305 
Table 4: Wind Characteristics for each case study — direction and speed. The average ship’s direction is also presented. 
Ship Name Wind Sector 
Average Wind 
Direction (°) 
Average Wind 
Speed (m/s) 
Average Ship 
Direction (°) 
7 
Ship1 SSE 
Ship2 | SSE 
Ship3 | SE 
Ship4 | 
157 
3,82 
275 
152 | 
4.58 
98 
:40- ] 
4.30 
278 
SSE 
“= SSE 
‘19 
| 
7 
2,95 
I8 
Ship 5 
119 
23.907 
9784 
306 
307 
308 
309 
310 
Similar to the initial boundary conditions for wind velocity, k and w consider formulas that 
are applied to perimetrical sides of the domain and concern vertical elevation profiles. Therefore, 
the formulas for k and w are calculated by the expressions in (Eq. 6-7), where turbulent viscosity 
constant C,, equals 0.09 (Shirzadi et al., 2017). 
k(z) 
_ ze 
Gy 
(bj 
(z)=— ! 
W(Z) = —' — 
K Cu Z + Z9 
(7) 
311 In contrast to perimetrical boundaries, velocity (U), k and w at the exhaust gas exit of the 
312 ship’s funnel boundary, are defined as uniform values, assuming that the exhaust gas velocity (V) 
313 is uniform over the whole area of the exhaust exit of the funnel. k and w are calculated by 
314 Equations 8 and 9, respectively, where /, is the turbulence intensity and L,; is the turbulence length 
315 scale. 
k 
WÜ — 
VI 
/ 
DL 
(5 
A 
“x 
+ } 
316 2.5 Estimation of exhaust mass flux 
317 
318 
319 
320 
321 
3272 
For estimating the exhaust flow rate at the funnel, this study examines the contribution of 
the Main Engine (ME) of the different ships. Emissions depend on the engines’ installed power 
and the current Load Factor (LF), which defines their operation. The engine characteristics and the 
load factor determine the flowrate of exhaust gas. The LF calculation for the ME is done by using 
the propeller law (Brown & Aldridge, 2019; EPA, 2009; Goldsworthy & Goldsworthy, 2015; 
Mackay et al., 2015; Yau et al., 2012), expressed by the following (Egqg. 10): 
14