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The 9th European Congress on Computational Methods in Applied Sciences and Engineering 
ECCOMAS Congress 2024 
3 – 7 June 2024, Lisboa, Portugal 
 
 
 
FINITE ELEMENT ANALYSIS OF A RIGID BODY ISOLATED WITH 
HIGH-DAMPING UNBONDED FIBER-REINFORCED ELASTOMERIC 
ISOLATORS 
GAETANO PIANESE
*
, NIEL VAN ENGELEN
†
 AND GABRIELE MILANI
*
 
*
 Department of Architecture, Built Environment and Construction Engineering (ABC), Politecnico di 
Milano, Piazza Leonardo da Vinci 32, 20133 Milan, Italy 
e-mail: gaetano.pianese@polimi.it, gabriele.milani@polimi.it 
 
† Department of Civil and Environmental Engineering, University of Windsor, 401 Sunset Ave., 
Windsor, Ontario N9B 3P4, Canada 
e-mail: niel.vanengelen@uwindsor.ca 
 
 
Key words: Finite element analysis, unbonded fiber-reinforced elastomeric isolator, non-
linear time history analysis, high-damping. 
 
Abstract. Fiber-reinforced elastomeric isolators (FREIs) stand as a recent advancement in 
seismic isolation technology, primarily designed to alleviate manufacturing and production 
costs. Unlike conventional steel-reinforced elastomeric isolators (SREIs), FREIs incorporate 
fiber fabric layers instead of steel laminas for reinforcement. This substitution not only reduces 
costs but also results in a seismic device with good isolation properties. Of particular 
significance are unbonded fiber-reinforced elastomeric isolators (UFREIs) when employed 
without bonding or fastening between the superstructure and foundations. In such 
configurations, UFREIs exhibit noteworthy lateral deformation, displaying high damping 
properties and lower stiffness compared to their bonded counterparts in traditional applications. 
This study engages in a comprehensive exploration of the seismic isolation characteristics of 
high-damping UFREIs. Utilizing the Finite Element (FE) software Abaqus, a rigid body 
isolated by two UFREIs has been modeled and subjected to 2D non-linear time history analyses. 
The results, encompassing acceleration, displacements, and horizontal forces of the rigid body, 
have been compared to experimental findings from a prior study conducted by the authors 
(shake table tests). Beyond the commendable isolation properties of devices, the results validate 
the UFREI FE model as a suitable representation for understanding device behavior in future 
structural analyses. This validation is particularly crucial, given the possibility of developing a 
model based on simple laboratory material tests involving rubber and fiber. 
 
  
Gaetano Pianese, Niel Van Engelen and Gabriele Milani. 
 2 
1 INTRODUCTION 
Fiber Reinforced Elastomeric Isolators (FREIs) have gained significant attention in recent 
years due to their ability to enhance the seismic performance of structures [1,2]. Unlike 
traditional steel-reinforced elastomeric isolators (SREIs), FREIs employ thin fiber layers as 
reinforcement. This distinction offers several advantages, such as simplified manufacturing 
processes, reduced weight of the isolators, and reduced costs. These characteristics make FREIs 
an attractive option for both upgrading existing structures and safeguarding new constructions 
in earthquake-prone regions, particularly in developing countries. 
FREIs can be installed using various methods, including fully bonded [3][1], unbonded 
(UFREI) [4][5][6], and partially bonded (PBFREI) [7][8][9] configurations. UFREI is 
especially noteworthy because it functions without direct bonding or mechanical fastening to 
the structure. Instead, it relies on friction between the isolator and the contact surfaces to 
transmit shear loads. This friction-based mechanism, which allows for rollover lateral 
deformation, enhances damping while reducing horizontal stiffness, thus improving the overall 
seismic response compared to similar bonded systems [10]. These unique features have spurred 
significant research interest, leading to numerous studies on the behavior and seismic 
performance of UFREIs. Although the mechanical properties of UFREIs are well-documented 
through both numerical simulations and experimental studies, their application in actual 
structures remains an active area of exploration [11]. Numerical modeling is a particularly 
valuable approach for assessing the seismic performance of FREIs in structural applications, as 
it provides a cost-effective alternative to manufacturing and experimental testing. 
In this paper, a numerical simulation of experimental shake table tests is performed in 
Abaqus [12]. A rigid body, isolated with two high-damping UFREIs, is subjected to 
unidirectional shake table tests. The time history analysis numerical results have been compared 
with the experimental ones to investigate the capacity of the finite element model (FEM), 
obtained from simple rubber material tests, to capture the lateral behavior of the device. This 
validation is crucial to determine if this tool can be used for future numerical structural 
applications. 
2 HIGH-DAMPING FIBER-REINFORCED ELASTOMERIC ISOLATORS AND 
SHAKE TABLE TESTS 
This study focused on seismic isolators specifically designed for the protection of low-rise 
masonry structures [13–16]. These are composed of alternating layers of high-damping rubber 
and glass fiber fabric. The isolators consist of high-damping rubber and glass fiber layers. The 
key geometric features and outcomes from the cyclic shear tests in terms of horizontal stiffness 
and damping ratios are presented in Table 1 and Table 2. The shear tests have been performed 
up to 200% of shear strain under a vertical pressure of 1.73 MPa. This vertical load was selected 
based on the conditions anticipated in the shake table tests to understand better the behavior of 
the isolators and the performance expectations. Further details on the experimental tests are 
available in [13]. 
Gaetano Pianese, Niel Van Engelen and Gabriele Milani. 
 3 
 
(a)  
 
(b) 
Figure 1: High-damping UFREI: (a) design and (b) structural application. 
Table 1: Geometrical characteristics of the high-damping UFREIs 
Height Base Rubber thickness Fiber thickness 
n° rubber 
layers 
n° fiber 
laminas 
Total rubber 
thickness 
[mm] [mm] [mm] [mm] [-] [-] [mm] 
67.0 200 4 0.5 15 14 60 
Table 2: UFREI cyclic shear test results 
Shear strain Horizontal stiffness Damping ratio 
[%] [kN/mm] [%] 
25 0.52 10.70 
50 0.41 9.97 
75 0.34 9.85 
100 0.29 9.84 
150 0.24 10.80 
200 0.23 11.60 
Shake table experiments were carried out in the Applied Dynamics Laboratory at McMaster 
University using a rigid block composed of two concrete slabs. The dimensions of the block 
were 2.80 meters by 2.00 meters by 0.40 meters, and it weighed approximately 110 kN, as 
shown in Figure 2. Each UFREI experienced a vertical load of 1.73 MPa and was aligned 
centrally along the block, separated by 1.30 meters in the North-South axis, which was the 
primary direction of testing. The block underwent testing with four different seismic events 
from earthquake records of Iran: the Tabas earthquake of 1978, with a peak ground acceleration 
(PGA) of 0.85 g, the 1990 Manjil earthquake, with a PGA of 0.51g, the Bam earthquake of 
2003, PGA of 0.81, and the 2017 Sarpol earthquake, with a PGA of 0.52 g. Due to constraints 
in the setup, each ground motion was compressed in time by a factor of two. The acceleration 
levels were gradually increased from 0.10 g PGA to their original values in increments of 0.10 
g. This stepwise approach facilitated a thorough analysis of the responses of the UFREIs to 
various acceleration levels and helped maintain the safety of the test setup by enabling the 
UFREI 
Glass 
fiber fabric 
High damping  
rubber 
Superstructure 
Foundation 
Gaetano Pianese, Niel Van Engelen and Gabriele Milani. 
 4 
detection of any potential slips or damages. Additional details on these experimental tests are 
described in [13]. In this study, not all test scenarios were executed numerically. Specifically, 
tests were selected at 0.20 g increments, starting at 0.10 g, and in the domain of stable response 
(i.e., no slip). 
  
  
(a) (b)  
Figure 2: Shake table test setup: (a) north-south and (b) west-east views. 
3 FINITE ELEMENT MODEL 
The setup of the experimental shake table tests was recreated in Abaqus (Figure 3). For the 
isolators, the rubber material was modeled using Yeoh and Maxwell’s hyperelastic and 
viscoelastic models using eight-node brick elements (C3D8RH). The glass fiber fabric layers 
embedded within the rubber [17] were modeled using a four-node doubly curved general-
purpose shell, accommodating finite membrane strains. They were characterized by isotropic-
elastic properties, with a Young’s modulus of 1500 MPa and a Poisson's ratio of 0.2 [18]. An 
in-depth description of this modeling process is thoroughly detailed in earlier research [19]. 
The shake table was modeled as a rigid body using four-node 3D bilinear rigid quadrilateral 
mesh elements. The concrete blocks were modeled collectively as a single entity with a Young’s 
modulus of 22000 MPa, a Poisson's ratio of 0.2, and a density of 2.50 x 10-9 tonne/mm3. This 
setup maintained a vertical pressure of 1.73 MPa on the isolators. Since the tests were conducted 
in a unidirectional manner, the concrete block was restricted in the Y direction, and additional 
constraints were applied to the shake table in the Y and Z directions. The shake table's reference 
point (RP) received the acceleration time history inputs along the X-axis. The interactions 
between the isolators and both the rigid block and the shake table were simulated using penalty 
surface contact with a friction coefficient of 1, a standard value chosen to avoid slipping [20]. 
Concrete 
block 
Concrete 
block 
Shake table Shake table 
UFREI 
Gaetano Pianese, Niel Van Engelen and Gabriele Milani. 
 5 
 
 
 
Figure 3: 3D FE model of the shake table setup. 
4 NUMERICAL RESULTS AND DISCUSSION 
The results from the non-linear time history analyses in the numerical model were compared 
with experimental data, focusing on the time histories of horizontal acceleration, displacement, 
and force. As an example, Figure 4 shows the time history of accelerations, displacements, and 
force for the Tabas 0.4 g ground motion test. Peak values from each earthquake record were 
identified for this comparison. Ratios of numerical model results to experimental data for each 
peak were computed. These results are summarized in Table 3. Additionally, the last row of the 
table displays the mean absolute error (MAE) percentage for all PGA amplitudes and ground 
motions examined. 
  
        (a)           (b) 
Gaetano Pianese, Niel Van Engelen and Gabriele Milani. 
 6 
 
(c) 
Figure 4: Non-linear time history results for the Tabas test at 0.40g: (a) comparison of the acceleration, (b) 
force, and (c) displacements. 
Table 3: Model to experimental results ratio for peaks 
Ground Motion PGA (g) Displacement Horizontal force Acceleration 
Bam 
0.11 1.42 1.10 1.17 
0.34 1.02 1.06 1.18 
0.40 0.97 1.13 1.17 
Tavas 
0.11 2.13 0.82 0.90 
0.39 1.04 1.00 1.07 
0.55 0.86 1.01 1.13 
0.66 1.01 1.18 1.23 
Manjil 
0.10 1.02 0.62 0.67 
0.25 1.51 0.83 1.14 
0.51 0.52 0.48 0.53 
Sarpol 
0.13 0.92 0.69 0.73 
0.27 1.20 0.96 1.16 
0.54 1.10 1.01 1.19 
MAE [%] 24.46 16.08 20.08 
The evaluation of the data showed that the highest MAE occurred in displacement 
measurements, reaching approximately 25%. The MAE for horizontal force was about 16%, 
while for acceleration, it was around 20%. Upon further inspection, the 3D FE model struggled 
to accurately simulate the behavior of the device at the smallest PGA amplitudes, typically 
associated with minimal shear strain, which was an anticipated outcome. As noted in prior 
studies, variations in the responses of the FE model, such as differences in stiffness and 
damping during low displacement cyclic shear tests, were observed [19]. Since the values at 
lower amplitudes are typically small, the resulting percentage errors can appear 
disproportionately large, potentially overstating the error's significance relative to the true scale 
of the measured values. To address this, a new MAE was computed, omitting the lowest PGA 
amplitudes from each set of ground motions. With this adjustment, the MAEs decreased to 
11.77% for displacements, 8.62% for horizontal force, and 13.38% for accelerations, bringing 
them below the 15% threshold, which is generally considered acceptable in engineering 
practices. 
Gaetano Pianese, Niel Van Engelen and Gabriele Milani. 
 7 
5 CONCLUSIONS 
This research evaluated the effectiveness of a 3D FE model, developed from simple material 
tests, in representing the seismic isolation performances of UFREIs. Specifically, shake table 
tests were simulated using Abaqus, and the resulting data, including displacement, horizontal 
forces, and acceleration time histories, were compared with experimental findings. The 
comparison focused on the peak values. 
The results showed that the UFREI 3D FE model had difficulty accurately simulating 
behavior at lower peak ground acceleration (PGA) levels (PGA ≤ 0.13 g), which are typically 
associated with low shear strain. However, the FE model showed a strong correlation with 
experimental results at higher PGA amplitudes, confirming the potential of using this tool for 
predicting seismic performance in structural applications. Additionally, the ability of the model 
to function without requiring calibration from UFREI cyclic shear test data emphasizes its 
practical value, especially when specific experimental data is unavailable, a common scenario 
during preliminary research phases. 
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[1] Van Engelen NC. Fiber-reinforced elastomeric isolators: A review. Soil Dynamics and 
Earthquake Engineering 2019;125:105621. 
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[2] Sheikh H, Van Engelen NC, Ruparathna R. A review of base isolation systems with 
adaptive characteristics. Structures 2022;38. 
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[4] Habieb AB, Valente M, Milani G. Base seismic isolation of a historical masonry 
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Engineering 2019;120:127–45. https://doi.org/10.1016/j.soildyn.2019.01.022. 
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Reinforced Neoprene Seismic Isolators Utilized in an Unbonded Application. Journal 
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[6] De Raaf MGP, Tait MJ, Toopchi-Nezhad H. Stability of fiber-reinforced elastomeric 
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[7] Van Engelen NC, Osgooei PM, Tait MJ, Konstantinidis D. Partially bonded fiber-
reinforced elastomeric isolators (PB-FREIs). Struct Control Health Monit 
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reinforced elastomeric bearings: Feasibility, effectiveness, aging effects, and low 
temperature response. Eng Struct 2019;179:120–8. 
https://doi.org/10.1016/j.engstruct.2018.10.043. 
[9] Van Engelen NC, Tait MJ, Konstantinidis D. Investigation of partially bonded fiber-
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Canadian Journal of Civil Engineering 2019;46. https://doi.org/10.1139/cjce-2018-
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[10] Toopchi-Nezhad H, Tait MJ, Drysdale RG. Bonded versus unbonded strip fiber 
reinforced elastomeric isolators: Finite element analysis. Compos Struct 2011;93. 
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[11] Thuyet VN, Deb SK, Dutta A. Mitigation of Seismic Vulnerability of Prototype Low-
Rise Masonry Building Using U-FREIs. Journal of Performance of Constructed 
Facilities 2018;32. https://doi.org/10.1061/(asce)cf.1943-5509.0001136. 
[12] Smith M. ABAQUS/Standard User’s Manual, Version 6.9. Dassault Systèmes Simulia 
Corp.; 2009. 
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isolated with high-damping unbonded fiber-reinforced elastomeric isolators. Structures 
2024;64. https://doi.org/doi.org/10.1016/j.istruc.2024.106595. 
[14] Pianese G, Van Engelen N, Toopchi-Nezhad H, Milani G. High-damping fiber-
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[15] Pianese G, Milani G, Milani F. Prediction of the optimal vulcanization of a fiber-
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[18] Ghorbi E, Toopchi-Nezhad H. Annular fiber-reinforced elastomeric bearings for 
seismic isolation of lightweight structures. Soil Dynamics and Earthquake Engineering 
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[19] Pianese G, Van Engelen N, Toopchi-Nezhad H, Milani G. An experimental and 
numerical insight into the unbonded and partially bonded high-damping fiber-
reinforced elastomeric . Soil Dynamics and Earthquake Engineering (Under Review) 
2024. 
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https://doi.org/10.1016/j.istruc.2021.08.095. 
  


Finite element analysis of a rigid body isolated with high-damping unbonded fiber-reinforced elastomeric isolators

Dunn, H.

Lahooti, M.

Chakraborty, N.

Gao, A.

Vortex Dynamics of Vertical-Axis Wind Turbines on Mars

Heidler, V.

Bublík, O.

Vimmr, J.

The 9th European Congress on Computational Methods in Applied Sciences and Engineering
ECCOMAS Congress 2024
3–7 June 2024, Lisboa, Portugal
CONVOLUTION NEURAL NETWORK FOR FLUID FLOW
SIMULATIONS IN CASCADE WITH OSCILLATING
BLADES
Václav Heidler1, Ondřej Bubĺık1 and Jan Vimmr1,2
1 NTIS - New Technology for the Information Society, Faculty of Applied Sciences, University
of West Bohemia, Technická 8, 30100 Pilsen, Czech Republic
2 Department of Mechanics, Faculty of Applied Sciences, University of West Bohemia,
Technická 8, 30100 Pilsen, Czech Republic
Key words: convolution neural network, compressible fluid flow, blade cascade, fluid-structure
interaction
Summary. The analysis of blade cascades for flutter onset is crucial for the operational safety
of turbomachinery. Despite significant advancements in computational power, comprehensive
CFD analysis remains a time-consuming task. This paper aims to mitigate the time demands
of CFD calculations by utilizing convolutional neural networks (CNNs). The developed model
is tested on a Fluid-Structure Interaction (FSI) analysis, revealing the conditions for flutter.
1 INTRODUCTION
Recent advances in deep learning have significantly impacted the field of computational fluid
dynamics (CFD), especially through the application of convolutional neural networks (CNNs).
These networks are capable of modeling flow characteristics, handling complex geometries, and
processing extensive datasets, making them invaluable for fluid flow predictions. Their ability
to learn from raw data and make real-time predictions has established CNNs as powerful tools
in various applications of fluid dynamics. Pioneering work [1] marked a significant milestone
by applying CNNs to predict steady fluid flow. In work [8] authors extended this approach to
predict unsteady turbulent fluid flows, inspiring numerous subsequent studies exploring CNN
applications in fluid dynamics, including works [10, 2, 3, 4].
This study aims to utilize a convolutional neural network to predict unsteady flow fields in
a cascade of oscillating blades. The primary motivation for using CNNs is their high prediction
speed, which addresses the significant time constraints of traditional CFD analyses. The de-
veloped neural network model is validated against the FlowPro CFD solver [6] in an unsteady
2D problem with a moving boundary. FlowPro is based on the Discontinuous Galerkin finite
element method and was also used for the generation of the training dataset for the model.
Further testing is conducted on an FSI task to reveal the conditions for flutter onset. The usage
of CNN in FSI analysis not only reduces the computational cost but also opens new avenues for
real-time and large-scale applications.
2 PROBLEM DESCRIPTION
In this work, we examine a system of bodies composed of three blades. Specifically, we focus
on solving a cross-section of the blade cascade, as the problem is defined in a 2D space. The
Václav Heidler, Ondřej Bubĺık and Jan Vimmr
motion of the first and third blades is prescribed by a harmonic function, as follows
y1 = A sin(2πf +Φ), y3 = A sin(2πf − Φ),
where A is the amplitude, f is the frequency and Φ is the phase angle. The middle blade is
free to move with one degree of freedom along the yy-axis, and its motion is governed by a
mass-spring model.
mÿ2 + ky2 = L,
where m is the blade mass, k is the blade stiffness and L is the lift force from the fluid, defined
using the flow field variables p, u, and v as follows:
L =
∮
Γ
(
pny −
1
Re
[(
∂v
∂x
+
∂u
∂y
)
nx + 2
∂v
∂y
ny
])
dl.
The situation is illustrated in Fig. 1. The stiffness k of the blade is chosen such that the natural
Figure 1: Problem setup
frequency of the oscillating blade matches the prescribed frequency f of the oscillating blades,
i.e., k = m(2πf)2.
2.1 Mesh generation and deformation
For the given problem, we consider a structured computational grid of size 128× 128 points
generated by an elliptic grid generator; see Fig. 3. The grid points entering the model vary
depending on the position of the blades. To compute the deformed grid, we use a simple
algorithm based on blending functions, which applies to computing grid deformation for a system
of rigid bodies. For each of the blades, we first precompute the so-called blending function bfb(x)
as a solution to the Laplace equation with the following Dirichlet boundary conditions
bfb(x) =
{
1 if x ∈ Γj , b = j,
0 if x ∈ Γj , b ̸= j
where Γj is the boundary of j-th blade.
Let x0ij = [x
0
ij , y
0
ij ] are the points of the initial undeformed mesh. Let x
b
t = [x
b, yb] is the
translation vector of a blade b. Then we can compute the points of the deformed mesh as follows
xij = x
0
ij +
∑
b
bfbijx
b
t
2
Václav Heidler, Ondřej Bubĺık and Jan Vimmr
Figure 2: Blending functions. The blue lines shows initial positions of blades.
Figure 3: Illustration of the Deformed State of the Mesh: The Blue Line Represents the Undeformed
Position of the Profiles.
3 NEURAL NETWORK MODEL
To predict unsteady incompressible fluid flow in blade cascade, we use a specialized con-
volutional encoder-decoder neural network known as U-Net [5], as depicted in Fig. 4. The
encoder compresses input data from the initial layer into an encoded representation by applying
convolutional filters followed by pooling layers, progressively down-sampling the data until it
is sufficiently compressed. The decoder, which mirrors the encoder, then increases the spatial
resolution and reduces the number of channels until the desired output is reconstructed. This
process involves upsampling and deconvolution, the inverse operations of pooling and convo-
lution. The architecture also includes skip connections, which concatenate each encoder layer
with its corresponding decoder layer. These connections ensure that partially encoded input
information from each encoder layer is available during output reconstruction. Consequently,
the number of input channels in the decoder is increased by the number of channels in the en-
coder due to this concatenation. The neural network’s input is a three-dimensional array with
3
Václav Heidler, Ondřej Bubĺık and Jan Vimmr
dimensions 128×128×8, containing eight values for each grid point: the x and y coordinates of
the grid points, corresponding boundary mark, mesh velocities ẋ and ẏ and flow field u, v and
p at time level tn. The boundary mark is a binary value, equal to 1 if the grid point is on the
boundary of the blade profile, and 0 if the grid point is within the fluid domain. The network
outputs the pressure and velocity fields at the grid points at time tn+1. The key parameters of
the developed CNN structure are summarized in Table 1.
Figure 4: Neural network architekture
Table 1: Hyperparameters of the U-Net
Parameter Value
Input shape 128× 128× 8
Output shape 128× 128× 3
Initial number of filters 12
Convolution frame 3× 3
Pooling frame 2× 2
Pooling function Max pooling
Activation function ReLU
Activation function at output Sigmoid
Depth 7
Trainable parameters 1,062,039
4 MODEL TRAINING AND VALIDATION
The proposed neural network model was trained using data from four CFD simulations.
In each simulation, the harmonic kinematic motion of the three blades was randomly set as
4
Václav Heidler, Ondřej Bubĺık and Jan Vimmr
yi = Ai sin(2πfi), i = 1, 2, 3. The amplitudes Ai and frequencies fi were randomly chosen from
the intervals A ∈ [0.05, 0.2] and f ∈ [0.1, 2.0]. The computation of the flow field was performed
using CFD software based on the discontinuous Galerkin finite element method [6]. The trained
model was validated on a random kinematic motion, see Fig. 6, where the lift force acting on
each blade over time is compared. The CFD calculation is shown in blue, and the neural network
prediction is shown in orange.
Figure 5: Comparison of the flow field predicted by the neural network (left) and the flow field computed
using CFD simulation (right).
5
Václav Heidler, Ondřej Bubĺık and Jan Vimmr
Figure 6: Comparison of lift between CFD simulation (blue) and neural network prediction (orange) for
the upper (left), middle (middle), and lower (right) blade.
5 FSI SIMULATION RESULTS
Consider the FSI problem described in the introductory section. For the upper and lower
blades, we set a harmonic motion with an amplitude of A = 0.15 and a frequency of f = 0.1.
The parameters for the middle blade are chosen as follows. The natural frequency is considered
the same as the oscillation frequency of the surrounding blades, i.e., fn = f = 0.1. For the
chosen mass m = 20, the spring stiffness is calculated as k = m(2πf)2 = 7.84. The goal of
this study is to observe the excitation of the middle blade depending on the phase angle Φ. We
performed a total of four simulations for the fundamental phase angles Φ = −π/2, −π/4, 0, π/4.
Figs.7-10 show the lift forces acting on the blades and the blade displacements over time. From
the graphs, it is evident that for the phase angles Φ = −π/2, −π/4, 0, the oscillation amplitude
of the middle blade remains limited. This indicates that the oscillation of the blade is damped
in these regimes. This situation is well characterized in Fig.11, which shows the energy absorbed
by the middle blade from the flow field. A dramatically different situation occurs for the phase
angle Φ = π/4, where the blade’s excitation occurs relatively quickly. This is again evident in
Fig.11, where a rapid increase in absorbed energy is shown. This case is highly susceptible to
flutter.
Figure 7: Lift (left) and y-displacement of the middle blade (right) for the phase angle Φ = −π/2.
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Václav Heidler, Ondřej Bubĺık and Jan Vimmr
Figure 8: Lift (left) and y-displacement of the middle blade (right) for the phase angle Φ = −π/4.
Figure 9: Lift (left) and y-displacement of the middle blade (right) for the phase angle Φ = 0.
Figure 10: Lift (left) and y-displacement of the middle blade (right) for the phase angle Φ = π/4.
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Václav Heidler, Ondřej Bubĺık and Jan Vimmr
Figure 11: Energy absorbed by middle blade during time.
6 CONCLUSIONS
In this work, a model for predicting unsteady flow in a blade cascade using a convolu-
tional neural network was developed. The model was used to analyze the onset of flutter in
a simple cascade consisting of three blades. The analysis showed that for the phase angles
Φ = −π/2, −π/4, 0, there is no excitation of the middle blade. However, for the phase angle
Φ = π/4, there is an unlimited growth in the oscillation amplitude of the middle blade, leading
to flutter. The obtained conclusion is in good agreement with generally accepted findings, where
the phase angle Φ = π/4 is characteristic of the onset of flutter and corresponds to the so-called
travelling waves, which are recorded in turbine disks [7].
The analyzed task demonstrates that the neural network-based model can produce excellent
results in a fraction of the computational time. The neural network can generate the flow
field up to three orders of magnitude faster than traditional CFD computations. The obtained
computational model can be extended to any number of blades using the Schwarz alternating
method.
7 ACKNOWLEDGEMENTS
This research is supported by project ”Investigation of 3D flow structures and their effects
on aeroelastic stability of turbine-blade cascades using experiment and deep learning approach”
GACR 24-12144S of the Grant Agency of the Czech Republic.
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Convolution Neural Network for Fluid Flow Simulations in Cascade with Oscillating Blades

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