=Paper=
{{Paper
|id=Vol-1490/paper24
|storemode=property
|title=Numeric simulation of the interaction between subsonic flow and a deformable profile blade on the compressor experiment phase
|pdfUrl=https://ceur-ws.org/Vol-1490/paper24.pdf
|volume=Vol-1490
}}
==Numeric simulation of the interaction between subsonic flow and a deformable profile blade on the compressor experiment phase==
https://ceur-ws.org/Vol-1490/paper24.pdf
Mathematical Modeling
Numeric simulation of the interaction between subsonic
flow and a deformable profile blade on the compressor
experiment phase
Mekhonoshina E.V., Modorskii V.Ya., Petrov V.Yu.
Perm National Research Polytechnic University
Abstract. The article investigates the numeric simulation of two-way
aeroelastic processes applied to the experimental phase of a compressor;
physical, mathematical, rigid and grid models of the system “gas – rotor –
stator” have been worked out; 2 FSI (two-way Fluid-Structure Interaction)
calculations have been performed on the evaluation of the interaction between a
gas-dynamic flow and a deformable rotor blade; the effect of voltage gain is
found in a blade, in an aeroelastic state compared with the transient calculations
of a stress-strain state.
Keywords: interdisciplinary calculation, experimental compressor stage
Citation: Mekhonoshina E.V., Modorskiy V.Ya., Petrov V.Yu. Numeric
simulation of the interaction between subsonic flow and a deformable profile
blade on the compressor experiment phase. Proceedings of Information
Technology and Nanotechnology (ITNT-2015), CEUR Workshop Proceedings,
2015; 1490: 211-218. DOI: 10.18287/1613-0073-2015-1490-211-218
Introduction
During the operation of compressors diverse vibrations may come out together
with increased dynamic loads on the bearings; they can initiate the decrease of
operating characteristics [1].
Blade machines produce vibrations for different reasons. For example, there might
be technological imbalances of shafts and other rotation parts, or imbalances by
assembly – all lead to vibrations. It’s also necessary to consider vibration processes in
magnetic suspensions. Vibration processes in labyrinth seals and in a gas-dynamic
tracks are also taken as key vibration factors [2, 3, 4, 5].
Moreover, the analysis of vibration and aerodynamics is carried out separately due
to the complexity of the calculations. Nowadays the vibrations in compressors cannot
be predicted as essential factors and are not taken into account.
1. Survey
The history of aeroelastic numeric calculations traces back to works related to an
asymmetric flutter that occurred during the flight on the bomber built by Handley
Page. In 1918 after the failure of the lower wing of the biplane Albatros D3 German
211
Information Technology and Nanotechnology (ITNT-2015)
Mathematical Modeling Mekhonoshina EV., Modorskiy VYa., Petrov VYu...
physicist Paul Richard Heinrich Blasius was the first to perform the analytical
calculations of a flutter. First numeric calculation of the aerodynamic power acting on
a harmonically vibrating thin plate in a two-dimensional flow was performed later in
1922 by W. Birnbaum in his thesis at Gottingen University [6, 7].
Since that time many researchers have referred to such issues of aeroelasticity. In
1972 A.S. Volmir described forced vibrations of the plate that was exposed to a
periodically varying transverse load [8]. The issue of aerohydroelasticity and its
component parts is thoroughly investigated in the following work [9]. The authors
consider the tasks where the impact of environment on structures operation is
necessary to consider and emphasize the always expanding scope of such tasks [9].
The main trend of the advance in technology is the increase of energy-and-mass
characteristics; hence loads are increasing and the mass of structures reduces at the
same time the stiffness of structures is coming down. In such a case unpredictable
effects might occur, such as a “flutter”. These kinds of issues are researched in the
following works [2]. The authors take a gas-elastic approach to calculate vibration
modes in power installations, give physical and mathematical models of a process,
and suggest a unified algorithm and solution method [2]. Lots of model task solutions
are given.
The researchers from the USA [10] did a review of associated numeric schemes.
They took one of the approaches to study the issue of a flutter [10]. The scientists
from three countries (ie. – China, Australia and USA), studied together the vibration
of wind turbine blades [11]. In the calculations the authors paid attention to the
interaction of gas flow and structure in the applied software ANSYS. The scientists
stress that the effect of such an interaction is essential and it has to be considered [11].
The scientists from China write about the interaction of a gas-dynamic flow and
structure with the profile NACA0012 [12]. Together with the idea of the following
work [2] it’s being suggested that the deformations change the flow field around the
structure, while the change in the field of a gas-dynamic pressure flow affects the
deformations as well [14].
As shown in [9] the solution of aeroelastic tasks requires theoretical methods of
elasticity, aeromechanics and vibrations. It’s necessary to simulate interdisciplinary
physical phenomena in order to solve such tasks. It’s complicated to calculate
together aerodynamics and rigidity as we deal with different mathematical models,
solution methods, the dynamics of calculated areas and approaches to discrete the
equations.
There are two variants of associating the equations of rigid body dynamic
deformation and the equations of gasdynamics: monolithic and consecutive [3]. By a
monolithic approach we use numeric schemes which result in the formation and
subsequent solution of a unified system of algebraic equations. A consecutive
approach is used to solve associated interdisciplinary tasks based on a separate
solution by the systems of equations for each subtask and requires the implementation
of calculation data exchange between the subtasks over a set period of time [3, 13]
with help of iteration procedures. Otherwise the synchronization is performed
directly. Such an approach is implemented in well known commercial products, such
as ANSYS, FlowVision, Abacus, CCM+, SolidWorks, LS-Dyna, Sysnoise
NASTRAN, OpenFOAM and FEStudio [14].
212
Information Technology and Nanotechnology (ITNT-2015)
Mathematical Modeling Mekhonoshina EV., Modorskiy VYa., Petrov VYu...
2. Physical model
This work suggests a fully associated non-standardized solution scheme for an
aeroelastic task applied to the simulation in the dynamical system
“gas-rotor-stator interaction” on the example of a compressor experiment phase.
Two domains have been considered: inlet guide vane (IGV) and the rotor itself.
The domain IGV is permanent, rotor domain is rotating with a constant angular rate.
The interaction of a gas-dynamic flow and rotor blade deformation is being
considered. Three-dimensional calculation model is given in the figure 1.
Fig. 1. – Three-dimensional calculation model of a compressor
We look at the sector that takes 1/12 of the structure. The sector is bounded by the
planes on which symmetry conditions are written. We consider the flow of an ideal
gas with the set properties; chemical processes are not considered; one-phase flow;
the calculations are performed without taking into account gravitation; the walls of
the structure neither absorb nor give off heat; the walls of the structure are rugged; the
coefficients of heat capacity don’t depend on the absolute temperature.
3. Mathematical model
Mathematical model is worked out based on the chosen physical model;
mathematical model includes two submodels. The submodel of gasdynamics is based
on the conservation laws of mass, momentum, energy, the equation of state of the
ideal compressible gas and encloses with the initial and boundary conditions.
Boundary conditions for gasdynamics are shown in the figure 2.
213
Information Technology and Nanotechnology (ITNT-2015)
Mathematical Modeling Mekhonoshina EV., Modorskiy VYa., Petrov VYu...
Fig. 2. – Boundary conditions for gas dynamic calculation
Mathematical model for the evaluation of a stress-strain state is written down as
follows [15, 16]:
mx cx kx F (t );
(1)
Where m – mass matrix; c – damping matrix; k - rigidity matrix; F(t) – load
vector; x – displacement.
At each moment these equations can be considered as a set of static equations of
equilibrium which take up the forces of inertia and damping as well. Time integration
by the Newmark method is used to solve these equations [15, 16]. We calculate the
increment between subsequent time points, integration step. Boundary conditions for
the structure are shown in Figure 3.
Fig. 3. – Boundary conditions for stress-strain state calculation
214
Information Technology and Nanotechnology (ITNT-2015)
Mathematical Modeling Mekhonoshina EV., Modorskiy VYa., Petrov VYu...
Afterwards we developed rigid body and grid models of the structure and gas
dynamic part. The number of the elements of the grid model of a gas dynamic rotor
track made up 56482 nodes and 51750 elements; of a gas dynamic stator track –
51863 nodes and 47490 elements; structures – 7728 nodes and 3378 elements.
4. Computational experiments
The solution is found by the iteration way. Two solvers – Transient Structural
(transient mechanics, finite element approach) and CFX Transient (gas dynamics,
finite volume approach) – are connected by data transfer. For the flow diagram of
such a solution refer to the following work [11].
The calculations are performed in the system of the computer engineering analysis
ANSYS 15.0 using the power of the high performance computing complex of
PNRPU. The duration of the calculations averages 4 hours on 16 cores «IntelXeon
E5-2680». We believe that the application of hybrid supercomputing systems with
graphics accelerators has great potential [17].
5. Results
According to the results of the computational experiments we found that the
dependence of the increment of displacements is specified by the aeroelasticity from
rotation speed at the control point which is located on the upper edge of the blade.
Figure 4 shows the diagram where in the vertical axis the difference of displacements
is given received by the calculation 2FSI and transient calculations of a stress-strain
state (calculated by the formula: ΔU=U2FSI-Utransient).
Fig. 4. – Aeroelasticity impact on the full movements at the control point on the upper edge of
the blade
In the horizontal axis the rotation of rotor speed is given. For the analysis we
selected the points which fit the period of time of the second peak occurrence by the
calculations 2FSI. At the same time the critical frequency of the rotation of the
215
Information Technology and Nanotechnology (ITNT-2015)
Mathematical Modeling Mekhonoshina EV., Modorskiy VYa., Petrov VYu...
compressor model phase was determined by the Campbell diagram which made up
1013,8 rad/s that determines the increase of movements by the rotation at the speeds
close to the critical speed.
In the computational experiment we received the dependence of the von Mises
stress σ time by the transient calculations (without considering FSI) and by the
calculations 2FSI for the rotor rotation speed ω=650 rad/s (see the figure 5).
Fig. 5. – Von Mises stress (ω=650 с-1)
We carried out the analysis of these dependences by diverse speeds of rotor
rotation. The following charts of the dependences Δσmax and Δσav from ω were
max
FSI
max
trans
worked out (figure 6a, 6b respectively), with max ,
max
trans
N N
FSI
trans FSI trans
av av av
, where av
FSI
1 , av
trans
1
.
trans
av
N N
We can see that at the frequencies close to the critical ones there is the increase of
von Mises stress related with aeroelastic effect.
Acknowledgements
Therese archis financed by the grant of the Russian scientific fund (project №14-
19-00877).
216
Information Technology and Nanotechnology (ITNT-2015)
Mathematical Modeling Mekhonoshina EV., Modorskiy VYa., Petrov VYu...
a)
b)
Fig. 6. – The increase of von Mises stress by considering aeroelastic effect: a – by maximum
values; b – by average values
References
1. Mekhonoshina EV, Modorsky VYa. Development of a technique of numerical modeling
of the aeroelastic work of Compressor. Scientific and technical bulletin of the Volga
region, 2014; 5: 264-268. [in Russian]
2. Modorsky VYa, Sokolkin YuV. Gas-elastic processes in power installations. Ed by
Sokolkin YuV. Moscow: Nauka, 2007. [in Russian]
3. Kopysov SP, Tonkov LE, Chernova AA. Bilateral binding when modeling interaction of
a supersonic stream and deformable plate. Comparison of numerical schemes and results
Experiment. Computational Continuum Mechanics, 2013; 6(1): 78-85. [in Russian]
217
Information Technology and Nanotechnology (ITNT-2015)
Mathematical Modeling Mekhonoshina EV., Modorskiy VYa., Petrov VYu...
4. Amarantov GN, Egorov MYu, Egorov SM, Egorov DM, Nekrasov VI. Numerical
modeling of intra chamber processes at an exit to an operating mode of the rocket engine
of solid fuel. Computational Continuum Mechanics, 2010; 3(3): 5-17. [in Russian]
5. Ganeev MS, Moiseyev VE, Skvortsova ZV. A nonlinear bend and stability of the
ellipsoidal cover interacting from Liquid. Computational Continuum Mechanics, 2011;
4(3): 32-40. [in Russian]
6. Arsentiev TP. The Abstract of the thesis "Fluctuations of a wing in a supersonic stream of
gas": PhD thesis abstract physical and mathematical science. SPb. University, St.
Petersburg, 2009; Source:
7. Blasius H. Über Schwingungserscheinungen an Einholmigen Unterflügeln. Zeitschrift für
fFugtechnik und Motorluftschiffahrt, 1925; 16: 39-42.
8. Volmir AS. Nonlinear dynamics of plates and Covers. Ed by Kildibekov IG. Moscow:
Nauka, 1972. [in Russian]
9. Gorshkov AG, Morozov VI, Ponomarev AT, Shklyarchuk FN. Aero hydroelasticity of
designs. Moscow: Fizmatlit, 2000. [in Russian]
10. Xiangying Ch, Ge-Cheng Zh, Ming-Ta Ya. Numerical simulation of 3-D wing flutter
with fully coupled fluid–structural interaction. Computers & Fluids, 2007; 36: 856–867.
11. Jianping Z, Liang G, Helen W, Aixi Zh, Danmei H, Jianxing R. The influence of wind
shear on vibration of geometrically nonlinear wind turbine blade under fluid–structure
interaction. Ocean Engineering, 2014; 84: 14-19.
12. Hefeng D, Chenxi W, Shaobin L, Zhen SXi. Numerical Research on Segmented Flexible
Airfoils Considering Fluid-structure Interaction. Procedia Engineering, 2015; 99: 57-66.
13. Farhat C, Lesoinne M. Two efficient staggered algorithms for the serial and parallel
solution of three-dimensional nonlinear transient aeroelastic problems. Computer Methods
in Applied Mechanics and Engineering, 2000; 182(3-4): 499-515.
14. Kopysov SP, Kuzmin IM, Rychkov VN, Tonkov LE. The divided approach at the
solution of the connected problems of FSI on hybrid computing systems. Works of the
international scientific conference “Parallel computing technologies (PAVT '2015)”.
Yekaterinburg: UrFU of the first President of Russia B. N. Yeltsin, 2015; 415-419. [in
Russian]
15. ANSYS Structural Analysis Guide, Release 15.0. Source: .
16. Wang E, Nelson T. Structural Dynamic Capabilities of ANSYS. Source: .
17. Golovashkin DL, Loganova LV. Solution of difference equations difference scheme with
cyclic boundary conditions on two-dimensional grid areas using multiple graphics
computing devices. Computer Optics, 2012; 36(4):534-540.
218
Information Technology and Nanotechnology (ITNT-2015)