Numerical Simulation and Validation in Scrubber Wash Water Discharge from Ships

Journal of Marine Science and Engineering

Article Numerical Simulation and Validation in Scrubber Wash Water Discharge from Ships

Yong-Seok Choi 1 and Tae-Woo Lim 2,* 1 Division of Marine System Engineering, Korea Maritime and Ocean University, Busan 49112, Korea; [email protected] 2 Division of Marine Engineering, Korea Maritime and Ocean University, Busan 49112, Korea * Correspondence: [email protected]

Received: 12 March 2020; Accepted: 7 April 2020; Published: 10 April 2020

Abstract: A regulation on the sulfur emissions of ships sailing in global sea areas has been enforced since 1 January 2020. In this new regulation, ships are required to use low-sulfur fuel oils or to install an after-treatment equipment, such as a scrubber. Open and hybrid scrubbers wash the exhaust gas using seawater and then discharge the wash water overboard. According to the regulation promulgated by the International Maritime Organization (IMO) Marine Environment Protection Committee (MEPC), the wash water must have a pH of 6.5 or higher at 4 m from the discharge point. Wash water is generally acidic, with a pH of 2.5–3.5, whereas seawater is alkaline, with a pH of approximately 8.2. The wash water is dispersed after being discharged overboard through a nozzle, and its pH is restored through dilution with the surrounding seawater. In this study, the pH was calculated by using a theoretical chemical reaction model, and then the dispersion of wash water was analyzed using CFD simulation. This study describes the process of selecting the appropriate turbulent Schmidt number in a wide range of nozzle diameters. Finally, the appropriate nozzle diameter was determined based on the initial pH of the discharged scrubber wash.

Keywords: CFD; dispersion; pH; turbulent Schmidt number; scrubber; wash water

1. Introduction In January 2020, the International Maritime Organization (IMO) enforced a regulation stipulating that the sulfur content of fuel used by ships sailing in the global sea area should be reduced from 3.5% to 0.5% [1,2]. In the future, it is expected that much attention will be given on regulations on emissions from ships. Shipping companies have searched for measures to comply with this new regulation on SOx emission. The most popular measure is the use of low-sulfur fuel oil (LSFO). For most ships that do not use LSFO, a scrubber was installed instead to remove SOx. Besides using LSFO or a scrubber, another option is to use alternative fuels, such as liquefied natural gas [3,4]. A scrubber is a washing system for exhaust gas. Scrubbers are classified into open-loop system, closed-loop system, and hybrid system, which combines the first two systems [5]. The open-loop system washes the exhaust gas using alkaline seawater and discharges the wash water overboard. This system has the simplest structure and is the most advantageous in terms of economic operation cost compared with the other types of scrubber [6]. The closed-loop system washes the exhaust gas using fresh water and then recycles the wash water using NaOH. The open-loop system and the hybrid system wash the exhaust gas using seawater, and discharge the wash water off-board because it is difficult to keep a large volume of wash water on-board. However, there has been a discussion on the harmful effects of scrubber wash water [7,8], and some European sea areas and U.S. coastal areas prohibit the discharge of scrubber wash water. The number of sea areas where the discharge of scrubber wash water is restricted may increase in the future.

J. Mar. Sci. Eng. 2020, 8, 272; doi:10.3390/jmse8040272 www.mdpi.com/journal/jmse J. Mar. Sci. Eng. 2020, 8, 272 2 of 17

Thus, shipping companies must install a closed-loop system scrubber or a hybrid scrubber to comply with the SOx regulations; when they opt to use an open-loop scrubber system, they must use LSFO in sea areas where wash water discharge is restricted. The current regulations stipulate that when stationary ships discharge scrubber wash water, the wash water at 4 m from the discharge point must have a pH of 6.5 or higher. Compliance to this regulation must be verified through experiments or through other equivalent scientifically proven methods, including numerical analysis, and must be certified by a classification society. Then the report must be kept on board [1]. Üplre et al. [9] theoretically and experimentally investigated the discharge of acidic turbulent jets in an alkaline environment. Their chemical model matched well with their titration experiment results. They introduced an empirical model of turbulent jets and integrated it with chemistry and fluid flow models. Also, Ülpre and Eames [10] conducted a physical and chemical research on the discharge of scrubber wash water from ships. To comply with the IMO’s regulation on scrubber wash water discharge from ships, they developed a procedure for the use of multiple ports. Turbulent jets have long been investigated because they are applied in various industries [11–13]. Studies in this field mainly focused on the velocity and concentration distributions of turbulent jets. With the development of numerical analysis, efforts have been made to match the experimental values with numerical analysis results. Pani et al. [14] proposed a point-source method to predict the velocity field of turbulent jets, and they found that their result agreed well with the CFD simulation. By considering the effect of buoyancy, Robinson et al. [15] conducted a numerical analysis on the mixing and dispersion of turbulent jets. They performed CFD simulation of two cases, namely, horizontal and angled jets, and then compared their result with published experimental results. In their numerical analysis, they applied the k-ε turbulence model and the Smagorinsky LES model, and they used adaptive mesh. Different results were obtained depending on the mesh quality. The simulation predicted the buoyant jet well, but it overestimated dispersion in a near field of the source. Choi et al. [16] determined, through CFD, the discharge velocity and dilution ratio under different discharge velocities and nozzle diameters. The discharge velocity from the turbulent jets exerted little effect on dilution. However, in the study, the CFD validation process was insufficient, so the dilution ratio according to the nozzle diameter seems to have a low reliability. In this study, the pH according to the dilution ratio of wash water and seawater was calculated through a theoretical chemical reaction model, and the volume fraction of wash water in the wash water-seawater mixture was calculated through CFD simulation. In addition, the pH was calculated by combining the dilution ratio, which was calculated using the theoretical chemical reaction model, and the volume fraction that was determined through CFD simulation. Furthermore, this paper details the accurate simulation method for turbulent jet flow under various nozzle diameters. Generally, the simulation of two-phase flow is implemented by using mixture model or volume of fluid (VOF) model. These models require a lot of time to calculate and are difficult to validate. In this study, the process in which the scrubber wash water is discharged and dispersed into the sea water is simulated solving the transport equation, and this method is highly dependent on the turbulent Schmidt number. Although studies that investigated the effect of Schmidt number on the flow have already been published, it is difficult to find a study that increases the reliability of the analysis by selecting the appropriate turbulent Schmidt number in the field of ship’s scrubber technology. Therefore, we propose herein the use of appropriate turbulent Schmidt numbers according to the nozzle diameter. This study proposes an accurate and easy-to-access approach to calculate the pH of scrubber wash water discharged from ships. Results of this study are expected to be useful to scrubber manufacturers, to ship-building companies, and to classification societies. J. Mar. Sci. Eng. 2020, 8, 272 3 of 17

2. Theoretical Analysis

2.1. Chemistry Reaction In this study, modeling was based on the acid-weak alkali reaction reported in the works of Ülpre et al. [9] and Ülpre [17]. These chemical reactions are detailed in said references. Seawater is a weak base buffer solution. A buffer solution is a solution that absorbs hydrogen ions even when a small amount of acid is added and thus causes almost no change in pH. The buffer capacity of seawater is 2 mainly determined by the HCO3− and CO3− ions [9,18]. The chemical equilibrium of the acid HA and the base MOH is expressed as follows:

h +i h +i H + M = [OH−] + [A−] (1)

The mass of acid (a) and base (b) are conserved by Equations (2) and (3):

CaVa = [A−](Va + Vb) (2)

h +i CbVb = [MOH] + M (Va + Vb) (3) where C indicates concentration and V indicates volume. When Equation (1) is substituted in Equation (2), the following equation is obtained:

h +i h +i CaVa = H + M [OH−] (Va + V ) (4) − b Furthermore, when Equation (4) is substituted in Equation (3), Equation (5) is obtained, and Equation (5) can be summarized as Equation (6). ! CaVa h +i CbVb = [MOH] + H + [OH−] (Va + Vb) (5) Va + Vb −

h +i h +i Va Ca H + [OH−] = V C + H [OH−] [MOH](Va + V ) (6) − b b − − b The ionization constants of water, acid, and base are deﬁned as follows:

h +i Kw = [OH−] H (7)

+ [H ][A−] Ka = (8) [HA] + [M ][OH−] Kw Kb = = (9) [MOH] Ka When Equation (9) is substituted in Equation (3), the following equation is obtained:      CbVb  [MOH](Va + V ) = C V   (10) b b b  [OH]  −  + 1 Kb

When Equations (10) and (8) are substituted in Equation (6), the following standard acid-alkali titration equation is obtained:

[ +] + Kw V Ca H [H+] b = − (11) V Cb + Kw a + + [H ] + 1+Kw/([H ]Kb) − [H ] J. Mar. Sci. Eng. 2020, 8, 272 4 of 17

In weak base reaction, Equation (11) can be expressed as:

+ Kw Ca [H ] + + Vb − [H ] Kw = for + Kb (12) V CbKb + Kw [H ] a + + [H ] + Kw/[H ] − [H ] In addition, the reaction of diprotic acid can be expressed as:

+ Ca(Ka1[H ]+2Ka1Ka2) + 2 + + + V ([H ] +Ka1[H ]+Ka1Ka2) [H ]+Kw/[H ] b = − (13) V Cb + + a + + [H ] Kw/[H ] (1+Kw/([H ]Kb)) −

14 2 The constants used in this study are as follows [9,19]: Kw = 10− , Ka1 = 1, Ka2 = 1.2 10− , 8 × K = 2.3 10 . Kw is the ionization constant of water, K , Ka and K are the ionization constants of b × − a1 2 b H2SO4 and HCO3−, respectively.

2.2. Turbulent Jets Pani et al. [14] proposed the following velocity distribution correlation and concentration distribution correlation in circular turbulent jets:

u Z 1 = 6.2 − (14) u0 D

C Z 1 = 5.26 − (15) C0 D where u is the velocity; u0 is the initial velocity at the discharge point; Z and D denote the axial distance and nozzle diameter, respectively; and C and C0 denote the concentration and initial concentration at the discharge point, respectively. Furthermore, Hodgson et al. [20] suggested the following concentration distribution correlation in circular turbulent jets: C Z 1 = 5.34 − (16) C0 D Equation (16) predicts a higher concentration than Equation (15), and a higher concentration indicates poor dilution. Thus, we adopted harsh conditions to minimize risks in this study. To verify the numerical analysis results, we compared the numerical analysis result with Equation (16).

3. Numerical Modeling Using the chemical reaction model described in Section2, the pH based on the dilution ratio of wash water and seawater can be calculated. Hence, the dilution ratio can be calculated by analyzing wash water dispersion without considering the chemical reaction in the numerical analysis. In the present study, CFD simulation was performed to simulate the discharge and dispersion process of wash water in seawater. Since the chemical reaction between wash water and seawater was assumed to occur 9 within a considerably short period of time (10− s) compared with the physical mixing process [21], it was assumed that the chemical reaction does not affect the physical mixing. In addition, since the wash water is mostly composed of seawater, we used the properties of the latter. However, wash water and seawater are assumed to be totally different fluids, and the concentration of wash water was calculated in the same manner as the volume fraction of wash water. In this study, the commercial code ANSYS-CFX V13.0 was used for CFD simulation. J. Mar. Sci. Eng. 2020, 8, 272 5 of 17

Since many studies have already reported that the k-ε model is appropriate for ﬂow analysis in order to simulate turbulent jets [15,22,23], our study also used the k-ε model. In this model, k and ε are expressed in their respective transport equations as follows [23,24]: " ! # ∂ ∂ µt ∂k ρujk = µ + + Pk ρε + Pkb (17) ∂xj ∂xj σk ∂xj − " # ∂ ∂ µt ∂ε ε ρujε = µ + + (Cε1Pk Cε2ρε + Cε1Pεb) (18) ∂xj ∂xj σε ∂xj k −

Pkb is deﬁned by an equation for Sct, as follows:

µt ∂T Pkb = βgi (19) Sct ∂xi where k and ε denote the turbulence kinetic energy and turbulence eddy dissipation, respectively; µt, β, and gi denote the turbulence viscosity, thermal expansion coefficient, and gravity vector, respectively. The constant values are as follows: Cε1 = 1.45, Cε2 = 1.9, σk = 1.0, σε = 1.3. Here, Sct is a turbulent Schmidt number, and the default value provided by ANSYS-CFX is 0.9. Sct is a major parameter that affects dispersion in the k-ε turbulence simulation [22,25] and is mainly obtained experimentally. Oliver et al. [22] suggested that Sct is approximately 0.7 when buoyancy is not considered, whereas it is 0.6 when buoyancy is considered. However, the appropriate Sct value is dependent on the nozzle diameter and shape and on the working fluid type. In this study, CFD was validated through the selection of the appropriate Sct which is dependent on the nozzle diameter. The objective of CFD simulation was to verify the volume fraction, which changes according to the dispersion of wash water. Therefore, the transport equation was solved by applying the volume fraction to the transport equation, defined as Equation (20), by using the volume fraction (vf ) as an additional variable without considering the complex detailed model of the two-phase flow [26]. The volume fraction of the wash water discharged from the nozzle was set as 1. Thus, the volume fraction of wash water in the initial external seawater of the nozzle is zero. ! ! ∂(ρv f ) µt + (ρuv f ) = ρα + v f + S (20) ∂t ∇· ∇· Scadd ∇

In Equation (20), Scadd, α, and S denote the turbulent Schmidt number, kinematic diﬀusivity, and source term of the additional variable, respectively.

3.1. Boundary Conditions The nozzle length was set as 20 times the nozzle diameter to simulate the fully developed flow of wash water discharged from the nozzle. A study [16] showed that the discharge velocity from a turbulent jet flow exerts almost no effect on dilution. In the present study, the dispersion of wash water according to the change in nozzle diameter was verified through CFD, and the CFD model was validated based on the existing literature. For the CFD simulation, nozzles with a diameter of 0.05–0.40 m were used. The discharge velocity of wash water from the nozzle is 1 m/s, and the opening condition was used for the exterior of the total domain. In actual flows, buoyancy can be generated by the temperature and density differences between the wash water and seawater, but buoyancy was ignored in this study. Compared with the results of studies that considered buoyancy, the present result showed that risk was minimized because the prevailing condition within 4 m from the discharge point is disadvantageous for dilution.

3.2. Mesh The quality of mesh used in CFD numerical analysis exerts a decisive effect on the result. In this study, hexahedral meshes were generated using ANSYS ICEM-CFD. Dense meshes were generated J. Mar. Sci. Eng. 2020, 8, 272 6 of 17 using the O-grid method for areas where the gradient of velocity and transport variables were expected to be large. In addition, mesh dependence was reviewed using approximately 180,000, 1.5 million, 3.3 million, and 4.8 million nodes for a nozzle diameter of 0.05 m. Figure1 shows the dimensionless velocity according to the axial distance of discharge for di fferent numbers of nodes. Dimensionless velocity is the local velocity divided by the maximum velocity. As the distance from the discharge point increased, variation in the results also increased depending on the number of meshes. At the point where the wash water is discharged from the nozzle, a rapid velocity gradient occurs due to the interaction of the wash water with the surrounding stagnant fluid. Hence, a sufficient number of meshes is required to simulate the dispersion phenomenon in this area. Therefore, 4.8 million meshes were selected based on the nozzle diameter of 0.05 m in this study. FigureJ. Mar. Sci.2 shows Eng. 2020 the, 8, hexahedralx FOR PEER REVIEW meshes used in this study. 6 of 17

J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 6 of 17 u / 0 u u / 0 u

FigureFigure 1. Mesh 1. Mesh independence independence on onthe the number number of of nodes. nodes.

FigureFigure 2. Hexahedral 2. Hexahedral mesh mesh for for CFD CFD simulations. simulations. Figure 2. Hexahedral mesh for CFD simulations. 4. Results4. Results

4.1.4. Results Titration4.1. Titration Curves Curves Figure 3 shows the titration curves of the chemical reaction model described in Section 2.1; this 4.1. TitrationFigure3 showsCurves the titration curves of the chemical reaction model described in Section 2.1; this model model describes the variations in pH as a function of the dilution ratio (𝑉⁄𝑉) of wash water at an describes the variations in pH as a function of the dilution ratio (V /Va) of wash water at an alkalinity Figurealkalinity 3 shows of 1800, the titration2200, and curves 2600 μofmol/kg, the chemical and at reactionan initial modelbpH of described2.5–3.5. When in Section the seawater 2.1; this of 1800, 2200, and 2600 µmol/kg, and at an initial pH of 2.5–3.5. When the seawater alkalinity was model describesalkalinity wasthe 2200variations μmol/kg, in thepH initial as a functionpH of 2.5 increasedof the dilution to 6.5 at ratio a dilution (𝑉 ⁄𝑉 ratio) of ofwash approximately water at an 2200 µmol/kg, the initial pH of 2.5 increased to 6.5 at a dilution ratio of approximately 3.81, and the alkalinity3.81, of and 1800, the initial2200, pHand of 3.52600 increased μmol/kg, to 6.5 and at a dilutionat an initial ratio ofpH approximately of 2.5–3.5. 0.35.When Table the 1 outlinesseawater initial pHthe of volume 3.5 increased fractions to (𝑉 6.5⁄𝑉 at+𝑉 a dilution) of the ratiodilution of approximatelyratio and wash wa 0.35.ter to Table achieve1 outlines a pH of the 6.5 volumebased alkalinity was 2200 μmol/kg, the initial pH of 2.5 increased to 6.5 at a dilution ratio of approximately fractionson (V thea/ (initialVa + VpH.)) When of the the dilution seawater ratio alkalinity and wash was water 1800 toμmol/kg, achieve dilution a pH of ratios 6.5 based of 4.66 on and the 0.42, initial 3.81, and the initial pHb of 3.5 increased to 6.5 at a dilution ratio of approximately 0.35. Table 1 outlines pH. Whenrespectively, the seawater should alkalinity be provided was 1800for theµmol initial/kg, pH dilution 2.5 and ratios 3.5 to ofbe 4.66pH of and 6.5. 0.42, For the respectively, dilution ratios, should ⁄ the volume4.66 andfractions 0.42 are (𝑉 converted𝑉 +𝑉 to) volume of the dilutionfraction of ratio wash and water wash of 0.18 wa andter to 0.70, achieve respectively. a pH of When 6.5 based the on the initialseawater pH. alkalinity When thewas seawater2600 μmol/kg, alkalinity the volume was fractions1800 μmol/kg, of the wash dilution water ratiosfor the ofinitial 4.66 pH and of 2.50.42, respectively,and 3.5 should to be pH be of provided 6.5 are 0.24 for and the 0.77 initial respectively. pH 2.5 and This 3.5 means to be that pH a ofrelatively 6.5. For large the amountdilution of ratios, sea 4.66 andwater 0.42 isare required converted to recover to volume the wash fraction water ofto wapH shof 6.5water at low of alkalinity0.18 and 0.70,compared respectively. to high alkalinity. When the seawaterOn alkalinity the other washand, 2600 a low μ mol/kg,initial pH the of washvolume water fractions requires of a thelarge wash amount water of seafor waterthe initial to recover pH of to 2.5 and 3.5 pHto be of pH6.5. of 6.5 are 0.24 and 0.77 respectively. This means that a relatively large amount of sea water is required to recover the wash water to pH of 6.5 at low alkalinity compared to high alkalinity. On the other hand, a low initial pH of wash water requires a large amount of sea water to recover to pH of 6.5.

J. Mar. Sci. Eng. 2020, 8, 272 7 of 17 be provided for the initial pH 2.5 and 3.5 to be pH of 6.5. For the dilution ratios, 4.66 and 0.42 are converted to volume fraction of wash water of 0.18 and 0.70, respectively. When the seawater alkalinity was 2600 µmol/kg, the volume fractions of the wash water for the initial pH of 2.5 and 3.5 to be pH of 6.5 are 0.24 and 0.77 respectively. This means that a relatively large amount of sea water is required to recover the wash water to pH of 6.5 at low alkalinity compared to high alkalinity. On the other hand, a low initial pH of wash water requires a large amount of sea water to recover to pH of 6.5. J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 7 of 17 pH

(a) Alkalinity: 1800 μmol/kg. pH

(b) Alkalinity: 2200 μmol/kg. pH

FigureFigure 3. Titration 3. Titration curves curves obtained obtained byby the th theoreticaleoretical chemical chemical reaction reaction model. model.

Table 1. Required dilution ratio and volume fraction depending on the initial pH of scrubber wash water under different seawater alkalinity values.

J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 8 of 17

J. Mar. Sci. Eng. 2020, 8, 272 8 of 17 Alkalinity Alkalinity Alkalinity Initial 1800 μmol/kg 2200 μmol/kg 2600 μmol/kg pHTable 1. RequiredDilution dilution Volume ratio and volumeDilution fraction dependingVolume on the initialDilution pH of scrubberVolume wash water underRatio diﬀerent seawaterFraction alkalinity values.Ratio Fraction Ratio Fraction

2.5 4.66 Alkalinity0.18 3.81 Alkalinity0.21 3.23Alkalinity 0.24 2.6Initial pH 3.63 1800 µmol0.22/kg 2.97 2200 µmol/kg0.25 2.512600 µmol/kg 0.28 2.7 2.83Dilution 0.26Volume 2.32Dilution Volume0.30 Dilution1.96 Volume0.34 2.8 2.22 Ratio 0.31Fraction 1.82Ratio Fraction0.36 Ratio1.54 Fraction0.39 2.9 2.51.74 4.660.36 0.18 1.43 3.81 0.41 0.21 3.231.21 0.240.45 3.0 2.61.37 3.630.42 0.22 1.12 2.97 0.47 0.25 2.510.95 0.280.51 3.1 2.71.08 2.830.48 0.26 0.88 2.32 0.53 0.30 1.960.75 0.340.57 2.8 2.22 0.31 1.82 0.36 1.54 0.39 3.2 2.90.85 1.740.54 0.36 0.70 1.43 0.59 0.41 1.210.59 0.450.63 3.3 3.00.67 1.370.60 0.42 0.55 1.12 0.64 0.47 0.950.47 0.510.68 3.4 3.10.53 1.080.65 0.48 0.44 0.88 0.70 0.53 0.750.37 0.570.73 3.2 0.85 0.54 0.70 0.59 0.59 0.63 3.5 0.42 0.70 0.35 0.74 0.29 0.77 3.3 0.67 0.60 0.55 0.64 0.47 0.68 3.4 0.53 0.65 0.44 0.70 0.37 0.73 4.2. CFD3.5 Validations 0.42 0.70 0.35 0.74 0.29 0.77

Figure 4 shows the variations in the dimensionless velocity (𝑢/𝑢) according to Equation (14), 4.2. CFD Validations which is the correlation reported by Pani et al. [14]; it also shows the change in 𝑆𝑐. In Figure 4, the x-axisFigure represents4 shows the the dimensionless variations in distance the dimensionless𝑍𝐷⁄. Equation velocity (14) ( isu 0a/ simpleu) according modelto that Equation has a linear (14), whichrelationship is the between correlation the reporteddimensionless by Pani velocity et al. and [14]; the it alsodimensionless shows the distance. change in Therefore,Sct. In Figure it is not4, thepossible x-axis to represents make accurate the dimensionless predictions distanceat the initial(Z/ Ddischarge,). Equation that (14) is, isat a a simple low dimensionless model that has distance. a linear relationshipThe results of between CFD simulation the dimensionless can be compared velocity to and Eq theuation dimensionless (14) only in distance. the region Therefore, with linearity it is not as possiblethe dimensionless to make accurate distance predictions increases. atIn thethis initial study, discharge, only the thattotal is, length at a low of 5 dimensionless m was considered distance. for Theanalysis, results because of CFD the simulation focus is canon the be comparedflow variable to Equation at the 4 m (14) point. only It in can the be region seen with that linearity𝑆𝑐 is a asmajor the dimensionlessparameter in the distance turbulent increases. jet flow. In this As study, 𝑆𝑐 increased, only the total the length dimensionless of 5 m was velocity considered also for increased, analysis, becausewhereas the the focus axial islocal on thevelocity ﬂow variable(u) decreased. at the 4At m a point. diameter It can of be 0.05 seen m, that a 𝑆𝑐Sc tvalueis a major of approximately parameter in the0.54 turbulent was found jet to ﬂow. match As bestSct increased,with the correlation the dimensionless reported velocityby Pani et also al. increased,[14]; at a diameter whereas of the 0.40 axial m, localthe 𝑆𝑐 velocity value (ofu) decreased.0.75 matched At best a diameter with th ofe said 0.05 m,correlation. a Sct value Figure of approximately 5 shows the 0.54𝑆𝑐 values was found that tomatch match best best with with Pani the et correlation al.’s [14] correlation reported byfor Pani each et nozzle al. [14 ];diameter. at a diameter The nozzle of 0.40 diameter m, the Sc andt value 𝑆𝑐 ofdisplayed 0.75 matched a nearly best linear with relationship, the said correlation. which can Figure be linearly5 shows interpolated the Sct values as follows: that match best with Pani et al.’s [14] correlation for each nozzle𝑆𝑐 diameter. = 0.619𝐷 The nozzle + 0.5007 diameter and Sct displayed a nearly(21) linear relationship, which can be linearly interpolated as follows: It should be noted that the 𝑆𝑐 derived by Equation (21) is valid only when the working fluid is seawater, when the nozzle diameter is 0.05–0.40Sc = 0.619 m,D and+ 0.5007 when the distance from the discharge point (21) is less than 5 m. /u 0 u

(a) D = 0.05 m.

Figure 4. Cont.

J. Mar. Sci. Eng. 2020, 8, 272 9 of 17 J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 9 of 17 J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 9 of 17 /u 0 /u u 0 u

(b) D = 0.40 m. (b) D = 0.40 m. ⁄ ⁄ FigureFigure 4.4. RelationshipRelationship betweenbetween dimensionlessdimensionless velocityvelocity(u𝑢0/u𝑢) andand dimensionlessdimensionless distancedistance(Z𝑍𝐷/D) Figure 4. Relationship between dimensionless velocity𝑢 ⁄𝑢 and dimensionless distance𝑍𝐷⁄ underunder didifferentﬀerent turbulentturbulent SchmidtSchmidt numbers.numbers. under different turbulent Schmidt numbers. t t Sc Sc

Figure 5. Relationship between validvalid turbulent Schmidt number and the nozzle diameter. Figure 5. Relationship between valid turbulent Schmidt number and the nozzle diameter.

ItFigure should 6 beshows noted the that inverse the Sc tofderived the volume by Equation fraction (21) according is valid onlyto Equation when the (20), working which ﬂuid is the is Figure 6 shows the inverse of the volume fraction according to Equation (20), which is the seawater,correlation when reported the nozzle by Hodgson diameter et is al. 0.05–0.40 [20]; it also m, and shows when the the variation distance in from 𝑆𝑐 the. As discharge with the point above is correlation reported by Hodgson et al. [20]; it also shows the variation in 𝑆𝑐. As with the above lessvelocity than distribution, 5 m. only the total length of 5 m was considered for analysis. As the 𝑆𝑐 increased, 𝑆𝑐 velocitythe inverseFigure distribution, 6of shows volume theonly fraction inverse the total decr of lengtheased, the volume of and 5 m the was fraction volume considered according fraction for analysis.increased. to Equation As In the other (20), whichwords, increased, isat thelow the inverse of volume fraction decreased, and the volume fraction increased. In other words, at low correlation𝑆𝑐, dispersion reported and by mixing Hodgson actively et al. oc [cur.20]; itAt also a diameter shows theof 0.05 variation m, the in 𝑆𝑐Scadd . of As 0.71 with matched the above best 𝑆𝑐, dispersion and mixing actively occur. At a diameter of 0.05 m, the 𝑆𝑐 of 0.71 matched best velocitywith the distribution, correlation onlyreported the total by Hodgson length of 5et m al. was [20]; considered at a diameter for analysis. of 0.40 As m, the theSc 𝑆𝑐addincreased, of 0.63 with the correlation reported by Hodgson et al. [20]; at a diameter of 0.40 m, the 𝑆𝑐 of 0.63 thematched inverse best of volumewith the fraction said correlation. decreased, Figure and the 7 volumeshows the fraction 𝑆𝑐 increased.values that In match other words,best with at lowthe matched best with the said correlation. Figure 7 shows the 𝑆𝑐 values that match best with the Sccorrelationadd, dispersion reported and by mixing Hodgson actively et al. occur. [20] for At each a diameter nozzle ofdiameter. 0.05 m, theIt canSc addbe oflinearly 0.71 matched interpolated best correlation reported by Hodgson et al. [20] for each nozzle diameter. It can be linearly interpolated withas follows: the correlation reported by Hodgson et al. [20]; at a diameter of 0.40 m, the Scadd of 0.63 matched as follows: best with the said correlation. Figure7 shows the Scadd values that match best with the correlation 𝑆𝑐 = −0.238𝐷 + 0.724 (22) reported by Hodgson et al. [20] for each𝑆𝑐 nozzle = −0.238𝐷diameter. It + can 0.724 be linearly interpolated as follows:(22)

Sc = 0.238D + 0.724 (22) add −

J.J. Mar. Mar. Sci. Sci. Eng. Eng. 20202020, ,88, ,x 272 FOR PEER REVIEW 1010 of of 17 17 J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 10 of 17 /vf 0 /vf 0 vf vf

(a) D = 0.05 m. (a) D = 0.05 m. /vf 0 /vf 0 vf vf

(b) D = 0.40 m. (b) D = 0.40 m. Figure 6. Relationship between volume fraction ratio𝑣𝑓 ⁄𝑣𝑓 and dimensionless distance𝑍𝐷⁄ Figure 6. Relationship between volume fraction ratio (v f0/v f ) and dimensionless distance (Z/D) Figure 6. Relationship between volume fraction ratio𝑣𝑓⁄𝑣𝑓 and dimensionless distance𝑍𝐷⁄ underunder different diﬀerent turbulent Schmidt numbers of additional variable. under different turbulent Schmidt numbers of additional variable. add add Sc Sc

FigureFigure 7. Relationship between between valid valid turbulent turbulent Schmidt Schmidt number number and nozzle and nozzle diameter diameter of additional of additional variable. Figure 7. Relationship between valid turbulent Schmidt number and nozzle diameter of additional variable. variable. Finally, numerical analysis was performed by setting the optimal Scadd for each nozzle diameter. FigureFinally,8 shows numerical the comparison analysis between was performed the volume by fractionsetting resultthe optimal of Hodgson 𝑆𝑐 etfor al. each [ 20] nozzle at 4 m 𝑆𝑐 diameter.fromFinally, the dischargeFigure numerical 8 shows point analysis the and comparison the resultwas performed of between the numerical theby volumesetting analysis. thefraction optimal It was result found of Hodgson that for the each numericalet al.nozzle [20] diameter. Figure 8 shows the comparison between the volume fraction result of Hodgson et al. [20] atanalysis 4 m from result the matched discharge well point with and the resultthe result obtained of the by numerical Hodgson etanalysis. al. [20]. It However, was found the thatSct andthe numericalat 4 m from analysis the discharge result matched point welland withthe result the resu of ltthe obtained numerical by Hodgson analysis. et It al. was [20]. found However, that thethe numerical analysis result matched well with the result obtained by Hodgson et al. [20]. However, the

J. Mar. Sci. Eng. 2020, 8, 272 11 of 17 J.J. Mar.Mar. Sci.Sci. Eng.Eng. 20202020,, 88,, xx FORFOR PEERPEER REVIEWREVIEW 11 11 ofof 1717

Scadd proposed in this study must be used under limited conditions. It should be noted that they are 𝑆𝑐𝑆𝑐 andand 𝑆𝑐𝑆𝑐 proposed proposed inin thisthis studystudy mustmust bebe usedused underunder limitedlimited conditions.conditions. ItIt shouldshould bebe notednoted thatthat theyvalidthey areare only validvalid when onlyonly buoyancy whenwhen buoyancybuoyancy is not considered, isis notnot considerconsider whened,ed, the whenwhen working thethe workingworking ﬂuid is fluidfluid seawater, isis seawater,seawater, when the whenwhen nozzle thethe nozzlediameternozzle diameterdiameter is 0.05–0.40 isis 0.05–0.400.05–0.40 m, and m,m, when andand thewhenwhen distance thethe distancedistance from the fromfrom discharge thethe dischargedischarge point point ispoint less isis than lessless 5 thanthan m. The55 m.m. CFD TheThe CFDpostCFD processingpostpost processingprocessing data isdatadata detailed isis detaileddetailed in Appendix inin AppendixAppendixA. A.A. vf at 4 m vf at 4 m

FigureFigure 8.8. ComparisonComparison betweenbetween existingexisting correlationcorrelation andand CFDCFD results. results.

TheThe CFDCFD resultsresults werewere comparedcompared withwith experimentalexperimental datadata availableavailable available inin in thethe the literatureliterature literature forfor for validation.validation. validation. PapanicolaouPapanicolaou andand ListList [27][27] [27] conducted the the experiment experimentalexperimentalal studystudy onon the the vertical turbulent buoyant jets usingusing lase-Dopplerlase-Doppler anemometry.anemometry. TheyThey verifiedverified veriﬁed thethe velocityvelocity velocity andand and concentrationconcentration concentration decaydecay decay experimentally,experimentally, experimentally, andand calculatedcalculatedcalculated the thethe momentum momentummomentum ﬂuxes fluxesfluxes using usingusing dimensionless didimensionlessmensionless parameters. parameters.parameters. Figure9 showsFigureFigure the 99 comparisonshowsshows thethe comparisonbetweencomparison the betweenbetween CFD results thethe CFDCFD and the resultsresults experimental andand thethe experimeexperime results obtainedntalntal resultsresults by obtainedobtained Papanicolaou byby PapanicolaouPapanicolaou and List [27 and].and It List wasList [27].found[27]. ItIt thatwaswas thefoundfound simulation thatthat thethe predictssimulationsimulation well predictspredicts the results wellwell from thethe resultsresults Papanicolau fromfrom PapanicolauPapanicolau and List [27 and].and ListList [27].[27]. /u /u 0 0 u u

FigureFigure 9. 9. ComparisonComparison betweenbetween thethe CFDCFD resultsresults andand thethe ex experimentalexperimentalperimental data*data* (*(* reproducedreproduced from from the the workwork of of Papanicolaou Papanicolaou and and List List (1988) (1988) [27]). [[27]).27]).

4.3.4.3. pHpH CalculationsCalculations TheThe volume volume fractionfractionfraction of ofof wash washwash water waterwater to toto achieve achieveachieve a pHaa pHpH of ofof 6.5 6.56.5 in in thein thethe wash washwash water-seawater water-seawaterwater-seawater mixture mixturemixture can canbecan determined bebe determineddetermined based basedbased on the onon titration thethe titrationtitration curves curvescurves obtained obtaobta ininedined Section inin SectionSection 4.1 and 4.14.1 presented andand presentedpresented in Table inin1. TableTable To achieve 1.1. ToTo achieveaachieve pH of a 6.5a pHpH by ofof mixing 6.56.5 byby with mixingmixing seawater withwith seawaterseawater that has that anthat alkalinity hashas anan alkalinityalkalinity of 2200 µ ofofmol 22002200/kg, μμ amol/kg,mol/kg, volume aa fraction volumevolume of fractionfraction 0.21 is ofrequiredof 0.210.21 isis when requiredrequired the washwhenwhen water thethe washwash has an waterwater initial hashas pH anan of initialinitial 2.5, and pHpH a volumeofof 2.5,2.5, andand fraction aa volumevolume of 0.74 fractionfraction is required ofof 0.740.74 when isis requiredtherequired initial whenwhen pH is the 3.5.the initial Theinitial volume pHpH isis fraction 3.5.3.5. TheThe at volumevolume 4 m from fractionfraction the discharge atat 44 mm point fromfrom was thethe calculated dischargedischarge through pointpoint waswas the calculatedCFDcalculated numerical throughthrough analysis thethe CFDCFD described numerinumeri above.calcal analysisanalysis describeddescribed above.above. FigureFigure 1010 showsshows thethe diameterdiameter requiredrequired toto achieveachieve aa pHpH ofof 6.56.5 atat 44 mm fromfrom thethe dischargedischarge pointpoint dependingdepending onon thethe initialinitial pH.pH. Moreover,Moreover, itit showsshows thethe relationshiprelationship betweenbetween pHpH andand nozzlenozzle diameterdiameter atat differentdifferent alkalinityalkalinity valuesvalues ofof seawater.seawater. AtAt aa lowlow alkalinity,alkalinity, aa largelarge amountamount ofof seawaterseawater isis requiredrequired toto

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J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 12 of 17 Figure 10 shows the diameter required to achieve a pH of 6.5 at 4 m from the discharge point restoredepending the pH on theof the initial wash pH. water, Moreover, so the itnozzle shows diameter the relationship must be betweensmall to facilitate pH and nozzledispersion. diameter The nozzleat diﬀerent diameter alkalinity should values be less of than seawater. 0.34 m At at athe low initial alkalinity, pH of a3.0 large and amount alkalinity of of seawater 2200 μmol/kg is required and lessto restore than 0.30 the m pH at of alkalinity the wash of water, 1800 μ somol/kg the nozzle to satisfy diameter the regulation must be. smallScrubber to facilitate manufacturers dispersion. can µ Themeasure nozzle the diameter pH of shouldwash water be less and than can 0.34 roughly m at the calculate initial pH the of 3.0nozzle and diameter alkalinity for of 2200 washmol water/kg µ discharge,and less than based 0.30 on m atthe alkalinity information of 1800 shownmol /inkg Figure to satisfy 10. the If the regulation. diameter Scrubber is too small manufacturers to discharge can enoughmeasure wash the pH water, of wash multiple water ports and can should roughly be considered. calculate the The nozzle wash diameter water discharged for wash water from discharge, multiple portsbased should on the informationnot interfere shownwith each in Figure other, 10and. If resear the diameterch on this is characteristic too small to discharge will be conducted enough wash as a water,future multipleplan. ports should be considered. The wash water discharged from multiple ports should not interfere with each other, and research on this characteristic will be conducted as a future plan.

Initial pH Initial

Figure 10. VariationVariation in the treatable initial pH with the designed nozzle diameter under different diﬀerent seawater alkalinity values.

5. Conclusions Conclusions Theoretical and numerical analysis was conducted to comply with the regulation on the scrubber scrubber wash water discharge from ships. In the theoreticaltheoretical chemical models, the pH was calculated based on the the initial initial pH pH and and dilution dilution ratio ratio [9,17]. [9,17 ].The The volume volume fraction fraction at 4 at m 4 from m from the discharge the discharge point point was wascalculated calculated through through dispersion dispersion analysis analysis of the of theturbulent turbulent jet jetflow. flow. The The results results of of this this study study are summarized as follows: 1. To simulate the dispersion phenomenon in turbulent jet flow, we solved the transport equation 1. To simulate the dispersion phenomenon in turbulent jet flow, we solved the transport equation by applying the volume fraction. Simulation was performed for nozzle diameters ranging from by applying the volume fraction. Simulation was performed for nozzle diameters ranging from 0.05 m to 0.40 m. The turbulent Schmidt number is a critical parameter that exerts a significant 0.05 m to 0.40 m. The turbulent Schmidt number is a critical parameter that exerts a significant effect on dispersion. An appropriate turbulent Schmidt number must be selected according to effect on dispersion. An appropriate turbulent Schmidt number must be selected according to the the nozzle diameter. The appropriate turbulent Schmidt numbers of the transport equations nozzle diameter. The appropriate turbulent Schmidt numbers of the transport equations were were calculated by comparing them with the existing correlations. The simulation results calculated by comparing them with the existing correlations. The simulation results obtained obtained within 5 m from the discharge point by using the calculated turbulent Schmidt within 5 m from the discharge point by using the calculated turbulent Schmidt numbers matched numbers matched well with the results obtained by Pani et al. [14] and Hodgson et al. [20]. well with the results obtained by Pani et al. [14] and Hodgson et al. [20]. 2. The volume fraction at 4 m from the discharge point was calculated through simulation, and 2. The volume fraction at 4 m from the discharge point was calculated through simulation, and titration curves were obtained by the theoretical chemical reaction model. The pH value at 4 m titration curves were obtained by the theoretical chemical reaction model. The pH value at 4 m can can be derived from the initial pH by applying the calculated volume fraction or dilution ratio be derived from the initial pH by applying the calculated volume fraction or dilution ratio to the to the titration curves. titration curves. 3. When the wash water has a low pH, a small diameter nozzle is required to restore the pH to 6.5 3. atWhen 4 m thefrom wash the water discharge has a lowpoint. pH, When a small the diameter seawater nozzle in the is requiredsurrounding to restore sea area the pH has to a 6.5 low at alkalinity,4 m from thea large discharge amount point. of seawater When the is seawaterrequired. in Hence, the surrounding a small diameter sea area nozzle has a lowmust alkalinity, be used toa largepromote amount dispersion. of seawater At isthe required. initial pH Hence, of 3.0 a small and diameteralkalinity nozzle of 2200 must μmol/kg, be used tothe promote nozzle µ diameterdispersion. should At the be initial less pHthan of 0.34 3.0 and m, and alkalinity at the of initial 2200 pHmol of/kg, 3.0 the and nozzle alkalinity diameter of 1800 should μmol/kg, be less µ itthan should 0.34 be m, less and than at the 0.30 initial m. pH of 3.0 and alkalinity of 1800 mol/kg, it should be less than 0.30 m. 4. For future research, we will improve the accuracy of the chemical reaction model through titration experiments by using wash water and seawater obtained from the scrubber of actual

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J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 13 of 17 4. For future research, we will improve the accuracy of the chemical reaction model through titration experimentsship engines. by Moreover, using wash we water intend and to seawater improve obtained the reliability from theof the scrubber CFD simulation of actual ship through engines. Moreover,comparison we with intend correlations to improve derived the reliability from more of varied the CFD turbulent simulation jet flows. through comparison with correlations derived from more varied turbulent jet ﬂows. Author Contributions: Conceptualization, Y.‐S.C. and T.‐W.L.; software, Y.‐S.C.; validation, Y.‐S.C. and T.‐W.L.; formal analysis, Y.‐S.C. and T.‐W.L.; investigation, Y.‐S.C. and T.‐W.L.; resources, Y.‐S.C. and T.‐W.L.; data Authorcuration, Contributions: Y.‐S.C. and T.Conceptualization,‐W.L.; writing—original Y.-S.C. draft and preparation, T.-W.L.; software, Y.‐S.C.; Y.-S.C.;writing—review validation, and Y.-S.C. editing, and Y.‐ T.-W.L.;S.C. formal analysis, Y.-S.C. and T.-W.L.; investigation, Y.-S.C. and T.-W.L.; resources, Y.-S.C. and T.-W.L.; data curation, and T.‐W.L.; visualization, Y.‐S.C. and T.‐W.L.; supervision, T.‐W.L.; project administration, Y.‐S.C. and T.‐W.L. Y.-S.C. and T.-W.L.; writing—original draft preparation, Y.-S.C.; writing—review and editing, Y.-S.C. and T.-W.L.; visualization,All authors Y.-S.C.have read and and T.-W.L.; agreed supervision, to the published T.-W.L.; version project of administration,the manuscript. Y.-S.C. and T.-W.L. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Funding: This research received no external funding.

ConﬂictsConflicts of of Interest: Interest:The The authors authors declare declare no no conﬂictconflict of interest.

AppendixAppendix A A. CFD CFD Post post Processing processing Data data FigureFigure A1 A1. shows shows the the calculation calculation result result forfor thethe volume fraction fraction distribution distribution of of wash wash water water using using thetheSc tand andScadd proposed proposed above above for each for each nozzle nozzle diameter. diameter. As shown As shown in the in ﬁgures, the figures, dispersion dispersion rapidly occursrapidly when occurs the nozzlewhen diameterthe nozzle is diameter small, and is the small, volume and fractionthe volume of wash fraction water of was wash relatively water was low at 4 mrelatively compared low to at when4 m compared the nozzle to when diameter the nozzle is large. diameter It was is found large. that It was the found dispersion that the of dispersion wash water wasof greatlywash water dependent was greatly on nozzle dependent diameter. on nozzle diameter.

(a)D = 0.05 m.

(b)D = 0.10 m.

Figure A1. Cont. J. Mar. Sci. Eng. 2020, 8, 272 14 of 17 J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 14 of 17

(c)D = 0.15 m.

(d)D = 0.20 m.

(e)D = 0.25 m.

Figure A1. Cont. J. Mar. Sci. Eng. 2020, 8, 272 15 of 17 J. Mar. Sci. Eng. 2020, 8, x FOR PEER REVIEW 15 of 17

(f)D = 0.30 m.

(g)D = 0.35 m.

(h)D = 0.40 m.

FigureFigure A1. A1.Volume Volume fraction fraction distributionsdistributions of wash wash water water under under different diﬀerent nozzle nozzle diameters. diameters.

References J. Mar. Sci. Eng. 2020, 8, 272 16 of 17

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