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IMPACT-2013
Modeling and Finite Element Analysis of a Micro Energy
Harvester
M. S. Bhuyan1, Burhanuddin Y. Majlis1 , Sawal H. M. Ali2, Masuri
Othman3 and Md. Shabiul Islam1 1Institute of Microengineering and
Nanoelectronics (IMEN), Universiti Kebangsaan Malaysia (UKM)
43600 UKM Bangi, Selangor, Malaysia. 2Department of Electrical,
Electronic and Systems Engineering, 43600 UKM Bangi, Selangor,
Malaysia. 3Ministry of Science, Technology and Innovation (MOSTI),
Federal Government Administrative Centre
62662 Putrajaya, Malaysia.
AbstractRemote energy efficiency for wireless micro sensor
devices in multimedia, signal processing and communication
technologies is of paramount interest not only for ensuring
continuous network operation despite primary battery limitations,
but also for reducing carbon footprint in communication systems.
Increasing demands of energy supply for micro devices, in
particular, with the advance of complex multimedia tasks, and
shorter communication distances as in sensors or machine-to-machine
communications, energy cost of signal processing becomes comparable
to transmit energy. Battery limitations can be partly alleviated by
energy harvesting technology that can collect various forms of
energy such as solar, wind, kinetic from ambient environment and
convert into electrical energy. In this work, device modeling and
Finite Element Analysis (FEA) of a Micro-Electro-Mechanical Systems
(MEMS) Energy Harvester (EH) is presented. The MEMS-EH converts
ambient fluid-flow into electrical energy by piezoelectric means. A
layered flexible cantilever that vibrates due to the fluid-flow
Krmn Vortex Street generated in the wake of a D-shaped bluff-body
is modeled in COMSOL Multiphysics. Different application modes were
carried out to investigate various response of the MEMS-EH and
feasibility of the design. Simulation of the MEMS-EH in Laminar
fluid Flow Regime showed von Mises effective stress 10.97 GPa and
the maximum displacement of the cantilever tip 60 m. The MEMS-EH
has no rotating part and without any tip mass. Design guideline of
the MEMS-EH model is presented in detail followed by simulation
results. From the analysis, the prospects of this fluid-flow driven
MEMS-EH device to function as an efficient kinetic energy
conversion into electricity for micro sensor is reported.
Keywords Finite Element Analysis (FEA); Energy Harvester (EH);
Fluid Induced Vibration (FIV) ; MEMS; Simulation
I. INTRODUCTION Networks of low-power micro sensor devices
are
increasingly being incorporated in many applications ranging
from environmental monitoring to automobile automations. However,
the real implementation of this technology is limited by the
ability of remote power-up. Most of these sensor devices operate
full day night and could be in locations where primary battery
replacement is quite difficult and costly [1]. Therefore, over the
past decade, researchers are continuously investigating for
innovative miniaturized Micro-Electro-Mechanical Systems (MEMS)
Energy Harvester (EH) device to convert ambient mechanical energies
such as vibrations or fluid flow, into
electricity [2]. Although at present, reported macro and meso
scale EH devices can produce power at milliwatt level, however,
insufficient power is still a major challenge while EH device
miniaturized into micro scale [3]. To overcome remote sensor
power-up problem, researchers to this end, have examined many
different methods of EH technologies including simple combustion in
micro-reactors, ambient vibration harvesting by electrostatic
transducers as well as electromagnetic transducers, Micro-Direct
Methanol Fuel Cells (DMFCs) and micro-solar cell arrays etc. [4].
One of the most studied methods to date, and one of the most
appealing due to its potential simplicity, involves the use of
piezoelectric EH in combination with ambient vibration. The
integration of piezoelectric MEMS-EH functionality with automotive
sensor devices becomes of interest because the evidence of large
amount of mechanical vibration that result during automotive
operation. Moreover, vibration-based energy harvesting is
especially attractive because the associated harvesters can be
scaled to incredibly small sizes and do not require the constant
addition of fuel, such as with combustion reactors and DMFCs.
Furthermore, unlike solar energy harvesting technology,
vibration-based energy harvesters may be packaged away from the
ambient environment to increase their device lifetimes and they can
be operated at all times throughout the day. In addition, this
environmentally friendly piezoelectric MEMS-EH device can have life
of more than twenty years that can provide safety, security of
supply and other benefits including ongoing life-cycle expenses of
automotive sensors [5].
COMSOL Multiphysics software allowed in selecting custom
material and properties for each part of the MEMS-EH by inputting
application environment specific values for the material and other
physical properties. Simulations using different application modes
in COMSOL is carried out to investigate various mechanical analysis
of the MEMS-EH considering automotive environment. The mechanical
outputs of the modeled MEMS-EH are used to evaluate its
performance. Design guidelines are presented in detail following
simulation results. Some interesting aspects that affect the
MEMS-EH output are discussed.
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Fig. 1. Illustration of the idea behind the operation of micro
MEMS-EH.
II. SIMULATION METHODOLOGY OF THE MEMS-EH
A. Model Description The design of analyzed MEMS-EH is based on
bi-layer
cantilever structure in the wake of a D-shaped bluff-body as
shown in Fig 1. The flexible cantilever layer and the supporting
D-shaped bluff-body are made from silicon, while Lead Zirconate
Titanate (PZT)-5A is used for piezoelectric film layer, which is
positioned on the top of the supporting layer and is poled along
the thickness direction resulting in transverse (d31) operation
mode described in Table 1. B. Operation Principle
Fluid flows through a rectangle micro channel, enters through
inlet with a fully developed laminar flow velocity profile, passes
over the D-shaped bluff-body and leaves through the outlet.
Interaction between fluid and the bluff-body creates pattern of
periodic alternating vortex shedding referred as von Karmans vortex
street [5] as shown in Fig. 2. The fluidic pressure impulse on the
piezoelectric cantilever results in short-term lift force. Since
the vortices, shedding in a periodic manner, the resulting lift
forces on the cantilever also vary periodically with time.
Variations in the lift force induce Vortex Induced Vibration (VIV),
which enables damped oscillation on the cantilever structure.
Consequently, the cantilever deflection causes mechanical stress
within the PZT-5H layer that results in the generation of
electrical energy based on piezoelectric effect.
TABLE I. MEMS-EH AND MICRO FLUID CHANNEL IN COMSOL.
Modeled Segment Property Range (m)
Micro Fluid Channel Length 200 Width 150 Height 150
Solid Cantilever Length 70 Width 50
Thickness 1
Peizoceramic layer Length 70 Width 50
Thickness 1 D-shaped bluff-body Diameter 20 D-shaped bluff-body
Length 150
Fig. 2. Von Krmn vortex streets forming in the wake of a
Bluff-body.
III. APPLICATION MODES IN COMSOL FOR THE MEMS-EH MODEL
FEA model of the MEMS-EH is realized within COMSOL Myltiphysics
by employing Solid Stress-Strain with Fluid Interaction application
mode and Piezo Solid application mode from MEMS Module Model
Library. The Solid Stress-Strain with Fluid Interaction application
mode includes Moving Mesh Arbitrary Lagrangian-Eulerian (ALE) and
Incompressible Navier-Stokes application modes by default.
A. Fluid Motion Fluid part of the model is solved with
Navier-Stokes
equations in spatial (deformed) coordinate system within the
flow channel. The fluid is incompressible and fluid motion is
governed by the following Navier-Stokes equations, solving for the
velocity field, u= (u, v) and the pressure, p: in the spatial
(deformed) moving coordinate system.
. I+(u+(u))]+(u.)u+ F (1)
. 0 (2) Where, I is the unit diagonal matrix, and F is the
volume
force affecting the fluid. The model neglects gravitation and
other volume forces affecting the fluid, so F=0. is the dynamic
viscosity, is the density.
B. Structural Mechanics The structural deformations are solved
using elastic
formulation and nonlinear geometry formulation to allow large
deformation, which uses the reference frame and is only active in
the beam. The bluff-body is fixed in the fluid channel so that it
cannot move in any direction. All other boundaries experience a
load from the fluid, given by,
F n. I u u (3)
Where n is the normal vector to the boundary. This load
represents a sum of pressure and viscous forces. In addition, the
predefined fluid load takes the area effect between the reference
frame for the solid and the moving ALE frame in the fluid into
account. C. Moving Mesh
The motion of deformed mesh is modeled using Winslow smoothing.
The Moving Mesh application, which defines the relation between the
spatial frame and the reference frame, solves mesh smoothing
equations in the fluid domain using the solid displacements to
define the coordinate transformations inside the beam. This mode
confirms fluid domain deforming along with the bluff structure.
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Fig. 3. MEMS-EH fixed constraints (red arrows) and load
(blue).
TABLE II. MEMS-EH MATERIAL USED FOR THE FEA ANALYSIS.
Subdomain Property Value Unit Fluid Density 1000 kg/m
3
Dynamic Viscosity 0.001 Pa.s D-shaped Bluff
body (Solid)
Youngs Module 8e6 Pa Poissons Ratio 0.33 -
Density 7850 kg/m3 PZT-5H Density 7500 kg/m3
IV. MEMS-EH SUBDOMAIN AND BOUNDARY IN COMSOL
A. Subdomais Physics MEMS-EH has total three subdomains; the
channel through
fluid flows is the fluid domain, D-shape bluff body and PZT-5H
layer are another two solid subdomains. PZT-5H used is a
transversely isotropic material, which is a special class of
orthotropic materials, has same properties in one plane (isotropic
behavior) and different properties in the direction normal to this
plane. The stress-charge form is selected for the constitutive
equation. For the polarization in the z direction in a 3-D
Cartesian coordinate system, respective data are used in
elasticity-matrix elements in the CE matrix, the piezoelectric
coupling-matrix in the e matrix, and the relative permittivities in
the rS matrix. Material properties parameters of the fluid,
D-shaped bluff body and piezoelectric material are provided in
Table 2.
B. Boundary Physics Fig. 3 shows, in Structural Mechanics
Application Mode,
boundary, D-shaped bluff body are constrained as fixed. In
contrast, the cantilever, protruding out of the trailing edge of
the D-shaped bluff body, is free, which experience a load during
fluid flows. This load represents a sum of pressure and viscous
forces. In Moving Mesh Application Mode, boundary conditions
control displacement of moving mesh with respect to initial
geometry. Motion of deformed mesh is modeled using Winslow
smoothing. At boundaries of the bluff body, this displacement is
the same as the Structural Mechanics deformation. At exterior
boundaries of flow domain, it is set to zero in all directions. The
Navier-Stokes equations are solved in the spatial (deformed)
coordinate system. In the Piezo Solid Application mode, Zero
charge/symmetry is selected for all the boundaries except the upper
and lower surface of the PZT-5H, which is grounded. At the inlet,
the model uses a fully developed laminar flow. Zero pressure is
applied at the outlet. At all other boundaries, no-slip conditions
are applied.
Fig. 4. Mesh of the MEMS-EH
C. Mesh Generation A mesh is a partition of the geometry model
into small
units of simple shapes. The MEMS-EH follows 3D meshing
techniques. Due to MEMS-EHs thin layer cantilever, advanced meshing
technique is used to avoid geometric scale variations problem. Mesh
quality is considered poor if dropping to less than 0.1 in a 3D
geometries model. MEMS-EH scale factor 1.0 was assigned for in the
x, y, and z directions. It should be noted that the FEM analyses of
the MEMS-EH was performed with the tetrahedral global mesh with
minimum element quality 0.3061. The mesh generator partitions the
sub-domains of the MEMS-EH into triangular mesh elements with 23865
Degree of Freedom (DoF). Total number of elements (tetrahedral) was
4152 and the number of boundary elements was found (Triangular)
2384. These values represented the maximum size able to accurately
mesh the smallest feature of the device (piezoelectric layer). As a
result, control meshes and/or finer meshes are unnecessary as the
default sizes prove to be more than adequate. Fig. 4 shows the mesh
of the MEMS-EH.
V. FEA SIMULATION RESULTS OF THE MEMS-EH The fluid-flow driven
MEMS-EH has been analyzed using
COMSOLs different application mode to simulate various
mechanical and electrical outputs for robust design consideration.
Fig. 5 shows the flow channel that expressing velocity field as a
directional vector. The changes in the fluid-flow due to the
D-shaped bluff body have a clear visible effect on the cantilever
and fluid-flow itself. Top and bottom surfaces of the cantilever
experience increased viscous and pressure
Fig. 5. The velocity field and the flow lines at flow velocity
of 1.5 m/s.
Load direction arrow
D-bluff body fixed constrain
Triangular mesh element
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Fig. 6. The von Mises effective stress on cantilever.
forces that cased cantilever deformation. Fluid-flow domain has
changed considerably. The color and direction of the streamlines
indicate the velocity and the direction of the flow. Fig. 6 shows
that the static analysis of von Mises effective stress maximum
value of 10.97 GPA. , which, compared with the materials yield
strength results in high utilization factor. Transient Analysis of
the MEMS-EH was carried out at excitation frequency of 500 Hz. The
purpose of this analysis was to find the transient response from a
harmonic load during the first five periods (10 ms). This analysis
solves for the transient solution of the displacements and
velocities as functions of time. Rayleigh damping, where damping
parameters were specified that are proportional to the mass (dM)
and stiffness (dK). Plot in Fig. 7 shows the displacement of the
cantilever tip, at ambient pressure at x-displacement (dashed
line), y-displacement (dashed-dotted line), and z-displacement
(solid line). Frequency response analysis of the MEMS-EH with
Rayleigh damping was to find the transient response with an
excitation frequency in the range 350650 Hz. Fig. 8 shows the tip
displacement amplitude as a function of the excitation frequency
range.
VI. CONCLUSION In summary, a FEA modeling of a MEMS-EH without
any rotating part that couples mechanical, piezoelectric and fluid
domain to convert fluid-flow driven kinetic energy into electricity
is presented in this paper. COMSOL Mechanical analysis results
confirm the probability of the fluid flow based MEMS-EH. The
addition of the D-shaped bluff-body made significant improvements
in vortex shedding frequency exerting on the cantilever, hence
greatly magnified the cantilever deflection. This design example
just begin to touch on the large potential for micro energy
harvesting from vortex shedding to provide power for many
beneficial sensors that could be used in and around fluid-flow
ducts. Benefits of this kind of MEMS-EH device can be seen as a
micro power source for sensors monitoring temperature and humidity
usually operating on a low duty cycle with as little as 1-20 W.
Other application areas such as liquid or gaseous water pipes and
natural gas lines also exhibit similar characteristics. This model
provides relatively high performance at low fluid-flow velocity,
and will ideally provide the necessary performance over a wider
range of fluid-flow velocities.
Fig. 7. Cantilever tip displacement (Transient Analysis)
Fig. 8. Displacement amplitude at excitation frequency range of
350-650 Hz
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