Fluid-Structure Interaction of Flexible Thin Sheet

By Josiah Cassidy

 

Introduction

The environmental effect and limited supplies of fossil fuel energies have prompted extensive study into the creation of innovative and diversified methods to produce electrical energy. Parallel to this, systems capable of cheaply producing limited amounts of energy to power remote or isolated devices, for which connection to the standard electrical network is unfeasible due to cost or technical complexity, have also received special attention. These two factors have heightened interest in methods capable of producing self-sustaining vibrations of a solid or flexible substrate and converting the accompanying mechanical energy into electrical power. The conversion of kinetic energy from geophysical movements such as tidal currents, winds, and river flows into electricity is particularly interesting due to this energy source’s widespread availability and low environmental impact. Several mechanisms, such as vortex-induced vibration, flutter, and coupled- mode flutter instability of the flexible plate in a steady flow, have been identified through research on fluid–structure interactions (FSI) [1]. In this scenario, it is well known that the flat equilibrium state of the plate becomes unstable above a certain flow velocity, at which point significant amplitude dynamic vibrations can form on the structure. The goal of the proposed project is to investigate the capacity to generate electrical power from the self-sustained oscillations of a flexible plate caused by this fluttering instability by converting mechanical strain into electric potential using multiple embedded piezo electronic sensors.

Methods

Through a set of water tunnel experiments, we investigated the onset of flexible plate’s dynamic instability and the occurrence of possible limit cycle oscillations as a function of flow velocity and geometrical dimensions. We studied the effect of the geometrical parameters, such as the ratio between the length, width, and thickness of the plate, on the onset of the instabilities. The flexible plate was fabricated by pouring silicon rubber into 3D-printed molds to ensure both shape accuracy and structural flexibility. During this process, multiple piezoelectric sensors were embedded at various locations across the plate. The experiments for the dynamic response measurement were conducted in a re-circulating water tunnel facility at FSI LAB at UMass Dartmouth. To be able to conduct the experiment in our water tunnel, we have also designed a setup that will secure the flexible plate in the water tunnel shown in Figure 1.

Figure 1: Model of Flexible Plate Setup

The structural response of the system was measured using the embedded piezoelectric sensors purchased with OUR grant funds. Each piezoelectric sensor was connected using full bridge rectifiers to separate inputs of the Arduino in order to collect each sensor’s data separately but simultaneously. As the flexible plate starts to oscillate, it causes a strain in the sensor which transfers data to the Arduino in the form of voltage measurements based on the amount of strain experienced. Using this setup, we performed experiments with various sensors locations along the flexible plate. This method allowed us to find how the strain in the sensor changes based on not only the fluid flow and the flexible plate’s aspect ratio but also the geometric location of the piezoelectric sensor. Throughout this spring semester, many changes needed to be made in order for this setup to operate accurately and efficiently. First, new molds need to be designed and 3D printed so that we can do testing with many different aspect ratio flexible plates. We also needed to adjust the mounting setup for the flexible plate so that it would be fixed securely in the water tunnel. We made these adjustments by redesigning the holder in SOLIDWORKS to better support the flexible plate when oriented vertically. Other modifications were added like screws to secure the flexible plate in place during testing. Next, we adjusted our Arduino setup in order to accommodate 4 data inputs. This allows us to read data from multiple piezos on a single flexible plate during testing at the same time. A picture of the flexible plate during testing in the water tunnel is shown below in Figure 2.

Figure 2: Flexible Plate in Water Tunnel

Results

Figure 3 shows one of our flexible plates and an example of piezo placement in the plate. Some preliminary results are shown in Figure 4.

Figure 3: Placement of piezoelectric sensors in flexible plate

Figure 4: Graph comparing voltage output to water tunnel speed

The y-axis shows average voltage which was found from data collection through the use of the Arduino. This data was streamed to an excel file where it was averaged for each water tunnel speed test. Across the x-axis is the speed of the water flow in the water tunnel in meters per second. From this preliminary testing, we observed a higher voltage output from piezos placed toward the front of the flexible plate when compared to the rear. This could be due to the greater amount of change in displacement that occurs at these water tunnel speeds. A sample time series of the sensor measurements is shown below in Figure 5 in which you can see the changes in voltage output as the flexible plate experiences displacement.

Figure 5: “Sample Time Series of Sensor Data”

Conclusion and Future Direction

While our current testing has started to grant some results, much more testing is required before anything definitive can be said. As this project continues into the next semester or two, much more testing in the water tunnel should be done with more aspect ratios and a wider variety of piezo placement. Researchers should also use other methods like computer simulations to determine exactly why certain piezo placements give higher voltage outputs. This combined with our current piezo experiments may lead to more accurate predictions of power output during varied conditions without the need for experimental testing.

Reference

[1] A.K. Pandey, G. Sharma, R. Bhardwaj, Flow-induced reconfiguration and cross-flow vibrations of an elastic plate and implications to energy harvesting, Journal of Fluids and Structures 122 (October 2023), 103977. https://doi.org/10.1016/j.jfluidstructs.2023.103977.