Modal Analysis of Coupled Fluid – Hani Aziz Ameen

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Modal Analysis of Coupled Fluid Structure Response of

Turbomachine

Asst. Prof. Dr. Hani Aziz Ameen

Dies and Tools Engineering DepartmentTechnical CollegeBaghdadIraq.E-mail:[email protected]

AbstractTo predict the dynamic characteristics of structures with containment

fluid, finite element representation of the pressure field within the fluid isemployed. ANSYS12 makes a convenient analysis procedure for this

purpose. Tenth mode shapes of each parts and assembly part of

turbomachinery is presented. The loading due to pressure was solved by

subjecting this pressure onto the fan blade surface, shaft and hollow shaft

using ANSYS12, finite element software by the coupledfield analysis. A

coupledfield analysis is a combination of analyses from different

engineering disciplines (physics fields) that interact to solve global turbo-

machinery problems, hence a coupledfield analysis is often referred to

as a multi- physics analysis. Loading due to fluid flow and rotational

velocity were subjected on the turbo machinery system. Results show that

the value of natural frequency in assembly part is less than the natural

frequency in individual parts.

Symbols

e volume of the structure

sS contacting surface of fluid and structure

fS boundary surface on which external load acts

f volume occupied by the fluid

ij components of stress tensor

means variationij components of strain tensor

s density of the structure

iu components of displacement

iu component of acceleration

in outward normal direction cosines on the contact boundary

p pressure of the fluid

iT prescribed boundary force for structure

f density of the fluid


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][ sK stiffness matrix of the structure

][ sM mass matrix of the structure

][A fluid- structure interaction matrix

][ fK stiffness matrix of pressure

}{F nodal point load vector acting on the structure

}{u unknown nodal displacement vector of the structure

circular frequency

i i-th empty mode of the structure

iC i-th generalized coordinate.

IntroductionTo estimate more accurately the dynamic characteristics of

turbomachinery, it is inevitable to include the influence of fluid motionsupon the structure in the course of the analysis. Up to the present, various

methods of dealing with the coupled fluid-structure dynamic behaviorhave been proposed. There are two different approaches adopting

different coordinates system. One is the Lagrangian approach which

expresses the fluid notion by the displacement function in the same

manner as the structure motion. The fluid is treated as an elastic solid

with a finite bulk modulus and a negligibly small shear modulus. Whenthe fluid is incompressiblem this approach has a shortpoint that it requires

the special technique such as a hybrid variational principle or a penaltymethod to suppress many rotary modes to be produced in the fluid.

Another is the Eulerian approach. In this approach the velocity field is

expressed by the gradient of a scalar function which represents thevelocity potential or the pressure field. As there is only one unknown

variable per nodal point, the number of total degrees of freedom is one-

third that of the Lagrangian approach. Since the Lagrangian approach is

less preferable to the Eulerian approach. ANSYS12 provides the the

virtual mass method based on the boundary integrals of the velocity

potential in the Eulerian approach, however, its application to a complexshaped fluid such as contained in a turbomachinery seems to be

inappropriate . Hence the finite element representation of the fluid has

been chosen. Zienkiewicz et al [1],[2], show the details of the theory used

in this research so only basic points are described in brief as below.

Basic Theory

On the assumptions that deformations of the structure and the fluid are

infintesmal and fluid motion is of the potential flow, the linear theory can

be adopted. Two variational principles are expressed as follows,[2]

For the structure


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0)( Fe s S

ii

S

iiiisijij dSuTdsupnduu&&

(1)

For the fluid

f

f Ssiiji pdsnudpp 0,,1 . (2)

Eq.(2) neglects the free surface waves.

Finite Element Formulation

According to the finite element displacement formulation, Eqs(1) and (2)

expressed as the following equations of matrices[3][4],

}{}{][}]{[}]{[ FpAuMuK tss . (3)

0}]{[}]{[ uApKf .(4)

In the first step, eigen modes of the structure without the fluid areobtained from the following equation [5],

0}]){[]([2 uMK ss ..(5)

The interaction and the external load terms are omitted in Eq.(2). From

the assumption, the coupled eigen mode of the structure with the fluid is

approximated by the linear superposition of the n modes from Eq.(5) as

follows[6] :

n

i

ii CCu

1

.. (6)

Substituting Eq.(6) into the equation which is derived by eliminating

pressure from Eqs.(3) and (4), the following equation is obtained.

0}]]{[][][}{}]{[}({}]{[}[{ 12 CAKAMK ftt

st

st

Where the external load vector is neglected. In the second step, this

reduced eigenvalue equation is solved .Once the structural components of the coupled fluid-structure modes are

obtained, corresponding pressure components in the fluid can be derived

from Eq.(4) and it is straight forward to incorporate these modes into

seimic response and/or response spectrum analysis using the standardrigid formats available in ANSYS12 [7][8]. The simplified flow diagram

of these run is shown in Fig.(1)

Model of Turbomachinery system by ANSYS12Turbomachine model can be descretizing as in Fig.(2) [9].

Results and DiscussionStructure model analysis is investigated in which the eigenvalue and

eigenvector for each parts individually and assembly of a turbomachinesystem is studied. Free vibration analysis consists of studying the

vibration characteristics of the rotor system, such as natural frequencyand mode shapes.The natural frequency and mode shapes of a rotor


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system are very important parameters in the design of a turbomachine

system for dynamic loading conditions and minimization of machine

failures. A detailed study in this paper is made using the formulation

presented in this paper on the fluid- structure interface. The free vibration

characteristics have been investigated by ANSYS12 software. The resultsreported the tenth structural eigenvalue and eigenvectors which are basedupon the behavior of each part of the rotor system individually (shaft, fan

and hollow shaft) and mixed with each one and with overall system, as

shown in figures (3), (4), (5), (6), (7), (8), (9), (10), (11) and (12).

It can be noticed from the figures that the natural frequency for every part

individually of a system (shaft, fan and hollow shaft) or assemblyincreased with increasing mode number for example, the rate of

increasing in natural frequency for shaft (44.5%), fan (27.32%), hollow

shaft (12.455%) and for assembly parts the rate of is increased (12.3%).

The value of natural frequency in assembly part is less than natural

frequency in individual part at same mode number and maximum natural

frequency is record by shaft, hollow shaft, fan, and system respectively.

ConclusionsEulerian representation of fluid by conventional solid elements of

ANSYS12 can put a dynamic modal response analysis of a coupled

containment fluid- structure system to practical use, so the

turbomachinery show the validity of the approach. In which the natural

frequencies for every part in turbo machinery (shaft, fan, hollow shaft)

individually or assembly increased with increasing mode number, the rateof increasing the natural frequency for shaft (44.5%), fan (27.3%), hollow

shaft (12.455%) and for assembly parts the rate of is increased (12.3%).

The value of natural frequency in assembly part is less than the natural

frequency in individual parts.

References[1] Zienkiewicz O.C. and Bettess P. Fluid- Structure Dynamic

Interaction and Wave Forces. An Introduction to Numerical Treatment,

Int. J. Meth. Eng. , Vol.13, No.1, PP.1, 1979[2] Zienkiewicz O.C. andNewton R.E. Coupled Vibrations of a

structure Submerged in a Compressible Fluid, Proc. Int. Symp. On FiniteElement Techniques, Stuttgart, pp.361, 1969.

[3] Matej Vesenjak Fluid Structure Interaction in Multiphase Mixing

Vessel, XXI ICTAM, 15-21 , Augest, 2004, Warsaw, Poland.

[4] Sadeghi M. and Liu F. Coupled Fluid- Structure Simulation for

Turbo machinery Blade Rows, 43rd

AIAA Aerospace science meetingand exhibit, 10-13 Jan, 2005.

[5] Mohammed Ishaquddin, Marimuthu R., Balakrishnan S.,Sivasubramonian B. and Handoo K.L. Frequency and Model pressure


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computation for Fluid- Structure Interaction Analysis, Proc. Of the Inter.

Confer. On Aerospace science and Technology, 26-28 June, 2008.

[6] Wafa A.S. Al-Janaby Theoretical and Experimental Study of an

Axial Fan Rotor Bearing System using Vibration Analysis Ph.D.

Thesis, University of Technology, 2007.[7] Nakasone Y. and Yoshimoto S. and Stolarski T.A. Engineeringanalysis with ANSYS software, 1st published, 2006 .

[8] Al-Zafrany A. Finite Element Methods , Cranfield University,

2006 .

[9] Hani Aziz Ameen , The Effect of CoupledField on the Vibration

Characteristics and Stresses of Turbomachinery System , EuropeanJournal of Scientific Research, ISSN 1450-216X Vol.41 No.4 (2010),

pp.606-626.


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Processor

Modeling

Structure Element

Bearing Element

Fluid Structure

element

Fluid142

Solid45

Fluid Element Fluid142

Shaft : Solid72

Fan : Solid72

Hollow shaft : Solid72

Combin14

Mesh the model by mesh tool and direct method

Given boundary condition for fluid and fluid structure (A)

Physics write fluid

Physics clear fluid

Given boundary condition for structure and structure fluid (B)

Physics write structure

Physics clear structure


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Fig.(1) Simplified flow diagrams for analysis of coupled fluid- structure

response in ANSYS12 software

Save

Solution

Physics read fluid

Solve

Physics read structure

Finish

Solution

Applied Load

Solve

Finish

Postprocessor

Pressure

OMEGA


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Fig.(2) Model Descretization [9]


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Fig.(3) First mode Shapes


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Fig.(4) second mode Shapes


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Fig.(5) Third mode Shapes


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Fig.(6) Fourth mode Shapes


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Fig.(7) Fifth mode Shapes


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Fig.(8) Sixth mode Shapes


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Fig.(9) Seventh mode Shapes


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Fig.(10) eighth mode Shapes


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Fig.(11) Ninth mode Shapes


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Fig.(12) Tenth mode Shapes


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The Author

Dr. Hani Aziz Ameen , Birth date 1971 in Baghdad-

Iraq, has Ph.D. in Mechanical Engineering Applied

Mechanics from the University of Technology Iraq

in 1998. He has more than 60 published papers and he

is an expert in the ANSYS software and finite element analysis.

Working in several universities and colleges (Technology University-

AlNahreen University- Tikrit UniversityTechnical College AlMusaib)

And now he is Asst. Professor in the Technical College Baghdad

Dies and Tools Engineering Department.

Mob.: 0780 289 7027

E-mail:[email protected]
mailto:[email protected]:[email protected]:[email protected]:[email protected]

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Modal Analysis of Coupled Fluid – Hani Aziz Ameen