Blade Circulation Research Articles

Influence of Rotor Inflow, Tip Loss, and Aerodynamics Modeling on the Maximum Thrust Computation in Hover

Comprehensive rotorcraft simulation codes are the workhorses for designing and simulating helicopters and their rotors under steady and unsteady operating conditions. These codes are also used to predict helicopters’ limits as they approach rotor stall conditions. This paper focuses on the prediction of maximum rotor thrust when hovering (due to stall limits) and the thrust and power characteristics when the collective control angle is further increased. The aerodynamic factors that may significantly affect the results are as follows: steady vs. unsteady aerodynamics, steady vs. dynamic stall, blade tip losses, curvature flow, yaw angle, inflow model, and blade-vortex interaction. The inflow model and tip losses are found to be the most important factors. For real-world applications vortex-based inflow models are considered the best choice, as they reflect the blade circulation distribution within the inflow distribution. Because the focus is on the impact of aerodynamic modeling on rotor stall, the blade design and its flexibility are intentionally not considered.

Impact of some design considerations on the wake recovery of vertical-axis turbines

Using delayed detached-eddy simulations, the objective of this paper is to show the effects of some design parameters on the wake recovery of vertical-axis turbines. To that end, the wake dynamics of a single-blade turbine is analyzed and compared for two different positions of blade attachment point and for two designs of blade support structures (struts). The results show that the chordwise position of the blade attachment point affects the temporal evolution of the blade circulation during the turbine revolution. More precisely, we demonstrate that an attachment point positioned near the trailing edge of the blade leads to a temporal vorticity distribution that is detrimental to the wake recovery. Moreover, we show that the use of tip struts, that are highly beneficial to the turbine efficiency, affects the spatial distribution of the vortex structures shed by the turbine as well as the wake recovery. The results presented in this paper suggest that the velocity recovery in the wake is highly dependent on the very near-wake vortex dynamics. Therefore, we can infer that any geometric parameter affecting the temporal and spatial distributions of the vorticity shed by the blades can significantly alter the wake recovery of vertical-axis turbines.

Extracting angles of attack from blade‐resolved rotor CFD simulations

AbstractThe distribution of the angles of attack over the span of a rotor blade, together with blade element theory, provides a useful framework to understand forces, performance and other fluid dynamic phenomena of axial‐flow rotors. However, the angle of attack is not straightforward to define for a three‐dimensional rotor, where the flow is perturbed by the blade circulation, shed vorticity and wake development.This paper evaluates six methods to extract the angles of attack from blade‐resolved CFD simulations of axial‐flow turbines. Simulations of two different rotors are presented: a low solidity rotor designed for wind and a higher solidity rotor designed for tidal stream energy conversion. Of the analysed methods, five were obtained from the literature and are tested in terms of their internal parameters. The remaining method is named the streamtube analysis method (SAM) and is presented as an improvement on analysis methods that azimuthally average the flow data on the rotor plane, referred to as azimuthal averaging techniques (AATs). The SAM method accounts for the expansion of the streamtubes in flow‐field velocity sampling and exhibits improved convergence on the internal parameters compared with AAT.The six methods are benchmarked in terms of the angles of attack, axial induction factors and the local lift and drag coefficients, identifying that most perform well and converge with each other despite the different underlying assumptions or modelling approaches. However, given the limitations and inherent dependency on internal parameters, the line averaging and SAM are suggested for general flow analysis application.

Investigations of tip-jet and exhaust jet development in a ducted fan

The major aim of this work is to investigate the tip-jet and exhaust jet development in a ducted fan as well as the impact on the fan’s performance. The flow field of the ducted fans under the solidity varied from 0.2 to 0.7 are simulated by using the shear-stress transport k-ω turbulence model with a refined high-quality structured grid. The exhaust jet trajectory, expanding range and the flow intersection of the jet and mainstream in the blade passage are analyzed. As the results suggest, the flow direction of the exhaust jet is deflected by the downwash and Coanda effect. The major decay region of the exhaust jet can extend at least 2 times the blade chord downstream from the blade trailing edge. The blade circulation is impacted by the tip-jet rather than the exhaust jet from the upstream when the blade tip pitch angle is 8°, and the fan solidity is less than 0.7. The blade tip thrust is reduced by the interruption from the exhaust jet when the blade tip pitch angle is 2°, and the fan solidity is larger than 0.3.

A strongly-coupled model for flexible rotors

A fluid–structure model describing the equilibrium state of a flexible blade rotor with its own wake is derived for various external axial flow conditions. The model is based on three building blocks. The two-dimensional lifting-line theory is first used to compute the local aerodynamic loads and the blade circulation profile. The blade deformation is then obtained by solving the nonlinear equations for bending and twisting angles deduced from a one-dimensional beam model. Finally, the wake is obtained using a Joukowski model. In this wake model, the wake of each blade is modeled by two small-core-size counter-rotating vortices emitted from the rotor axis and blade tip. The velocity field induced by these vortices is computed using the Biot–Savart law. We show that, in the rotor frame, we can obtain a stationary vortex structure for almost any vertical flight regimes. This wake solution can then be used to compute the induced velocity in the rotor plane and apply the two-dimensional lifting-line theory again. By iterating a few times this loop, we converge toward a nonlinear solution of the problem for which the aerodynamics loads, blade deformation and wake structure are compatible.As illustration, this newly-developed model is applied to two rotors. We analyze the effects of the external wind conditions, geometry and material properties of the blades on the blade deformation and wake characteristics. We show that we can describe slow descending regimes for which the classical momentum theory does not apply.

Discussion: “Unsteady RANS Simulations of Wells Turbine Under Transient Flow Conditions” (Hu and Li, ASME J. Offshore Mech. Arct. Eng., 140(1), p. 011901)

The work by Hu and Li (2018, “Unsteady RANS Simulations of Wells Turbine Under Transient Flow Conditions,” ASME J. Offshore Mech. Arct. Eng., 140(1), p. 011901) presents the numerical simulation of a high-solidity Wells turbine by means of a computational fluid dynamics (CFD) (Reynolds-averaged Navier–Stokes (RANS)) approach. A key aspect highlighted by the authors is the presence of a hysteretic loop in the machine's performance curves, due (according to their explanation) to the interaction of vortices shed by the blade with the blade circulation, which is responsible for the aerodynamic forces. It is our opinion that this work contains some serious errors that invalidate the results. In this brief discussion, we aim to demonstrate how the hysteresis found and discussed by the authors should not be present in the turbine analyzed in Hu and Li (2018, “Unsteady RANS Simulations of Wells Turbine Under Transient Flow Conditions,” ASME J. Offshore Mech. Arct. Eng., 140(1), p. 011901), and it is unlikely to be present in any Wells turbine. The fact that Hu and Li find hysteresis in their simulations is most likely caused by numerical errors due to an insufficient temporal discretization. This and other inaccuracies could have been avoided with a more careful consideration of the available literature.

Numerical simulation of flow behavior of particles in a liquid-solid stirred vessel with baffles

Flow behavior of particles is simulated by means of two-fluid model combining with kinetic theory of granular flow in a liquid-solid stirred vessel with baffles. The Huilin-Gidaspow drag model is used to obtain interphase interaction of liquid and solids phases. The virtual mass force is considered in simulations. The moving reference frame is applied to the rotation of numerical domain. Predictions are compared with experimental data measured by Pianko-Oprych et al. (2009) in a liquid-solid stirred vessel. This comparison shows that the present model can capture the liquid-solid flow in a liquid-solid stirred vessel. The distributions of velocity and solids volume fraction are predicted at the different heights. The effects of particle density on flow behavior of particles are generally scarce using CFD. Simulations indicate the stirred vessel consists of three regions based on distributions of velocity and turbulent kinetic energy, they are blade circulation region, conical induced region and near-wall region. As an increasing of the impeller speed, the turbulence kinetic and solids phase velocity rise, and the particles fluctuation is intensified.

Stall-Warning Approach Based on Aeroacoustic Principle

In a fan/compressor, the pass of the blade is a periodic event and this periodicity deteriorates when rotating stall is gradually approached. The present work studies this periodicity of the pressure signal and explains when and why this periodicity deterioration happens from the perspective of the aeroacoustic principle. A theoretical analysis shows that the change of blade circulation has a close association with rotating stall and can be reflected on the periodicity deterioration of pressure signals sampled by a near-field dynamic pressure sensor located on the casing wall. A defined parameter , which can revalue this periodicity, has the potential to be a stall-warning criterion. Then, a stall-warning approach is developed in terms of this feature. The values of are calculated by the pressure signals of several blade pitches based on the current and the previous shaft periods. Statistical estimations are conducted on within statistical windows by calculating the probabilities of less than a threshold. The relevant experiments are carried out on a low-speed compressor, a transonic compressor, and a low-speed fan. The results show that the proposed approach has the capability of generating a stall-warning signal sufficiently in advance of the modal wave and spike in turbomachinery.

Angle of attack distribution on wind turbines in yawed flow

This paper presents a new approach to model the induction for wind turbines in yawed flow to find the effective angle of attack distribution along the blades. There is an inherent difficulty in determining the angle of attack required by aeroelastic codes as input to tabulated airfoil data. Unlike two-dimensional (2D) conditions where the angle of attack is the angle between the unperturbed flow and the airfoil chord, for the rotating blade, the incoming flow is bended because of rotation and affected by the induction of the blade circulation and the tip and root vortices, making the definition of the angle of attack uncertain. In this work, the analogy with 2D potential flows suggests that a coupling term between the unperturbed geometric angle of attack and the unitary velocity in the radial direction should be included to calculate the effective angle of attack seen by the blade strips. The model introduces two radially dependent interferences on the geometric angle, obtained from axial flow conditions that give the effective angle of attack under arbitrarily yawed flow conditions. The model gives a uniform treatment to the radial flows associated with yawed conditions or coned rotors and can be applied directly to calculate the effective angle of attack distribution on coned rotors in yawed flow. The accuracy of the method compares with results obtained from conventional or higher degree of complexity methods. The model can be incorporated into blade element momentum theory codes as an option to calculate angle of attack distributions. Copyright © 2015 John Wiley & Sons, Ltd.

Comparison of the near‐wake between actuator‐line simulations and a simplified vortex model of a horizontal‐axis wind turbine

AbstractThe flow around an isolated horizontal‐axis wind turbine is estimated by means of a new vortex code based on the Biot–Savart law with constant circulation along the blades. The results have been compared with numerical simulations where the wind turbine blades are replaced with actuator lines. Two different wind turbines have been simulated: one with constant circulation along the blades, to replicate the vortex method approximations, and the other with a realistic circulation distribution, to compare the outcomes of the vortex model with real operative wind‐turbine conditions (Tjæreborg wind turbine). The vortex model matched the numerical simulation of the turbine with constant blade circulation in terms of the near‐wake structure and local forces along the blade. The results from the Tjæreborg turbine case showed some discrepancies between the two approaches, but overall, the agreement is qualitatively good, validating the analytical method for more general conditions. The present results show that a simple vortex code is able to provide an estimation of the flow around the wind turbine similar to the actuator‐line approach but with a negligible computational effort. Copyright © 2015 John Wiley & Sons, Ltd.

Efficiency gain of low-speed axial flow rotors due to forward sweep

The paper aims at discovering the relationship between the spanwise gradient of blade circulation and the total efficiency gain due to forward sweep, in the case of low-speed axial flow fans, at the design point. For this purpose, an extensive set of literature data have been processed and evaluated by statistical means. A trend function has been established for quantifying the aforementioned relationship. By such means, it has been pointed out that the efficiency gain due to forward sweep tends to increase with the spanwise gradient of blade circulation. This means that the purposeful incorporation of forward sweep in the design process offers an increased potential for efficiency improvement in the case of rotors of controlled vortex design. The maximum efficiency gain has been observed to be 2% to 3%, due to an in-house developed design method. It has been noted that the efficiency improvement due to forward sweep tends to be minor for free-vortex rotors. Furthermore, the efficiency tends to deteriorate if spanwise decreasing blade circulation occurs in forward-swept rotors. Remarks have been made on the means of simultaneous reduction of loss and noise related to low-speed axial fans, for a prescribed aerodynamic performance.

A solution‐based stall delay model for horizontal‐axis wind turbines

AbstractThis work proposes a new solution‐based stall delay model to predict rotational effects on horizontal‐axis wind turbines. In contrast to conventional stall delay models that correct sectional airfoil data prior to the solution to account for three‐dimensional and rotational effects, a novel approach is proposed that corrects sectional airfoil data during a blade element momentum solution algorithm by investigating solution‐dependent parameters such as the spanwise circulation distribution and the local flow velocity acting at a section of blade. An iterative process is employed that successively modifies sectional lift and drag data until the blade circulation distribution is converged. Results obtained with the solution‐based stall delay model show consistent good agreement with measured data along the National Renewable Energy Laboratory Phase VI and Model Experiments in Controlled Conditions rotor blades at low and high wind speeds. Copyright © 2014 John Wiley & Sons, Ltd.

A simplified vortex model of propeller and wind-turbine wakes

AbstractA new vortex model of inviscid propeller and wind-turbine wakes is proposed based on an asymptotic expansion of the Biot–Savart induction law to account for the finite vortex core size. The circulation along the blade is assumed to be constant from the blade root to the tip approximating a turbine with maximum power production for given operating conditions. The model iteratively calculates the tip-vortex path, allowing the wake to expand/contract freely, and is afterward able to evaluate the velocity field in the whole domain. The ‘roller-bearing analogy’, proposed by Okulov and Sørensen (J. Fluid Mech., vol. 649, 2010, pp. 497–508), is used to determine the vortex core size. A comparison of the main outcomes of the present model with the general momentum theory is performed in terms of the operating parameters (namely the number of blades, the tip-speed ratio, the blade circulation and the vortex core size), demonstrating good agreement between the two. Furthermore, experimental data have been compared with the model outputs to validate the model under real operating conditions.

Forward Blade Sweep Applied to Low-Speed Axial Fan Rotors of Controlled Vortex Design: An Overview

An overview is given on the research maintained by the author about the design aspects of three-dimensional blade passage flow in low-speed axial flow industrial fan rotors, affected by spanwise changing design blade circulation due to controlled vortex design (CVD), blade forward sweep (FSW), and their combination. It was pointed out that, comparing the CVD method to the free vortex design, the fluid in the blade suction side boundary layer has an increased inclination to migrate radially outward, increasing the near-tip blockage and loss. It was concluded that the benefit of FSW, in terms of moderating loss near the tip, can be better utilized for the rotors of the CVD, in comparison to the free vortex design. Compared to the free vortex design, the FSW applied to the blades of the CVD was found to also be especially beneficial in loss reduction away from the endwalls, via shortening the flow paths on the suction side—in any case being elongated by the radially outward flow due to CVD—and thus, reducing the effect of wall skin friction. The necessity of correcting the swept blades was pointed out for matching with the prescribed CVD circulation distribution.

Numerical simulation of clocking effect on blade unsteady aerodynamic force in axial turbine

To give an insight into the clocking effect and its influence on the wake transportation and its interaction, the unsteady three-dimensional flow through a 1.5-stage axial low pressure turbine is simulated numerically by using a density-correction based, Reynolds-Averaged Navier-Stokes equations commercial CFD code. The 2nd stator clocking is applied over ten equal tangential positions. The results show that the harmonic blade number ratio is an important factor affecting the clocking effect. The clocking effect has very small influence on the turbine efficiency in this investigation. The difference between the maximum and minimum efficiency is about 0.1%. The maximum efficiency can be achieved when the 1st stator wake enters the 2nd stator passage near blade suction surface and its adjacent wake passes through the 2nd stator passage close to blade pressure surface. The minimum efficiency appears if the 1st stator wake impinges upon the leading edge of the 2nd stator and its adjacent wake of the 1st stator passes through the mid-channel in the 2nd stator. The wake convective transportation and the blade circulation variation due to its impingement on the subsequent blade are the main mechanism affecting the pressure variation in blade surface.

Radial fluid migration and endwall blockage in axial flow rotors

The article presents an analytical model for systematic investigation of the effects stimulating or retarding radial outward migration of fluid in the suction side (SS) boundary layer of the blades of axial flow rotors, contributing to increased near-tip loss and promoting tip stalling. With application of the model to an experimental case study, coupled with evaluation of detailed flow measurement data, it has been pointed out that the outward migration and near-tip accumulation of high-loss fluid are intensified by the controlled vortex design (CVD) style. This phenomenon is related to the SS outward flow associated with the vortices shed from the blade of spanwise changing circulation. It has been found that the outward migration, and consequently, the endwall blockage at the casing, becomes more pronounced as the intensity of shed vortices due to CVD increases. Based on experimental data, it has been pointed out that the increase in axial displacement thickness is approximately proportional to the radial gradient of blade circulation. Based on the purposeful use of the analytical model, forward blade sweep was found to be especially beneficial for the rotors of CVD, as a means for moderating outward migration along the suction surface.

Aerodynamic effects of forward blade skew in axial flow rotors of controlled vortex design

Comparative studies have been carried out on two axial flow fan rotors of controlled vortex design (CVD), at their design flowrate, in order to investigate the effects of circumferential forward skew on blade aerodynamics. The studies were based on computational fluid dynamics (CFD), validated on the basis of global performance and hot wire flow field measurements. The computations indicated that the forward-skewed blade tip modifies the rotor inlet condition along the entire span, due to its protrusion to the relative inlet flow field. This leads to the rearrangement of spanwise blade load distribution, increase of losses along the dominant part of span, and converts the prescribed spanwise blade circulation distribution towards a free vortex flow pattern. Due to the above, reduction in both total pressure rise and efficiency was established. By moderation of the radial outward flow on the suction side, being especially significant for non-free vortex blading, forward sweep was found to be particularly useful for potential reduction of near-tip loss in CVD rotors. Application of reliable CFD-based design systems was recommended for systematic consideration and control of both load- and loss-modifying effects due to non-radial blade stacking.

Effect of a Winglet on Normal Blade-Vortex Interaction

The flowfielddownstreamof abladeinteracted normallywith awinglet-generated doublevortexwasinvestigated experimentally. Similar to the baseline (with no winglet) interaction, the passage of the double vortex over the blade significantly altered the blade circulation distribution, causing negative vorticity to be shed into its wake, which, together with the turbulent wake motions, acted to trigger the turbulent decay of the vortex core, resulting in an increaseinitssizeandlossofcirculation.Forajunction vortexinteracted directlywith thebladeleadingedge,apair of two counter-rotating vortices, similar to the baseline interaction case, was observed at 1.5 chords downstream of the blade trailing edge. Qualitatively, the variation in double vortex-blade separation distance produced large variations in the vortex core parameters associated with the junction vortex, whereas minor changes for the tip vortex.

Mechanism of Hysteretic Characteristics of Wells Turbine for Wave Power Conversion

A Wells turbine for wave power conversion has hysteretic characteristics in a reciprocating flow. The counterclockwise hysteretic loop of the Wells turbine is opposite to the clockwise one of the well-known dynamic stall of an airfoil. In this paper, the mechanism of the hysteretic behavior was elucidated by an unsteady three-dimensional Navier-Stokes numerical simulation. It was found that the hysteretic behavior was associated with a streamwise vortical flow appearing near the blade suction surface. In the accelerating process of axial flow velocity, the vortex is intensified to enlarge the flow separation area on the blade suction surface. In the decelerating flow process, the flow separation area is reduced because of the weakened vortex. Therefore, the aerodynamic performance in the accelerating flow process is lower than in the decelerating flow process, unlike the dynamic stall. Based on the vortex theorem, the mechanism to vary the intensity of the vortex can be explained by the trailing vortices associated with the change in the blade circulation.

Mechanism of Hysteretic Characteristics of Wells Turbine.

A Wells turbine for wave power conversion has hysteretic characteristics in a reciprocating flow. The counterclockwise hysteretic loop of the Wells turbine is opposite to the clockwise one of the well-known dynamic stall of an airfoil. In this paper, the mechanism of the hysteretic behavior was elucidated by an unsteady 3-dimensional Navier-Stokes numerical simulation. It was found that the hysteretic behavior was associated with a streamwise vortical flow appearing near the blade suction surface. In the accelerating process of axial flow velocity, the vortex is intensified to enlarge the flow separation area on the blade suction surface. In the decelerating flow process, the flow separation area is reduced because of the weakened vortex. Therefore, the aerodynamic performance in the accelerating flow process is lower than in the decelerating flow process, unlike the dynamic stall. Based on the vortex theorem, the mechanism to vary the intensity of the vortex is explained by the trailing vortices associated with change in the blade circulation.