Numerical Analysis of the Propeller with Economical Cap by CFD
Yoshihisa Okada*, Kenta Katayama* and Akinori Okazaki*
Propeller Design department, Nakashima Propeller Co.,Ltd.
688-1, Joto-Kitagata, Higashi-ku, Okayama 709-0625, Japan
E-mail: yoshihisa@nakashima.co.jp - Web page : http: // www.nakashima.co.jp
1.Introduction
In recent years, the ship speed and the propeller load increase more and more. Especially, the tendency isremarkable at container ship. When the horsepower per unit area is 700-800 kW/m2 or more and the ship speed
is 22-23 knots or more, Mikael Grekula et al.1) pointed out that the rudder erosion should be occurred. JuergenFriesch2) described the causes of rudder erosion were propeller tip-vortex cavitation, propeller hub-vortex
cavitation and etc. and he introduced a new twisted rudder TW05 to reduce the risk of cavitation erosion in hispaper. However, it is considered that the cavitation of the propeller should be disappeared in front of the rudder.
Yamasaki et al.3) developed Non-Hub vortex(NHV) propeller. The features of this NHV propeller isconfirmed an increase in efficiency due to the decrease of the hub vortex. Special propeller caps with similar
characteristics are known, for example PBCF developed by Ouchi4) et al. Kawamura et al.5) investigated thecharacteristics of PBCF on model and full scale Reynolds number by CFD. Recently, there are special caps bysome manufacturers, however there are no published paper for design of these special caps by CFD.
This paper describes that the development of economical propeller cap for prevention of rudder erosion. Theauthors carried out the optimaization of economical propeller cap by CFD, and the performance of the propeller
with economical cap was confirmed by model test.
Keywords

CFD・Propeller・Economical Cap・Diffusion effect・Hub vortex・Rudder erosion

List of symbols

2.Analysis by CFD
2-1.Propeller Particulars and Analysis Models
MPNo.1&2 are analyzed by CFD, MPNo.1, has 6 blades, is for large container vessel and MPNo.2, has 5 blades,
is for bulk carrier. Table1 and Fig.1 show the propeller particulars and profile. MPNo.1 has the large blade areaand large skew angle and MPNo.2 has the small blade area and medium skew angle. These propellers aredesigned to confirm the difference regarding the performance of the propeller with cap by the difference ofpropeller profile.

MPNo.1

MPNo.2

Fig.1 Propeller Profile

RANS calculations are performed by SOFTWARE CRADLE SCRYU/Tetra Ver.10 which is a commercial CFD
code and is based on a finite volume method with an unstructured grid. The Shear Stress k-ω model is applied tothe turbulence model of the present simulations. The authors simulated the flow field around a propeller in nonuniform wake flow. The computational domain is composed of the inner rotational part including the propeller
and the outer stationary part. The stationary part and the rotational part are connected discontinuously. Constantvelocity and zero pressure are prescribed at the inlet and the outlet boundary, respectively. Fig.2 shows thecomputational domain. The numerical mesh is an unstructured grid, and basic cells are tetrahedral and prismatic
cells are applied to near the blade surface for resolving the boundary layer. The first layer thickness of the prismlayer was set to a non-dimensional wall distance for a wall-bounded flow (y+ in short) =1. The total number ofelements was about 32 million.

Fig2. Analysis Model for CFD

2-2.Analysis of General Propeller Caps
Firstly, the performance of the general propeller caps was analyzed by CFD. Fig.3 shows the profile of thegeneral propeller caps. The contraction type is typically used in many propeller manufacturers. Straight type anddiffusion type has sometimes adopted as countermeasure against hub vortex cavitation. In this analysis,Reynolds number is abt.2×106 considering calculation cost and scale effectContraction type

Straight type

Diffusion type

Fig.3 Profile of General Propeller caps

Fig.4 shows the pressure distribution behind the propeller caps by CFD result. The blue part represents the lowpressure which is the cause of the hub vortex cavitation. In MPNo.1, contraction type generates the low pressurepart behind the propeller cap. The low pressure part generated by straight type is smaller than contraction type
and the part by diffusion type is still smaller. Compared with MPNo.1, the low pressure part in MPNo. 2 issmaller. Namely, it is estimated that the hub vortex generated by 5blades propeller is weaker than the vortex by 6blades propeller. As well as MPNo.1, it is shown by Fig.4 that the reduction of the low pressure part by straightcap in MPNo.2. From above results, it can diffuse the hub vortex when the propeller cap is straight or diffusion
type. However, these propeller caps still generate large low pressure part.
Next, it was visualized how hub vortex is generated by CFD for design of economical cap.
Fig.5 shows the isosurface which represents the flow of tangential direction of a certain velocity. The flow
generated at trailing edge was concentrated at the center of propeller cap rear. If the concentration of tangential
flows is prevented, it is expected that the hub vortex is weakened. It is named “diffusion effect” in this paper. In
addition, it was confirmed that the low pressure part decreases on straight type or diffusion type due to diffusion
effect.

MPNo.1

MPNo.2Contraction type

Straight type

Diffusion type

Contraction type

Straight typeFig.4 Pressure distribution behind the Propeller caps (MPNo.1&2)

Fig.5 Visualization of Hub Vortex generation for MPNo.2
The authors confirmed the following items by numerical analysis of CFD.
1) The low pressure part on MPNO.1 has 6 blades is larger than on MPNo.2 has 5blades.
2) The cap of straight type or diffusion type can reduce low pressure part than contraction type by diffusion
effect.
3) Hub vortex is occurred by concentration of several tangential flows generated from propeller blade root.

2-3.Design of Economical Cap
It is important to prevent the concentration of the tangential flow at the center of the propeller cap rear for areduction of the hub vortex. Therefore, the design concept of an economical cap is prevention of theconcentration of tangential flows, and the authors designed three economical caps as follows. Fig.6 shows theprofile of the designed the economical caps.
Case-1 : Straight fins, and the end of fins is concentrated at the center of propeller cap rear.
Case-2 : Straight fins same as Case-1, and the end of fins is separated at the center of propeller cap rear.
Case-3 : Taper fins, and the end of fins is separated at the center of propeller cap rear.

Case-1Case-2Case-3Fig.6 Profile of Economical Propeller caps for MPNo.2
Fig.7 shows the isosurface of tangential flow visualized by same way of Fig.5 on the economical caps. In all ofthem, the diffusion effect is confirmed. In Case-1, weak hub vortex is occurred at the center of propeller cap rear,and the tangential flows are induced to the part of concentration of the fins at cap rear. Therefore, the authors
judged the edge of fins should be separated at the center of propeller cap for prevention of hub vortex. Fig.8
shows the pressure distribution of each economical cap, and the low pressure part (blue area) of each economical
cap is reduced than the general caps. The effect of reducing the low pressure part of the CASE-3 is higher thanCase-1 and Case-2. Therefore the authors designed the economical cap for MPNo.1&2 based on Case-3, andmade a comparison between the economical cap and the contraction type about the propeller characteristics withthose cap.
Fig.9 & 10 shows the comparison of the propeller characteristics with the economical cap and the contraction
type, and the components of KT & KQ of the propeller characteristics for MPNo.1&2. KT of propeller witheconomical cap is larger than with contraction type. Moreover, KQ is smaller. As the results, the propeller
efficiency became to increase. From the figure of the components of KT and KQ, the authors confirmed that KTof propeller cap increased and KQ of propeller cap decreased. In MPNo.1, KQ of the boss is decreased in a rangeof high J. Regarding the propeller efficiency, MPNo.1 is increased max.1.23% and MPNo.2 is increased
max.0.61 % by economical cap.
Fig.11 shows the pressure distribution of the propeller cap. The contraction type has the large low pressurepart (blue area) at the propeller cap rear. In the economical cap, the high pressure part (yellow and red area) on
the cap is increased by fins, and the low pressure part of the boss also reduced by economical cap.

Case-3Case-2Case-1

Fig.7 Tangential Flow of Economical caps for MPNo.2

Case-1Case-2Case-3Fig.8 Pressure distribution behind Economical caps for MPNo.2

Fig.9 Comparison of Propeller Characteristics for MPNo.1 (Economical/Contraction)

Fig.10 Comparison of Propeller Characteristics for MPNo.2 (Economical/Contraction)

Contraction type

Economical cap

Fig.11 Comparison of Pressure distribution of Contraction type and Economical Cap for MPNo.1

3. Confirmation by Model Test
3-1. Procedure of Model Test
Fig.12 shows the measurement equipment for economical cap. Model test was carried out by circulating water
channel in West Japan Fluid Engineering Laboratory Co., Ltd.. This model test was carried out at Reynolds
number of abt.4×105, and was adopted reverse POT for measurement of the characteristics of the propeller withcap.

Flow direction
Fig.12 Measurement Equipments for the Propeller Characteristics by Reverse POT

3-2. Model Test Results
Fig.13 shows the comparison of the propeller characteristics by model test results. In MPNo.1, the propeller
efficiency is increased max. 1.28% because Kt of economical cap is increased and KQ is almost decreased. InMPNo.2, the propeller efficiency is increased max.0.69% because KT is increased and KQ is slightly increased.
For the increase in propeller efficiency by model test, was almost the same as numerical analysis by CFD.
However, on MPNo.2, the difference tendency between model test and CFD regarding KQ was observed.

Fig.13 Comparison of Propeller Characteristics by Model Test (Economical/Contraction)
Fig.14 shows the photograph of flow visualization of the hub vortex. The flow visualization test by air injection
method was conducted to confirm the strength of the hub vortex. In comparison with the contraction types,
MPNo.1 generated strong hub vortex compared with MPNo.2. In the results of both propellers, the hub vortexwas disappeared on the economical cap.
MPNo.1

Contraction type

MPNo.2

Economical cap

Contraction type

Economical cap

Fig.14 Flow Visualisation Test for the Hub Vortex

4. Conclusions
In numerical analysis by CFD and the motel test, the authors were confirmed that the following.
1) Diffusion effect of the hub vortex by economical cap was confirmed by CFD and the model test.
2) The increase of total efficiency by the economical cap was confirmed by CFD and the model test.
According to CFD result, the effect of an improvement of the efficiency was by the fins on the economicalcap.
3) About the increase of efficiency by economical cap in model test, MPNo.1 was max.1.28% and MPNo.2
was max.0.69%. In addition, almost the same results could be confirmed by CFD analysis.
4) Therefore, it is expected that prevention of rudder erosion and improvement of efficiency by economicalcap.
After this, the authors will try the numerical analysis of economical cap including hull by CFD, and confirmation
the efficiency in actual operation.

5. References
1. Mikael Grekula and Per Lindell, “Cavitation EROSION Damage on Semi-Spade Rudders”, The Swedish Club
Letter 1-2007
2. Juergen Friesch, “RUDDER EROSION DAMAGES CAUSED BY CAVITATION”, CAV2006, Aug.,2006.
3. S.Yamasaki, “High Efficiency Propellers - NHV Propeller with Smallest Blade Area”, IPS’10, Apr.,2010.
4. K.Ouchi, “Effect and Application of PBCF(Propeller Boss Cap Fins)”, Journal of M.E.S.J., Vol.27, No.9,
1992.
5. T.Kawamura, “Model and full scale CFD analysis of propeller boss cap fins (PBCF)”, Journal of Marine
Science and Technology, Vol.17, Dec.,2012.