Hydrodynamic optimization of pre-swirl stator by CFD and model testing

DOI 10.3233/ISP-130092 IOS Press

Hydrodynamic optimization of pre-swirl stator by CFD

and model testing

Keunjae Kim

_{, Michael Leer-Andersen}

_{, Sofia Werner}

_{, Michal Orych}

and Youngbok Choi

a_{SSPA Sweden AB, Gothenburg, Sweden}

b_{FLOWTECH International AB, Gothenburg, Sweden}

c_{Daewoo Shipbuilding and Marine Engineering Co., Ltd., Seoul, Korea}

With environmental concerns becoming one of the most important issues facing the shipping/ship-building industry today, SSPA has witnessed strong demand for the development of energy saving devices (ESD). SSPA anticipates that the demand will be greater to respond to new requirements set by the IMO regulation on energy efficient design index (EEDI).

SSPA has been involved in many joint research projects in developing energy saving solutions. Daewoo Shipbuilding and Marine Engineering Co. Ltd. (DSME) has developed several ESDs in cooperation with SSPA, where SSPA has tested most of the ESDs designed by DSME over the last 10 years. The pre-swirl stator (PSS) is a device mounted on the stern boss just upstream of the propeller (see Fig. 6 or Fig. 33). It is designed to generate pre-swirl flow to the propeller in order to gain a favorable interaction with the propeller that improves the propulsive efficiency and results in a power reduction.

This paper is a full description of one of the developments of PSS from the early design stage, opti-mization phase, and confirmation by model tests to validation through sea trial tests.

Keywords: Hydrodynamic optimization, Energy Saving Device (ESD), Pre-swirl Stator (PSS), Computa-tional Fluid Dynamic (CFD)

1. Introduction

Although propellers are regarded as reasonably efficient in transforming mechan-ical engine power with efficiency in the range of 70 percents, significant energy loss still incurred. Retaining the energy loss is one of most effective way to improve the overall propulsion efficiency using various energy saving devices (ESD). Many ESD’s are used to enhance the flow into the propeller aiming at increasing propulsion efficiency as well as reducing energy loss.

SSPA has been working with optimum design of ESD for the improvement of overall propulsion efficiency. The first research work performed was SSPA’s par-ticipation in the European project VIRTUE, carried out during 2004–2009, which

*_{Corresponding author. E-mail: keunjae.kim@sspa.se.}

focused on the development of the approach for predicting hull/propeller interac-tion [8]. Thereafter, extensive internal SSPA research work has been performed by Kim et al. [9] and Kim and Bathfield [10] in this area under H. Hammars fond dur-ing 2009–2010 to investigate the incorporation of the effect of propeller and energy saving devices in viscous flow computation.

Promising results were obtained for a limited test computation made for several ship types. The use of potential-flow based method for estimating the propeller per-formance (solving the flow with RANS code) behind ship seems a sufficiently com-plete and accurate approach for predicting the thrust, torque and rotation rate for the propeller in order to achieve correct ranking between different design alternatives.

In the present paper, a case study for the development of PSS for an Aframax product carrier will be presented from early design stage, optimization phase and confirmation by model tests to validation through sea trial tests.

The base line design selected for the development of PSS is the latest hull form/propeller design developed by DSME throughout a number of model tests at SSPA during the years. The resistance and propulsion performance quality of the base line design evaluated based on SSPA statistics is absolute best among 200 Afra-max P/C tested. Three to six PSS blades have been investigated in various config-urations on single screw ships over the years. The stator configuration selected for the present optimization is four bladed with a diameter equal to the propeller di-ameter. A wide range of PSS design parameter variation studies was performed by SHIPFLOW. Five design parameters were investigated; no. of stator blades, diame-ter of stators, angular position of blades, stator blade pitch angle and twisted stator blades. The parameterization and the grid generation of PSS are performed with SHIPFLOW XGRID and RANS simulation is made with SHIPFLOW XCHAP.

This type of CFD computation is very challenging since it requires full simu-lation of propeller open water characteristics, resistance and self-propulsion tests with a high level of accuracy that is capable of predicting small differences in flow characteristics, as well as the relative ranking of propulsion efficiency due to small variations in design parameters for PSS.

Based on evaluation of power gain and detail analysis of flow characteristics, four most interesting PSS configurations were selected for confirmation by model test-ing. The model test results confirmed the conclusion drawn from the SHIPFLOW simulation in the relative ranking between four tested PSS configurations.

After further refinements were made with propeller design and PSS configuration, the final PSS configuration was selected. The computation indicates that around 4% power gain can be achieved by the final PSS as compared to the base line design, while somewhat larger gains were predicted by model tests (5.7%). The speed trial at full load condition confirmed that the vessel is performing around 0.25 knots better at the trial power (or around 5% less power required at 15.0 knots) in comparison with the model test predictions.

The developed PSS has become the standard configuration for DSME for a wide range of hull types including VLCCs, Tankers, Bulkers, Ro-Ro ships and Containers.

The DSME PSS has been successfully applied to various ship types, with an average reduction of 4–6 percent in propulsion power.

2. Numerical method

SHIPFLOW includes three flow analysis modules: Free surface wave elevation can be computed with the potential flow solver (XPAN), thin boundary layer and transition can be evaluated with the boundary layer method (XBOUND) and a wake region resolved in the Reynolds Averaged Navier–Stokes (RANS) solver, the CHAP-MAN code.

The CHAPMAN code is a relatively new viscous solver included in SHIPFLOW under the name XCHAP and the Reynolds Averaged Navier–Stokes equations are solved for steady incompressible flow using a finite volume method. First order Roe scheme is used for the convective terms and flux correction is added to obtain a higher order of accuracy. In the code three turbulence models are implemented, the

kω-SST, kω-BSL models and the explicit algebraic stress model, EASM. No wall

functions are used in the code and the model equations are integrated to the wall. The momentum, pressure and turbulence equations are solved in a coupled manner with the alternating direction implicit (ADI) method.

2.1. Lifting line method

SHIPFLOW also includes a lifting line based propeller analysis module (LL). In this model, a finite-bladed propeller is first replaced with an infinite-bladed propeller. Then series of vortex systems, such as bound vortices, hub vortices and free (trail-ing) vortices, are distributed to represent the propeller. The slipstream contraction is not considered in this model because the pitch and the radius of each vortex line are assumed to be constant. Only the steady part of induced tangential and axial velocity is taken into account, although this method is mainly proved for lightly loaded pro-pellers by Hough and Ordway [6]. The method used in the calculations of the induced velocities of propeller can be found in [2]. The determination of the non-dimensional blade circulation is made by incorporating a method based on Goldstein’s Kappa the-ory (see [4]). The viscous drag of the blade is calculated in an approximate way by an empirical formula for blade section drag. The principle of this method is briefly described by Zhang [19] and Li [14].

2.2. Modelling propeller/hull interaction by body force approach

The effect of the propeller is introduced in the RANS simulation as a body force for numerical modelling of propeller. By applying the body forces to discretized cells on the propeller disk, the flow is accelerated in the same way as suction of the flow by the propeller. The body force is calculated by propeller analysis code which is

run iteratively with the RANS solver. The velocity computed by the RANS solver over the whole domain, subtracting the induced velocity estimated by the propeller analysis code, leads to a effective wake. This effective wake is used as the inflow to the propeller analysis code, which calculates axial and tangential body forces. These forces are then returned to the RANS solver in an iterative manner.

The interactive coupling between the RANS solver XCHAP and the lifting line model via body forces is completed with the following procedure at regular intervals, normally every 10 iteration in the RANS solver:

(i) Interpolate the current approximation of the velocity field to an embedded cylindrical grid concentric with the propeller.

(ii) Obtain the effective wake on the blade of the propeller by subtracting the propeller-induced velocities obtained in the previous iteration from the ve-locity field.

(iii) Run the propeller model in the effective wake and calculate the blade circu-lation, forces and torques.

(iv) Distribute the computed forces over the volume cells in the cylindrical grid. (v) Interpolate the forces from the cylindrical grid to the computation grid and

introduce them in the right-hand side of the N-S equations.

The fluid that passes through the propeller disk cells has thus acquired a body force and is accelerated so that the time averaged action of the propeller is simulated. The sum of the forces will give the fluid passing through the propeller disc a longitudinal and angular momentum consistent with the thrust and torque on the propeller. At convergence the two models are matched in the sense that the absolute wake com-puted by the RANS method, at points sampled in a circular disc in the middle of the cylindrical grid, will be equal to the total wake computed by the propeller model at the same points.

The present method based on CHAPMAN/LL coupling has been validated through a number of test cases. Extensive comparative studies have been made by Han [5]. CHAPMAN has been coupled with another propeller analysis module MPUF-3A based on lifting surface method (vortex lattice method), which was devel-oped by Lee [13]. Comparative computations have been made with CHAPMAN/LL and CHAPMAN/MPUF couplings for hull/propeller interaction and propeller/rudder interaction. The comparative study has been continued by Kim [7] for propeller– hull–rudder interaction problem. Quite promising results were obtained from both methods. The action of propeller, even in the viscous wake of the ship hull, is to a large extent determined by lift effects that can be modelled by such a relatively simple lifting line method.

3. Uncertainty estimation on standard self-propulsion test simulation

This section will present the results of verification and validation exercise made for estimation of numerical accuracy of SHIPFLOW in standard self-propulsion

sim-ulation. The present results were presented at Gothenburg 2010 Workshop on CFD in Ship Hydrodynamics, held on December 8–10, 2010 in Gothenburg, Sweden.

Verification study has been performed for KCS (MOERI 3600 teu container-ship) with four geometrically similar grids generated using grid refinement ratio

r_G(= hi/h1) of 20.4; the finest g1 (10.0 M grid points), fine g2 (4.0 M), medium

g3(1.6 M) and coarse g4(0.7 M). The procedure used for uncertainty estimation is

based on a least squares variant of the Grid Convergence Index method proposed by Eca and Hoekstra [3].

The error estimation is made using extrapolation formula with exponent

φi = φ0+ α· hp_i, (1)

where φiis the numerical solution of any local or integral scalar quantity on a given

grid (designated by the subscripti), φ0 is the estimated exact solution, α is a

con-stant, hiis a parameter which identifies the representative grid cell size and p is the

observed order of accuracy. The three unknown φ0, α and p are determined by a best

root mean square fit using the solution obtained on the four grids. In the present V&V study, the following procedure is used:

• Determine the observed order of accuracy, p, from the available data.

• For 0.95  p < 2.05, UGis estimated with the Grid Convergence Index

pro-posed and the standard deviation USof the fit:

UG= 1.25|δRE| + US. (2)

The extrapolated value is taken as δRE = φ0− φ1, where φ1is the value from

the finest grid and the standard deviation of the fit, USis given by

US=

n

i=1(φi− (φ0+ αhp_i))2

n− 3 .

• For 0 < p < 0.95, the same error estimate is made but is then compared with

the data rangeΔM multiplied by the safety factor 1.25, so that UGis obtained

from:

UG= min(1.25|δRE| + US,ΔM), (3)

whereΔM is the maximum difference between all the solutions available

ΔM = max  |φi− φj|  with 1 i  n ∩ 1  j  n. IfΔM > 1.25|δRE| + USthen φ0= φ1.

• For p  2.05 UG= max  1.25|δRE∗ | + US,ΔM  , (4)

where δRE∗ is calculated from a function with fixed p = 2 fitted to the data. The

extrapolated value is φ0= φ1+ δ∗RE.

• If monotonic convergence is not observed

UG= 3ΔM and φ0= φ1. (5)

Resistance and self-propulsion simulations are made at Td = 10.8 m (fixed even

keel condition) and design speed Fr = 0.26 (Re = 1.4·107in model scale). The self-propulsion computation was carried out at the ship point following the experimental procedure. Thus, the rate of revolutions of the propeller n is to be adjusted to obtain force equilibrium in the longitudinal direction considering the applied towing force (Skin Friction Correction, SFC), i.e.

T = RT(SP)− SFC, (6)

where T is the computed thrust, RT(SP) is the total resistance at self-propulsion and

SFC = 30.272 N or towing force coefficient Ctow = 1.330· 10−3(from the tests).

Typically, with current version of SHIPFLOW, this type of simulation is made with double model flow and so a wave resistance correction (Cw = 0.538· 10−3) were

made. The applied towing force coefficient in the simulation is 0.7914· 10−3.

3.1. Uncertainty estimation of resistance coefficients

The results of the resistance prediction are summarised in Table 1. In addition to resistance coefficients obtained for the four grids, the estimated iterative uncertainty in percentage of the converged solution is given.

For the viscous pressure resistance coefficient, the estimated iterative uncertainty is rather high; 13.9% in the finest grid g1and 6% in the fine grid g2while almost 0%

for the two coarse grids. The iterative uncertainty is estimated in relative variation in percentage compared with a converged solution. Figure 1 shows a typical conver-gence history of the viscous pressure resistance prediction with the finest grid g1.

In the present study, the convergence solution is obtained by taking an average value of the last 4,000 iterations. The iterative uncertainty is originated from the non-linearity of RANS equations and the turbulence model solved in CFD. A nonlinear EASM turbulence model is used in the present calculation and it suffers from a high level of uncertainty.

On the other hand, very small, almost equal to 0%, iterative variation is observed on the viscous frictional resistance for all grids tested (see Fig. 2 for g2grid). It seems

that the iterative uncertainty estimation for frictional resistance component is quite reliable.

Table 1

Resistance prediction for KCS

Grid C_F Std CPV Std CT Std ·103 _%C F ·103 %CPV ·103 %CT EFD 3.550 g1 2.759 0.03 0.283 13.9 3.580 1.11 g2 2.745 0.01 0.304 6.05 3.586 0.52 g3 2.713 0.00 0.352 0.03 3.603 0.00 g4 2.637 0.00 0.463 0.01 3.637 0.00 E%D _−0.85 ε12%S1 0.53 7.36 0.17 U_I/ε12 0.049 1.88 6.53 p_G/p_G,th 1.53 1.50 1.45 Φ0 2.770 0.267 3.574 Φ0,p=2 2.794 0.233 3.564 U_S 6.204· 10−4 6.204· 10−4 6.204· 10−4 U_G%S1 5.57 79.4 1.99 Notes:

(1) Comparison error, E%D = [(D− S)/D] ∗ 100, where D is the EFD value and S is the simulation value.

(2) Relative change in solution: ε12%S1= [(S1− S2)/S1]∗ 100, “1” refers to the finest grid. (3) Iterative uncertainty U_Iis based on fine grid solution.

(4) p_Gis the estimated order of accuracy and p_G,this the theoretical order of accuracy. (5) U_Gis the grid uncertainty.

Fig. 1. Iteration convergence history in resistance computation with g1grid. (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/ISP-130092.)

Fig. 2. Iteration convergence history in resistance computation with g2grid. (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/ISP-130092.)

Fig. 3. Convergence of resistance coefficients as function of grid refinement ratio. (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/ISP-130092.)

As expected from the well known fact that the variation of pressure resistance and frictional resistance is opposite as the grid density changes. As the number of grid cells increases, the pressure resistance decreases with a variation as high as 38%, while the frictional resistance increases with much smaller variation of 4.7%. However, the pressure resistance is a small ratio (around 10%) of total resistance and the impact of pressure resistance component on the uncertainty of total resistance is limited.

Figure 3 presents the convergence of resistance components including form factor and mean wake with the grid refinement. Monotonic convergence is obtained for the resistance coefficients; pG/pG,thare around 1.5. The estimated grid uncertainty

UG%S1is 1.59.

3.2. Uncertainty estimation of self-propulsion factors

The predicted self-propulsion factors (KT, KQ and rps) and force coefficients

(CF, CP and CT) for all four grids are presented in Table 2. The force coefficients

Table 2

Force coefficients, self-propulsion simulation for KCS

Grid K_T K_Q rps C_F· 103 CPV· 103 CT· 103 0.170 0.0288 9.50 3.966 g1 0.179 0.0306 9.28 2.755 0.637 3.994 g2 0.180 0.0307 9.27 2.740 0.660 4.002 g3 0.184 0.0312 9.26 2.709 0.711 4.022 g4 0.185 0.0314 9.24 2.633 0.825 4.061 %stdev 0.68 0.55 0.26 0.02 5.17 0.84 E%D _{−5.34 −6.26} 2.33 −0.71 ε12%S1 0.365 0.350 0.079 0.538 3.517 0.193 U_I/ε12 0.003 0.0005 0.0021 0.0009 0.009 0.0063 p_G/p_G,th 0.131 0.06 0.0001 1.53 1.46 1.30 Φ0 0.156 0.0219 257.0 2.765 0.619 3.986 Φ0,p=2 0.178 0.0310 9.276 2.789 0.585 3.976 U_S 0.001 0.0018 5· 10−4 7· 10−4 2· 10−4 9· 10−4 U_G%S1 15.02 12.4 0.155 3.266 21.467 1.195

condition. The total force coefficient CT is sum of total drag and towing force

coef-ficient.

For the force coefficients, the estimated iterative uncertainty is much lower level as compared to the corresponding coefficients from resistance prediction. Due to action of propeller, the flow characteristic is more accelerated near the stern of the ship with much reduced vortical/separated flows. Another interesting point is a large increase of pressure force component. This is due to suction of the flow by the propeller, due to the pressure near stern area decreases resulting in the increase of the pressure force component.

The observed order of grid convergence accuracy for all predicted self-propulsion factors and force components are shown in Fig. 4. Monotonic convergence is ob-tained; pG/pG,this around 1.4 for all force coefficients, but between 0 and 1 for all

propulsive factors. The estimated grid uncertainty UG%S1= 15% and 12% for KT

and KQand <1% for rps.

The present study indicates monotonic convergence for all integrated quantities; the estimated order of accuracy is higher than second order for force coefficients but more likely to be first order for self-propulsion factors.

4. Test hull

The selected test ship is a 42 m beam Aframax product carrier representing the state of the art in design today.

Fig. 4. Convergence of force coefficients and self-propulsion factors as function of grid refinement ratio. (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/ISP-130092.)

4.1. Ship hull

Main geometrical particulars of hull for PSS design are summarized in Table 3. For proprietary reasons the exact lines can not be shown, but a perspective view of hull is given in Fig. 5.

Table 3

Main dimension parameters, DSME Aframax product carrier

Hydrostatics Design Ballast

Length between perpendiculars LPP [m] 240.00 240.00

Beam B [m] 42.00 42.00 Draft, fore T_F [m] 13.60 6.70 Draft, average T_M [m] 13.60 7.45 Draft, aft T_A [m] 13.60 8.20 Waterline length LWL [m] 244.40 237.71 Beam in waterline BWL [m] 42.00 42.00 Volume V [m3] 114300 58807

Wetted surface SHULL [m2] 14494 11073

Fig. 5. Perspective view of hull geometry.

4.2. Propeller

The propellers tested is fixed, right turning, four bladed propellers with a diameter of 7.3 m. The propeller geometrical properties can be found in Table 4.

4.3. PSS

Various energy saving devices can be applied, but the practically applicable de-vices should be simple, relatively cheap to install, easy to maintain and most im-portantly, the ESD design should have a solid scientific back ground. The pre-swirl stator (PSS) is a device mounted on the stern boss just upstream of the propeller (see Fig. 6 or Fig. 33). It is designed to generate a pre-swirl flow into the propeller in order to gain a favorable interaction with the propeller action that improves the propulsive efficiency and results in a power reduction.

Table 4

Propeller geometrical parameters

No of blades 4

Diameter [m] 7.3

Hub diameter [m] 1.168 Expanded blade area ratio 0.513 Pitch ratio at 0.75R 0.637 Mean pitch ratio, P/D 0.637

Fig. 6. PSS model set-up for CFD computation. (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/ISP-130092.)

5. Numerical computation

Resistance and self-propulsion simulations were made at design speed and draft conditions in model scale as given in Table 5.

Assuming that the effect of free surface on wake flow is rather small, all computa-tion made are restricted to double-model flow in which the free surface is assumed to be flat and treated as a symmetry plane. In the self-propulsion simulation, the towing force Ra is applied and the propeller rpm adjusted until the self-propulsion point is reached; i.e. the propeller thrust force produced by propeller plus towing force may balance the resistance force (the increase of the resistance force acting on the hull due to the propeller suction in the self-propulsion situation). The towing force is based on model–ship correlation, roughness allowance and wave resistance correction.

5.1. Grid topology

Computations were performed using zonal approach; XCHAP is used only for the stern/wake flow part and XBOUND for the thin boundary layer flow calculation around the forebody. In stern/wake flow computation, the overlapping grid technique [16,17] with structured components was used to achieve high quality cells for the background hull and appendages. As illustrated in Fig. 6, the grids consists of one background grid (covering the whole fluid domain) with an additional overlapping refinement grid covering the stern of the ship and six overlapping component grids for four pre-swirl stator blades, one propeller and one rudder.

Table 5 Computation condition

Draft [m] T_d= 13.6

Mean draft [m] T_M = 13.863

Trim angle α_H1=−0.1258◦

Ship speed Vs [knots] Vs = 15.0 Froude number (based on LPP = 239 m) Fn = 0.1594 Reynolds number (based on LPP = 239 m) Re = 8.462· 106 Wetted surface as set in Towing tank [m2] WSA = 14,494

Towing force [N] Ra = 14.48 N

6. Simulations

The simulations were carried out in several steps. Performance of base line hull form (hull + propeller + rudder) was evaluated first and was used for reference in comparison of power reduction with PSS. The PPS computations were made for a base PSS configuration with the 4 blades initially set at what was tentatively expected to be the optimum configuration. Thereafter the base configuration was optimized through systematic variation study with five design parameters. Full scale simulation was completed with the finally selected PSS configuration.

Predicted flow quantities include resistance, wake and propulsion factors (thrust, torque and rpm) in model scale. The evaluation of propulsion performance was made by comparison of the value of Qn(torque× rpm).

6.1. Base line hull simulation without PSS

6.1.1. Resistance

The predicted resistance components are compared with the test results in Fig. 7. The total resistance is slightly under predicted with a deviation of 2.75%.

6.1.2. Wake

The predicted model scale wake at Vs = 15.0 knots is compared with measured wake at the propeller plane in Figs 8 and 9. In the comparison the predicted wakes are shown in the left and the measured wake to the right.

In general the calculation predicts the wake flow characteristics well in several aspects. Both calculations and experiments indicated that the fluid moves in upward and inward direction and forming a pair of bilge vortices. The center position of bilge vortices is well predicted. Some minor difference can be seen in the upper (345◦–15◦) and lower part (150◦–210◦) close to the symmetry plane. The longitu-dinal bilge vortical flow predicted in upper part is not strong enough while much stronger wake is predicted at the shifted position in upper direction in the computa-tion. Possible reason for this is stair case representation of HO type grid around stern contour line.

Fig. 7. Resistance coefficient. (Colors are visible in the online version of the article; http://dx.doi.org/ 10.3233/ISP-130092.)

Fig. 8. Comparison of total nominal wake at propeller plane, left: SHIPFLOW prediction, right: experi-ment.

6.1.3. POW

The open water characteristics of the propeller were calculated at a wide range of advance ratios from J = 0.2–0.7. The computed results are compared with the mea-surement data in Fig. 10. It is observed that the thrust and torque are well predicted for most frequent operating range between J = 0.4 and J = 0.6, but under predicted for lower J than 0.2.

6.1.4. Self-propulsion

The calculation was started from the converged solution from resistance compu-tation. The predicted thrust and torque coefficient are well within 5.4% and 10.6% deviations for thrust and torque from the measured one (see Fig. 11).

Fig. 9. Comparison of total wake fraction and transversal velocities, left: SHIPFLOW prediction, right: experiment. (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/ISP-130092.)

Fig. 10. Comparison of POW characteristics. (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/ISP-130092.)

The under prediction of T and Q can be partly explained by the fact that the applied towing force in the simulation is somewhat higher than the required and this may result in light propeller loading condition when obtaining force equilibrium by adjusting the propeller rpm during self-propulsion iteration. In the simulation, the towing force applied is RA= 13.532 N (towing force coefficient Ctow= 1.212·

10−3), which is obtained from model-full scale skin friction correction (Ca= 1.749·

10−3) and wave resistance correction (Cw= 0.0626· 10−3).

It should also be mentioned that the propeller diameter is different in the measure-ments and computations: the measure wake is made based on 7.4 m propeller while the computation is made for 7.3 m propeller.

Fig. 11. Self-propulsion simulation results, model scale. (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/ISP-130092.)

6.2. Base PSS configuration simulation

A base reference computation was made for the base PSS configuration selected; the 4-bladed stator was initially set at what was tentatively expected to be the opti-mum combination of blade pitch angles (Fig. 6). As can be seen in the figure, the base PSS configuration has one center blade mounted horizontally on the starboard side (denoted as SC) and three on the port side. The port side blades are mounted at 45◦ intervals; one in upper side (denoted as PU) and another one in lower side (denoted as PL) from center blade (denoted as PC), which is mounted horizontally. The effect of PSS on the improvement of propulsion efficiency was investigated in detail analysis of local flow quantities around the stator blades.

6.2.1. Resistance

Resistance is computed only for the base configuration and compared with the bare hull resistance. Very small but practically no increase in resistance is made by the stator less than 0.6%.

6.2.2. Self-propulsion

The evaluation of propulsion efficiency is made by comparison of Qnvalue in

model scale. The predicted Qnvalues are given in Fig. 12. The computation indicates

that 2.8% power gain can be achieved by adding the PSS.

6.3. Hydrodynamic effect of PSS

The gain in propulsion efficiency achieved can be explained by the increase of angle of attack of inflow to the propeller, caused by an increased wake fraction and counter-rotating pre-swirl flow generated by the PSS. These effects will be examined further in the following sub-sections.

Fig. 12. Comparison of Qnvalue for bare hull and base PSS configuration. (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/ISP-130092.)

6.3.1. Pre-swirl

Velocity distributions predicted by resistance simulation with and without PSS are compared at different planes; Xc(at the center of the PSS chord) in Fig. 13 and Xp

(propeller plane) in Fig. 14. A favorable change in tangential velocities is noted in Fig. 14, where more counter-rotating swirl is generated by the PSS. In the bare hull case, the water flows in upward and inward direction and forming a pair of bilge vortices. The effect of the PSS is visible in the right side of Figs 13 and 14; the port bilge vortices are disappeared and tip vortices are generated from the four PSS blades. Flow separation is visible on the inner part of the starboard blade.

Figure 15 shows the tangential velocities in r/R = 0.4 and r/R = 0.8, as an example (positive values means clockwise rotating flow, looking forward). With a right turning propeller, negative (or decreasing) tangential velocities means a flow that rotate in the opposite direction to the propeller slip stream, i.e. pre-swirl. Fig-ure 15 indicates that for the investigated case, the tangential velocities decreases (i.e. pre-swirl is produced) in the entire inner part, and mainly on the port side at the outer radii in the propeller disk. The resultant net effect is an increase of the pre-swirl for all radii, as shown in Fig. 16.

The effect of the pre-swirl is clearly illustrated in Fig. 17, which shows a compar-ison of the rotational velocity behind the propeller from self-propulsion simulations with and without PSS. The asymmetry of the contours can be observed, where the rotational velocity component at the starboard side is nulled by the propeller-induced tangential velocity. This is the reason why only one blade is placed in starboard side. It is clearly noted that the loss of rotating energy is considerably diminished by the stator, also illustrated by Fig. 18, which shows the decrease in transversal velocity.

6.3.2. Wake

Another favorable change is seen in the color contour plots in Figs 13 and 14, where the velocity magnitude in the propeller plane is de-creased by the presence of the PSS. This is mainly due to the reduction of the axial component. The mean

Fig. 13. Velocity distribution at Xc, left: bare hull, right: base PSS (resistance simulation). (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/ISP-130092.)

Fig. 14. Velocity distribution at Xp, left: bare hull, right: base PSS (resistance simulation). (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/ISP-130092.)

axial wake fractions computed from resistance simulation are 0.62 for the bare hull without PSS and 0.68 for PSS.

6.3.3. Angle of attack

The flow ahead of the propeller for the case without PSS is of course symmetric, but the blade angle of attack is higher on the starboard side than on the port side as propeller rotates clockwise direction. Thus the propeller performs more efficiently while rotating on the starboard side. In the propeller slip stream, the up and inward flow is cancelled on starboard side while the transverse rotation velocity is increased on port side. This phenomenon can be seen in velocity vector plot behind the pro-peller (Fig. 20).

Figure 20 shows how the PSS changes the flow direction to the propeller blades (r/R = 0.7 is shown in the figure as an example). Such a favorable change for the present case is registered on the entire part for the inner radii (Fig. 15 top) and mainly on the port side for the outer radii in the propeller disk (Fig. 15 bottom).

The resulting approximate angle of attack on the propeller blades are shown in Fig. 21 for radii 0.4 and 0.8 (taking into account propeller pitch, rate of revolution and induced velocities from the propeller blades). It is seen that the angle of attack

Fig. 15. Tangential velocity from resistance simulation, top: r/R = 0.4, bottom: r/R = 0.8. (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/ISP-130092.)

increases almost everywhere with the PSS. For the inner radii on the starboard side, the favorable effect does not come from the change in tangential velocities, but from the reduction of the axial velocities. This is the area where the PSS blades separate, which gives a decrease of axial velocity, as seen in Figs 13 and 14. The mean angle

Fig. 16. Mean tangential velocities (resistance simulation). (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/ISP-130092.)

Fig. 17. Transversal velocity distribution at X_B (1.9 m behind propeller position), left: without PSS, right: with base PSS (self-propulsion). (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/ISP-130092.)

of attack versus radii is shown in Fig. 22. By increasing the angle of attack to the propeller, it can deliver the same thrust at a smaller rate of revolution. This results in higher propulsion efficiency. However, a practical limitation which has to be consid-ered is the lower rpm limit of the engine. The propeller pitch has to be decreased to get a proper power-rpm matching.

Figure 22 shows that there are larger variations of propeller angle of attack with the PSS compared to the bare hull case. This may result in unwanted propeller cavitation induced problems – erosion as well as vibration/noise, which should be investigated carefully with cavitation tunnel tests.

Obviously, an increase in resistance when fitting a PSS is also an unfavorable effect, but the increase is smaller than 0.6% (0.1% by PU and SC blades, 0.2% by

Fig. 18. Difference in transversal velocity between base PSS and no PSS. (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/ISP-130092.)

Fig. 19. Velocity distribution at X_B(self-propulsion, bare hull). (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/ISP-130092.)

PC and PL blades).

The PSS design should be done based on optimum trade-off between the power reduction (favorable effect) and maximum allowable resistance increase/cavitation risk.

6.3.4. Effect of propeller on PSS

Figure 23 shows the local flow around stator PU with resistance and self-propulsion computation respectively. It is quite evident that the propeller induced flow strongly affects the flow over the stator as mainly the axial velocity component over the stator is increased especially close to the root of the stator. The wake behind the stator blade is therefore also affected. For that reason examining the flow over and behind the stator using only resistance computations is not sufficient.

Fig. 20. Angle of attack on propeller, top: port side, bottom: starboard side. (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/ISP-130092.)

Figure 24 illustrates the importance of including the suction effect of flow by propeller when analyzing flow characteristics around stator blades. On the pressure side (bottom pictures) of all portside blades the difference in Cp(dynamic pressure

Fig. 21. Propeller blade angle of attack from self-propulsion simulations, top: r/R = 0.4, bottom: r/R = 0.8. (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/ISP-130092.)

pressure zone indicating the risk of flow separation is much higher with an acting propeller than without. This is due to the change in angle of attack and increase of axial flow velocity as the propeller accelerates the flow.

7. Optimization

Starting from initial PSS configuration, optimization was carried out through a variation of the following five design parameters:

Fig. 22. Mean propeller blade angle of attack (self-propulsion simulations). (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/ISP-130092.)

Fig. 23. Velocity contours and streamlines on PU (base PSS), left: resistance, right: self-propulsion. (Col-ors are visible in the online version of the article; http://dx.doi.org/10.3233/ISP-130092.)

• No of stator blades; • Diameter of stator blade; • Angular position of stator blade; • Stator blade pitch angle; • Twisted stator blade.

All design parameter variations investigated are summarized in Table 6. The de-sign parameters were systematically varied for one parameter at a time. The optimum configuration of PSS is determined based on comparison of the propulsion perfor-mance index Qn(torque×rpm). Once the best PSS configuration was found for each

parameter setting, the parameter were kept for the remainder of the simulations. Obviously using a formal optimization, for example generic algorithm, would have been beneficial as the above described procedure does not couple the

param-Fig. 24. Cpon port side blade. Resistance (left), self-propulsion (right). Top: suction side, bottom: pressure side. (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/ISP-130092.)

eters. However, the considerable CPU time required for each parameter set renders such an approach not feasible within a reasonable time frame.

7.1. Optimization – No. of stator blades

Stators with three to six blades have previously been investigated on single screw ships over the years. The stator configuration selected as the base PS configuration for the present optimization study has four blades.

As the propeller rotates in the clock wise direction, the propeller blades meet favorable counter rotating flow when rotating on the starboard side due to an up-ward flow generated from stern of the ship. This led to a basic question whether the starboard stator contributes with any efficiency gain and further investigations were made for four different configurations as listed in Table 6.

The predicted Qnvalue is presented in Fig. 25. The computation results indicate

Table 6

All PSS configurations investigated through five design parameters variation study

PSS PU PC PL SC Remarks

No of stator blades 1 Y Y Y Y Initial configuration 2 Y Y Y N No starboard stator blade 3 Y Y Y H Half size of starboard blade

4 N Y Y Y No PU stator blade

Diameter 11 Y Y Y Y D_S= 0.9D_P

12(1) Y Y Y Y D_S= 1.0D_P

13 Y Y Y Y D_S= 1.1D_P

14 Y Y Y Y D_S= 1.2D_P

Angular position 21 345◦ 300◦ 255◦ 120◦ Rotated by 30◦clockwise 22 330◦ 285◦ 240◦ 105◦ Rotated by 15◦clockwise 23(1) 315◦ 270◦ 225◦ 90◦ Initial configuration 24 300◦ 255◦ 210◦ 75◦ Rotated by−15◦clockwise Stator pitch angle 31 −8 0 0 0 PU stator blade pitch angle variation

32 −4 0 0 0

33(1) 0 0 0 0

34 4 0 0 0

35 0 −8 0 0 PC stator blade pitch angle variation

36 0 −4 0 0

37 0 4 0 0

38 0 0 −8 0 PL stator blade pitch angle variation

39 0 0 −4 0

40 0 0 4 0

41 0 0 8 0

42 0 4 4 −8 SC stator blade pitch angle variation

43 0 4 4 −4

44 0 4 4 0

45 0 4 4 4

46 0 4 4 8

Twisted blade 51 Y Y Y Y Twisted all portside blade

52 Y Y Y Y Twisted starboard blade

33 Y Y Y Y Best from PU/PL variation

40 Y Y Y Y Best from PC variation

44 Y Y Y Y Best from SC variation

Note: Positive sign for the change of pitch angle is defined as the angle of attack of the flow to the stator blade become larger.

Fig. 25. Comparison of Qnvalue for various starboard side stator configurations. (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/ISP-130092.)

concluded from this study that four stator blades seem to be good choice for further optimization study.

7.2. Optimization – Diameter of stator blade

The next optimization study was to find an optimum diameter of stator blade. The influence of diameter of stator blade (DS) is investigated by increasing or reducing

the diameter from initial stator configuration, which is equal to propeller diameter (DP) by 10% and 20% as shown in Table 6.

The result of self-propulsion simulation made is presented in Fig. 26. It can be seen that the stator blades with a size similar to propeller diameter seem to be opti-mum. Considering possible risk of unfavorable influence of stator blade tip vortex on propeller cavitation for the case of PSS 11 and possible increase of resistance due to 10% larger diameter of stator blade for the case of PSS 13, the PSS 12 was selected for further optimization study.

7.3. Optimization – Angular position of stators

Another design parameter investigated is the angular position of the stator blade. A systematic variation of angular position was made by rotating stator blades from original position; all blades rotated clockwise by 15◦and 30◦for PSS 21 and PSS 22, while rotated counter clockwise by 15◦for PSS 24 as listed in Table 6.

The influence of angular position of stator blade on propulsion efficiency is pre-sented in Fig. 27. The predicted Qn value is quite sensitive to angular position of

stator blade especially the port side stator rotated to lower part from the original position. On the other hand, no practical differences in the predicted Qnvalues are

noted when rotated in clockwise direction. It can be concluded that the initial angular position of stator is still the optimum.

Fig. 26. Comparison of Qn value due to diameter variation of stator blade. (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/ISP-130092.)

Fig. 27. Comparison of Qnvalue due to the change of angular position of stator. (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/ISP-130092.)

7.4. Optimization – Stator blade pitch angle

Systematic variation of pitch angles of stator blades was made for self-propulsion simulation to find an optimum pitch angle starting from the initial stator configura-tion. Blade angles were systematically varied for one blade at a time. Once the best angle was found for a blade that angle was kept for the remainder of the simulations. Total sixteen stator blade pitch angle variations was investigated as listed in Table 6 and the predicted Qnvalues are compared in Fig. 28.

Although the difference in Qnis somewhat small, the comparison study clearly

indicates the likely optimum range of pitch angle for each stator blade. The initial pitch angle turns out to be rather close to the optimum and the best five are those who has the same or 4◦ reduced pitch angle of port side stator blade while having the base pitch angle setting for starboard center stator blade. The initial pitch angle

Fig. 28. Comparison of Qnvalue for all stator blade pitch angle variation. (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/ISP-130092.)

Fig. 29. Velocity distribution at X_C(left) and X_P (right) from resistance simulation, PSS 46. (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/ISP-130092.)

for SC stator blade seems to be the optimum and any increase or decrease of the pitch angle does not give any further improvement.

Comparative plots of the wake for the stator configuration with the largest pitch angle variation relative to the base stator (PSS 46 from Table 6) is shown in Fig. 29. Comparing with Fig. 13, no significant difference but some noticeable change in local flow behind the PSS can be found. As can be seen in the figure the blades produce more lift as pitch angle increases. Much stronger tip vortices are generated from all four PSS blades and some change of flow direction due to lift generated by high pith angle can be seen in Fig. 29. The inner part of starboard stator blade produce high lift with large separated flow behind.

However the change of wake flow due to high lift pitch angle is not favorable direction. The counter-rotating tangential velocities are decreased in starboard and lower part of port side. The reduction of axial wake is not as much as pitch angle increase (mean wake fraction is 0.599 for base PSS while 0.606 for PSS 46).

Fig. 30. Velocity and streamline trace from resistance simulation, left: base PSS, right: PSS 46. (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/ISP-130092.)

Figure 30 show a comparison between local stator flow for the base PSS and the PSS 46. It should be noted that the streamlines are projected to their respective planes and as such does reflect the actual flow exactly.

In the above plots the complexity of the flow around the stators can be observed. The lift is inversed as move along the stator blade from the root to the tip. At the root clearly detached flow exists below the stator, while the same flow feature is seen above the blade at the tip.

Proper alignment of the blade is therefore important to create a desirable lift, but also to ensure that cavitation and vibration is not occurred both on the stator and the propeller blades due to separated flow originating from the stators.

7.5. Optimization – Twisted stator blade

An overall assessment for port side stator is that three stator seems to be effec-tive and contribute 60–70% of the total power gain achieved. As pointed out in the previous section, the lift developed by the outer part of the blades is a little bit too excessive while no significant effect on lift by the inner part of the blade is created. This brought an idea with twisted pitch angle (linearly varying from +4◦at the root to−4◦at the tip relative to the initial constant pitch angle) especially for port side stators. The computation indicated this is the way to go for further improvement: without putting any special efforts, most promising result can be obtained for the first twisted portside PSS (see PSS 51 in Table 6) as can be seen in comparison made with the best configurations of each port side blade (see Fig. 31). However, no further investigation was made on this idea as this is not preferred by DSME due to practical difficulties foreseen during manufacturing of stator blades.

8. Confirmation by model testing

Based on the evaluation of power gain and detailed analysis of flow characteristics four PSS configurations are selected and tested in the towing tank. The four selected for confirmation by model testing are PSS 32, 34, 40 and 44, which are marked in red

Fig. 31. Comparison of Qnvalue of twisted portside stator blade. (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/ISP-130092.)

Fig. 32. Comparison of Qn for PSS configurations investigated from optimization study. (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/ISP-130092.)

in the Fig. 32. The four configurations are selected among the better than average, but sufficiently wide variation in PSS configurations in order to investigate if the same conclusion can be obtained from model tests in the relative ranking made by comparison of propulsion performance Qnindex from SHIPFLOW simulation.

A scaled ship, propeller and stator model were manufactured (see Fig. 33) and confirmation tests have been performed at SSPA’s towing tank (L = 260 m, B = 10 m, D = 5 m). The comparative measurements were made at Vs = 15.0 knots and design draft Td = 12.5 m with the same set-up of the model during the same

day. Test methods and calculation principles for the resistance and self-propulsion tests were made according to ITTC 78 method and full scale performance prediction of the test results are made based on ITTC 99 method as described in model test report [18].

Comparison is made for all tested PSS configurations in Figs 34 and 38. Figures 34 and 35 illustrate very good correlation between SHIPFLOW simulation and model test results in relative ranking of Qn. Although SHIPFLOW predicted lower Qn

than the measured one the ranking is correct and so the comparison of Qnshould be

useful for selecting the best configuration between various alternative designs. It is also quite promising to see from Figs 36–38 that reasonable correlation is achieved not only Qnbut also all propulsion quantities (T , Q and rps).

Fig. 33. PSS mounted on a ship model for towing tank testing. (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/ISP-130092.)

Fig. 34. Comparison of propulsion performance index Qnfor the selected PSS configurations. (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/ISP-130092.)

Fig. 35. Comparison of propulsion performance index Qnfor the selected PSS configurations. (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/ISP-130092.)

9. Further refinement of propeller and PSS design

Further design improvements have been made through a new propeller design and PSS configuration.

Fig. 36. Comparison of thrust T , model scale. (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/ISP-130092.)

Fig. 37. Comparison of torque Q, model scale. (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/ISP-130092.)

Fig. 38. Comparison of propeller revolution, model scale. (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/ISP-130092.)

First a refinement of propeller design was made in order to increase 3–4% rpm for correcting the rpm reduced by introduction of PSS. The graphical comparison of the predicted POW efficiency of two propellers P1 (original propeller) and P2 (new propeller design) is made in Fig. 39.

After due consideration of propeller cavitation performance, the portside upper stator blade is removed and three stator blade with reduced pitch angle was selected as the final design. Very small increase (0.5%) in resistance is made as can be seen in Fig. 40, which is mainly due to increase of viscous pressure resistance of the stator blades.

The predicted wake for the final selected PSS design is compared with the mea-sured wake at propeller plane in Figs 41 and 42. Comparing with the base hull wake

Fig. 39. Comparison of POW characteristics of P1 and P2 propellers. (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/ISP-130092.)

Fig. 40. Resistance coefficients for final PSS, model scale. (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/ISP-130092.)

in Figs 8 and 9, the change in wake flow characteristics due to the final PSS is fairly well predicted and fair comparison can be made with the measured wake, although all small details in peak to peak wake variations behind portside stator blades are not accurately captured in Fig. 43. This indicates that the no. of grid (5.4M cells) used is still not sufficiently fine enough in order to capture such a detail change of flow characteristics.

The power reduction achieved from design improvements of propeller and PSS configurations is demonstrated in Fig. 44. Total improvement predicted by SHIPFLOW is 4%, which is somewhat under predicted than the model test predic-tion (5.7%).

As discussed earlier the change in wake by PSS is in favor of propulsion efficiency, but the large reduction of axial velocities (see Fig. 42) will lead to sudden increase of propeller blade angles of attack and this may be resulted in unwanted propeller cavitation induced problem.

Fig. 41. Comparison of total nominal wake of the final PSS at propeller plane, left: SHIPFLOW prediction, right: experiment.

Fig. 42. Comparison of total wake fraction and transversal velocities, left: SHIPFLOW prediction, right: experiment. (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/ISP-130092.)

The cavitation tests were performed with special care for two loading conditions corresponding to NCR power at design and ballast draft with 15% sea margin. The test program comprised cavitation observations, pressure pulse measurements and cavitation erosion tests. The propeller was subjected to erosion tests at ballast MCR condition without sea margin for an extended time of 60 min. This is extreme test condition for the propeller considering the fact that ballast NCR for a testing time

Fig. 43. Comparison of circumferential distribution of total wake fraction, left: SHIPFLOW prediction, right: experiment.

Fig. 44. Power reduction. (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/ ISP-130092.)

of 30 min is SSPA standard procedure. The cavitation test results showed that the propeller is entirely satisfactory in cavitation performance (see Fig. 45): the pressure pulse values are moderate and no vibration problems due to propeller excitation are expected. And further the erosion tests did not show any indication of erosion [15].

10. Full scale performances

In order to make sure that the final PSS configuration confirmed from model tests/model scale CHAPMAN simulations could still be an optimum in full scale

Fig. 45. Cavitation extension at ballast NCR condition. (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/ISP-130092.)

Fig. 46. Resistance coefficients for final PSS, full scale. (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/ISP-130092.)

operation, full scale simulations were performed for the base hull with and without the final PSS configuration.

10.1. Resistance

The predicted resistance components for the base hull with and without PSS are presented in Fig. 46. The increase in resistance by PSS is larger (2.4%) in full scale than in model scale (0.5%).

The predicted resistance of appendage in model and full scale is compared in Fig. 47. This is mainly due to the fact that the PSS operates in a flow field where a larger part of the stator is experiencing close to free stream velocity due to the more concentrated wake in full scale.

10.2. Wake

The predicted full scale wake with and without PSS is compared in Figs 48 and 49. Comparing the model scale wake in Figs 8 and 9 and Figs 41 and 42, no hooks were

Fig. 47. Resistance increase of appendages in full scale. (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/ISP-130092.)

Fig. 48. Comparison of computed nominal wake in full scale, left: bare hull, right: final PSS.

noted and the small separation below the stern bulb noted in the predicted wake contours at full scale.

Figures 50 and 51 shows velocity distribution at model scale (left) in comparison to full scale (right) from resistance simulation for the final PSS. The boundary layer is relatively thinner in full scale. It is clearly seen that the bilge vortical flow in the upper part and separated flow in the lower part of propeller disk, which occurred in model scale, but not occurred and/or occurred over the small region in full scale. Other noticeable difference is the stronger vortical flows generated in the outer radii of the two port side stator blades, which can be responsible for the increase of drag. On the other hand, the detached flows at the inner radii of all blades (especially starboard center) become smaller in full scale.

Velocity distributions from self-propulsion simulation are given in Fig. 52. The suction effect of the propeller can clearly be seen; the boundary layer becomes even

Fig. 49. Comparison of total wake fraction and transversal velocities at propeller plane, left: bare hull, right: final PSS. (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/ ISP-130092.)

Fig. 50. Velocity distribution at Xcfrom resistance simulation for final PSS, left: model scale, right: full scale. (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/ISP-130092.)

thinner and a large acceleration of axial velocity occurs on the starboard side. The strong vortical flow still remains at the outer radii of all stator blades. This indicates again that the idea of twisted stator blade (linearly decreasing pitch angle in the inner radii and increasing in the outer radii) could work in full scale as well.

10.3. Self-propulsion

The evaluation of propulsion efficiency in full scale is made by comparison of Qn

value in the similar way as in model scale and presented in Fig. 53. The computation indicates 3% power reduction can be achieved by the final PSS as compared to the bare hull.

Fig. 51. Velocity distribution at Xpfrom resistance simulation for final PSS, left: model scale, right: full scale. (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/ISP-130092.)

Fig. 52. Velocity distribution at Xc(left) and Xp(right), from full scale self-propulsion simulation for final PSS. (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/ISP-130092.)

It is very promising results confirming that hydrodynamic effects of PSS on the improvement of propulsion performance are fully working in full scale as well as model scale. The 3% power reduction can be explained by increase of angle of at-tack as shown in Fig. 54. The increase in mean angle of atat-tack is quite comparable between model and full scale.

This can be clearly seen from the comparison of transverse velocity distribution shown in Figs 55 and 56. The loss of rotational energy is considerably diminished by the PSS.

10.4. Full scale speed trials

The developed final PSS was fitted on the ships and a speed trial was performed in East-Southern sea of Korea on 16 January 2012, in good weather condition. The vessel was very close to the fully loaded condition with mean draft of 13.6 m at about even keel. The sea trial was performed by DSME [1] under inspection of ship owner and classification society. The sea trial results were analyzed according to ISO 15016 – Guidelines for the assessment of speed and power performance by analysis of speed trial data. The results of speed trial [1] showed that the vessel is performing around 0.25 knots better in comparison with the model test predictions.

Fig. 53. Power reduction estimated in full scale. (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/ISP-130092.)

Fig. 54. Mean propeller angle of attack (black: without PSS; red: final PSS). (The colors are visible in the online version of the article; http://dx.doi.org/10.3233/ISP-130092.)

11. Conclusions

In the present paper, a design optimization study of PSS for an Aframax product carrier has been presented from early design stage, SHIPFLOW simula-tion/optimization phase, and confirmation by model tests to validation through sea trial tests. Some interesting findings were obtained during the course of the work and the following conclusions can be drawn:

Estimation of numerical accuracy. SHIPFLOW has been applied for the

Fig. 55. Transverse velocity at full scale self-propulsion without PSS (left) and with PSS (right) at Xp. (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/ISP-130092.)

Fig. 56. Transverse velocity at full scale self-propulsion without PSS (left) and with PSS (right) at X_B. (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/ISP-130092.)

resistance, POW and self-propulsion simulation has been presented in the results of verification and validation exercise made for KCS (MOERI 3600 teu containership) with four geometrically similar grids. The V&V study indicates:

• monotonic convergence for all integrated quantities,

• the estimated order of accuracy is higher than second order for force

coeffi-cients,

• more likely to be first order for self-propulsion factors.

Hydrodynamic effect of PSS. The hydrodynamic effect of PSS was investigated

through a detail analysis of local flow characteristics and they can be summarized as:

• The gain in propulsion efficiency achieved is mainly due to the angle of attack

on the propeller blades are increased by the PSS.

• The increase of angle of attack is caused by an increased wake fraction and

counter-rotating pre-swirl flow generated by the PSS.

• The rotational energy in the slip stream is reduced with the PSS.

• The flow over the PSS is highly affected by the working propeller, therefore the

Optimization. A wide range of design parameter variation studies was performed

and the optimum configuration of PSS is determined based on comparison of Qn

index. Only four PSS configurations were model tested for validation purpose. Some concluding remarks are:

• The model test results confirmed the conclusion drawn from the SHIPFLOW

simulation in the relative ranking between four tested PSS configurations.

• This identical ranking indicates that the SHIPFLOW simulation can be used

with confidence in optimum design stage of ESDs.

• Power reduction by the PSS predicted with CFD simulations correlated well

with model test

Later studies have indicated that the magnitude of the ranking are quite sensitive to the grid resolution around the stators and an improvement of a factor 2–3 closer to the model tests have been achieved. The ranking does remain the same no matter the refinement level.

Power reduction achieved by final PSS. After further refinements were made with

propeller design and PSS configuration, the final PSS configuration was selected.

• The computation indicates that around 4% power gain can be achieved by the

final PSS as compared to the base line design, while somewhat larger gains were predicted by model tests (5.7%).

• The full scale computation confirms that hydrodynamic effects of PSS on the

improvement of propulsion performance are fully working in full scale as well as model scale.

• The sea trial showed that the vessel is performing around 0.25 knots better in

comparison with the model test predictions.

The final but most important conclusion drawn from the present study is that the design optimization of ESDs is now possible with current capabilities of SHIPFLOW simulation – resistance and self-propulsion. SHIPFLOW simulation coupled to model testing can be a cost effective approach to develop an optimum configuration of ESDs for the future.

12. Future work

An important recommendation for future work is to perform full scale simula-tion from the optimizasimula-tion phase to make sure that the optimum PSS configurasimula-tion obtained from model tests/model scale SHIPFLOW simulation could still be the op-timum in full scale operation.

Acknowledgements

This study was financially supported by Daewoo Shipbuilding and Marine Engi-neering Co., Ltd. The authors would like to express their sincere gratitude to DSME

for the productive cooperation and special permission to use the results from model and sea trial tests.

References

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