Dynamic Responses of Composite Marine Propeller in Spatially Wake

Transcription

1 Dynamic Responses of Composite Marine Propeller in Spatially Wake Dynamic Responses of Composite Marine Propeller in Spatially Wake Y. Hong a, X.D. He a,*, R.G. Wang a, Y.B. Li a, J.Z. Zhang a, H.M. Zhang a and X. Gao b a Center for Composite Materials and Structures, School of Astronautics, Harbin Institute of Technology, Harbin, , China b College of Shipbuilding Engineering, Harbin Engineering University, Harbin, , China Summary Dynamic responses of a composite marine propeller in spatially wake were investigated in this paper. A hydroelastic model was developed to identify the response characteristics of the composite propeller blades using a finite element method (FEM) coupled with a computational fluid dynamics (CFD) method. Rotational effects and added mass were considered. A coupled matrix was established and solved by the Newton-Raphson numerical procedure. The dynamic characteristics and responses of the composite blade were calculated and compared with those of the counterpart rigid blade. Effects of various parameters, including the layer lamination and fiber orientation were investigated. 1. Introduction Propeller blades are the key structural units in shafting system of the marine industries. In the operational condition, composite propeller blades subjects the hydrodynamic pressure and centrifugal force, the high vibrations are caused by the harmonic loading on the blade due to an unsteady hydrodynamic environment and highly flexible rotating blades. However, the vibration control and hydroelastic stability are required tightly in the processing of design for the composite propeller blades. Thus, the structural dynamics of the composite propeller blades and the related stability and vibratory characteristics should be extensively paid attention. In recent years, considerable researches have directed towards the composite marine propeller for its excellent foreground 1-2. The evaluation of stress and strength 3-4, the optimization of stacking sequence and the improvement of hydrodynamic performance 5 have been completed by Smithers Rapra Technology, 2011 Lin and his partners for the composite propeller, respectively. The effective modulus method and the finite element method are used in the structural analysis in turn. The PSF-2 program (a special software for analyzing the flow field of propeller in steady and subcavitating flows) is applied for the fluid analysis of the composite propeller. Although it is easily to find numerous literature references about the dynamic studies of other composite blades, such as the composite wind turbine blade and the composite rotor blade 6-8, there are few reports about the structural dynamics analysis of the composite propeller. Until recently, Young presented a coupled boundary element (BEM) and finite element (FEM) approach to investigate the structural dynamic characteristics of the flexible composite propeller So, the structural responses in spatially wake and dynamic characteristics of the composite propeller blade are investigated using a 3-D FEM/CFD coupling algorithm in this paper. The CFD method based on Reynolds Averaged Navier-Stokes (RANS) equation is used for fluid analysis in place of conventional methods (such as: PSF-2 program and VLM method) based on the potential theory. The results of the composite blade are compared with those of the counterpart rigid blade. The effects of the lamination parameters are discussed. 2. Theoretical background 2.1 Dynamic Analysis of Composite Blade Figure 1 shows the composite propeller rotating with a constant angular velocity W about a fixed axis. In order to analyzing the dynamic response of the composite propeller in spatially wake, the finite element model of a reference blade is constructed by using a layered solid element 11. Compared with other element types, the layered solid element can exactly match the three-dimensional physical geometry of the blade on a ply-by-ply basis, and it can handily utilize the designability of composite material by setting the parameters of Real Constants 12. Figure 2 shows the finite element model of the reference blade. The Polymers & Polymer Composites, Vol. 19, Nos. 4 & 5,

2 Y. Hong, X.D. He, R.G. Wang, Y.B. Li, J.Z. Zhang, H.M. Zhang and X. Gao Figure 1. The coordinate system of the propeller Figure 2. The finite element model of the composite blade solve this problem, the hydroelastic model is presented. 2.2 Hydroelastic Model The hydroelastic model of the composite blade is developed by using a 3-D FEM/CFD coupled method. The CFD method based on Reynolds Averaged Navier-Stokes (RANS) equation is used for fluid analysis in place of conventional methods based on the potential theory (such as PSF- 2, VLM, BEM). The fluid is assumed to be viscid and incompressible. With these assumptions, the hydrodynamic characteristics of the composite propeller can be obtained by applying the general-purpose CFD software ANSYS CFX 12. Combining the equation (2)-(3) with the results of the hydrodynamic pressure, the generalized fluid force {F h } can be considered as three parts: (4) Where F h (1), F h (2) and F h (3) is fluid force, radiation force and restoring force, respectively. F h (2) and F h (3) can be further expressed as: (5) dynamic equation of the composite blade can be expressed as: (1) Where [M], [C] and [K] are the mass, the damping and total stiffness matrices, respectively, Ü, Ù and U are the acceleration, velocity and displacement vectors, respectively. On the right side of the equation (1), the external load {F} acting on the blade includes the generalized fluid force {F h } normal to the surface of the blade and the centrifugal force {F r }. And the force of the fluid acting on the blade can be expressed as: (2) In which da is the interaction boundary between fluid and structure, n is its outward normal vector. P is the total hydrodynamic pressure acting on the blade, it can be decomposed into two parts: (3) Where P and P r are the hydrodynamic v pressure due to rotation and elastic deformation, respectively. In order to (6) It can be seen from equations (5) and (6) that the matrix, and describe the corresponding parts of hydrodynamic force which are respectively in phase with the acceleration, velocity and displacement of the blade vibrating in water. So they are called added mass, added damping and added stiffness matrixes, respectively. Substituting equations (4)-(6) into equation (1), the hydroelastic vibrating equation of the composite blade can be expressed as: 406 Polymers & Polymer Composites, Vol. 19, Nos. 4 & 5, 2011

3 Dynamic Responses of Composite Marine Propeller in Spatially Wake It can be solved by using the commercial FEM /CFD software ANSYS/ANSYS CFX Results and discussion To analyze the dynamic characteristics and responses of the composite propeller, the numerical modelling is completed for a model propeller, which has seven blades, expanded area ratio of 0.75 and diameter of 22 cm. Table 1 lists the properties of the materials used in the calculation. The finite element model of the composite blade, generated by the software ANSYS, is shown in Figure 2. The stacking sequence of the composite blade is symmetric with respect to the middle surface, following the order 30º, 30º, 45º, 45º, 0º, 0º, 0º, from the pressure and suction surfaces to the camber surface, respectively. The x-direction of the blade serves as the reference direction of the fiber. The model consists of 510 layered solid elements. The root of the propeller blade is fixed to simulate the boundary condition of a real blade. The hydrodynamic pressure is calculated by the software CFX. The spatially wake distribution, imposed using the CEL feature of the software CFX, is shown in Figure 3. Figure 4 shows the natural frequencies of the composite blade (C1 blade) in air and water, respectively. It is clear that the natural frequencies of the composite blade in water are less than those of the composite blade in air due to the influence of the added mass. Compared these results with those of the counterpart rigid blade, we can see that the influence of the added mass is larger for the composite blade than that for the rigid blade. It is probably due to that the composite blade is greatly lighter than the rigid blade, the ratio between structure tonnage and structure mass increases, (7) so the influence of the added mass increases. Figure 5 displays the mode shapes of the C1 blade. Mode 1 is the longitudinal bending mode. Mode 2 is the twist mode. Mode 3 and 4 combine these different effects. Figure 3. The spatially wake distribution of the propeller The dynamic responses of the composite blade in spatially wake are calculated by using the 3-D FEM/CFD coupling algorithm. Figure 6 presents the displacement of the tip node during a rotation for the C1 blade and the rigid blade. It is clear that the results appear the oscillation characteristics. Figure 4. The natural frequencies of the composite and rigid blades Table 1. Material properties Properties UC SC Metal Longitudinal modulus E 1 (Pa) 1.35e e e11 Transverse modulus E 2 (Pa) 9.4e e10 In-plane shear modulus G 12 (Pa) 5e9 4.9e9 In-plane Poisson s ratio ν Density r (kg/m 3 ) Polymers & Polymer Composites, Vol. 19, Nos. 4 & 5,

4 Y. Hong, X.D. He, R.G. Wang, Y.B. Li, J.Z. Zhang, H.M. Zhang and X. Gao Figure 5. The mode shapes of the composite blade (C1 blade) Figure 6. Comparisons of the tip node displacement during a rotation for the composite and rigid blades 408 Polymers & Polymer Composites, Vol. 19, Nos. 4 & 5, 2011

5 Dynamic Responses of Composite Marine Propeller in Spatially Wake By choosing the same scope of variable, we can see that the displacement of the composite blade are larger than that of the rigid blade. That is because that composite materials has higher elasticity. Due to the different hydroelastic effects for the composite and the metal, the smaller oscillation is occurred around the rotation angle θ=180 degree for the composite blade, and the smaller oscillation is occurred around the rotation angle θ=90 and θ=270 degree for the rigid blade. Figure 7 shows the principal stress of the tip node during a rotation for the C1 blade and the rigid blade. The similar oscillation characteristics are displayed. But the maximum principal stresses during a rotation both appear around the rotation angle θ=150 degree. To compare the effect of the lamination parameters on the dynamic responses of the composite blade, three stacking sequences are used and discussed. Table 2 presents three symmetric stacking sequences. Figure 8 presents Figure 7. Comparisons of the tip node stress during a rotation for the composite and rigid blades Table 2. Three symmetric stacking schemes Stacking schemes C1 blade [0 2 /45 2 /90 4 /45 6 /90 6 /45 6 /90 6 ] s C2 blade [30 2 /45 2 /0 4 /45 6 /0 6 /45 6 /0 6 ] s C3 blade [-15 2 /90 2 /0 4 /90 6 /0 6 /90 6 /0 6 ] s Figure 8. Comparisons of the maximum displacement during a rotation for three composite blades Polymers & Polymer Composites, Vol. 19, Nos. 4 & 5,

6 Y. Hong, X.D. He, R.G. Wang, Y.B. Li, J.Z. Zhang, H.M. Zhang and X. Gao the maximum displacement during a rotation for three composite blades. It is clearly that the C2 blade has a smaller displacement in all of direction than other blades. That is because that the fibre orientation of 30 degree on the surface of the blade, compared with the fiber orientation of 0 and -15 degrees, is much helpful to control the deformation of the composite blade. At the same time, we can see that the composite blade with different lamination parameters exhibits different oscillation tendencies. The smaller oscillation is occurred around the rotation angle θ=180 degree for the C1 blade, and the smaller oscillation is occurred around the rotation angle θ=30 and θ=330 degree for the C2 and C3 blades. Figure 9 presents the maximum principal stress during a rotation for three composite blades. The maximum principal stresses of the C2 and C3 blades are smaller than that of the C1 blade. That is because that the fibre orientation of 0 degree, compared with the fiber orientation of 45 and 90 degrees, is much helpful to reduce the principal stress of the composite blade. 5. Conclusions The dynamic responses of a composite marine propeller in spatially wake are investigated using a 3-D FEM/CFD coupling algorithm. The dynamic characteristics of the composite blade are different from those of the rigid blade. The effect of the added mass on the composite blade is greatly larger than that of on the rigid blade. Compared with the counterpart rigid blade, the dynamic responses of the composite blade during a rotation exhibit different variation tendencies due to the different elastic characteristics of the composites and the metal. On the other hand, the lamination parameters have a great influence on the dynamic characteristics of the composite blade. The fibre orientation of 30 degree is much helpful to control the deformation of the composite blade, and the fibre orientation of 0 degree is much helpful to reduce the principal stress the composite blade. Figure 9. Comparisons of the maximum principal stress during a rotation for three composite blades Acknowledgement This work is supported by Program for Changjiang Scholars and Innovative Research Team in University References 1. Mouritz A.P., Gellert E., Burchill P., and Challis K., Review of advanced composite structures for naval ships and submarines, Composite Structures, 53 (2001) Marsh G., A new start for marine propellers, Reinforced Plastics, Lin G.F., Comparative stressdeflection analyses of a thickshell composite propeller blade, Technical Report, David Taylor Research Center, DTRC/SHD , Lin H.J., Strength evaluation of a composite marine propeller blade, Journal of Reinforced Plastics and Composites, 24 (2005) Lee Y.J. and Lin C.C., Optimized design of composite propeller, Mechanics of Advanced Materials and Structures, 11 (2004) Wang J.H., Qin D.T., and Lim T.C., Dynamic analysis of horizontal axis wind turbine by thin-walled beam theory, Journal of Sound and Vibration, 329 (2010) Bauchau O.A. and Chiang W., Dynamic Analysis of Bearingless Tail Rotor Blades Based on Nonlinear Shell Models, Journal of Aircraft, 31(6) (1994) Carlos E.S.C., Sang J.S., and Matthew L.W., Dynamic response of active twist rotor blades, Smart Materials and Structures, 10 (2001) Young Y.L., Fluid-stucture interaction analysis of flexible composite marine propellers, Journal of Fluids and Structures, 24 (2008) Liu Z. and Young Y.L., Utilization of bend-twist coupling for performance enhancement of composite marine propellers, Journal of Fluids and Structures, 25 (2009) Polymers & Polymer Composites, Vol. 19, Nos. 4 & 5, 2011

7 Dynamic Responses of Composite Marine Propeller in Spatially Wake 11. Taylor R.L. and Beresford P.J., A Non-Conforming element for stress analysis, International Journal for Numerical Methods in Engineering, 10 (1976) ANSYS. ANSYS Version 12.0 Documentation, Qing L.D., Validation of RANS predictions of open water performance of a highly skewed propeller with experiments, Conference of Global Chinese Scholars on Hydrodynamics, Watanabe T., Kawamura T., Takekoshi Y., and Maeda M., Simulation of steady and unsteady cavitations on a marine propeller using a RANS CFD code, Fifth International Symposium on Cavitations, Polymers & Polymer Composites, Vol. 19, Nos. 4 & 5,

8 Y. Hong, X.D. He, R.G. Wang, Y.B. Li, J.Z. Zhang, H.M. Zhang and X. Gao 412 Polymers & Polymer Composites, Vol. 19, Nos. 4 & 5, 2011