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A numerical study for effectiveness of a wake equalizing duct
ARTICLE IN PRESS
Ocean Engineering 34 (2007) 2138–2145 www.elsevier.com/locate/oceaneng
A numerical study for effectiveness of a wake equalizing duct Fahri C - elik Yildiz Technical University, Department of Naval Architecture, Besiktas-Istanbul, Turkey Received 29 December 2006; accepted 17 April 2007 Available online 27 April 2007
Abstract A numerical study is carried out for calculating effect of the wake equalizing duct (WED) on the propulsion performance of a chemical tanker. Analysis is performed using a CFD tool based on the solution of Reynolds averaged Navier–Stokes (RANS) equation. Computations are carried out for several arrangements of WED for a number of ship speeds. Total 56 runs are achieved, and the results are compared with each other. It can be concluded from this study that propeller characteristics and resistance of the ship are slightly affected by the presence of the WED, but an additional thrust is produced by the WED. It is also found that the maximum gain obtained by using an appropriate WED design is about 10%. r 2007 Elsevier Ltd. All rights reserved. Keywords: Wake equalizing duct; Energy saving; Propeller; Propulsion
1. Introduction Marine propellers are the most common propulsion systems owing to the high efficiency supplied by them; nevertheless, it is possible to improve its propulsive performance using additional auxiliary propulsor devices (unconventional propulsors). During the last three decades considerable research and development activities have taken into place within this context. Most of these devices are used to improve propulsive efficiency, but some of them aims to improve other performance characteristics, such as cavitation, vibration, noise, manoeuvrability, etc. It can be found more review studies about various unconventional propulsors in Glover (1987), ITTC (1990), Blaurock (1990), Patience (1991), Breslin and Andersen (1994), and Carlton (1994). One of the energy saving devices used widely in ships is the wake equalizing duct (WED) (Schneekluth’s duct) (Fig. 1). It consists of two aerofoil sectioned half-ring ducts integrated to the hull in front of upper region of the propeller. Some important parameters for the effectiveness of the WED are the angles of duct axis to ship’s center line plane, longitudinal positions, inner diameters, profile Fax: +90 212 236 4165.
E-mail address: [email protected]. 0029-8018/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.oceaneng.2007.04.006
section shapes, angles of section to duct axis and lengths of the half-ring ducts. It is assumed that the WED accelerates the inflow of the upper region of the propeller where the flow is slow relative to the lower region of the propeller; and it improves the uniformity of the wake over the propeller disc, so the propeller efficiency is increased. In addition, a well-designed WED reduces the amount of flow separation at the after body, generates an additional thrust as in the accelerating type of duct, reduces the propellerexcited vibrations due to the uniform wake, and improves the steering qualities because of the more straightened flow coming to the rudder. If the WED is installed to an existing ship, constructional changes and modifications in propeller design are not needed. A WED can also be used in combination with other energy saving devices such as vane wheel and asymmetric stern (Schneekluth, 1986). Schneekluth (1986) reports that the effectiveness of a WED is most evident if the ship speed is between 12 and 18 knots and its block coefficient is higher than 0.6. By now, most of the studies related to the estimation of the effect of the WED on propulsion characteristics of a ship have been carried out based on model tests. But it is difficult to extrapolate the powering performance from model tests (especially for very large ships) due to the Reynolds number effects (scale effects) stated in ITTC (1999). At higher Reynolds numbers the scale effects occurs
ARTICLE IN PRESS F. C - elik / Ocean Engineering 34 (2007) 2138–2145
Fig. 1. The wake equalizing duct (Wartsila, 2005).
more evidently, in such cases it is recommended that selfpropulsion tests should be performed to reduce these effects (ITTC, 1999). In addition, numerical flow computations as an alternative of the model tests can also be used to estimate the effectiveness of the WED. Extensive experimental tests are performed for a tanker with and without WED to investigate the scale effects in the HYKAT (hydrodynamics and cavitation tunnel) in the Hamburg Ship Model Basin by Friesch and Johannsen (1994). In their study it is concluded that the WED has a positive effect on powering performance of the ship at full scale, but it is difficult to predict this positive effect from model tests. Korkut (2006) gives an experimental study on the effect of the WED for a river going general cargo ship. In his study two different hull forms are generated from the original hull form of the vessel to optimize the stern flow. The results obtained from resistance, self-propulsion and flow visualizations tests on powering characteristic of the ship are presented. The computational methods using mostly the Reynolds averaged Navier–Stokes (RANS) equations are also applied to the ship hydrodynamics to predict the propulsion performance of ships. There are a number of studies in this context; one of these is carried out by Abdel-Maksoud (2003), where the resistance and propulsion characteristics for a container ship with and without propeller are computed using a commercial CFD code, CFX. The numerical results are compared with experimental ones and the differences between the total resistance coefficients obtained from CFD and those of the measurements are found about 6%. A numerical study on the effect of the WED for a tanker with higher block coefficient is presented by Ok (2004). A CFD code Comet based on finite volume method is used for numerical computations. As propeller does not exist at the after body, especially the Reynolds number effects are investigated for various ship speeds. As a result it is found that the WED causes an additional power requirement for propulsion and a moderate resistance increase compared to the case of the ship without duct, and so it is concluded that an inappropriate duct causes a substantial resistance and power requirements.
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Besides Abdel-Maksoud (2003) and Ok (2004) stated above, Watanabe et al. (2003), Sanchez-Caja et al. (2000) and Gul et al. (2005) investigated viscous flow around ship hull and propeller. In these studies commercial RANS solvers are used to predict the propulsion performance or resistance of ship and propeller, and it is shown that the difference between the results obtained from numerical methods and model tests is acceptable. As conclusion it can be said that CFD is now the more preferred means of testing alternative to analyze flow around ship and propeller before experimental testing takes place. In this study, a numerical investigation based on RANS method is carried out to find the most appropriate WED arrangement for a chemical tanker. As a RANS solver, commercial software called Fluent is performed. The computations are carried out for the ship alone, the ship with propeller, ship with WED alone, ship with WED and the propeller in the speed range of 10–16 knots. The WED arrangements are obtained by selecting three various angles of duct section and two longitudinal positions of the duct. In order to reduce the computation time, the aft body of the ship behind the parallel body is taken into account instead of complete hull. 2. CFD analysis 2.1. Geometrical properties of ship A chemical tanker is taken into account in order to investigate numerically the influence of WED on the powering characteristics of ship. The ship has a hydrodynamically modern design, one screw propeller and C B ¼ 0:77 block coefficient. The main particulars of the ship are given in Table 1. As can be seen from Fig. 2 which shows cross-sections of chemical tanker, the ship has a bulb and transom stern. 2.2. Propeller data The propeller geometry (Fig. 3) used in CFD analysis is designed as using an improved lifting line method developed by C - elik and Gu¨ner (2006). The blade section geometry of the propeller is generated using NACA66 thickness with a ¼ 0:8 mean line distributions for all radii. The design input data of propeller for chemical tanker is given in Table 2. Table 1 Main particulars of ship Length between perpendiculars, LBP (m) Waterline length, LWL (m) Breadth, B (m) Depth, D (m) Draught, T (m) Displacement, D (ton) Block coefficient, C B Design speed, V s (knot)
87.55 89.38 14.26 6.85 5.42 5500 0.77 14
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length of duct is selected as a quarter of diameter. Flows around the stern are investigated for the following cases given in Table 3 for ship with and without propeller. 2.4. Numerical method
Fig. 2. Cross-sections of chemical tanker.
Fig. 3. Geometry of the propeller.
2.5. Grid generation
Table 2 Propeller design input data Delivered power, PD (kW) Design speed, V s (knot) Rate of rotation, RPM Propeller diameter, D (m) Number of blades, Z Pitch ratio, P=D at 0.7R Blade area ratio, ðAE =A0 Þ Wake ð1 wN Þ
In CFD analysis, the solution is carried out by numerically solving RANS equations. As a RANS solver, a commercial CFD code (based on finite volume method) Fluent 6.2.16 is used. Detailed descriptions of the numerical method can be found in the User’s Guide of this code (2004). In this work, the flow is assumed to be incompressible and turbulent corresponding to Reynolds numbers investigated between 4:48 108 and 7:177 108 . The k2e (standard) model is chosen as the turbulence model (Launder and Spalding, 1972). The governing equations are discretized using a second-order upwind interpolation scheme, and the discretized equations are solved using SIMPLE algorithm. The solution is considered converged when the continuity residual is lower than 104 and velocity residuals are lower than 105 , which is obtained for cases of with propeller at almost 600 and for cases of without propeller at almost 400 iterations. All numerical computations were performed on the computer IBM with 2 GB RAM, Pentium 4 2.7 GHz CPU.
3246 14 150 3.5 4 1.081 0.60 0.697
2.3. The WED arrangements There are a number of parameters for design and effective arrangements of the WED, such as the inner diameter, profile section shape, length, the angle of section, the angle of axis of half rings, and the longitudinal and vertical location. In this study, the analyses are carried out for six various duct arrangements by means of changing two parameters of WED, which are the angle of section and longitudinal location, and the best geometry and position of duct for improving propulsion performance of ship are investigated. The general location of WED can be seen in Fig. 4. By changing the angle of duct section ðfÞ, different radius of leading edge ðRin Þ is obtained while the radius of trailing edge ðRout Þ, vertical location and length of duct (DC) are kept constant. The radius of trailing edge ðRout Þ is selected as half diameter of propeller and the
The ship hull geometry shown in Fig. 2 is modeled using Maxsurf ship design program, the WED and propeller geometries are generated in Rhino CAD program and all geometries are imported to Fluent pre-processor Gambit for grid generation and description of boundary conditions. As known one of the most significant parameters in numerical flow simulations is the quality of mesh. This affects directly the accuracy of solution and required number of iterations (CPU time). For this purpose, the computational domain modeling flow around the ship hull is split into 13 parts. Twelve of these parts are stationary and the one is moving domain which rotates with propeller together. For the surfaces which belong to the propeller, duct and the stern of ship the computational grids are generated using triangular mesh elements, and the other surfaces of ship are meshed using quadrilateral mesh elements. Generating surface meshes, computational domains are filled with hexahedral, tetrahedral and wedge volume mesh elements where appropriate. The grid spacing is finer near hull surface in order to compute the viscous flow effects more correctly. The numerical grid is kept constant for all Reynolds numbers corresponding to ship speeds. Fig. 5 shows the computational grids around after body for the present simulation.
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Fig. 4. Location of the WED at the after body of ship.
Table 3 The wake equalizing duct arrangements
Case Case Case Case Case Case Case
1 2 3 4 5 6 7
Angle of duct section ðfÞ (degree)
Longitudinal position of duct (from A.P.) (m)
No duct 18 18 14 14 10 10
3.25 2.95 3.25 2.95 3.25 2.95
The number of total cells used in volume mesh for cases of ship without and with propeller is approximately 1,050,000 and 1,250,000, respectively. On the ship hull, propeller and duct surfaces, the nonslip wall condition is imposed. On the water surface, the slip wall condition is imposed and the shearing stress components are set to 0. On the outer boundary, the symmetry boundary condition is applied. 2.6. Validation of the numerical method Numerical resistance tests were carried out by Gul et al. (2005) for 2650 DWT tanker by using CFD code Fluent.
Fig. 5. Computational grids around the stern of ship.
Model experiments of tanker were performed at BSHC (Bulgarian Ship Hydrodynamics Centre). Main particulars of the ship: length of water line LWL ¼ 81:04 m, breadth B ¼ 12:5 m and drought T ¼ 4:70 m. In their study frictional, residual and total resistance values of ship were calculated at different Froude numbers ðF n Þ corresponding to 8, 10 and 12 knots of ship speed using the turbulence flow model and the free surface condition
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Table 4 Comparison of the resistance coefficients obtained from CFD and model tests (Gul et al., 2005) Froude number ðF n Þ
0.1563 0.1954 0.2216
Residual resistance coefficient C R 103
Frictional resistance coefficient C F 103
Total resistance coefficient C T 103
Experiment
CFD (Fluent)
ITTC 57
CFD (Fluent)
Experiment
CFD (Fluent)
0.6982 1.2730 2.3241
0.6462 1.2403 2.2234
1.7475 1.6969 1.6693
1.7596 1.6908 1.6498
2.4457 2.9699 3.9935
2.4059 2.9311 3.8732
on the water surface. Resistance coefficients obtained from CFD were compared with those of experimental results (Table 4). As can be seen in Table 4, differences between residual, frictional and total resistance coefficients are about 4.7%, 0.7%, 2%, respectively. This shows that differences are acceptable. 3. Results and discussions As mentioned before, the aim of using a WED can be summarized as follows: improving the propeller efficiency owing to the homogeneity of the wake obtained by accelerating the inflow to upper part of propeller, reducing the propeller-excited vibrations, reducing the viscous resistance force by decreasing the flow separation at the stern of ship, and generating an additional thrust, so improving propulsion efficiency. In this study for three various duct geometries and two longitudinal locations, whether the ducts provide the advantages stated above is investigated numerically. The most appropriate duct geometry and whose location is found in terms of gain supplied (reduction of power required for propulsion). First the numerical flow analyses around the stern of ship without propeller for all cases are performed in order to obtain the nominal wake distribution at propeller plane. Then the flow analyses for all cases of ship with propeller are carried out. And the effective wake distributions, viscous pressure and frictional resistance forces affecting ship hull and duct surfaces, thrust of ducts, thrust and torque coefficients of propeller are computed. 3.1. Resistance The total resistance force affecting a ship hull can be mainly subdivided into two components: wave resistance caused by the gravity of the earth and viscous resistance caused by viscosity of water. Viscous resistance force can be also subdivided into two components: frictional resistance and viscous pressure resistance. In this study the wave resistance and free surface effects are omitted, so it is assumed that the water surface is calm. Frictional resistance depends on the wetted surface area of the ship hull, viscosity of water and ship speed. Because
the duct surface area is negligible comparing to the ship hull surface area, as expected, it is found that the difference of frictional resistance forces between ship with duct and without duct is insignificant for all cases analyzed. It is hoped that the most effected resistance component is the viscous pressure force by use of WED. The duct may reduce the viscous pressure resistance by reducing the flow separations at after body. In these numerical simulations, it is found that there is not any considerable flow separation on the path lines around the stern of ship for all cases. So for all duct variants and locations, the viscous pressure resistance forces remain constant for both cases of ship with and without duct. Because the ship has a modern design, the stern of ship is well designed hydrodynamically. The path lines and velocity vectors around after body of the ship at the most effective attachment, which is Case 6, are presented in Figs. 6 and 7, respectively. 3.2. Thrust produced by WED As seen in Fig. 8, the ducts generate a positive thrust for all duct cases between 10 and 15.4 knots of ship speed. In Cases 2 and 3, the thrust produced by duct decreases with increasing ship speed, and after 15.4 knots the duct gives a negative thrust (resistance). In Cases 4 and 5, the trend of curves is similar to 2 and 3, but they show a gradual decrease with ship speed. Nevertheless, the ducts in Cases 4 and 5 supply a considerable amount of positive thrust as seen in Fig. 8. In Cases 6 and 7, where the angle of duct section ðfÞ is 10 , the maximum thrusts are obtained from ducts, and goes up a little with ship speed. At design speed of ship that the maximum thrust of duct is supplied as 28.553 kN by the duct in Case 6 is shown in Fig. 8. Despite the duct in Case 6 generates maximum positive thrust, it is insufficient to say that it has effective duct geometry and its position is the most appropriate. For this reason, it is necessary to compare the propulsion efficiencies for cases of the ship with and without duct. Fig. 9 shows the axial velocity distributions around WED for ship with and without propeller for Case 6. As expected the axial velocity inside of WED is higher than outside of WED, and the axial velocity inside of WED increases by presence of the propeller.
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Fig. 6. Path lines around the stern of ship for Case 6.
the propeller by improving the uniformity of wake. In this study for all duct cases investigated, it seems that the WED does not change the propeller open water efficiency, positive or negative. As shown in Fig. 10, the wake distribution at the propeller disc is modified a little by using WED, but there is not any significant influence of this modification on propeller efficiency. Likewise, the other propeller characteristics (thrust and torque coefficients; K T , K Q ) also nearly remains constant for both cases of the ship with and without WED. As Fig. 11 shows the variation of the average wake in the speed range of 10–16 knots for Case 6, Fig. 12 shows the open water characteristics of the propeller for Case 6. Although the propeller characteristics are affected very little by the presence of the duct, the propulsive efficiency is increased considerably for some duct cases owing to an additional positive thrust generated by the duct (Fig. 13). At ship design speed the maximum increasing of the propulsive efficiency (gain or power saving) is found 9.743% with the duct in Case 6. It is an important amount of reduction of power required for propulsion.
Fig. 7. Velocity vectors on the stern of ship for Case 6. 35.0
Thrust ofduct (kN)
30.0
Case 2
Case 3
Case 4
Case 5
Case 6
Case 7
25.0
4. Conclusions
20.0 15.0 10.0 5.0 0.0 -5.0
10
11
12
13
14
15
16
Ship speed (knot)
Fig. 8. Variation of thrust produced by WED with ship speed.
3.3. Propulsion As mentioned above, main purpose of use of a WED (as stated by Schneekluth, 1986 which developed the wake equalizing duct) is to increase the open water efficiency of
The wake equalizing duct (WED) is one of the most commonly used energy saving devices for improving the propulsion performance of a ship; and reducing the propeller-excited vibrations and viscous resistance forces. In this study a numerical investigation, in order to find out the most effective duct geometry and longitudinal location from among six duct cases, is carried out for a chemical tanker with C B ¼ 0:77. The propulsion characteristics, path lines over the after body and viscous resistance forces are analyzed for case of the ship combined with propeller and the WED at various ship speeds. In order to reduce the required CPU time, the aft body of ship is taken into account rather than full body. The numerical computations are performed using a commercial RANS solver Fluent 6.2.16.
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Fig. 9. Axial velocity distributions around WED for Case 6: (a) ship with propeller; (b) ship without propeller.
0.750 0.740 0.730 0.720 0.710 0.700 0.690 0.680 0.670 0.660 0.650 10
0.8
0.6 0.5 0.4 0.3 0.2 11
12 13 14 Ship speed (knot)
15
16
Fig. 11. Variation of the average wake with ship speed for Case 6.
The results obtained from numerical simulations can be summarized as follows:
Kt 10Kq η
0.7 KT 10KQ η
Average wake (1-w)
Fig. 10. The nominal wake distributions: (a) ship with WED (Case 6); (b) ship without WED.
In all duct cases and ship speeds, the nominal and effective wake distributions are affected very little by the
0.1 0.300
0.400
0.500
0.600
0.700
0.800
0.900
Advance coefficient (JA) Fig. 12. The open water characteristics of the propeller for Case 6.
attachment of the duct, and so are the average wakes. That the average and effective wake will not be changed is also reported by Schneekluth (1986). The average
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12.0
Case 2
Case 3
Case 4
Case 5
Case 6
Case 7
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his colleagues, I˙slam Yilmaz and Can Kocaman for their helps in design stage of ship form.
10.0
Gain (%)
8.0
References
6.0 4.0 2.0 0.0 -2.0 10
11
-4.0
12 13 14 Ship speed (knot)
15
16
-6.0
Fig. 13. Variation of gains obtained using WED for various duct arrangements.
nominal wake fraction of the chemical tanker at the propeller disc is found approximately 0.303. The viscous resistance forces of ship are not changed with ducts. For all cases analyzed, the propeller propulsive characteristics nearly remain constant. For all duct cases at the design speed of ship, the ducts generates a positive thrust, which reaches a significant amount especially in Cases 6 and 7. The maximum contribution to the power saving is supplied by the duct in Case 6. The duct in this case at the design speed of ship causes an increasing of 9.7% at the propulsive efficiency. Whereas the effectiveness of the duct arrangements depends on the angle of duct section strongly, it is affected a little with the longitudinal location of WED for analyzed cases.
The overall conclusion can be stated that a well-designed WED can improve the propulsion characteristics of a ship considerably; otherwise, it can cause a negative effect. Therefore in designing a WED for a specific ship hull, the extensive studies for duct variants including the various parameters of duct (such as the angle of duct section, the length of duct, the angle of duct axis, etc.) must be carried out for the best ship propulsive performance. Acknowledgments The author wishes to thank Prof. Mesut Gu¨ner for his valuable discussions and suggestions, and also thanks to
Abdel-Maksoud, M., 2003. Numerical and experimental study of cavitation behaviour of a propeller. Sprechtag Kavitation, Hamburg. Blaurock, J., 1990. An appraisal of unconventional aft body configurations and propulsion devices. Marine Technology SNAME 27 (6), 325–336. Breslin, J.P., Andersen, P., 1994. Hydrodynamics of Ship Propeller. Cambridge University Press, Cambridge. Carlton, J.S., 1994. Marine Propellers and Propulsion. ButterworthHeinemann Ltd., Oxford. C - elik, F., Gu¨ner, M., 2006. An improved lifting line model for the design of marine propellers. Marine Technology and SNAME News 43 (2), 100–113. Fluent 6.2.16 User’s Guide, Fluent Inc., 2004. Friesch, J., Johannsen, C., 1994. Propulsion optimization tests at high Reynolds numbers. SNAME Transactions 102, 1–21. Glover, E.J., 1987. Propulsive devices for improved propulsive efficiency. Transactions of the Institute of Marine Engineers 99, 23–29. Gul, Y., Kaydihan, L., Cehreli, Z.N., Ucar, G., Esirgemez, E., 2005. CFD Application for hydrodynamic design of ships. Naval Architect and Marine Technology 163 (in Turkish). ITTC, The Propulsor Committee, 1990. Proceedings of the 19th International Towing Tank Conference (ITTC), vol. 1, Madrid, Spain, pp. 109–160. ITTC, 1999. Final report of the specialist committee on unconventional propulsors. 22nd International Towing Tank Conference, Seoul, Korea and Sanghai, China. Korkut, E., 2006. A case study for the effect of a flow improvement device (a partial wake equalizing duct) on ship powering characteristics. Ocean Engineering 33 (2), 205–218. Launder, B.E., Spalding, D.B., 1972. Lectures in Mathematical Models of Turbulence. Academic Press, London, England. Maxsurf Ship Design Program: hwww.formsys.comi. Ok, J.P., 2004. Numerical investigation of scale effects of Schneekluth’s duct. Ph.D. Thesis, Hamburg Technical University, Germany. Patience, G., 1991. Developments in marine propellers. Proceedings of the Institute of Mechanical Engineers 205, pp. 1–12. Sanchez-Caja, A., Rautaheimo, P., Siikonen, T., 2000. Simulation of the incompressible viscous flow around a ducted propeller using a RANS equation solver. 23rd Symposium on Naval Hydrodynamics, Val de Reuil, 2000. Schneekluth, H., 1986. Wake equalizing duct. The Naval Architect 103, 147–150. Warstila hhttp://www.wartsila.com/Wartsila/docs/en/ship_power/media_ publications/marine_news/2005_1/replacing_fpp.pdfi. Watanabe, T., Kawamura, T., Takekoshi, Y., Maeda, M., Rhee, S.H., 2003. Simulation of steady and unsteady cavitation on a marine propeller using a RANS CFD code. Proceedings of the Fifth International Symposium on Cavitation (CAV2003), Osaka, Japan.
Ocean Engineering 34 (2007) 2138–2145 www.elsevier.com/locate/oceaneng
A numerical study for effectiveness of a wake equalizing duct Fahri C - elik Yildiz Technical University, Department of Naval Architecture, Besiktas-Istanbul, Turkey Received 29 December 2006; accepted 17 April 2007 Available online 27 April 2007
Abstract A numerical study is carried out for calculating effect of the wake equalizing duct (WED) on the propulsion performance of a chemical tanker. Analysis is performed using a CFD tool based on the solution of Reynolds averaged Navier–Stokes (RANS) equation. Computations are carried out for several arrangements of WED for a number of ship speeds. Total 56 runs are achieved, and the results are compared with each other. It can be concluded from this study that propeller characteristics and resistance of the ship are slightly affected by the presence of the WED, but an additional thrust is produced by the WED. It is also found that the maximum gain obtained by using an appropriate WED design is about 10%. r 2007 Elsevier Ltd. All rights reserved. Keywords: Wake equalizing duct; Energy saving; Propeller; Propulsion
1. Introduction Marine propellers are the most common propulsion systems owing to the high efficiency supplied by them; nevertheless, it is possible to improve its propulsive performance using additional auxiliary propulsor devices (unconventional propulsors). During the last three decades considerable research and development activities have taken into place within this context. Most of these devices are used to improve propulsive efficiency, but some of them aims to improve other performance characteristics, such as cavitation, vibration, noise, manoeuvrability, etc. It can be found more review studies about various unconventional propulsors in Glover (1987), ITTC (1990), Blaurock (1990), Patience (1991), Breslin and Andersen (1994), and Carlton (1994). One of the energy saving devices used widely in ships is the wake equalizing duct (WED) (Schneekluth’s duct) (Fig. 1). It consists of two aerofoil sectioned half-ring ducts integrated to the hull in front of upper region of the propeller. Some important parameters for the effectiveness of the WED are the angles of duct axis to ship’s center line plane, longitudinal positions, inner diameters, profile Fax: +90 212 236 4165.
E-mail address: [email protected]. 0029-8018/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.oceaneng.2007.04.006
section shapes, angles of section to duct axis and lengths of the half-ring ducts. It is assumed that the WED accelerates the inflow of the upper region of the propeller where the flow is slow relative to the lower region of the propeller; and it improves the uniformity of the wake over the propeller disc, so the propeller efficiency is increased. In addition, a well-designed WED reduces the amount of flow separation at the after body, generates an additional thrust as in the accelerating type of duct, reduces the propellerexcited vibrations due to the uniform wake, and improves the steering qualities because of the more straightened flow coming to the rudder. If the WED is installed to an existing ship, constructional changes and modifications in propeller design are not needed. A WED can also be used in combination with other energy saving devices such as vane wheel and asymmetric stern (Schneekluth, 1986). Schneekluth (1986) reports that the effectiveness of a WED is most evident if the ship speed is between 12 and 18 knots and its block coefficient is higher than 0.6. By now, most of the studies related to the estimation of the effect of the WED on propulsion characteristics of a ship have been carried out based on model tests. But it is difficult to extrapolate the powering performance from model tests (especially for very large ships) due to the Reynolds number effects (scale effects) stated in ITTC (1999). At higher Reynolds numbers the scale effects occurs
ARTICLE IN PRESS F. C - elik / Ocean Engineering 34 (2007) 2138–2145
Fig. 1. The wake equalizing duct (Wartsila, 2005).
more evidently, in such cases it is recommended that selfpropulsion tests should be performed to reduce these effects (ITTC, 1999). In addition, numerical flow computations as an alternative of the model tests can also be used to estimate the effectiveness of the WED. Extensive experimental tests are performed for a tanker with and without WED to investigate the scale effects in the HYKAT (hydrodynamics and cavitation tunnel) in the Hamburg Ship Model Basin by Friesch and Johannsen (1994). In their study it is concluded that the WED has a positive effect on powering performance of the ship at full scale, but it is difficult to predict this positive effect from model tests. Korkut (2006) gives an experimental study on the effect of the WED for a river going general cargo ship. In his study two different hull forms are generated from the original hull form of the vessel to optimize the stern flow. The results obtained from resistance, self-propulsion and flow visualizations tests on powering characteristic of the ship are presented. The computational methods using mostly the Reynolds averaged Navier–Stokes (RANS) equations are also applied to the ship hydrodynamics to predict the propulsion performance of ships. There are a number of studies in this context; one of these is carried out by Abdel-Maksoud (2003), where the resistance and propulsion characteristics for a container ship with and without propeller are computed using a commercial CFD code, CFX. The numerical results are compared with experimental ones and the differences between the total resistance coefficients obtained from CFD and those of the measurements are found about 6%. A numerical study on the effect of the WED for a tanker with higher block coefficient is presented by Ok (2004). A CFD code Comet based on finite volume method is used for numerical computations. As propeller does not exist at the after body, especially the Reynolds number effects are investigated for various ship speeds. As a result it is found that the WED causes an additional power requirement for propulsion and a moderate resistance increase compared to the case of the ship without duct, and so it is concluded that an inappropriate duct causes a substantial resistance and power requirements.
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Besides Abdel-Maksoud (2003) and Ok (2004) stated above, Watanabe et al. (2003), Sanchez-Caja et al. (2000) and Gul et al. (2005) investigated viscous flow around ship hull and propeller. In these studies commercial RANS solvers are used to predict the propulsion performance or resistance of ship and propeller, and it is shown that the difference between the results obtained from numerical methods and model tests is acceptable. As conclusion it can be said that CFD is now the more preferred means of testing alternative to analyze flow around ship and propeller before experimental testing takes place. In this study, a numerical investigation based on RANS method is carried out to find the most appropriate WED arrangement for a chemical tanker. As a RANS solver, commercial software called Fluent is performed. The computations are carried out for the ship alone, the ship with propeller, ship with WED alone, ship with WED and the propeller in the speed range of 10–16 knots. The WED arrangements are obtained by selecting three various angles of duct section and two longitudinal positions of the duct. In order to reduce the computation time, the aft body of the ship behind the parallel body is taken into account instead of complete hull. 2. CFD analysis 2.1. Geometrical properties of ship A chemical tanker is taken into account in order to investigate numerically the influence of WED on the powering characteristics of ship. The ship has a hydrodynamically modern design, one screw propeller and C B ¼ 0:77 block coefficient. The main particulars of the ship are given in Table 1. As can be seen from Fig. 2 which shows cross-sections of chemical tanker, the ship has a bulb and transom stern. 2.2. Propeller data The propeller geometry (Fig. 3) used in CFD analysis is designed as using an improved lifting line method developed by C - elik and Gu¨ner (2006). The blade section geometry of the propeller is generated using NACA66 thickness with a ¼ 0:8 mean line distributions for all radii. The design input data of propeller for chemical tanker is given in Table 2. Table 1 Main particulars of ship Length between perpendiculars, LBP (m) Waterline length, LWL (m) Breadth, B (m) Depth, D (m) Draught, T (m) Displacement, D (ton) Block coefficient, C B Design speed, V s (knot)
87.55 89.38 14.26 6.85 5.42 5500 0.77 14
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length of duct is selected as a quarter of diameter. Flows around the stern are investigated for the following cases given in Table 3 for ship with and without propeller. 2.4. Numerical method
Fig. 2. Cross-sections of chemical tanker.
Fig. 3. Geometry of the propeller.
2.5. Grid generation
Table 2 Propeller design input data Delivered power, PD (kW) Design speed, V s (knot) Rate of rotation, RPM Propeller diameter, D (m) Number of blades, Z Pitch ratio, P=D at 0.7R Blade area ratio, ðAE =A0 Þ Wake ð1 wN Þ
In CFD analysis, the solution is carried out by numerically solving RANS equations. As a RANS solver, a commercial CFD code (based on finite volume method) Fluent 6.2.16 is used. Detailed descriptions of the numerical method can be found in the User’s Guide of this code (2004). In this work, the flow is assumed to be incompressible and turbulent corresponding to Reynolds numbers investigated between 4:48 108 and 7:177 108 . The k2e (standard) model is chosen as the turbulence model (Launder and Spalding, 1972). The governing equations are discretized using a second-order upwind interpolation scheme, and the discretized equations are solved using SIMPLE algorithm. The solution is considered converged when the continuity residual is lower than 104 and velocity residuals are lower than 105 , which is obtained for cases of with propeller at almost 600 and for cases of without propeller at almost 400 iterations. All numerical computations were performed on the computer IBM with 2 GB RAM, Pentium 4 2.7 GHz CPU.
3246 14 150 3.5 4 1.081 0.60 0.697
2.3. The WED arrangements There are a number of parameters for design and effective arrangements of the WED, such as the inner diameter, profile section shape, length, the angle of section, the angle of axis of half rings, and the longitudinal and vertical location. In this study, the analyses are carried out for six various duct arrangements by means of changing two parameters of WED, which are the angle of section and longitudinal location, and the best geometry and position of duct for improving propulsion performance of ship are investigated. The general location of WED can be seen in Fig. 4. By changing the angle of duct section ðfÞ, different radius of leading edge ðRin Þ is obtained while the radius of trailing edge ðRout Þ, vertical location and length of duct (DC) are kept constant. The radius of trailing edge ðRout Þ is selected as half diameter of propeller and the
The ship hull geometry shown in Fig. 2 is modeled using Maxsurf ship design program, the WED and propeller geometries are generated in Rhino CAD program and all geometries are imported to Fluent pre-processor Gambit for grid generation and description of boundary conditions. As known one of the most significant parameters in numerical flow simulations is the quality of mesh. This affects directly the accuracy of solution and required number of iterations (CPU time). For this purpose, the computational domain modeling flow around the ship hull is split into 13 parts. Twelve of these parts are stationary and the one is moving domain which rotates with propeller together. For the surfaces which belong to the propeller, duct and the stern of ship the computational grids are generated using triangular mesh elements, and the other surfaces of ship are meshed using quadrilateral mesh elements. Generating surface meshes, computational domains are filled with hexahedral, tetrahedral and wedge volume mesh elements where appropriate. The grid spacing is finer near hull surface in order to compute the viscous flow effects more correctly. The numerical grid is kept constant for all Reynolds numbers corresponding to ship speeds. Fig. 5 shows the computational grids around after body for the present simulation.
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Fig. 4. Location of the WED at the after body of ship.
Table 3 The wake equalizing duct arrangements
Case Case Case Case Case Case Case
1 2 3 4 5 6 7
Angle of duct section ðfÞ (degree)
Longitudinal position of duct (from A.P.) (m)
No duct 18 18 14 14 10 10
3.25 2.95 3.25 2.95 3.25 2.95
The number of total cells used in volume mesh for cases of ship without and with propeller is approximately 1,050,000 and 1,250,000, respectively. On the ship hull, propeller and duct surfaces, the nonslip wall condition is imposed. On the water surface, the slip wall condition is imposed and the shearing stress components are set to 0. On the outer boundary, the symmetry boundary condition is applied. 2.6. Validation of the numerical method Numerical resistance tests were carried out by Gul et al. (2005) for 2650 DWT tanker by using CFD code Fluent.
Fig. 5. Computational grids around the stern of ship.
Model experiments of tanker were performed at BSHC (Bulgarian Ship Hydrodynamics Centre). Main particulars of the ship: length of water line LWL ¼ 81:04 m, breadth B ¼ 12:5 m and drought T ¼ 4:70 m. In their study frictional, residual and total resistance values of ship were calculated at different Froude numbers ðF n Þ corresponding to 8, 10 and 12 knots of ship speed using the turbulence flow model and the free surface condition
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Table 4 Comparison of the resistance coefficients obtained from CFD and model tests (Gul et al., 2005) Froude number ðF n Þ
0.1563 0.1954 0.2216
Residual resistance coefficient C R 103
Frictional resistance coefficient C F 103
Total resistance coefficient C T 103
Experiment
CFD (Fluent)
ITTC 57
CFD (Fluent)
Experiment
CFD (Fluent)
0.6982 1.2730 2.3241
0.6462 1.2403 2.2234
1.7475 1.6969 1.6693
1.7596 1.6908 1.6498
2.4457 2.9699 3.9935
2.4059 2.9311 3.8732
on the water surface. Resistance coefficients obtained from CFD were compared with those of experimental results (Table 4). As can be seen in Table 4, differences between residual, frictional and total resistance coefficients are about 4.7%, 0.7%, 2%, respectively. This shows that differences are acceptable. 3. Results and discussions As mentioned before, the aim of using a WED can be summarized as follows: improving the propeller efficiency owing to the homogeneity of the wake obtained by accelerating the inflow to upper part of propeller, reducing the propeller-excited vibrations, reducing the viscous resistance force by decreasing the flow separation at the stern of ship, and generating an additional thrust, so improving propulsion efficiency. In this study for three various duct geometries and two longitudinal locations, whether the ducts provide the advantages stated above is investigated numerically. The most appropriate duct geometry and whose location is found in terms of gain supplied (reduction of power required for propulsion). First the numerical flow analyses around the stern of ship without propeller for all cases are performed in order to obtain the nominal wake distribution at propeller plane. Then the flow analyses for all cases of ship with propeller are carried out. And the effective wake distributions, viscous pressure and frictional resistance forces affecting ship hull and duct surfaces, thrust of ducts, thrust and torque coefficients of propeller are computed. 3.1. Resistance The total resistance force affecting a ship hull can be mainly subdivided into two components: wave resistance caused by the gravity of the earth and viscous resistance caused by viscosity of water. Viscous resistance force can be also subdivided into two components: frictional resistance and viscous pressure resistance. In this study the wave resistance and free surface effects are omitted, so it is assumed that the water surface is calm. Frictional resistance depends on the wetted surface area of the ship hull, viscosity of water and ship speed. Because
the duct surface area is negligible comparing to the ship hull surface area, as expected, it is found that the difference of frictional resistance forces between ship with duct and without duct is insignificant for all cases analyzed. It is hoped that the most effected resistance component is the viscous pressure force by use of WED. The duct may reduce the viscous pressure resistance by reducing the flow separations at after body. In these numerical simulations, it is found that there is not any considerable flow separation on the path lines around the stern of ship for all cases. So for all duct variants and locations, the viscous pressure resistance forces remain constant for both cases of ship with and without duct. Because the ship has a modern design, the stern of ship is well designed hydrodynamically. The path lines and velocity vectors around after body of the ship at the most effective attachment, which is Case 6, are presented in Figs. 6 and 7, respectively. 3.2. Thrust produced by WED As seen in Fig. 8, the ducts generate a positive thrust for all duct cases between 10 and 15.4 knots of ship speed. In Cases 2 and 3, the thrust produced by duct decreases with increasing ship speed, and after 15.4 knots the duct gives a negative thrust (resistance). In Cases 4 and 5, the trend of curves is similar to 2 and 3, but they show a gradual decrease with ship speed. Nevertheless, the ducts in Cases 4 and 5 supply a considerable amount of positive thrust as seen in Fig. 8. In Cases 6 and 7, where the angle of duct section ðfÞ is 10 , the maximum thrusts are obtained from ducts, and goes up a little with ship speed. At design speed of ship that the maximum thrust of duct is supplied as 28.553 kN by the duct in Case 6 is shown in Fig. 8. Despite the duct in Case 6 generates maximum positive thrust, it is insufficient to say that it has effective duct geometry and its position is the most appropriate. For this reason, it is necessary to compare the propulsion efficiencies for cases of the ship with and without duct. Fig. 9 shows the axial velocity distributions around WED for ship with and without propeller for Case 6. As expected the axial velocity inside of WED is higher than outside of WED, and the axial velocity inside of WED increases by presence of the propeller.
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Fig. 6. Path lines around the stern of ship for Case 6.
the propeller by improving the uniformity of wake. In this study for all duct cases investigated, it seems that the WED does not change the propeller open water efficiency, positive or negative. As shown in Fig. 10, the wake distribution at the propeller disc is modified a little by using WED, but there is not any significant influence of this modification on propeller efficiency. Likewise, the other propeller characteristics (thrust and torque coefficients; K T , K Q ) also nearly remains constant for both cases of the ship with and without WED. As Fig. 11 shows the variation of the average wake in the speed range of 10–16 knots for Case 6, Fig. 12 shows the open water characteristics of the propeller for Case 6. Although the propeller characteristics are affected very little by the presence of the duct, the propulsive efficiency is increased considerably for some duct cases owing to an additional positive thrust generated by the duct (Fig. 13). At ship design speed the maximum increasing of the propulsive efficiency (gain or power saving) is found 9.743% with the duct in Case 6. It is an important amount of reduction of power required for propulsion.
Fig. 7. Velocity vectors on the stern of ship for Case 6. 35.0
Thrust ofduct (kN)
30.0
Case 2
Case 3
Case 4
Case 5
Case 6
Case 7
25.0
4. Conclusions
20.0 15.0 10.0 5.0 0.0 -5.0
10
11
12
13
14
15
16
Ship speed (knot)
Fig. 8. Variation of thrust produced by WED with ship speed.
3.3. Propulsion As mentioned above, main purpose of use of a WED (as stated by Schneekluth, 1986 which developed the wake equalizing duct) is to increase the open water efficiency of
The wake equalizing duct (WED) is one of the most commonly used energy saving devices for improving the propulsion performance of a ship; and reducing the propeller-excited vibrations and viscous resistance forces. In this study a numerical investigation, in order to find out the most effective duct geometry and longitudinal location from among six duct cases, is carried out for a chemical tanker with C B ¼ 0:77. The propulsion characteristics, path lines over the after body and viscous resistance forces are analyzed for case of the ship combined with propeller and the WED at various ship speeds. In order to reduce the required CPU time, the aft body of ship is taken into account rather than full body. The numerical computations are performed using a commercial RANS solver Fluent 6.2.16.
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Fig. 9. Axial velocity distributions around WED for Case 6: (a) ship with propeller; (b) ship without propeller.
0.750 0.740 0.730 0.720 0.710 0.700 0.690 0.680 0.670 0.660 0.650 10
0.8
0.6 0.5 0.4 0.3 0.2 11
12 13 14 Ship speed (knot)
15
16
Fig. 11. Variation of the average wake with ship speed for Case 6.
The results obtained from numerical simulations can be summarized as follows:
Kt 10Kq η
0.7 KT 10KQ η
Average wake (1-w)
Fig. 10. The nominal wake distributions: (a) ship with WED (Case 6); (b) ship without WED.
In all duct cases and ship speeds, the nominal and effective wake distributions are affected very little by the
0.1 0.300
0.400
0.500
0.600
0.700
0.800
0.900
Advance coefficient (JA) Fig. 12. The open water characteristics of the propeller for Case 6.
attachment of the duct, and so are the average wakes. That the average and effective wake will not be changed is also reported by Schneekluth (1986). The average
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12.0
Case 2
Case 3
Case 4
Case 5
Case 6
Case 7
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his colleagues, I˙slam Yilmaz and Can Kocaman for their helps in design stage of ship form.
10.0
Gain (%)
8.0
References
6.0 4.0 2.0 0.0 -2.0 10
11
-4.0
12 13 14 Ship speed (knot)
15
16
-6.0
Fig. 13. Variation of gains obtained using WED for various duct arrangements.
nominal wake fraction of the chemical tanker at the propeller disc is found approximately 0.303. The viscous resistance forces of ship are not changed with ducts. For all cases analyzed, the propeller propulsive characteristics nearly remain constant. For all duct cases at the design speed of ship, the ducts generates a positive thrust, which reaches a significant amount especially in Cases 6 and 7. The maximum contribution to the power saving is supplied by the duct in Case 6. The duct in this case at the design speed of ship causes an increasing of 9.7% at the propulsive efficiency. Whereas the effectiveness of the duct arrangements depends on the angle of duct section strongly, it is affected a little with the longitudinal location of WED for analyzed cases.
The overall conclusion can be stated that a well-designed WED can improve the propulsion characteristics of a ship considerably; otherwise, it can cause a negative effect. Therefore in designing a WED for a specific ship hull, the extensive studies for duct variants including the various parameters of duct (such as the angle of duct section, the length of duct, the angle of duct axis, etc.) must be carried out for the best ship propulsive performance. Acknowledgments The author wishes to thank Prof. Mesut Gu¨ner for his valuable discussions and suggestions, and also thanks to
Abdel-Maksoud, M., 2003. Numerical and experimental study of cavitation behaviour of a propeller. Sprechtag Kavitation, Hamburg. Blaurock, J., 1990. An appraisal of unconventional aft body configurations and propulsion devices. Marine Technology SNAME 27 (6), 325–336. Breslin, J.P., Andersen, P., 1994. Hydrodynamics of Ship Propeller. Cambridge University Press, Cambridge. Carlton, J.S., 1994. Marine Propellers and Propulsion. ButterworthHeinemann Ltd., Oxford. C - elik, F., Gu¨ner, M., 2006. An improved lifting line model for the design of marine propellers. Marine Technology and SNAME News 43 (2), 100–113. Fluent 6.2.16 User’s Guide, Fluent Inc., 2004. Friesch, J., Johannsen, C., 1994. Propulsion optimization tests at high Reynolds numbers. SNAME Transactions 102, 1–21. Glover, E.J., 1987. Propulsive devices for improved propulsive efficiency. Transactions of the Institute of Marine Engineers 99, 23–29. Gul, Y., Kaydihan, L., Cehreli, Z.N., Ucar, G., Esirgemez, E., 2005. CFD Application for hydrodynamic design of ships. Naval Architect and Marine Technology 163 (in Turkish). ITTC, The Propulsor Committee, 1990. Proceedings of the 19th International Towing Tank Conference (ITTC), vol. 1, Madrid, Spain, pp. 109–160. ITTC, 1999. Final report of the specialist committee on unconventional propulsors. 22nd International Towing Tank Conference, Seoul, Korea and Sanghai, China. Korkut, E., 2006. A case study for the effect of a flow improvement device (a partial wake equalizing duct) on ship powering characteristics. Ocean Engineering 33 (2), 205–218. Launder, B.E., Spalding, D.B., 1972. Lectures in Mathematical Models of Turbulence. Academic Press, London, England. Maxsurf Ship Design Program: hwww.formsys.comi. Ok, J.P., 2004. Numerical investigation of scale effects of Schneekluth’s duct. Ph.D. Thesis, Hamburg Technical University, Germany. Patience, G., 1991. Developments in marine propellers. Proceedings of the Institute of Mechanical Engineers 205, pp. 1–12. Sanchez-Caja, A., Rautaheimo, P., Siikonen, T., 2000. Simulation of the incompressible viscous flow around a ducted propeller using a RANS equation solver. 23rd Symposium on Naval Hydrodynamics, Val de Reuil, 2000. Schneekluth, H., 1986. Wake equalizing duct. The Naval Architect 103, 147–150. Warstila hhttp://www.wartsila.com/Wartsila/docs/en/ship_power/media_ publications/marine_news/2005_1/replacing_fpp.pdfi. Watanabe, T., Kawamura, T., Takekoshi, Y., Maeda, M., Rhee, S.H., 2003. Simulation of steady and unsteady cavitation on a marine propeller using a RANS CFD code. Proceedings of the Fifth International Symposium on Cavitation (CAV2003), Osaka, Japan.