## 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 \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Wind Speed** & **Wind Direction** & **0\({}^{\circ}\)** & **15\({}^{\circ}\)** & **45\({}^{\circ}\)** & **90\({}^{\circ}\)** & **180\({}^{\circ}\)** & **315\({}^{\circ}\)** & **345\({}^{\circ}\)** \\ \hline
10 knots & \(\bigcirc\) & \(\bigcirc\) & \(\bigcirc\) & \(\bigcirc\) & \(\bigcirc\) & \(\bigcirc\) & \(\bigcirc\) \\
15 knots & \(\bigcirc\) & \(\bigcirc\) & \(\bigcirc\) & \(\bigcirc\) & \(\bigcirc\) & \(\bigcirc\) & \(\bigcirc\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Satisfaction with the comfortable NO\({}_{2}\) concentration, 0.5 ppm, based on modified pipes. Figure 18: Perspective views of isosurfaces of 0.5 ppm NO\({}_{2}\) for different wind directions of (**a**) 0\({}^{\circ}\), (**b**) 15\({}^{\circ}\), (**c**) 45\({}^{\circ}\), (**d**) 90\({}^{\circ}\), (**e**) 180\({}^{\circ}\), (**f**) 315\({}^{\circ}\) and (**g**) 345\({}^{\circ}\) under wind speed of 15 knots (modified design of pipes). 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 NO\({}_{2}\) was distributed over the deck in most cases. Meanwhile, no areas of exhaust smoke with 0.5 ppm NO\({}_{2}\) 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 NO\({}_{2}\) 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. Conceptualization, S.-M.J. and S.P. ; methodology, K.-L.J. and S.-M.J.; validation, H.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. This work was supported by a research fund from Chosun University (K207177007-1). Not applicable.