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Showing papers on "Airfoil published in 2001"


Journal ArticleDOI
TL;DR: In this article, the effect of the actuation frequency, actuator location, and momentum coefficient on flow separation on a symmetric airfoil with synthetic jet actuators is investigated.
Abstract: Control of flow separation on an unconventional symmetric airfoil using synthetic (zero net mass flux) jet actuators is investigated in a series of wind tunnel tests. The symmetric airfoil comprises the aft portion of a NACA four-digit series airfoil and a leading edge section that is one-half of a round cylinder. The experiments are conducted over a range of Reynolds numbers between 3.1 × 10 5 and 7.25 × 10 5 . In this range, the flow separates near the leading edge at angles of attack exceeding 5 deg. When synthetic jet control is applied near the leading edge, upstream of the separation point, the separated flow reattaches completely for angles of attack up to 17.5 deg and partially for higher angles of attack. The effect of the actuation frequency, actuator location, and momentum coefficient is investigated for different angles of attack. The momentum coefficient required to reattach the separated flow decreases as the actuators are placed closer to the separation point. In some cases, reattachment is also achieved when the actuators are placed downstream of the stagnation point on the pressure side of the airfoil

563 citations


Journal ArticleDOI
TL;DR: In this article, a review of the physical mechanisms of the periodic shock motion on airfoils at transonic flow conditions are associated with the phenomenon of buffeting, and various modes of shock wave motion for different flow conditions and airfoil configurations are described.

333 citations


Journal ArticleDOI
TL;DR: In this paper, the effect of variation of the amplitude of the pitching motion on the force coefe cient was investigated and it was shown that the critical parameter for thrust generation is not the reduced frequency but the Strouhal number based on the maximum excursion of the trailing edge.
Abstract: Ae niteelemente owsolverbasedonunstructuredgridsisemployedforstudyingtheunsteadye owpastoscillating airfoils. The viscous e ow past a NACA0012 airfoil at various pitching frequencies is simulated. The variation of the force coefe cient with reduced frequency is compared to experimental and other numerical studies. The effect of variation of the amplitude of the pitching motion on the force coefe cient shows that the critical parameter for thrust generation is not the reduced frequency but the Strouhal number based on the maximum excursion of the trailing edge. The e ow about theairfoil in a combined pitching and heaving motion, a modefound in many insects, is also simulated. The effects of varying the phase angle between the pitch and the heave motions is studied. The thrust coefe cient was compared with experimental studies and good agreement is obtained. It is found that the maximumthrustcoefe cient isobtained forwhen thepitchmotionleads theheavemotion by 120 deg andmaximum propulsive efe ciency occurs at a phase angle of 90 deg.

206 citations


Journal ArticleDOI
TL;DR: In this article, a code-friendly version of the Durbin model is proposed to enhance numerical stability, which alleviates the stiffness problem associated with the original model caused by the boundary conditions at walls.

191 citations


01 Aug 2001
TL;DR: It is found that transition modelling is to a large extent responsible for the poor quality of the computational results for most of the considered airfoils.
Abstract: The aim of this work is two-sided. Firstly, experimental results obtained for numerous sets of airfoil measurements (mainly intended for wind turbine applications) are collected and compared with computational results from the 2D Navier-Stokes solver EllipSys2D, as well as results from the panel method code XFOIL. Secondly, we are interested in validating the code EllipSys2D and finding out for which air-foils it does not perform well compared to the experiments, as well as why, when it does so. The airfoils are classified according to the agreement between the numerical results and experimental data. A study correlating the available data and this classification is performed. It is found that transition modelling is to a large extent responsible for the poor quality of the computational results for most of the considered airfoils. The transition model mechanism that leads to these discrepancies is identified. Some advices are given for elaborating future airfoil design processes that would involve the numerical code EllipSys2D in particular, and transition modelling in general. (au)

165 citations


Patent
29 Aug 2001
TL;DR: In this paper, a wind harnessing system using a plurality of self supporting airfoil kites for production of useful power is described, where the kites are attached to a pivotal control housing by control lines 58 L and 58 R and support lines 60 L and 60 R and the entire process repeats starting with power stroke 140 a.
Abstract: A wind harnessing system using a plurality of self supporting airfoil kites 50 for production of useful power. The system comprising multiple airfoil kites 50 in tandem attached to a pivotal control housing 32 by control lines 58 L and 58 R and support lines 60 L and 60 R. Control lines 58 L and 58 R can change length with respect to the length of support lines 60 L and 60 R to control the airfoil kites' 50 angle-of-attack, pitch angle, direction of flight, and flight speed. The length of control lines 58 L and 58 R are controlled from ground station 30 by a movable pulley system in control housing 32 to adjust the airfoils' direction to follow a specific flight path 140. Control lines 58 R and 58 L and support lines 60 R and 60 L are also wound on a power shaft and pulley system in control housing 32. As the airfoil kites are propelled by the wind at very-high speed, the airfoils generate a powerful AXIAL force. The control lines 58 L and 58 R and support lines 60 L and 60 R are then reeled-out under this AXIAL tension causing the power shaft and pulley system in control housing 32 to turn a generator to generate electricity. After airfoil kites 50 have finished their reel-out power stroke 140 a, the airfoil's pitch angle is made negative so they can be reeled-in by their control and support lines using a minimum of force along path 140 b. Once the airfoils have been rewound to the proper distance, the airfoils are again angled for high-speed operation to generate powerful AXIAL force and reeled-out along 140 c to provide another power stroke. The airfoil kites are then reeled-in again along path 140 d and the entire process repeats starting with power stroke 140 a. Since the force to rewind the airfoils is much less than the force generated during reel-out, there is net power generated.

138 citations


Journal ArticleDOI
TL;DR: In this article, the authors derived an approximation for the Green's function with respect to the leading and trailing edges of an airfoil for high frequencies, where the acoustic wavelength is assumed to be large relative to the airfoin thickness, but no restriction on its magnitude relative to.
Abstract: Approximations are derived for the three-dimensional, time-harmonic acoustic Green's function whose normal derivative vanishes on the surface of an airfoil of finite thickness and chord for source locations in the neighbourhood of either the leading or trailing edge. The acoustic wavelength is assumed to be large relative to the airfoil thickness, but no restriction is placed on its magnitude relative to . A multiple scattering calculation is performed for high frequencies that involves an expansion in terms of the successive scattering of waves from the leading and trailing edges of the airfoil. The 'principal subseries' of the expansion is summed and shown to provide an excellent approximation for the Green's function when κ 0 ≥ 1, where κ 0 is the acoustic wavenumber. The solution is extended down to κ 0 = 0 by interpolation with the corresponding Green's function for an airfoil of acoustically compact chord. The results extend the single scattering approximation introduced by R. K. Amiet (AIAAJ. 12 1970), and are illustrated by application to the problem of trailing-edge noise generated by nominally steady, low Mach number flow past the airfoil. Experiments and numerical simulations of such flows often include acoustic frequencies that are sufficiently small that the usual assumption of trailing-edge noise theory, that the airfoil is semi-infinite, is not valid.

121 citations


Journal ArticleDOI
TL;DR: In this article, the authors investigated the performance of an optimized nonuniform rational B-spline (NURBS) geometrical representation for the aerodynamic design of wings.
Abstract: The geometric representation and parameterization used in an aerodynamic wing design process determines the number of design variables and influences the smoothness of the wing representation. In an attempt to reduce the number of design variables while preserving good smoothness properties, the present research investigates the performance of an optimized nonuniform rational B-spline (NURBS) geometrical representation for the aerodynamic design of wings. As a first step, an approach is described whereby optimal spatial positions and weights of a fixed number of NURBS control points is determined using a quasi-Newton optimization algorithm to approximate a general airfoil section. The resulting optimized NURBS representation significantly reduces the number of design variables needed to define accurately a wing section while ensuring good smoothness properties. In a second step, the NURBS control point positions and weights are used as design variables in an aerodynamic optimization problem. This methodology results in a rapid and robust design process, as illustrated by examples of aerodynamic optimization for two- and three-dimensional cases

117 citations


Journal ArticleDOI
TL;DR: In this article, a proof-of-concept microtab design and the multi-disciplinary techniques used to fabricate and test the tabs are compared, and the results demonstrate the significant potential for using microtabs for active load control.
Abstract: Micro-electro-mechanical (MEM) translational tabs are introduced for active load control on aerodynamic surfaces such as wind turbine rotor blades. Microtabs are mounted near the trailing edge of rotor blades, deploy approximately normal to the surface, and have a maximum deployment height on the order of the boundary-layer thickness. Deployment of the tab effectively changes the sectional chamber of the rotor blade, thereby changing its aerodynamic characteristics. A tab with tab height to blade section chord ratio, h/c, of 0.01 causes an increase in the section lift coefficient, C 1 , of approximately 0.3, with minimal drag penalty. This paper presents a proof of concept microtab design and the multi-disciplinary techniques used to fabricate and test the tabs. Computational and experimental wind tunnel results for a representative airfoil using fixed as well as remotely actuated tabs are compared. Although the specifics of load control limitations, including actuation and response times will require further research, the results presented demonstrate the significant potential for using microtabs for active load control.

111 citations


Journal ArticleDOI
TL;DR: In this paper, a sensitivity analysis code based either on a direct method or on an adjoint method is proposed to evaluate the sensitivity derivatives of an aerodynamic objective function and its derivatives can be evaluated robustly and efficiently.
Abstract: In the application of gradient-based methods to practical aerodynamic design problems, one of the major concerns is an accurate and efficient calculation of sensitivity derivatives of an aerodynamic objective function. Sensitivity derivatives can be evaluated robustly and efficiently by using a sensitivity analysis code based either on a direct method or on an adjoint method. An adjoint method is preferable in aerodynamic designs because it is more economical when the number of design variables is larger than the total number of an objective function and constraints.

103 citations


Journal ArticleDOI
TL;DR: In this article, a detailed investigation of two-dimensional airfoil stalling characteristics has been conducted, revealing low-frequency and highly unsteady e owin some cases and large-scalethree-dimensional structures in other cases.
Abstract: Recent investigations of two-dimensional airfoil stalling characteristics have revealed low-frequency and highly unsteady e owin somecases and large-scalethree-dimensionalstructuresin other cases.Thelatterwerereferred to as “ stall cells” and can form on two-dimensional cone gurations where the ends of the airfoil model are e ush with tunnelsidewallsorend plates.Thispaperpresentsresultsofdetailedinvestigationsofthestalling characteristicsof several airfoils that exhibited both low-frequency unsteadiness and large-scale three-dimensional structures. The airfoils were wind-tunnel tested in a two-dimensional cone guration. The primary measurements were spanwise wakevelocityand mini-tufte owvisualization. Theresultsshowedthatairfoilswithtrailing-edgeseparationsatand above maximum lift (static stall )exhibited stall-cell patterns. Conversely, airfoils that had leading-edge separation bubblesthatgrewinsizeastheangleofattackwasincreasedintostalldevelopedthelow-frequency,highlyunsteady e ow. This unsteadiness was found to be essentially two dimensional. Therefore, the development of either of these phenomenaappearstobedeterminedbythecharacteristicsoftheboundary-layerseparationleadinguptothestall.

Proceedings ArticleDOI
08 Jan 2001
TL;DR: This work presents the development of compact, high-power synthetic jet actuators for realistic flow separation control applications and demonstrates the developed SJA technology in representative, flow separation Control problems, including control of steady separation/stall.
Abstract: Although strong potential of synthetic jets as flow separation control actuators has been demonstrated in the existing literature, there is a large gap between the synthetic jet actuators (SJA) used in laboratory demonstrations and the SJAs needed in realistic fullscale applications, in terms of compactness, weight, efficiency, control authority and power density. In most cases, the SJAs used in demonstrations are either too large or too weak for realistic applications. In this work, we present the development of compact, high-power synthetic jet actuators for realistic flow separation control applications and demonstrate the developed SJA technology in representative, flow separation control problems, including control of steady separation/stall. The developed actuators are compact enough to fit in the interior of a 14.75" chord, NACA0015 wing, have maximum power of 2.0 HP and can produce (for the tested conditions) exit velocities as high as 80 m/sec. Flow separation control was demonstrated over a 14.75" chord, NACA 0015 wing at angles of attack and free stream velocities as high as 25 degrees and 45 m/s, respectively and pressure data was acquired over the wing for a range of conditions. INTRODUCTION The separation of the boundary layer is associated with large energy losses, and in most applications adversely affects the aerodynamic loads in the form of lift loss and drag increase. Therefore, there is a strong incentive to delay or manipulate the occurrence of flow separation. For example, if the separation of the boundary layer formed over a bluff body is delayed, the pressure drag is greatly reduced; also separation delay will permit the operation of an airfoil/wing at higher angles of attack. Me Cormick (2000) showed that delay or elimination of separation * Research Assistant, Aerospace Engineering Department, Student Member AIAA. § Associate Professor, Aerospace Engineering Department, Member AIAA Copyright © 2000 by J. L. Gilarranz and O. K. Rediniotis. Published by the American Institute of Aeronautics and Astronautics, Inc. with permission. can increase the pressure recovery in a diffiiser. Hence, separation control is of great importance to most of the systems involving fluid flow, such as air, land or underwater vehicles, turbomachines, diffusers, etc. Many researchers have developed and tested methods of separation control in a variety of applications. Gad-el-Hak and Bushnell (1991) provide a comprehensive review on the research in the area of separation control previous to the year 1991. Typically the separation control techniques may be grouped in two categories: passive and active techniques. Most of the techniques, developed for passive separation control, may be found in the review by Gad-el-Hak and Bushnell (1991). Some of the parameters affecting the selection of a separation control technique include, but are not limited to: weight of system, power consumption (active type), power density, parasitic drag of device, size, reliability, cost and efficiency. Active separation control methods have included the application of: • steady boundary layer suction to remove the low momentum fluid. • wall heat transfer to control and modify the viscosity of the fluid. • moving walls in order to use the no-slip condition at the surface to energize the fluid close to the wall. • momentum addition to the boundary layer by steady blowing. • oscillatory blowing and suction. In the recent years the development of the socalled "synthetic jet" or "zero mass flux" devices and their potential for flow control has received a great amount of attention from the fluid dynamics community. This type of systems mostly involves small-scale, low-energy, typically high-frequency actuators, whose operation is based on the concentrated input of energy at high receptivity regions of the flowfield. They take advantage of the physical flow evolution processes to amplify the applied disturbance, which stands apart from the traditional brut force 1 American Institute of Aeronautics and Astronautics c)2001 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization.


Patent
09 Oct 2001
TL;DR: In this article, a turbine airfoil section having an internal cavity and a plurality of indentations on the inner surface of the internal cavity is described, where the indentations provide enhanced heat transfer.
Abstract: A turbine airfoil section having an internal cavity and a plurality of indentations on the inner surface of the internal cavity is described. The indentations provide enhanced heat transfer for cooling the internal cavity of an airfoil thereby improving the life of the airfoil and optimizing the efficiency of the engine by minimizing the amount of compressor bleed air required. Advantageously, this cooling scheme also does not restrict the cooling flow within the internal cavity. The indentations may have varying patterns and alternative geometric configurations.

Journal ArticleDOI
TL;DR: In this paper, the aeroelastic response to time-dependent external excitation of a two-dimensional rigid/elastic-lifting surface in incompressible flow field featuring plunging-pitching coupled motion is addressed.

Journal ArticleDOI
TL;DR: In this paper, the authors analyzed dynamic stall control on a NACA 0015 airfoil, where leading-edge excitation had effectively eliminated the dynamic stall vortex and signie cantly attenuated trailing-edge separation.
Abstract: Dynamic e ow separation and its control over a stationary dee ected surface are used to demonstrate the timescale disparity between the process of dynamic stall, which is dominated by the dynamic stall vortex (DSV), and the excitation-induced large coherent structures that effect its control. Appreciation of this disparity provided a framework for analyzing dynamic stall control on a NACA 0015 airfoil, where leading-edge excitation had effectively eliminated the DSV and signie cantly attenuated trailing-edge separation. Within this framework, a comparisonofstaticandairfoilphase-lockeddynamicpressuredataacquiredin thevicinity ofmaximum incidence (® o 25 deg) revealed that chordwise pressure distributions were independent of the airfoil pitching frequency and that the generation and advection of LCSs were not signie cantly affected by the dynamic airfoil pitching motion.Furthermore,disparitiesbetweenstaticanddynamicdatadiminishedastheexcitationfrequencyincreased relative to the airfoil pitching frequency. Oscillations of the aerodynamic coefe cients induced by the excitations were negligibly small but served to regulateairfoil cycle-to-cycle disparities typical of the baselinepoststall regime.

Patent
08 Feb 2001
TL;DR: In this paper, the annulus profile of the hot gas path is defined in conjunction with the airfoil profile and the profile of inner and outer walls by the Cartesian coordinate values given in Tables I and II, respectively.
Abstract: A first-stage nozzle vane includes an airfoil having a profile according to Table I. The annulus profile of the hot gas path is defined in conjunction with the airfoil profile and the profile of the inner and outer walls by the Cartesian coordinate values given in Tables I and II, respectively. The airfoil is a three-dimensional bowed design, both in the airfoil body and in the trailing edge. The airfoil is steam and air-cooled by flowing cooling mediums through cavities extending in the vane between inner and outer walls.

Journal ArticleDOI
TL;DR: In this paper, the authors describe power requirements for micro air vehicles, flying in the Reynolds number regime of similar to 10(5), and three flight modes have been researched: fixed wing, rotary wing and flapping wing.
Abstract: This paper describes power requirements for micro air vehicles, flying in the Reynolds number regime of similar to 10(5). Three flight modes have been researched: fixed wing, rotary wing and flapping wing. For each mode, the literature in the public domain has been reviewed to obtain appropriate lift and drag coefficient data at these low Reynolds numbers. Energy and power requirements for the three flight modes have been calculated and an optimisation procedure has been utilised to evaluate the most efficient flight mode and configuration for a variety of specified missions. The effect of wind-speed on the optimal solution has been examined. It has been discovered that when there is no hover requirement, fixed wing flight is always most energy efficient for the micro air vehicle. However, if there is a hover requirement, the suitability of flapping or rotary wing flight is dependent on the mission profile and ambient windspeed.

Journal ArticleDOI
TL;DR: In this article, the authors considered the requirements of conceptual wing design with particular emphasis on the representation of airfoil sections and proposed a combination of optimization algorithms and computational fluid dynamics for the development of improved aerodynamic designs.
Abstract: The combination of optimization algorithms and computational fluid dynamics offers promise for the development of improved aerodynamic designs. Optimization strategies have a common reuirement for representation of geometry by a number of design parameters. For wing design the parameterization is generally separable into a representation of the planform and the representation of airfoil sections at a number of spanwise positions. The representation of airfoil sections is considered here with particular emphasis on the requirements of conceptual wing design.

Journal ArticleDOI
TL;DR: The PSU 94-097 airfoil as discussed by the authors was designed for use on winglets of high-performance sailplanes and was tested in the Penn State Low-Speed, Low-Turbulence Wind Tunnel from Reynolds numbers of 2.4 × 10 5 to 1.0 × 10 6.
Abstract: The PSU 94-097 airfoil has been designed for use on winglets of high-performance sailplanes. The design problem is difficult because the airfoil must operate over a wide range of Reynolds numbers, and this range includes values that are relatively low. To validate the design tools, as well as the design itself, the airfoil was tested in the Penn State Low-Speed, Low-Turbulence Wind Tunnel from Reynolds numbers of 2.4 × 10 5 to 1.0 × 10 6 . In addition to transition-free measurements, potential drag reductions using artificial turbulators were explored, although the benefits were found to be limited for this application. Finally, performance predictions from two well-known computer codes are compared to the data obtained experimentally, and both are found to generate results that are in good agreement with the wind-tunnel measurements. Nomenclature CP pressure coefficient, (pl - p∞ )/q∞ L. lower surface R Reynolds number based on free-stream conditions and airfoil chord S. boundary-layer separation location, xS/c T. boundary-layer transition location, xT/c U. upper surface c airfoil chord cd profile-drag coefficient cl section lift coefficient cm section pitching-moment coefficient about the quarter-chord point p static pressure, Pa (lbf/ft 2

Journal ArticleDOI
TL;DR: In this article, a design philosophy for low Reynolds number airfoils that judiciously combines the tailoring of the airfoil pressure distribution using a transition ramp with the use of boundary-layer trips is presented.
Abstract: A design philosophy for low Reynolds number airfoils that judiciously combines the tailoring of the airfoil pressure distribution using a transition ramp with the use of boundary-layer trips is presented Three airfoils with systematic changes to the shape of the transition ramp have been designed to study the effect of trips on the airfoil performance The airfoils were wind-tunnel tested with various trip locations and at Reynolds numbers of 100,000 and 300,000 to assess the effectiveness of the design philosophy The results show that the design philosophy was successfullyusedin integratinga boundary-layertrip from theoutsetin theairfoildesignprocessFortheReynolds numbers and the range of airfoil shapes considered, however, airfoils designed with trips do not hold any clear advantage over airfoils designed for good performance in the clean condition

Journal ArticleDOI
TL;DR: In this article, a re-bladed LP turbine with ultra high lift aerofoils is described, achieving a further reduction of approximately 11% in aerofoil count and significant reduction in turbine weight.
Abstract: The original LP turbine of the BR715 engine featured “High Lift” blading, which achieved a 20% reduction in aerofoil numbers compared to blading with conventional levels of lift - reported in Cobley et al. (1997). This paper describes the design and test of a re-bladed LP turbine with new “Ultra High Lift” aerofoils, achieving a further reduction of approximately 11% in aerofoil count and significant reductions in turbine weight. The design is based on the successful cascade experiments of Howell et al. (2000) and Brunner et al. (2000). Unsteady wake - boundary layer interaction on these low Reynolds number aerofoils is of particular importance in their successful application. Test results show the LP turbine performance to be in line with expectation. Measured aerofoil pressure distributions are presented and compared with the design intent. Changes in the turbine characteristics relative to the original design are interpreted by making reference to the detailed differences in the two aerofoil design styles.Copyright © 2001 by ASME

Patent
13 Jul 2001
TL;DR: The second-stage nozzles have vanes comprising airfoil profiles substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I with the X,Y and Z values commencing at the radially innermost aerodynamic section of the air-foil and then made relative to that section for the Z coordinate values.
Abstract: The second-stage nozzles have vanes comprising airfoil profiles substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in inches in Table I with the X, Y and Z values commencing at the radially innermost aerodynamic section of the airfoil and then made relative to that section for the Z coordinate values. The X, Y and Z values may be scaled as a function of the same constant or number to provide a scaled-up or scaled-down airfoil section for the nozzle.

Patent
22 Oct 2001
TL;DR: In this paper, the authors presented a repair method for a gas turbine airfoil with specified nominal dimensions, which is based on removing at least a portion of at least one section of the airframe to create at least 1 deficit of material relative to the specified nominal dimension, and then inserting a second material, having a creep life that is at least substantially equal to the creep life of the first material, and a fatigue life equal to fatigue life.
Abstract: Methods for repairing and manufacturing a gas turbine airfoil, and the airfoil repaired and manufactured with such methods are presented with, for example, the repair method comprising providing an airfoil having specified nominal dimensions, the airfoil comprising a first material, the first material having a creep life and a fatigue life, the airfoil further comprising a leading edge section and a trailing edge section; removing at least one portion of at least one section of the airfoil to create at least one deficit of material for the airfoil relative to the specified nominal dimensions, the at least one section selected from the group consisting of the leading edge section and the trailing edge section; providing at least one insert comprising a second material, the second material having a creep life that is at least substantially equal to the creep life of the first material, and a fatigue life that is at least substantially equal to the fatigue life of the first material; and disposing the at least one insert onto the airfoil such that the at least one deficit of material is substantially eliminated.

Patent
28 Jun 2001
TL;DR: The second-stage buckets have airfoil profiles substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I wherein Z is a perpendicular distance from a plane normal to a radius of the turbine centerline.
Abstract: The second-stage buckets have airfoil profiles substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in inches in Table I wherein Z is a perpendicular distance from a plane normal to a radius of the turbine centerline and containing the X and Y values with the Z value commencing at zero in the X, Y plane at the radially innermost aerodynamic section of the airfoil and X and Y are coordinate values defining the airfoil profile at each distance Z. The X and Y values may be scaled as a function of the same constant or number to provide a scaled-up or scaled-down airfoil section for the bucket. The second-stage wheel has sixty buckets.

01 May 2001
TL;DR: In this paper, the problem of broadband noise generated by turbulence impinging on a downstream blade row is examined from a theoretical viewpoint, and the results for sound power spectra in terms of 3D wavenumber spectra of the turbulence are derived.
Abstract: The problem of broadband noise generated by turbulence impinging on a downstream blade row is examined from a theoretical viewpoint. Equations are derived for sound power spectra in terms of 3 dimensional wavenumber spectra of the turbulence. Particular attention is given to issues of turbulence inhomogeneity associated with the near field of the rotor and variations through boundary layers. Lean and sweep of the rotor or stator cascade are also handled rigorously with a full derivation of the relevant geometry and definitions of lean and sweep angles. Use of the general theory is illustrated by 2 simple theoretical spectra for homogeneous turbulence. Limited comparisons are made with data from model fans designed by Pratt & Whitney, Allison, and Boeing. Parametric studies for stator noise are presented showing trends with Mach number, vane count, turbulence scale and intensity, lean, and sweep. Two conventions are presented to define lean and sweep. In the "cascade system" lean is a rotation out of its plane and sweep is a rotation of the airfoil in its plane. In the "duct system" lean is the leading edge angle viewing the fan from the front (along the fan axis) and sweep is the angle viewing the fan from the side (,perpendicular to the axis). It is shown that the governing parameter is sweep in the plane of the airfoil (which reduces the chordwise component of Mach number). Lean (out of the plane of the airfoil) has little effect. Rotor noise predictions are compared with duct turbulence/rotor interaction noise data from Boeing and variations, including blade tip sweep and turbulence axial and transverse scales are explored.

Journal ArticleDOI
TL;DR: Results for several grid convergence studies show that this higher-order approach produces a substantial reduction in numerical error in the computation of single- and multielement aerodynamic models, both subsonic and transonic.
Abstract: A higher-order spatial discretization is presented for the solution of the thin-layer Navier ‐Stokes equations with application to two-dimensional turbulent aerodynamic e ows. The terms raised to a level of accuracy consistent with third-order global accuracy include the inviscid and viscous e uxes, the metrics of the generalized curvilinear coordinate transformation, the diffusive e uxes in the turbulence model, the numerical boundary schemes, and the numerical integration technique used to calculate forces and moments. Given the presence of grid and e ow singularities, third-order convergence behavior is not expected. The motivation is to reduce the numerical error on a given grid or to reduce the grid density required to achieve specie ed error levels. Results for several grid convergence studies show that this higher-order approach produces a substantial reduction in numerical error in the computation of single- and multielement aerodynamic e ows, both subsonic and transonic. Comparisons with a well-established second-order algorithm demonstrate that signie cant savings in computing expense, typically factors of three to four, can be achieved using the higher-order discretization.

Journal ArticleDOI
TL;DR: In this paper, a NACA 0012 airfoil is simulated using both particle and continuum approaches, in three different conditions: supersonic, transonic, and low subsonic.
Abstract: Raree ed gas e ows around a NACA 0012 airfoil are simulated using both particle and continuum approaches Three different conditions are considered: supersonic, transonic, and low subsonic In all three cases, the continuum approach solves the Navier ‐Stokes equations with a slip boundary condition on the airfoil surface For the supersonic and transonic cases, the particle method employed is the direct simulation Monte Carlo method Because of problems with this method at the low subsonic condition, caused by excessive statistical e uctuations, a new particle method called the information preservation technique is applied The computed density and velocity e owe elds are compared with experimental data and found to be in generally good agreement Some interesting features in the surface pressure distributions along the airfoil are found for these low-Reynolds-number e ows

Journal ArticleDOI
TL;DR: In this article, an incremental iterative approach for differentiating advanced flow codes is successfully demonstrated on a two-dimensional inviscid model problem using ADIFOR 3.0 and is proven to yield accurate first-order aerodynamic sensitivity derivatives.
Abstract: An efficient incremental iterative approach for differentiating advanced flow codes is successfully demonstrated on a two-dimensional inviscid model problem. The method employs the reverse-mode capability of the automatic differentiation software tool ADIFOR 3.0 and is proven to yield accurate first-order aerodynamic sensitivity derivatives. A substantial reduction in CPU time and computer memory is demonstrated in comparison with results from a straightforward, black-box reverse-mode applicaiton of ADIFOR 3.0 to the same flow code. An ADIFOR-assisted procedure for accurate second-rder aerodynamic sensitivity derivatives is successfully verified on an inviscid transonic lifting airfoil example problem. The method requires that first-order derivatives are calculated first using both the forward (direct) and reverse (adjoinct) procedures; then, a very efficient noniterative calculation of all second-order derivatives can be accomplished. Accurate second derivatives (i.e., the complete Hesian matrices) of lift, wave drag, and pitching-moment coefficients are calculated with respect to geometric shape, angle of attack, and freestream Mach number.

Proceedings ArticleDOI
TL;DR: In this article, the effects of high freestream turbulence on the boundary layer development of a stator vane airfoil were examined, showing that the mean velocity profiles appeared to be more consistent with laminar profiles.
Abstract: High freestream turbulence levels have been shown to greatly augment the heat transfer on a gas turbine airfoil. To better understand these effects, this study has examined the effects elevated freestream turbulence levels have on the boundary layer development along a stator vane airfoil. Low freestream turbulence measurements (0.6 percent) were performed as a baseline for comparison to measurements at combustor simulated turbulence levels (19.5 percent). A two-component LDV system was used for detailed boundary layer measurements of both the mean and fluctuating velocities on the pressure and suction surfaces. Although the mean velocity profiles appeared to be more consistent with laminar profiles, large velocity fluctuations were measured in the boundary layer along the pressure side at the high freestream turbulence conditions. Along the suction side, transition occurred further upstream due to freestream turbulence.