Examination of Impaction Efficiency of Sea-Salt Particle for an Airborne Sea-Salt and a Corrosion Sensor Using CFD Model

Abstract

To improve estimation of sea salt deposition distributions on structural surfaces such as that of an airborne sea salt and corrosion sensor, we numerically simulated approaching flows with particles around a vertical flat plate. This is a typical object that mimics a sensor with a support plate. We used a computational fluid dynamics (CFD) model based on the unsteady Reynolds averaged Navier–Stokes equation. After validating the results by comparison with existing studies for flows with particles around a cylinder, we examined the changes in particle impaction efficiency on the plate with different approaching flow directions (0, 45 deg) and particle diameters (5 × 10⁻⁶–1.6 × 10⁻⁴ m). The impaction efficiency increases rapidly with particle diameter, whereas the influence of flow direction is small. Such increases in impaction efficiency are due to contributions from inertial impaction, and thus the variation in Stokes number with wind speed and the plate size can be used to predict the flow and particle conditions required for increases in impaction efficiency. The efficiencies for small particles on the front surface of the plate are higher than those on a cylinder. The impactions of small particles on the plate are locally activated by flow separations around a bluff body, whereas those on a cylinder are caused by intercepts without flow separations.

 

This Paper was Originally Published in Japanese in Zairyo-to-Kankyo 71 (2022) 253–262. The abstract and the captions of Table 1 and Figs. 1–12 were slightly modified.

1. Introduction

Methods for estimating corrosion rates under various meteorological conditions have been investigated and reflect the aging of steel structures such as steel towers and bridges. Empirical equations for corrosion rates with environmental parameters have been proposed and applied to create corrosion rate maps based on exposure tests of major materials such as steel and zinc [1]. Furthermore, machine learning techniques such as artificial neural networks, which can account for the complicated dependencies of the corrosion rates on many variables, have recently been used to increase the precision of estimation methods [2, 3]. However, such estimations require prior accumulation of sufficient observational data [4]. In addition, local environmental corrections are needed, such as for the high sea salt concentration near a coast [5], the high frequency of strong winds [6, 7], and the long duration of high humidity [8].

Computational fluid dynamics (CFD) has become a powerful tool for evaluating the spatial distribution of the environment, along with improvements in computational capabilities. By comparison with observations, Suto et al. [9, 10] have confirmed the applicability of a CFD code, NuWiCC-ST, to changes in sea salt concentration in the air, which is one of the environmental parameters controlling the corrosion rate along with the complex terrain and heterogeneous ground surface conditions. Moreover, they have developed a mapping procedure that combines statistical methods to estimate the period average of sea salt particles. Fujii et al. [11], Obata et al. [12], Noguchi et al. [13], and Ohnishi et al. [14] have also attempted estimates of more detailed sea salt distributions in the air including near structures such as bridges.

However, sea salt deposition on structural surfaces has not yet been quantitatively assessed. One of the reasons is the dependence of deposition on the airflow in the immediate vicinity of the structure, which generally results in complex flow fields such as boundary layer flows along the structural surface and wake flows including flow separation behind the structure [15–17]. CFD calculations of sea salt concentration or flux in the air are often qualitatively compared with observed sea salt deposition [9]. This is also consistent with the fact that the influence of airflow in the vicinity of observation equipment has become a factor in standardizing methods for observing and understanding the environment of sea salt corrosion [18, 19].

In this study, we investigate the particle impaction efficiency on a vertical rectangular flat plate, which is the typical geometry of a structure containing a corrosion sensor installed on a fixture [20]. The aim is to refine the evaluation of sea salt impaction on sensors. We numerically simulate unsteady flows around the plate with the unsteady Reynolds averaged Navier–Stokes equation (URANS) [21], which can capture unsteady flow fields such as vortices developing behind the plate. Additionally, we calculate particle transport with a Lagrangian scheme [22] to evaluate changes in the impaction efficiency of sea salt particles on a structural surface with particle diameter and wind direction.

2. Numerical Set-Up

2.1 Object

The numerical simulations targeted air flows with sea salt particles around a vertical square flat plate. The width of the plate was set equal to the height, H = 0.1 m, and the thickness was set to 0.01 m. This corresponds to the dimensions of sea salt and corrosion sensors such as the ACM sensor installed on a fixture [20]. The speed of the approaching flow, Ua, was set to 10 m/s on the basis of the conditions for sea salt generation over the sea due to whitecaps [6, 7, 9, 10]. Two wind directions were considered: 0 deg, which was directly opposite to the normal direction of the vertical plate, and 45 deg, which was inclined to the vertical plate. Six particle diameters (Dp = 5 × 10⁻⁶ m, 9 × 10⁻⁶ m, 1.6 × 10⁻⁵ m, 2.9 × 10⁻⁵ m, 5.2 × 10⁻⁵ m, and 1.6 × 10⁻⁴ m) were considered, corresponding to the conditions in previous studies [9, 10].

2.2 Numerical method and condition

We implemented particle transport models using the solver pimple Foam within the open source CFD code OpenFOAM, which is based on the finite volume method and has advantages in reproducing complex airflow fields near structures. The basic equations for the airflow field are the mass conservation equation (the continuity equation) and the momentum conservation equation (the Navier Stokes equation) for a single-phase, incompressible fluid with Reynolds decomposition with unsteady terms. The GAMG algorithm for pressure and the DILU-PBiCG algorithm for other physical quantities were used as matrix solvers. The second-order Back–Euler and the second-order central difference schemes were used for time integration and spatial discretization, respectively. Turbulence was treated using the Kato–Launder model [23], which is suitable for reproducing the airflow around rectangular structures. Compared with the k–ω SST SAS, which is suitable for reproducing a boundary layer flow, the Kato–Launder model has been confirmed to describe the separation flow around a vertical flat plate in more detail.

Figure 1 depicts the numerical domain with the grid arrangement and coordinate system used in this study, where panels (a) and (b) show the grid arrangement for the entire computational domain and near the vertical plate, respectively. The numerical domain was set to −0.5 m < x < 1.0 m, −0.5 m < y < 1.0 m, and −0.5 m < z < 0.5 m in the streamwise, spanwise, and vertical directions, respectively; the origin of the coordinate system was set at the center of the vertical plate surface. The numerical grid was created using the OpenFOAM tool blockMesh and was based on a hexahedral mesh with variable spacing, and the spacing near the plate surface was set to 5 mm. The non-slip boundary condition was used on the plate surfaces. A constant and uniform wind speed was applied to the inlet boundary, and free and slip conditions were applied to the outlet and side boundaries, respectively.

Fig. 1

Grid arrangement for the numerical domain (a) and near the vertical plate (b) with the coordinate system in (b); the unit is [m].

After 5 sec. of airflow simulation, particles were added from 5 sec. to 6 sec., and particle transport was calculated until 8 sec. The time steps of the numerical simulations were adjusted so that the Courant number was less than 0.5. Particle motion was described by a Lagrangian scheme assuming 1-way coupling with the airflows [22]. Interparticle interferences such as aggregation and the effects of Brownian motion were neglected. The drag force on the particles was treated only as a function of the particle Reynolds number Re with the particle diameter as the characteristic length, assuming the particles to be spherical. The effects of the Basset force, Magnus effect, and Saffman lift force were neglected. Particles were injected into the computational domain from the 10⁶ points with an area of 0.1 m × 0.1 m located in front of the vertical plate. An average of 1 particle/sec. was injected from each point. To improve the uniformity of the spatial particle distribution, we randomized the points and the time intervals for particle injections. We also performed simulations with different numbers of particles and time intervals and confirmed that there was no significant difference between the results obtained with the particle input amounts and method used here and the statistical convergence of the calculated impaction efficiencies.

To validate our method, we performed three-dimensional unsteady simulations for a flow around a cylinder, which has been reported in previous studies, including the formation of organized vortices in wake regions. The turbulence model was replaced with k–ω SST SAS to reproduce the boundary layer flows that developed along the cylinder surface. The reproducibility of the unsteady flow behavior around an obstacle under high Reynolds number was investigated in terms of the time series of the lift coefficient C_L and the drag coefficient C_D at Re = 10⁵; the Reynolds number is based on the cylinder diameter. As an example, Fig. 2 presents the time histories of C_L and C_D calculated for a cylinder with an aspect (diameter-to-length) ratio of 9. The horizontal axis is the dimensionless time t^* based on the approaching wind speed and the cylinder diameter. The time-averaged values of C_L and C_D are approximately 0 and 1, which are consistent with a previous study [24]. The dominant frequency and the amplitude modulations of the time history of C_L are also consistent with the previous study [24]. The probability density functions (PDFs) of the instantaneous lift coefficient C_L are shown in Fig. 3 to clarify the amplitude modulations of C_L. The horizontal axis is the fluctuating component normalized by the RMS value. The PDFs show two extreme values that differ from those for the Gaussian distribution [24], corresponding to the time history shown in Fig. 2. The simulations were also performed for a cylinder with aspect ratios of 1 and 4. These simulations show that the time histories and PDFs of C_D and C_L change with decreasing aspect ratio owing to the enhanced rocking as the aspect ratio decreases. As for particle transport and impaction, the impaction efficiencies on the front and back surfaces of a cylinder were examined for various Reynolds and Stokes numbers in two-dimensional simulations, in accordance with previous studies. The impaction efficiencies were consistent with those in previous studies, including the differences between the front and back surfaces of the cylinder and the dependencies on the Reynolds and Stokes numbers [25, 26].

Fig. 2

Time series of instantaneous lift and drag force coefficients, C_L and C_D, of the cylinder.

Fig. 3

Probability density function of the lift force coefficient of the cylinder.

3. Numerical Results

3.1 Airflow and particle transport around a vertical flat plate

Figures 4 and 5 present the contours of the time-averaged streamwise and spanwise components of the wind velocity, Umeanx and Umeany, in the horizontal (x–y) plane including the center of the vertical plate (z = 0) for wind approaching at 0 deg and 45 deg, respectively. The vertical component Umeanz was found to be close to zero for both wind directions (figure omitted). For the wind approaching at 0 deg, strong lateral roundabouts appear after deceleration and stagnation in front of the plate. A wake with decreasing wind speed is generated behind the plate owing to the wind-shielding effects of the vertical plate with the downstream extension of the wake region, which recovers the wind speed deficit. Such flow patterns are consistent with previous studies [27, 28]. The profiles of Umeanx and Umeany are nearly symmetrical about the central axis, but a slight asymmetry occurs in the deceleration regions. This is probably because the integration time used in this study was kept quite short owing to the computational cost limitations; a small-time step was set to capture the particle transport process. Longer integration times would be required to obtain convergent statistics on wind speed fluctuations in the low-frequency range associated with organized vortices. Therefore, the quantitative evaluation of the impaction efficiencies on the back surface of the plate, which was not the subject of this study, should be interpreted with caution. For the 45 deg approaching wind, the asymmetry of the flow pattern is caused by the inclination of the plate. However, for the 0 deg approaching wind, deceleration in front of the plate, strong lateral roundabouts, and a wake with decreasing wind speed behind the plate are generated.

Fig. 4

Contours of time-averaged streamwise (a) and spanwise (b) velocities for a flow approaching at 0 deg in the horizontal plane at the plate center.

Fig. 5

Contours of time-averaged streamwise (a) and spanwise (b) velocities for a flow approaching at 45 deg in the horizontal plane at the plate center.

Figures 6 and 7 show snapshots of the instantaneous streamwise component of wind velocity, Ux, with the instantaneous particle distribution in the horizontal (x–y) plane including the center of the vertical plate (z = 0) for the 0 deg and 45 deg approaching winds, respectively. These are the results at the end of the computation (t = 8 sec.). Many particles exist in front of the plate regardless of the direction of the approaching wind, including the deceleration region. In the wake region behind the plate, particle distributions associated with organized vortices [27] are observed. The distributions show the effect of particle diameter on particle transport. Particles with small diameters follow the flow patterns of organized vortices, except near the center of the vortices where strong centripetal forces act, and are entrained even into the deceleration region behind the plate. As the particle diameter increases, the particles deviate from the flow pattern of the organized motions and attenuate the mixture in the deceleration region behind the plate. The number of particles behind the plate decreases compared with that in front of the plate. For the largest particles (Dp = 1.6 × 10⁻⁴ m), a constant mixing width is generated regardless of the downstream location of the deceleration region behind the plate, whereas the wake region has a downstream extension.

Fig. 6

Snapshots of particles with Dp = 5 (a), 9 (b), 16 (c), 29 (d), 52 (e), and 160 (f) ×10⁻⁶ m and streamwise velocity for a flow approaching at 0 deg.

Fig. 7

Snapshots of particles with Dp = 5 (a), 9 (b), 16 (c), 29 (d), 52 (e), and 160 (f) ×10⁻⁶ m and streamwise velocity for a flow approaching at 45 deg.

Figures 8 and 9 illustrate the particle transport in the immediate vicinity of the plate. The results at the end of the calculation (t = 8 sec.) are used for illustration. The particle color refers to the residence time of the particles in the airflow. The residence time for all particle diameters is as short as 0.02 sec.–0.05 sec. before approach to the plate, regardless of the direction of the approaching wind. Around the plate, the residence time is affected by the particle diameter. The residence time of some particles with small diameters (Dp = 5 × 10⁻⁶ m, 9 × 10⁻⁶ m, and 1.6 × 10⁻⁵ m) is as long as 0.15 sec. in front of the plate and as long as 0.05 sec.–0.1 sec. behind the plate. The residence time decreases with increasing particle diameter and is close to 0.02 sec.–0.05 sec., which reduces the change in the resistance time from the approaching flow regions to the near-plate regions. Note that, for the wind approaching at 45 deg, particles with a long residence time are mixed near the leading edge of the plate (right side of the figure).

Fig. 8

Snapshots of particles with aging in the near-surface region with Dp = 5 (a), 9 (b), 16 (c), 29 (d), 52 (e), and 160 (f) ×10⁻⁶ m for a flow approaching at 0 deg.

Fig. 9

Snapshots of particles with aging in the near-surface region with Dp = 5 (a), 9 (b), 16 (c), 29 (d), 52 (e), and 160 (f) ×10⁻⁶ m for a flow approaching at 45 deg.

3.2 Particle impact on a vertical flat plate

Table 1 summarizes the results for the particle impaction efficiency η_f, defined as the ratio of the number of particles impacting on the front surface of the vertical plate to the total number of particles input, for the winds approaching at 0 deg and 45 deg. The number of particles impacting the back surface of the plate is extremely limited, and the impaction efficiency is also very low, as shown in Figs. 8 and 9. The impaction efficiency η_f is approximately 0.1 when the particle diameter Dp is smaller than 10⁻⁵ m, and it is almost 1 when the particle diameter Dp is larger than 10⁻⁴ m, regardless of the direction from which the wind approaches. The impaction efficiencies of small particles for the wind approaching at 45 deg exceed those for 0 deg, whereas for large particles, the η_f values for 0 deg exceed those for 45 deg. This shows the effect of wind direction.

Table 1 Particle impaction efficiency at the front side of the vertical plate for a flow approaching at θ = 0 deg (a) and 45 deg (b) for particles with Dp = 5, 9, 16, 29, 52, and 160 × 10⁻⁶ m.

Figures 10 and 11 show the contours for the spatial distribution of the number of particles impinging on the front surface of the plate. When the direction of the approaching wind is 0 deg, the number of impinging particles has maxima at the four corners of the plate for particles with a diameter less than 10⁻⁵ m. The distribution becomes uniform as the particle diameter increases. When the wind direction is 45 deg, the distribution tends to be uniform as the particle diameter increases, but the number of particle impingements increases in the upstream intercept (right side of the figure) non-uniformly in the spanwise direction (y direction).

Fig. 10

Spatial distribution at the front surface of impacting particles with Dp = 5 (a), 9 (b), 16 (c), 29 (d), 52 (e), and 160 (f) ×10⁻⁶ m for a flow approaching at 0 deg.

Fig. 11

Spatial distribution at the front surface of impacting particles with Dp = 5 (a), 9 (b), 16 (c), 29 (d), 52 (e), and 160 (f) ×10⁻⁶ m for a flow approaching at 45 deg.

4. Discussion

Numerical simulations were performed for the particle transport accompanying the airflow around a vertical flat plate and the particle impact on the plate surface. Special attention was paid to the effects of particle diameter and direction of the approaching wind. The impaction efficiency on the plate surface rapidly changes with the particle diameter, whereas the effects of wind direction are insignificant. At the back side of the plate, when the particle diameter is small, the particles follow the organized vortex and are mixed in the deceleration region except near the center of the vortex where strong centripetal force acts, whereas the large particles mainly move in the same direction as the approaching wind.

The particle diameter for such an abrupt change in particle transport and impaction behavior, which was 10⁻⁵ m–10⁻⁴ m for an approaching wind speed Ua = 10 m/s, was generally normalized using the Stokes number, St [St = ρ_pD_p²Uc/(18νLc) [22, 25], where ν and ρ_p are the kinematic viscosity of air and the density of the particle]. The Stokes number is a nondimensional parameter governing particle transport in flow fields. In the calculation of the Stokes number, the selections of the characteristic velocity Uc and the characteristic length Lc are crucial. Here, we choose the approaching wind speed, Ua, and the plate size, H, for Uc and Lc, respectively. This is because the flow pattern with the rapid bending with the wind speed in the vicinity of the front surface of the plate corresponds to the approaching flow, as shown in Figs. 4 and 5. For the kinematic viscosity of air and the density of sea salt, ν = 1.5 × 10⁻⁵ m²/s and ρ_p = 1 × 10³ kg/m³, respectively, the Stokes numbers for our conditions are estimated to be 0.01, 0.03, 0.1, 0.3, 1.0, and 10.0. This reveals consideration of a wide Stokes number range, including the small number region, which is insufficiently discussed in previous studies [22]. The particle impaction efficiencies at the front plate surface listed in Table 1 are presented against the Stokes number in Fig. 12. A sudden change in the impaction efficiency is observed at a threshold value of St ≅ 10⁻¹–10⁰ regardless of the wind direction: the impaction efficiency is approximately 0.1 when the Stokes number is smaller than 10⁻¹, and almost 1 when the Stokes number is larger than 10⁰. The Stokes number that gives this abrupt change in impact efficiency is consistent with those for the front of a cylinder [25, 26], which means this threshold Stokes number is independent of the structural geometry.

Fig. 12

Change in particle impaction efficiency at the front side of the plate with Stokes number St for flows approaching at 0 deg and 45 deg. The dashed line is calculated with the formula for particle impaction efficiency on a cylinder proposed by Makkonen [29].

It should be emphasized that the efficiency for small Stokes number for the vertical plate (η_f ≅ 0.1) is much larger than that for cylinders [25, 26]. The efficiency estimated using an empirical formula for a cylinder surface [29], also shown in Fig. 12, becomes lower than that for the flat plate with decreasing Stokes number. Particle impactions with a small Stokes number following the airflow are mainly due to contacting the cylinder surface [25, 26]. In the front of the flat plate, unlike the cylinder, wind speed locally increases and the streamline becomes more bent with the airflow deceleration (Figs. 4–7). Therefore, the ratio of the particle relaxation time to the time scale of passage through the structure, which is expressed by the Stokes number, is not uniform at the front surface of the vertical plate, and a region that locally activates particle collisions is generated. This corresponds to the fact that the spatial distribution of impaction on the front surface of the plate for small particle diameters has maxima at the four corners and upstream intercept (right side of the figure) when the wind approaches at 0 deg and 45 deg (Figs. 10 and 11). The non-dimensional parameter R (= Dp/H), which indicates the contribution of particle contact following the airflow to the cylinder surface, is approximately 10⁻³ even for the largest particles, which is small enough for neglecting contact effects [30].

5. Conclusion

This study aimed to refine the evaluation of sea salt deposition on structural surfaces considering airborne salinity and corrosion sensors. A CFD model based on URANS was used to numerically simulate an approaching flow with sea salt particles around a vertical rectangular plate, which represents the typical shape of a sensor installed on a fixing jig. We examined the changes in impaction efficiency with the direction of the approaching wind (0 deg and 45 deg) and the particle diameter, and presented physical interpretations based on insights into the airflow and particle transport processes.

The impaction efficiency η_f of a particle on the front surface of a vertical plate increased rapidly with increasing particle diameter, whereas the effect of wind direction on the efficiency was small. This rapid increase was due to the inertial effect of large-diameter particles. The Stokes number, which is a non-dimensional parameter related to the wind speed of the approaching flow and the size of the structure, was found to be effective in predicting such changes in the impaction efficiency. The impaction efficiency was approximately 0.1 when the Stokes number was smaller than 10⁻¹, and almost 1 when the Stokes number was larger than 10⁰, corresponding to values for impaction on a cylinder surface [25, 26]. This indicates that the efficiency increases with the Stokes number regardless of structural geometry.

However, there exist quantitative differences between the impaction efficiencies of a vertical plate and cylinder surface under a small Stokes number. The impaction efficiency at the front of the vertical surface (η_f ≅ 0.1) was higher than that for cylinders [25, 26, 29]. This difference in impaction efficiency is due to the difference in airflow deceleration near surfaces with and without curvature. At the front of a cylinder, the airflow deceleration is not as pronounced as at the front of a vertical plate, and impactions are caused by direct contact between particles following the airflow and the cylinder surface [25]. Contrary to this, at the front of the vertical plate, the local increase in wind speed and bending of the streamline become more pronounced as the airflow slows down. The ratio of the relaxation time of the particles to the time scale of their passage through the structure, which is indicated by the Stokes number, is not uniform, and a region is locally generated that activates particle impact.

These results suggest the importance of particle diameter in correcting impaction efficiency when observing and making maps for sea salt particles. Long-term, wide-area maps and multi-point observations generally require evaluating corrosion and impaction of sea salt particles, and thus particle diameter dependencies should be carefully considered with special attention to locally changing flow fields in front of the structural surface. The permeability of the structure must also be considered because it is closely related to the flow patterns near the surface. When the particle diameter is large (St ≅ 10⁻¹), the spatial distribution of the particles on the front surface of a vertical plate is almost uniform, indicating that the plate size has a small effect on the impact efficiency.

Long-term particle residence, which occurs under a small Stokes number, may be due to the influence of deposition processes other than impaction, such as turbulent diffusion [26]. We will perform further research on evaluating deposition considering elementary processes other than impaction with the effect of wind velocity fluctuations included in the approaching wind [31].

Acknowledgments

We developed the research plan and the numerical setup through discussions with Drs. Yasuhiko Hori, Takashi Nishihara, Tomomi Ishikawa, Atsushi Hashimoto, and Ayumu Sato, and Mr. Kazuyasu Goto of CRIEPI. Dr. Yuzuru Eguchi of CRIEPI provided useful advice on interpreting the simulation results. We express our deepest gratitude to them.

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