Actuator Disc Theory Research Articles

Feasibility Study of Using Flexible Solar Panels for Powered-Parachute Flying Vehicles

Objectives: To assess the potential of using the flexible solar cells to provide the powered parachute vehicles (PPC) with the necessary power for cruise flight. Methods/Analysis: The power required for a typical PPC with three different types of flexible solar cells was determined based on the actuator disk theory. The necessary area and mass of the solar cells needed to generate the required power are also determined. Findings: It was found that the available solar cells in the market can be used to cover the PPC parafoil and generate the required power. However, there is a trade-off between the efficiency, flexibility, and cost of the solar cells. Application/Improvement: The proposed idea of covering the parafoil’s surface with solar cells, with the aim of increasing the endurance of the PPC vehicles, was found to be feasible. This technology can be adopted for military and civilian applications. Keywords: Parafoil, Paraglider, Powered Parachute, Solar, Solar Powered

Comparison of actuator disc flows representing wind turbines and propellers

Actuator disc theory is the basis for rotor design and analysis, valid for discs representing wind turbine rotors as well as propellers. In Froude’s momentum theory swirl is absent, in Joukowsky’s momentum theory this is included. The momentum theory including swirl, developed in WES, 2:307-316,2017, as well as potential flow calculations have been expanded to propeller discs. For the rotational speed Ω → ∞ the classical Froude results are recovered. For low values of Ω the propeller discs show an expanding instead of contracting wake, like wind turbine discs. Both flow regimes show a complete blockage of the flow for a low but non-zero Ωmin. For all wind turbine discs, so irrespective of Ω, the velocity in the meridian plane, is constant at the disc, for all propeller discs this is not.

An integrated numerical method for wind turbine flow simulation, sound generation and propagation

The scope of the paper is to present an efficient numerical method that predicts: (a) wind turbine aerodynamic loads and power; (b) wind turbine noise source; (c) long distance wind turbine noise source propagation. The numerical methods involved in this study are a combination of Computational Fluid Dynamics (CFD) and wind turbine aeroacoustic methods. The results from the CFD simulation provide necessary information of wind turbine power and thrust etc. The 2D Actuator Disc (AD) theory is applied for such a purpose. The computational efficiency becomes very high while using a steady 2D CFD approach. The flow geometry at each blade element is required for wind turbine noise source calculations. The predicted wind turbine noise source is the starting field for long distance noise propagation model which is based on solving the Parabolic Equations (PE) in the frequency domain. Results showed that the integrated wind turbine flow-acoustic prediction method is capable of calculating wind turbine aerodynamic, aerodynamic noise source and long range sound propagation.

Assessment of the Malaysian tidal stream energy resource using an upper bound approach

In this paper, an upper bound approach is used to determine the maximum power available to tidal stream turbines placed at five sites along the west coast of Peninsular Malaysia. A depth-averaged hydrodynamic model of the Malacca Strait is built and validated against field measurements. Actuator disc theory is then used to introduce rows of tidal stream turbines as line sinks of momentum and to determine the maximum time-averaged power available to rows of both moderately sized and very large turbines, placed strategically at the locations of highest naturally occurring kinetic energy flux. Results suggest that although the Malaysian tidal stream energy resource is not large enough to make a significant contribution to the country’s energy mix, there may yet be opportunities to use low-speed tidal turbines in small-scale and off-grid electricity generation schemes. Methods are described in detail and links to source codes and results are provided to encourage the application of this simple, yet effective resource assessment methodology to other promising tidal energy sites.

Scaling law for the lift force of autorotating falling seeds at terminal velocity

We provide a scaling law for the lift force of autorotating falling seeds at terminal velocity to describe the relation among the lift force, seed geometry and terminal descending and rotating velocities. Two theories, steady wing-vortex theory and actuator-disk theory, are examined to derive the scaling law. In the steady wing-vortex theory, the strength of a leading-edge vortex is scaled with the circulation around a wing and the lift force is modelled by the time derivative of vortical impulse, whereas the conservations of mass, linear and angular momentum, and kinetic energy across the autorotating falling seed are applied in the actuator-disk theory. To examine the validity of the theoretical results, an unsteady three-dimensional numerical simulation is conducted for flow around an autorotating seed (Acer palmatum) during free fall. The sectional lift coefficient predicted from the steady wing-vortex theory reasonably agrees with that from the numerical simulation, whereas the actuator-disk theory fails to provide an estimation of the sectional lift coefficient. The weights of 11 different species of autorotating falling seeds fall on the scaling law derived from the steady wing-vortex theory, suggesting that even a simple theoretical approach can explain how falling seeds support their weights by autorotation once the circulation from a leading-edge vortex is properly included in the theory.

Sensitivity Analysis to Control the Far-Wake Unsteadiness Behind Turbines

We explore the stability of wakes arising from 2D flow actuators based on linear momentum actuator disc theory. We use stability and sensitivity analysis (using adjoints) to show that the wake stability is controlled by the Reynolds number and the thrust force (or flow resistance) applied through the turbine. First, we report that decreasing the thrust force has a comparable stabilising effect to a decrease in Reynolds numbers (based on the turbine diameter). Second, a discrete sensitivity analysis identifies two regions for suitable placement of flow control forcing, one close to the turbines and one far downstream. Third, we show that adding a localised control force, in the regions identified by the sensitivity analysis, stabilises the wake. Particularly, locating the control forcing close to the turbines results in an enhanced stabilisation such that the wake remains steady for significantly higher Reynolds numbers or turbine thrusts. The analysis of the controlled flow fields confirms that modifying the velocity gradient close to the turbine is more efficient to stabilise the wake than controlling the wake far downstream. The analysis is performed for the first flow bifurcation (at low Reynolds numbers) which serves as a foundation of the stabilization technique but the control strategy is tested at higher Reynolds numbers in the final section of the paper, showing enhanced stability for a turbulent flow case.

Generic Analytical Thrust-Force Model for Flapping Wings

The purpose of this paper is to propose a generic analytical flapping-wing cycle-average thrust-force estimation method by implementing elongated body theory into actuator disk theory. Compared with previous a flapping-wing analysis based on actuator disk theory, the proposed method relates wing geometry and kinematics directly to induced velocity, and the periodical pressure pulsation correction factor measurement for every different flapping-wing design is no longer necessary. The proposed method is much simpler than unsteady aerodynamics or computational implementations, and thus the complex multiparameter optimization can be avoided at the early design stage of flapping-wing vehicles. Theoretical deviation of the proposed thrust model is evaluated by a numerical simulation method, and a correction term is proposed. The corrected method is then validated by wind-tunnel experiments on an 850-cm-wing-span active-twisting flapping-wing model and experimental data from previous studies that were over large parameter ranges. The results suggest that the proposed method is valid for the flapping-wing cycle-average thrust estimation over a large range of variables. Theoretical deductions about the effects of dominant factors of flapping-wing propulsion behavior and application of the present method in both passive- and active-twisting flapping-wing designs are also discussed.

Experimental analysis on the dynamic wake of an actuator disc undergoing transient loads

The Blade Element Momentum model, which is based on the actuator disc theory, is still the model most used for the design of open rotors. Although derived from steady cases with a fully developed wake, this approach is also applied to unsteady cases, with additional engineering corrections. This work aims to study the impact of an unsteady loading on the wake of an actuator disc. The load and flow of an actuator disc are measured in the Open Jet Facility wind tunnel of Delft University of Technology, for steady and unsteady cases. The velocity and turbulence profiles are characterized in three regions: the inner wake region, the shear layer region and the region outside the wake. For unsteady load cases, the measured velocity field shows a hysteresis effect in relation to the loading, showing differences between the cases when loading is increased and loading is decreased. The flow field also shows a transient response to the step change in loading, with either an overshoot or undershoot of the velocity in relation to the steady-state velocity. In general, a smaller reduced ramp time results in a faster velocity transient, and in turn a larger amplitude of overshoot or undershoot. Time constants analysis shows that the flow reaches the new steady-state slower for load increase than for load decrease; the time constants outside the wake are generally larger than at other radial locations for a given downstream plane; the time constants of measured velocity in the wake show radial dependence.The data are relevant for the validation of numerical models for unsteady actuator discs and wind turbines, and are made available in an open source database (see Appendix).

Numerical analysis of a diffuser-augmented hydrokinetic turbine

The current work presents a novel way to evaluate the interaction effects in a diffuser-augmented hydrokinetic turbine (DAHT) under the terms presented on the generalized actuator disc theory described by Jamieson (2011). Transient RANS CFD methods are employed to obtain the performance, thrust, and average flow speeds at the turbine plane in simulations performed in three comparable cases: bare turbine, bare diffuser and diffuser-augmented turbine. After validating the bare turbine case comparing numerical results against the experiments presented by Fontaine et al. (2013), the axial induction factors are obtained for the three cases based on the average speeds of the turbine plane. The analysis of the results shows the importance of considering rotor-diffuser interaction for the design of diffuser-augmented devices, and that these interaction effects are just as relevant as the bare diffuser and the bare turbine characteristics.

Joukowsky actuator disc momentum theory

Abstract. Actuator disc theory is the basis for most rotor design methods, albeit with many extensions and engineering rules added to make it a well-established method. However, the off-design condition of a very low rotational speed Ω of the disc is still a topic for scientific discussions. Several authors have presented solutions of the associated momentum theory for actuator discs with a constant circulation, the so-called Joukowsky discs, showing the efficiency Cp → ∞ for the tip speed ratio λ → 0. The momentum theory is very sensitive to the choice of the radius δ of the core of the centreline vortex as the pressure and velocity gradients become infinite for δ → 0. Usually the vortex core area is not included in the momentum balance, as it vanishes for δ → 0. However, the pressure in the vortex core behaves as a Delta function and so contributes to the balance, thereby cancelling the singular behaviour. Applying this in the momentum balance results in Cp → 0 for λ → 0, instead of Cp → ∞. The Joukowsky actuator disc theory is confirmed by a very good match with numerically obtained results. At the disc the velocity in the meridian plane is shown to be constant. The Joukowsky calculations give higher Cp values than corresponding solutions for discs with a Goldstein-based wake circulation published in literature.

A comparison of numerical and analytical predictions of the tidal stream power resource of Massachusetts, USA

The coastal waters of Massachusetts, USA encompass tidal phenomena that generate flows of sufficient magnitude for commercially viable power extraction. We examine the tidal power resource of the Massachusetts coastal region with two high-resolution hydrodynamic tidal models: a regional model encompassing the coastal waters of southeastern New England and a local domain model of Cape Cod Canal. Both models have been subject to comprehensive skill assessment using available surface elevation and ADCP measurements. Based on the model results, we identify five high-energy sites (Cape Cod Canal, Muskeget Channel, Quicks Hole, Robinson Hole and Woods Hole) for evaluation of the maximum extractable tidal power. The power extraction at these sites is modeled using linear momentum actuator disk theory applied to a cross-channel array of turbines. Of the sites evaluated, Muskeget Channel has the greatest resource, with an estimated maximum extractable power of 24 MW. The estimated total power available from all five sites is 44 MW. These estimates agree within 21% with predictions from analytical approaches at all sites. Potential applications for the models include: providing developers with an initial assessment of the resource, guiding observation programs for further study of the resource, and facilitating optimization of turbine array design.

The power available to tidal turbines in an open channel flow

Linear momentum actuator disc theory is extended to address the power available to a tidal turbine array spanning the cross-section of an open channel flow. A generalised formulation is presented, which relaxes constraints in previous models on the Froude number of the flow and the geometry of the turbine array, and also considers the effects of far-wake mixing on the overall power removed from the flow. In the limiting case of no free surface deformation, the rigid lid model is recovered. Blockage, the ratio of turbine frontal area to the cross-sectional area of the surrounding flow passage, has the greatest effect on available power, with the peak power coefficient increasing by 55% from 0·60 to 0·93 as the blockage ratio increases from 0·05 to 0·20. A further 3% increase in peak power coefficient is achieved as the Froude number increases from 0·05 to 0·20. The efficiency of energy extraction may be determined relative to the total power extracted from the flow, comprising the power available to the turbines, and the power dissipated in wake mixing. Higher blockage turbines operating at low thrust coefficients are shown to be more efficient than lower blockage turbines.

Impact of channel blockage on the performance of axial and cross-flow hydrokinetic turbines

This work investigates the effect of channel blockage on the performance of axial and cross-flow turbines with the objective of filling a gap in the literature on suitable blockage corrections for cross-flow turbines. Our investigation is based on 3D computational fluid dynamics simulations at high Reynolds number. Blockage corrections are proposed for axial and cross-flow hydrokinetic turbines. These corrections allow the estimation of the drag, power and tip speed ratio of the theoretically unconfined turbine, based on results of the confined turbine. It is found that a blockage correction based on a simple linear momentum actuator disk theory, is quite adequate when applied to both axial and low-solidity cross-flow turbines. Results suggest that for the 3-bladed (high-solidity) cross-flow turbine, this method slightly underpredicts the correction factor, more so for drag than for power. Normalizing with the bypass flow velocity improves the drag correction. For both technologies, the power extracted is found to be almost insensitive to blockage when dynamic stall is present. To discriminate between lateral and vertical confinement is usually not required, the performance being mostly dependent on the blockage ratio (ratio of turbine and channel frontal areas) unless the confinement asymmetry differs by more than a factor of 3.

Momentum theory of Joukowsky actuator discs with swirl

Actuator disc theory is the basis for most rotor design methods, be it with many extensions and engineering rules added to make it a well-established method. However, the off-design condition of a very low rotational speed Ω of the disc is still a topic for scientific discussions. Several authors have presented solutions of the associated momentum theory for actuator discs with a constant circulation, the so-called Joukowsky discs, showing the efficiency Cp → ∞ for Ω → 0. The momentum balance is very sensitive to the choice of the vortex core radius δ as the pressure and velocity gradients become infinite for δ → 0. Viscous vortex cores do not show this singular behaviour so an inviscid core model is sought which removes the momentum balance sensitivity to singular flow. A vortex core with a constant δ does so. Applying this results in Cp → 0 for Ω → 0, instead of Cp → ∞. The Joukowsky actuator disc theory is confirmed by a very good match with the numerically obtained results. It gives higher Cp values than corresponding solutions for discs with a Goldstein-based wake circulation published in literature.

A control-oriented dynamic wind farm flow model: “WFSim”

In this paper, we present and extend the dynamic medium fidelity control-oriented Wind Farm Simulator (WFSim) model. WFSim resolves flow fields in wind farms in a horizontal, two dimensional plane. It is based on the spatially and temporally discretised two dimensional Navier-Stokes equations and the continuity equation and solves for a predefined grid and wind farm topology. The force on the flow field generated by turbines is modelled using actuator disk theory. Sparsity in system matrices is exploited in WFSim, which enables a relatively fast flow field computation. The extensions to WFSim we present in this paper are the inclusion of a wake redirection model, a turbulence model and a linearisation of the nonlinear WFSim model equations. The first is important because it allows us to carry out wake redirection control and simulate situations with an inflow that is misaligned with the rotor plane. The wake redirection model is validated against a theoretical wake centreline known from literature. The second extension makes WFSim more realistic because it accounts for wake recovery. The amount of recovery is validated using a high fidelity simulation model Simulator fOr Wind Farm Applications (SOWFA) for a two turbine test case. Finally, a linearisation is important since it allows the application of more standard analysis, observer and control techniques.

Performance enhancement of downstream vertical-axis wind turbines

Increased power production is observed in downstream vertical-axis wind turbines (VAWTs) when positioned offset from the wake of upstream turbines. This effect is found to exist in both laboratory and field environments with pairs of co- and counter-rotating turbines, respectively. It is hypothesized that the observed production enhancement is due to flow acceleration adjacent to the upstream turbine due to bluff body blockage, which would increase the incident freestream velocity on appropriately positioned downstream turbines. A low-order model combining potential flow and actuator disk theory captures this effect. Additional laboratory and field experiments further validate the predictive capabilities of the model. Finally, an evolutionary algorithm reveals patterns in optimized VAWT arrays with various numbers of turbines. A “truss-shaped” array is identified as a promising configuration to optimize energy extraction in VAWT wind farms by maximizing the performance enhancement of downstream turbines.

Two-scale momentum theory for very large wind farms

A new theoretical approach is proposed to predict a practical upper limit to the efficiency of a very large wind farm. The new theory suggests that the efficiency of ideal turbines in an ideal very large wind farm depends primarily on a non-dimensional parameter λ/Cf0, where λ is the ratio of the rotor swept area to the land area (for each turbine) and Cf0 is a natural friction coefficient observed before constructing the farm. When X/Cf approaches to zero, the new theory goes back to the classical actuator disc theory, yielding the well-known Betz limit. When λ/Cf0 increases to a large value, the maximum power coefficient of each turbine reduces whilst a normalised power density of the farm increases asymptotically to an upper limit. A CFD analysis of an infinitely large wind farm with ‘aligned’ and ‘displaced’ array configurations is also presented to validate a key assumption used in the new theory.

An analytical model for a full wind turbine wake

An analytical wind turbine wake model is proposed to predict the wind velocity distribution for all distances downwind of a wind turbine, including the near-wake. This wake model augments the Jensen model and subsequent derivations thereof, and is a direct generalization of that recently proposed by Bastankhah and Porté-Agel. The model is derived by applying conservation of mass and momentum in the context of actuator disk theory, and assuming a distribution of the double-Gaussian type for the velocity deficit in the wake. The physical solutions are obtained by appropriate mixing of the waked- and freestream velocity deficit solutions, reflecting the fact that only a portion of the fluid particles passing through the rotor disk will interact with a blade.

The Actuator Disc Concept in Phoenics

This study presents two models to simulate a wind turbine. This is done by employing the 1D momentum actuator disc theory in PHOENICS, a general purpose computational fluid dynamics software. To test the general applicability of these models, single wind turbine simulations are conducted using eight different wind turbine models from two manufacturers. The simulations are performed by imposing sheared inflow with hub height wind speeds ranging from 3 m/s up to 25 m/s. A range of computational parameters are investigated, including the resolution of the domain, the thickness of the actuator disc and the iterative convergence criteria. To investigate the wake development produced by these methods, a comparison study is performed with the more complex large-eddy simulation software EllipSys3D using an actuator disc approach for validation purposes. The resulting wind turbine thrust and power outputs from PHOENICS are compared with the experimental power curves and thrust values provided by the manufacturers for each wind turbine. The results show that actuator disc methods are able to provide a reasonable estimation of the conventional wind turbine power and thrust output with low computational effort. Moreover, the results from the preliminary comparison of the wake produced from these two rotor models compare well with the wake produced by the actuator disc in EllipSys3D.

Calibrating the Loss Coefficient of a Porous Plate

AbstractMarine structures are sometimes represented in coastal ocean circulation models as a porous plate that exerts drag on the flow and dissipates energy. Such a representation requires that a loss coefficient be specified to reduce the flow speed to some prescribed fraction of the upstream incident flow. To provide guidance and a framework for this problem, the case of a uniform channel that is partially blocked by a porous structure is considered. Drawing on existing results from actuator disc theory, simple analytical relations are presented for the dependence of the flow speed through a porous plate on the loss coefficient. It is shown that limitations on representing structures with high hydrodynamic loading using an actuator disc in an unbounded region can be avoided by allowing for weak geometrical blockage by lateral boundaries.