Hydro-elastic analysis of marine propellers based on a BEM-FEM coupled FSI algorithm

International Journal of Naval Architecture and Ocean Engineering.
2014.
Sep,
6(3):
562-577

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

- Published : September 30, 2014

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Marine propeller
;
Composite material
;
Fluid-structure interaction (FSI)
;
Boundary element method (BEM, Panel method)
;
Finite element method (FEM)
;
Steady state analysis
;
Unsteady transient analysis
;
Acoustic medium

INTRODUCTION

- Research background

A marine propeller operates in the complex flow field called the ship’s wake and the transition of flow angle of attack leads to rapid changes in pressure distribution on the propeller blade. As the trend of high power engines follows increases in vessel size, a marine propeller is being exposed to various risks including cavitation erosion, pressure fluctuation-induced vibration, underwater radiation noise, etc.
Compared with propellers made of metal, those made of composite materials - a combination of two or more physically / chemically heterogeneous materials - have superior properties for managing these risks. Composite materials are light weight, and have high stiffness and better sound absorption ability (
ITTC, 2005
). Despite their higher costs, the excellent manufacturing and maintenance ability of an additive production process is expanding the application of composite materials to all industrial areas, including aviation, environment/energy, information, electricity, automobile and household supplies.
Attempts are being made to use composite materials in the marine propeller blades of warships, submarines, and torpedoes for two reasons. First, composites can improve chance of survival because their good sound absorption ability reduces noncevitating propeller noise. Second, their blade deformation characteristics of the wake distribution delays cavitation inception and reduces cavitation volume. Their superior properties have led to their expanded application in yachts, tugs, and fishing boats. Composite materials also make it possible to reduce A/S costs for preventing heat damages in shaft systems, and to simplify the vessel stern structures due to their light weight - less than half the weight of Nickel-Aluminum-Bronze (NAB) alloy (
ITTC, 2005
).
The amount and geometry of a composite material’s deformation from the acting load can be controlled with different combinations of laminated material, stacking order, and ply angle. Thus, if its deformable characteristics can be properly considered at the design stage, a composite propeller can reduce fuel oil consumption in its operating profile compared with an NAB propeller which does not change shape (
Young, 2007a
;
2007b
;
2008
).
While recognizing these virtues, the difficulty is that it is not easy to accurately and practically simulate the hydro-elastic behavior of the composite marine propellers. These simulation difficulties act as a barrier to the accurate prediction of propulsion performance, initial geometry decisions, and strength evaluations at the propeller design stage.
- Previous studies

Inviscid numerical methodologies for calculating the flow field around propeller blades include the lifting line method, the lifting surface method (or vortex-lattice method, VLM), and the boundary element method (BEM). These inviscid methods are widely used in propeller performance prediction because of their short computing times and general usability. Computational fluid dynamics (CFD) analyses (RANS, LES, etc.) that consider the viscous effect tend to use a propeller flow analysis, which requires increased computing power. Even though the viscous flow analyses give a more accurate solution, BEM-based FSI analysis is performed in this study due to the considerations of computing time for the evaluation of propeller design applications.
The lifting line theory, proposed by
Prandtl (1921)
, and the VLM, which was applied to the propeller by
Kerwin et al. (1978)
, are useful methods for initial propeller design due to their ease of calculation. They have limitations, however, when considering three-dimensional blade geometry, BEM is introduced to achieve a more accurate FSI analysis. BEM, also called the panel method, was adapted to the propeller by dividing the potential basis and velocity basis methods of
Hess and Valarezo (1985)
,
Lee (1987)
,
Kerwin et al. (1987)
,
Hoshino (1989)
, etc. After
Lee (1987)
showed the excellent performance of the potential basis method, this method has been mainly used in the field of propeller analysis.
Hsin (1990)
and
Suh et al. (1992)
proposed the Kutta condition and
Greeley and Kerwin (1982)
and
Lee (1987)
introduced the flow-adapted grid to include a propeller wake roll-up model for improved convergence in the BEM analysis. These methods apply to the BEM code, KPA14, used in this study.
Various other numerical and experimental studies have also been conducted to analyze composite material (or elastomer) propellers.
Lin and Lin (1996)
simulated the elastic behavior of marine propellers in noncavitating conditions with a VLMFEM interaction.
Young (2007a
;
2008)
showed a hydro-elastic response of a composite propeller in steady/unsteady conditions by using BEM-FEM FSI and validated the results with model test results. In particular, Young’s study conducted BEM analysis to predict the hydrodynamic damping effect for unsteady behavior such as blade “fluttering” induced by a change in inflow conditions at the hull behind the wake field.
Chen et al. (2006)
evaluated the behavior of the composite marine propeller in four-cycle inflow conditions by performing model tests and a numerical simulation.
Motley et al. (2009)
and
Blasques et al. (2010)
studied optimum material stacking to improve propulsion efficiency and
Jang et al. (2012)
proposed a reverse engineering procedure for the initial design of an elastomer propeller considering blade deformation.
Lee et al. (2009)
,
Lee et al. (2012)
and
Lee et al. (2013)
have carried out the study of the relationship between manufacturing and performance of flexible (composite) propeller.
- Objective

The hydro-elastic analysis of a flexible marine propeller, which is a simplified orthotropic-homogeneous material model of a composite propeller, has been developed to accurately and efficiently predict the propeller’s propulsion performance and evaluate its strength. For practical use in the propeller design stage, the inviscid potential-based BEM code, KPA14, is used to calculate the loads on the blades. A commercial Finite Element Analysis (FEA) solver (Abaqus Standard) is introduced for predicting blade deformation and evaluating propeller strength. An interface between these two solvers is developed to analyze the hydro-elastic behavior of the composite-material propeller, and the accuracy and usability of the developed algorithm are confirmed by comparing our results with the model test results in previously published literature.
FORMULATION AND NUMERICAL METHODS

The flow field around the propeller blade, the structural deformation, and their relationship at the blade surface are numerically formulated for the FSI analysis to predict the performance of the marine propeller.
- Governing equation of the flow field around the propeller blades

As mentioned in the previous section, the potential basis analysis, from the studies of
Hsin (1990)
,
Suh et al. (1992)
,
Greeley and Kerwin (1982)
and
Lee (1987)
, are applied to analyze the steady or unsteady flow fields. We assume that the flow field consists of the three-dimensional closed boundary
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- S∞:Sblade+Shub
- p: point induced velocity potential is calculated
- q: point positioned singularity
- R( p; q): distance betweenpandq

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- Structural equations of motion for blade deformation

The equation of motion for the structural deformation corresponding to the propeller blade fixed coordinate is as Eq. (10),
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- Fluid-structure interaction

Assuming that deformation of the blade for the inflow variation is relatively large and that the change in the hydrodynamic characteristics due to geometrical alteration is not small, the FSI effect must be applied for the estimation on each hydrodynamic force and structural deformation. We propose using a two-way coupled FSI analysis that includes structural nonlinear analysis because the amount of blade deformation is not small to assume linear according to
Young (2008)
. To analyze strictly for the elastically vibrating response due to the changing flow field in the ship’s wake, the “wet” condition (considering not only hydrodynamic pressure distribution on blade but including hydrodynamic added mass/damping effect) must be considered. The acoustic fluid medium finite element model is adapted to consider this effect. This acoustic medium model was applied to ship hull vibration in contact with water by
Paik (2010)
.
Let the fluid field around propeller blade be compressible and inviscid then the equation of equilibrium is as follows:
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METHODOLOGY FOR HYDRO-ELASTICTY ANALYSIS OF A PROPELLER BLADE

Based on the formulated mathematical model, we implement a steady and unsteady transient FSI algorithm to predict the performance and evaluate the structure of the flexible propeller.
- Basic concept of FSI analysis

A basic interface structure of the two-way coupled FSI, shown in
Fig. 4
, consists of a BEM panel code (KPA14) for calculating the hydrodynamic force acting on the blade surface and a nonlinear FEM solver (Abaqus Standard) for calculating the structural deforming response, rotational body force (Coriolis force and centrifugal force), and added mass damping of the unsteady transient flow condition.
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- Process for initial geometry prediction

The pattern of blade deformation depends on the properties of the materials used in manufacture and the ply stacking condition such as the main orientation, as well as the loads acting on the blade. This means that the process of predicting the initial blade geometry, which is dependent on the materials and ply stacking conditions, requires that the design geometry be determined at given propeller execution conditions.
Assuming that the optimum geometry for the propeller design condition is the “A” blade and the flexible propeller is manufactured with this geometry and is in operation, its shape would be deformed to “B”. The “B” blade has completely different geometry than the optimal design in
Fig. 5
. Thus, the initial design process should be adapted to the geometry design of the marine propeller with the shape of the “C” blade, which is estimated by the reverse engineering method presented by
Jang (2012)
. Then, the blade would be changed to the target geometry for the existing driving conditions. The reverse engineering algorithm for blade initial design shown below
Fig. 6
.
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- Unsteady transient FSI procedure

Time domain-based FSI analysis of the propeller’s blade position in the wake field is required to more accurately predict the performance and evaluate the structural strength. Rotating blades in the nonuniform inflow flow field have a “fluttering” vibration behavior caused by the change in pressure distribution and blade deformation from the response of the pressure load on the surface. Unlike the aviation propeller and wind turbine blade which act in low density air, the marine propeller cannot ignore the damping effect of the added mass on the blade surface and vibrates in the ship’s wake. Thus, in this study, we considered the hydrodynamic damping effect of the added mass by applying the acoustic medium around the propeller blades.
To perform unsteady transient analysis (dynamic analysis of Abaqus Standard), it is impossible to carry out the prediction of deformed shape at
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VALIDATIONS

A comparison and review of experimental and computational results in the literature were conducted to verify the BEM-FEM-based steady and transient FSI analysis presented in this study. Since published references that contain both measured experimental data as well as the geometric/material properties of propellers is limited, the propellers validated in each analysis are different.
- Steady state analysis

Chen et al. (2006)
and
Young (2008)
present results for their experiments and FSI analysis of a six-bladed 610 mm diameter carbon fiber reinforced plastic propeller, manufactured at A.I.R. Fertigung-Technologie, GmbH in Hohen Luckow, Germany, and tested in the Naval Surface Warfare Center, Carderock Division (NSWCCD). In particular,
Young (2008)
conducted the validation of the proposed analytical method using the BEM-FEM FSI algorithm to compare the thrust, torque, and efficiency of a full-scaled open water model test for a “rigid” propeller P5471 and a “flexible” propeller P5479.
In this study, we validate this analytical method by comparing our results with
Young’s (2008)
experimental and analytical results for propeller P5479. The geometry of propeller P5479 is shown in
Fig. 8
. This is a useful exercise for our verification because this propeller has significant hydro-elastic behavior. Isotropic homogeneous material (not a real ply stack model) is applied in the analysis. The material properties extracted by
Liu et al. (2007)
are E
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- Unsteady transient analysis

A marine propeller operates in the complex flow field condition known as the ship’s wake. The composite material marine propeller, in particular, must undergo hydro-elastic response analysis for unsteady conditions because its shape changes according to the blade position in the wake. Therefore, consideration of its structural safety, such as the risk of delamination due to fatigue and accurately predicting its performance, cannot be ignored.
The damping induced by the hydrodynamic added mass significantly affects the elastic response of the propeller blade in water. Thus hydro-elastic analysis that considers the so called “wet” condition effect should be conducted. In the research of
Chen et al. (2006)
,
Young (2007a
;
2008)
, and
Motley et al. (2009)
, this elastic vibration effect was estimated using the potential- based BEM and the results were applied directly to the structural mass and damping coefficients.
In this study, however, the added mass effect is considered by adapting the acoustic medium field and applying it as a pressure component on the blade surface directly. We compare the results from our proposed method with the measured and calculated results of
Chen et al. (2006)
.
The propeller used in the analysis is a P5475 (
Fig. 10
), which deforms in actual conditions significantly enough to validate the analysis algorithm and the Laser Doppler Velocimetry (LDV) measured result of the pitch deformation published in
Chen et al. (2006)
. Material properties of the P5475 are E
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- Natural frequency analysis for dynamic stability evaluation

Natural frequency analyses of propeller P5479 rotating at 909RPM for “dry” and “wet” conditions are conducted and the analyzed natural frequencies of each mode are compared with the measured (“wet” condition, mode 1) and calculated results of
Young (2008)
in
Fig. 14
. And the blade shapes under “wet” conditions for each mode are shown in
Fig. 15
.
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CONCLUSIONS

Since a flexible (or composite material) propeller is affected not only by the pressure changes acting on the blade but also the body forces from the rotational motion, such as the centrifugal force, the Coriolis force, and the “fluttering” hydro-elastic behavior in wake field; it is not easy to predict the propulsion performance, the initial geometry with respect to deformation, and the structural strength at the design stage.
The BEM-FEM-based practical hydro-elastic algorithm for a flexible marine propeller is developed for blade and ply orientation design to address performance prediction and structural evaluation. The study contents are as follows:
- 1) BEM code does not consider viscous effect and effective wake. However, it still gives sufficient accuracy and short computing time to apply propeller design stage. Therefore BEM-FEM FSI methodology is proposed for practical application to flexible marine propeller design instead of the more elaborate CFD-FEM FSI analysis.
- 2) Panel code (KPA14) is used for hydrodynamic analysis to predict pressure loads on the propeller blade and a commercial FEA tool (Abaqus 6.12 Standard, Static and Dynamic option) is used for nonlinear analysis to calculate blade deformation and evaluate strength. An interface code is developed to connect these two analysis tools and perform FSI analysis.
- 3) A three-dimensional continuum shell element is introduced for the FEA, which has merits in its easy modeling of composite material ply and its ability to reflect the structural behavior of objects having three-dimensional geometry.
- 4) The hydrodynamic damping effect of added mass, which is induced by the elastic behavior of the propeller blade, are applied to the FEM for acoustic fluid mediums and as composing system equations of motion for pressure on the surface and the structural deformation of blade geometry, unlike existing studies.
- 5) A validation study for the proposed steady and unsteady transient algorithm for composite propeller FSI analysis is conducted by comparing our study results with published experimental and analytical results on flexible propellers composed of orthotropic-homogeneous materials. As a result, the usefulness of the proposed practical methodology was confirmed.

Acknowledgements

This research was supported partly by the Industrial Convergence Strategic Technology Development Program (No. 1004- 4499) funded by the Ministry of Trade, Industry and Energy (Korea).

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Citing 'Hydro-elastic analysis of marine propellers based on a BEM-FEM coupled FSI algorithm
'

@article{ E1JSE6_2014_v6n3_562}
,title={Hydro-elastic analysis of marine propellers based on a BEM-FEM coupled FSI algorithm}
,volume={3}
, number= {3}
, journal={International Journal of Naval Architecture and Ocean Engineering}
, publisher={The Society of Naval Architects of Korea}
, author={Lee, Hyoungsuk
and
Song, Min-Churl
and
Suh, Jung-Chun
and
Chang, Bong-Jun}
, year={2014}
, month={Sep}