Ship Optimization Based on Fully-Parametric Models for Hull, Propeller and Rudder

Abstract

The purpose of ship optimization is to reduce the resistance of the ship and improve the propulsive efficiency of the propeller. Taking the design of the hull, propeller and rudder as an example, the integration optimization of ship speed performance based on the fully-parametric model was described in detail. Based on the parent hull, stock propeller and flat plate rudder, the fully-parametric coupling models of ship, propeller and rudder were established. The fully-parametric optimization method was used to optimize the optimal combination of hull, propeller and rudder with low resistance, high efficiency and appropriate propeller light running margin. The models were tested in the towing tank to verify the speed performance of the two sets of hulls, propellers and rudders. It was found that the ship integration optimization method based on the fully-parametric model excavated the improvement space of the ship’s speed performance from the overall level and realized the integration optimization of the fully-parametric model. The design of hull, propeller and rudder achieved the best speed performance. Compared with the initial design, the speed performance was greatly improved. By analyzing the effects of the hull, propeller and rudder separately, it was found that these parts have different effects on speed performance improvement, and ultimately can maximize the overall comprehensive income; CFD calculation and model test results had a good agreement.

1. Introduction

To realize the ship’s energy saving and emission reduction, and make the ship have good speed performance, we can optimize the hull lines to minimize its resistance and improve the propeller’s propulsive efficiency. In the process of ship design, to reduce the resistance and improve the propulsion efficiency, there were mainly the following means: Reduce the resistance by optimizing hull lines to get low resistance performance. Improve the propulsion efficiency of the propeller. The propeller configuration can be optimized; hydrodynamic energy-saving devices can also be used, such as a high-efficiency energy-saving rudder, compensation fan duct, hub cap fin, twisted rudder, rudder ball and rudder fin, etc., to improve the propeller propulsion efficiency.

At present, the conventional optimization methods in ship design have been optimizing hull lines, propeller, rudder and hydrodynamic energy-saving device, respectively, and the optimization process was independent. The disadvantage is that each of the hull lines, propeller, rudder and hydrodynamic energy-saving device may be optimized to the extreme, but when they were combined together, their comprehensive speed performance was not necessarily the best. Campana et al. (2016) [1]; Campana et al. (2009) [2]; Campana et al. (2006) [3] optimized many engineering ships and got good results in the model tests. In the study, the scientific optimization algorithm was used, and wave-making resistance and seakeeping were used as objective functions. Benini (2003) [4] introduced a multi-objective optimization method of B-screw series propeller that made use of an evolutionary algorithm, maximizing both efficiency and thrust coefficient with a constraint determined by cavitation. The results were given in the form of diagrams, which can be implemented on a common personal computer and used to derive optimal screw configurations in real time. Takekoshi (2005) [5] used a vortex lattice method to evaluate the performance and the time-dependent pressure distribution on the blade surface in a non-uniform flow, while efficient optimization algorithms are used to modify the blade sections. By this method, the propeller efficiency was improved by 1.2% under the constrains of constant thrust and a prescribed margin for face cavitation. Chen J H [6] conducted a B-series propeller design to use a GA for both hydrodynamic efficiency and vibration consideration. The objective function was set by users who can freely weigh the relative importance of efficiency and vibration. GAs were successfully shown to be able to obtain an optimal set of parameters, leading to efficient performance and low vibration. Ahn (2012) [7] found that a large inflow angle and fast inflow velocity in the vicinity of ±0.7 R from the shaft center may cause cavitation. Also, an X-Twisted rudder has relatively small inflow angles along the rudder span compared with a semi-balanced rudder. Cavitation tests with respect to the rudder types and twisted angles showed the effectiveness of twist on cavitation and the tendency according to the twist. The resistance, self-propulsion and maneuvering tests showed ship speed was improved with good maneuvering performance in the case of the X-Twisted rudder. Especially, it was found out that maneuvering performance between port and starboard was well balanced compared with semi-balanced rudders. Kim (2014) [8] found the twisted versions have greater performance driven by increased hull efficiency from less thrust deduction fraction and more effective wake fraction and decreased propeller rotating speed. Cheng (2020) [9] found when the twisted angle of the leading edge increases from 4.0 to 6.0 degree, the delivery power would decrease. There is no big effect on the delivery power with rudders with different twisted trailing edges. Further, the rudder bulb with an ellipse section has a good speed performance, especially when used in the sailing ship. All the studies have shown that each of hull lines, propeller and rudder can be optimized to the extreme, respectively.

Aimed at the defects of conventional optimization methods, the integration optimization technology of ship speed performance based on the fully-parametric model was the best choice, which can comprehensively optimize the speed performance and obtain the best case.

Fully-parametric optimization refers to one technique, which can be used to generate the fully-parametric models of hull, propeller, rudder and hydrodynamic energy-saving device, and achieve the purpose of changing the geometric shape by changing the characteristic parameters. The fully-parametric model was established in the software CAESES 4.0. Integration refers to the coupling of the hull, propeller, rudder and hydrodynamic energy-saving device. According to the scientific optimization algorithm and meeting the constraint conditions, lots of schemes were generated, and CFD software (STAR-CCM+ 14.02) was used for numerical calculation analysis and evaluation. With the speed performance as the objective function, the best combination of cases was found. Sun (2020) [10] studied the navigation performance of the DTMB5415 twin-screw ship under cruise and maximum speed. The accuracy and feasibility of the calculation method were verified by comparing the simulation results of ship resistance, open water performance of propeller and self-propelled point at the maximum navigation speed with the experimental results. Cheng (2022) [11] studied the influence of the mutual interference among hull, propellers and rudder on the propulsion efficiency and found the decrease in spacing between the propeller and the rudder was prominently helpful in increasing propeller efficiency, and moving the propeller and rudder backwards as a whole was extremely useful to improve the propeller propulsion efficiency. Through open water, self-propelled and cavitation tests, You (2003) [12] found optimizing the propulsion system of the ship–propeller–rudder of the mother ship effectively improved the resistance performance and reduced the adverse cavitation effects under high-speed conditions.

In this paper, the design of a ship, propeller and rudder was taken as an example. Firstly, through the model test results of the parent ship, we knew that the residual resistance coefficient of the hull was high, and the resistance was high too. The propulsion efficiency was low, and the propeller light turning margin was 8.55%, which was higher than the design requirement. Secondly, a fully-parametric coupling model of hull, propeller and rudder was established based on the parent hull lines, stock propeller and flat rudder. The optimal combination case of hull, propeller and rudder with low resistance, high efficiency and appropriate propeller light turning margin was optimized based on the ship speed performance as the objective function and the integrated optimization design concept. Finally, a model test was carried out in the towing tank to verify the speed performance of the two sets of hull, propeller and rudder cases before and after optimization, which provided technical support for the integrated optimization of the ship’s fully-parametric models.

2. Main Dimensions of Ship, Propeller and Rudder

A fully-parametric coupling model of hull, propeller and rudder was established in this paper, and the influence of hull, propeller and rudder on the speed performance was studied by using an integration optimization method. The scale ratio of ship model, propeller model and rudder model was 1:27.328, the models are shown in Figure 1, Figure 2 and Figure 3 and its main parameters are listed in

Table 1. Main dimensions of ship, propeller and rudder.

Ship		Propeller		Rudder
Item	Value	Item	Value	Item	Value
The length between perpendiculars LPP/m	169.0	Diameter D/m	6.7	Area S/m	28.2
Breadth B/m	28.4	Pitch P/D	0.899	Balanced ratio e	0.324
Design draft Td/m	8.5	Number of Blades N	5	Aspect ratio λ	1.534

.

3. Integrated Optimization Based on Fully-Parametric Models

3.1. Establishment of Fully-Parametric Models

3.1.1. Establishment of Fully-Parametric Hull Model

Feature curves such as the transverse section area curve, design waterline, flat bottom line, deck top line, tangential angle of design waterline, tangential angle of flat bottom line and tangential angle of deck top line were extracted from the parent ship, and the feature curves defined by feature parameters were introduced to approximate the feature curves extracted based on the parent ship, respectively. On this basis, the meta-surface function in CAESES (2021) [13] software was applied to establish the fully-parametric hull model, as shown in Figure 4.

3.1.2. Establishment of Fully-Parametric Propeller Model

The chord length, pitch, camber, thickness, skew, rake, camber distribution and thickness distribution of the stock propeller were extracted, and the characteristic curves defined by the characteristic parameters were introduced to approximate the characteristic curves extracted from the stock propeller respectively. On this basis, the meta-surface function in CAESES software was applied to establish the fully-parametric propeller model, as shown in Figure 5.

3.1.3. Establishment of Fully-Parametric Rudder

Characteristic parameters such as rudder blade area, height of rudder blade, height of bottom of rudder blade from baseline, chord length of upper section of rudder blade and height of center line of rudder ball of were extracted, and the characteristic curve was established through the characteristic parameters, and then the meta-surface function in CAESES software was applied to establish the fully-parametric model of the rudder, as shown in Figure 6.

3.1.4. Fully-Parametric Coupling Models of Hull, Propeller and Rudder

After the fully-parameter models of hull, propeller and rudder were established respectively, they were coupled together through boolean operation to realize the integration combination of hull, propeller and rudder, as shown in Figure 7. The stern enlargement is shown in Figure 8.

3.2. Determination and Scope of Feature Parameters and Constraints

The feature curves were controlled by the feature parameters, and the fully-parametric geometric configuration of the hull, propeller and rudder was formed by the characteristic curves, which were coupled together to realize the integration of ship design. Then, the feature parameters can be used as the design variables of ship optimization, the ship speed performance can be used as the objective function, and the ship can be numerically simulated by the scientific optimization algorithm under constrained conditions. Therefore, the fully-parametric model was the foundation, the integration was the guarantee, the constraint was the requirement and the performance at design speed was the objective.

However, the fully-parametric model of hull, propeller and rudder had lots of feature parameters, 65 hull feature parameters, 10 propeller feature parameters and 7 rudder feature parameters, a total of about 82 feature variables. If all of them were used as design variables, the current computer numerical calculation ability was difficult to achieve, and it was not necessary according to design experience. Therefore, according to the actual engineering design requirements and model test results, the feature parameters that had a greater impact on the speed performance can be sorted out and analyzed as design variables, and the range of design variables can be narrowed to achieve the purpose of improving design quality and reducing calculation amount.

In general, the feature parameters of the hull included length between perpendiculars, breadth, design draft, bilge rise angle, bilge radius, transverse section position, centroid, transom height, inlet angle of the design waterline of fore-body, fullness of the design waterline of fore-body, tangential angle of the design waterline of fore-body, section area curve at design draft, outlet angle of the design waterline of aft-body, fullness of the design waterline of aft-body, tangential angle of the design waterline of aft-body and so on. There were 65 feature parameters for hull. However, according to the requirements of engineering design, general arrangement and ship model test results, most of the ship’s feature parameters did not need to change, such as length between perpendiculars, breadth, design draft and displacement. Based on the previous experience and sensitivity study, many feature variables were not sensitive to the objective such as bilge rise angle and bilge radius. Therefore, feature variables can be reduced as much as possible to improve the optimization efficiency. Finally, considering the engineering design period and design experience, only the following 8 feature variables were selected in this optimization, which can basically meet the optimization requirements. The initial value was extracted from the feature curve of the parent ship, as listed in

Table 2. The variables of parameter model for ship.

Serial Number	Symbols	Variable Name	Initial Value	Range
1	Dwl-Entry Angel	Fore design waterline entry angle parameters	6	1~10
2	Dwl-Fullness	Fore design waterline fullness parameters	0.53	0.48~0.58
3	FlareDwl	Tangential angle parameter of bow design waterline	35.6	30~40
4	Fore-Sac	Fore-section area curve parameters	0.88	0.865~0.90
5	Transom Height	Transom height parameter	9.53	9.1~9.9
6	Diag-Fullness	Stern design waterline fullness parameters	0.65	0.58~0.70
7	TanAtDiag-Fullness	Stern design waterline tangential angle parameters	0.58	0.5~0.65
8	Aft-Sac	Aft-section area curve parameters	0.92	0.9~0.94

. Constraint conditions: the displacement could not be less than 26,719 m³, and not more than 27,000 m³. the position of the center of buoyancy varied within the range of ±1% on the basis of the parent ship; considering the overall layout requirements and limit points, the appropriate value range of each feature variable was finally selected, as listed in Table 2.

A total of 10 propeller variables can be used as feature parameters. However, model tests showed that the propeller had low propulsion efficiency and large light running margin. In order to improve the propeller propulsion efficiency and reduce the light turning margin, the propeller chord length, pitch and camber were selected as feature parameters according to design experience, and the extreme value was searched in a small range. The initial value was extracted from the stock propeller, as shown in

Table 3. The variables of parameter model for the propeller.

Serial Number	Symbols	Variable Name	Initial Value (0.7 R)	Range
1	Chord	Chord length	1697.5 mm	1527.8~1782.4 mm
2	Pitch	Pitch	5960.1 mm	5840.9~6258.1 mm
3	MaxCamber	Camber	31.6 mm	28.5~33.2 mm

. Constraint conditions: under the model scale, the propeller rotating speed was controlled within 7.9 rps~8.0 rps, which can satisfy the range of 4–6% of the propeller light running margin. The variation range of characteristic parameters was estimated according to the constraint condition phase, as shown in Table 3.

The fully-parametric model of rudder was mainly controlled by 7 characteristic parameters, such as the area of rudder blade, the height of rudder blade, the height of the bottom of the rudder blade from the base line, the chord length of the upper section of the rudder blade, the twist angle, the twist height and the height of the center line of the rudder ball. The twist angle of the rudder was an important parameter to control the rudder configuration, and the appropriate twist angle can effectively improve the propeller propulsion efficiency and reduce the propulsion power, as an optimization variable. With regard to the twisted angle, the part above the rudder bulb was twisted to left side from stern to stem and the part below the rudder bulb was twisted to the right side. The constraint was that the angle of distortion was greater than 0. According to the research and analysis, the performance of the rudder would decrease correspondingly when the angle of distortion exceeds 10°, so the variation range of the twisted angle is shown in

Table 4. The variables of parameter model for the rudder.

Serial Number	Symbols	Variable Name	Initial Value	Range
1	Twist_angle	Twist Angle	0	0~10°

.

3.3. Optimization Algorithm

According to the analysis of engineering design, a total of 12 characteristic variables of hull, propeller and rudder were selected. Under the given variable range, objective function, constraints and the total number of models to be generated, Sobol Method, a quasi-random algorithm with good convergence, was used for uniform sampling. As long as there were enough samples, the samples within the whole range of changes can be fully represented, and the best case can be quickly found. Considering there were 12 feature variables in the optimization, it was representative enough to generate 1000 calculation cases based on our study, as shown in Figure 9.

3.4. Numerical Calculation and Optimization Result Analysis

After the fully-parametric model of the target ship was established and the feature parameters were determined, the numerical simulation based on CFD can be carried out. Firstly, the fully-parametric model of hull, propeller and rudder was derived by the commercial software CAESES. Secondly, the corresponding macro commands and calculation files were recorded in the commercial software STARCCM+ (2019) [14] and output files such as resistance Rt, thrust T and torque Q in model scale were generated. Finally, self-propulsion simulation was performed with STARCCM+ full viscous flow, as shown in Figure 10. The computer with 256 cores was used for calculations.

3.4.1. Analysis of Integration Optimization Results Based on Fully-Parametric Model

By controlling the changes of hull, propeller and rudder through characteristic parameters, the calculated speed Vm of self-propulsion numerical simulation of each scheme was 1.821 m/s, and the corresponding Froude number Fr was 0.232, which corresponded to the real ship speed of 18.5 kn. Among the 1000 cases, some did not meet the displacement requirements and some did not meet the rotating speed requirements. So those numerical calculations were not carried out, and finally 800 cases met the requirements. Two different rotating speed cases were calculated for each case. According to the line interpolation method, the rotating speed and torque under the model scale of each scheme were obtained, and the hull propulsion power PD was calculated by the formula PD = 2 × π × n × Q. The calculation results were shown in Figure 11, where case 0 was the parent ship, the propulsion power was too large, and case 479 was the optimal case. The analysis of mesh convergence has been done (2023) [15].

Table 5. The numerical simulation results.

Condition Number	Initial Scheme	Optimal Scenario
RPM n/(1/s)	8.115	7.990
Thrust T/(N)	36.355	34.538
Torque Q/(N * m)	1.478	1.426
Propulsion power PD/(w)	75.341	71.607
Difference Δ/(%)	-	−4.96%

Note: Δ = (P_D (optimal scheme)/P_D (initial scheme) − 1) * 100%.

showed the propeller rotating speed n, thrust T and torque Q of the initial case 0 (parent ship, stock propeller and flat rudder) and the optimal case 479 (the integrated coupling of the optimal ship, propeller and twisted rudder). The hull propulsion power PD under the model scale and the hull propulsion power deviation ratio between the two cases were obtained by calculation. It can be seen from the table that the speed performance of the optimal scheme was improved by 4.96% compared with the initial case, which was a very considerable increase.

In order to facilitate the analysis of the optimization results, the hull, propeller and rudder of the optimal case were studied and analyzed respectively. The initial case is no. 1, and the optimal case is no. 4, as shown in

Table 6. The different cases.

Case No.	Hull	Propeller	Rudder
1	parent ship	stock propeller	flat rudder
2	optimal ship	stock propeller	flat rudder
3	optimal ship	optimal propeller	flat rudder
4	optimal ship pe	optimal propeller	optimal rudder

.

3.4.2. Result Analysis Based on the Fully-Parametric Hull Model

The optimized hull lines had the same main dimensions as the parent ship, the displacement was 26,739 m³, and the position of the center of buoyancy was 1.75% after the ship middle, all of which meet the constraints of the constraints. Case 1 and 2 adopt the same stock propeller and flat rudder, just to compare the influence of hull lines on propulsion power. Using the same numerical setting for calculation, the calculation speed Vm of the self-propulsion numerical simulation of the two cases was 1.821 m/s. The two cases were calculated with two different rotating speed respectively. According to the line interpolation method, the rotating speed and torque under the model scale of each case were obtained, and the hull propulsion power PD was calculated by the formula. The calculation results are shown in

Table 7. The numerical simulation results.

Condition Number	Case 1	Case 2
RPM n/(1/s)	8.115	8.070
Thrust T/(N)	36.355	34.800
Torque Q/(N * m)	1.478	1.430
Propulsion power PD/(w)	75.341	72.509
Difference Δ/(%)	-	−3.76%

Note: Δ = (P_D (m)/P_D (n) − 1) * 100%; n = 1, m = 2.

.

According to the numerical calculation results, the propulsion power of case 2 was reduced by 3.76% compared with case 1. Figure 12 showed the comparison of waveforms on the hull surface. Near stations 18–19, the wave crest of case 2 was lower than that of case 1. Near stations 13–15, the trough of case 2 was shallower than that of case 1, indicating that the wave pattern of case 2 was flatter and the resistance performance was better.

Figure 13 is a comparison of pressure distribution on the hull surface. Near stations 18–19, the high pressure value of case 2 was smaller than that of case 1, and the range of high pressure was also smaller. Near stations 13–15, the low pressure area of case 2 was smaller and larger than that of case 1. Near the stern 5 stations, the low pressure area of case 2 was smaller than that of case 1, indicating that the pressure distribution of case 2 was more stable and reasonable than that of case 1, and the resistance performance was better.

To sum up, the numerical value, wave pattern distribution on the hull surface and pressure distribution on the hull surface reflected that the ship speed performance based on integrated optimization had been greatly improved.

The comparison between the parent ship and the optimized ship obtained by the integrated optimization based on the fully-parametric model is shown in Figure 14. It was found that the bow narrowed near the design draft and widened on the bilge. The stern narrowed; the displacement remained the same. Through self-propulsion numerical simulation, the propulsion power was reduced by 3.76%, which was a very significant reduction in ship optimization. This was mainly due to the narrowing of the waterline near the design draft of the bow, which made the shoulders smoother and the water flow smoother, and the widening of the bilge line, which made the pressure distribution on the bilge more reasonable and the viscosity resistance lower. The narrowing of the stern improved wake flow and propeller propulsion efficiency.

3.4.3. Result Analysis Based on Fully-Parametric Propeller Model

The optimized propeller had the same diameter and blade number as the stock propeller. At 0.7R, the chord length was 1549 mm, the pitch was 6070 mm and the maximum camber was 29 mm, all of which met the constraints. Case 2 and 3 adopt the same hull and flat rudder, and the effect of propeller on propulsion power was only compared here. Using the same numerical setting for calculation, the calculation speed Vm of the self-propulsion numerical simulation of the two cases was 1.821 m/s. The two cases were calculated with two different rotating speed respectively. According to the line interpolation method, the rotating speed and torque under the model scale of each case were obtained, and the hull propulsion power PD was calculated by the formula. The calculation results are shown in

Table 8. The numerical simulation results.

Condition Number	Case 2	Case 3
RPM n/(1/s)	8.070	7.992
Thrust T/(N)	34.800	34.644
Torque Q/(N * m)	1.430	1.441
Propulsion power PD/(w)	72.509	72.346
Difference Δ/(%)	-	−0.22%

Note: Δ = (P_D (m)/P_D (n) − 1) * 100%; n = 2, m = 3.

.

According to the numerical calculation results, the propulsion power of case 3 was reduced by 0.22% compared with case 2, the rotating speed was changed from 8.07 per second to 7.992 and the light running margin was reduced accordingly. After conversion, the design requirements of 4~7% light running margin were met. Compared with the pressure distribution of propeller blade in Figure 15a,b, it can be seen that the optimal propeller adjusted the thrust distribution so that the thrust was evenly distributed on the blade to improve the thrust efficiency of the propeller. The high pressure area (red area) of the stock propeller in the leading side area was larger than that of the optimal propeller, indicating that the cavitation performance of the optimized propeller had been better improved. By adjusting the pitch, chord length and camber distribution, the optimized propeller improved the pressure distribution on the blade surface, reduced the blade cavitation and effectively improved the propeller efficiency. By comparing the propeller blade back pressure distribution in Figure 15c,d, it can be seen that at the 12 o’clock position, the low pressure area was similar, which had little impact on propeller performance. Propeller rotation would drive the water flow behind the propeller to rotate. Since the circumferential rotation speed was perpendicular to the forward direction of the ship, it did not contribute to the ship’s propulsion. The greater the rotating speed of the water behind the propeller, the greater the loss of efficiency. As can be seen from the comparison in Figure 16, the rotational water velocity after the optimal propeller was significantly lower than that of the stock propeller.

3.4.4. Result Analysis Based on Fully-Parametric Rudder Model

The profile form of the twisted rudder obtained by optimization was unchanged; only the distortion angle was changed, the best twisted angle was 4°. Case 3 and 4 used the same hull and design propeller, just to compare the influence of the change of rudder twisted angle on the propulsion power. Using the same numerical setting for calculation, the calculation speed Vm of the self-propulsion numerical simulation of the two cases was 1.821 m/s. The two cases were calculated two different rotating speeds respectively. According to the line interpolation method, the rotating speed and torque under the model scale of each case were obtained and the hull propulsion power PD was calculated through the formula. The calculation results are shown in

Table 9. The numerical simulation results.

Condition Number	Case 3	Case 4
RPM n/(1/s)	7.992	7.990
Thrust T/(N)	34.644	34.538
Torque Q/(N * m)	1.441	1.426
Propulsion power PD/(w)	72.346	71.607
Difference Δ/(%)	-	−1.02%

Note: Δ = (P_D (m)/P_D (n) − 1) * 100%; n = 3, m = 4.

.

According to the numerical calculation results, the propulsion power of case 4 was reduced by 1.02% compared with case 3, and the propeller speed changed little, which met the engineering requirements for the light running margin. Figure 17a,b showed the low pressure distribution of the optimal twisted rudder with a 4° angle and a flat rudder. It can be seen that compared with the flat rudder, the optimal rudder had a more uniform pressure distribution, small low pressure area, relatively large low pressure value, lower resistance and better performance. Figure 17c,d showed the high pressure distribution of the optimal twisting rudder with a 4° angle and a flat rudder, from which it can be seen that the range of high pressure region of the optimal twisting rudder with a 4 degree angle was relatively smaller than that of the flat rudder. Similarly, the resistance was reduced and the performance was better.

4. Model Test Verification

4.1. Test Models

The ship hull, propeller and rudder were optimized by the integrated optimization method based on the fully-parametric models, and the model scale was the same as that of CFD numerical simulation, with a scale of 1:27.328, as shown in Figure 18, Figure 19 and Figure 20. Model tests were done in the towing tank (2020) [16].

4.2. Comparison of Test Results

The model test was carried out under the design draft, and a total of four cases 1–4 in Table 7 were tested, with the speed ranging from 17 kn to 19.5 kn.

The results of case 1 and 2 in

Table 10. The test results.

Speed	Case 1		Case 2			Case 3			Case 4
Vs	PD	N	PD	N	Δ21/%	PD	N	Δ31/%	PD	N	Δ41/%
kn	kW	rpm	kW	rpm	-	kW	rpm	-	kW	rpm	-
17	6489	88.7	6155	87.8	−5.14%	6186	86	−4.67%	6066	85.5	−6.52%
17.5	7157	91.6	6817	90.7	−4.75%	6834	88.8	−4.51%	6701	88.4	−6.37%
18	7896	94.6	7548	93.7	−4.40%	7547	91.7	−4.42%	7438	91.4	−5.79%
18.5	8728	97.8	8384	96.8	−3.95%	8380	94.8	−3.99%	8261	94.5	−5.35%
19	9651	101	9354	100.1	−3.08%	9292	97.9	−3.72%	9215	97.8	−4.52%
19.5	10,786	104.4	10,457	103.7	−3.05%	10,363	101.2	−3.92%	10,387	101.4	−3.70%

Note: Δ = (P_D (m)/P_D (n) − 1) * 100%; N = 1, m = 2, 3 and 4.

showed that with the same propeller and rudder, the speed performance of the optimal ship was significantly better than that of the parent ship. At the design speed of 18.5 kn, the propulsion power was reduced by 3.95%. It can be seen from

Table 11. Predicted ship speed.

No.	Ship	Propeller	Rudder	Speed Vs/kn	Rotating Speed N/rpm
1	parent ship	stock propeller	flat rudder	18.44	100.5
2	optimal ship	stock propeller	flat rudder	18.63	100.7
3	optimal ship	optimal propeller	flat rudder	18.65	98.7
4	optimal ship	optimal propeller	optimal rudder	18.70	98.9

that under the rated power, the speed was increased from 18.44 kn to 18.63 kn, exceeding the requirements of the design requirement. However, the propeller rotating speed changed little. It can be seen from the calculation results in

Table 12. The light running margin.

Case	1	2	3	4
N/rpm	100.5	100.7	98.7	98.9
Light running margin	7.14%	7.36%	5.22%	5.44%

that the propeller light running margin does still not meet the design requirements. Compared with the test results, the CFD numerical simulation results had good consistency.

As shown in the results of case 2 and 3 in Table 10, under the condition of the same hull lines and rudder, the propulsion power of the optimal propeller had little change but slightly improved compared with the stock propeller at different speeds. It can be seen from Table 11 that under the rated power, the ship speed was basically unchanged, but the propeller speed decreased to a certain extent. It can be seen from the calculation results in Table 12 that the propeller light running margin of 5.22% met the design requirements of 4~6%. The CFD numerical simulation results also reflected that the optimal propeller had no obvious effect in terms of propulsion efficiency, but the rotating speed was reduced to a certain extent, which was in good agreement with the model test results.

The results of case 3 and 4 in Table 10 showed that under the same hull lines and propeller, the optimal rudder had a certain amount of reduced hull propulsion power compared with the flat rudder at different speeds. At the design speed of 18.5 kn, the propulsion power decreased by 1.36%. It can be seen from Table 11 that under the rated power (PD = 9930 kW), the ship speed increased by 0.05 kn, which further improved the speed performance of the ship, and the propeller rotating speed remained basically unchanged. It can be seen from the calculation results in Table 12 that the propeller light running margin of 5.44% also met the design requirements of 4~6%. Compared with the test results, the CFD numerical simulation results had a good consistency and met the requirements of engineering design.

5. Conclusions

Taking the research and development of hull, propeller and rudder as an example, this paper elaborated the integrated optimization research of ship speed performance based on fully-parametric models. It was found that the application of the integrated optimization technology of ship speed performance based on the fully-parametric model was helpful to improve the quality of ship comprehensive research and development and design efficiency. At the same time, this method also reduced the over-dependence of R&D personnel on design experience, and quickly developed excellent ships that met the market demand. The following conclusions can be drawn:

• When establishing a coupled parametric models of hull, propeller and rudder, take them as a whole system, and study the improvement space of ship speed performance from the whole level.
• The hull integrated optimization method based on the fully-parametric model did not need manual intervention in the CFD optimization process, and can save human resources by obtaining the final results of all cases and analyzing them uniformly.
• In the design process, there was no need to iterate repeatedly. One person can complete the design of the hull, propeller and rudder. Under the premise of enough computing conditions, generally in 7 to 8 weeks it can finish the optimization work. However, using the traditional design method, for the hull design, one person needed 5~6 weeks, for the propeller design one person needed 2~3 weeks, and for the rudder design one person needed 2~3 weeks. Compared with the two methods, not only was the design quality was improved, but also the manpower and time were saved.
• Based on the fully-parametric coupling model, through the scientific optimization algorithm, under the constraint conditions and with the speed performance of the objective, this optimized the speed performance of the hull, propeller and rudder. Compared with the initial case, it had a great of improvement, reducing the ship’s propulsion power by about 5%.
• The integrated optimization method based on the fully-parametric model was decomposed into hull, propeller and rudder, and it would be found that each sub-item had different effects on speed performance improvement, and the ultimate goal was to achieve the largest overall comprehensive income.
• The numerical simulation results were in good agreement with the model test results.