Piezoelectric energy harvester for scavenging steady internal flow energy: a numerical investigation

Abstract

The wake-induced vibration of a thin piezoelectric (PZT) actuator is examined to explore some aspects of vortex-based energy harvesting. Simulations are conducted at Re = 200, various blockage ratios (0.08 ≤ b ≤ 0.5), and using the PZT actuator on the hosted diaphragm. The endeavor of the present investigation is to discover the effects of vortices and wall confinements at different longitudinal and lateral spacing ratios on the performance of PZT. As an objective of the current study, the aim is to determine the optimal position of the PZT to generate a significant amount of vibration so that maximum energy can be captured. Another connotation of this study regards the possibility of employing a flexible diaphragm on internal walls and harvesting energy, as a self-sufficient system, for remote sensing applications. The longitudinal distance between the center of the upstream cylinder and the center of the diaphragm varies (X_D = 1.0–3.0), while the importance of the blockage ratio on energy harvesting is studied for a laminar flow. The effect of confinement has been incorporated into the present model so that the lift force of a bluff body can be expressed as a function of the blockage ratio. Assuming that the upstream cylinder is stationary, the flexible diaphragm and PZT in the wake of the cylinder can be considered fixed–fixed and cantilever, respectively. Initially, the influence of spacing ratio on downstream wake is investigated by modeling flow around a coupled cylinder-diaphragm. Based on the numerical results, key spacing ratios, longitudinally and laterally, are discovered and introduced for the second part of the simulation. Then, the dynamic response of a flexible PZT and its generated voltage are explored in the second part. Numerical investigations are conducted using two-way fluid structural interaction, and all necessary equations, including fluidic and structural equations, formulated and discussed methodically. Moreover, the present results provide a practical way of designing a system for capturing internal flow energy, which has been poorly documented up to now.

Appendix

The properties of the lead zirconate titanate (PZT-2).

Compliance

$$ C_{E} = \left[ {\begin{array}{*{20}l} {11.6} \hfill & { - 3.33} \hfill & { - 4.97} \hfill & { 0} \hfill & { 0} \hfill & { 0} \hfill \\ { - 3.33} \hfill & {11.6} \hfill & { - 4.96} \hfill & 0 \hfill & 0 \hfill & 0 \hfill \\ { - 4.97} \hfill & { - 4.97} \hfill & {14.8} \hfill & 0 \hfill & 0 \hfill & 0 \hfill \\ {0.00 } \hfill & {0.00 } \hfill & { 0.00 } \hfill & {45} \hfill & { 0.0 } \hfill & {0.00} \hfill \\ {0.00 } \hfill & {0.00} \hfill & { 0.00} \hfill & {0.0 } \hfill & {45} \hfill & {0.00} \hfill \\ {0.00} \hfill & { 0.00} \hfill & {0.00} \hfill & {0.0} \hfill & {0.0} \hfill & {29.9} \hfill \\ \end{array} } \right] \times 10^{ - 12 } {\text{m}}^{2} /{\text{N}} $$

Piezoelectric coupling

$$ e = \left[ {\begin{array}{*{20}l} {0.0} \hfill & {0.0} \hfill & {0.0} \hfill & {0.0} \hfill & {440} \hfill & {0.0} \hfill \\ {0.0} \hfill & {0.0} \hfill & {0.0} \hfill & {440} \hfill & {0.0} \hfill & {0.0} \hfill \\ { - 60} \hfill & { - 60} \hfill & {152} \hfill & {0.0} \hfill & {0.0} \hfill & {0.0} \hfill \\ \end{array} } \right] \times 10^{ - 12 } C/N $$

Relative permittivity

$$ \varepsilon_{{s/\varepsilon_{0} }} = \left[ {\begin{array}{*{20}c} {990} & {0.0} & {0.0} \\ {0.0} & {990} & {0.0} \\ {0.0 } & {0.0 } & {450} \\ \end{array} } \right] $$