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Fluid-structure interaction Simulation for Hydro-elastic Performance of marine Propeller at Full-Scale

In this study, CFD-FEM bi-directional fluid structure interaction (FSI) methodology using STAR-CCM+ is adapted for the hydro-elastic interaction simulation of the propeller at full-scale. To validate the FSI simulation reliabilities, the open-water curve of the rigid and NAB propellers VP1304 at model scale are computed. Then, the propeller KP505 is employed for the open-water test to study scale effect and hydro-elastic performance. The change of thrust coefficient, torque coefficient, efficiency, stress distribution, deformation are presented. From the results, the hydrodynamic difference due to scale effect and hydro-elastic performance are observed. Analysis of structural response of NAB propeller shows that scale effect plays a role.


INTRODUCTION
The hydrodynamic characteristics of propellers are usually studied at model scale and model openwater tests are regarded as an effective method to predict the performance of marine propellers at fullscale. For the limitations of the test condition, the rotation speed of the model propeller cannot be large enough, which inevitably lead to the Reynolds number of the model propeller far smaller than of the full-scale propeller. With the development of computer performance, full-scale CFD simulation receive more attention. Jung-Kyu Choi [1] computed model and full-scale propeller under the open-water condition using different wall treatments. Results shows that the wall function calculation as an efficient calculation is recommended for the full-scale calculation due to the large Reynolds number. Sun [2] performed DES calculations of the model and full-scale propellers VP1304 to analyze scale effect on the wake dynamics. All of this suggest that more efforts to directly estimate the performance On the other hand, under the effect of fluid pressure, the structure of blade undergoes deformation progress, which cause the change of longitudinal and skew angle. Propeller designers couldn't handle this situation by traditional theory and empirical methods because they all are based on a rigid blade. FSI methodology has been used to study the hydro-elastic performance. Young [3] studied hydroelastic performance of a composite propeller by a BEM-FEM method and model test. P. J. Maljaars et al. [4] carry out the non-uniform flow hydro-elastic analysis of the flexible propellers in cavitating and non-cavitating conditions, based on BEM-FEM method. Conventional boundary element method has a reasonable accuracy and computational efficiency, however BEM ignore effect of viscous flow, which has a limitation of prediction of blade boundary layer and wake region. Moreover, the effect of scale effect on propeller couldn't be calculated quantitatively. Cao [5] computed different materials of propeller VP1304 under the open-water condition using CFD-FEM method.
In this paper, Bi-directional CFD-FEM fluid structure interaction method is used for hydro-elastic simulation. STAR-CCM+ is used as a solver for FSI analysis. The results of simulation of model propeller VP1304 under the open-water test condition are compared with the experiment and FSI simulation result of Cao [5]. The rigid and NAB propeller KP505 at model and full scale is analyzed using Bi-directional CFD-FEM method.

NUMERICAL METHODS
In this paper, CFD simulation of rigid ones and FSI simulation of NAB ones under open-water condition using STAR-CCM+ solver. Sliding mesh and mesh morphing technique is used to evaluate the hydrodynamic performance and structural deformation respectively.

Fluid Analysis Method
The fluid is assumed to be an incompressible fluid, which follows the generally accepted assumption about fluid around a marine propeller. Therefore, the governing equations are solved by the Navier-Stokes equations (1) and (2) of unsteady turbulent as follows: where U i =(U, V, W) is the velocity component in the X i =(x, y, z) direction; P is static pressure; μ is the dynamic viscosity of fluid; ρ is fluid density; expresses the Reynolds stress, and requires a turbulence model to close. In this study, K-ω SST model is applied for turbulence model and commercial CFD program.
The calculation domain is divided into two parts-the stationary domain and the rotating domain, and the calculation domain of propeller VP1304 is shown in Figure 1. The Stationary domain should be large enough, which has the length of 10D, with 7D cylindrical diameter, to ensure that the out boundary will not influence the analysis of the near-propeller fluid flow. The rotating domain has the length of 1.2D, with 1.6D cylindrical diameter. The internal interface is established to transmit the data. The velocity of inlet boundary is set at advance speed V A . On the outlet boundary, the static pressure outlet is imposed, with 0 Pa reference pressure. Fluid solver time step is set at 1° of propeller rotation per step.

Solid Analysis Method
The equations (3) and (4) of motion for the structural deformation of the propeller blade is as follows: where M s is the mass matrix; C s is the damping matrix; K s is the stiffness matrix, representing the material mass, damping and stiffness of propeller blade; , , are acceleration, velocity, and displacement of the structure element; F ST represents the all loads acting on the structure. The structural analysis of structural response is conduct with STAR-CCM+ solver, which also has FEA solver module.
In this study, the blades of propeller VP1304 and propeller KP505 material is set at Ni-Al Bronze (NAB), which properties are ρ=7400 kg/m 3 , E=124 GPa, υ=0.33. solid solver time step is also set at 1° of propeller rotation per step.

Coupling Method
In this study, FSI analysis is performed by bi-directional coupling method, and the coupling time step is the same as the time step of fluid and solid solver. the analysis progress as follows [6]: 1) CFD analysis to calculate pressure distributions at the blade surface.
2) FEM analysis to calculate deformation is performed with pressure as load condition.
3) Morphing CFD mesh based on deformation data. 4) Return to step 1) and perform CFD calculation for deformed propeller.

VERIFICATION AND VALIDATION
To verify the validation of mesh convergence and the FSI method, propeller VP1304 open-water curve has been computed, which compared with the experimental reports on SMP'11 workshop. The advance coefficient J, advance speed V A , thrust coefficient K T , torque coefficient K Q and efficiency η can be calculated through equations (5) and (6) as follows: While the calculation domain for propeller VP1304 has been explained in section Ⅱ, polyhedral mesh and trimmed cell mesh were adobted for rotating domain and stationary domain espectively. Different grid refinement was used for the propeller leading edge, trailing edge, and wake region. For the solid analysis, tetrahedral mesh was generated.
Propeller rotational speed n is 15 rps, with the scale ratio λ=12. Eight cases with eight different advance coefficients were run, and Figure 3 shows the open water curves, both the experimental results and the computed at model scale using CFD and CFD-FEM(FSI). Comparing the CFD results with the experimental results, the open-water characteristics of rigid propeller shows consistent tendency and maximum errors of KT and KQ occur at J=0.4006 and J=1.3308 respectively. Also, comparing the FSI results with the CFD and experimental results, the open-water characteristics of traditional NAB propeller are slightly smaller than rigid propeller, and more consistent with experiment results at J variation.

ANALYSIS AND DISCUSSION
In this section, scale effect and hydro-elastic performance influence on propeller hydrodynamic characteristics and structural response will be discussed. To minimize the grid size effect, the grid topologies for the model and full-scale propellers were the same, except for the absolute near-wall spacing. As explain by Jung-Kyu Choi [1], full-scale calculation using the high y + wall treatment nearly make no difference due to large Reynolds number, so y + is close to 80 for full-scale propeller calculation. Also, the calculation domain, boundry condions, material selection and other settings are the same, which have been mentioned (section Ⅱ, Ⅲ).  Figures 4 and 5 show the open-water performmance of rigid and NAB propeller under the model and full-scale condition. Figure 4 compares CFD simulation results with experiment and ITTC scale correction results respectively. It can be observed that K T at full-scale increases, while K Q decreases, compared with K T and K Q at model-scale. The reason can be explained in airfoil lift test of Fiddes [7]: the increase of Reynolds number will lead to the increase of lift force and decrease of drag force on blade section.   The thrust coefficient and torque coefficient respectively include the pressure components K T P and K Q P and the friction components K T F and K Q F . The distribution of each component is shown in Figure  6. It is observed that scale effect have greater effect on friction component of torque coefficient at J variation, though friction component is relatively small. Comparing NAB propeller with rigid propeller at full-scale, pressure componets decreases, especially under heavy load condition, while friction component increase slightly.  To analyze the deformation distribution of model and full-scale propeller, dimensionless relative deformation ∆X r is defined as ∆X r =∆X/D×100%, where D represents diameter. The relative deformation distribution at the centerline of blade pressure side(J=0.8) is shown in Table 1. For the full-scale propeller, relative deformation is much high than that of model-scale.

CONCLUSION
Full-scale CFD simulation avoids the scale effect on the traditional model test and FSI simulation have accurate ability to predict hydro-elastic performance by coupling fluid and structure. In this study, to estimate the scale effect and hydro-elastic performance influence on propeller hydrodynamic characteristics and structural response, CFD-FEM methodology using STAR-CCM + is adapted. Two kinds of marine propeller, VP1304 and KP505 are employed for open-water calculation. Analysis shows that scale effect and hydro-elastic performance affect hydrodynamic characteristics and structural response interatively, such as: (1) the thrust coefficient and torque coefficient of the fullscale NAB propeller decrease more than that of the model-scale, compared with rigid propeller; (2) moreover, scale effect and hydro-elastic performance have different influence on the friction coefficient and pressure coefficient respectively; (3) The structural response of NAB propeller have some difference in model and full-scale. the relative deformation of full-scale propeller is much high than of model-scale.
In a future work, we will try to apply the FSI methodology to the propeller KP505 behind the container vessel KCS, and conduct self-propulsion simulation.