Unsteady Kutta condition at high values of the reduced frequency parameter

The aerodynamic performance of blunt trailing edge airfoils generated from the DU- 91-W2-250, DU-97-W-300 and DU-96-W-350 airfoils by enlarging the thickness of trailing edge symmetrically from the location of maximum thickness to chord to the trailing edge were analyzed by using CFD and RFOIL methods at a chord Reynolds number of 3 × 106. The goal of this study is to analyze the aerodynamic performance of blunt trailing edge airfoils with different thicknesses of trailing edge and maximum thicknesses to chord. The steady results calculated by the fully turbulent k-ω SST, transitional k-ω SST model and RFOIL all show that with the increase of thickness of trailing edge, the linear region of lift is extended and the maximum lift also increases, the increase rate and amount of lift become limited gradually at low angles of attack, while the drag increases dramatically. For thicker airfoils with larger maximum thickness to chord length, the increment of lift is larger than that of relatively thinner airfoils when the thickness of blunt trailing edge is increased from 5% to 10% chord length. But too large lift can cause abrupt stall which is profitless for power output. The transient characteristics of blunt trailing edge airfoils are caused by blunt body vortices at low angles of attack, and by the combined effect of separation and blunt body vortices at large angles of attack. With the increase of thickness of blunt trailing edge, the vibration amplitudes of lift and drag curves increase. The transient calculations over-predict the lift at large angles of attack and drag at all angles of attack than the steady calculations which is likely to be caused by the artificial restriction of the flow in two dimensions.

Unsteady flow models of wings and airfoils have been studied to understand the aerodynamic performance of natural flyers and provide improved maneuverability for micro aerial vehicles (MAVs). Vortex methods have been extensively applied to reduce the dimensionality of these aerodynamic models, based on the proper estimation of the distribution and evolution of the vortices in the wake. In such modeling approaches, one of the most fundamental questions is how the vortex sheets are generated and released from the leading and trailing edges. To study the formation of the trailing-edge vortex sheet, the classical Kutta condition is extended to unsteady situations following the physical sense that flow cannot turn around a sharp edge. This condition can be readily applied to a flat plate or an airfoil with cusped trailing edge since the direction of the forming vortex sheet is known to be tangential to the trailing edge. However, for a non-cusped trailing edge, the direction of the forming vortex sheet is ambiguous. In this study, to remove any ad-hoc condition, a novel analytical formulation is provided to determine the angle of the trailingedge vortex sheet. The derivation of this equation only requires momentum conservation in the direction normal to the forming vortex sheet. The aerodynamic model together with the proposed unsteady Kutta condition is verified by comparing flow structures and force calculations with experimental results for airfoils in steady and unsteady background flows.

The diffraction of externally generated sound in a uniformly moving flow at the trailing edge of a semi-infinite flat plate is studied. In particular, the coupling of the sound field to the hydrodynamic field by way of vortex shedding from the edge is considered in detail, both in inviscid and in viscous flow.In the inviscid model the (two-dimensional) diffracted fields of a cylindrical pulse wave, a plane harmonic wave and a plane pulse wave are calculated. The viscous proess of vortex shedding is represented by an appropriate trailing-edge condition. Two specific cases are compared, in one of which the full Kutta condition is applied, and in the other no vortex shedding is permitted. The results show good agreement with Heavens’ (1978) observations from his schlieren photographs, and confirm his conclusions. It is further demonstrated, by an explicit expression, that the sound power absorbed by the wake may be positive or negative, depending on Mach number and source position. So the process of vortex shedding does not necessarily imply an attenuation of the sound.In the viscous model a high-Reynolds-number approximation is constructed, based on a triple-deck boundary-layer structure, matching the harmonic plane wave outer solution to a known incompressible inner solution near the edge, to obtain the viscous correction to the Kutta condition.

The trailing edge of high pressure gas turbine blade in aeroengine is usually designed as thin as possible to achieve higher aerodynamic efficiency. However, as the inlet temperature of modern gas turbine is continuously increasing, thermal stress in a thin trailing edge will become much significant, resulting in possibilities of erosion and creep problems. To find a balance between these two conflicting goals, one method is the use of pressure-side cutback, which extends into the coolant slot to get film cooling and also achieves a thin trailing edge. Due to the interactions between mainstream and coolant flow, film cooling effect on trailing edge cutback is significantly affected by the vortex shedding downstream the cooling slot. To resolve the coherent flow structures and understand their role on film cooling effect on trailing-edge cutback, this paper implemented a Very Large Eddy Simulation (VLES) model into the solver ANSYS Fluent with user defined functions. By introducing a resolution control factor, the turbulence viscosity predicted by transient SST k-ω model was corrected and the VLES computations were realized in the whole computational region. With the VLES method, film cooling effectiveness distributions on trailing-edge cutback at three blowing ratios were computed and compared against the experimental data. The coherent unsteadiness in cutback region was visualized to reveal the mixing process between mainstream and coolant flow. The numerical accuracies between different unsteady prediction methods, i.e. URANS (Unsteady Reynolds Averaged Navier-Stokes), SAS (Scale-Adaptive Simulation), DES (Detached Eddy Simulation), DDES (Delayed-Detached Eddy Simulation), SBES (Stress-Blended Eddy Simulation), and VLES were compared with respect to the resolutions of cooling effect and vortex shedding. The results show that the periodic vortex shedding induced by the interactions between mainstream and coolant is the main factor that affecting the cooling performance on cutback. VLES method has a comparable accuracy in predicting the film cooling effect on trailing edge cutback with DDES and SBES approaching. In the detached shear layer, VLES method exhibits a good ability to resolve coherent unsteadiness caused by vortex shedding. Compared with URANS and SAS methods, the VLES method has a higher accuracy in resolving the periodic vortex shedding and film cooling effectiveness distributions, especially in low blowing ratio cases.

Results from an experimental study of the aerodynamic and aeroacoustic properties of a atback version of the TU Delft DU97-W-300 airfoil are presented for a chord Reynolds number of 3 10 6 . The data were gathered in the Virginia Tech Stability Wind Tunnel, which uses a special aeroacoustic test section to enable measurements of airfoil self-noise. Corrected wind tunnel aerodynamic measurements for the DU97-W-300 are compared to previous solid wall wind tunnel data and are shown to give good agreement. Aeroacoustic data are presented for the atback airfoil, with a focus on the amplitude and frequency of noise associated with the vortex-shedding tone from the blunt trailing edge wake. The effect of a splitter plate attachment on both drag and noise is also presented. Computational Fluid Dynamics predictions of the aerodynamic properties of both the unmodied DU97-W-300 and the atback version are compared to the experimental data. Technical risks associated with the use of atback airfoils for the inboard region of wind turbine blades include increased aerodynamic noise and increased aerodynamic drag. Both of these penalties are the result of the blunt trailing edge shape and the wake that is produced by this shape. The relatively low pressure at the blunt base results in a much larger drag force than for a conventional airfoil shape. The effect of this drag penalty on rotor thrust and torque coefcient for typical inboard twist angles is not severe, and in fact can be offset by the additional lift that a atback airfoil generates. 3 Consideration of drag reducing devices such as splitter plates or trailing edge serrations may be desireable to further boost performance, however. The increased noise from the atback is due primarily to the vortex shedding phenomenon associated with bluff- body wakes. The vortex shedding often leads to tonal noise, similar to the Aeolian tones of o w past circular cylinders. The intensity of bluff-body vortex shedding tones at low Mach number scales with the sixth power of the relative o w velocity. Broadband aeroacoustic noise sources associated with turbulent boundary layer-trailing edge interaction scale with the fth power of the relative o w velocity. Since outboard o w velocities are much higher than those encoun- tered inboard, the overall aerodynamic noise levels of a rotor incorporating inboard atback shapes will likely continue to be dominated by outboard trailing edge noise. However, two aspects of the atback noise source may be cause for concern. First, the vortex-shedding noise from atbacks is likely to be contained in a relatively low-frequency band (50-200 Hz). Some community noise regulations have separate low-frequency noise standards apart from considera- tion of A-weighted sound, which emphasize higher frequencies to which the human ear is more sensitive. Second, the

Aerodynamic properties of an airfoil can be modified by trapping concentrations of vorticity close to the trailing edge. Experimental work has shown that synthetic jet actuators can be used to manipulate and control this trapped vorticity. A time-resolved detailed model is used to simulate the action of tangential-blowing synthetic jet actuators mounted near the trailing edge of the airfoil at low angle of attack. This detailed model resolves the temporal and spatial scales involved in the synthetic jet dynamics. The detailed synthetic jet model along with the Computational Fluid Dynamics (CFD) computations in which they are embedded are validated against wind tunnel data acquired by Dr Ari Glezer’s group at Georgia Tech. Numerical results show the effects of the actuators on the vortical structure of the flow, as well as on the aerodynamic properties. The main effect of the actuation on the time averaged vorticity field is a bending of the separation shear layer from the actuator toward the airfoil surface, resulting in changes in the aerodynamic properties. Similar to the experimental observations, full actuation of the suction side actuator reduces the pitching moment and increases the lift force, while the pressure side actuator increases the pitching moment and reduces the lift force. The effectiveness of the actuator is measured by the change in the aerodynamic properties of the airfoil in particular the lift (�Cl) and moment (�Cm) coefficients. Computational results for the actuator effectiveness show very good agreement with the experimental values over the range of 2 ◦ to 10 ◦ . While the actuation modifies the global pressure distribution, the most pronounced effects are near the trailing edge in which a spike in the pressure coefficient ( Cp), consistent with experimental results, is observed.

D EFINED as the “nonpropulsive noise of an aircraft in flight” in [1], noise produced by airframe components becomes significant during the approach-to-land phase of aircraft operations. Research efforts on identifying and understanding the noise sources associated with the individual airframe components, in particular, high-lift systems, have been undertaken by many researchers [2]. It has been confirmed experimentally in [3–5], and analytically by using empirical methods [6], that both leading-edge slats and trailing-edge flap side edges are the most important noise contributors from the high-lift systems to overall noise levels of an aircraft in approach. The high-lift noise, intuitively thinking, is configuration dependent. Any increase in the deflection angle of slat and flap will lead to an increase in overall noise level. The larger the deflection angles are, the higher the noise level will be. This is due to the fact that the highlift components are more loaded when their deflection angles are increased, generatingwhat is referred to as the loading noise. Further, higher deflection angles may induce stronger vortex shedding and turbulent wake downstream which causes higher noise. Such intuitions were supported by experiments conducted at NASA Langley Research Center in 1998 and 2002 [7], which revealed that slat noise is generated due to its configuration setting angles. Khorrami et al. [8] hypothesized with 2-D unsteady computation that the vortex shedding at the slat trailing edge was responsible for the additional highfrequency spike observed only at higher slat angles. An acoustic whistling mechanism at the slat gap due to vortex shedding was later proposed by Tam and Pastouchenko [9] and Agarwal [10]. The theory supported that the simple vortex shedding and feedback mechanism resonating with gap tone frequency caused noise amplification and propagation. Similar observations were made for flap noise, as reported in [11,12]. Both references reported that the measured noise level at higher flap deflection angles exceeded the predicted noise level, which suggests that there might be an additional source contributor, most likely vortex instabilities, as a result of its interaction with the nearby flap upper surface. It may be noted that such phenomenon was not seen at lower settings of flap angles. These observations may infer that high-lift device noise level is directly affected by the configuration setting angles of slats and flaps. In general, high-lift device noise sources are present at wide frequency ranges of low-to-mid andmid-to-high. At a fixed observer location, under a constant flow speed, slat noise is dominant in the low-to-midfrequency range, and flap side-edge noise is dominant at the mid-to-high-frequency range as shown by both Guo and Joshi [13] and Guo et al. [14]. In this study, the proposed technique uses reduced deployment angles of both high-lift devices simultaneously to achieve the most effective noise reduction in different frequency domains. Aerodynamics performance also has to be carefully monitored to ensure no significant loss is present. The objective of the current Note is to examine the effectiveness of a microtab device in airframe noise reduction. Reducing deployment setting angles of both slats and flaps, the associated noise can be alleviated. Loss in aerodynamic lift, as a result of the reduced highlift settings, is compensated by use of a microtab device. The microtab device can be viewed as a small spanwise strip located at the pressure side of flap near the trailing edge, similar to a Gurney flap (Fig. 1). While deployed normal to local airfoil surface, the microtab device alters the local flowfield which leads to increased effective camber, and hence improves lift-to-drag ratio, similar to that of a Gurney flap introduced by Liebeck [15]. In the present work, a threedimensional numerical analysis is presented and compared to sound pressure level (SPL) of the proposed microtab configuration at a specified far-field location to that of the baseline, that is, conventional configuration in approach, to see if any reduction in noise can be achieved.

: This report describes the design and numerical analysis of a turbine cascade suitable to research the vortex shedding and shock waves coupling. This follows the very successful research model that was used to drive a 60% increase in lift beyond the state-of-the-art for Low Pressure Turbines (LPTs). The selected turbine flow passage enhanced the vortex shedding intensity by using a relatively large trailing edge diameter. This geometry is both government-owned and generic. So, the geometry and all experimental data produced in the study will be distributable throughout the research community, and this can further increase knowledge about the flow field and additional means to control. A potential solution that is being explored is the use of pulsed cooling ejection to control both the vortex shedding and trailing edge shock patterns. The present research may guide aerodynamic designers to novel concepts to modulate shock waves. The current research is high relevance for the design of compact and light future fluid machinery. While the results of such an investigation have bearing on transonic turbines and compressors in particular, the physics that dominate the flow are fundamental and could have applicability to any flow that is dominated by both shocks and vertical disturbances.

Three elongated bluff bodies with a chord-to-thickness ratio of seven have been studied experimentally at a Reynolds number based on body thickness of 3 × 104. The defining feature of elongated bluff bodies is the interaction between trailing edge Kármán vortex shedding and leading edge separation-reattachment. We have used particle image velocimetry with different body geometries to investigate this interaction for three distinct cases: (i) small leading edge separation-reattachment length; (ii) large leading edge separation-reattachment length; and (iii) one case in between these bounds. The leading edge separation-reattachment is a significant source of spanwise enstrophy. Thus, changes in the wake enstrophy distribution are of particular interest. We have examined the time-averaged distribution and production of both the turbulent kinetic energy and the spanwise enstrophy in the near wake region utilizing proper orthogonal decomposition on the vorticity field to distinguish between turbulence and the periodic contribution of the trailing edge vortex shedding. A significant increase in the lateral distribution of spanwise enstrophy is observed – exceeding the typical bounds of the near wake – which is due to the leading edge separation-reattachment and the resulting scale of the flow at the trailing edge. As a result, strengthening the leading edge flow, which tends to weaken the trailing edge vortex shedding, may lead to enhanced mixing in the wake.

The silent flight achieved by owls is attributed to their unique wing morphologies, characterized by leading-edge (LE) serrations, trailing-edge (TE) fringes, and a velvet-like surface. The specific morphological effects of LE serrations and TE fringes on aeroacoustic performance have been widely studied, but the LE–TE aeroacoustic interaction remains poorly understood. This paper describes a simulation-based study of the aeroacoustic characteristics of owl-inspired TE fringes and their interplay with LE serrations by combining large-eddy simulations of unsteady near-field flow structures with the Ffowcs Williams–Hawkings equation for sound radiation. Using owl-inspired LE serrated and TE fringed wing models, it is verified that TE fringes enable a pronounced high-frequency sound reduction at angles of attack (AoAs) of 5–15° while achieving comparable aerodynamic performance to a clean model. The near-field vortex dynamics, pressure distributions, and velocity spectra reveal that TE fringes suppress flow separation and vortex shedding in the vicinity of the TE, consequently reducing local velocity fluctuations and far-field overall sound pressure levels. Furthermore, the combination of TE fringes and LE serrations enables a remarkable reduction in overall sound pressure levels at all AoAs, and their aeroacoustic interplay is responsible for stabilizing velocity fluctuations over the suction surface, which suppress both low- and high-frequency sound. Our results demonstrate that TE fringes are a robust sound reduction device in resolving the trade-off between aerodynamic force production and sound reduction, while LE serrations and TE fringes complement one another as an effective noise-reducing biomimetic design.

The silent flight achieved by owls is attributed to their unique wing morphologies, characterized by leading-edge (LE) serrations, trailing-edge (TE) fringes, and a velvet-like surface. The specific morphological effects of LE serrations and TE fringes on aeroacoustic performance have been widely studied, but the LE–TE aeroacoustic interaction remains poorly understood. This paper describes a simulation-based study of the aeroacoustic characteristics of owl-inspired TE fringes and their interplay with LE serrations by combining large-eddy simulations of unsteady near-field flow structures with the Ffowcs Williams–Hawkings equation for sound radiation. Using owl-inspired LE serrated and TE fringed wing models, it is verified that TE fringes enable a pronounced high-frequency sound reduction at angles of attack (AoAs) of 5–15° while achieving comparable aerodynamic performance to a clean model. The near-field vortex dynamics, pressure distributions, and velocity spectra reveal that TE fringes suppress flow separation and vortex shedding in the vicinity of the TE, consequently reducing local velocity fluctuations and far-field overall sound pressure levels. Furthermore, the combination of TE fringes and LE serrations enables a remarkable reduction in overall sound pressure levels at all AoAs, and their aeroacoustic interplay is responsible for stabilizing velocity fluctuations over the suction surface, which suppress both low- and high-frequency sound. Our results demonstrate that TE fringes are a robust sound reduction device in resolving the trade-off between aerodynamic force production and sound reduction, while LE serrations and TE fringes complement one another as an effective noise-reducing biomimetic design.

The flowfield and sound generated by turbulent flow passing over the trailing edge of an airfoil was studied experimentally. The airfoil geometries considered were thin, flat models that provided canonical, zero-pressure-gradient, turbulent boundary layers upstream of the trailing edge. The Reynolds number based on the chord was . A trailing edge with a symmetric, tapered, sharp edge was studied first. This allowed the use of a simple scattering theory to predict the radiated sound based on boundary-layer surface pressure. Second, a series of blunt, asymmetric, trailing-edge models were studied. The lower surface of the edge was flat, while the upper surface was rounded with a 45 deg trailing-edge angle. Three models were considered, which provided a variation in the ratio of model thickness to thickness of the approach boundary layer. Particle image velocimetry measurements were obtained to provide insight into the local flowfield dynamics that generated the sound. Acoustic measurements from the blunt edges indicated that the high-frequency sound primarily resulted from scattering from the lower surface. At lower frequency, the radiated sound was found to have significantly higher amplitude compared to the sharp-edged case. This was caused by the large-scale motions in the wake resulting from the separated flow at the trailing edge. In the case of where the boundary layers were thin compared to the trailing edge, discrete vortex shedding and tonal sound were observed. When the boundary layers were thicker, the elevated sound levels were broadband.

The paper presents a linear analytical model to predict the frequency characteristics of the discrete oscillations of the jet-edge feedback cycle. The jet is idealized as having top-hat profile with vortex-sheet shear layers, and the nozzle from which it issues is represented by a parallel plate duct. At a stand-off distance h, a flat plate is inserted along the centreline of the jet, and a sinuous instability wave with real frequency w is assumed to be created in the vicinity of the nozzle and to propagate towards the splitter plate. Its interaction with the splitter plate produces an irrotational feedback field which, near the nozzle exit, is a periodic transverse flow producing singularities at the nozzle lips. Vortex shedding is assumed to occur, alleviating the singularities and allowing a trailing-edge Kutta condition to be satisfied; this Kutta condition is claimed to be the phase-locking criterion. The shed vorticity develops into a sinuous spatial instability, and the cycle of events is repeated periodically. Problems corresponding to the various physical processes described are analysed, for in viscid flow with vortex-sheet shear layers and aligned flat-plate boundaries, and solved in an appropriate asymptotic sense by Wiener-Hopf methods. Calculation of the phase changes occurring in the constituents of the cycle gives an equation for the frequency w in the Nth ‘stage’ as a function of jet width 2b, jet velocity U0, standoff distance h, and stage label N: \[ \omega b/U_0 = (b/h)^{\frac{3}{2}}[4\pi(N-{\textstyle\frac{3}{8}})]^{\frac{3}{2}}. \] The variations with b, U0, h and N are in excellent agreement with edge-tone experiments; the principal disagreement lies in the overall numerical factor $(4\pi)^{\frac{3}{2}}$ and explanations are given for this. Possible effects associated with the inclusion of displacement thickness fluctuations in the splitter-plate boundary layers, and the enforcement of a leading-edge Kutta condition, are also considered and shown not to affect the frequencies of the operating stages.

Trailing edge bluntness noise reduction using porous treatments

The application of the Kutta condition to unsteady flows has been controversial over the years, with increased research activities over the 1970s and 1980s. This dissatisfaction with the Kutta condition has been recently rejuvenated with the increased interest in low-Reynolds-number, high-frequency bio-inspired flight. However, there is no convincing alternative to the Kutta condition, even though it is not mathematically derived. Realizing that the lift generation and vorticity production are essentially viscous processes, we provide a viscous extension of the classical theory of unsteady aerodynamics by relaxing the Kutta condition. We introduce a trailing-edge singularity term in the pressure distribution and determine its strength by using the triple-deck viscous boundary layer theory. Based on the extended theory, we develop (for the first time) a theoretical viscous (Reynolds-number-dependent) extension of the Theodorsen lift frequency response function. It is found that viscosity induces more phase lag to the Theodorsen function particularly at high frequencies and low Reynolds numbers. The obtained theoretical results are validated against numerical laminar simulations of Navier–Stokes equations over a sinusoidally pitching NACA 0012 at low Reynolds numbers and using Reynolds-averaged Navier–Stokes equations at relatively high Reynolds numbers. The physics behind the observed viscosity-induced lag is discussed in relation to wake viscous damping, circulation development and the Kutta condition. Also, the viscous contribution to the lift is shown to significantly decrease the virtual mass, particularly at high frequencies and Reynolds numbers.