Vortex Shedding Induced Energy Harvesting from Piezoelectric Materials in HVAC Flows Weinstein L A1, Cacan M R1, So P M1 and Wright P K1, 2 1 The Department of Mechanical Engineering, UC Berkeley, CA 94720-1740 2 The Center for Information Technology Research in the Interest of Society, Berkeley, CA 94720-1764 E-mail:
[email protected],
[email protected] Abstract. A cantilevered piezoelectric beam is excited in an HVAC flow. This excitation is amplified by the interactions between a) an aerodynamic fin attached at the end of the piezoelectric cantilever and b) the vortex shedding downstream from a bluff body placed in the air-flow ahead of the fin/cantilever assembly. Positioning of small weights along the fin enables the ability to tune the energy harvester to operate at resonance for flow velocities from 2 - 5 m/s, which are characteristic of HVAC ducts. In a 15 cm diameter air duct, power generation of 200 µW for a flow speed of 2.5 m/s and power generation of 3 mW for a flow speed of 5 m/s was achieved. These power outputs are sufficient to power a wireless sensor node for HVAC monitoring systems or other sensors for smart building technology.
Vortex Shedding Induced Energy Harvesting from Piezoelectric Materials in HVAC Flows 2 1. Introduction In recent years, radio, microprocessor and sensor technologies have made considerable advancements enabling the use of wireless sensor nodes for the monitoring of various systems. Battery technology has not kept pace with these enabling technologies for wireless sensor networks, so battery powered nodes must be replaced frequently. Over the lifetime of a sensor node, this is expensive, environmentally detrimental and labor intensive. A more elegant solution is the use of energy harvesting to create devices that draw power from ambient sources such as light, heat or vibrations. A robust energy harvesting device combined with rechargeable batteries could extend node lifetimes and eliminate the need to change replaceable batteries. This paper investigates the particular case of energy harvesting from HVAC systems. HVAC systems were chosen since they offer an attractive environment for energy harvesting from fluid flow due to the predictable nature of their flow and their prevalence in buildings. Airflow in HVAC systems is typically unidirectional with a slug-shaped velocity profile and operating speeds from 2 to 5 m/s ‡. While other environments such as liquid or gaseous water pipes and natural gas lines also exhibit similar characteristics, they offer a more challenging environment in which to work. These environments could implement a similar harvester using the foundation of the results in this paper assuming the right steps were taken to protect the harvester from potential damage. Experimental testing in an HVAC system was beneficial as it is the simplest and safest system for conducting research. Harvesting localized flow power from HVAC systems then offers an opportune method to power a sensor and low power radio that can be run on low duty cycle with as little as 100 µW [1]. Benefits of this kind of device can be seen through the monitoring of temperature and humidity of the air, allowing the efficiency and performance of HVAC systems to be improved. HVAC systems also act as a convenient point to monitor air quality and safety for public buildings. These examples just begin to touch on the large potential for energy harvesting in HVAC systems to provide power for many beneficial sensors that could be used in and around air ducts. There exists a multitude of harvesting strategies for fluid flow, some specifically targeting HVAC systems and some with broader intended applications. Despite the many studies previously conducted on energy harvesters from fluid flow, there still exists a gap in harvesting capability. While many are capable of providing the 100 µW desired for powering a wireless sensor node, few can do so in the entire range of flow speeds typical of HVAC ducts, particularly at speeds below 3 m/s. Some researchers have designed traditional wind turbine technology on a smaller scale or turbines paired with piezoelectric materials to operate efficiently at the centimeter scale. The traditional turbine technologies are promising, with work by Federspiel et al achieving efficiencies approaching 10% [3] and work by Howey et al achieving power outputs approaching 100 ‡ http://www.engineeringtoolbox.com/flow-velocity-air-ducts-d_388.html accessed June 28, 2011
Vortex Shedding Induced Energy Harvesting from Piezoelectric Materials in HVAC Flows 3 µW at 3 m/s using less than 10 cm2 of cross sectional area [2], but these techniques use rotating parts which is undesirable for long-term applications. Myers et al have combined turbines with piezoelectrics and managed to achieve a cut in speed of around 2.5 m/s [4], but the rotating machinery is still undesirable. This concern is addressed in many novel approaches that do not currently exist at the utility scale include harvesting using aeroelastic flutter, wake galloping and many other fluids dynamics phenomena. The Windbelt [5] which uses aeroelastic flutter, shows power outputs in the mW range, but its cut in speed of 3 m/s renders it unable to harvest from the entire HVAC flow range. A new technique from Jung et al [6] uses wake galloping, which yields impressive power outputs, but their harvester is too large to be accommodated by most HVAC ducts and it is unclear if the efficiency would scale down with a smaller device. Work by Zhu et al using oscillatory drag on a cantilevered fin is very promising with power outputs sufficient for wireless sensor nodes at wind speeds as low as 2 m/s [7], but the design depends on gravity, and therefore installation in a vertical HVAC duct, which might not always be available. Ji et al have developed a harvester using an acoustic resonant cavity (similar in principle to a harmonica) which has impressive mW scale power outputs but suffers from a cut in speed around 3 m/s [8]. Other novel techniques include flapping foils [9] and vortex shedding to induce motion in a membrane parallel to the flow [10] and while they hold potential they are not yet mature enough to compete with the other harvesters. Another strategy that avoids rotating machinery which is ultimately pursued in this paper is that of flapping piezoelectrics, which has a wide range of previous work. Pobering et al have investigated cantilevers attached to a flow obstacle, but appreciable power outputs have only been reported for flow speeds far greater than would be encountered in an HVAC duct [11]. Work investigating a cantilever placed in unsteady flow has been performed by Akaydin et al but similarly the power outputs are insufficient for running a wireless sensor node in the HVAC flow speed regime [12]. Flapping “flaglike” piezoelectric bimorphs have been pursued by Robbins et al [13] for air flow, and Taylor et al [14] for water flow, and while they come closer to the desired performance, they do not achieve the 100 µW target below 3 m/s. Finally, Oh et al implemented a leaf-like design for a piezoelectric harvester, but the power output was insufficient for powering a wireless network node [15]. The strategy pursued in this paper in order to achieve 100 µW in HVAC flow conditions is coupling vortex shedding from a bluff obstacle in the air flow to a fin attached to a piezoelectric bender. When piezoelectrics are deformed, they convert mechanical energy into electrical energy through their crystalline structure. By attaching the fin to the bender, the deflection of the bender can be maximized and its response can be better tuned for various flows. This setup provides relatively high performance at low flow speeds, and will ideally provide the necessary performance over a wider range of flow speeds than other harvesters. The small cross-sectional area exposed to the air flow and size of the device make it an ideal energy harvester for HVAC systems. Figure 1 shows a line drawing in to familiarize the reader with the
Vortex Shedding Induced Energy Harvesting from Piezoelectric Materials in HVAC Flows 4 basic principle by which the harvester operates.
Vortex Street
Incoming Flow
Fin Bluff Obstacle
Piezoelectric Bender
Figure 1: Diagram illustrating idea behind the operation of the harvester While the strategy in this paper is similar to what has been pursued by others [11] [12] [15], the addition of a fin in this particular configuration is novel in the literature. The attachment of the fin to the tip of the bender is beneficial as the magnitude of force acting on the cantilever can be greatly magnified. Additionally, the upstream obstacle can be designed such that the excitation frequency is matched with the natural frequency of the bender, further increasing bender deflection. This design is poorly suited for environments where the flow direction is unknown, as the fin would not always lie in the wake of the obstacle. For the unidirectional HVAC environment, this issue is not a concern. For these reasons, this device offers competitive performance in its intended application of harvesting from HVAC flow. 2. Model The mechanical input for the system is achieved through vortex shedding off a cylindrical obstacle. Vortex shedding is a phenomenon in which air flowing past a blunt object creates a periodic oscillating pressure field behind it, often referred to in fluid dynamics as a Karman vortex street (Figure 2) [16]. The frequency at which vortices shed from the bluff body is described by the Strouhal relation (1). f = (St ∗ D)/v
(1)
Where f is the frequency of the periodic oscillation, St is the Strouhal Number, D is the diameter of the obstacle, and v is the fluid velocity across the obstacle. The Reynolds number Re of interest for our analysis is given in (2). Re = (D ∗ v)/ν
(2)
Where D is the diameter of the obstacle, v is the fluid velocity across the obstacle, and ν is the kinematic viscosity of air. The obstacle used with our device, a cylinder of diameter 2.5 cm, at typical HVAC flow speeds corresponds to Reynolds numbers from about 3000 to 8000. For this range
Vortex Shedding Induced Energy Harvesting from Piezoelectric Materials in HVAC Flows 5
Figure 2: Streamline diagram of vortex shedding phenomenon
the Strouhal Number is assumed to be constant at 0.21 [16]. The shedding frequency for a range of flow speeds from 2 to 5 m/s correlates to a frequency range of 16 to 40 Hz. Vortices shed from the blunt obstacle exert a force on the fin of the harvester due to pressure differentials on each side of the fin. A simple Bernoulli relation is used to determine the pressure differential (3), which corresponds to the force exerted on the fin. 1 (3) P = ρ(v12 − v22 ) 2 Where P is the difference in pressure, ρ is the density of the air, and v is the velocity with subscripts denoting side of the fin. Velocity from a vortex can be modeled as (4). vθ = Γ/2r
(4)
Where vθ is the tangential velocity relative to the vortex center, Γ is the vortex strength, and r is the distance from the vortex center. Integrating (3) where v1 is the average centerline velocity, and v2 is the average centerline velocity minus vθ substituted from (4) across the area of the fin yields the force exerted on the fin (5). Z L 1 F = hρΓ (Γ/4r2 − vc /r) dx. 2 (5) 0 p 2 2 r = (x − xc ) + yc Where F is the force, h is the height of the fin, ρ is the density of air, Γ is the vortex strength, L is the length of the fin, vc is the average centerline velocity, and r is the distance from the vortex center to a point on the fin, decomposed into xc (distance in the stream-wise direction) and yc (distance perpendicular to the stream). Varying the position of the vortex center xc shows how the forces change in time as the vortex passes the fin. This shows that an acceptable approximation for force on the fin is given in (6). F = Fmax sin (ωt)
(6)
Where Fmax is the value of F when xc = L/2, i.e. when the vortex is at the midpoint of the fin. Fmax is proportional to velocity squared due to the fact that Γ is proportional
Vortex Shedding Induced Energy Harvesting from Piezoelectric Materials in HVAC Flows 6 to vc [16]. ω is the shedding frequency of the vortices (which must match the frequency of vortices passing the fin). For design considerations the fin and bender system was modeled as a one degree of freedom spring mass damper. To achieve maximum power output from the bender, input excitations from vortex shedding should match the natural frequency of the bender. This is because for low damping (ζ
