Energy harvesting via thermo-piezoelectric transduction within a heated capillary

Piezoelectric (PZT) transduction is a method of converting external vibrations (kinetic energy) into electricity through the piezoelectric effect which occurs only in certain “active” materials (i.e., PZT materials) that create a voltage due to rearrangement of their crystal lattice dipoles during strain. In general, PZT generator efficiency can be improved by designing for application-specific input vibration, electrical load, natural frequency, mechanical damping ratio, electromechanical coupling coefficient, and more.^1–5 Significant research in the area of applied piezoelectricity generation has been performed over the last two decades,^6–8 including studies into harvesting fluid motion to drive PZT generators.^9,10 Goushcha et al. used a strain gage (used as a PZT sensor surrogate) attached to a cantilever beam to harvest energy (∼2 mW of circuit power) from a self-advancing vortex created with an audio speaker to produce ∼2 mW of circuit power.⁹ Wang and Ko converted vibrational energy from fluid flow into electrical energy using a PZT film placed over a diaphragm covering a pressure chamber in-line with the fluid channel.¹⁰ These vibrations had a pressure amplitude of 1.2 kPa at a frequency of 26 Hz, which produced an output peak-to-peak voltage (V_pp) of 2.2 V with an instantaneous power of 0.2 μW.

An oscillating heat pipe (OHP) is a two-phase heat transfer device that operates when subjected to a sufficient temperature gradient.^11,12 It exists as an evacuated/sealed, serpentine-arranged capillary channel (or tube) that is partially filled with a fluid (e.g., water and refrigerant), with the ratio of the added liquid volume to the internal channel volume defined as the OHP fill/charge ratio. The capillary structure meanders repetitiously through a heat reception and rejection zone (i.e., the evaporator and condenser, respectively). During operation, heat is transferred from the OHP evaporator, which, at a minimum/critical temperature difference (or heat flux),^12–14 triggers the evaporation of various-sized, internal saturated liquid slugs which are randomly distributed along the serpentine channel/tube. Due to the non-uniform mass distribution along the OHP serpentine structure, vaporization creates an unsteady pressure gradient that drives fluid oscillation and circulation; hence, no wicking structure is required. Fluid oscillations within an OHP typically occur over a frequency spectrum less than 10 Hz.^15–18 Although vapor growth and contraction drive OHP operation, the temperature difference across the OHP length can result in significant sensible heat transfer between the evaporator and condenser.^19,20 A major OHP operational limit, known as evaporator dry-out, occurs when the heat flux to the evaporator inhibits liquid from returning to it for re-evaporation.²¹ 

Since OHPs are lightweight and readily manufacturable, require no power source to operate, and have a relatively high thermal conductivity (on-the-order of 10³ < k_eff < 10⁴ W/m K), they warrant use in several electronic and aerospace thermal management applications. More recently, however, OHPs have been investigated as platforms for energy harvesting and conversion by taking advantage of the thermally driven, self-sustaining flow within them. Monroe et al. built an OHP capable of ferrofluidic induction by positioning a solenoid in proximity to the internal oscillating motion of a nanoferromagnetic working fluid suspension within an OHP.²² In these experiments, an ∼0.8 mV peak-to-peak voltage was measured across the solenoid. Zabek et al. demonstrated energy harvesting using an array of pyroelectric elements mounted on the surface of a flat-plate OHP.²³ The OHP had surface temperature variations of ∼5 K at frequencies of ∼0.45 Hz due to internal fluid oscillations. These fluid oscillations resulted in surface heating/cooling rates that drove thermal-to-electric conversion as evidenced by measured, maximum open circuit voltages (VOC) near 0.8 V. Piezoelectric actuators have also been used to stimulate the fluid within OHPs for improved thermal performance. Zhao et al. placed PZT ceramics along the evaporator surface of a 6-turn copper OHP in which the ultrasonic sound (1 kHz) produced from the PZT ceramics reduced the heat input required to initiate fluid oscillations by approximately 67%.²⁴ 

The current study investigates an energy harvesting method for converting waste heat (or an available temperature difference) into electrical energy through means of a thermally actuated OHP. A PZT transducer is placed directly within a section of the OHP, and the impact of the PZT transducer on the heat transfer ability of the OHP is measured.

Two similar 4-turn tubular OHPs (d_i = 3.25 mm and d_o = 4.8 mm) were constructed by bending copper capillary tubing (C12200 alloy). One of the OHPs included a PZT harvester, i.e., the “Pz-OHP,” while the other acted as the “control OHP” without a PZT harvester. The internal diameter of the OHP tubing was selected to ensure capillarity of the working fluid by having a Bond number ≤2, i.e., D_i < $2γg(ρl−ρv)$⁠, where γ is the surface tension, ρ_l is the liquid density, ρ_v is the vapor density, and g is the local gravitational acceleration.²⁵ 

A section of square brass tubing (C26000 alloy: w_i = 3.25 mm and w_o = 4.0 mm) was installed in-line with a centrally located capillary tube within the adiabatic section (section between the evaporator and condenser) of both OHPs. The square tubing was used for encapsulating the PZT transducer while providing ample space for its oscillatory deflection during Pz-OHP operation. For the Pz-OHP, two openings were cut along one side of the square tube to allow the PZT to form a bow spring, as shown in Fig. 1. This specific harvesting configuration was selected as to reduce its pressure drop and mechanical fatigue during OHP operation. A viewing port (polycarbonate window) was added to one side of the square tube to observe the fluid as it oscillated across and around the PZT. This viewing port was included only to provide visual confirmation of the working fluid's state inside the square tubing. While thermal and voltage data were being collected, the OHP was entirely insulated to minimize heat loss.

A macrofiber composite (MFC) PZT transducer (Smart Material, M-8503-P2) was used for energy harvesting. The active PZT element was 3 mm × 85 mm and sealed within an oversized, environmental coating strip (8 mm × 113 mm). The coating strip was trimmed to allow the active PZT to move inside the 3.25 mm square tube. The leads for the PZT were on opposite ends of the transducer and located outside the OHP/harvester assembly. All mating surfaces were sealed with a two-part epoxy adhesive (J-B KWIK).

As shown in Fig. 1, twelve type-T thermocouples (TCs) were affixed to the outside walls of the OHPs to quantify their thermal performance. The OHPs were first evacuated to less than ∼1 Pa before being charged with high-performance liquid chromatography (HPLC)-grade water to an 80% (±2%) filling ratio. After filling, the charging tube was pneumatically crimped to create a hermetic seal. Aluminum cooling and heating blocks were used to control OHP thermal boundary conditions. Grooves (r ≈ 2.4 mm) were machined into both pairs of blocks to match the external geometry of the OHP tubes to ensure an interference fit and maximal contact area. To further decrease the thermal contact resistance, grooves were coated with a thin layer of thermal paste (Omegatherm 201) prior to their fastening against the OHP. Two 300 W cartridge heaters were embedded in the heating blocks, and their power output was controlled using a variable autotransformer (Variac, Staco Energy) and digital multi-meter (DMM). A recirculating bath (PolyScience AD15R-30-A11B) was used to continuously route 15 °C cooling water through the cooling blocks. A schematic of the experimental setup is shown in Fig. 2. The entire assembly was wrapped in fiberglass insulation to inhibit heat loss to the environment. Based on the surface temperature of the insulation, heat loss was estimated to be ≤5% at higher power inputs. A small section of the insulation surrounding the OHP was temporarily removed in order to visualize the internal flow through the installed viewing port at various heat inputs. Images of the fluid moving in the viewing port (∼240 × 140 pixel frame) were recorded using a digital camera with a resolution of 1.20 μm/pixel at 120 fps.

A National Instruments data acquisition (DAQ) system (cDAQ-9178 chassis with NI-9213 temperature and NI 9205 voltage modules) collected temperature and voltage data, while LabVIEW SignalExpress was used to record and manage data. The DAQ sampled the TCs and PZT open circuit voltages (VOC) at 100 Hz and 500 Hz, respectively. The PZT voltage signal was routed to the DAQ through a passive 40 Hz low-pass filter to eliminate high-frequency noise (i.e., noise above 250 Hz). A fourth-order Butterworth 0.75–40 Hz band-pass (BP) filter was applied to remove information not associated with fluid motion and to remove any 60 Hz interference from nearby electrical systems. Tests began at heat inputs of 10 W and then 50 W, followed by 50 W increments until maximum temperature oscillation spikes reached ∼100 °C.

Both the Pz-OHP and control OHP were found to operate after a heat input of 50 W as evidenced by their surface temperatures (i.e., TC1-TC12) oscillating with respect to time. These temperature oscillations are known to be a direct result of the thermally driven internal fluid pulsations within the OHPs,^26,27 and this was confirmed through the use of the installed viewing port. An example of a vapor plug passing through the viewing port is given in Fig. 3; the time interval between frames is 8.33 ms. Representative temperature oscillations at TC6 and TC7 during 150 W are shown in Fig. 4(a).

The internal fluid motion proved capable of driving the repetitious deflection of the bow-configured PZT material within the Pz-OHP as evidenced by a recorded voltage signal. Representative VOC signals are given in Fig. 4 for heat inputs 150 W and 400 W. In Fig. 4(a), it may be seen that the characteristic voltage signal possesses low-frequency, random spikes in response to the internal fluid motion within the Pz-OHP. Due to the pressure drop across the PZT, the frequency and amplitude of the temperature oscillations in its vicinity are more aperiodic and exaggerated, respectively. The PZT harvester was found to be capable of producing a time-varying open-circuit voltage (VOC) with peak-to-peak amplitudes typically ranging between 10 and 60 mV for heat inputs up to ∼400 W.

The phase-change heat transfer occurring within the Pz-OHP aids its ability to pump fluid through tube segments, including that of the harvesting region. As a result, a weak correlation between temperature and voltage peaks is observable when comparing the VOC signal with the temperature signals shown in Fig. 4(a). When local temperature rises are interrupted and rapidly reduced in magnitude due to latent heat transfer, a voltage spike with the corresponding magnitude results. There were intermittent periods when the fluid in a Pz-OHP tube would temporarily lock up and cease moving due to pressure balancing—an occurrence observed for some OHPs.²⁸ During these periods, which may be observed to occur at ∼85 and ∼275 s in Fig. 4(a) for the harvesting tube, no voltage generation occurs and temperature increases linearly.

A maximum peak-to-peak voltage, $VOCpp,max$⁠, was calculated using the difference in the minimum and maximum VOC at each heat input. The largest 1% positive and negative voltage data were also averaged to estimate $VOC¯max$ and $VOC¯min$ in order to quantify an average peak-to-peak voltage as shown in the following equation:

The VOC_RMS was calculated to include periods of zero voltage generation. The aggregated voltage data vs. heat input for the Pz-OHP is shown in Fig. 5.

From Fig. 5, it is seen that the Pz-OHP provided the maximum voltage output at heat inputs between 350 W and 400 W. Maximum $VOCpp,max$⁠, $VOC¯pp$⁠, and $VOCRMS$ occurred at a heat input of 400 W with values of 63.0, 53.6, and 12.1 mV, respectively. Due to large-amplitude fluid displacements occurring during the more intermittent OHP operation phase just above its start-up,²⁹ relatively large VOC amplitudes were measured at heat inputs of 50 W and 100 W. For heat inputs between 100 W and 300 W, the generated VOC is less in magnitude but more consistent over time as the operating behavior of the OHP stabilizes. The higher VOC generation at heat inputs >350 W can be attributed to the flow regime within the OHP transitioning, thus allowing more liquid mass to pass across the PZT for greater deflection.

The steady-state OHP heat transport capability was quantified on a per-tube basis via an effective thermal conductivity defined by Eq. (2). The heat transfer through the square harvesting tube (i.e., t5, meaning the 5th tube section from left in Fig. 1) and two adjacent round tubes (t3 and t7) were analyzed. The temperature differences, $ΔT$⁠, used for Eq. (1) coincide with locations spanning the adiabatic region by distance, $Δx$⁠, i.e., TC3 and TC5 and TC8 and TC10 for the round tubes and TC6 and TC7 for the square tube [see Fig. 1(a)].

In Eq. (2), $Atube$ is the cross-sectional area of the tube section and the heat transfer is assumed approximately equal to the electrical power input, i.e., q$≅$P. The effective tube thermal conductivities corresponding to the Pz-OHP and the control OHP are shown in Fig. 6.

As shown in Fig. 6, both OHPs possessed relatively high thermal conductivities between 10 and 20 kW/m K; however, due to the non-uniform fluid distribution within the OHPs, a slight tube-to-tube variation existed. The effective thermal conductivities increased with heat input until approximately 300 W. At heat inputs greater than 300 W, the Pz-OHP performance started to decline because it achieves evaporator dry-out. The control OHP possessed a higher heat input limitation and did not experience evaporator dry-out until approximately 500 W. These results confirm that the pressure drop of the PZT harvesting module hinders the ability of fluid to flow throughout the OHP capillary structure at higher heat inputs in which the pressure drop is exaggerated due to higher flow velocities.

For both OHPs, the square tube section (t5) consistently yielded the highest thermal conductivity because it had a smaller wall thickness and 24% more flow area. Interestingly, the square tube section of the Pz-OHP possessed a higher thermal conductivity than that of the control OHP for heat inputs between 100 W and 250 W. This can be attributed to the increased forced convection heat transfer between the evaporator and condenser due to the pressure drop imposed by the PZT material, resulting in faster fluid speeds across it. Note that the impact of harvesting on thermal performance is localized only to the harvesting region as there was no discernible difference between k_eff,t3 and k_eff,t7 for either OHP at heat inputs less than 300 W. At heat inputs ≥300 W, the difference in heat transport ability between the Pz-OHP and control OHP became more apparent with k_eff,t3 and k_eff,t7 decreasing for the Pz-OHP. This behavior is most likely due to evaporator dry-out within the Pz-OHP at power inputs ≥300 W, resulting in the reduction of fluid oscillations and the decrease in k_eff.

This work has demonstrated a unique means for thermal-to-kinetic-to-electrical energy conversion through the use of a thermally driven PZT transducer integrated within an oscillating heat pipe (OHP) partially filled with water. The enthalpy of the fluid encapsulated within the operating OHP was used to repetitiously deflect a PZT transducer configured as a bow spring. For the investigated piezoelectric OHP (Pz-OHP), low-frequency (∼1 Hz) fluid “pulses” were observed to occur across the flexed PZT transducer, resulting in its deflection and production of measureable voltage spikes ranging between 24 and 63 mV. The PZT material was found to deflect in concert with internal fluid motion in the vicinity of the harvesting region for heat inputs up to 400 W. The Pz-OHP maintained an effective thermal conductivity on-the-order of 10 kW/m K; however, due to the pressure drop across the PZT transducer, the heat transfer limit of the OHP was reduced by approximately 20%.

The investigated Pz-OHP is not a traditional heat engine; instead, it is a heat transport device with the added feature of in-situ power generation. Future work should focus on tailoring the Pz-OHP for a more dedicated role of electrical power generation. Since fluid motion within the OHP generally depends on working fluid, operating orientation, temperature difference, and evaporator area, they can be manipulated for maximal thermo-piezoelectric transduction in a given operating environment (e.g., heat flux and cooling conditions). The fluid oscillations can be “tuned” to operate at a frequency near the natural frequency of installed PZT transducers for maximal power generation. Although additional research is needed to optimize the piezoelectric OHP harvester design for useful power output, the presented proof-of-concept demonstrates a passive method for combined energy harvesting and thermal management.

This work was funded by the National Science Foundation (Award No. #1660446). This research was not funded or endorsed by ERDC or Sandia National Laboratories. Any opinions, findings, conclusions, or recommendations expressed herein do not necessarily reflect the views of ERDC or Sandia National Laboratories.