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8/6/2019 Dynamic Characteristics of Turbo Machine System, Hani Aziz Ameen
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Dynamic Characteristics of Turbomachinery system
Asst. Prof. Dr. Hani Aziz Ameen
Dies and Tools Engineering Department
Technical College /BaghdadIraq.E-mail:[email protected]
Abstract
To predict the dynamic characteristics of structures with containment
fluid, finite element representation of the pressure field within the fluid is
employed. 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 usingANSYS12, 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 toas 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 variation
ij 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
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iT prescribed boundary force for structure
f density of the fluid
][ 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.
Introduction
To estimate more accurately the dynamic characteristics of
turbomachinery, it is inevitable to include the influence of fluid motions
upon the structure in the course of the analysis. Up to the present, various
methods of dealing with the coupled fluid-structure dynamic behavior
have 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 penalty
method 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 virtualmass method based on the boundary integrals of the velocity potential in
the Eulerian approach, however, its application to a complex shaped fluidsuch 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.
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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
0)( Fe s S
ii
S
iiiisijij dSuTdsupnduu (1)
For the fluid
f
f
Ss
iiji pdsnudpp 0,,1
. (2)
Eq.(2) neglects the free surface waves.
Finite Element FormulationAccording 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 are
obtained from the following equation [5],
0}]){[]([2 uMK ss ..(5)
The interaction and the external load terms are omitted in Eq.(2). Fromthe assumption, the coupled eigen mode of the structure with the fluid is
approximated by the linear superposition of the n modes from Eq.(5) asfollows[6] :
n
iii 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 f
tt
s
t
s
t
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 standard
rigid formats available in ANSYS12 [7][8]. The simplified flow diagram
of these run is shown in Fig.(1)
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Model of Turbomachinery system by ANSYS12
Turbomachine model can be descretizing as in Fig.(2) [9].
Results and Discussion
Structure model analysis is investigated in which the eigenvalue and
eigenvector for each parts individually and assembly of a turbomachine
system is studied. Free vibration analysis consists of studying the
vibration characteristics of the rotor system, such as natural frequency
and mode shapes.The natural frequency and mode shapes of a rotor
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 based
upon 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 partindividually of a system (shaft, fan and hollow shaft) or assembly
increased with increasing mode number for example, the rate of
increasing in natural frequency for shaft (44.5%), fan (27.32%), hollowshaft (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 naturalfrequency is record by shaft, hollow shaft, fan, and system respectively.
Conclusions
Eulerian 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 naturalfrequencies for every part in turbo machinery (shaft, fan, hollow shaft)
individually or assembly increased with increasing mode number, the rate
of 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 naturalfrequency in individual parts.
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References
[1] Zienkiewicz O.C. and Bettess P. Fluid- Structure DynamicInteraction 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 astructure Submerged in a Compressible Fluid, Proc. Int. Symp. On Finite
Element Techniques, Stuttgart, pp.361, 1969.
[3] Matej Vesenjak Fluid Structure Interaction in Multiphase MixingVessel, 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 meeting
and exhibit, 10-13 Jan, 2005.
[5] Mohammed Ishaquddin, Marimuthu R., Balakrishnan S.,Sivasubramonian B. and Handoo K.L. Frequency and Model pressure
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-Jana by 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. Engineering
analysis 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 VibrationCharacteristics and Stresses of Turbomachinery System , European
Journal 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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