Bending Vibration Analysis of Pipes and Shafts Arranged in Fluid Filled Tubular Spaces Using FEM By Desta Milkessa Under the guidance of : Prof. Dr.Eng. Patrick Kaeding Dipl.-Ing. Michael Holtmann Developed at: Germanischer Lioyd, Hamburg Feb., 2012 University of Rostock Naval Architecture and Marine Ocean Engineering 1
Introduction: FSI Fluid Dynamics Structural Dynamic ASSUMPTIONS! Compressible and Irrotational flow No body and viscous forces (inviscid) Mean density and pressure are uniform Small disturbances Medium at rest and Homogeneous Acoustic Fluid Fluid Structure Interface Methods To Solve FSI Monolithic approach: Partitioned approach: University of Rostock Naval Architecture and Ocean Engineering 2
Engineering Applications 1. Ship stern Tube 2. Overboard discharge line Tube Shaft Video University of Rostock Naval Architecture and Ocean Engineering 3
Objective Objective and Scientific Contribution Develop acoustic FSI-FEM using ANSYS. Perform vibration analysis, parametric study and mesh adaptation. Determine shaft, and pipes vibration characteristic. Determine added mass coefficient of the components Finally to propose quick and simple formulae for added mass. Contribution Determine the effect of surrounding fluid on important construction members. Make known important design parameters for complex FSI of concerned problems. University of Rostock Naval Architecture and Ocean Engineering 4
Bending Vibration Analysis Of Shaft And Tube Coupled With Fluids Part-1 BVA of stern tube Part-2 BVA of OVBD Discharge line Infinite fluid Assumptions Material: Steel (shaft, tube, and caisson) and Fiber reinforced pipe Fluid part : Acoustic fluid Boundary cond. : Simply supported for part-1 and rigidly fixed for part-2 University of Rostock Naval Architecture and Ocean Engineering 5
Acoustic FSI FE Model Techniques (ANSYS) Boundary Conditions and Interfaces Definitions Displacement (U x, U y, U z ) and pressure DOF for fluid in contact Only pressure DOF for other domain (KEYOPT(2)=1) University of Rostock Naval Architecture and Ocean Engineering 6
Frequency (Hz) CASE-1 Bending Vibration of Solid Elastic Dry Shaft and Elastic Tube Validation with analytical result 25 Dry Shaft Natural frequency 20 15 10 5 0 0.0 0.1 0.2 0.3 0.4 0.5 Analytical Result Radius of shaft (mm) ANSYS 2D Result Problems with 2D models r2=0.18m r2=0.3555m r2=0.5688m University of Rostock Naval Architecture and Ocean Engineering 7
CASE-2 BVA of Solid Elastic Shaft in Infinite Fluid 2r1 r4 Determination of proper infinite fluid outer extreme Identification of proper mesh size r4=(2-3)r1 Set pressure zero at 2 to 3 times of outer diameter (error <1%) University of Rostock Naval Architecture and Ocean Engineering 8
CASE-3 BVA of Solid Elastic Shaft in Fluid Filled Rigid Tube L = lambda/2 2D Model 3D Model Theoretical added mass M a f CmA This result will be compared with ANSYS 2D and 3D Graph used to determine Cm (Grim O., 1975) University of Rostock Naval Architecture and Ocean Engineering 9
CASE-3 Models Validation with Theoretical results As shaft radius increases As tube radius decreases University of Rostock Naval Architecture and Ocean Engineering 10
CASE-4 BVA of Solid Elastic Shaft in Fluid Filled Elastic Flexible Tube Immersed in Infinite Fluid Main assumptions Simply supported Acoustic fluid and initially at rest Acoustic FSI-3D Model Pressure distribution for shaft resonance Pressure distribution for tube resonance University of Rostock Naval Architecture and Ocean Engineering 11
Added Mass Coefficient of Stern Tube Shaft cm as r1 increases Tube Cm as r1 increases Shaft cm as r2 decreases Tube Cm as r2 decreases Added mass= M a f C m A University of Rostock Naval Architecture and Ocean Engineering 12
Hydrodynamic mass coefficient % decrement in frequency Comparison of Different CASES 80.00 70.00 60.00 50.00 40.00 30.00 20.00 10.00 0.00 70 60 50 40 30 20 10 0 Comparison of CASE-2,3,4 0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34 r1(m) % decr. for CASE-2 % decr. for-case-3 Hydrodynamic coefficient comparison Cm-CASE-2 (ANSYS-3D) Cm-CASE-3 (ANSYS-3D) Cm-CASE-4 (ANSYS-3D) 0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34 r1 (m) University of Rostock Naval Architecture and Ocean Engineering 13 CASE-2 CASE-3 CASE-4 CASE-4 50% more affected as compared to CASE-3
Frequency % Decrement 70 60 50 40 30 20 10 Frequency % Decrement Comparison of Percentage Decrement in Shaft and Tube Natural Frequency As r1 increases % DECR.-SHAFT FREQ. % DECR.-TUBE FREQ. 0 0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34 r1 (m) As r2 decreases 70 60 50 40 30 20 10 % DECR.-SHAFT FREQ. % DECR.-TUBE FREQ. 0 0.23 0.25 0.27 0.29 0.31 0.33 0.35 r2 (m) University of Rostock Naval Architecture and Ocean Engineering 14 -Shaft frequency affected much as with change in its radius. As the gap decreases the natural frequency of shaft increase and of the tube decreases
Influence of Density Only fluid between shaft and tube changed Shaft natural frequency influenced more. University of Rostock Naval Architecture and Ocean Engineering 15
Harmonic Analysis -2kN harmonic force applied at the center on shaft. To determine steady state response of shaft and tube. To validate modal analysis. To determine vibration transmission from shaft to tube and vice versa through fluid. CASE-2 CASE-4 (m) (m) (Hz) (Hz) University of Rostock Naval Architecture and Ocean Engineering 16
PART-2 Bending vibration Analysis of OVBD Line Real model Simplified model Assumptions: Ballast water considered as infinite fluid Caisson rigidly fixed at 4 points! Pipe rigidly fixed at two extremes University of Rostock Naval Architecture and Ocean Engineering 17
Natural frequency of Pipe (Hz) Pipe natural frequency 1.40 1.20 WETTED MODE-1 DRY MODE-1 1.00 0.80 0.60 75% 0.40 0.20 0.00 0 0.25 0.5 0.75 1 Ballast fluid level (1=full) Mode-2 76% (3.9-0.9Hz) Mode-3 74% (8.4-2. 2Hz) -Almost no effect of ballast water University of Rostock Naval Architecture and Ocean Engineering 18
Natural frequency of Caisson (Hz) Caisson natural frequency 20 18 WETTED MODE-1 DRY MODE-1 16 14 33% 41% 45% 46% 12 46% 10 8 6 0.00 0.25 0.50 0.75 1.00 Ballast fluid level (1=full) -Much affected by ballast water University of Rostock Naval Architecture and Ocean Engineering 19
Effect of Ballast Water on Wetted In and Out Caisson Mode-1 Bottom Mode-2 Bottom Top Top Frequency percentage decrement University of Rostock Naval Architecture and Ocean Engineering 20
Forced OVBD System Without Ballast Water (10^-2) (10^-3) (m) Zoomed out (10^-5) (Hz) 2kN harmonic force applied to the pipe at the center University of Rostock Naval Architecture and Ocean Engineering 21
Conclusion and Future Direction o Acoustic FSI FEM can simulate BVA with minimum error. o Stern tube BV much affected by added mass o Added mass coefficient depend on absolute dimension of shaft and tube, not only on ratio. o Added mass coefficient of shaft increase as gap decreases o Added mass coefficient of tube decrease as the gap decreases o Natural frequency and added mass of OVBD discharge line are much affected by surrounding fluid. o No influence of ballast water on pipe natural frequency o Caisson frequency depend on ballast water condition as well University of Rostock Naval Architecture and Ocean Engineering 22
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