct cross-correlation method [3] .

3. Numerical Approach of Motion of Sea-Water Mists

Above mentioned flow visualization was executed in the wind tunnel, but it is difficult to use the sea-water mist as tracer particle. Because wind tunnel was corroded by salt, author, therefore, attempts numerical approach to understand the collision of sea-water mists. Also, velocity data obtained by PIV are used in a whole flow field.

These behaviors of sea-water mists are given by equation of translate motion of particle (or droplet) [4] as following Equation (1):

$\begin{array}{l}\frac{\text{d}}{\text{d}t}\left({\rho }_l{V}_l{u}_l\right)+\frac{\text{d}}{\text{d}t}\left(\beta {\rho }_G{V}_l{u}_l\right)+{\rho }_l{V}_{l}g+V_l\nabla p-V_l\mu \left({\nabla }^2{u}_G\right)\\ +\frac{1}{2}{\rho }_G\left(\text{π}{r}_l^2\right)C_D\left|u_l-u_G\right|\left(u_l-u_G\right)+F_L=0.\end{array}$ (1)

where, 1st term to 7th terms mean inertia force, added inertia force, gravity force, pressure gradient force, viscos force, drag force and lift force. $u$ is velocity vector, $r$ and $d$ are a radius and a diameter of particle, $p$ is the pressure, $g$ is gravity acceleration vector, $\rho$ is density, $\mu$ is viscosity, $V$ is volume of a particle, and $\beta$ is virtual mass coefficient. Drag force coefficient $C_D$ used equation known as Newtonian resistance and equation proposed by Shiller and Naumann [5] . Subscript $l$ and $G$ mean sea-water mist particle and air, respectively. Approximate equation of Suffman’s lift force defined by Mei [6] is given as Lift force $F_L$ .

In real case, the diameter of the sea-water mist has the range of a few micro-meters to several ten micro-meters. In this simulation, a diameter of droplet $d$ sets to 10 μm and the standard deviation of droplet σ_d sets to 5 μm. Initial positions of droplets are located randomly in whole cavities. Time marching method set to 1st order Euler method. Droplet position in the next step is calculated by velocity $u_l$ given by Equation (1) and the time interval dt = 5 ms. Interaction between droplets don’t consider. When droplets impinge to wall, it is judged that droplets bonded to the wall. At the time of impinging, bonded wall position (left, center and right wall) and impinging wall height are recorded to investigate a degree for each height of wall.

4. Results and Discussions

4.1. Flow Visualization and PIV Results

Figure 2 and Figure 3 show smoke trajectory images at L/H = 0.5 and 2, respectively. These images are made by an average of 100 frame sequence images and image enhancement. For these figure, authors added to some arrow to recognize the stream direction.

From Figure 2 at L/H = 0.5, smoke stream moves to almost parallel to plate below the bridge beam and rotate to counter-clockwise in each cavity. From Figure 3 at L/H = 2, smoke stream moves separately from the left wall, rotate to counter-clockwise in the right cavity. The smoke streams from the downstream cavity moves to upstream cavity and rotate to clockwise in the upstream cavity.

Figure 4 and Figure 5 show averaged velocity vector maps at L/H = 0.5 and 2,

respectively. These results are obtained as time average of 3000 frame velocity vectors (1 second). Color bar means u/U which is defined the rate of the magnitude of each velocity vector to the inlet velocity U. That is, blue means 0m/s and red mean 5 m/s.

From Figure 4, velocities have about 5 m/s between bridge beam and plate and flow direction was parallel to the bridge beam and plate. In two cavities, velocities rotate to counter-clockwise and the magnitude of velocities is a half times less than main flow velocity U. Since velocities in both cavities is faster than out of plane velocity, there is no influence of three-dimensional flow.

Flow of Figure 4 at L/H = 0.5 is different from flow of Figure 5 at L/H = 2. From Figure 5, main flow separates toward plate wall largely below the left wall.

The separated flow goes over the downstream cavity and the right wall. Therefore, flow in the downstream cavity rotates to counter-clockwise, countercurrent flow under the center wall are obtained from the downstream cavity to the upstream cavity, and flow in the upstream cavity rotates to clockwise. The magnitudes of velocities in two cavities are slower than ones in Figure 4. Especially, since flow in upper area of downstream cavity is slower, influence of three-dimensional flow is included slightly.

Table 2 shows the relation of the rotation direction in two cavities. In this experience, flow at L/H = 1 is similar to one at L/H = 0.5. From above results, flow

○ means counter clockwise flow; × means clockwise flow.

structure as shown in Figure 4 change to one as shown in Figure 5, when 1 < L/H < 2.

4.2. Numerical Simulation on Collision of Sea-Water Mist Particles

Numerical approach of sea-water mist particles is executed. Figures 6(a)-(d) and Figures 7(a)-(d) show the probability density function (PDF) distribution of the collision of sea-water mist particles at the all side wall at the L/H = 0.5 and 2. Figure 6(a) and Figure 6(b), Figure 7(a) and Figure 7(b) show on left and right wall in area A of the upstream cavity and Figure 6(c) and Figure 6(d), Figure 7(c) and Figure 7(d) show on left and right wall in area B of the downstream cavity. h means the height on the wall. A vertical axis means the rate h/H of the position of wall to bridge height.

Flow both of their upstream and downstream cavities rotates to counter clockwise, mist particles which flow into these cavities from main flow impinge to right wall in these cavities. As shown in Figure 6(b) and Figure 6(d), there are many collisions of particles at h/H < 0.1, and as h/H becomes higher, PDF of collision decreases. In the Figure 6(a) of the opposite side of the upstream cavity, many mist particles move to downward and to almost parallel along the left wall. Therefore, there are many collisions of particles at h/H < 0.1, and as h/H becomes lower, PDF of collision increases. In the Figure 6(d) of the opposite side of the downstream cavity, many mist particles move to downward and impinge to the left wall. Therefore, there are many collisions of particles near h/H = 0.6, and as h/H becomes lower, PDF of collision decreases.

In Figure 7, Flow in the upstream cavity rotates to clockwise and one in the downstream cavity rotates to counter-clockwise as shown in Figure 5. Many mist particles which flow into these cavities impinge to the left wall in the upstream cavity and to the right wall in the downstream cavity. In Figure 7(a), there are many particle collisions when height is lower at the L/H < 0.5, and as h/H becomes higher, PDF of collision decreases. Peak of the collision is at the h/H = 1 because there is secondary flow in this corner and particles was trapped in the corner vortex. In the Figure 7(b) of the opposite side of Figure 7(a), many mist particles move to downward and impinge to the right wall. Therefore, PDF of collisions is higher when range of h/H is 0.1 to 0.5. In Figure 7(d), many mist particle mender to upward and impinge to the right wall. Therefore, when h/H is less than 0.7, there is a peak of PDF of collision at h/H = 0.6. There is a secondary flow in the corner, when h/H is larger than 0.7, PDF of collision are larger again. In Figure 7(c) of the opposite side of Figure 7(d), many mist

particles move to downward slowly and to almost parallel along the left wall. PDF distribution is almost equivalent in whole height.

5. Conclusions

The author was interested in the relationship between corrosion of sea-water mist and flow structure. Two approaches were attempted. One was flow visualization and PIV to understand the flow structures around bridge beams, and another was numerical approach of collision of sea-water mists.

From the visualization and PIV, authors revealed that flow at L/H = 0.5 rotates to counter-clockwise in two cavities and also flow at L/H = 2 rotates to counter-clockwise in the downstream cavity and to clockwise in the upstream cavity and countercurrent flow from the downstream cavity to the upstream cavity.

From the numerical approach on collision of water-sea mist particle, probability density function of collision was higher at the impinging point in two cavities and it was easy for corrosion to progress in the position.