Performance Evaluation of Combined Wind-Assisted Propulsion and Organic Rankine Cycle Systems in Ships

Abstract

With the increasingly stringent regulation of ship carbon emissions by the International Maritime Organization (IMO), improving ship energy efficiency has become a key research direction in the current shipping industry. This paper proposes and evaluates a comprehensive energy-saving solution that integrates a wind-assisted propulsion system (WAPS) and an organic Rankine cycle (ORC) waste heat power generation system. By establishing an energy efficiency simulation model of a typical ocean-going cargo ship, the appropriate optimal system configuration parameters and working fluids are determined based on minimizing the total fuel consumption, and the impact of these two energy-saving technologies on fuel consumption is systematically analyzed. The simulation results show that the simultaneous use of these two energy-saving technologies can achieve the highest energy efficiency, with the maximum fuel savings of approximately 21%. This study provides a theoretical basis and engineering reference for the design of ship energy-saving systems.

1. Introduction

As the global shipping industry accelerates its low-carbon transformation, the International Maritime Organization (IMO) has imposed mandatory constraints on carbon emissions throughout the life cycle of ships through regulatory frameworks such as the ship energy efficiency design index (EEDI), carbon intensity index (CII), and energy efficiency existing index (EEXI) [1,2]. In this context, the development of ship energy-saving technologies has become an important research direction in the field of marine engineering and shipping [3].

Currently, there are many types of ship energy-saving technologies, including speed optimization, route optimization, air lubrication systems, hull optimization design, drag reduction technology, electric propulsion systems, hybrid power technology, wind-assisted propulsion technology, waste heat recovery, and alternative energy (such as hydrogen energy and solar energy) [4,5,6,7,8,9,10,11,12,13]. Among them, the wind-assisted propulsion system (WAPS) has been widely studied in the design and application of wind propulsion and propulsion performance evaluation due to its good adaptability to ship deck space and has also seen significant progress in terms of development and commercial adoption [14]. The system is mainly suitable for ships with large open deck areas, such as bulk carriers and oil tankers [15].

Seddiek et al. investigated installing four Flettner rotors on a bulk carrier with a deadweight of 80,533 MT operating between Egypt and France. Their results showed that each rotor could produce an average net output of 384 kWh, leading to the total annual fuel savings of 1693 tons, or approximately 22.28% of the ship’s fuel consumption [16]. Li et al. proposed a polygonal sail composed of sails and cylinders applied to a 300,000-ton tanker [17]. Essentially, this sail functions as a super large Flettner rotor, which can produce a maximum propulsive power of 2005 kW under 20 m/s wind speed with a spin ratio of k = 1. Ammar et al. studied the application of four Flettner rotors on bulk carriers. They estimated the maximum CO₂ emission reductions of 5089 tons per year for the Damietta–Dunkirk route [18].

Considering that the energy wasted by the engine exhaust gas accounts for about 25% of the fuel energy, the organic Rankine cycle (ORC), as a mature low-grade heat recovery solution, is an important solution to improve energy efficiency [19,20].

Mondejar et al. used the ORC system to support a passenger ship power grid, delivering 22% of the total power demand [21]. However, there are few studies on the impact of the ORC system on the fuel consumption of an entire ship. Konur et al. combined a diesel generator (D/G) set simulation and an ORC system model to study the use of the ORC system to support the reduction of the number of generators or D/G loads during operation, improving energy efficiency and reducing the total fuel consumption by 5.16% [22]. However, this study used a fixed D/G load with different operating modes over a two-year period rather than the actual voyage load changes for the simulation study.

Although wind-assisted propulsion and waste heat recovery systems have shown significant energy-saving potential in theory and engineering applications, the current research mostly focuses on the performance analysis of a single system. The fuel-saving and emission reduction effects of the combination of WAPS and ORC energy-saving technologies have not been fully considered.

This paper aims to analyze the feasibility of using a WAPS and an ORC to evaluate the decarbonization potential of the shipping industry. The main contributions are as follows: (1) a comparison of the WAPS and ORC technology combinations in onboard applications; (2) consideration of the impact of new technologies on the fuel consumption of the ME and D/Gs.

The rest of this paper is organized as follows. Section 2 introduces the energy-saving technology system and model validation. Section 3 establishes a fuel consumption model with multiple influencing parameters. Section 4 demonstrates the application of the model through case studies. Finally, Section 5 draws conclusions and outlines the impact of the two energy-saving technologies on the fuel consumption of the entire ship.

2. Mathematical Model of the WAPS and ORC Technologies

2.1. Wind-Assisted Propulsion System

The WAPS is based on the Magnus principle. When the wind blows towards the rotating rotor, the air on one side of the rotor accelerates due to the rotation of the rotor, while the air on the other side is decelerated. This creates a low-pressure area and a high-pressure area. This pressure difference produces a lift perpendicular to the direction of the airflow, as shown in Figure 1 [23].

The performance of Flettner rotors is affected by ship speed ($V_s$), true wind speed ($V_t$), and wind direction ($\gamma$). This is because, for a moving ship, changes in ship speed, true wind speed, and wind direction affect the apparent wind speed ($V_a$) of the ship. The relationship is shown in Figure 2, where $\gamma$ is the true wind direction from meteorological data and $\beta$ is the apparent wind direction.

The apparent wind speed (V_a) and the apparent wind direction of the ship can be calculated from the true wind speed ($V_t$), wind direction angle ($\gamma$), and ship speed ($V_s$) using Equations (1) and (2) [24].

$$V_a=\sqrt{V_t^2+V_s^2-2V_t{V}_s\mathit{cos}\gamma }$$

(1)

$$\beta =\mathit{arccos}\left({\displaystyle \frac{V_t^2-V_a^2-V_s^2}{-2V_a{V}_s}}\right)$$

(2)

The rotational speed ($U_{rot}$) of the Flettner rotor can be expressed as a function of the rotation coefficient ($C_{rot}$) and the apparent wind speed relative to the ship, as shown in Equation (3).

$$U_{rot}=C_{rot}\cdot V_a$$

(3)

The power required to operate the rotor ($P_{w,con}$) can be expressed as a function of overcoming friction resistance, as shown in Equation (4) [18]:

$$P_{w,\mathit{con}}=\left[\left({\displaystyle \frac{0.455}{{(lo{g}_{10}\left(Re\right))}^{2.58}}}-{\displaystyle \frac{1700}{Re}}\right)\cdot {\rho }_A\cdot {\displaystyle \frac{{U_{\mathit{rot}}}^2}{2}}\cdot R_A \right]\cdot U_{\mathit{rot}},$$

(4)

where ${\rho }_A$ is the air density, R_A is the rotor surface area, and $Re$ is the Reynolds number. The Reynolds number is calculated as follows:

$$Re={\displaystyle \frac{{\rho }_A\cdot C_{\mathit{rot}}\cdot V_A\cdot L_{Ry}}{\mu }},$$

(5)

where $L_{Ry}$ is the characteristic length of the rotor and $\mu$ is the dynamic viscosity of air.

The effective Flettner rotor power (P_s) in the direction of the ship can be determined from the effective force ($F_x$) in the direction of ship motion (x–x) and the ship speed.

$$P_s=F_x\cdot V_s$$

(6)

$F_x$ can be determined by the lift coefficient (C_L) and the drag coefficient ($C_D$), as shown in Equation (7):

$$F_x=\left(C_L\cdot \mathit{sin}\beta -C_D\cdot \mathit{cos}\beta \right)\cdot \left({\displaystyle \frac{{\rho }_A\cdot V_a^2}{2}}\right)\cdot A,$$

(7)

where $A$ is the maximum projected area of the Flettner rotor to the wind. $C_L$ and $C_D$ can be calculated as functions of spin ratio ($\mathrm{SR}$), as shown in Equations (8) and (9). These equations are valid for a Flettner rotor with an aspect ratio of 6 and a rotor diameter equal to half of the diameter of the disc at the top of the rotor [25].

$$\begin{gathered} C_L=-0.0046{ \mathrm{S}R}^5+0.1145{ \mathrm{S}R}^4-0.9817{ \mathrm{S}R}^3 \\ +3.1309{ \mathrm{S}R}^2-0.1039 \mathrm{S}\mathrm{R} \end{gathered}$$

(8)

$$\begin{gathered} C_D=-0.0017{ \mathrm{S}R}^5+0.0464{ \mathrm{S}R}^4-0.4424{ \mathrm{S}R}^3 \\ +1.7243{ \mathrm{S}R}^2-1.641 \mathrm{SR}+0.6375 \end{gathered}$$

(9)

2.2. Organic Rankine Cycle

The ORC is usually used in the waste heat recovery system of engines and generally consists of an expander, condenser, pump, and heater or evaporator. A simple Rankine cycle diagram is shown in Figure 3.

The working process is as follows: the working fluid undergoes a non-isentropic compression process (1–2) driven by the pump, which increases its pressure and turns it into a high-pressure subcooled liquid. During the constant-pressure heat absorption process (2–4), the working fluid absorbs heat from the external heat source through the heater or evaporator and is then evaporated into a high-pressure saturated or superheated vapor. In the isentropic expansion process (4–5), the high-temperature and high-pressure saturated or superheated vapor expands and performs work, converting thermal energy into mechanical energy. Finally, in the constant pressure condensation process (5–1), the working fluid is condensed into a liquid state by the condenser at constant pressure [26].

By using an ORC system on ships, waste heat can be used to generate electricity, thereby reducing the power requirements from the D/Gs, reducing dependence on traditional fuels, and reducing the ship’s operating costs and environmental impact.

The ORC system temperature entropy (T-S) diagram is shown in Figure 4.

In step 1–2, the working fluid is pressurized through the working fluid pump, and the power $W_{pump}$ consumed by the working fluid pump can be expressed as follows:

$$W_{pump}=m_w\left(h_2-h_1\right)={\displaystyle \frac{m_w\left(h_{2s}-h_1\right)}{{\eta }_{pump}}} ,$$

(10)

where h_2s is the isentropic enthalpy of the working fluid after being compressed, ${\eta }_{pump}$ is the isentropic efficiency of the working fluid pump, and $m_w$ is the mass flow rate of the organic working fluid in the system, which can be calculated using Equation (11):

$$m_w={\displaystyle \frac{Q_{\mathit{tot}}\cdot \left(1-\epsilon \right)}{h_4-h_2}} ,$$

(11)

where $Q_{\mathit{tot}}$ is the heat contained in the diesel engine flue gas and $\epsilon$ is the heat loss rate of the heat exchanger. $Q_{\mathit{tot}}$ can be calculated as follows:

$$Q_{\mathit{tot}}=m_{\mathit{ex}}\cdot c_{\mathit{ex}}\cdot \left(T_{\mathit{ex},\mathit{in}}-T_{\mathit{ex},\mathit{out}}\right),$$

(12)

where $m_{\mathit{ex}}$ is the mass flow rate of diesel engine exhaust gas, c_ex is the average constant pressure specific heat capacity of exhaust gas, and $T_{\mathit{ex},\mathit{in}}$ and $T_{\mathit{ex},\mathit{out}}$ are the inlet temperature and the outlet temperature of waste heat, respectively.

The 2–4 process of the evaporator can be expressed as follows:

$$Q_{\mathit{evap}}=m_w\left(h_4-h_2\right)$$

(13)

The 4–5 process of the expander can be expressed as follows:

$$W_{exp}=m_w\left(h_4-h_5\right)=m_w\left(h_4-h_{5s}\right){\eta }_{exp}$$

(14)

The 5–1 process of the condenser can be expressed as follows:

$$m_c={\displaystyle \frac{m_w\left(h_5-h_1\right)}{\left(1-\epsilon \right)\cdot c_{\mathit{cw}}\cdot \left(T_{\mathit{cw},\mathit{out}}-T_{\mathit{cw},\mathit{in}}\right)}}$$

(15)

where $m_c$ is the mass flow rate of cooling water, $c_{\mathit{cw}}$ is the average constant pressure specific heat capacity of cooling water, and $T_{\mathit{cw},\mathit{in}}$ and $T_{\mathit{cw},\mathit{out}}$ are the inlet temperature and the outlet temperature of the cooling water, respectively.

2.3. Model Verification

The established WAPS and ORC models were verified using data from the literature. The WAPS simulation model was verified using the system parameters and experimental data presented in [24]. The coefficient of lift and the coefficient of drag were set to 12.5 and 0.2, respectively. The true wind speed was set to a constant value of 5 m/s, and the vessel speed was set to a constant of 15 knots.

Table 1. WAPS model verification against [24].

	y = 70°			y = 180°			y = 260°
	Paper	Results	Error (%)	Paper	Results	Error (%)	Paper	Results	Error (%)
Crot = 2	40.36	40.34	0.05	−4.73	−4.74	0.21	54.18	54.14	0.07
Crot = 3	39.48	39.45	0.08	−8.58	−8.59	0.17	52.31	52.27	0.08
Crot = 4	37.82	37.80	0.05	−15.76	−15.79	0.19	48.81	48.76	0.10
Crot = 5	35.18	35.15	0.09	−27.22	−27.26	0.15	43.23	43.17	0.14
Crot = 6	31.34	31.30	0.13	−43.87	−43.94	0.16	35.12	35.02	0.20

presents a comparison of net power output results from the simulation model with those from the literature. The table shows the changes in net power output when the rotation coefficient values (C_rot) are 2, 3, 4, 5, and 6. The maximum relative error is 0.21%, and the minimum relative error is 0.05%. The errors are within an acceptable range, hence verifying the developed model.

After verifying the accuracy of the model, in subsequent simulations, the rotor height was set to 24 metres and the diameter was 4 metres. The lift coefficient and the drag coefficient were calculated using Equations (8) and (9) based on the parameters applicable to a rotor aspect ratio of AR = 6.

Several organic fluids with relatively high critical temperatures were selected as candidate working fluids, and their thermal properties are listed in

Table 2. Fluid properties for ORC waste heat recovery [27].

Working Fluid	Molecule Weight (g/mol)	Normal Boiling Point (K)	Critical Temperature (K)	Critical Pressure (kPa)	GWP	ODP	ASHRAE 34
Cyclohexane	84.16	353.9	553.6	4075.0	−4.74	0	A3
Benzene	78.11	353.2	562.1	4894.0	−8.59	0	B2
Toluene	92.14	383.8	591.8	4126.3	43.94	0	A3

.

The simulation model of the ORC system established in this paper was verified using the system parameters and experimental data presented by [27]. The exhaust gas inlet and outlet temperatures were set to 300 °C and 105 °C, respectively, the condensation temperature was 38 °C, and the working fluid mass flow rate was 7139 kg/h. Three working fluids, cyclohexane, benzene and toluene, were used, and the relationship between the exhaust gas outlet temperature and the evaporation temperature of different working fluids was fitted according to the data in the literature. The simulation results of the model in this paper were compared with the results in the literature, as shown in

Table 3. ORC model verification against [27].

Type of Working Fluid	Cyclohexane			Benzene			Toluene
	Paper	Results	Error (%)	Paper	Results	Error (%)	Paper	Results	Error (%)
Evaporation temperature (K)	518.3	518.4	0.02	479.8	479.7	0.02	477.2	479.7	0.52
Working fluid mass flow (kg/s)	0.62	0.602	3.23	0.68	0.67	1.47	0.67	0.67	0
System net power (kW)	90.1	91.67	1.74	90.8	91.71	1.00	89.2	89.65	0.50
System thermal efficiency (%)	21.2	21.17	0.14	21.3	21.41	0.52	21	21.29	1.38

. The system parameters and performance, including the evaporation temperature, the working fluid flow rate, the system net output work, and the system thermal efficiency, were compared. The maximum relative error was 3.23%, and the minimum relative error was 0%. The error was within an acceptable range, hence verifying the developed model.

3. Ship Fuel Consumption Model

The WAPS and ORC technologies can each be used separately, or WAPS can be used in conjunction with the ORC to provide power. Due to factors such as financial budget, ship layout space, and emission reduction requirements, the two technologies can be provided in different combinations for different types of ships.

Firstly, a fuel consumption model for a ship without any energy-saving technologies is established. Then, based on the impact of the two technologies on the propulsion power of the ME and the electrical load demand of D/Gs, fuel consumption models for ships with different combinations of these technologies are developed.

3.1. Fuel Consumption Model for Ships Without Any Energy-Saving Technologies

During sailing, a ship overcomes both air and water resistance. Air resistance primarily consists of wind resistance, while water resistance is categorized into added resistance attributed to the environment and static resistance. Thus, the total resistance ($R$) is the sum of wind resistance ($R_{\mathit{wind}}$), wave-added resistance ($R_{\mathit{wave}}$), and static resistance ($R_t$), expressed as Equation (16):

$$R=R_t+R_{\mathit{wind}}+R_{\mathit{wave}}$$

(16)

Static resistance is determined using Equation (17) [28]:

$$R_t=R_f\left(1+k_1\right)+R_{\mathit{app}}+R_w+R_b+R_{\mathit{tr}}+R_a,$$

(17)

where $R_f$ is the frictional resistance, $R_{\mathit{app}}$ is the appendage resistance, $R_w$ is the wave-making resistance, $R_b$ is the bulbous bow resistance, $R_{\mathit{tr}}$ is the transom resistance, and $R_a$ is the model correlation resistance.

The wind resistance can be obtained by Equation (18):

$$R_{\mathit{wind}}=0.5\cdot {\rho }_A\cdot A_S\cdot V_{\mathit{wind}}\cdot C_a,$$

(18)

where ${\rho }_A$ is the density of air, $A_S$ is the positive projected area on the ship above the waterline, $V_{\mathit{wind}}$ is the wind speed, and $C_a$ is the air coefficient resistance.

The wave-added resistance is calculated by Equation (19) [29]:

$$R_{\mathit{wave}}=0.64\cdot {{\xi }_w}^2\cdot B^2\cdot C_B\cdot {\rho }_S/L,$$

(19)

where ${\xi }_w$ is the characteristic wave height, $B$ is the breadth of the ship, $C_B$ is the block coefficient, ${\rho }_S$ is the density of sea water, and $L$ denotes the length of the ship.

To overcome resistance, the ship’s main engine generates a certain amount of power, which is transmitted through the shaft system to rotate the propeller and produce thrust, driving the ship forward. When the ship is sailing steadily, the propeller thrust balances the hull resistance. This relationship is described by Equations (20) and (21):

$$R=T_E=\left(1-t\right)\cdot T,$$

(20)

$$P_E=T_E\cdot V_S=R\cdot V_S,$$

(21)

where $T_E$ is the effective thrust of the propeller, $t$ is the thrust deduction fraction, $T$ is the thrust from the main engine, $P_E$ is the effective power of the propeller, and $V_S$ is the speed through water.

The power output from the main engine is subject to various frictional losses during the transmission process, resulting in the propeller receiving less power than the main engine produces. After receiving the power, the propeller, through its interaction with the hull, converts it into effective power, which is used to overcome the hull resistance and propel the ship forward. The power transfer relationships are illustrated by Equations (22) and (23):

$$P_D={\displaystyle \frac{P_E}{{\eta }_0\cdot {\eta }_H\cdot {\eta }_R}},$$

(22)

$$P_B={\displaystyle \frac{P_D}{{\eta }_G\cdot {\eta }_S}},$$

(23)

where $P_D$ is the power received by the propeller, $P_B$ is the main engine power output, ${\eta }_0$ is the propeller open water efficiency, ${\eta }_H$ is the hull efficiency, ${\eta }_R$_R is the relative rotation efficiency, ${\eta }_G$ is the gearbox efficiency, and ${\eta }_S$ is the shafting transmission efficiency.

The hull efficiency can be expressed by Equation (24):

$${\eta }_H={\displaystyle \frac{1-t}{1-w}},$$

(24)

where $t$ is the thrust deduction factor and $w$ represents the wake fraction.

The propeller thrust can be calculated by Equation (25):

$$T=K_T\cdot {\rho }_s\cdot n^2\cdot D^4,$$

(25)

where $K_T$ is the thrust coefficient, $n$ is the propeller speed, and D is the propeller diameter.

The propeller advance coefficient can be calculated using Equation (26), and the open water efficiency can be determined using Equation (27):

$$J={\displaystyle \frac{V_a}{nD}}={\displaystyle \frac{\left(1-w\right)\cdot V_s}{nD}},$$

(26)

$${\eta }_0={\displaystyle \frac{K_T}{K_Q}}\cdot {\displaystyle \frac{J}{2\pi }},$$

(27)

where $J$ is the propeller advance coefficient, $V_a$ is the advance speed, and $K_Q$ is the torque coefficient.

From Equations (20)–(27), the power of the main engine that is necessary to ensure the movement of the vessel can be determined using Equation (28):

$$P_B={\displaystyle \frac{2\pi \rho D^5{n}^3{K}_Q}{{\eta }_S{\eta }_G{\eta }_R}}$$

(28)

The propeller torque coefficient and advance coefficient can be obtained based on Equation (29) and the open water characteristic curves of the specific propeller shown in Figure 5.

Equation (29) can be derived by solving Equations (20), (25), and (26) simultaneously:

$${\displaystyle \frac{K_T}{J^2}}={\displaystyle \frac{T_E}{\rho \left(1-t\right){(1-w)}^2{V_s}^2{D}^2}}$$

(29)

Figure 6 shows the specific fuel oil consumption (SFOC) of the main engine, which will be used in the case study in Section 4. In general, the fuel consumption of the main engine can be determined using Equations (30) and (31):

$$q_m=P_B\cdot g_m,$$

(30)

$$F{C}_m={\displaystyle \sum }_{i=1}^n{q}_{m,i}\times t_i,$$

(31)

where $q_m$ is the hourly fuel consumption of the ship, $g_m$ represents the SFOC of the main engine, FC_m is the total fuel consumption of the ME, $t$ is the runtime of the engine (h), and $i$ represents the index of each one-hour voyage segment.

The D/G fuel consumption rate is provided by the manufacturer for a specific load and can be used to estimate the fuel consumption of the generator under different loads. The average D/G fuel consumption rate values used in this study are shown in Figure 7 [31].

Figure 7 shows the fuel consumption when the generator installed power is 500 kW. The fuel consumption rate of the D/Gs under different loads is calculated using quadratic polynomial regression analysis. The fuel consumption of the D/Gs (FC_g) for power generation can be given by Equations (32) and (33):

$$P_g=P_{g,a},$$

(32)

$$F{C}_g={\displaystyle \sum }_{i=1}^n{q}_{\mathrm{g},\mathrm{j}}\left(P_g\right)\times t_j,$$

(33)

where $P_g$ is the power demand of the D/Gs, $P_{g,a}$ is the D/G power demand for a specific activity, $q_{\mathrm{g}}$ is the consumption rate (kg/h), $t$ is the time the generator is running (h), $j$ is the number of D/Gs in operation, and $a$ is the vessel activity type.

Figure 8 shows the power transmission mode of the ship for both electrical load and propulsion.

Overall, from the above analysis and Figure 8, it can be seen that the total fuel consumption of the ship (FC) can be expressed by the sum of the ME fuel consumption and the D/G fuel consumption, as shown in Equation (34):

$$FC=F{C}_m+F{C}_g$$

(34)

3.2. Fuel Consumption Model for Ships with WAPS

For ships equipped with WAPS using Flettner rotors, their operation primarily relies on the thrust power provided by the Flettner rotors in combination with the propulsion power from the main engine. Together, these forces overcome the resistance experienced by the vessel during navigation, propelling it forward. This relationship is described by Equations (35) and (36):

$$\left(R-F_x\right)=T_E=\left(1-t\right)\cdot T,$$

(35)

$$P_E=T_E\cdot V_S=\left(R-F_x\right)\cdot V_S$$

(36)

Additionally, WAPS requires extra electrical power to drive the motor that rotates the Flettner rotor. Therefore, the D/G power demand for ships equipped with WAPS can be calculated using Equation (37):

$$P_g=P_{g,a}+P_{w,\mathit{con}}$$

(37)

3.3. Fuel Consumption Model for Ships with the ORC

The installation of an ORC system on a ship to recover the energy from the exhaust heat of the main engine has no effect on the ship’s resistance. It mainly converts the recovered heat energy into mechanical energy, and ultimately converts waste heat energy into electrical energy, providing electricity for the ship. Therefore, the power demand relationship of the D/Gs after installing the ORC system is as shown in Equations (38) and (39):

$$P_{\mathit{exp}}=W_{exp}·{\eta }_{exp},$$

(38)

$$P_g=P_{g,a}+W_{\mathit{pump}},$$

(39)

where $P_{\mathit{exp}}$ is the electrical power generated by the ORC and ${\eta }_{exp}$ is the efficiency of converting the mechanical work of the expander into electrical energy.

3.4. Fuel Consumption Model for Ships with WAPS and the ORC

For ships equipped with both WAPS and the ORC, the thrust provided by the Flettner rotor overcomes the resistance encountered by the ship during navigation, which can reduce the effective thrust of the propeller, and the ORC system recovers the waste heat energy of the main engine to generate electrical energy for use to supply the electrical load. Therefore, the effective thrust of the propeller can be calculated using Equations (35) and (36). The D/G power requirement can be calculated using Equation (40):

$$P_g=P_{g,a}+P_{w,\mathit{con}}+W_{\mathit{pump}}$$

(40)

In summary, the ship energy consumption modelling process of different technology combinations is shown in Figure 9, which includes the following steps in

Table 4. Fuel consumption calculation process for ME, D/Gs, and ORC savings.

System	Step	Description	Reference
ME	(1)	Calculate the ship hull resistance according to environmental factors and ship sailing speed.	Formulas (16) to (19)
	(2)	Calculate the effective thrust.	Formulas (20) and (35)
	(3)	Obtain the propeller advance coefficient $J$ and the torque coefficient.	Formula (29), Figure 5
	(4)	Obtain the propeller speed.	Formula (26)
	(5)	Calculate the main engine output power and obtain the SFOC.	Formula (28), Figure 6
	(6)	Calculate the main engine energy consumption.	Formula (31)
D/Gs	(1)	Determine the D/G power demand based on the vessel type, size, activity.	Formula (32)
	(2)	Calculate the electrical load for different technology combinations.	Formulas (37), (39) and (40)
	(3)	Calculate the D/G energy consumption using consumption rates.	Figure 7, Formula (33)
ORC savings	(1)	Calculate the equivalent fuel consumption savings using D/G consumption rates for ORC-generated electricity.	Figure 7, Formula (38)

.

4. Case Study

4.1. Study Case Description

The impact of different energy-saving technology combinations on the fuel consumption of the ME and D/G was compared through a case study. A Handymax bulk carrier was used as the reference ship for this study. Bulk carriers were chosen because they have relatively large space on deck to install Flettner rotors. This vessel’s route runs from East Port Said to Vistino (see Figure 10), and the wind rose diagram corresponding to this route is presented in Figure 11. The vessel’s daily operating parameters are provided in Appendix A, and the main parameters of the target ship are shown in

Table 5. Main parameters of the target ship.

Ship Parameters	ME and D/G
Length: 190 m	ME model: 6S50ME-C10.7
Breadth: 32.26 m	ME MCR power: 1 × 9500 kW
Deadweight tonnage: 53,000 t	ME speed: 125 RPM
Design draft: 11.5 m	D/G MCR power: 3 × 500 kW

.

The electrical distribution system model of the Handymax bulk carrier using the two energy saving technologies is shown in Figure 12.

As can be seen from Figure 12, the ORC generates electricity by recycling the heat of the ME exhaust gas and supplies this electricity to the WAPS and other electrical loads of the ship. When the power supply is insufficient, additional ship generators can be started to supply power. The D/G power demand for other electrical loads on the ship, besides the energy-saving technologies, varies depending on the ship type, size, and activity (at berth, manoeuvring, at sea, etc.).

Table 6. Handymax bulk carrier electrical power requirements.

Vessel		Power Demand (kW)
Type	Size (dwt)	Berth	Anchor	Man.	Sea
Bulk carrier	35,000–59,999	150	250	680	260

summarises the power demand characteristics of Handymax bulk carriers considered in this study [32].

Since the application of new technologies will increase the load of the generator, the load sharing of the generator affects the fuel consumption, and therefore fuel costs and emissions produced by the ship’s generators. It is necessary to formulate a reasonable generator power allocation strategy to give full scope to the energy saving potential of the new technology and optimise the overall fuel consumption.

If the generator is operated at 90% capacity (instead of 40%), then a fuel and cost saving of about 7% can be achieved [33]. Therefore, the load sharing limit of the generator is set to 90% load, as shown in Figure 13.

That is, when the first generator reaches 90% load, the second generator is started, and the load demand is evenly divided between the two generators until both generators reach 90% load, then the next generator is brought online, and the total load is evenly distributed between the generators.

4.2. The Impact of Energy-Saving Technology Combinations on ME and D/Gs Fuel Consumption

Figure 14A shows the fuel consumption of the ME and D/Gs for WAPS when the ORC waste heat recovery technology is not used. Figure 14B,C show the situation when using the ORC technology alone and when combining WAPS with ORC. The “ORC saving” in Figure 14B,C represents the fuel consumption saved by using ORC technology.

When using WAPS technology, the adjustment of the rotation coefficient parameters has a significant impact on the fuel consumption of the ME and D/Gs. From Figure 14A, it can be seen that as the rotation coefficient increases from 1 to 6, the fuel consumption of the ME decreases by 14.95%, from 314.46 t to 267.45 t, but the fuel consumption of the D/Gs increases by 48.82%, from 23.98 t to 46.85 t. Considering both the fuel savings from the ME and the increased fuel consumption of the D/Gs, the overall fuel consumption is lowest when the Flettner rotor rotational coefficient is set to 4. Therefore, when using Flettner rotors, it is not a case of simply increasing the rotation coefficient, because although increasing the rotation coefficient can reduce the fuel consumption of the main engine, it will cause the fuel consumption of the D/Gs to increase and potentially exceed the ME saving. The lowest overall fuel consumption needs to be considered to determine the appropriate rotation coefficient. It is worth mentioning that when the Flettner rotor rotational coefficient is set to 5, the existing three D/Gs on the ship are unable to provide sufficient power to drive the Flettner rotors under challenging wind conditions while sailing on the target route. Although the rotational coefficient value of 5 is not the optimal setting in the case presented in this paper, certain routes or ship types may encounter scenarios where the installed generators cannot sustain the optimal rotational speed of the Flettner rotors in the WAPS system due to insufficient power being available.

Similarly, when using different working fluids for the ORC waste heat recovery, the equivalent fuel consumption for the electrical energy generated by the ORC ranges from high to low as Benzene 31.42 t, Cyclohexane 31.40 t and Toluene 31.01 t. At the same time, the main engine fuel consumption remains constant at 326.06 t, while the fuel consumption of the D/Gs shows minimal variation, around 24.30 t. Considering that the power consumption of the pumps in the ORC system could increase the fuel consumption of the ship’s D/Gs, the equivalent fuel consumption of the entire ship is the lowest when using Benzene as the ORC working fluid, which is 318.94 t. It is important to note that, regardless of the working fluid employed, the equivalent fuel consumption saving for electrical energy produced by the ORC exceeds the fuel consumption of D/Gs. This implies that installing the ORC power generation equipment on ships can significantly reduce the fuel consumption of D/Gs.

When the ORC is used in combination with WAPS, the equivalent fuel consumption saved by the ORC technology is lower than when used alone. This is because WAPS will reduce the power of the ME and thereby reduce the mass flow rate of exhaust gas emitted and hence the production capacity of the ORC. When using the combination of WAPS and ORC, setting C_rot = 4 and Benzene, the fuel consumption of the whole ship is the lowest at 276.32 t. Therefore, when using the two-technology combination of WAPS, and ORC under these conditions achieves the lowest fuel consumption of the whole ship.

4.3. Comparison of Fuel-Saving Effects of Energy-Saving Technology Combinations

To provide a more intuitive illustration of the operational status of the combined energy-saving technologies along the route, a trajectory map of the energy system operation (Figure 15) was created. In this map, colour-coded segments indicate the status of the energy-saving systems along the voyage: black represents no energy-saving system in operation, blue indicates operation of WAPS only, yellow indicates operation of the ORC device only, and red indicates simultaneous operation of both WAPS and ORC systems.

As shown in Figure 15, during most of the voyage, the two energy-saving technologies can be effectively combined to reduce the vessel’s energy consumption. However, near the destination, around the Vistino port area, both systems become inactive. This is due to the vessel decelerating as it approaches the port, resulting in a speed that is too low and an unfavourable wind angle for the WAPS to operate. Additionally, the low engine load in this phase leads to insufficient waste heat for the ORC system to function.

Moreover, it can be observed that in the eastern Mediterranean region (approximately from the Suez Canal to Greece), the WAPS is hardly used, and the ORC system operates independently. This is due to the highly unfavourable relative wind direction, close to 0 degrees, resulting in poor aerodynamic performance and the inability to generate net thrust. Additionally, in the coastal areas of Western Europe, the Baltic Sea, and the Gulf of Finland, there are periods when wind speeds are too low and wind directions are unfavourable, causing the WAPS to be ineffective.

Furthermore, near the northern coast of Algeria in the Mediterranean Sea, there are situations where only the WAPS system can operate while the ORC system cannot. This occurs because WAPS can provide the majority of the vessel’s thrust, which reduces the power output and exhaust of the ME, thereby preventing the ORC system from running properly.

Figure 16 compares the amount and percentage of fuel saved per voyage using WAPS and ORC individually and when using the combination of WAPS and ORC.

It can be observed that when the two technologies are adopted at the same time, the fuel saving level is the highest, close to 74 t, which exceeds one-fifth of the total fuel consumption. When a single energy-saving technology is used alone, WAPS achieves the highest fuel savings, while ORC has the lowest, with fuel saving rates of 13.27% and 8.85%, respectively. It is worth noting that although WAPS can save the most energy, due to the large amount of electrical load it requires, when the wind speed is very high, the installed power of the existing diesel generators on board may not be able to meet the optimal operation of WAPS, and additional generator sets would be needed otherwise, the power required to drive the Flettner rotor would have to be reduced by reducing the rotation coefficient.

5. Discussion

The transverse force generated by the rotor could potentially influence the vessel’s drift and maneuverability. However, to simplify the current model and focus on evaluating the fuel-saving potential, this effect has not been included at this stage. Additionally, there is a limitation in extending these results to other voyages or seasons, since the performance is inherently dependent on specific routes and weather conditions at particular times.

Future research will aim to incorporate the effects of transverse forces, as well as the impact of varying weather patterns across different seasons and routes, to provide a more comprehensive evaluation of the technologies.

6. Conclusions

This paper takes a Panamax bulk carrier as the research focus and considers a combination of WAPS and ORC technologies to reduce the ME power and recover the waste heat from the engine exhaust. Taking the lowest fuel consumption of the whole ship as the evaluation standard, the appropriate WAPS parameters and the working fluid for the ORC are selected to determine the optimal parameter combination.

(1)

A combination of two energy saving is defined, and the rotation coefficient of WAPS is set to 4, and the fuel saving effect is best when benzene is used as the working fluid. A voyage from the East Port Said to Vistino can save 73.58 t of fuel, reducing the fuel consumption of the whole ship by 21.03%.

(2)

The fuel saving effects of using WAPS and ORC individually, as well as their combination, was compared. The voyage fuel savings rates for WAPS, ORC, and the combination of WAPS and ORC were 8.85%, 13.27%, and 21.03%, respectively.

(3)

When using WAPS, a large amount of electricity is required to drive the Flettner rotor. Especially when the rotor rotation coefficient is large or the wind speed is high, additional D/Gs may be needed to drive it.

(4)

When green technology is used, the equivalent fuel consumption generated by ORC will be reduced. This is because of the load on the main engine is reduced, resulting in a reduction in the net power generated by ORC. At the same time, when using new technologies, the fuel consumption of the D/Gs is significantly higher than when not using technologies. Therefore, when evaluating the impact of green technologies on the efficiency of main engines, the overall fuel consumption should be considered at the same time to obtain more meaningful results.