Sharp Trailing Edge Research Articles

Hydrodynamic analysis of an underwater glider wing using ANSYS fluent as an investigation tool

The analysis of the hydrodynamic behavior of the modified trailing edge of an underwater glider wing was conducted using ANSYS Fluent 18.1. The procedure was carried out using the computational fluid dynamics (CFD) approach. A standard four digits NACA0016 aerofoil profile was selected while the geometry points were extracted from NACA online aerofoil generator using Solidworks, which enabled the creation of the 3D wing profile. Since the focus of the study is more toward hydrodynamic behavior or the influence of the modified round trailing edge as opposed to the normal sharp trailing edge, coefficient of lift (CL), coefficient of drag (Cd), coefficient of pressure (Cp) and the drag polar (Cd/CL) are very crucial parameters and have an influence on the accuracy of the results. The results showed lift and drag coefficient are a function of the angle of attack (AOA) and free stream velocities. The investigation showed the optimal design point of the AOA of 12° at the corresponding speed of 0.26 m/s. The critical AOA matched with the optimal design point of 12°. The results also showed that Cp is higher closer to the fuselage and therefore explains why more structural rigidity must be provided in this region of high stress concentration. The drag and lift curve corresponded to the typical wing characteristics of the published experiment data regardless of the operating conditions.

Circulation dynamics of small-amplitude pitching airfoil undergoing laminar-to-turbulent transition

This study is motivated by the non-linear behavior of the lift response of a pitching airfoil with a small amplitude and frequency where a linear behavior is expected. The validated γ−Reθ transition model coupled with k−ωSST (shear stress transport) turbulence model was utilized to solve the unsteady Reynolds-averaged Navier–Stokes (URANS) equations for a harmonically pitching NACA 0012 at Reynolds numbers 75×103, 200×103 and reduced frequencies 0.05−0.3. First, the numerical setup was validated against experimental results for a pitching airfoil undergoing laminar-to-turbulent transition. Then, the circulation dynamics were investigated following an exact derivation of the Kutta condition. Unlike the classical Kutta condition which assumes a vanishing pressure loading at the sharp trailing-edge, it is shown that the transition induces non-linearity in the lift dynamics by creating a significant pressure variation across the boundary layer in the vicinity of the trailing-edge, affecting the development of the bound circulation around the airfoil. Moreover, the effects of reduced frequency, pitching amplitude and Reynolds number on the circulation dynamics were studied in both frequency and time domains. The results shed light on the further enhancement of potential flow-based solutions to capture non-linearity in the lift dynamics due to transition.

Skimming impacts and rebounds of smoothly shaped bodies on shallow liquid layers

Investigated in this paper is the coupled fluid–body motion of a thin solid body undergoing a skimming impact on a shallow-water layer. The underbody shape (the region that makes contact with the liquid layer) is described by a smooth polynomic curve for which the magnitude of underbody thickness is represented by the scale parameter C. The body undergoes an oblique impact (where the horizontal speed of the body is much greater than its vertical speed) onto a liquid layer with the underbody’s trailing edge making the initial contact. This downstream contact point of the wetted region is modelled as fixed (relative to the body) throughout the skimming motion with the liquid layer assumed to detach smoothly from this sharp trailing edge. There are two geometrical scenarios of interest: the concave case (C<0 producing a hooked underbody) and the convex case (C > 0 producing a rounded underbody). As C is varied the rebound dynamics of the motion are predicted. Analyses of small-time water entry and of water exit are presented and are shown to be broadly in agreement with the computational results of the shallow-water model. Reduced analysis and physical insights are also presented in each case alongside numerical investigations and comparisons as C is varied, indicating qualitative analytical/numerical agreement. Increased body thickness substantially changes the interaction structure and accentuates inertial forces in the fluid flow.

Noise source location and scaling of subsonic upper-surface blowing

This paper deals with the topic of upper surface blowing noise. Using a model-scale rectangular nozzle of an aspect ratio of 10 and a sharp trailing edge, detailed noise contours were acquired with and without a subsonic jet blowing over a flat surface to determine the noise source location as a function of frequency. Additionally, velocity scaling of the upper surface blowing noise was carried out. It was found that the upper surface blowing increases the noise significantly. This is a result of both the trailing edge noise and turbulence downstream of the trailing edge, referred to as wake noise in the paper. It was found that low-frequency noise with a peak Strouhal number of 0.02 originates from the trailing edge whereas the high-frequency noise with the peak in the vicinity of Strouhal number of 0.2 originates near the nozzle exit. Low frequency (low Strouhal number) follows a velocity scaling corresponding to a dipole source where as the high Strouhal numbers as quadrupole sources. The culmination of these two effects is a cardioid-shaped directivity pattern. On the shielded side, the most dominant noise sources were at the trailing edge and in the near wake. The trailing edge mounting geometry also created anomalous acoustic diffraction indicating that not only is the geometry of the edge itself important, but also all geometry near the trailing edge.

Watch Your Adjoints! Lack of Mesh Convergence in Inviscid Adjoint Solutions

It has been long known that 2D and 3D inviscid adjoint solutions are generically singular at sharp trailing edges. In this paper, a concurrent effect is described by which wall boundary values of 2D and 3D inviscid continuous and discrete adjoint solutions based on lift and drag are strongly mesh dependent and do not converge as the mesh is refined. Various numerical tests are performed to characterize the problem. Lift-based adjoint solutions are found to be affected for any flow condition, whereas drag-based adjoint solutions are affected for transonic lifting flows. A (laminar) viscous case is examined as well, but no comparable behavior is found, which suggests that the issue is exclusive to inviscid flows. It is argued that this behavior is caused by the trailing edge adjoint singularity.

Understanding the secondary separation from an inclined square cylinder with sharp and rounded trailing edges

The steady separated flow past a square cylinder at 45° incidence and having a sharp/rounded base is a unique kind of separated flow around a symmetric bluff obstacle. At low Reynolds numbers (Re ≈ 6–8), this flow displays diverse features that are not known to be displayed by common symmetric bluff bodies, such as circular/square cylinders at zero incidence. The uniqueness of this flow was first highlighted by Kumar et al. [“Steady separation of flow from an inclined square cylinder with sharp and rounded base,” Comput. Fluids 171, 29–40 (2018)] in their recent numerical investigation concerning the onset of initial separation. They reported detailed flow kinematics resulting from separation of the laminar boundary layer via secondary mode, primary mode, and their combination. In this work, based on stabilized finite-element computations, the fluid dynamic aspects of primary and secondary separation are delved. The parameters considered are the normalized corner radius at the cylinder base and Re. Exploration of the influence of base radius on the occurrence/absence of the secondary separation is the main objective. The occurrence of secondary separation is a function of base radius. It occurs only with small or no rounding at the base, i.e., when the pressure gradient close to the base is favorable or mildly adverse. Irrespective of the base radius, the onset of secondary separation occurs at a constant Re value of 7.3. The drag decays as Re−0.62; it becomes invariant when Re is held constant. A new nondimensional parameter η accommodating the effects of pressure recovery and radius of curvature is introduced. The drag exhibits no sensitivity to η.

The influence of reduced Reynolds number on the wake of the DrivAer estate vehicle

Experiments on vehicle aerodynamics were conducted in a low-speed water channel at a Reynolds number two orders of magnitude lower than that of typical full-scale studies. Particle Image Velocimetry (PIV) measurements, focused on the wake of a realistic estate passenger vehicle model, were obtained and compared with existing wake measurements from full-scale wind-tunnel tests. The combination of sharp and rounded trailing edges present on the geometry impacts properties of the separating shear layers, although the general wake structures are qualitatively similar. In both cases, the wake remains dominated by the upwash from the underbody exit diffuser outflow. Effects of the reduced Reynolds number on the spectral content of the wake velocity field downstream of the recirculation region are also documented.

An Investigation of Damages in Low Power Wind Turbine Blades

Data in the literature about the various types of damages in wind turbines which may result during manufacturing or operation is not enough. In the current work, a number of 18 blades of 300 kW and 81 blades of 100 kW power wind turbines are inspected using visual test (VT) and if needed using liquid penetrant test (PT) when needed. The location and size of discontinuities found are measured and documented. Types of discontinuities are categorized into four main ‎groups: 1) Transverse cracks and longitudinal cracks, 2) Hair line surface cracks, coating pores, surface damages, holes or ‎penetrations, 3) Edge cuts or crushing ‎and side separation, and 4) reworked areas.‎ The gathered data are analyzed to allocate the different forms of discontinuities about the blade length, to establish an indication of the rotor blades working conditions. It is found that the transverse carks are concentrated at the highly loaded and geometric change region of trailing edge. Longitudinal cracks up to 59 cm long are detected also at the region of the geometric change; i.e. in the root and the cover of the aerodynamic zone. Edge damages such as edge cuts or crushing and partial side separation are found in the sharp trailing edge. Surface and coating damages are observed on the leading edge due to erosion.

Mean velocity behaviour in the near wake of long slender cylinder with a sharp trailing edge at a high Reynolds number

ABSTRACTA simple eddy viscosity model is applied to the governing equations to establish the behaviour of the mean velocity in the turbulent axisymmetric near wake. The near wake develops from a long slender cylinder which is kept parallel to the flow and is developing under zero streamwise pressure gradient. The upstream turbulent boundary layer on the body of revolution is fully developed. In the inner layer of the flow downstream of the trailing edge, the turbulent inner layer of the upstream boundary layer grows into the initial logarithmic layer, and as a consequence, the centreline velocity in the near wake is shown to increase logarithmically with streamwise distances for large streamwise distances. The analysis further leads to two regions of the near wake flow (the inner near wake and the outer near wake), similar to that of a fully developed turbulent boundary layer, for which the governing equations have been derived. The matching between these two regions leads to a logarithmic variation in the normal direction. Also shown is the variation of the square of the wake width which varies logarithmically with streamwise distance in the near wake. These features are validated by comparison with available experimental data.

Singular and Discontinuous Solutions of the Adjoint Euler Equations

This study analyzes the behavior of solutions to the quasi-one-dimensional and two-dimensional adjoint Euler equations at singularities, including shocks, sonic points/lines, and sharp trailing edges. In the quasi-one-dimensional case the analysis reveals a wide variety of behaviors beyond the continuous-at-shocks/singular-at-sonic-points standard lore, whereas in the two-dimensional case the adjoint shock structure is carefully examined. Several issues regarding the numerical computation of adjoint solutions are also discussed.

Panel Method for Ducted Propellers with Sharp Trailing Edge Duct with Fully Aligned Wake on Blade and Duct

A low-order panel method is used to predict the performance of ducted propellers. A full wake alignment (FWA) scheme, originally developed to determine the location of the force-free trailing wake of open propellers, is improved and extended to determine the location of the force-free trailing wakes of both the propeller blades and the duct, including the interaction with each other. The present method is applied on a ducted propeller with sharp trailing edge duct, and the predicted results over a wide range of advance ratios, with or without full alignment of the duct wake, are compared with each other, as well as with results from RANS simulations and with measurements from an experiment.

Developed liquid film passing a trailing edge under the action of gravity and capillarity

We consider the asymptotic structure of a steady developed viscous thin film passing the sharp trailing edge of a horizontally aligned flat plate under the weak action of gravity acting vertically and surface tension. The surprisingly rich details of the flow in the immediate vicinity of the trailing edge are elucidated both analytically and numerically. As a central innovation, we demonstrate how streamline curvature serves to regularise the edge singularity apparent on larger scales via generic viscous–inviscid interaction. This is shown to be provoked by weak disturbances of accordingly strong exponential downstream growth, which we trace from the virtual origin of the flow towards the trailing edge. They represent a prototype of the precursor to free interaction in the most general sense, which, interestingly, has not attracted due attention previously. Moreover, we delineate how an increased effect of gravity involves marginally choked flow at the edge.

Vortex shedding characteristics of the wake of a thin flat plate with a circular trailing edge

The near and very near wake of a thin flat plate with a circular trailing edge are investigated with direct numerical simulations (DNS). Data obtained for two different Reynolds numbers (based on plate thickness, D) are the main focus of this study. The separating boundary layers are turbulent in both cases. An earlier investigation of one of the cases (Case F) showed shed vortices in the wake that were about 1.0D to 4.0D in spanwise length. Considerable variation in both the strength and frequency of these shed vortices was observed. One objective of the present investigation is to determine the important contributors to this variability in strength and frequency of shed vortices and their finite spanwise extent. Analysis of the data shows that streamwise vortices in the separating boundary layer play an important role in strengthening/weakening of the shed vortices and that high/low-speed streaks in the boundary layer are important contributors to variability in shedding frequency. Both these features of the boundary layer contribute to the finite extent of the vortices in the spanwise direction. The second plate DNS (Case G, with 40% of the plate thickness of Case F) shows that while shedding intensity is weaker than obtained in Case F, many of the wake features are similar to that of Case F. This is important in understanding the path to the wake of the thin plate with a sharp trailing edge where shedding is absent. Here we also test the efficacy of a functional relationship between the shedding frequency and the Reynolds numbers based on the boundary layer momentum thickness (Reθ) and D (ReD); data for developing this behavioral model is from Cases F & G and five earlier DNSs of the flat plate wake.

Blunt-Wavy Combined Trailing Edge for Wind Turbine Blade Inboard Performance Improvement

Aerodynamic performance of wind turbine blade inboard is improved by modifying its trailing edge shape. A combined trailing edge modification design with blunt trailing edge and a span-wise wavy trailing edge is used. Designing blunt trailing edge at the blade inboard makes the flow become more attached than the conventional sharp trailing edge. The span-wise wavy trailing edge breaks up the Karman vortex shedding generated by the blunt trailing edge. The Sandia National Laboratory 100 meter blade, SNL100-03 was used as a baseline model. Rotating blade simulations are performed with the full-scale isolated rotor condition. Aerodynamic performance analysis and aeroacoustic performance analysis of the modified turbine blades are performed. By using the blunt-wavy combined trailing edge modification, the massive flow separation at the inboard of the baseline blade is prevented successfully. Delayed Detached Eddy Simulation (DDES) with a modified laminar-turbulent transition model (Medida - Baeder model) is used for better prediction of flow separation.

Computational and Experimental Investigation of Camber-Morphing Airfoils for Reverse Flow Drag Reduction on High-Speed Rotorcraft

Through computational fluid dynamics simulations and wind tunnel tests, this study examines a NACA 63-218 airfoil in reverse flow at Rec=375,000 and demonstrates reduction in reverse flow drag through the introduction of reflex camber. Of the three contributors to drag—ram pressure on the upper surface near the trailing edge, suction on the lower surface near the trailing edge, and bluff body separation at the rounded nose—reflex camber (where the camber line near the trailing edge of the airfoil is deflected upward) influences the first two, reducing exposure to ram drag on the upper surface while rotating the suction on the lower surface away from the direction of drag. Particle image velocimetry and surface pressure measurements were utilized in experiment to directly compare with the results obtained through simulation. As expected, the flow was dominated by separation over the sharp trailing edge, where at moderate angles of attack (α &lt;190°), a separation bubble was observed; the use of reflex camber reduced the extent of this separation. The simulations (unsteady Reynolds-averaged Navier–Stokes with and without the Spalart–Allmaras turbulence model) captured the reduction in separation at the trailing-edge well, as there was good agreement between the velocity fields when compared to experiments. This yielded maximum drag reductions near 60% for a 10° reflex camber, compared to reductions near 50% in experiments. Even greater percentage reductions in drag (up to 70%) were observed with a larger 15° reflex angle (not tested experimentally) for nose-up pitch angles greater than 5°in reverse flow. With simulations at a higher Reynolds number (1.5 million) showing very similar drag reductions, using reflex camber over inboard blade sections appears to have significant promise for alleviating reverse flow drag on edgewise rotors at high advance ratio.

Shed vortex structure and phase-averaged velocity statistics in symmetric/asymmetric turbulent flat plate wakes

The near wake of a flat plate is investigated via direct numerical simulations. Many earlier experimental investigations have used thin plates with sharp trailing edges and turbulent boundary layers to create the wake. This results in large θ/DTE values (θ is the boundary layer momentum thickness toward the end of the plate and DTE is the trailing edge thickness). In the present study, the emphasis is on relatively thick plates with circular trailing edges (CTEs) resulting in θ/D values less than one (D is the plate thickness and the diameter of the CTE) and vigorous vortex shedding. The Reynolds numbers based on the plate length and D are 1.255 × 106 and 10 000, respectively. Two cases are computed: one with turbulent boundary layers on both the upper and lower surfaces of the plate (statistically the same, symmetric wake, Case TT) and the other with turbulent and laminar boundary layers on the upper and lower surfaces, respectively (asymmetric case, Case TL). The data and understanding obtained are of considerable engineering interest, particularly in turbomachinery where the pressure side of an airfoil can remain laminar or transitional because of a favorable pressure gradient and the suction side is turbulent. Shed-vortex structure and phase-averaged velocity statistics obtained in the two cases are compared here. The upper negative shed vortices in Case TL (turbulent separating boundary layer) are weaker than the lower positive ones (laminar separating boundary layer) at inception (a factor of 1.27 weaker in terms of peak phase-averaged spanwise vorticity at the first appearance of a peak). The upper vortices weaken rapidly as they travel downstream. A second feature of interest in Case TL is a considerable increase in the peak phase-averaged, streamwise normal intensity (random component) with increasing streamwise distance (x/D) that occurs near the positive vortex cores. This behavior is observed for a few diameters in the near wake. This is counter to Case TT where the peak value essentially decreases with increasing x/D. Both these effects are examined in detail, and the important contributors are identified.

Comparative Study of Aerodynamic and Aeroacoustic Behavior of Flat Plate Airfoils With Different Trailing Edge Geometry

The present study compares the aerodynamic and aeroacoustic behavior of the flow past two flat plate airfoils; viz. blunted trailing edge and sharp trailing edge, having a fixed aspect ratio of 1.867. The study is performed experimentally showing variance in lift and drag at two different velocity of 20m/s and 30m/s and at different angles of attack, viz. 5°, 12°, 20°, 25°, 30°. All the models are prepared by mild steel and the studies are conducted using 300×300×1000 mm subsonic wind tunnel. Results show that the drag coefficient in sharp trailing edge reduces significantly by a maximum amount of 22%. The lift coefficient, however, does not change significantly. Uncertainty analysis performed shows that maximum percentage of uncertainty in each case is less than 5%. Aero acoustic measurement of the noise radiated by the trailing edge of the two flat plates is performed in a reflecting environment at a velocity of 20m/s and at two different angles of attack of 10° and 15° with ¼’’ inch far field microphone mounted near the trailing edge of the airfoil in the test section. The spectra obtained indicate that the noise from the sharp trailing edge is consistently lower than the blunt trailing edge. Thus, this paper adequately demonstrates the role of trailing edge in modifying the aerodynamic as well as aero acoustic characteristic.

Aerofoil broadband and tonal noise modelling using stochastic sound sources and incorporated large scale fluctuations

The present work discusses modifications to the stochastic Fast Random Particle Mesh (FRPM) method featuring both tonal and broadband noise sources. The technique relies on the combination of incorporated vortex-shedding resolved flow available from Unsteady Reynolds-Averaged Navier-Stokes (URANS) simulation with the fine-scale turbulence FRPM solution generated via the stochastic velocity fluctuations in the context of vortex sound theory. In contrast to the existing literature, our method encompasses a unified treatment for broadband and tonal acoustic noise sources at the source level, thus, accounting for linear source interference as well as possible non-linear source interaction effects. When sound sources are determined, for the sound propagation, Acoustic Perturbation Equations (APE-4) are solved in the time-domain. Results of the method's application for two aerofoil benchmark cases, with both sharp and blunt trailing edges are presented. In each case, the importance of individual linear and non-linear noise sources was investigated. Several new key features related to the unsteady implementation of the method were tested and brought into the equation. Encouraging results have been obtained for benchmark test cases using the new technique which is believed to be potentially applicable to other airframe noise problems where both tonal and broadband parts are important.

Reduced frequency effects on combined oscillations, angle of attack and free stream oscillations, for a wind turbine blade element

The dynamic stall phenomenon in horizontal axis wind turbines causes significant energy waste and sometimes wind turbine failure. For modeling a deep dynamic stall phenomenon of a horizontal axis wind turbine blade element, a numerical simulation of an oscillating NREL's S809 airfoil has been performed at Reynolds number of 106 in an unsteady incident velocity; the velocity oscillates with the same frequency as the airfoil oscillation but with different phase difference (ϕ). Since the sliding mesh technique has been applied for the airfoil oscillation, an O-type grid is created resulting in the reduced number of mesh layers. A specific correction improves the quality of the O-type mesh near the sharp trailing edge. For the combined oscillations, the effects of the reduced frequency (k) in the range of 0.05≤k≤0.15 are investigated with the phase differences of ϕ=−π2, +π2,π. The results show their significant dependency on k at specific ϕ values in particular at ϕ=−π2. Combined effects of k and ϕ can change the aerodynamic loads during dynamic stall significantly compared to loads from a case with a steady incident velocity. These significant changes in the flow structure and aerodynamic loads can affect the wind turbine performance during the dynamic stall phenomenon.

A study of computational methods for wake structure and base pressure prediction of a generic SUV model with fixed and rotating wheels

This study is an evaluation of the computational methods in reproducing experimental data for a generic sports utility vehicle (SUV) geometry and an assessment on the influence of fixed and rotating wheels for this geometry. Initially, comparisons are made in the wake structure and base pressures between several CFD codes and experimental data. It was shown that steady-state RANS methods are unsuitable for this geometry due to a large scale unsteadiness in the wake caused by separation at the sharp trailing edge and rear wheel wake interactions. unsteady RANS (URANS) offered no improvements in wake prediction despite a significant increase in computational cost. The detached-eddy simulation (DES) and Lattice–Boltzmann methods showed the best agreement with the experimental results in both the wake structure and base pressure, with LBM running in approximately a fifth of the time for DES. The study then continues by analysing the influence of rotating wheels and a moving ground plane over a fixed wheel and ground plane arrangement. The introduction of wheel rotation and a moving ground was shown to increase the base pressure and reduce the drag acting on the vehicle when compared to the fixed case. However, when compared to the experimental standoff case, variations in drag and lift coefficients were minimal but misleading, as significant variations to the surface pressures were present.