7/28/2019 Modal Analysis of Coupled Fluid Hani Aziz Ameen
1/19
1
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 coupled- field analysis. A
coupled- field analysis is a combination of analyses from different
engineering disciplines (physics fields) that interact to solve global turbo-
machinery problems, hence a coupled- field 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
7/28/2019 Modal Analysis of Coupled Fluid Hani Aziz Ameen
2/19
2
][ 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
7/28/2019 Modal Analysis of Coupled Fluid Hani Aziz Ameen
3/19
3
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
7/28/2019 Modal Analysis of Coupled Fluid Hani Aziz Ameen
4/19
4
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
7/28/2019 Modal Analysis of Coupled Fluid Hani Aziz Ameen
5/19
5
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.
7/28/2019 Modal Analysis of Coupled Fluid Hani Aziz Ameen
6/19
6
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
7/28/2019 Modal Analysis of Coupled Fluid Hani Aziz Ameen
7/19
7
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
7/28/2019 Modal Analysis of Coupled Fluid Hani Aziz Ameen
8/19
8
Fig.(2) Model Descretization [9]
7/28/2019 Modal Analysis of Coupled Fluid Hani Aziz Ameen
9/19
9
Fig.(3) First mode Shapes
7/28/2019 Modal Analysis of Coupled Fluid Hani Aziz Ameen
10/19
10
Fig.(4) second mode Shapes
7/28/2019 Modal Analysis of Coupled Fluid Hani Aziz Ameen
11/19
11
Fig.(5) Third mode Shapes
7/28/2019 Modal Analysis of Coupled Fluid Hani Aziz Ameen
12/19
12
Fig.(6) Fourth mode Shapes
7/28/2019 Modal Analysis of Coupled Fluid Hani Aziz Ameen
13/19
13
Fig.(7) Fifth mode Shapes
7/28/2019 Modal Analysis of Coupled Fluid Hani Aziz Ameen
14/19
14
Fig.(8) Sixth mode Shapes
7/28/2019 Modal Analysis of Coupled Fluid Hani Aziz Ameen
15/19
15
Fig.(9) Seventh mode Shapes
7/28/2019 Modal Analysis of Coupled Fluid Hani Aziz Ameen
16/19
16
Fig.(10) eighth mode Shapes
7/28/2019 Modal Analysis of Coupled Fluid Hani Aziz Ameen
17/19
17
Fig.(11) Ninth mode Shapes
7/28/2019 Modal Analysis of Coupled Fluid Hani Aziz Ameen
18/19
18
Fig.(12) Tenth mode Shapes
7/28/2019 Modal Analysis of Coupled Fluid Hani Aziz Ameen
19/19
19
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]