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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from highly unsteady fluid flows using piezoelectric materials, J. Intel. Mat. Sys. Struct. vol. 21 126378, 2010.

[4] Ming Zhaoa and Liang Chengb, Numerical simulation of vortex-induced vibration of four circular cylinders in a square configuration, Journal of Fluids and Structures, vol. 31, 2012.

[5] C.H.K. Williamson and G.L. Brown, A Series in to represent the Strouhal-Reynolds number relationship of the cylinder wake, J. Fluids Struct., vol. 12, 1998.

von Mises effective stress maximum

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