John O. Dabiri

Potential order-of-magnitude enhancement of wind farm power density via counter-rotating vertical-axis wind turbine arrays

Modern wind farms comprised of horizontal-axis wind turbines (HAWTs) require significant land resources to separate each wind turbine from the adjacent turbine wakes. This aerodynamic constraint limits the amount of power that can be extracted from a given wind farm footprint. The resulting inefficiency of HAWT farms is currently compensated by using taller wind turbines to access greater wind resources at high altitudes, but this solution comes at the expense of higher engineering costs and greater visual, acoustic, radar, and environmental impacts. We investigated the use of counter-rotating vertical-axis wind turbines (VAWTs) in order to achieve higher power output per unit land area than existing wind farms consisting of HAWTs. Full-scale field tests of 10-m tall VAWTs in various counter-rotating configurations were conducted under natural wind conditions during summer 2010. Whereas modern wind farms consisting of HAWTs produce 2–3 W of power per square meter of land area, these field tests indicate that power densities an order of magnitude greater can potentially be achieved by arranging VAWTs in layouts that enable them to extract energy from adjacent wakes and from above the wind farm. Moreover, this improved performance does not require higher individual wind turbine efficiency, only closer wind turbine spacing and a sufficient vertical flux of turbulence kinetic energy from the atmospheric surface layer. The results suggest an alternative approach to wind farming that has the potential to concurrently reduce the cost, size, and environmental impacts of wind farms.

Lagrangian analysis of fluid transport in empirical vortex ring flows

In this paper we apply dynamical systems analyses and computational tools to fluid transport in empirically measured vortex ring flows. Measurements of quasisteadily propagating vortex rings generated by a mechanical piston-cylinder apparatus reveal lobe dynamics during entrainment and detrainment that are consistent with previous theoretical and numerical studies. In addition, the vortex ring wake of a free-swimming Aurelia aurita jellyfish is measured and analyzed in the framework of dynamical systems to elucidate similar lobe dynamics in a naturally occurring biological flow. For the mechanically generated rings, a comparison of the net entrainment rate based on the present methods with a previous Eulerian analysis shows good correspondence. However, the current Lagrangian framework is more effective than previous analyses in capturing the transport geometry, especially when the flow becomes more unsteady, as in the case of the free-swimming jellyfish. Extensions of these results to more complex flow geometries is suggested.

Flow patterns generated by oblate medusan jellyfish: field measurements and laboratory analyses

SUMMARY Flow patterns generated by medusan swimmers such as jellyfish are known to differ according the morphology of the various animal species. Oblate medusae have been previously observed to generate vortex ring structures during the propulsive cycle. Owing to the inherent physical coupling between locomotor and feeding structures in these animals, the dynamics of vortex ring formation must be robustly tuned to facilitate effective functioning of both systems. To understand how this is achieved, we employed dye visualization techniques on scyphomedusae (Aurelia aurita) observed swimming in their natural marine habitat. The flow created during each propulsive cycle consists of a toroidal starting vortex formed during the power swimming stroke, followed by a stopping vortex of opposite rotational sense generated during the recovery stroke. These two vortices merge in a laterally oriented vortex superstructure that induces flow both toward the subumbrellar feeding surfaces and downstream. The lateral vortex motif discovered here appears to be critical to the dual function of the medusa bell as a flow source for feeding and propulsion. Furthermore, vortices in the animal wake have a greater volume and closer spacing than predicted by prevailing models of medusan swimming. These effects are shown to be advantageous for feeding and swimming performance, and are an important consequence of vortex interactions that have been previously neglected.

Introduction to Focus Issue: Lagrangian Coherent Structures

The topic of Lagrangian coherent structures (LCS) has been a rapidly growing area of research in nonlinear dynamics for almost a decade. It provides a means to rigorously define and detect transport barriers in dynamical systems with arbitrary time dependence and has a wealth of applications, particularly to fluid flow problems. Here, we give a short introduction to the topic of LCS and review the new work presented in this Focus Issue.

Fluid entrainment by isolated vortex rings

Of particular importance to the development of models for isolated vortex ring dynamics in a real fluid is knowledge of ambient fluid entrainment by the ring. This time-dependent process dictates changes in the volume of fluid that must share impulse delivered by the vortex ring generator. Therefore fluid entrainment is also of immediate significance to the unsteady forces that arise due to the presence of vortex rings in starting flows. Applications ranging from industrial and transportation, to animal locomotion and cardiac flows, are currently being investigated to understand the dynamical role of the observed vortex ring structures. Despite this growing interest, fully empirical measurements of fluid entrainment by isolated vortex rings have remained elusive. The primary difficulties arise in defining the unsteady boundary of the ring, as well as an inability to maintain the vortex ring in the test section sufficiently long to facilitate measurements. We present a new technique for entrainment measurement that utilizes a coaxial counter-flow to retard translation of vortex rings generated from a piston–cylinder apparatus, so that their growth due to fluid entrainment can be observed. Instantaneous streamlines of the flow are used to determine the unsteady vortex ring boundary and compute ambient fluid entrainment. Measurements indicate that the entrainment process does not promote self-similar vortex ring growth, but instead consists of a rapid convection-based entrainment phase during ring formation, followed by a slower diffusive mechanism that entrains ambient fluid into the isolated vortex ring. Entrained fluid typically constitutes 30% to 40% of the total volume of fluid carried with the vortex ring. Various counter-flow protocols were used to substantially manipulate the diffusive entrainment process, producing rings with entrained fluid fractions up to 65%. Measurements of vortex ring growth rate and vorticity distribution during diffusive entrainment are used to explain those observed effects, and a model is developed to relate the governing parameters of isolated vortex ring evolution. Measurement results are compared with previous studies of the process, and implications for the dynamics of starting flows are suggested.

A viscosity-enhanced mechanism for biogenic ocean mixing

Recent observations of biologically generated turbulence in the ocean have led to conflicting conclusions regarding the significance of the contribution of animal swimming to ocean mixing. Measurements indicate elevated turbulent dissipation—comparable with levels caused by winds and tides—in the vicinity of large populations of planktonic animals swimming together. However, it has also been noted that elevated turbulent dissipation is by itself insufficient proof of substantial biogenic mixing, because much of the turbulent kinetic energy of small animals is injected below the Ozmidov buoyancy length scale, where it is primarily dissipated as heat by the fluid viscosity before it can affect ocean mixing. Ongoing debate regarding biogenic mixing has focused on comparisons between animal wake turbulence and ocean turbulence. Here, we show that a second, previously neglected mechanism of fluid mixing—first described over 50 years ago by Charles Darwin— is the dominant mechanism of mixing by swimming animals. The efficiency of mixing by Darwin’s mechanism is dependent on animal shape rather than fluid length scale and, unlike turbulent wake mixing, is enhanced by fluid viscosity. Therefore, it provides a means of biogenic mixing that can be equally effective in small zooplankton and large mammals. A theoretical model for the relative contributions of Darwinian mixing and turbulent wake mixing is created and validated by in situ field measurements of swimming jellyfish using a newly developed scuba-based laser velocimetry device. Extrapolation of these results to other animals is straightforward given knowledge of the animal shape and orientation during vertical migration. On the basis of calculations of a broad range of aquatic animal species, we conclude that biogenic mixing via Darwin’s mechanism can be a significant contributor to ocean mixing and nutrient transport.

On the estimation of swimming and flying forces from wake measurements

SUMMARY The transfer of momentum from an animal to fluid in its wake is fundamental to many swimming and flying modes of locomotion. Hence, properties of the wake are commonly studied in experiments to infer the magnitude and direction of locomotive forces. The determination of which wake properties are necessary and sufficient to empirically deduce swimming and flying forces is currently made ad hoc. This paper systematically addresses the question of the minimum number of wake properties whose combination is sufficient to determine swimming and flying forces from wake measurements. In particular, it is confirmed that the spatial velocity distribution (i.e. the velocity field) in the wake is by itself insufficient to determine swimming and flying forces, and must be combined with the fluid pressure distribution. Importantly, it is also shown that the spatial distribution of rotation and shear (i.e. the vorticity field) in the wake is by itself insufficient to determine swimming and flying forces, and must be combined with a parameter that is analogous to the fluid pressure. The measurement of this parameter in the wake is shown to be identical to a calculation of the added-mass contribution from fluid surrounding vortices in the wake, and proceeds identically to a measurement of the added-mass traditionally associated with fluid surrounding solid bodies. It is demonstrated that the velocity/pressure perspective is equivalent to the vorticity/vortex-added-mass approach in the equations of motion. A model is developed to approximate the contribution of wake vortex added-mass to locomotive forces, given a combination of velocity and vorticity field measurements in the wake. A dimensionless parameter, the wake vortex ratio (denoted Wa), is introduced to predict the types of wake flows for which the contribution of forces due to wake vortex added-mass will become non-negligible. Previous wake analyses are re-examined in light of this parameter to infer the existence and importance of wake vortex added-mass in those cases. In the process, it is demonstrated that the commonly used time-averaged force estimates based on wake measurements are not sufficient to prove that an animal is generating the locomotive forces necessary to sustain flight or maintain neutral buoyancy.

Fish schooling as a basis for vertical axis wind turbine farm design

Most wind farms consist of horizontal axis wind turbines (HAWTs) due to the high power coefficient (mechanical power output divided by the power of the free-stream air through the turbine cross-sectional area) of an isolated turbine. However when in close proximity to neighboring turbines, HAWTs suffer from a reduced power coefficient. In contrast, previous research on vertical axis wind turbines (VAWTs) suggests that closely spaced VAWTs may experience only small decreases (or even increases) in an individual turbines power coefficient when placed in close proximity to neighbors, thus yielding much higher power outputs for a given area of land. A potential flow model of inter-VAWT interactions is developed to investigate the effect of changes in VAWT spatial arrangement on the array performance coefficient, which compares the expected average power coefficient of turbines in an array to a spatially isolated turbine. A geometric arrangement based on the configuration of shed vortices in the wake of schooling fish is shown to significantly increase the array performance coefficient based upon an array of 16 x 16 wind turbines. The results suggest increases in power output of over one order of magnitude for a given area of land as compared to HAWTs.

The role of optimal vortex formation in biological fluid transport

Animal phyla that require macro-scale fluid transport for functioning have repeatedly and often independently converged on the use of jet flows. During flow initiation these jets form fluid vortex rings, which facilitate mass transfer by stationary pumps (e.g. cardiac chambers) and momentum transfer by mobile systems (e.g. jet-propelled swimmers). Previous research has shown that vortex rings generated in the laboratory can be optimized for efficiency or thrust, based on the jet length-to-diameter ratio (L/D), with peak performance occurring at 3.5<L/D<4.5. Attempts to determine if biological jets achieve this optimization have been inconclusive, due to the inability to properly account for the diversity of jet kinematics found across animal phyla. We combine laboratory experiments, in situ observations and a framework that reduces the kinematics to a single parameter in order to quantitatively show that individual animal kinematics can be tuned in correlation with optimal vortex ring formation. This new approach identifies simple rules for effective fluid transport, facilitates comparative biological studies of jet flows across animal phyla irrespective of their specific functions and can be extended to unify theories of optimal jet-based and flapping-based vortex ring formation.

Energy exchange in an array of vertical-axis wind turbines

We analyze the flow field within an array of 18 counter-rotating, vertical-axis wind turbines (VAWTs), with an emphasis on the fluxes of mean and turbulence kinetic energy. The turbine wakes and the recovery of the mean wind speed between the turbine rows are derived from measurements of the velocity field using a portable meteorological tower with seven, vertically-staggered, three-component ultrasonic anemometers. The data provide insight to the blockage effect of both the individual turbine pairs within the array and the turbine array as a whole. The horizontal and planform kinetic energy fluxes into the turbine array are analyzed, and various models for the roughness length of the turbine array are compared. A high planform kinetic energy flux is measured for the VAWT array, which facilitates rapid flow recovery in the wake region behind the turbine pairs. Flow velocities return to 95% of the upwind value within six rotor diameters downwind from each turbine pair. This is less than half the recovery distance behind a typical horizontal-axis wind turbine (HAWT). The observed high level of the planform kinetic energy flux is correlated with higher relative roughness lengths for the VAWT array as compared to HAWT farms. This result is especially relevant for large wind farms with horizontal dimensions comparable to the height of the atmospheric boundary layer. As shown in recent work and confirmed here, the planform kinetic energy flux can be the dominant source of energy in such large-scale wind farms.