Dispersion Simulations of Exhaust Smoke Discharged from Anchor-Handling Tug Supply Vessel under Various Wind Conditions

Abstract

Exhaust smoke discharged from marine vessels and offshore plants not only contaminates the hull and cargo but is also the main cause of deterioration in the crew’s health and working environment. Rules and regulations have been implemented and have become stricter in recent decades. In this study, the exhaust smoke flow around an anchor-handling tug supply vessel in a stationary state, which has been seldom studied, is analyzed using computational fluid dynamics. The study investigates the effect of changing the wind speed and direction, which primarily affects the flow and dispersion of the smoke, to verify the suitability of the environment for the crew. To assess the environment, the recommended and comfortable concentrations of NO₂ are used. The results demonstrate that a higher wind speed worsens the effect of the exhaust flow on the environment, owing to lower-pressure values and regions behind the structures. The emission of exhaust smoke is unsatisfactory when the wind flows from the side or rear of the vessel, instead of from the bow. Differing from previous studies conducted on general merchant vessels in navigating conditions, it was found that side winds can also have detrimental environmental effects in the stationary state. Adopting the original design of exhaust pipes leads to the distribution of exhaust smoke over the deck, exceeding the recommended exposure limit. Increasing the height of the pipes is identified as a simple but effective method to facilitate the smooth discharge of exhaust smoke.

1. Introduction

Rules and regulations have been implemented for decades to control marine emissions because they are harmful to both the environment and human health. Air pollutants emitted by ships increase annually and will continue to increase in the future, owing to the growth of global trade. Air pollutants emitted by ships arriving to and departing from ports significantly affect the air quality in coastal areas and hundreds of kilometers inland. Additionally, air pollutants contribute to global atmospheric change. Exhaust gases from marine diesel engines include nitrogen, oxygen, carbon dioxide (CO₂), carbon monoxide (CO), sulfur oxides (SOx), nitrogen oxides (NOx), hydrocarbons, water vapor, and smoke. Nitrogen and sulfur oxides are of particular concern as threats to vegetation, the environment, and human health. Focusing on marine vessels and offshore plants, the high-temperature exhaust smoke discharged from exhaust gases not only contaminates the hull and cargo and damages the antenna but is also the main culprit that deteriorates the operation environment of the crew [1,2].

In most ships, the exhaust pipe is located above the accommodation and navigation rooms. Because the accommodation is composed of simple planes, when a relatively high wind speed occurs, owing to the ship’s operation or wind, a zone with low pressure appears around the accommodation and separation occurs. When the exhaust smoke is discharged from the low-pressure area, it remains around the ship because it cannot escape to the outside, where the pressure is high. In addition, the vortex generated around the exhaust pipe interferes with the normal operation of the anemometer, and high-temperature exhaust smoke may cause thermal damage to the machinery around the exhaust smoke.

A simple but effective method to reduce damage and contamination caused by exhaust smoke is to change the design of the pipe and relocate it to a place where the pressure is high and the vortex is low. However, this should be performed by considering various aspects. For instance, the height of the exhaust pipe is subject to air draft restrictions on the port route, and its shape affects noise. In addition, when the height of the exhaust pipe located above the navigation room increases, vibrations occur, which necessitates structural reinforcement. Therefore, the exhaust pipe must be appropriately designed by considering the operating conditions such as wind direction, wind speed, and engine load. The adoption of contemporary exhaust gas treatment systems, such as scrubbers, is one of the most well-established and effective methods to mitigate the harmful effects of exhaust gases, and a review of these systems for compliance with the limits specified recently by the International Maritime Organization (IMO) is available in [3].

Several rules and regulations relevant to marine emissions have been implemented. The IMO Tier 3 NOx emission standards have been in effect since 1 January 2016. These apply only to new marine diesel engines of 130 kW or more installed on ships with a keel construction date of 1 January 2016 and operating within designated emission control areas. The IMO Stage 3 nitrogen oxide emission level is 80% lower than the emission level stipulated in the IMO Stage 1 nitrogen oxide emission standard. This standard can be achieved by applying a secondary emission control system. SOx can be reduced by decreasing the sulfur content of the fuel. In October 2008, the Marine Environment Protection Committee of the IMO agreed to gradually reduce the maximum sulfur content in fuels used in ships. Under the revised Marpol Annex VI regulations, the global limit on sulfur content was reduced to 0.5% on 1 January 2020. The limit applicable to sulfur oxide emission control areas was reduced to 0.1% from 1 January 2015. In Australia, the working time for gases that are harmful to the human body is regulated [4]. For an exposure standard, three forms, namely peak limitation, short-term exposure limit (STEL), and eight-hour time-weighted average, have been suggested. Peak limitation refers to the maximum or peak airborne concentration of a substance determined over the shortest analytically practical period, which does not exceed 15 min. The STEL is the time-weighted average maximum airborne concentration of a substance calculated over a 15 min period. Eight-hour time-weighted average (TWA) is the maximum average airborne concentration of a substance when calculated over an eight-hour working day for a five-day working week. For NO₂, 5 ppm STEL and 3 ppm TWA were suggested.

Model tests and computational fluid dynamics (CFD) analyses are primarily performed to observe the flow phenomenon around exhaust pipes. The model test has been widely performed in the past and offers excellent accuracy; however, it requires a significant amount of time and money to obtain all the information regarding the flow field. CFD has been used extensively recently; however, the amount of data accumulated, such as those from model tests, are insufficient. Hence, a review of various design conditions can be provided rapidly and economically. Isyumov and Tanaka [5] summarized the law of similarity for exhaust smoke and suggested a method for an accurate simulation. Kulkani et al. [6] summarized studies pertaining to ship exhaust smoke flow by performing tests and CFD simulations after 1930. Additionally, Kulkani et al. [7] conducted an exhaust smoke flow experiment using a simple vessel and superstructure. Camelli and Lohner [8] simulated the temperature and concentration of exhaust smoke around ships via large eddy simulations. Park et al. [1] computed the exhaust smoke temperature around a container ship and verified the CFD results via a ship trial. Park et al. [2] conducted a parametric study pertaining to the design parameters affecting exhaust smoke. Li et al. [9] simulated the weakening effect of the exhaust smoke of a ship traveling at various wind speeds, ship speeds, exhaust smoke velocities, and temperatures. Regarding exhaust smoke flow, numerous numerical studies have been conducted to investigate the turbulent boundary layer and wake around ships (Reddy et al. [10]; Syms [11]). Roper et al. [12] observed the flow around a ship during helicopter take-off and landing via CFD simulations and real-line measurements. Forrest and Owen [13] predicted the wake of a ship via detached eddy simulations and compared the results with the measurement results from an actual ship. The different plume behaviors of the exhaust from different numbers of container ship stacks were quantitatively analyzed based on mass fraction via CFD simulation [14]. The effects of the efflux velocity, operational conditions, stack geometry, and buoyancy on the exhaust dispersion of generic frigates have been investigated numerically [15].

Most studies relevant to exhaust smoke flow from a ship have been conducted for the navigating status, i.e., under the condition that a high relative wind speed and the wind direction affect the flow fields. This is appropriate for general merchant ships but not for special-purpose vessels, such as drill ships, offshore plants, and operation support vessels. For the latter, the exhaust smoke flow is primarily affected by wind because they operate in a stationary state at sea.

Therefore, in this study, the exhaust smoke flow around an anchor-handling tug supply vessel in a stationary state is analyzed via CFD simulation. By changing the wind speed and direction, we assess whether the environment is suitable for the crew members. The commercial CFD software (https://www.ansys.com/products/fluids, accessed on 4 June 2023), ANSYS Fluent, is used for the grid system and numerical simulations.

2. Numerical Methods

2.1. Governing Equations

For compressible turbulent flows, the governing equations are the continuity and Navier–Stokes equations, as shown in Equations (1) and (2).

(1)$\frac{\partial \rho }{\partial t}+\nabla ·\left(\rho \overrightarrow{v}\right)=0,$

(2)$\frac{\partial \left(\rho \overrightarrow{v}\right)}{\partial t}+\nabla ·\left(\rho \overrightarrow{v}\overrightarrow{v}\right)=-\nabla P+\nabla ·\stackrel{=}{\tau }+\rho \overrightarrow{g},$

where $\rho$ and $t$ are the density and time, respectively; and $\overrightarrow{v}$ is the velocity vector. In Equation (2), $P$ is the static pressure, $\stackrel{=}{\tau }$ the stress tensor, and $\overrightarrow{g}$ the gravitational acceleration vector.

To predict the behavior of the exhaust gas, the transport equation for the local mass fraction of the chemical species ($Y_i$), as shown in Equation (3), was adopted.

(3)$\frac{\partial \left(\rho Y_i\right)}{\partial t}+\nabla ·\left(\rho \overrightarrow{v}{Y}_i\right)=-\nabla ·\overrightarrow{J_i}+R_i+S_i,$

where $\overrightarrow{J_i}$ is the diffusion flux of species $i$ and $R_i$ is the net rate of production of species $i$ by chemical reactions. $S_i$ is the rate of formation due to the addition of the dispersed phase.

2.2. Numerical Algorithm and Schemes

The transient Reynolds-averaged Navier–Stokes (RANS) and species transport equations were numerically solved by discretizing the finite volume method. As for the RANS simulations, a turbulence model for the realizable $k$-$ϵ$ model [16] was adopted to accurately predict the spreading rate of both planar and round jets, since the realizable $k$-$ϵ$ model yielded favorable results in a parametric study pertaining to exhaust smoke from a ship based on turbulence models confirmed by the authors’ previous studies [1,2].

The velocity and pressure were coupled using a semi-implicit method for a pressure-linked equation algorithm. The convection and diffusion terms of the governing and $k$-$ϵ$ transport equations were discretized via a second-order upwind and a central differencing scheme, respectively. The temporal term was discretized using the Crank–Nicholson scheme. An algebraic multigrid method was adapted to accelerate solution convergence. The computations were continued until the residuals of all solution variables were less than ${10}^{-6}$. The numerical solver, schemes, and models used in this study were the same as those applied in the authors’ previous studies [1,2]. In those studies, the analysis focused on exhaust smoke from a navigating ship, and the results were validated through comparison with experimental data.

3. Numerical Simulations

3.1. Validation Test

To confirm the accuracy of the present numerical schemes and methods for the mixed flow of exhaust smoke and wind, a CFD simulation of coaxial and confined jet flows was performed [17]. The mixed flow is related to the velocity ratio, i.e., $Ru=U_{out}/U_{in}$, where $U_{in}$ is the jet velocity from the circular pipe, and $U_{out}$ is the co-flow velocity, as shown in Figure 1. Because of the axisymmetric shape, an axisymmetric boundary condition was applied at the bottom. The diameter $D$ of the circular pipe was 11.5 mm, whereas the $U_{in}$ and $U_{out}$ were 10 and 0.4 m/s, respectively. Hence, the velocity ratio $Ru$ was 0.04.

Figure 2a,b show the velocity magnitude contours in the measuring section and entire computational domain, respectively. Based on the figures, the two different velocities resulted in a shear flow, and the flow fields were mixed. The axial velocity distributions obtained from the simulation at $x/D=3$ were compared with those measured using two-dimensional particle image velocimetry [17]. Although a minor discrepancy was indicated at approximately $y=0.02$, consistency was demonstrated between the results, as shown in Figure 3.

3.2. Dispersion of Exhaust Smoke Gases

Numerical simulations were performed by changing the wind speeds and directions to predict the dispersion of exhaust smoke from the exhaust gas pipes of an anchor-handling tug supply vessel and to verify whether the environment was suitable for crews.

3.2.1. Modeling, Computational Domain, and Boundary Conditions

The modeled geometry of the anchor-handling tug supply vessel is shown in Figure 4. The scale ratio of the model was 1/100, which is generally used in a wind tunnel test for smoke tests for a ship. The dimensions of the vessel and domains were normalized by the length of the ship $L$.

Figure 5 shows the computational domain of the modeled ship. A Cartesian coordinate system was adopted, in which the positive x-axis was aligned with the flow direction, the positive y-axis was the right-side direction, and the positive z-axis was the vertical upward direction. The origin of the coordinate system was the center of the vessel. The dimensions of the computational domain were set to $-3\le x/L\le 3,-3\le y/L\le 3$, $0\le z/L\le 2$.

The boundary conditions [18] are summarized in Table 1. The wind speed $\left(U_{wind}\right)$ entering the vessel was imposed on the inlet and side boundaries of the domain. Mass-flow inlet conditions were applied to the ends of the two main exhaust pipes, i.e., the inlets.

3.2.2. Grid Uncertainty Assessment

To determine the appropriate level of the grid system, a grid dependency test was performed by adopting the procedure proposed by Celik et al. of the American Society of Mechanical Engineers [19]. The effects of the grid systems on the NO₂ concentration measured 1 m after the exhaust pipe were examined, as shown in Figure 6. Only NO₂ was considered because the NO contained in the exhaust smoke reacted with oxygen and easily transformed into NO₂.

For the numerical simulations, the typical operating conditions were assumed as follows: the load of the main engine was 25% of the maximum continuous rating, that of the auxiliary engine was 100%, and the head wind was 15 knots. For the boundary conditions of the exhaust gas pipes, 300 ppm and 900 ppm of NO₂ concentrations from the main and auxiliary engines, respectively, were assumed to be mixed with air. The corresponding mass-flow rates for the two concentrations above were 8000 and 6000 kg/h, respectively.

Three levels of unstructured grid systems were investigated, for which the total numbers of grids were 807,000, 1,711,000 and 3,559,000. The grids near the exhaust pipes are shown in Figure 7.

The representative cell (h) ratio between each grid system was maintained at approximately 1.28, whereas the expansion ratio of the spatial grid was maintained constant. The apparent order ($p$) of this method can be expressed as

(4)$p=\frac{1}{\mathrm{l}\mathrm{n}\left(r_{21}\right)}\left|\ln \left|{ϵ}_{32}/{ϵ}_{21}\right|+q\left(p\right)\right|,$

(5)$q(p)=\ln \left(\frac{r_{21}^p-1·sgn\left(\frac{{ϵ}_{32}}{{ϵ}_{21}}\right)}{r_{32}^p-1·sgn\left(\frac{{ϵ}_{32}}{{ϵ}_{21}}\right)}\right),$

where $r_{21}=h_2/h_1$ and $r_{32}=h_3/h_2$. Meanwhile, ${ϵ}_{32}={\varphi }_3-{\varphi }_2\mathrm{a}\mathrm{n}\mathrm{d}{ϵ}_{21}={\varphi }_2-{\varphi }_1$, where ${\varphi }_k$ is the solution for the kth grid. The NO₂ concentration was measured at a position equal to the exhaust pipe height and $1.5L$ away from the stern.

The order was calculated using a fixed-point iteration. The extrapolated values were calculated as follows:

(6)${\varphi }_{ext}^{21}=\left(r_{21}^p{\varphi }_1-{\varphi }_2\right)/\left(r_{21}^p-1,\right)$

The approximate relative error ($e_a^{21}$), extrapolated relative error ($e_{ext}^{21}$), and fine-grid convergence index were calculated, in addition with the apparent order (${\mathrm{G}\mathrm{C}\mathrm{I}}_{fine}^{21}$).

(7)$e_a^{21}=\left|\frac{{\varphi }_1-{\varphi }_2}{{\varphi }_1}\right|,$

(8)$e_{ext}^{21}=\left|\frac{{\varphi }_{ext}^{12}-{\varphi }_2}{{\varphi }_{ext}^{12}}\right|,$

(9)${\mathrm{G}\mathrm{C}\mathrm{I}}_{fine}^{21}=\frac{1.25e_a^{21}}{r_{21}^p-1},$

The error due to the grids was estimated to be approximately 4%, as shown in Table 2, where the details of the grid convergence tests are listed.

3.2.3. Computational Cases

Because the anchor-handling tug supply vessel was operated in a stationary position, the vessel speed was set to 0. When designing a ship, considering the design at sea state is important and should be taken into account. The wind velocity, period, and amplitude of significant waves are determined based on the sea status. In this study, wind speeds of 10 m/s and 15 m/s were chosen to correspond to sea statuses of 5 and 7, respectively. These wind speeds are commonly used in smoke tests conducted by shipbuilding companies. Regarding the wind direction, more cases were selected for winds blowing from the fore-body of the ship as shown in Figure 8. This decision was made because the vertical distance between the exhaust pipes and the deck in the aft-body of the ship is lower than that in the fore-body, resulting in a relatively worse environmental effect.

The medium-level grid systems mentioned in the previous subsection were selected for the simulations. For each wind direction, the ship was rotated along the wind direction and the grids were regenerated. Figure 9 shows the representative grid systems in the y = 0 plane when the wind direction was 0°. As shown in the figure, extremely fine grids were generated around the exhaust pipe in the wake region, and relatively dense grids were used on the deck where the exhaust smoke remained.

3.2.4. Simulation Results

As previously mentioned, exhaust gases from exhaust pipes contain NOx and SOx, which are harmful to humans and can contaminate deck structures. Australia regulates the amount of time workers can work in environments with harmful gases, with a recommended exposure limit of 1.5 ppm of NO₂ for an 8 h workday. Specifically, the maximum concentration of NO₂ based on the number of hours worked is defined as follows:

(10)$\mathrm{T}\mathrm{W}\mathrm{A}(h)=\frac{8\times \left(24-\mathrm{h}\right)\times \mathrm{T}\mathrm{W}\mathrm{A}\left(8\right)}{16 \mathrm{h}},$

where h represents the number of hours a worker works.

TWA(8) is sufficiently small to represent the recommended exposure limit of 1.5 ppm of NO₂ concentration for an 8 h workday. If a worker worked for 5 h, then the maximum exposure to NO₂ is 2.85 ppm. In the present study, the recommended exposure limit for NO₂ concentration was set to 1.5 ppm based on the eight-hour TWA. The comfortable exposure limit for this concentration was assumed to be 0.5 ppm.

Figure 10 and Figure 11 show the perspective and top views of the isosurfaces of 1.5 ppm of NO₂ for different wind directions under a wind speed of 10 knots.

As shown in the figures, the exhaust smoke distributed over the deck, i.e., the area that did not satisfy the recommended exposure limit increased, except when the wind directions were 0°, 15°, and 90°. Differing from previous studies conducted on general merchant vessels in navigating conditions, it was found that side winds of 45° and 315° could also have detrimental environmental effects since a strong relative wind due to the ship’s advancing did not exist. Therefore, more careful investigation is needed to estimate the effect of the exhaust smoke from special-purpose vessels operating in a stationary state. Figure 12 shows the streamlines when the wind speed was 10 knots and the wind direction was 0°. When the wind entered the vessel, the flow stagnated behind the accommodation and the exhaust smoke diffused toward the deck. The contour maps of the pressure coefficient $\left(C_P=p/\frac{1}{2}\rho U_{wind}^2\right)$ for this case are shown in Figure 13. The $C_P$ behind the accommodation exhibited lower values, owing to the incoming wind. This stagnant flow can be easily predicted because the pressure behind the accommodation decreases as the wind magnitude increases. Owing to this pressure gradient, one can predict that the higher the wind, the worse the exhaust flow is. In addition, if the exhaust gases enter lower-pressure regions, then they are likely to stagnate and not be able to escape. To smoothly discharge the exhaust smoke, a larger height of the exhaust pipe is preferable.

Figure 14 shows the contour maps of $C_P$ when the wind direction was 45°. Lower values and regions were observed compared with the case of 15°. Hence, one may conclude that the reduction in the exhaust gases around the back of the accommodation, as shown in Figure 10c, was due to the abovementioned lower-pressure values and regions.

The worse working conditions at a wind direction of 45° are attributable to the geometry of the structures on the deck. When the wind direction was 0°, the structure gradually increased upwind, whereas when the wind direction was 45°, the structure elevated abruptly along the wind-blowing direction. When the structure elevated sequentially, the pressure increased when the wind hit the structure, and the pressure drop behind the structure was relatively low; however, when the structure was elevated abruptly, the pressure in front of the structure increased, whereas the pressure behind the structure decreased. Therefore, the exhaust gas flows under the 45° wind direction were not smoother than those under a 0° wind direction. For the case of the 90° wind direction, a strong downward flow is expected, owing to the rapid change in the structural height; however, the adverse effects are likely to be insignificant, owing to the small width of the deck. For the case of the 180° wind direction, exhaust gases may enter residential areas. Measures are required to address this issue.

As the wind speed increased to 15 knots, NO₂ distributed across the deck over a large area, as shown in Figure 15 and Figure 16, and the targeted exposure limit was not satisfied in all cases. This may have been caused by the lower-pressure values and regions behind the structures when the incoming wind speed increased, as expected. The results of verifying the recommended NO₂ concentration, 1.5 ppm, are summarized in Table 3.

As explained earlier, the height of the exhaust pipe can affect the exhaust gas flow. Therefore, the original heights of the pipes, 2.1m, were increased by 50%, and simulations were performed to confirm their effectiveness.

Figure 17 and Figure 18 show the perspective views of isosurfaces of comfortable NO₂ concentrations (0.5 ppm) for different wind directions under wind speeds of 10 and 15 knots, respectively. As clearly shown in the figures, exhaust smoke was discharged smoothly and did not propagate to the deck in the wind direction. Additionally, the comfortable NO₂ concentration, i.e., 0.5 ppm, not the targeted exposure limit of the recommended NO₂ concentration, 1.5 ppm, was satisfied for all cases when modified pipes were adopted. The results of verifying the comfortable NO₂ concentration, 1.5 ppm, are summarized in Table 4.

The authors want to point out that the present RANS simulations with the realizable $k$-$ϵ$ model are valid for the steady state. Therefore, there may be a necessity to perform unsteady simulations with proper turbulence models considering a ship’s motion due to waves for special cases. More cases of wind directions and speed are also needed to be tested for the different types of vessels.

4. Conclusions

The exhaust smoke flow around an anchor-handling tug supply vessel in a stationary state, which has been seldom studied, was investigated via CFD simulation to verify whether the environment was suitable for crew members. First, simulations of coaxial and confined jet flows were performed to confirm the accuracy of the current numerical schemes and methods for mixed exhaust smoke and wind flows. The axial velocity profiles obtained from the simulations agreed well with the experimental results.

The main simulations were performed under a combination of two wind speeds, 10 and 15 knots, and seven different wind directions. The results showed that the higher the wind speed, the worse the effect of the exhaust flow on the environment was, owing to the lower-pressure values and regions behind the structures. Owing to the shape of the structure, exhaust smoke emission was unsatisfactory when the wind flowed from the side or rear rather than from the bow of the vessel. This is because the stagnant flow caused by the shape of the structure is closely related to the exhaust smoke flow. Differing from previous studies conducted on general merchant vessels in navigating conditions, it was found that side winds could also have detrimental environmental effects since a strong relative wind due to the ship’s advancing did not exist. When the original design of the exhaust pipes was adopted, exhaust smoke with 1.5 ppm NO₂ was distributed over the deck in most cases. Meanwhile, no areas of exhaust smoke with 0.5 ppm NO₂ were in contact with the deck or hull for all cases when a simple design change was adopted, i.e., by increasing the height of the exhaust pipe.

For future studies, it is necessary to further investigate the effect of turbulence models and find the optimum design of exhaust pipes via changing the design parameters of the pipes. The effect of the wind speed and height of the pipe on the structural soundness will also be checked. Additionally, two-phase unsteady simulations will be conducted to account for the ship’s six degrees-of-freedom motion induced by waves and to identify local fluctuations in undesirable NO₂ behaviors. If there are available experimental or numerical results, numerical studies utilizing current numerical methods will be performed, and the results will be compared. These will contribute to a more comprehensive understanding of exhaust smoke flow and its environmental impact in relation to ship design.

Author Contributions

Conceptualization, S.-M.J. and S.P.; methodology, K.-L.J. and S.-M.J.; validation, H.J.J. and S.P.; formal analysis, H.J.J. and S.P.; investigation, K.-L.J. and S.-M.J.; resources, S.P.; writing—original draft preparation, S.P.; writing—review and editing, S.-M.J. and S.P.; visualization, H.J.J., K.-L.J. and S.P.; supervision, K.-L.J. and S.P.; funding acquisition, S.-M.J. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Not applicable.

Conflicts of Interest

The authors declare no conflict of interest.

Nomenclature

$C_P$	pressure coefficient (-)
$D$	diameter of the circular pipe (m)
$\overrightarrow{g}$	gravitational acceleration vector (ms−2)
$h$	height of representative cell (m)
${⬚}_i$	index of species (-)
$\overrightarrow{J_i}$	diffusion flux of species $i$ (kgm−3s−1)
$k$	turbulent kinetic energy (m−2s−2)
$L$	length of ship (m)
$P$	pressure (Pa)
$p$	apparent order (-)
$R_i$	net rate of production of species i by chemical reactions (kgm−2s−1)
$S_i$	rate of creation by addition from the dispersed phase (kgm−2s−1)
$R_{ij}$	cell ratio hj/hi (-)
$Ru$	velocity ratio (-)
$t$	time (s)
$\overrightarrow{v}$	velocity vector (ms−1)
$U_{in}$	jet velocity from the circular pipe (ms−1)
$U_{out}$	co-flow velocity (ms−1)
$U_{wind}$	wind velocity (ms−1)
$\overrightarrow{v}$	velocity vector (ms−1)
$Y_i$	mass fraction of the chemical species i (-)
$ϵ$	dissipation rate of turbulence (m2s−3 m)
${ϵ}_{\mathrm{i}\mathrm{j}}$	difference between solution of ith grid and jth grid (-)
$\rho$	density (kgm−3)
$\stackrel{=}{\tau }$	stress tensor (Nsm−2)

Footnotes

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Figures and Tables

Figure 1. Computational domain, grid systems, and boundary conditions for co-flow jet mixing problem.

Figure 2. Contour maps of velocity magnitude in (a) measuring section and (b) whole domain for co-flow jet mixing problem.

Figure 2. Contour maps of velocity magnitude in (a) measuring section and (b) whole domain for co-flow jet mixing problem.

Figure 3. Comparison of axial velocity profiles at [Forumla omitted. See PDF.] plane for co-flow jet mixing problem.

Figure 4. Modeled geometry of target vessel.

Figure 5. Computational domain and boundaries with zoomed area near the pipes in a pink rectangular.

Figure 6. NO2 concentration measurement point for grid dependency test.

Figure 7. Grid systems of (a) coarse, (b) medium and (c) fine levels near exhaust pipes for grid dependency tests.

Figure 8. Selected wind directions.

Figure 9. Typical grid systems at y = 0 plane when wind direction was 0°.

Figure 10. Perspective views of isosurfaces of 1.5 ppm NO2 for different wind directions of (a) 0°, (b) 15°, (c) 45°, (d) 90°, (e) 180°, (f) 315° and (g) 345° under wind speed of 10 knots (original design of pipes).

Figure 11. Top views of isosurfaces of 1.5 ppm NO2 for different wind directions of (a) 0°, (b) 15°, (c) 45°, (d) 90°, (e) 180°, (f) 315° and (g) 345° under wind speed of 10 knots (original design of pipes).

Figure 12. Streamlines near vessel with wind speed of 10 knots and 0° direction.

Figure 13. Pressure coefficient contours at y = 0 plane under wind speed of 10 knots and 0° direction.

Figure 14. Pressure coefficient contours under wind speed of 10 knots and 45° direction.

Figure 15. Perspective views of isosurfaces of 1.5 ppm NO2 for different wind directions of (a) 0°, (b) 15°, (c) 45°, (d) 90°, (e) 180°, (f) 315° and (g) 345° under wind speed of 15 knots (original design of pipes).

Figure 16. Top views of isosurfaces of 1.5 ppm NO2 for different wind directions of (a) 0°, (b) 15°, (c) 45°, (d) 90°, (e) 180°, (f) 315° and (g) 345° under wind speed of 15 knots (original design of pipes).

Figure 17. Perspective views of isosurfaces of 0.5 ppm NO2 for different wind directions of (a) 0°, (b) 15°, (c) 45°, (d) 90°, (e) 180°, (f) 315° and (g) 345° under wind speed of 10 knots (modified design of pipes).

Figure 17. Perspective views of isosurfaces of 0.5 ppm NO2 for different wind directions of (a) 0°, (b) 15°, (c) 45°, (d) 90°, (e) 180°, (f) 315° and (g) 345° under wind speed of 10 knots (modified design of pipes).

Figure 18. Perspective views of isosurfaces of 0.5 ppm NO2 for different wind directions of (a) 0°, (b) 15°, (c) 45°, (d) 90°, (e) 180°, (f) 315° and (g) 345° under wind speed of 15 knots (modified design of pipes).

Table 1

Boundary conditions.

Boundaries		v	p	k	$\mathit{ϵ}$	${\mathit{Y}}_{\mathit{i}}$
Ship	Hull	No slip	Zero gradient	Zero gradient
	Pipe inlet	Fixed value		Fixed value
Domain	Inlet	Fixed value	Zero gradient	Fixed value		Zero gradient
	Outlet	Zero gradient	Fixed value	Zero gradient
	Sides	Fixed value	Zero gradient	Fixed value
	Top	Zero gradient
	Bottom	Zero gradient	Free slip	Zero gradient

Table 2

Results of grid uncertainty assessment.

	Coarse	Medium	Fine
Total number of meshes	807,000	1,711,000	3,559,000
Representative cell ($h$)	93.11	119.59	152.68
Ratio of h	-	1.27	1.28
NO2 concentration [ppm]	0.3957	0.3719	0.3681
Difference rate	-	2.3%	1.2%
Apparent order ($p)$	2.9
Extrapolated value (${\varphi }_{ext}^{21})$	0.3492
Approximate relative error ($e_a^{21})$	3.27%
Extrapolated relative error ($e_{ext}^{21})$	3.11%
Grid convergence index (${\mathrm{G}\mathrm{C}\mathrm{I}}_{fine}^{21})$	3.77%

Table 3

Satisfaction with the recommended NO₂ concentration, 1.5 ppm, based on original pipes.

	Wind Direction	0°	15°	45°	90°	180°	315°	345°
Wind Speed
10 knots		○	○	ⅹ	○	ⅹ	ⅹ	ⅹ
15 knots		ⅹ	ⅹ	ⅹ	ⅹ	ⅹ	ⅹ	ⅹ

Table 4

Satisfaction with the comfortable NO₂ concentration, 0.5 ppm, based on modified pipes.

	Wind Direction	0°	15°	45°	90°	180°	315°	345°
Wind Speed
10 knots		○	○	○	○	○	○	○
15 knots		○	○	○	○	○	○	○

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