A general model for trailing edge serrations simulation on wind turbine airfoils

Trailing edge serrations(TESs) are capable of noticeably suppressing the turbulent trailing edge noise induced by rotating wind turbine blades and become an integral part of a blade. However, the challenges involved in the dimensional design of serration height 2 h, wavelength λ and flap angle are Φ yet to be dealt with in a satisfactory manner. To address the problem, a general model for simulating the effects of serrations on the hydrodynamic and aeroacoustic performance is proposed due to its ease of use and relatively low requirements for user input. The solid serrations are replicated by momentum sources calculated by its aerodynamic forces. Then, a case relevant to wind turbine airfoil is examined, a hybrid improved delay detached eddy simulation(IDDES) method coupled with FW-H integration is deployed to obtain the flow features and far-field sound pressure level. It is found that the modeling method could reproduce the flow field and noise as serrated airfoil.     

Experimental investigation of a blunt trailing edge flow field with application to sound generation

The unsteady lift generated by turbulence at the trailing edge of an airfoil is a source of radiated sound. The objective of the present research was to measure the velocity field in the near wake region of an asymmetric beveled trailing edge in order to determine the flow mechanisms responsible for the generation of trailing edge noise. Two component velocity measurements were acquired using particle image velocimetry. The chord Reynolds number was 1.9 × 10⁶. The data show velocity field realizations that were typical of a wake flow containing an asymmetric periodic vortex shedding. A phase average decomposition of the velocity field with respect to this shedding process was utilized to separate the large scale turbulent motions that occurred at the vortex shedding frequency (i.e., those responsible for the production of tonal noise) from the smaller scale turbulent motions, which were interpreted to be responsible for the production of broadband sound. The small scale turbulence was found to be dependent on the phase of the vortex shedding process implying a dependence of the broadband sound generated by the trailing edge on the phase of the vortex shedding process.     

Contribution to the theory of thin-profile trailing edge separation

The conditions of nonsymmetric trailing edge flow with separation are investigated. Solutions of the equations for the interaction zone in the neighborhood of the trailing edge of a thin profile at an angle of attack of the order O(Re^–1/16) in the separated flow regime are constructed numerically. It is shown that for this zone a solution exists up to a certain angle of attack. In all the regimes the value of the friction on the upper surface at the very end of the trailing edge remains a positive quantity. The solution of the equations in the separated flow regimes is found to be nonunique. The flow over the leading edge is assumed to be unseparated, and the separation at the trailing edge, if present, is assumed to be localized in the interior of the boundary layer. The flow over a Kutta profile at zero angle of attack is taken as an example. In this case the satisfaction of the Chaplygin-Joukowsky condition at the trailing edge ensures smooth flow over both the trailing and leading edges.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 55–59, July–August, 1989.     

Supersonic flow around the trailing edge of a thin profile

The method of mergeable asymptotic expansions has recently been used effectively in investigations devoted to the study of boundary layer interaction with an external inviscid flow at high subcritical Reynolds numbers Re. The asymptotic analysis permits obtaining a limit pattern of the flow around a solid as Re þ, and determining the similarity and quantitative regularity laws which are in good agreement with experimental results. Thus by using the method of mergeable asymptotic expansions it is shown in [1–4] that near sites with high local curvature of the body contour and flow separation and attachment points, an interaction domain appears that has a small length on the order of Re^-3/8. In this flow domain, which has a three-layer structure, the pressure distribution in a first approximation already depends on the change in boundary-layer displacement thickness, while the induced pressure gradient, in turn, influences the flow in the boundary layer. An analogous situation occurs in the neighborhood of the trailing edge of a flat plate where an interaction domain also appears [5, 6]. The flow in the neighborhood of the trailing edge of a flat plate around which a supersonic viscous gas flows was examined in [7]. Numerical results in this paper show that the friction stress on the plate surface remains positive everywhere in the interaction domain, and grows on approaching the trailing edge. The supersonic flow around the trailing edge of a flat plate at a small angle of attack was investigated in [8, 9], Supersonic flow of a viscous gas in the neighborhood of the trailing edge of a flat plate at zero angle of attack is examined in [10], but with different velocity values in the inviscid part of the flow on the upper and lower sides of the plate. The more general problem of the flow around the trailing edge of a profile with small relative thickness is investigated in this paper.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 36–42, May–June, 1981.     

Solution of Navier-Stokes equations near the trailing edge of a plate

The appearance of a local singularity in the solutions for the neighborhood of the trailing edge of a plate in a sub- or supersonic flow makes it necessary to consider the flow in the local region which is described in the first approximation by the Navier-Stokes equations for an incompressible gas. In this paper numerical solutions are obtained for such a region for both a thin plate and a plate with thickness. The streamline patterns and the distributions of the flow functions over the surface of the plate and in the wake behind it are presented. For the plate with finite thickness, a numerical solution is obtained in a wide range of variation of the local Reynolds number.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 173–176, July–August, 1985.     

Turbulence modelling of the shear layers in the trailing edge region of a modern rear-loaded airfoil at incidence

After carefull analysis in a turbulent zero-pressure gradient flow, various simple algebraic turbulence models were applied to the almost separated flow on the upperside of an airfoil at incidence. The Johnson-King and Horton non-equilibrium (or rate equation) models give clearly improved results.     

Turbulent flow of a fluid in the neighborhood of the trailing edge of a plate at zero angle of attack

The laminar flow regime of an incompressible fluid at the trailing edge of a plate was studied by Stewartson and Messiter [1, 2] by means of the method of matched asymptotic expansions. In. the present paper, this method is used to analyze the same problem, but in the case of turbulent flow in the boundary layer and the wake. A system of linear equations of elliptic type with variable coefficients is obtained for the averaged values of the flow parameters in the main part of the boundary layer and the wake that is responsible for the change in the displacement thickness. A solution of this system is constructed by the Fourier method in the case of a power law of the velocity in front of the interaction region.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 17–23, November–December, 1983.     

Numerical evaluation of the aerodynamic influence of the helicopter composite blade trailing edge tabs

In classical composite helicopter rotor blade production, a small flat tab must be formed along the entire trailing edge, in order to enable proper merging of the upper and the lower surface plies during manufacturing. By this, the original airfoil shape is altered. Such fixed tabs have been added in a range of possible angular positions to several existing asymmetrical helicopter airfoils, and their capability to change the moment coefficient about the aerodynamic center of the airfoils was initially analyzed. Although usual tabs are proportionally small, angular domains in which they do not remarkably change the required nearly zero aerodynamic moment, were quantified as very narrow. In the next stage, an algorithm has been defined and implemented: (a) for the determination of optimum angular tab positions for several asymmetrical airfoils, that satisfy the moment requirement (for such airfoils optimum tab direction cannot be known in advance), and (b) for the reduction of the influence of eventual inherent numerical errors of applied software to a minimum. The accuracy of this algorithm has been verified on a symmetrical airfoil, for which the optimum tab position is readily known. In the next step, the tab influence on other aerodynamic airfoil characteristics, and the influence on flight performance of a light helicopter from an on-going project, has been analyzed. Several possible tab design concepts were defined, and some characteristic aspects of their implementation were considered. At the level of preliminary helicopter performance calculations, the influence of the two general outcomes of the tab designs were analyzed, one that preserves initial relative airfoil thickness, and another which leads to its reduction. In the first case, the influence of the slight increase of drag coefficient was taken into account, while in the second one, the decrease of drag coefficient, accompanied with necessary additional strengthening and added blade mass was considered. In both cases applied modifications proved to have moderate direct influence on helicopter flight performance, compared with a hypothetic case that the original airfoil without tab could have been used instead. General conclusions have imposed the need for very careful approach in tab design for asymmetrical airfoils, which must be primarily focused on the tab’s potential remarkable influence on the aerodynamic moment.     

Effect of trailing edge shape on hydrodynamic damping for a hydrofoil

Flow induced vibration on a hydrofoil may be significantly reduced with a slight modification of the trailing edge without alteration of the hydrodynamic performance. Particularly, the so called Donaldson trailing edge shape gave remarkable results and is being used in a variety of industrial applications. Nevertheless, the physics behind vibration reduction is still not understood. In the present study, we have investigated the hydrodynamic damping of a 2D hydrofoil with Donaldson trailing edge shape. The results are compared with the same hydrofoil with blunt trailing edge. The tests are carried out in EPFL high speed cavitation tunnel and two piezoelectric patches are used for the hydrofoil excitation in non-intrusive way. It was found that the hydrodynamic damping is significantly increased with the Donaldson cut. Besides, as the flow velocity is increased, the hydrodynamic damping is found to remain almost constant up to the hydrofoil resonance and then increases linearly, for both tested trailing edge shapes and for both first bending and torsion modes.     

Three-dimensional wake dynamics of a blunt and divergent trailing edge airfoil

The wake dynamics of an airfoil with a blunt and divergent trailing edge is investigated experimentally at relatively high Reynolds. The near wake topology is examined versus different levels of free stream turbulence FST and angles of attack, while the downstream wake evolution is characterized at various levels of FST. The FST is found to have a significant effect on the shapes of turbulence profiles and on the downstream location where the flow reaches its quasi-asymptotic behavior. Streamwise vortices (ribs) corresponding to spanwise variations of turbulence quantities are identified in the near wake region. Simultaneous multi-point hot-wire measurements indicate that their spatial arrangement is similar to Williamson’s (Ann Rev Fluid Mech 29:477–539, 1996) mode B laminar wake flow topology. The results suggest that the statistical spanwise distribution of ribs is independent of FST effects and angle of attack as long as the vortex shedding Strouhal number remains approximately similar.     

Stochastic estimation of flow near the trailing edge of a NACA0012 airfoil

A stochastic estimation technique has been applied to simultaneously acquired data of velocity and surface pressure as a tool to identify the sources of wall-pressure fluctuations. The measurements have been done on a NACA0012 airfoil at a Reynolds number of Re _c  = 2 × 10⁵, based on the chord of the airfoil, where a separated laminar boundary layer was present. By performing simultaneous measurements of the surface pressure fluctuations and of the velocity field in the boundary layer and wake of the airfoil, the wall-pressure sources near the trailing edge (TE) have been studied. The mechanisms and flow structures associated with the generation of the surface pressure have been investigated. The “quasi-instantaneous” velocity field resulting from the application of the technique has led to a picture of the evolution in time of the convecting surface pressure generating flow structures and revealed information about the sources of the wall-pressure fluctuations, their nature and variability. These sources are closely related to those of the radiated noise from the TE of an airfoil and to the vibration issues encountered in ship hulls for example. The NACA0012 airfoil had a 30 cm chord and aspect ratio of 1.     

Some three-dimensional effects during vortex generation at a straight edge

For vortices generated by an impulsively started flow about a straight sharp edge bounded by side-walls, one might expect the vortex-flow in the mid-plane to remain unaffected by the walls for a time. Experiments in water using rectangular nozzles with generally moderate width-to-height ratios showed that a flow was initiated from the walls into the vortex core and towards the mid-plane. This flow set in at the same time as the main flow began. The fastest mass transport took place near the junction between the edge and the walls. This water moved within the vortex axis with an initially constant velocity approximately a third of that of the main flow, independent of the width, the height and the edge-angle within a surprisingly large range of these parameters. A further feature of the wall-near flow is the appearance and growth of a region of vortex breakdown in the core near the wall. In the mid-plane a flow was initiated directed radially outwards from the centre of the vortex. This flow was also short lived, beginning both before the axis became significantly distorted, as well as before any noticeable axial velocity gradient near the mid-plane existed. This radial motion seems thus to be the most sensitive measure of the flow in the mid-plane becoming three-dimensional. During this time the forces associated with the axial and radial flow may be significant. Despite the abovementioned relatively fast secondary flow, the trajectory of the vortex-centre in the mid-plane seems unaffected.     

Transient studies of screw and edge dislocation generation at crack edges

Exact transient analyses of the generation of screw and edge dislocations at the edges of stationary cracks subjected to the diffraction of, respectively, plane SH- and SV-waves, and their subsequent arrest are performed. The solutions are examined in light of a dislocation emission criterion which is based, simultaneously, on standard dislocation force concepts and quasi-static emission studies.This examination allows expressions for the times of emission and arrest, the distances traveled by the dislocations, and the dynamic stress intensity factors to be derived in terms of parameters such as dislocation speed and yield stress. These expressions exhibit distinctive dynamic effects and reveal several features of the generation process:In particular, the times and distances are, while on a micromechanical scale, not necessarily insignificant, and imply that purely brittle fracture may not easily occur. Then, edge dislocation emission would appear to occur at a preferred speed, while screw dislocation emission apparently prefers to take place quasi-statically.Examination of a general incident waveform class shows that a continuous wave could cause dislocation generation to occur before a step-stress wave can. Moreover, the emission process depends upon a weighted time history of the incident wave stress, not its instantaneous value. This, in turn, implies that dislocation emission does not necessarily shield the crack edge by lowering the dynamic stress intensity factor. Finally, unless the dislocations are allowed to decelerate to zero speed upon arrest, a repetitious process of start-stop motion can in principle take place.     

Investigation of aerodynamic effects of coolant ejection at the trailing edge of a turbine blade model by PIV and pressure measurements

In order to simulate the thick trailing edges of turbine blades a slotted plate profile together with a newly designed nozzle was installed into the high-speed wind tunnel of the DLR Göttingen. At different supersonic Mach numbers and at four coolant flow rates in the range of 0–2.5% pressure distribution measurements and probe measurements were performed. The flow field was visualized by schlieren photos and the instantaneous velocity field was quantitatively investigated by Particle Image Velocimetry (PIV). The measurements of the velocity field gave an insight into stationary effects, for example the change of shock strength with coolant flow rate, and instationary effects such as the existence of a vortex street in the wake. The PIV technique offers special advantages for the investigation of transonic flow fields, but also yields to special experimental difficulties, which are also described in this article. Measured losses display a maximum at the downstream Mach number 1. This is strongly related to the behaviour of the base pressure. A loss minimum is achieved at moderate coolant flow rates, showing that an optimum coolant flow rate exists. The loss was analysed and separated into the loss contributions from the profile upstream of the trailing edge and the mixing loss due to the coolant flow.     

Effects of a vectored trailing edge jet on delta wing vortex breakdown

Flow visualization was used to study the effects of a vectored trailing edge jet on the leading edge vortex breakdown of a 65° delta wing. The experimental results indicated that there is little effect of the jet on the leading edge vortex breakdown when the angle of the vectored jet is less than 10°. With the increase of the vectored angle ß, the effect of the jet on the flow becomes stronger, i.e., the jet delays the leading edge vortex breakdown in the direction of the vectored jet, and accelerates breakdown of the other leading edge vortex. Moreover, the effect of the jet control tends to be weaker with the angle of attack.