Sharp Trailing Edge Research Articles

Performance enhancement of a semi-active flapping foil energy harvester via airfoil with modified trailing edge and jet flap

This paper aims to numerically study effectiveness of the use of a suitable combination of an airfoil with modified trailing edge and jet flap in enhancing the energy harvesting performance of a semi-active flapping foil. The configuration of the proposed airfoil is created by referring to the method of generating a blunt trailing edge airfoil. The most promising airfoil profile is obtained by only thickening the rear part of the original airfoil to reach a thickness of 2% chord, which can apparently promote the energy capturing capability of a semi-active flapping foil when compared with its conventional counterpart with a sharp trailing edge airfoil. Furthermore, a jet flap, an active flow control technique, is then applied on the aft portion of the modified airfoil and the effectiveness of this combination is assessed by a comparison with that of the passive flow control device, Gurney flap. The present findings suggest that this combination can be much more effective than a Gurney flap in significantly increasing the energy harvesting efficiency of the semi-active flapping foil over a wide range of operating conditions, and also has the advantage of structural integrity, which make it more suitable for harsh environment applications.

An effective simulation scheme for the prediction of aerodynamic environment under hypersonic conditions characterized by NACA0012

Currently, aerodynamic environment prediction research into scramjet-propelled vehicles characterized by NACA0012 under hypersonic conditions is relatively sparse. Two-dimensional external flow field models are established, and then through validation tests, we perform a systematic investigation between simulation parameters and prediction accuracy, and an effective aerodynamic environment prediction simulation scheme under hypersonic conditions is proposed. Unlike under incompressible conditions, the maximum accuracy decline could be attributed to the inappropriate choice of the sharp trailing edge modeling method, but the definition formula is still preferred. In particular, for the two modeling data point sources, Airfoil tools and NACA4, the numerical performance of the latter is better than the former, and the calculation accuracy negatively correlates with the number of data points offered by both of them. Moreover, for the mesh cells near the shock, the cell Reynolds number and aspect ratio values should be no smaller than 16 and not exceed 380, respectively, and the recommended values for the far field distance, the turbulence model and flux type are 16L, Spalart-Allmaras, and ROE flux type. Under hypersonic conditions, the aerodynamic environment characterized by NACA0012 predicts a maximum temperature of approximately 1856.85 °C, with an average temperature change rate of 77 °C/s. Meanwhile, the top sound pressure level and the vibration acceleration could reach up to 145 dB and 182 g, respectively.

Computational investigation of the effect of the trailing edge thickness on the wind turbine performance

Trailing edge (TE) thickness is a manufacturing constraint in blade design, especially for airfoils with a sharp TE. To achieve a specific TE thickness, blade geometry is often modified during the design process, typically in the outer zone of the blade where the airfoil’s TE is thinner. This area has a significant impact on energy production and loads. Quantifying the effect of TE thickness modifications is crucial for making informed design decisions.Therefore, this study quantifies and compares the impact of linear and polynomial geometry modifications on airfoil aerodynamics and turbine performance. Xfoil and OpenFAST were used to calculate these performance variations in the well-known NREL 5 MW wind turbine. The TE thickness of the model was modified to meet various manufacturing constraints, ranging from no restriction to a limit of 12mm TE thickness.In terms of the aerodynamic behavior of the airfoils, the maximum efficiency of airfoils with low relative thickness decreases as the TE thickness increases. Annual Energy Production shows a reduction of up to 0.42% for the worst case, while blade root loads increase by up to 20%. For low relative thickness airfoils, the linear method has proven to be a better option with less impact on performance.

A boundary element analysis of quasi-potential inviscid incompressible flow in multiply connected airfoil wing

AbstractThe quasi-potential flow in a doubly linked airfoil wing with a sharp trailing edge can be solved using a high-order boundary-element method (BEM). A bicubic Hermite spline interpolation is used to express the unknown, with node derivatives given by finite difference method. The revolutionary traits apply to bleeding-edge settings; specifically, challenges relating to the three-dimensional problem of multiply connected domains are investigated. Numerical validation examples were utilized to assess the implemented BEM approach.

A similarity approach to the turbulent near-wake of a long slender cylinder with a sharp trailing edge at zero pressure gradient

A high Reynolds number wake flow developing under zero pressure gradient from a long slender axisymmetric cylinder with sharp trail ending is investigated. The main focus is the flow domain immediately behind the trailing edge, where the fully developed upstream turbulent boundary layers separated by the body, unite under no body constraints and the boundary layer identity and characteristics are gradually lost. Similarity solutions for the streamwise mean velocity and centreline velocity are obtained in which the region exhibits the log law of the fully developed boundary layer. A critical assessment of inner near wake characteristic length is done.

Computational and Experimental Investigation of FX 63-137 Airfoil at Low Reynolds Numbers

In this study, the capability of the present day RANS based CFD solver in predicting the characteristics of the FX 63-137 airfoil at a low Reynolds number is carried out. The Reynolds number considered in the present work varies between 0.08 to 0.2 million. Computational simulations were carried out on both sharp trailing edge and blunt trailing edge FX 63-137 airfoils. The comparison between the two FX 63-137 airfoils brings out the effect of the trailing edge on the aerodynamic coefficients. Experimental tests were conducted on the FX 63-137 airfoil for these low Reynolds numbers at the MART facility of CSIR-NAL to validate the CFD simulations. Further, the present MART tunnel data is compared against the experimental data available in the literature. This comparison will show the differences in the experimental results between the tunnels and how the CFD simulations compare against them.

Refining Kutta’s Flow over a Flat Plate: Necessary Conditions for Lift

In this paper, we present a variational theory of lift that, unlike Kutta’s theory, is derived from first principles in mechanics: Hertz’s principle of least curvature. In this theory, the unique value of circulation is determined by minimizing the Appellian of the flowfield. Interestingly, it recovers the Kutta condition in the special case of an airfoil with a sharp trailing edge. In this paper, we apply such a theory to the classical problem of the flow over a flat plate. The resulting ideal flow does not match Kutta’s solution in this case; it results in a nonlifting solution for any uncambered, fore-aft symmetric shape, confirming experimental findings in superfluids. This result provides necessary conditions for lift generation in an ideal fluid. For a real fluid over a flat plate with a sharp leading edge, viscosity plays an important role, leading to a flow separation at the leading edge, even at small angles of attack. This separation bubble creates asymmetry in the outer inviscid flowfield (outside the bubble), which enables lift. This problem is discussed in the light of the developed variational theory of lift and some historical details about the development of Kutta’s theory.

Experimental Investigation of Fenestron Noise

The noise radiation of an EC135 Fenestron is investigated by means of flight tests. The noise emission was measured with ground microphones during several different maneuvers. These include hover, rearward flight, and forward flight at different combinations of the side slip angle and the airspeed. In hover, a high level of broadband noise is observed. A comparison with available engine noise data suggested that engine noise is not dominant in hover. In rearward flight, the Fenestron may encounter a relatively clean aerodynamic inflow. However, the measurements do not indicate a reduction in noise radiation of the Fenestron. For rearward flight, a significant increase in main rotor noise is observed. Flights at different combinations of the side slip angle and airspeed show that the Fenestron radiates high levels of tonal noise at high-speed flight at negative side slip. The most likely cause for this is a highly disturbed inflow caused by flow separations of the diffusor outlet edge and the sharp trailing edges of the stator blades. Measurements of the tail boom yaw moment and Fenestron drive shaft torque imply that a reverse flow is possible at medium airspeed, while the Fenestron thrust does not reverse sign. Only at higher airspeeds and negative side slip, it is possible to achieve a thrust reversal in addition to a flow reversal.

Influence Analysis of Simulation Parameters on Numerical Prediction of Compressible External Flow Field Based on NACA0012 Airfoil under Hypersonic Speed

Currently, the influence of numerical parameters on the prediction accuracy of the compressible external flow field characterized by a NACA0012 airfoil under hypersonic speed, especially the influence analyses of the trailing edge shape, the modeling methods, and the adopted data points on it are relatively sparse. In this paper, using three modeling approaches and two data point sources, six NACA0012 airfoils are designed including two types of trailing edge shapes. Unlike under the incompressible external flow field, the comparative analysis shows that though the optimal accuracy is obtained by the sharp trailing edge, the improper sharp trailing edge design could result in a greater error ratio than that of the blunt trailing edge. Similarly, the definition formula could provide the best performance, while in other cases, NACA4 is preferred and the selection between them depends on the adopted data point source. Furthermore, the increase in the number of the adopted two types of data points would lead to a decrease in prediction accuracy. According to the comparison among all the optimal total error ratios, the suggested configuration is the sharp trailing edge based on the definition formula adopting 200 points sourced from NACA4 + 16 m far-field distance + SA turbulence model + ROE flux type and the best result is 2.05%.

Analytic adjoint solutions for the 2-D incompressible Euler equations using the Green's function approach

The Green's function approach of Giles and Pierce (J. Fluid Mech., vol. 426, 2001, pp. 327–345) is used to build the lift and drag based analytic adjoint solutions for the two-dimensional incompressible Euler equations around irrotational base flows. The drag-based adjoint solution turns out to have a very simple closed form in terms of the flow variables and is smooth throughout the flow domain, while the lift-based solution is singular at rear stagnation points and sharp trailing edges owing to the Kutta condition. This singularity is propagated to the whole dividing streamline (which includes the incoming stagnation streamline and the wall) upstream of the rear singularity (trailing edge or rear stagnation point) by the sensitivity of the Kutta condition to changes in the stagnation pressure.

Investigation of blade design parameters for performance improvement of hydraulic cross flow turbine

Micro hydro power plant offers the cheapest renewable as well as a clean energy resource having abundant room for development. Cross flow turbine is easy to manufacture and maintain, operable in off-grid remote areas with negligible civil work requirement leading to its high popularity in developing countries. The present study numerically investigates the effect of different blade design parameters on the performance of hydraulic cross flow turbine using Ansys-CFX®. Firstly, a comparative analysis of the full turbine and half turbine model is performed. Then, the blade leading and trailing edge is varied considering four distinct geometric profiles with varying rotational speeds of 100–240 rpm. Moreover, the blade exit angle is varied from 50° to 100°, keeping a consistent rotational speed of 180 rpm. The results are presented in terms of the torque generated, and the turbine efficiency. In addition, the localized flow around the blades is elaborated using the flow velocity contours and streamlines. The geometric combination with a circular profile for the blade leading edge followed by a sharp trailing edge transpired maximum turbine efficiency. Moreover, the optimal blade exit angle lies between 55° and 60° contrary to the general practice of radial exit.

A panel method for the prediction of unsteady performance of ducted propellers in ship behind condition

In this article, a boundary element method (BEM) is used to predict the unsteady performance of ducted propellers in open water and ship behind condition. To improve the accuracy of a potential flow solver with highly viscous problems, such as flow separation near a blunt body, section profiles of the model duct have to be modified from a blunt trailing edge duct to a sharp trailing edge duct. The present method modifies the duct profiles based on the predicted streamlines by coupling a potential flow solver with a viscous flow solver. For the prediction of effective wakes, a BEM/RANS coupling scheme is utilized to account for viscous interactions between the non-axisymmetric hull and ducted propellers. The effective wakes are predicted using different configurations of hull/propeller geometry to investigate how the flow field is influenced by the hull/propeller interactions along with the hull appendages. The predicted open water performance and unsteady results are compared to experimental measurements and results from unsteady Reynolds-averaged Navier–Stokes (URANS) simulations over a range of loading conditions. Comparisons are also made between the predicted effective wakes from ducted propellers and open propellers.

The Effect of Single-Sided Ribs on Heat Transfer and Pressure Drop Within a Trailing Edge Internal Channel of a Gas Turbine Blade

Abstract Convective cooling in a gas turbine blade internal trailing edge channel is often insufficient at the sharp trailing edge. This study examines convective heat transfer and pressure drop within a simplified nonrotating trailing edge channel. The internal passage has been modeled as a right triangular channel with a 9 deg angle sharp corner. A copper plate was heated from underneath via a uniform heat flux heater and examined via infrared thermography for two cases: smooth wall and single-sided ribbed wall. Nonuniformity in the heat flux due to conduction is corrected by a Reynolds-averaged Navier–Stokes (RANS) conjugate heat transfer calculation, which was validated by the mean velocity, friction factor, and temperature fields from experiments and large eddy simulation (LES). Nusselt number distributions illustrate that surface heat transfer is increased considerably with ribs and coupled with the vortices in the flow. Heat transfer at the sharp corner is increased by more than twofold due to ribs placed at the center of the channel due to secondary flow. The present single-sided ribbed channel utilizes secondary flow toward the corner and is presumed to have better thermal performance than a dual-sided ribbed channel. Thus, it is important to set the appropriate rib length within the channel.

Analysis of Influence of Different Parameters on Numerical Simulation of NACA0012 Incompressible External Flow Field under High Reynolds Numbers

Currently, influence analysis of simulation parameters, especially the trailing edge shape and the corresponding modeling method on the force coefficients of NACA0012 under a high Reynolds number, is relatively sparse. In this paper, two trailing edge shapes are designed by three modeling methods and combined with three far-field distances to establish eighteen two-dimensional external flow fields. The same number of structured grids are generated by a unified grid strategy and the SST k-omega and the Spalart–Allmaras models are adopted to solve the NS equations to realize the numerical simulations. Unlike under low Reynolds numbers, the analysis results show that although the accuracy difference between the sharp trailing edge and the blunt trailing edge decreases as the attack angle range increases, the former is preferred in all studied ranges. As to the corresponding modeling methods, the NACA4 and the definition formula are preferred, the choice of which depends on the studied range. In particular, a greater number of data points adopted into the definition formula is not necessarily better. Considering the error ratios comprehensively, the simulation configurations of sharp trailing edge + 20 m far-field distance + SA/SST/SST/SST/SST/SA turbulence model obtains optimal simulation effects.

Aeroacoustic Investigation of Trailing-Edge Finlets

Wind tunnel testing and embedded large eddy simulations are employed to study the noise reduction of trailing-edge finlets on an airfoil. Trailing-edge finlets are shown to increase the distance between the highly energetic fluid particles and the sharp trailing edge. Experiments were conducted at different angles of attack. Wind tunnel measurements confirm that finlets reduce the broadband noise radiated by the airfoil. Results also reveal that the noise reduction of finlets is dependent on the airfoil angle of attack, and that the highest noise reduction is obtained at the largest angle of attack tested.

ПОЛУАНАЛИТИЧЕСКИЙ МЕТОД В ЗАДАЧЕ ОБТЕКАНИЯ КРЫЛОВОГО ПРОФИЛЯ С ОСТРОЙ ЗАДНЕЙ КРОМКОЙ ПОТОКОМ ИДЕАЛЬНОЙ ЖИДКОСТИ

In the present work we propose a method to study a two-dimensional flow of non-viscous fluid around an airfoil with a sharp trailing edge, by the double-layer potential theory. The circulation of velocity vector is modeled by the potential of a point vortex whose center is located inside the boundary contour. The magnitude of the circulation is defined on the basis of the Joukowski-Chaplygin postulate. There are presented some results for a Joukowski rudde, as well as for the airfoil in the form of a pair of interacting circles. It is performed a comparison of the circulation with its theoretical value.

Developed liquid film passing a smoothed and wedge-shaped trailing edge: small-scale analysis and the ‘teapot effect’ at large Reynolds numbers

Recently, the authors considered a thin steady developed viscous free-surface flow passing the sharp trailing edge of a horizontally aligned flat plate under surface tension and the weak action of gravity, acting vertically, in the asymptotic slender-layer limit (J. Fluid Mech., vol. 850, 2018, pp. 924–953). We revisit the capillarity-driven short-scale viscous–inviscid interaction, on account of the inherent upstream influence, immediately downstream of the edge and scrutinise flow detachment on all smaller scales. We adhere to the assumption of a Froude number so large that choking at the plate edge is insignificant but envisage the variation of the relevant Weber number of$O(1)$. The main focus, tackled essentially analytically, is the continuation of the structure of the flow towards scales much smaller than the interactive ones and where it no longer can be treated as slender. As a remarkable phenomenon, this analysis predicts harmonic capillary ripples of Rayleigh type, prevalent on the free surface upstream of the trailing edge. They exhibit an increase of both the wavelength and amplitude as the characteristic Weber number decreases. Finally, the theory clarifies the actual detachment process, within a rational description of flow separation. At this stage, the wetting properties of the fluid and the microscopically wedge-shaped edge, viewed as infinitely thin on the larger scales, come into play. As this geometry typically models the exit of a spout, the predicted wetting of the wedge is related to what in the literature is referred to as the teapot effect.

Unsteady flow structures behind a shark denticle replica on the wall: Time-resolved particle image velocimetry measurements

Experiments were performed to determine the unsteady flow structures of a shark denticle replica with three longitudinal ridges of different elevations and sharp trailing edges. Time-resolved particle image velocimetry measurements were conducted to capture the time-varying flow fields behind a shark denticle replica and contoured denticle, using the latter as a benchmark configuration for comparison. The flow fields in the streamwise and spanwise planes were obtained experimentally to determine the highly three-dimensional flow behavior. The flow dynamics of the unsteady superimposed flow structures behind the denticle replica are illustrated in terms of the time-averaged flow fields, statistical flow quantities, dominant vortex structures, and their phase-dependent evolution processes. The findings demonstrate that the denticle replica reduces the size and stability of the recirculation zone, suppressing flow separation. The velocity fluctuations and Reynolds shear stresses of the denticle replica are higher than those of the contoured denticle. Proper orthogonal decomposition analysis on the fluctuating velocity fields reveals alternating clockwise and counterclockwise vortices that convect along the streamwise direction, which correspond to decomposed flow structures, such as counter-rotating vortex pairs in the spanwise plane. These aspects are considered to be signatures of a hairpin-shaped vortex based on the phase-averaging analysis of the unsteady three-dimensional behavior. A hairpin-shaped vortex makes a concerted contribution to fluid mixing between the central wake region and surrounding area. As the fluid flows downstream, fast detachment of the hairpin-shaped vortex is recognized away from the wall to the main stream, which in turn attenuates the flow structure signatures in the spanwise plane. A low-frequency swinging motion of the fluid is also identified in the central wake region, which enhances fluid mixing on the two sides of the wake.

A Parametric Study on the LES Numerical Setup to Investigate Fan/OGV Broadband Noise

In the present paper, large eddy simulations are performed to study two different mechanisms of Fan/OGV broadband noise: airfoil self-noise and turbulence interaction noise. Firstly, the current study focuses on the prediction of airfoil self-noise from a thin plate with a sharp trailing edge and a chord-based Reynolds number of the order of 106. The boundary layer is tripped to trigger transition to turbulence, and a parameter study is performed to study the influence of the near-wall modeling, grid topology and refinement in the near-wall and wake regions, the spanwise domain extent, and the tripping method. Empirical and analytical models, as well as available DNS data are used for validation purposes. Secondly, the interaction noise from a thin plate impinged by an incoming synthetic turbulent flow is studied. For both cases, far-field acoustic spectra are compared to Amiet’s models for leading and trailing edge noise showing a good agreement.

Wakes of thin flat plates: Intermittency, cessation of vortex shedding and the emergence of an intermediate-wake instability

The near and intermediate wake regions of thin flat plates with both sharp and circular trailing edges (TEs) are investigated with direct numerical simulations (DNSs). The TE is circular in two of the cases (IN & NS) and sharp in one of them (ST). The separating boundary layers are turbulent in all cases. The main objective here is to explore the effect of significantly reducing the Reynolds number (ReD, based on circular TE diameter, D) on the flow in the TE region, in particular the vortex shedding process (Cases IN and NS). Intermittent shedding is observed in Case IN. Case NS, with half the TE diameter of Case IN, is an essentially non-shedding case. The second objective is to understand the reasons underlying the findings of an earlier experimental wake investigation (sharp TE) where a broadband peak was observed in centerline cross-stream velocity (v) spectra. Case ST from the present study showed a wake instability resulting in spanwise vortices. The instability is intermittent and contributes to a broadband peak in the centerline v spectrum. Cases IN & NS also exhibit a similar wake instability in the intermediate wake and a corresponding spectral (v) broadband peak. The third objective is to study the distributions of the time-averaged velocity statistics in thin plate wakes. The turbulent stresses and, the budget terms for the streamwise intensity, obtained in Case IN, are included and discussed here. All the budget terms contribute appreciably to the overall budget in the transport equation for streamwise normal intensity.