1 University of Rostock | Naval Architecture and Ocean Engineering February 2012 University of Rostock | Naval Architecture and Marine Engineering

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

2 University of Rostock | Naval Architecture and Ocean Engineering February 2012

Introduction: FSI

Fluid Dynamics Structural Dynamic

Acoustic Fluid

ASSUMPTIONS!

Compressible and Irrotational flow

No body and viscous forces (inviscid)

Mean density and pressure are uniform

Small disturbances

Medium at rest and Homogeneous

Fluid Structure Interface

Methods To Solve FSI

Monolithic approach: Partitioned approach:

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Engineering Applications

1. Ship stern Tube 2. Overboard discharge line

Tube

Shaft Video

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Objective and Scientific Contribution

Objective

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.

5 University of Rostock | Naval Architecture and Ocean Engineering February 2012

Bending Vibration Analysis Of Shaft And Tube Coupled

With Fluids

Part-1 BVA of stern tube Part-2 BVA of OVBD Discharge line

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

Infinite fluid

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Acoustic FSI FE Model Techniques (ANSYS)

Boundary Conditions and Interfaces Definitions

Displacement (Ux, Uy, Uz) and pressure DOF for fluid in contact

Only pressure DOF for other domain (KEYOPT(2)=1)

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CASE-1 Bending Vibration of Solid Elastic Dry Shaft and

Elastic Tube

Validation with analytical result

Problems with 2D models

r2=0.18m r2=0.3555m r2=0.5688m

0

5

10

15

20

25

0.0 0.1 0.2 0.3 0.4 0.5 Fre

qu

en

cy (

Hz)

Radius of shaft (mm)

Dry Shaft Natural frequency

Analytical Result ANSYS 2D Result

8 University of Rostock | Naval Architecture and Ocean Engineering February 2012

CASE-2 BVA of Solid Elastic Shaft in Infinite Fluid

Determination of proper infinite fluid outer extreme Identification of proper mesh size

2r1

r4

r4=(2 - 3)r1

Set pressure zero at 2 to 3 times of outer diameter (error <1%)

9 University of Rostock | Naval Architecture and Ocean Engineering February 2012

CASE-3 BVA of Solid Elastic Shaft in Fluid Filled Rigid Tube

2D Model 3D Model

Graph used to determine Cm (Grim O., 1975)

ACM mfa

Theoretical added mass

This result will be compared with ANSYS 2D and 3D

L = lambda/2

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CASE-3 Models Validation with Theoretical results

As shaft radius increases As tube radius decreases

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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

12 University of Rostock | Naval Architecture and Ocean Engineering February 2012

Added Mass Coefficient of Stern Tube

Shaft cm as r1 increases

Shaft cm as r2 decreases

Tube Cm as r1 increases

Tube Cm as r2 decreases

Added mass= ACM mfa

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Comparison of Different CASES

0.00

10.00

20.00

30.00

40.00

50.00

60.00

70.00

80.00

0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34

% d

ecre

men

t in

fre

qu

ency

r1(m)

Comparison of CASE-2,3,4

% decr. for CASE-2 % decr. for-CASE-3

0

10

20

30

40

50

60

70

0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34

Hyd

rod

ynam

ic m

ass

coef

fici

en

t

r1 (m)

Cm-CASE-2 (ANSYS-3D) Cm-CASE-3 (ANSYS-3D) Cm-CASE-4 (ANSYS-3D)

Hydrodynamic coefficient comparison

CASE-4 50% more affected

as compared to CASE-3

CASE-2

CASE-3

CASE-4

14 University of Rostock | Naval Architecture and Ocean Engineering February 2012

Comparison of Percentage Decrement in Shaft and

Tube Natural Frequency

-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

0

10

20

30

40

50

60

70

0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34 Fre

qu

en

cy %

De

cre

me

nt

r1 (m)

% DECR.-SHAFT FREQ. % DECR.-TUBE FREQ.

0

10

20

30

40

50

60

70

0.23 0.25 0.27 0.29 0.31 0.33 0.35

Fre

qu

en

cy %

De

cre

me

nt

r2 (m)

% DECR.-SHAFT FREQ.

% DECR.-TUBE FREQ.

As r1 increases

As r2 decreases

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Influence of Density

•Only fluid between shaft and

tube changed

•Shaft natural frequency

influenced more.

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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.

(m)

CASE-2

(Hz)

CASE-4

(m)

(Hz)

17 University of Rostock | Naval Architecture and Ocean Engineering February 2012

PART-2 Bending vibration Analysis of OVBD Line

Assumptions:

Ballast water considered as infinite fluid

Caisson rigidly fixed at 4 points! Pipe rigidly fixed at two extremes

Real model Simplified model

18 University of Rostock | Naval Architecture and Ocean Engineering February 2012

Pipe natural frequency

Mode-2 – 76% (3.9 - 0.9Hz) Mode-3 – 74% (8.4 - 2. 2Hz) -Almost no effect of ballast water

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

0 0.25 0.5 0.75 1

Natu

ral fr

eq

uen

cy o

f P

ipe

(H

z)

Ballast fluid level (1=full)

WETTED MODE-1

DRY MODE-1

75%

19 University of Rostock | Naval Architecture and Ocean Engineering February 2012

Caisson natural frequency

-Much affected by ballast water

6

8

10

12

14

16

18

20

0.00 0.25 0.50 0.75 1.00

Natu

ral fr

eq

uen

cy o

f C

ais

so

n (

Hz)

Ballast fluid level (1=full)

WETTED MODE-1

DRY MODE-1

46%

33% 41%

45% 46%

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Effect of Ballast Water on Wetted In and Out Caisson

Mode-1 Mode-2

Frequency percentage decrement

Bottom

Top

Bottom

Top

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Forced OVBD System Without Ballast Water

2kN harmonic force applied to the pipe at the center

(m)

(Hz)

(10^-2) (10^-3)

(10^-5)

Zoomed out

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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

23 University of Rostock | Naval Architecture and Ocean Engineering February 2012

THANK YOU

FOR YOUR ATTENTION!