Deep Ocean Vortex Power Sensors

Utilizing Deep Ocean Currents to Power Extended Duration Sensors

Leverett Bezanson and John Thornton

Progeny Systems San Diego, CA

[email protected]

Nick Konchuba and Shashank Priya Center for Energy Harvesting Materials and Systems (CEHMS), Virginia Tech

Blacksburg, VA [email protected]

Abstract- Energy harvesting has the potential to save billions of dollars and create ground breaking technologies for sustainable ocean

monitoring systems. Replacement of batteries from the sensors deployed on sea floor is expensive and tedious process. The cost of maintenance for battery operated equipments in the deep waters may be prohibitive. Thus, it is highly desirable to develop a system that harnesses energy to prolong the life of these sensors or transducers and reduce the maintenance costs. The low energy density environment of the sea floor limits the methods that can be used for energy harvesting. Vortex Induced Vibrations (VIV) due to fluid flow plagues structures and cables in the undersea environment. The energy produced can be very destructive and the effect has been analyzed for many years. It is this phenomenon that Progeny has been investigating to power the undersea sensors. This will be accomplished by applying the force produced by VIV to piezoelectric cymbal generators and storing the energy in secondary batteries. Progeny Systems has teamed with Center for Energy Harvesting Materials and Systems (CEHMS), Virginia Tech, whom are leader in the vibration energy harvesting field, and have successfully demonstrated the power generation capability of cymbal under laboratory conditions using the boundary conditions derived from VIV. Extensive analytical modeling and ATILA based FEM analysis was conducted to optimize the performance of the cymbal transducers.

I. INTRODUCTION

SURVIVE was developed for submarine tracking transducers deployed for training missions under a Phase I SBIR supported by NAVAIR. The technology can be applied to any underwater system that has similar power requirements. The Supply Utilizing Vortex Induced Vibration Energy (SURVIVE) is a sea floor power supply that can power components that have either short duration medium power draw or a low power steady draw. To exemplify, this system could power surveillance arrays,

oceanographic sensors of many varieties, or health monitoring systems of deep ocean oil platforms. The objective of SURVIVE is to prolong the life of electronics up to 10 years without undergoing mandatory maintenance. Risks that can decrease the lifespan are fatigue of the vibrating rod or the generators, and the cycle limitations of the batteries. This paper describes each subsystem of energy conversion sequentially. Each section includes the current design and verification simulations and experiments.

Section II details the initial mechanical conversion of the slow moving currents found on the ocean floor into oscillatory compression and tension stress that can be applied on to piezoelectric cymbal transducers. This section includes simulations and mathematical models that were developed to optimize the mechanical design and output power characteristics. Section III includes the laboratory tests on the cymbal generator array. A prototype of three generators was built and characterized through experimentation to verify the multi-physics models and simulations. Section IV outlines the electrical conversion and summation of the energy and how it is applied to the battery pack. Also included in this section are the characteristics of the chosen battery chemistry and the available loads that the supply can drive. Simulations on the switched power supply were done with SIMPLIS, along with MATLAB models of performance. Section V provides a look into the future research and configurations that is possible for the SURVIVE structure.

Fig. 1. Solid Model of SURVIVE

978-1-4244-4333-8/10/$25.00 ©2010 IEEE

II. MECHANICAL ANALYSIS, DESIGN AND SIMULATIONS

A. Analysis and Design of Vibrating Cantilever

SURVIVE is based on harvesting energy from water motion by including a electromechanical transducer that can vibrate close to the resonance in the flow as a result of the vortex’s created around the structure. This is referred to as Vortex Induced Vibration (VIV). The vortex street wake is similar regardless of the geometry of the structure. As the vortices are shed from various facets, alternating surface pressures are induced on the structure which then causes the vibration of the structure. Typically, engineers analyze the prevailing environment, wind or current, to ensure that structure designs will not resonate when forced at those environmental conditions. This is accomplished by evaluating the expected vibration frequency which would be caused by the fluid flow and ensuring that the structural design does not have a similar resonant frequency. In the case of SURVIVE, the premise was to design the structure to resonate at the same frequency as the vortex street and harvest the energy created. The ability to design this mechanism is shown in the following analysis. Vortex shedding from a structure in a current flow is a function of Reynolds number, Re given as [1]: (1)

Where is the free stream velocity and is the characteristic dimension . The Strouhal number (S) is a dimensionless

proportionality constant between the predominant frequency of vortex shedding and the free stream velocity divided by the characteristic dimension give as [1]:

(2) Where is vortex shedding frequency. At Re < 105, S is a maximum of 0.22 at Re=103. In the transitional range, 3x105 < Re <

3x106, researchers have found that very smooth surface cylinders has a chaotic, disorganized, high-frequency wake and S as high as 0.5 [1]. The environment analyzed had a 0.25 m/s average current. To keep the rod at a reasonable length it was found that the current must be amplified from all directions. A proprietary structure was created to achieve an amplified current across the face of the rod from different directions. A cylinder can be used to maximize the omni-directional power conversion and achieve the higher modes of vibration which create the load needed to drive piezoelectric cymbal transducers. The lateral and fore-aft force per unit length can be written as [2]:

(3)

Where Cd is coefficient of drag, Cl is coefficient of lift and ρ is the density of seawater. The coefficient of lift has been shown

in literature to be a function of tip amplitude. A curvefit of experimental data for a pivoted rod at resonance with vortex shedding is provided in Ref. [1]. The in-line frequency has been proven to vibrate at twice the lateral frequency. The cylinder structure was designed to have a resonant frequency for the transverse case. The resonant frequency of a cantilever can be calculated as [3]:

(4) Where fn is the Natural frequency, Kn is the mode number, E is the modulus of elasticity, I is the moment of inertia, g is the acceleration, w is the load per unit length, and l is the length of beam. The net force was applied at the center of the length of the rod, or at 1.1m. The resultant moment felt at the base of the rod was found to be 37.5 N-m for in-line vibration. By analyzing the structure as a simply supported beam with a moment applied to the center of the beam we calculated the length of the beam to achieve the desired force applied to the structure. We hoped to achieve a 60N time varying force at the simple supports then the length of the beam, diameter of the plate which mounts the cylindrical rod, was 0.625m. The resulting resonant frequency was designed to be 60 Hz which could be achieved for the electromechanical transducers.

B. Simulations

Several simulations were conducted to verify the calculations and optimize the design. These simulations incorporated the electrical load and parameters such as input frequencies and forces were varied to achieve the power output in the desired range. The electronics and batteries could last 15 to 20 years. Therefore, other factor that will affect the system life is the fatigue of the vibrating rod. COSMOS is structural analysis software that is an add-on to the SolidWorks® Solid Modeling program. FEA and

fatigue analyses were done on several different materials to begin the material selection process for the prototype and production system. The analysis was started by deflecting the rod in the 3rd mode of vibration which is the baseline VIV configuration to achieve the desired load on the wobble plate. One concern was the longevity of the rod under strain. Figs. 2 and 3 show the conservative analysis done on a titanium rod after a year of constant vibration. Even with the high safety factor applied and the base statically constrained, which would not be the case during deployment since the transducers will compress taking the brunt of the load, the titanium rod easily passed. With a treated metal and solid machined design it was easy to infer that the life limitation will not be the rod failing. Figure 4 shows the MATLAB simulation created by using the underlying equations from the previous section. This allows for a design that can be easily modified and changed to meet the changing requirements of any sensor that would want to use the SURVIVE as its power source. A multi-physics simulation of the flow across the rod is underway using CD-Adepco software.

III. GENERATOR PROTOTYPES AND EXPERIMENTS

A. Cymbal Generator Design The design of cymbal transducer was based upon two factors: amplification factor and electromechanical resonance frequency.

These two factors have guided the geometric constraints and selection of materials for the transducer. The amplification factor determines the effectiveness of the cymbal as a mechanical transformer and is approximately proportional to the ratio φc/2dc. The magnitude of axial load transferred in the transverse direction is proportional to cos(θ). A small θ is desirable, however if θ is too small then the cavity volume is nonexistent and the transducer loses its amplification properties. Based on the literature survey of published information [4 - 6], the ratio φc/2dc was set to 7. These symbols and relationships are shown in Fig. 5 and Table 1. The mechanical load specifications were fixed at 60 N at 60 Hz for the cymbal to be mounted in a container with an overall diameter of 0.66m. The literature review also showed that a 29 mm diameter cymbal transducer could generate 10 mW of power from a 70 N dynamic load at an operating frequency of 60 Hz [6]. Based on this result, the SURVIVE unit requires approximately 100 transducers in order to generate output power in the range of 0.6-1.0 W. The simplest possible way to array the transducers would be to vertically stack them in the housing with permitted number of rows. The stacking concept was used as the basis for constraining the overall diameter of cymbal. For a stack of N transducers of equal mass and stiffness, the resonant frequency of stack was related to the resonant frequency of one transducer by the following relation:

(5) This relationship was verified using ANSYS. For two different cap materials, the number of cymbals in the stacks was varied

from 1 to 32 showing that the frequency varies as 1/N, for any number of N transducers, as shown in Fig. 6. The mechanical resonance of a 29 mm cymbal was approximately 15kHz. This preliminary analysis suggests that 160 transducers would be needed per stack reducing the height to approximately 0.6 m. The cymbal caps were made of steel because of its rigidity, strength, and electrical properties. While 160 is much too tall however even a stack of 10 greatly reduces the resonant frequency.

Fig. 2 COSMOS Simulation of Rod Undergoing VIV.

Fig. 2 Titanium Stress Simulation for 1 Year

Fig. 4 MATLAB Simulation of Governing VIV Equations and Parameters

TABLE I: PARAMETERS OF DESIGNED CYMBAL TRANSDUCER

B. Prototype and Experimental Results An experimental investigation was conducted to determine the

electrical characteristics of cymbal transducer and verify the modeling results. Fig. 7 shows a picture of two completed transducers. The steel caps of the transducers were bonded to piezoelectric disk using a thin layer of epoxy cured at 80oC. Silver powder was mixed with the epoxy to provide electrical connection between the ceramic and steel caps. This allows wires to be directly soldered to the caps and not just the piezoelectric disk. The transducers were placed on an ABS plastic plate fixed to the shaker. A wooden frame was placed on top of the cymbal and shaker and a force transducer was placed between the cymbal and the frame. The leads of the cymbal were connected to a bread board used to perform a resistor sweep. The SigLAB DAQ was used to record the output of the force transducer and the voltage across the load resistance. The cymbal was excited under varying frequency, pre-stress, and dynamic load. The electromechanical resonance of the cymbal was found to be located at 10 kHz. The fabricated cymbal has slight asymmetries in the caps which results in a spurious

responseError! Reference source not found.. The damped capacitance of cymbal was measured to be 3.47nF using an impedance analyzer. The resistor sweep was performed under an input sinusoidal excitation of amplitudes 5 and 11N at 60 Hz under two different pre-stress conditions. The optimal resistance was in the vicinity of 700 kΩ. This magnitude was close to that determined analytically using the following expression: (6)

With increasing pre-stress, the power output should increase as long as there is no change in the mounting condition and mechanical damping. The experimental results show that the output power decreases with increase in pre-stress which could be related to following conditions: wooden material selected for housing the transducer increases the damping, epoxy used to hold the cap and ceramic disk is detached, and vertical force is not aligned with the cymbal axis of symmetry. Further experiments are needed to eliminate all these factors. The energy harvesting frequencies selected for the experiments in the range of 10-200 Hz are far below the electromechanical resonance of the transducer which lowers the

Parameter Symbol Value Units

Cavity Depth dc 2.175 mm

Cavity Diameter φcav 29.8 mm

Cap Top Diameter φcap 9.8 mm

Cap Thickness tc 0.3 mm

Piezo Thickness tp 2 mm

Piezo Diameter φp 32.8 mm

Overall Diameter φ 37.83 mm Fig. 5 ANSYS model with Pertinent Dimensions

Fig. 6 Inverse Relationship Between the resonance Frequency of One Transducer and a Stack of N Transducers

Fig. 7 Picture of Prototyped Transducers

response. An array of cymbals can be used and mounting mechanism to achieve mechanical resonance. This will be investigated on a 3-element array. The results show that I the operating frequency of the cymbal is increased then it will result in higher output power.

ATILA FEM software was used for optimizing the dimensions of cymbal. The dimensions used in the model were taken from the fabricated transducer to match the results from testing. The piezoelectric material parameters in the model (PZT5AH) differ slightly from the actual material used in the fabricated cymbal. Steel with a 210 GPa Young’s modulus was chosen for the cap material. The impedance of the modeled cymbal was found to be close enough to that of tested cymbal illustrating the validity of FEM in further optimization of the performance. The electromechanical resonance was slightly higher in the calculated curve than in the experimental data. As mentioned earlier, there could be several factors for this difference in the calculated and measured data, mainly related to the asymmetry and epoxy layer. The epoxy used to bond the caps with the ceramic disk may lead to dampening thus reducing the frequency in the model estimation.

Fig. 8, shown above depicts the voltage and power variation at various frequencies. Only the dynamic force was modeled in ATILA due to limitations imposed by the interface. The model correctly estimates the optimal load resistance of 700 kΩ as shown in Fig. 9. The magnitude of voltage and power is less as compared to the experimentally measured values. The pre-stress in the experiments might result in higher output powers as piezoelectric charge is higher under stress-biased condition. The variation in the results could also be related to the difference in the material parameters. The model does under predict the experimental data, providing a more conservative estimate which will be useful in design of the arrays. The cymbal could not be tested at the operating point specified for the SURVIVE unit; the model was used to extrapolate the harvester performance outside of the test region (5-11N). The results of the FEM model are expected to underestimate real values based on results reported in literature. It was found that ~6mW can be harvested from one cymbal transducer under desired operating conditions. At 60 Hz, the cymbal was predicted to generate an output voltage of 80 V and the output power of 6mW across a 700 kΩ load.

C. Array Design

In order to achieve the necessary power requirements, an appropriate array structure was designed. This structure was designed to provide equal force distribution on all transducers reducing the space requirement within the housing by reducing the overall height and filling the inner regions of the container. The end product is intended to eliminate or reduce some of the drawbacks of stacking which includes transducer voltage phase mismatch, inefficient use of space in the housing, and resonance matching. With a solid mounting structure attached to the cantilever-driven top plate, this array will allow transducers to fill the cavity more efficiently without compromising the dynamics of the system. A section view of the Impulsive Resonating Array is shown in Fig. 10, and the Orthepedic view in Fig. 11. The device is mounted on a platform through spring elements. Cymbal transducers will be placed on a base platform with very small clearance between the top cap and the base of the sprung mass. An input force from the top will excite the mass at resonance and create a bouncing pattern on the cymbals. This array has the advantage that it can be easily made into a revolved section and fit well into the container. The array could also potentially be stacked should more cymbals be required. The spring elements will suspend a mass tuned to the input frequency. The resonating structure will drive the cymbals with an impulse response but allow all cymbals to receive an equal amount of force.

Fig. 8 Frequency Vs Power and Voltage of Experiment

Fig. 9 Power Vs Electrical Load

IV. ELECTRICAL TOPOLOGY AND ENERGY ANALYSIS

A. Electronic Design The output of piezoelectric generators can be modeled as a voltage source so every oscillating generator that is in phase can

be wired together in series. Even with the described array designed there will be many out of phase portions that cannot be applied simultaneously to the batteries otherwise they would sink power from one another. To combat this problem a system was designed such that a pulse charge can be applied to a battery pack at a low rate without causing undesirable effects like venting or a balance mismatch. The stages of converting all of the AC power sources into a DC pulses are shown in Fig. 12. The stages of energy conversion circuitry are AC to DC conversion, impedance matching DC to DC conversion, and active control with feedback.

As seen from the diagram the groups of generators are wired in series which will raise the voltages (already on the order of 80 V). This topology produces very high voltages which will dictate the use of simply using regular low voltage drop diodes in a bridge rectifier to convert to DC. Actively controlled switch mode MOSFETS were originally considered until it was found that it would make virtually no difference in the overall efficiency because of the high voltages involved and the added complexity of having to switch the FETs. At the output of the bridge rectifier a DC-DC converter was implemented as opposed to attempting to directly charge the battery with the very high voltage. This dramatically increases the efficiency due to the impedance matching of the ideal resistance and the ideal pulse charge that will not harm the battery pack or create heat and reduce efficiency [7]. Taking some of the characteristic provided from the generator a simulation of an ideal buck converter using 8 generators in series was simulated to obtain the efficiency of the conversion. This is shown in Fig. 13. This simulation was performed using SIMPLIS circuit simulation software specifically for switch mode power supplies. The simulation yielded efficiency over 80% which could charge the battery pack from full depletion in 16 weeks with the simulated stack.

A microcontroller monitors the output voltages of every buck converter and the state of the battery to apply the correct PWM to the switch mode supplies as well as individually pulse charge the pack with the correct voltage and duration. It will also ensure that the stages do not pulse simultaneously. Rows of batteries could be added and balanced with the same microcontroller if more power is needed. The power consumption of the microcontroller can be very small due to the advancements in processing efficiency and the development of specialized PWM controllers that are readily available from multiple sources [8].

Fig. 12 Topology of Energy Conversion Circuitry

Fig. 10 Impulsive Resonating Array Fig. 11 Orthopedic view of Impulsive Resonating Array

B. Energy Storage Configuration and Experiment There are several different ways to store energy. Most types were

eliminated from this system because of capacity or self discharge. Two options emerged from the selection as viable storage devices: Lithium-Ion (and variations such as Lithium Polymer) or Nickel Metal Hydride. Lithium–Ion is desirable for its energy density however it does have high self discharge rates when kept at a full charge. There is also safety issues along with complex circuitry required for recharging. In the new era of hybrid vehicles, the Nickel Metal Hydride Hybrid chemistry has advanced to meet the initial challenge. NiMH batteries used to have high self discharge rates, but with new developments, the chemistry only self-discharges at 1% per month which is on par with discharge of Lithium-ion [9] NiMH can also be trickle charged at the right voltage without the worry of venting or damaging the battery. The batteries have an average cycle lifespan of 1000 cycles. Experiments are needed to find the longevity of the batteries, but according to the manufacturer specifications the batteries can last for ten years in a charged state.

A piece of information that was illusive is the minimum wattage that is required to charge NiMH hybrid batteries. The data sheets for the cells only state what the maximum charge rate is but not the minimum. To answer this question we procured the batteries from AccuEvolution one of the few companies producing D size NiMH Hybrids. Fig. 14 shows the uncharged 10Ah battery pack. Fig. 15 shows the voltage after 3 days of charge proving that we only need 5mA to charge the battery which equates to 0.120W. At this rate the batteries would be charged in six months. The transducer system required a 10 day use 6 times a year with these requirements in mind the SURVIVE system was designed to produce 0.66W on average to charge 40 batteries in 30 days. The batteries came pre-charged so they were first discharged completely, then recharged for three days, and discharged again. Further experiments are underway to establish time periods that are needed with pulse charging.

time/mSecs 10mSecs/div

0 10 20 30 40 50

2

4

6

8

10

12

Fig. 13 SIMPLIS simulation showing improved voltage output (mA vs mS).

Fig. 14 Discharged NiMH battery pack under 5mA charge. Fig. 15 NiMH Pack After Three Days of Charge Showing the Rise in Voltage

SUMMARY

The Supply Utilizing Vortex Induced Vibration Energy (SURVIVE) can be subdivided into three main subsystems: the mechanical cantilever, the piezoelectric cymbal generator array and the power supply electronics. The design targets ocean current of 0.25 m/s. After some initial analysis, it was found that the current velocity can be amplified. The accelerated current flows across the VIV rod which causes a transverse and an along-flow vibration. The VIV rod was designed to resonate at the frequency that is driven by the flow conditions. The dominant force and frequency after amplification was 60 N and 60Hz. The VIV rod was attached to a wobble plate that sandwiches multiple stacks of cymbal generators. The plate applies alternating compression and tension on these stacks. A cymbal generator was utilized due to its structural integrity and ability to amplify the forces applied on them. Each generator was found to generate a minimum of 6mW in the given conditions. If 300 generators are used, 150 will be under load and produce a continuous power of 0.9W. The power supply electronics must match the high impedance of the generator with the low impedance of the NiMH Hybrid batteries. The power supply must also sum the power from the generators which will be out-of-phase. After an AC-DC conversion with a simple bridge rectifier, a DC-DC buck converter was used to match impedances. The converter was used in discontinuous mode to sum the generators and has a total simulated efficiency of 80% leaving 0.72W to charge a 480Wh battery within 33 days. The energy provided from the charge will be enough to power several different types of sensors that reside on the ocean floor. This can be seen as a system that wakes up and consumes the full charge of the battery OR a system that will consistently use less power than is produced over a determined period of time.

ACKNOWLEDGMENT

This work was supported by NAVAIR and the offices at NUWC under a Phase I SBIR. The authors would like to thank John Rego for providing his support during the effort.

REFERENCES [1] Blevins, Robert. Flow Induced Vibration 2nd ed. Malabar, Florida. 2001 Krieger: 40-65 [2] Kundu, P and Cohen, I. Fluid Mechanics 4th ed. Dania, Florida. Academic Press. 2008 Chpt 6 [3] Young, Warren C. and Budynas. Roark’s Formulas for Stress and Strain 7th ed. New York Mcgraw Hill 2002 pg. 764 [4] Kim H, Priya S, Uchino K (2006) Modeling of piezoelectric energy harvesting using cymbal transducers. Jpn. J. Appl. Phys. Part 1-Reg. Papers 45(7):

5836–5840 [5] Kim H, Priya S, Uchino K, Newnham RE (2005) Piezoelectric energy harvesting under high prestressed cyclic vibrations. J. Electroceram. 15: 27–34 [6] Kim H, Batra A, Priya S, Uchino K, Markley D, Newnham RE, Hofmann HF (2004) Energy harvesting a using piezoelectric “Cymbal” transducer in

dynamic environment. Jpn. J. Appl. Phys. 43: 6178–6183 [7] Ottman, Geffrey K., Heath F. Hofmann, and George A. Lesieutre, Optimized Piezoelectric Energy Harvesting Circuit Using Step-Down Converter in

Discontinuous Conduction Mode, IEEE Transactions on Power Electronics, Vol. 18, No. 2, March 2003 [8] Priya, Shashank and Daniel Inman (Editors), Energy Harvesting Technologies, Springer Science and Business Media, LLC, 2009 [9] Author unknown, AccuEvolution D size data sheet, www.accuevolution.com