Optimization of energy saving device combined with a propeller using real-coded genetic algorithm

Tomohiro Ryu
,
Takashi Kanemaru
,
Shiro Kataoka
,
Kiyoshi Arihama
,
Akira Yoshitake
,
Daijiro Arakawa
,
Jun Ando

International Journal of Naval Architecture and Ocean Engineering.
2014.
Jun,
6(2):
406-417

This is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

- Published : June 30, 2014

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Propeller
;
Turbo-Ring
;
Energy saving device
;
SQCM
;
Hub vortex
;
Genetic algorithm
;
Optimization

INTRODUCTION

Recently, many energy saving devices are developed to improve propulsive performance and reduce CO
TURBO-RING

Turbo-Ring is an energy-saving device equipped behind a propeller (
Fig. 1
). It has small blades and rotates with the pro-peller in the same direction. The rotational speed of Turbo-Ring is the same as the propeller rotational speed. The diameter of Turbo-Ring is 40% of propeller, and the number of blades is the same as the number of propeller blades. Turbo-Ring blade has reverse camber to propeller blade. Therefore, the Turbo-Ring generates the opposite thrust and torque in the propeller slipstream, as shown in
Fig. 2
. As a result, the thrust and torque decrease. Then, the propeller efficiency improves because the decrement of torque is larger than that of thrust. The propeller efficiency improves about 1.5-2.5% by Turbo-Ring in the ship wake.
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CALCULATION METHOD

In order to calculate the characteristic of propeller with Turbo-Ring, we use a simple surface panel method “Source and Quasi-Continuous vortex lattice Method (SQCM)” which was developed in Kyushu University. The detail of SQCM is described in the paper (
Ando et al., 1995
). Furthermore, the authors expanded SQCM into the method which theoretically treats the hub vortex as a root side tip vortex. And the reasonable results were obtained about the hub surface flow and the mirror image effect between the root of propeller blade and the hub surface. The detail of hub vortex model is described in the paper (
Kanemaru et al., 2012
).
In this paper, we apply the hub vortex model to both propeller and Turbo-Ring in order to express the phenomena by the interaction such as the strength of hub vortex, the complicated flow around the Turbo-Ring in the propeller slipstream, the resistance acting on boss cap. The hub vortex model of the Turbo-Ring is the same to that of the propeller and applied behind the propeller as shown in
Fig. 3
. The singularity distributions of these models including their surface panels are solved simultaneously. As the result, the strength of hub vortex is expressed as the sum of the strength by propeller and Turbo-Ring. Moreover, the wake alignments of both propeller and Turbo-Ring are taken into consideration by the method described in the papers (
Kanemaru and Ando, 2007
;
2011
). In order to keep the robustness in wake alignment, the radial positions of the vortex lattice node are fixed, and only pitch transformation of the wake sheet is taken into consideration. The wake alignment is considered from the trailing edge to the position of 1/4 rotation on the wake sheet, and a geometrical pitch model is applied after 1/4 rotation. The detail of the geometrical pitch model is described in the paper (
Ando et al., 1995
).
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CALCULATED RESULTS

- Propeller and Turbo-Ring for calculation

In this study, we designed an original propeller with no skew and rake. The chord distribution in the radial direction is expressed by a simple formula. We also designed an original Turbo-Ring by our standard design method. We call it “TR-ORG”.
Table 1
shows the principal particulars of the original propeller and
Table 2
shows the principal particulars of TR-ORG.
Principal particulars of original propeller.

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Principal particulars of TR-ORG.

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Parameters of Turbo-Rings.

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- • The panel nodal points of the propeller and Turbo-Ring should be in the same positions in the radial direction..

- Experiment

We manufactured the models of original propeller and six kinds of Turbo-Ring (TR-ORG, A~E) and carried out the reverse propeller open tests. The experiments were carried out in the towing tank of Shipbuilding Research Centre of Japan.
Fig. 6
shows the model propeller and Turbo-Rings.
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- Results and discussion

Figs. 7
and
8
show the comparison of calculated and experimental characteristics of the original propeller with TR-ORG. The characteristics of the original propeller only are also shown in these figures.
Fig. 7
shows the thrust and torque coefficients, and
Fig. 8
shows the propeller efficiency. The thrust and torque of Turbo-Ring are non-dimensionalized by propeller diameter. In the experimental results, the torque decreases and propeller efficiency increases by equipment of Turbo-Ring. The calculated results show the similar tendency to the experimental results.
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OPTIMIZATION METHOD

- Real-coded genetic algorithm

The genetic algorithm (GA) is a stochastic optimization technique inspired by the evolution process of natural life. In GA, selection is performed in the population of a certain generation so that an individual with high fitness to the objective function in the optimization problem survives with high probability. Furthermore, the population of the next generation is formed by crossover and mutation. As alternation of generations proceeds, the individuals with higher fitness increase, and the most suit-able solution is provided. The above is a basic concept of GA. In general, an individual is expressed by binary string of 0 or 1 of the suitable number per one design variable in GA. And this binary string is transformed to the design variable which is a real number. The chromosome of each individual is expressed by binary strings of the same number as the number of the design variables. Spaces expressed by binary strings and real numbers are called genotype and phenotype spaces, respectively. The mapping from phenotype to genotype is called coding. The GA with coding by binary string is called binary-coded GA. And binary-coded GA is applied to various problems. On the other hand, several GAs which use the real number directly to express an individual have been proposed. This kind of GA is called real-coded GA.
It has been reported that real-coded GA can surely find the optimum solution if the design variables are continuous in func-tion optimization problems (
Ono et al., 1999
). In the present study, the real-coded GA using Unimodal Normal Distribution Crossover (UNDX) as a crossover operator is adopted. This GA was applied to the lens design problem, which is known as a difficult problem, and its usefulness was confirmed (
Ono et al., 2000
). UNDX proposed by
Ono et al. (1999)
is a kind of cross-over operator in real-coded GAs. Each individual is defined by a real number vector and the dimension of the vector space is the same number as the number of design variables
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- Design variables and objective function

In the present method, the improved Turbo-Ring and propeller have the same chord, skew, rake and maximum blade thick-ness distributions in the radial direction as the original Turbo-Ring and propeller. The number of the blade is also the same. Thickness and camber distributions in the chord-wise direction may be used the same ones as the original Turbo-Ring and pro-peller or other distributions may be adopted. The blade section used for the improved Turbo-Ring and propeller is called basic blade section. In the present study, NACA66 a = 0.8 section is used as the basic blade section.
Pitch and maximum camber distributions in the radial direction are selected as the design variables. These shapes are ap-proximated by parabolic functions.
Optimization is conducted to maximize the efficiency of the propeller with Turbo-Ring. When the Turbo-Ring and pro-peller are optimized simultaneously, the improved propeller thrust should be greater than or equal to the original propeller thrust. This is the constraint condition in the present optimization problem.
As the constraint condition for cavitation performance, the amplitude of fluctuating pressure at the 1st blade frequency above propeller center calculated by
Holden’s method (1979)
is considered. First the fluctuating pressure amplitude of the original propeller at the 1st blade frequency is calculated and determined the upper limit of the fluctuating pressure amplitude. If the cavity area is required not to exceed the original one, equivalent value to the original amplitude of fluctuating pressure at the 1st blade frequency is imposed as the upper limit.
- Procedure of optimization

In GA, it is very important to use a generation-alternation model which can avoid the early convergence and suppress the evolutionary stagnation. In the present study, Minimal Generation Gap (MGG) model proposed by
Satoh et al. (1997)
is adopted.
The procedure of optimization for improving the efficiency of the propeller with Turbo-Ring is described as follows:
RESULTS OF OPTIMIZATION

- Optimized Turbo-Ring and propeller

We optimized the original Turbo-Ring “TR-ORG” using the real-corded genetic algorithm described in the preceding sec-tion. The diameter of Turbo-Ring is 40% of propeller diameter. Furthermore, we also optimized the Turbo-Ring and propeller blades simultaneously. We call this combination Turbo-Ring and propeller “P&TR (OPT)”. As shown in
Table 4
, we define the names of the optimized Turbo-Rings and propeller.
Figs. 15
and
16
show the pitch and maximum camber distribution of the optimized Turbo-Rings and propeller.
Definition of propeller with turbo-ring.

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- Results and discussion

Fig. 17
shows the calculated efficiency of the propeller with Turbo-Ring. As can be seen from
Fig. 17
, the propeller effi-ciency becomes higher than that of ORG by optimization of the Turbo-Ring blades. In case of simultaneous optimization of the Turbo-Ring and propeller, the propeller efficiency becomes much higher than that of ORG.
Fig. 18
shows the experimental result. Unlike the calculated result, there is little difference in the propeller efficiency between ORG and TR (OPT). In case of simultaneous optimization of the Turbo-Ring and propeller, the propeller efficiency becomes higher than that of ORG like the calculation.
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CONCLUSION

A method to improve the performance of the propeller with Turbo-Ring using real-coded genetic algorithm was developed. In this method, the simple surface panel method “SQCM” used as the estimation method for the propeller characteristics was expanded by considering the hub vortices and the wake alignments of the propeller and Turbo-Ring. The accuracy of the esti-mation method was confirmed by the model experiment.
In the optimization of the Turbo-Ring only and in the simultaneous optimization of the Turbo-Ring and propeller, the experimental propeller efficiency was improved compared to the propeller without Turbo-Ring in the both cases. Especially, the simultaneous optimization of the Turbo-Ring and propeller is effective for the improvement of the efficiency of the propeller with Turbo-Ring.
The present optimization method will be applied to the design of practical propeller with Turbo-Ring for further energy saving in ship propulsion.
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Citing 'Optimization of energy saving device combined with a propeller using real-coded genetic algorithm
'

@article{ E1JSE6_2014_v6n2_406}
,title={Optimization of energy saving device combined with a propeller using real-coded genetic algorithm}
,volume={2}
, url={http://dx.doi.org/10.2478/IJNAOE-2013-0188}, DOI={10.2478/IJNAOE-2013-0188}
, number= {2}
, journal={International Journal of Naval Architecture and Ocean Engineering}
, publisher={The Society of Naval Architects of Korea}
, author={Ryu, Tomohiro
and
Kanemaru, Takashi
and
Kataoka, Shiro
and
Arihama, Kiyoshi
and
Yoshitake, Akira
and
Arakawa, Daijiro
and
Ando, Jun}
, year={2014}
, month={Jun}