Numerical Solution of Compressible Steady Flows around the RAE 2822 Airfoil

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Kryštůfek P.

2014-03-01

Full Text Available The article presents results of a numerical solution of subsonic, transonic and supersonic flows described by the system of Navier-Stokes equations in 2D laminar compressible flows around the RAE 2822 airfoil. Authors used FVM multistage Runge-Kutta method to numerically solve the flows around the RAE 2822 airfoil.

Active Control of Flow Separation Over an Airfoil

Science.gov (United States)

Ravindran, S. S.

1999-01-01

Designing an aircraft without conventional control surfaces is of interest to aerospace community. In this direction, smart actuator devices such as synthetic jets have been proposed to provide aircraft maneuverability instead of control surfaces. In this article, a numerical study is performed to investigate the effects of unsteady suction and blowing on airfoils. The unsteady suction and blowing is introduced at the leading edge of the airfoil in the form of tangential jet. Numerical solutions are obtained using Reynolds-Averaged viscous compressible Navier-Stokes equations. Unsteady suction and blowing is investigated as a means of separation control to obtain lift on airfoils. The effect of blowing coefficients on lift and drag is investigated. The numerical simulations are compared with experiments from the Tel-Aviv University (TAU). These results indicate that unsteady suction and blowing can be used as a means of separation control to generate lift on airfoils.

CFD Prediction of Airfoil Drag in Viscous Flow Using the Entropy Generation Method

Directory of Open Access Journals (Sweden)

Wei Wang

2018-01-01

Full Text Available A new aerodynamic force of drag prediction approach was developed to compute the airfoil drag via entropy generation rate in the flow field. According to the momentum balance, entropy generation and its relationship to drag were derived for viscous flow. Model equations for the calculation of the local entropy generation in turbulent flows were presented by extending the RANS procedure to the entropy balance equation. The accuracy of algorithm and programs was assessed by simulating the pressure coefficient distribution and dragging coefficient of different airfoils under different Reynolds number at different attack angle. Numerical data shows that the total entropy generation rate in the flow field and the drag coefficient of the airfoil can be related by linear equation, which indicates that the total drag could be resolved into entropy generation based on its physical mechanism of energy loss.

Nonlinear power flow feedback control for improved stability and performance of airfoil sections

Science.gov (United States)

Wilson, David G.; Robinett, III, Rush D.

2013-09-03

A computer-implemented method of determining the pitch stability of an airfoil system, comprising using a computer to numerically integrate a differential equation of motion that includes terms describing PID controller action. In one model, the differential equation characterizes the time-dependent response of the airfoil's pitch angle, .alpha.. The computer model calculates limit-cycles of the model, which represent the stability boundaries of the airfoil system. Once the stability boundary is known, feedback control can be implemented, by using, for example, a PID controller to control a feedback actuator. The method allows the PID controller gain constants, K.sub.I, K.sub.p, and K.sub.d, to be optimized. This permits operation closer to the stability boundaries, while preventing the physical apparatus from unintentionally crossing the stability boundaries. Operating closer to the stability boundaries permits greater power efficiencies to be extracted from the airfoil system.

Airfoil shape optimization using non-traditional optimization technique and its validation

Directory of Open Access Journals (Sweden)

R. Mukesh

2014-07-01

Full Text Available Computational fluid dynamics (CFD is one of the computer-based solution methods which is more widely employed in aerospace engineering. The computational power and time required to carry out the analysis increase as the fidelity of the analysis increases. Aerodynamic shape optimization has become a vital part of aircraft design in the recent years. Generally if we want to optimize an airfoil we have to describe the airfoil and for that, we need to have at least hundred points of x and y co-ordinates. It is really difficult to optimize airfoils with this large number of co-ordinates. Nowadays many different schemes of parameter sets are used to describe general airfoil such as B-spline, and PARSEC. The main goal of these parameterization schemes is to reduce the number of needed parameters as few as possible while controlling the important aerodynamic features effectively. Here the work has been done on the PARSEC geometry representation method. The objective of this work is to introduce the knowledge of describing general airfoil using twelve parameters by representing its shape as a polynomial function. And also we have introduced the concept of Genetic Algorithm to optimize the aerodynamic characteristics of a general airfoil for specific conditions. A MATLAB program has been developed to implement PARSEC, Panel Technique, and Genetic Algorithm. This program has been tested for a standard NACA 2411 airfoil and optimized to improve its coefficient of lift. Pressure distribution and co-efficient of lift for airfoil geometries have been calculated using the Panel method. The optimized airfoil has improved co-efficient of lift compared to the original one. The optimized airfoil is validated using wind tunnel data.

Numerical solution of viscous flow around an airfoil with a flap via the random vortex method

Energy Technology Data Exchange (ETDEWEB)

Ghadiri, B.; Nazari, D. [Tarbiat Modares Univ., Dept. of Mechancial Engineering, Tehran (Iran, Islamic Republic of)]. E-mail: Ghadirib@modares.ac.ir; Nazari_d@yahoo.com

2003-07-01

The unsteady and incompressible flow around an airfoil with a flap is analyzed via a random vortex method. The Navier-Stokes equations, in the form of vorticity, is split into diffusion and convection parts according to the fractional step method. A random Walk method is used to solve the diffusion equation and the Cloud-in-Cell (CIC) method to solve the Euler's equation. The sequence mapping transformations is used to map the uniform flow around an airfoil with a flap onto a circular cylinder with a uniform flow velocity. The pressure and force coefficients are computed for an airfoil with a flap attached for different angle of attack; agreement with experimental data is good. (author)

Numerical solution of viscous flow around an airfoil with a flap via the random vortex method

International Nuclear Information System (INIS)

Ghadiri, B.; Nazari, D.

2003-01-01

The unsteady and incompressible flow around an airfoil with a flap is analyzed via a random vortex method. The Navier-Stokes equations, in the form of vorticity, is split into diffusion and convection parts according to the fractional step method. A random Walk method is used to solve the diffusion equation and the Cloud-in-Cell (CIC) method to solve the Euler's equation. The sequence mapping transformations is used to map the uniform flow around an airfoil with a flap onto a circular cylinder with a uniform flow velocity. The pressure and force coefficients are computed for an airfoil with a flap attached for different angle of attack; agreement with experimental data is good. (author)

Hybrid immersed boundary method for airfoils with a trailing-edge flap

DEFF Research Database (Denmark)

Zhu, Wei Jun; Behrens, Tim; Shen, Wen Zhong

2013-01-01

In this paper, a hybrid immersed boundary technique has been developed for simulating turbulent flows past airfoils with moving trailing-edge flaps. Over the main fixed part of the airfoil, the equations are solved using a standard body-fitted finite volume technique, whereas the moving trailing......-edge flap is simulated using the immersed boundary method on a curvilinear mesh. An existing in-house-developed flow solver is employed to solve the incompressible Reynolds-Averaged Navier-Stokes equations together with the k-ω turbulence model. To achieve consistent wall boundary conditions at the immersed...... boundaries the k-ωturbulence model is modified and adapted to the local conditions associated with the immersed boundary method. The obtained results show that the hybrid approach is an efficient and accurate method for solving turbulent flows past airfoils with a trailing-edge flap and that flow control...

Composite airfoil assembly

Science.gov (United States)

Garcia-Crespo, Andres Jose

2015-03-03

A composite blade assembly for mounting on a turbine wheel includes a ceramic airfoil and an airfoil platform. The ceramic airfoil is formed with an airfoil portion, a blade shank portion and a blade dovetail tang. The metal platform includes a platform shank and a radially inner platform dovetail. The ceramic airfoil is captured within the metal platform, such that in use, the ceramic airfoil is held within the turbine wheel independent of the metal platform.

Numerical investigation on exterior conformal mappings with application to airfoils

International Nuclear Information System (INIS)

Mohamad Rashidi Md Razali; Hu Laey Nee

2000-01-01

A numerical method is described in computing a conformal map from an exterior region onto the exterior of the unit disk. The numerical method is based on a boundary integral equation which is similar to the Kerzman-Stein integral equation for interior mapping. Some examples show that numerical results of high accuracy can be obtained provided that the boundaries are smooth. This numerical method has been applied to the mapping airfoils. However, due to the fact that the parametric representation of an air foil is not known, a cubic spline interpolation method has been used. Some numerical examples with satisfying results have been obtained for the symmetrical and cambered airfoils. (Author)

On generalized fractional vibration equation

International Nuclear Information System (INIS)

Dai, Hongzhe; Zheng, Zhibao; Wang, Wei

2017-01-01

Highlights: • The paper presents a generalized fractional vibration equation for arbitrary viscoelastically damped system. • Some classical vibration equations can be derived from the developed equation. • The analytic solution of developed equation is derived under some special cases. • The generalized equation is particularly useful for developing new fractional equivalent linearization method. - Abstract: In this paper, a generalized fractional vibration equation with multi-terms of fractional dissipation is developed to describe the dynamical response of an arbitrary viscoelastically damped system. It is shown that many classical equations of motion, e.g., the Bagley–Torvik equation, can be derived from the developed equation. The Laplace transform is utilized to solve the generalized equation and the analytic solution under some special cases is derived. Example demonstrates the generalized transfer function of an arbitrary viscoelastic system.

Unsteady lift forces on highly cambered airfoils moving through a gust

Science.gov (United States)

Atassi, H.; Goldstein, M.

1974-01-01

An unsteady airfoil theory in which the flow is linearized about the steady potential flow of the airfoil is presented. The theory is applied to an airfoil entering a gust. After transformation to the W-plane, the problem is formulated in terms of a Poisson's equation. The solutions are expanded in a Fourier-Bessel series. The theory is applied to a circular arc with arbitrary camber. Closed form expressions for the velocity and pressure on the surface of the airfoil are obtained. The unsteady aerodynamic forces are then calculated and shown to contain two terms. One in an explicit closed analytical form represents the contribution of the oncoming vortical disturbance, the other depends on a single quadrature and accounts for the effect of the wake.

Comprehensive performance comparison of airfoil fin PCHEs with NACA 00XX series airfoil

Energy Technology Data Exchange (ETDEWEB)

Chen, Fei, E-mail: chenfei@iet.cn [Institute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing 100190 (China); Heating Technology Research and Development Center, Beijing District Heating Group, Beijing 100028 (China); Zhang, Lishen, E-mail: lishenzhang@sina.com [Heating Technology Research and Development Center, Beijing District Heating Group, Beijing 100028 (China); Huai, Xiulan, E-mail: hxl@iet.cn [Institute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing 100190 (China); Li, Jufeng, E-mail: lijufeng.net@163.com [Nuclear and Radiation Safety Center, Ministry of Environmental Protection, Beijing 100082 (China); Zhang, Hang, E-mail: zhanghang@iet.cn [Institute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing 100190 (China); Liu, Zhigang, E-mail: zgliu9322@163.com [Energy Research Institute of Shandong Academy of Sciences, Jinan, Shandong 250014 (China)

2017-04-15

Highlights: • Pressure drop of NACA 0020 airfoil fin PCHE reduces strikingly in comparison with the zigzag PCHE. • Pressure drop of NACA 00XX airfoil fin PCHE decreases as airfoil thickness increases. • Heat transfer performance of NACA 00XX airfoil fin PCHE increases as airfoil thickness rises. • Comprehensive performance of NACA 00XX airfoil fin PCHE degrades as airfoil thickness increases. - Abstract: Printed circuit heat exchanger (PCHE) can be used in supercritical carbon dioxide (S-CO{sub 2}) Brayton cycle. The present study compares NACA 0020 airfoil fin PCHE with conventional zigzag PCHE by numerical analysis. Pressure drop of the former has a striking reduction while maintaining excellent heat transfer performance. Comparison on four NACA 00XX series airfoil fin PCHEs is performed to investigate the influence of airfoil profile on flow and heat transfer performance. With a fixed vertical pitch, heat transfer performance of NACA series airfoil fin PCHE increases as airfoil thickness increases. However, comprehensive performance, in which both flow and heat transfer are taken into account, degrades with increasing airfoil thickness. Among four NACA airfoil fin PCHEs presented in this paper, NACA 0010 airfoil fin PCHE demonstrates the best comprehensive performance.

Comprehensive performance comparison of airfoil fin PCHEs with NACA 00XX series airfoil

International Nuclear Information System (INIS)

Chen, Fei; Zhang, Lishen; Huai, Xiulan; Li, Jufeng; Zhang, Hang; Liu, Zhigang

2017-01-01

Highlights: • Pressure drop of NACA 0020 airfoil fin PCHE reduces strikingly in comparison with the zigzag PCHE. • Pressure drop of NACA 00XX airfoil fin PCHE decreases as airfoil thickness increases. • Heat transfer performance of NACA 00XX airfoil fin PCHE increases as airfoil thickness rises. • Comprehensive performance of NACA 00XX airfoil fin PCHE degrades as airfoil thickness increases. - Abstract: Printed circuit heat exchanger (PCHE) can be used in supercritical carbon dioxide (S-CO_2) Brayton cycle. The present study compares NACA 0020 airfoil fin PCHE with conventional zigzag PCHE by numerical analysis. Pressure drop of the former has a striking reduction while maintaining excellent heat transfer performance. Comparison on four NACA 00XX series airfoil fin PCHEs is performed to investigate the influence of airfoil profile on flow and heat transfer performance. With a fixed vertical pitch, heat transfer performance of NACA series airfoil fin PCHE increases as airfoil thickness increases. However, comprehensive performance, in which both flow and heat transfer are taken into account, degrades with increasing airfoil thickness. Among four NACA airfoil fin PCHEs presented in this paper, NACA 0010 airfoil fin PCHE demonstrates the best comprehensive performance.

Unsteady flow model for circulation-control airfoils

Science.gov (United States)

Rao, B. M.

1979-01-01

An analysis and a numerical lifting surface method are developed for predicting the unsteady airloads on two-dimensional circulation control airfoils in incompressible flow. The analysis and the computer program are validated by correlating the computed unsteady airloads with test data and also with other theoretical solutions. Additionally, a mathematical model for predicting the bending-torsion flutter of a two-dimensional airfoil (a reference section of a wing or rotor blade) and a computer program using an iterative scheme are developed. The flutter program has a provision for using the CC airfoil airloads program or the Theodorsen hard flap solution to compute the unsteady lift and moment used in the flutter equations. The adopted mathematical model and the iterative scheme are used to perform a flutter analysis of a typical CC rotor blade reference section. The program seems to work well within the basic assumption of the incompressible flow.

An efficient finite differences method for the computation of compressible, subsonic, unsteady flows past airfoils and panels

Science.gov (United States)

Colera, Manuel; Pérez-Saborid, Miguel

2017-09-01

A finite differences scheme is proposed in this work to compute in the time domain the compressible, subsonic, unsteady flow past an aerodynamic airfoil using the linearized potential theory. It improves and extends the original method proposed in this journal by Hariharan, Ping and Scott [1] by considering: (i) a non-uniform mesh, (ii) an implicit time integration algorithm, (iii) a vectorized implementation and (iv) the coupled airfoil dynamics and fluid dynamic loads. First, we have formulated the method for cases in which the airfoil motion is given. The scheme has been tested on well known problems in unsteady aerodynamics -such as the response to a sudden change of the angle of attack and to a harmonic motion of the airfoil- and has been proved to be more accurate and efficient than other finite differences and vortex-lattice methods found in the literature. Secondly, we have coupled our method to the equations governing the airfoil dynamics in order to numerically solve problems where the airfoil motion is unknown a priori as happens, for example, in the cases of the flutter and the divergence of a typical section of a wing or of a flexible panel. Apparently, this is the first self-consistent and easy-to-implement numerical analysis in the time domain of the compressible, linearized coupled dynamics of the (generally flexible) airfoil-fluid system carried out in the literature. The results for the particular case of a rigid airfoil show excellent agreement with those reported by other authors, whereas those obtained for the case of a cantilevered flexible airfoil in compressible flow seem to be original or, at least, not well-known.

The flow of an incompressible electroconductive fluid past a thin airfoil. The parabolic profile

Directory of Open Access Journals (Sweden)

Adrian CARABINEANU

2014-04-01

Full Text Available We study the two-dimensional steady flow of an ideal incompressible perfectly conducting fluid past an insulating thin parabolic airfoil. We consider the linearized Euler and Maxwell equations and Ohm's law. We use the integral representations for the velocity, magnetic induction and pressure and the boundary conditions to obtain an integral equation for the jump of the pressure across the airfoil. We give some graphic representations for the lift coefficient, velocity and magnetic induction.

Numerical Solution of Inviscid Compressible Steady Flows around the RAE 2822 Airfoil

Science.gov (United States)

Kryštůfek, P.; Kozel, K.

2015-05-01

The article presents results of a numerical solution of subsonic, transonic and supersonic flows described by the system of Euler equations in 2D compressible flows around the RAE 2822 airfoil. Authors used FVM multistage Runge-Kutta method to numerically solve the flows around the RAE 2822 airfoil. The results are compared with the solution using the software Ansys Fluent 15.0.7.

Leading-Edge Noise Prediction of General Airfoil Profiles with Spanwise-Varying Inflow Conditions

NARCIS (Netherlands)

Miotto, Renato Fuzaro; Wolf, William Roberto; De Santana, Leandro Dantas

2018-01-01

This paper presents a study of the leading-edge noise radiated by an airfoil undergoing a turbulent inflow. The noise prediction of generic airfoil profiles subjected to spanwise-varying inflow conditions is performed with the support of Amiet’s theory and the inverse strip technique. In the

Leading-Edge Noise Prediction of General Airfoil Profiles with Spanwise-Varying Inflow Conditions

NARCIS (Netherlands)

Miotto, Renato Fuzaro; Wolf, William Roberto; De Santana, Leandro Dantas

This paper presents a study of the leading-edge noise radiated by an airfoil undergoing a turbulent inflow. The noise prediction of generic airfoil profiles subjected to spanwise-varying inflow conditions is performed with the support of Amiet’s theory and the inverse strip technique. In the

A parameter identification problem arising from a two-dimensional airfoil section model

International Nuclear Information System (INIS)

Cerezo, G.M.

1994-01-01

The development of state space models for aeroelastic systems, including unsteady aerodynamics, is particularly important for the design of highly maneuverable aircraft. In this work we present a state space formulation for a special class of singular neutral functional differential equations (SNFDE) with initial data in C(-1, 0). This work is motivated by the two-dimensional airfoil model presented by Burns, Cliff and Herdman in. In the same authors discuss the validity of the assumptions under which the model was formulated. They pay special attention to the derivation of the evolution equation for the circulation on the airfoil. This equation was coupled to the rigid-body dynamics of the airfoil in order to obtain a complete set of functional differential equations that describes the composite system. The resulting mathematical model for the aeroelastic system has a weakly singular component. In this work we consider a finite delay approximation to the model presented in. We work with a scalar model in which we consider the weak singularity appearing in the original problem. The main goal of this work is to develop numerical techniques for the identification of the parameters appearing in the kernel of the associated scalar integral equation. Clearly this is the first step in the study of parameter identification for the original model and the corresponding validation of this model for the aeroelastic system

Airfoils for wind turbine

Science.gov (United States)

Tangler, James L.; Somers, Dan M.

1996-01-01

Airfoils for the blade of a wind turbine wherein each airfoil is characterized by a thickness in a range from 16%-24% and a maximum lift coefficient designed to be largely insensitive to roughness effects. The airfoils include a family of airfoils for a blade 15 to 25 meters in length, a family of airfoils for a blade 1 to 5 meters in length, and a family of airfoils for a blade 5 to 10 meters in length.

Generalized estimating equations

CERN Document Server

Hardin, James W

2002-01-01

Although powerful and flexible, the method of generalized linear models (GLM) is limited in its ability to accurately deal with longitudinal and clustered data. Developed specifically to accommodate these data types, the method of Generalized Estimating Equations (GEE) extends the GLM algorithm to accommodate the correlated data encountered in health research, social science, biology, and other related fields.Generalized Estimating Equations provides the first complete treatment of GEE methodology in all of its variations. After introducing the subject and reviewing GLM, the authors examine th

Implementation of different turbulence model to find proper model to estimate aerodynamic properties of airfoils

Science.gov (United States)

Sogukpinar, Haci; Bozkurt, Ismail

2018-02-01

In this paper, aerodynamic calculations of NACA 4 series airfoil of 0012 are performed by using Finite-Volume Method and obtained results are compared with experimental data to correlate the numerical accuracy of CFD approximation. Then other airfoils are simulated with k-ɛ, k-w Spalart-Allmaras and SST model. The governing equations are the Reynolds-Averaged-Navier-Stokes (RANS) equations. The performance of different airfoils (NACA 0008, 0009, 0010, 0012, 0015, 0018, 0021, 0024) at different angle of attack are investigated and compared with most used turbulence models for industrial applications. According to the results of the comparison of numerical calculations and experimental data, k-w and SST models are considered to be closest to experimental results for the calculation of the lift coefficient.

Performance assessment of Darrieus wind turbine with symmetric and cambered airfoils

Energy Technology Data Exchange (ETDEWEB)

Cisse, H.; Trifu, O.; Paraschivoiu, I. [Ecole Polytechnique, Montreal, PQ (Canada). Dept. de Genie Mecanique

2007-07-01

This paper outlined the wind turbine and design software used to predict the flow conditions and performance of a straight-bladed Darrieus wind turbine. Three different blade sections were considered, notably the NACA 0018; the SNLA NLF 18/50 symmetrical airfoil; and the FX63-137 cambered airfoil. The numerical predictions of the flow conditions during the operation of the rotors were also presented. Torque yield for each blade section under a variety of operating conditions was presented. The numerical software program used in the study was based on a double-multiple streamtube model which considered a partition of the rotor in streamtubes and considered each of the 2 blade elements as an actuator disk. The actuator disk theory was based on a theory of momentum conservation. Wind velocities were determined in order to calculate forces acting on the actuator disks. A second set of equations was used to determine the forces acting on the upwind and downwind blade elements. Equations were also derived for the downwind interference factor. The following 3 main sets of data were used: (1) a geometry definition of the wind turbine; (2) operational conditions; and (3) main control parameters. Results of the study showed that the cambered airfoil blade section produced 10 times more torque in turbine starting conditions than the NACA 0018. Laminar airfoil lift to drag ratio at low angles of attack, and the use of appropriate Reynolds numbers resulted in higher efficiency. The large static stall angle of the cambered airfoil allowed higher power outputs than symmetrical airfoils. It was concluded that the starting torque of a Darrieus turbine can be increased by using a cambered blade section. 13 refs., 19 figs.

Mechanism of unconventional aerodynamic characteristics of an elliptic airfoil

Directory of Open Access Journals (Sweden)

Sun Wei

2015-06-01

Full Text Available The aerodynamic characteristics of elliptic airfoil are quite different from the case of conventional airfoil for Reynolds number varying from about 104 to 106. In order to reveal the fundamental mechanism, the unsteady flow around a stationary two-dimensional elliptic airfoil with 16% relative thickness has been simulated using unsteady Reynolds-averaged Navier–Stokes equations and the γ-Reθt‾ transition turbulence model at different angles of attack for flow Reynolds number of 5 × 105. The aerodynamic coefficients and the pressure distribution obtained by computation are in good agreement with experimental data, which indicates that the numerical method works well. Through this study, the mechanism of the unconventional aerodynamic characteristics of airfoil is analyzed and discussed based on the computational predictions coupled with the wind tunnel results. It is considered that the boundary layer transition at the leading edge and the unsteady flow separation vortices at the trailing edge are the causes of the case. Furthermore, a valuable insight into the physics of how the flow behavior affects the elliptic airfoil’s aerodynamics is provided.

Application of an upwind Navier-Stokes code to two-dimensional transonic airfoil flow

International Nuclear Information System (INIS)

Rumsey, C.L.; Thomas, J.L.; Anderson, W.K.; Taylor, S.L.

1987-01-01

An upwind-biased implicit approximate factorization Navier-Stokes algorithm is applied to a variety of steady transonic airfoil cases, using the NACA 0012, RAE 2822, and Jones supercritical airfoils. The thin-layer form of the compressible Navier-Stokes equations is used. Both the CYBER 205 and CRAY 2 supercomputers are utilized, with average computational speeds of about 18 and 16 microsec/gridpoint/iteration, respectively. Lift curves, drag polars, and variations in drag coefficient with Mach number are determined for the NACA 0012 and Jones supercritical airfoils. Also, several cases are computed for comparison with experiment. The effect of grid density and grid extent on a typical turbulent airfoil solution is shown. An algebraic eddy-viscosity turbulence model is used for all of the computations. 10 references

Study of two-dimensional flow by triangular unstructured grid around airfoil with dynamic ground effect

International Nuclear Information System (INIS)

Haghbin, S.; Farahat, S.

2004-01-01

In this paper, the numerical solution of two-dimensional incompressible viscid flow by triangular unstructured grid around airfoil with dynamic ground effect and by using geometric conservation law (GCL) has been represented. In this analysis, after the mesh generation for physical model, for the purpose of adaption of meshes with physical condition, the mesh adaption method has been used. Also, for increasing the speed of results convergence, the Multigrid method has been applied to the solver of governing equations. Because of the movement of meshes in this analysis, by using a spring simulation, the generated meshes have been moved and in every time step for the purpose of controlling the quality of meshes, by considering the EquiAngle Skew coefficient (EAS) and the volume of each mesh, the meshes that had a large EAS and a volume more than and less than defined maximum and minimum value, have been removed and then regenerated. Also, because the continuity and momentum conservations law were insufficient to work with these moving grids, the geometric conservation law was combined with the other conservation laws and a general equation was obtained for the dynamic meshes. For solving this general equation, the Simple Algorithm has been used. According to the results, the dynamic ground effect causes unsteadiness and also the Lift coefficient is increased vibrationally. And with respect to the type of airfoil, the Drag coefficient can decrease or increase vibrationally. (author)

Study of two-dimensional flow by triangular unstructured grid around airfoil with dynamic ground effect

Energy Technology Data Exchange (ETDEWEB)

Haghbin, S.; Farahat, S. [Sistan and Baluchestan Univ., Dept. of Mechanical Engineering, Zahedan (Iran, Islamic Republic of)]. E-mail: sadegh_haghbin@yahoo.com

2004-07-01

In this paper, the numerical solution of two-dimensional incompressible viscid flow by triangular unstructured grid around airfoil with dynamic ground effect and by using geometric conservation law (GCL) has been represented. In this analysis, after the mesh generation for physical model, for the purpose of adaption of meshes with physical condition, the mesh adaption method has been used. Also, for increasing the speed of results convergence, the Multigrid method has been applied to the solver of governing equations. Because of the movement of meshes in this analysis, by using a spring simulation, the generated meshes have been moved and in every time step for the purpose of controlling the quality of meshes, by considering the EquiAngle Skew coefficient (EAS) and the volume of each mesh, the meshes that had a large EAS and a volume more than and less than defined maximum and minimum value, have been removed and then regenerated. Also, because the continuity and momentum conservations law were insufficient to work with these moving grids, the geometric conservation law was combined with the other conservation laws and a general equation was obtained for the dynamic meshes. For solving this general equation, the Simple Algorithm has been used. According to the results, the dynamic ground effect causes unsteadiness and also the Lift coefficient is increased vibrationally. And with respect to the type of airfoil, the Drag coefficient can decrease or increase vibrationally. (author)

Applications of Laplace transform methods to airfoil motion and stability calculations

Science.gov (United States)

Edwards, J. W.

1979-01-01

This paper reviews the development of generalized unsteady aerodynamic theory and presents a derivation of the generalized Possio integral equation. Numerical calculations resolve questions concerning subsonic indicial lift functions and demonstrate the generation of Kutta waves at high values of reduced frequency, subsonic Mach number, or both. The use of rational function approximations of unsteady aerodynamic loads in aeroelastic stability calculations is reviewed, and a reformulation of the matrix Pade approximation technique is given. Numerical examples of flutter boundary calculations for a wing which is to be flight tested are given. Finally, a simplified aerodynamic model of transonic flow is used to study the stability of an airfoil exposed to supersonic and subsonic flow regions.

Geometrical effects on the airfoil flow separation and transition

KAUST Repository

Zhang, Wei

2015-04-25

We present results from direct numerical simulations (DNS) of incompressible flow over two airfoils, NACA-4412 and NACA-0012-64, to investigate the effects of the airfoil geometry on the flow separation and transition patterns at Re=104 and 10 degrees incidence. The two chosen airfoils are geometrically similar except for maximum camber (respectively 4%C and 0 with C the chord length), which results in a larger projection area with respect to the incoming flow for the NACA-4412 airfoil, and a larger leeward surface curvature at the leading edge for the NACA-0012-64 airfoil. The governing equations are discretized using an energy conservative fourth-order spatial discretization scheme. An assessment on the two-point correlation indicates that a spanwise domain size of 0.8C is sufficiently large for the present simulations. We discuss flow separation at the airfoil leading edge, transition of the separated shear layer to three-dimensional flow and subsequently to turbulence. Numerical results reveal a stronger adverse pressure gradient field in the leading edge region of the NACA-0012-64 airfoil due to the rapidly varying surface curvature. As a result, the flow experiences detachment at x/C=0.08, and the separated shear layer transition via Kelvin-Helmholtz mechanism occurs at x/C=0.29 with fully developed turbulent flow around x/C=0.80. These flow development phases are delayed to occur at much downstream positions, respectively, observed around x/C=0.25, 0.71 and 1.15 for the NACA-4412 airfoil. The turbulent intensity, measured by the turbulent fluctuations and turbulent Reynolds stresses, are much larger for NACA-0012-64 from the transition onset until the airfoil trailing edge, while turbulence develops significantly downstream of the trailing edge for the NACA-4412 airfoil. For both airfoils, our DNS results indicate that the mean Reynolds stress u\\'u\\'/U02 reaches its maximum value at a distance from the surface approximately equal to the displacement

Reinforced Airfoil Shaped Body

DEFF Research Database (Denmark)

2011-01-01

The present invention relates to an airfoil shaped body with a leading edge and a trailing edge extending along the longitudinal extension of the body and defining a profile chord, the airfoil shaped body comprising an airfoil shaped facing that forms the outer surface of the airfoil shaped body...

Closed loop steam cooled airfoil

Science.gov (United States)

Widrig, Scott M.; Rudolph, Ronald J.; Wagner, Gregg P.

2006-04-18

An airfoil, a method of manufacturing an airfoil, and a system for cooling an airfoil is provided. The cooling system can be used with an airfoil located in the first stages of a combustion turbine within a combined cycle power generation plant and involves flowing closed loop steam through a pin array set within an airfoil. The airfoil can comprise a cavity having a cooling chamber bounded by an interior wall and an exterior wall so that steam can enter the cavity, pass through the pin array, and then return to the cavity to thereby cool the airfoil. The method of manufacturing an airfoil can include a type of lost wax investment casting process in which a pin array is cast into an airfoil to form a cooling chamber.

The generalized Airy diffusion equation

Directory of Open Access Journals (Sweden)

Frank M. Cholewinski

2003-08-01

Full Text Available Solutions of a generalized Airy diffusion equation and an associated nonlinear partial differential equation are obtained. Trigonometric type functions are derived for a third order generalized radial Euler type operator. An associated complex variable theory and generalized Cauchy-Euler equations are obtained. Further, it is shown that the Airy expansions can be mapped onto the Bessel Calculus of Bochner, Cholewinski and Haimo.

Effect of Reynolds Number on Aerodynamics of Airfoil with Gurney Flap

Directory of Open Access Journals (Sweden)

Shubham Jain

2015-01-01

Full Text Available Steady state, two-dimensional computational investigations performed on NACA 0012 airfoil to analyze the effect of variation in Reynolds number on the aerodynamics of the airfoil without and with a Gurney flap of height of 3% chord are presented in this paper. RANS based one-equation Spalart-Allmaras model is used for the computations. Both lift and drag coefficients increase with Gurney flap compared to those without Gurney flap at all Reynolds numbers at all angles of attack. The zero lift angle of attack seems to become more negative as Reynolds number increases due to effective increase of the airfoil camber. However the stall angle of attack decreased by 2° for the airfoil with Gurney flap. Lift coefficient decreases rapidly and drag coefficient increases rapidly when Reynolds number is decreased below critical range. This occurs due to change in flow pattern near Gurney flap at low Reynolds numbers.

Computer investigations of the turbulent flow around a NACA2415 airfoil wind turbine

Science.gov (United States)

Driss, Zied; Chelbi, Tarek; Abid, Mohamed Salah

2015-12-01

In this work, computer investigations are carried out to study the flow field developing around a NACA2415 airfoil wind turbine. The Navier-Stokes equations in conjunction with the standard k-ɛ turbulence model are considered. These equations are solved numerically to determine the local characteristics of the flow. The models tested are implemented in the software "SolidWorks Flow Simulation" which uses a finite volume scheme. The numerical results are compared with experiments conducted on an open wind tunnel to validate the numerical results. This will help improving the aerodynamic efficiency in the design of packaged installations of the NACA2415 airfoil type wind turbine.

Validation of the CQU-DTU-LN1 series of airfoils

DEFF Research Database (Denmark)

Shen, Wen Zhong; Zhu, Wei Jun; Fischer, Andreas

2014-01-01

The CQU-DTU-LN1 series of airfoils were designed with an objective of high lift and low noise emission. In the design process, the aerodynamic performance is obtained using XFOIL while noise emission is obtained with the BPM model. In this paper we present some validations of the designed CQU......, the designed Cl and Cl/Cd agrees well with the experiment and are in general higher than those of the NACA airfoil. For the acoustic features, the noise emission of the LN118 airfoil is compared with the acoustic measurements and that of the NACA airfoil. Comparisons show that the BPM model can predict...

Airfoil System for Cruising Flight

Science.gov (United States)

Shams, Qamar A. (Inventor); Liu, Tianshu (Inventor)

2014-01-01

An airfoil system includes an airfoil body and at least one flexible strip. The airfoil body has a top surface and a bottom surface, a chord length, a span, and a maximum thickness. Each flexible strip is attached along at least one edge thereof to either the top or bottom surface of the airfoil body. The flexible strip has a spanwise length that is a function of the airfoil body's span, a chordwise width that is a function of the airfoil body's chord length, and a thickness that is a function of the airfoil body's maximum thickness.

Shape Optimization of NREL S809 Airfoil for Wind Turbine Blades Using a Multiobjective Genetic Algorithm

Directory of Open Access Journals (Sweden)

Yilei He

2014-01-01

Full Text Available The goal of this paper is to employ a multiobjective genetic algorithm (MOGA to optimize the shape of a well-known wind turbine airfoil S809 to improve its lift and drag characteristics, in particular to achieve two objectives, that is, to increase its lift and its lift to drag ratio. The commercially available software FLUENT is employed to calculate the flow field on an adaptive structured mesh using the Reynolds-Averaged Navier-Stokes (RANS equations in conjunction with a two-equation k-ω SST turbulence model. The results show significant improvement in both lift coefficient and lift to drag ratio of the optimized airfoil compared to the original S809 airfoil. In addition, MOGA results are in close agreement with those obtained by the adjoint-based optimization technique.

Unsteady Thick Airfoil Aerodynamics: Experiments, Computation, and Theory

Science.gov (United States)

Strangfeld, C.; Rumsey, C. L.; Mueller-Vahl, H.; Greenblatt, D.; Nayeri, C. N.; Paschereit, C. O.

2015-01-01

An experimental, computational and theoretical investigation was carried out to study the aerodynamic loads acting on a relatively thick NACA 0018 airfoil when subjected to pitching and surging, individually and synchronously. Both pre-stall and post-stall angles of attack were considered. Experiments were carried out in a dedicated unsteady wind tunnel, with large surge amplitudes, and airfoil loads were estimated by means of unsteady surface mounted pressure measurements. Theoretical predictions were based on Theodorsen's and Isaacs' results as well as on the relatively recent generalizations of van der Wall. Both two- and three-dimensional computations were performed on structured grids employing unsteady Reynolds-averaged Navier-Stokes (URANS). For pure surging at pre-stall angles of attack, the correspondence between experiments and theory was satisfactory; this served as a validation of Isaacs theory. Discrepancies were traced to dynamic trailing-edge separation, even at low angles of attack. Excellent correspondence was found between experiments and theory for airfoil pitching as well as combined pitching and surging; the latter appears to be the first clear validation of van der Wall's theoretical results. Although qualitatively similar to experiment at low angles of attack, two-dimensional URANS computations yielded notable errors in the unsteady load effects of pitching, surging and their synchronous combination. The main reason is believed to be that the URANS equations do not resolve wake vorticity (explicitly modeled in the theory) or the resulting rolled-up un- steady flow structures because high values of eddy viscosity tend to \\smear" the wake. At post-stall angles, three-dimensional computations illustrated the importance of modeling the tunnel side walls.

Generalization of Einstein's gravitational field equations

Science.gov (United States)

Moulin, Frédéric

2017-12-01

The Riemann tensor is the cornerstone of general relativity, but as is well known it does not appear explicitly in Einstein's equation of gravitation. This suggests that the latter may not be the most general equation. We propose here for the first time, following a rigorous mathematical treatment based on the variational principle, that there exists a generalized 4-index gravitational field equation containing the Riemann curvature tensor linearly, and thus the Weyl tensor as well. We show that this equation, written in n dimensions, contains the energy-momentum tensor for matter and that of the gravitational field itself. This new 4-index equation remains completely within the framework of general relativity and emerges as a natural generalization of the familiar 2-index Einstein equation. Due to the presence of the Weyl tensor, we show that this equation contains much more information, which fully justifies the use of a fourth-order theory.

Airfoil design and optimization

Energy Technology Data Exchange (ETDEWEB)

Lutz, T. [Stuttgart Univ. (Germany). Inst. fuer Aerodynamik und Gasdynamik

2001-07-01

The aerodynamic efficiency of mildly swept wings is mainly influenced by the characteristics of the airfoil sections. The specific design of airfoils is therefore one of the classical tasks of aerodynamics. Since the airfoil characteristics are directly dependent on the inviscid pressure distribution the application of inverse calculation methods is obvious. The direct numerical airfoil optimization offers an alternative to the manual design and attracts increasing interest. (orig.)

Semi-empirical model for prediction of unsteady forces on an airfoil with application to flutter

Science.gov (United States)

Mahajan, A. J.; Kaza, K. R. V.; Dowell, E. H.

1993-01-01

A semi-empirical model is described for predicting unsteady aerodynamic forces on arbitrary airfoils under mildly stalled and unstalled conditions. Aerodynamic forces are modeled using second order ordinary differential equations for lift and moment with airfoil motion as the input. This model is simultaneously integrated with structural dynamics equations to determine flutter characteristics for a two degrees-of-freedom system. Results for a number of cases are presented to demonstrate the suitability of this model to predict flutter. Comparison is made to the flutter characteristics determined by a Navier-Stokes solver and also the classical incompressible potential flow theory.

Numerical computation of gust aerodynamic response for realistic airfoils : Application of Amiet’s theory

NARCIS (Netherlands)

Miotto, Renato Fuzaro; Wolf, William Roberto; de Santana, Leandro Dantas

2016-01-01

Current knowledge on the noise generation mechanisms of an airfoil subjected to a turbulent flow indicates that an increment to the airfoil thickness leads to a reduction of the leading-edge noise. This effect is generally attributed to the turbulence distortion occurring close upstream the airfoil

Influence of ice accretion on the noise generated by an airfoil section

International Nuclear Information System (INIS)

Szasz, Robert-Zoltan; Ronnfors, Matilda; Revstedt, Johan

2016-01-01

Highlights: • The noise generated by ice accreted airfoils is investigated using a hybrid approach. • The roughness of the ice surface is found to have an important effect on the radiated noise. • Ice was found to damp lower frequencies and amplify higher ones. - Abstract: We investigate the noise generated by an airfoil section. Three cases are considered, one with a clean airfoil and two cases with airfoils with ice accretion. The amount of ice is the same in the two cases with ice accretion, but the surface of the accreted ice layer is smoother in one of them. The noise is computed using a hybrid approach. First the flow and the acoustic sources are computed. Second, the noise propagation is predicted by solving an inhomogeneous wave equation. The results indicate that in this case the accreted ice layer leads to a decrease of the radiated noise levels, especially in the lower frequency range.

Computation of airfoil buffet boundaries

Science.gov (United States)

Levy, L. L., Jr.; Bailey, H. E.

1981-01-01

The ILLIAC IV computer has been programmed with an implicit, finite-difference code for solving the thin layer compressible Navier-Stokes equation. Results presented for the case of the buffet boundaries of a conventional and a supercritical airfoil section at high Reynolds numbers are found to be in agreement with experimentally determined buffet boundaries, especially at the higher freestream Mach numbers and lower lift coefficients where the onset of unsteady flows is associated with shock wave-induced boundary layer separation.

Experimental study of wind-turbine airfoil aerodynamics in high turbulence

Energy Technology Data Exchange (ETDEWEB)

Devinant, Ph.; Laverne, T.; Hureau, J. [Laboratoire de Mecanique et d' Energetique Ecole Superieure de l' Energie et des Materiaux Universite d' Orleans, rue Leonard de Vinci F-45072 , Cedex 2 Orleans (France)

2002-06-01

Wind turbines very often have to operate in high turbulence related, for example, with lower layers atmospheric turbulence or wakes of other wind turbines. Most available data on airfoil aerodynamics concerns mainly aeronautical applications, which are characterized by a low level of turbulence (generally less than 1%) and low angles of attack. This paper presents wind tunnel test data for the aerodynamic properties-lift, drag, pitching moment, pressure distributions-of an airfoil used on a wind turbine when subjected to incident flow turbulence levels of 0.5-16% and placed at angles of attack up to 90. The results show that the aerodynamic behavior of the airfoil can be strongly affected by the turbulence level both qualitatively and quantitatively. This effect is especially evidenced in the angle of attack range corresponding to airfoil stall, as the boundary layer separation point advances along the leeward surface of the airfoil.

Nozzle airfoil having movable nozzle ribs

Science.gov (United States)

Yu, Yufeng Phillip; Itzel, Gary Michael

2002-01-01

A nozzle vane or airfoil structure is provided in which the nozzle ribs are connected to the side walls of the vane or airfoil in such a way that the ribs provide the requisite mechanical support between the concave side and convex side of the airfoil but are not locked in the radial direction of the assembly, longitudinally of the airfoil. The ribs may be bi-cast onto a preformed airfoil side wall structure or fastened to the airfoil by an interlocking slide connection and/or welding. By attaching the nozzle ribs to the nozzle airfoil metal in such a way that allows play longitudinally of the airfoil, the temperature difference induced radial thermal stresses at the nozzle airfoil/rib joint area are reduced while maintaining proper mechanical support of the nozzle side walls.

Parametric analyses on dynamic stall control of rotor airfoil via synthetic jet

Directory of Open Access Journals (Sweden)

Qijun ZHAO

2017-12-01

Full Text Available The effects of synthetic jet control on unsteady dynamic stall over rotor airfoil are investigated numerically. A moving-embedded grid method and an Unsteady Reynolds Averaged Navier-Stokes (URANS solver coupled with k-ω Shear Stress Transport (SST turbulence model are established for predicting the complex flowfields of oscillatory airfoil under jet control. Additionally, a velocity boundary condition modeled by sinusoidal function has been developed to fulfill the perturbation effect of periodic jet. The validity of present CFD method is evaluated by comparisons of the calculated results of baseline dynamic stall case for rotor airfoil and jet control case for VR-7B airfoil with experimental data. Then, parametric analyses are conducted emphatically for an OA212 rotor airfoil to investigate the effects of jet control parameters (jet location, dimensionless frequency, momentum coefficient, jet angle, jet type and dual-jet on dynamic stall characteristics of rotor airfoil. It is demonstrated by the calculated results that efficiency of jet control could be improved with specific momentum coefficient and jet angle when the jet is located near separation point of rotor airfoil. Furthermore, the dual-jet could improve control efficiency more obviously on dynamic stall of rotor airfoil with respect to the unique jet, and the influence laws of dual-jet’s angles and momentum coefficients on control effects are similar to those of the unique jet. Finally, unsteady aerodynamic characteristics of rotor via synthetic jet which is located on the upper surface of rotor blade in forward flight are calculated, and as a result, the aerodynamic characteristics of rotor are improved compared with the baseline. The results indicate that synthetic jet has the capability in improving aerodynamic characteristics of rotor. Keywords: Airfoil, Dynamic stall characteristics, Flow control, Moving-embedded grid methodology, Navier-Stokes equations, Parametric

Darrieus wind-turbine airfoil configurations

Science.gov (United States)

Migliore, P. G.; Fritschen, J. R.

1982-06-01

The purpose was to determine what aerodynamic performance improvement, if any, could be achieved by judiciously choosing the airfoil sections for Darrieus wind turbine blades. Ten different airfoils, having thickness to chord ratios of twelve, fifteen and eighteen percent, were investigated. Performance calculations indicated that the NACA 6-series airfoils yield peak power coefficients at least as great as the NACA. Furthermore, the power coefficient-tip speed ratio curves were broader and flatter for the 6-series airfoils. Sample calculations for an NACA 63 sub 2-015 airfoil showed an annual energy output increase of 17 to 27% depending upon rotor solidity, compared to an NACA 0015 airfoil. An attempt was made to account for the flow curvature effects associated with Darrieus turbines by transforming the NACA 63 sub 2-015 airfoil to an appropriate shape.

Impingement of water droplets on wedges and diamond airfoils at supersonic speeds

Science.gov (United States)

Serafini, John S

1953-01-01

An analytical solution has been obtained for the equations of motion of water droplets impinging on a wedge in a two-dimensional supersonic flow field with a shock wave attached to the wedge. The closed-form solution yields analytical expressions for the equation of the droplet trajectory, the local rate of impingement and the impingement velocity at any point on the wedge surface, and the total rate of impingement. The analytical expressions are utilized to determine the impingement on the forward surfaces of diamond airfoils in supersonic flow fields with attached shock waves. The results presented include the following conditions: droplet diameters from 2 to 100 microns, pressure altitudes from sea level to 30,000 feet, free-stream static temperatures from 420 degrees to 460 degrees R. Also, free-stream Mach numbers from 1.1 to 2.0, semi-apex angles for the wedge from 1.14 degrees to 7.97 degrees, thickness-to-chord ratios for the diamond airfoil from 0.02 to 0.14, chord lengths from 1 to 20 feet, and angles of attack from zero to the inverse tangent of the airfoil thickness-to-chord ratio.

A generalization of the simplest equation method and its application to (3+1)-dimensional KP equation and generalized Fisher equation

International Nuclear Information System (INIS)

Zhao, Zhonglong; Zhang, Yufeng; Han, Zhong; Rui, Wenjuan

2014-01-01

In this paper, the simplest equation method is used to construct exact traveling solutions of the (3+1)-dimensional KP equation and generalized Fisher equation. We summarize the main steps of the simplest equation method. The Bernoulli and Riccati equation are used as simplest equations. This method is straightforward and concise, and it can be applied to other nonlinear partial differential equations

A new algebraic turbulence model for accurate description of airfoil flows

Science.gov (United States)

Xiao, Meng-Juan; She, Zhen-Su

2017-11-01

We report a new algebraic turbulence model (SED-SL) based on the SED theory, a symmetry-based approach to quantifying wall turbulence. The model specifies a multi-layer profile of a stress length (SL) function in both the streamwise and wall-normal directions, which thus define the eddy viscosity in the RANS equation (e.g. a zero-equation model). After a successful simulation of flat plate flow (APS meeting, 2016), we report here further applications of the model to the flow around airfoil, with significant improvement of the prediction accuracy of the lift (CL) and drag (CD) coefficients compared to other popular models (e.g. BL, SA, etc.). Two airfoils, namely RAE2822 airfoil and NACA0012 airfoil, are computed for over 50 cases. The results are compared to experimental data from AGARD report, which shows deviations of CL bounded within 2%, and CD within 2 counts (10-4) for RAE2822 and 6 counts for NACA0012 respectively (under a systematic adjustment of the flow conditions). In all these calculations, only one parameter (proportional to the Karmen constant) shows slight variation with Mach number. The most remarkable outcome is, for the first time, the accurate prediction of the drag coefficient. The other interesting outcome is the physical interpretation of the multi-layer parameters: they specify the corresponding multi-layer structure of turbulent boundary layer; when used together with simulation data, the SED-SL enables one to extract physical information from empirical data, and to understand the variation of the turbulent boundary layer.

INVARIANTS OF GENERALIZED RAPOPORT-LEAS EQUATIONS

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Elena N. Kushner

2018-01-01

Full Text Available For the generalized Rapoport-Leas equations, algebra of differential invariants is constructed with respect to point transformations, that is, transformations of independent and dependent variables. The finding of a general transformation of this type reduces to solving an extremely complicated functional equation. Therefore, following the approach of Sophus Lie, we restrict ourselves to the search for infinitesimal transformations which are generated by translations along the trajectories of vector fields. The problem of finding these vector fields reduces to the redefined system decision of linear differential equations with respect to their coefficients. The Rapoport-Leas equations arise in the study of nonlinear filtration processes in porous media, as well as in other areas of natural science: for example, these equations describe various physical phenomena: two-phase filtration in a porous medium, filtration of a polytropic gas, and propagation of heat at nuclear explosion. They are vital topic for research: in recent works of Bibikov, Lychagin, and others, the analysis of the symmetries of the generalized Rapoport-Leas equations has been carried out; finite-dimensional dynamics and conditions of attractors existence have been found. Since the generalized RapoportLeas equations are nonlinear partial differential equations of the second order with two independent variables; the methods of the geometric theory of differential equations are used to study them in this paper. According to this theory differential equations generate subvarieties in the space of jets. This makes it possible to use the apparatus of modern differential geometry to study differential equations. We introduce the concept of admissible transformations, that is, replacements of variables that do not derive equations outside the class of the Rapoport-Leas equations. Such transformations form a Lie group. For this Lie group there are differential invariants that separate

Direct Numerical Simulation of Flows over an NACA-0012 Airfoil at Low and Moderate Reynolds Numbers

Science.gov (United States)

Balakumar, P.

2017-01-01

Direct numerical simulations (DNS) of flow over an NACA-0012 airfoil are performed at a low and a moderate Reynolds numbers of Re(sub c)=50 times10(exp 3) and 1times 10(exp 6). The angles of attack are 5 and 15 degrees at the low and the moderate Reynolds number cases respectively. The three-dimensional unsteady compressible Navier-Stokes equations are solved using higher order compact schemes. The flow field in the low Reynolds number case consists of a long separation bubble near the leading-edge region and an attached boundary layer on the aft part of the airfoil. The shear layer that formed in the separated region persisted up to the end of the airfoil. The roles of the turbulent diffusion, advection, and dissipation terms in the turbulent kinetic-energy balance equation change as the boundary layer evolves over the airfoil. In the higher Reynolds number case, the leading-edge separation bubble is very small in length and in height. A fully developed turbulent boundary layer is observed in a short distance downstream of the reattachment point. The boundary layer velocity near the wall gradually decreases along the airfoil. Eventually, the boundary layer separates near the trailing edge. The Reynolds stresses peak in the outer part of the boundary layer and the maximum amplitude also gradually increases along the chord.

Vertical axis wind turbine airfoil

Science.gov (United States)

Krivcov, Vladimir; Krivospitski, Vladimir; Maksimov, Vasili; Halstead, Richard; Grahov, Jurij Vasiljevich

2012-12-18

A vertical axis wind turbine airfoil is described. The wind turbine airfoil can include a leading edge, a trailing edge, an upper curved surface, a lower curved surface, and a centerline running between the upper surface and the lower surface and from the leading edge to the trailing edge. The airfoil can be configured so that the distance between the centerline and the upper surface is the same as the distance between the centerline and the lower surface at all points along the length of the airfoil. A plurality of such airfoils can be included in a vertical axis wind turbine. These airfoils can be vertically disposed and can rotate about a vertical axis.

Generalized quantal equation of motion

International Nuclear Information System (INIS)

Morsy, M.W.; Embaby, M.

1986-07-01

In the present paper, an attempt is made for establishing a generalized equation of motion for quantal objects, in which intrinsic self adjointness is naturally built in, independently of any prescribed representation. This is accomplished by adopting Hamilton's principle of least action, after incorporating, properly, the quantal features and employing the generalized calculus of variations, without being restricted to fixed end points representation. It turns out that our proposed equation of motion is an intrinsically self-adjoint Euler-Lagrange's differential equation that ensures extremization of the quantal action as required by Hamilton's principle. Time dependence is introduced and the corresponding equation of motion is derived, in which intrinsic self adjointness is also achieved. Reducibility of the proposed equation of motion to the conventional Schroedinger equation is examined. The corresponding continuity equation is established, and both of the probability density and the probability current density are identified. (author)

Parametric analyses for synthetic jet control on separation and stall over rotor airfoil

Directory of Open Access Journals (Sweden)

Zhao Guoqing

2014-10-01

Full Text Available Numerical simulations are performed to investigate the effects of synthetic jet control on separation and stall over rotor airfoils. The preconditioned and unsteady Reynolds-averaged Navier–Stokes equations coupled with a k − ω shear stream transport turbulence model are employed to accomplish the flowfield simulation of rotor airfoils under jet control. Additionally, a velocity boundary condition modeled by a sinusoidal function is developed to fulfill the perturbation effect of periodic jets. The validity of the present CFD procedure is evaluated by the simulated results of an isolated synthetic jet and the jet control case for airfoil NACA0015. Then, parametric analyses are conducted specifically for an OA213 rotor airfoil to investigate the effects of jet parameters (forcing frequency, jet location and momentum coefficient, jet direction, and distribution of jet arrays on the control effect of the aerodynamic characteristics of a rotor airfoil. Preliminary results indicate that the efficiency of jet control can be improved with specific frequencies (the best lift-drag ratio at F+ = 2.0 and jet angles (40° or 75° when the jets are located near the separation point of the rotor airfoil. Furthermore, as a result of a suitable combination of jet arrays, the lift coefficient of the airfoil can be improved by nearly 100%, and the corresponding drag coefficient decreased by 26.5% in comparison with the single point control case.

Aerodynamics of a thin airfoil flying over and in proximity to a wavy-wall surface. ; Lifting surface theory

Energy Technology Data Exchange (ETDEWEB)

Ando, S [Nagoya University, Nagoya (Japan); Ichikawa, M [Government Industrial Research Institute, Nagoya, Nagoya (Japan)

1991-05-04

Aerodynamic characteristics of a thin airfoil flying over and in proximity to a wavy-wall surface such as uneven ground or water surface were analyzed two-dimensionally by lifting surface theory in the simplest fundamental case only. The theoretical equation was simplified assuming that flow is inviscid and incompressible, all disturbances are sufficiently small, the wall surface is sinusoidal and rigid, and the wall moves in the same direction as free stream but with a constant velocity different from that of the stream. The equation was verified in the case where an airfoil with a constant angle-of-attack flies over a flat ground surface, and calculations were made with a set of important parameters such as mean airfoil height from the wall, wave length of the wall surface and the wall velocity. The whole effect of wavy wall proximity was divided into the first and second-order ground effects. The first one was just Kemp{prime}s upwash problem, and the second one was revealed through the present study which becomes significant for lower airfoil heights. 18 refs., 5 figs.

Numerical Study on Turbulent Airfoil Noise with High-Order Schemes

DEFF Research Database (Denmark)

Zhu, Wei Jun; Shen, Wen Zhong; Sørensen, Jens Nørkær

2009-01-01

step, the incompressible pressure and velocity form input to the acoustic equations. In this paper, sound generation from a NACA 0012 airfoil in turbulent flow condition is studied. The noise source regions are found at the trailing edge and the strength of the sources is depended on the Reynolds...

Pressure distribution over an NACA 23012 airfoil with an NACA 23012 external-airfoil flap

Science.gov (United States)

Wenzinger, Carl J

1938-01-01

Report presents the results of pressure-distribution tests of an NACA 23012 airfoil with an NACA 23012 external airfoil flap made in the 7 by 10-foot wind tunnel. The pressures were measured on the upper and lower surfaces at one chord section on both the main airfoil and on the flap for several different flap deflections and at several angles of attack. A test installation was used in which the airfoil was mounted horizontally in the wind tunnel between vertical end planes so that two-dimensional flow was approximated. The data are presented in the form of pressure-distribution diagrams and as graphs of calculated coefficients for the airfoil-and-flap combination and for the flap alone.

Turbulent flow simulation of the NREL S809 airfoil

Energy Technology Data Exchange (ETDEWEB)

Guerri, Ouahiba; Bouhadef, Khadidja; Harhad, Ameziane

2006-05-15

Numerical computations are carried out for the NREL S809 airfoil. The flow is modelled using an unsteady incompressible Reynolds Averaged Navier-Stokes solver. Two turbulence models (SST {kappa}/{omega}of Menter and RNG {kappa}/{epsilon}) are applied to close the RANS equations. All computations are performed assuming fully turbulent flow. The flow field is analyzed at various angles of attack from 0 to 20 degrees. Lift and drag forces are obtained from the computations by integrating the pressure and shear stress over the blade surface. The performance of the two turbulence models is compared and the influence of the free stream turbulence intensity is checked. The results confirm the satisfactory performance of the SST {kappa}/{omega} model of Menter for modelling turbulent flow around airfoils. (author)

Compressible flows with periodic vortical disturbances around lifting airfoils. Ph.D. Thesis - Notre Dame Univ.

Science.gov (United States)

Scott, James R.

1991-01-01

A numerical method is developed for solving periodic, three-dimensional, vortical flows around lifting airfoils in subsonic flow. The first-order method that is presented fully accounts for the distortion effects of the nonuniform mean flow on the convected upstream vortical disturbances. The unsteady velocity is split into a vortical component which is a known function of the upstream flow conditions and the Lagrangian coordinates of the mean flow, and an irrotational field whose potential satisfies a nonconstant-coefficient, inhomogeneous, convective wave equation. Using an elliptic coordinate transformation, the unsteady boundary value problem is solved in the frequency domain on grids which are determined as a function of the Mach number and reduced frequency. The numerical scheme is validated through extensive comparisons with known solutions to unsteady vortical flow problems. In general, it is seen that the agreement between the numerical and analytical results is very good for reduced frequencies ranging from 0 to 4, and for Mach numbers ranging from .1 to .8. Numerical results are also presented for a wide variety of flow configurations for the purpose of determining the effects of airfoil thickness, angle of attack, camber, and Mach number on the unsteady lift and moment of airfoils subjected to periodic vortical gusts. It is seen that each of these parameters can have a significant effect on the unsteady airfoil response to the incident disturbances, and that the effect depends strongly upon the reduced frequency and the dimensionality of the gust. For a one-dimensional (transverse) or two-dimensional (transverse and longitudinal) gust, the results indicate that airfoil thickness increases the unsteady lift and moment at the low reduced frequencies but decreases it at the high reduced frequencies. The results show that an increase in airfoil Mach number leads to a significant increase in the unsteady lift and moment for the low reduced frequencies, but a

A new solution-adaptive grid generation method for transonic airfoil flow calculations

Science.gov (United States)

Nakamura, S.; Holst, T. L.

1981-01-01

The clustering algorithm is controlled by a second-order, ordinary differential equation which uses the airfoil surface density gradient as a forcing function. The solution to this differential equation produces a surface grid distribution which is automatically clustered in regions with large gradients. The interior grid points are established from this surface distribution by using an interpolation scheme which is fast and retains the desirable properties of the original grid generated from the standard elliptic equation approach.

Profile catalogue for airfoil sections based on 3D

Energy Technology Data Exchange (ETDEWEB)

Bertagnolio, F.; Soerensen, Niels N.; Johansen, Jeppe

2006-12-15

This report is a continuation of the Wind Turbine Airfoil Catalogue which objective was, firstly to provide a database of aerodynamic characteristics for a wide range of airfoil profiles aimed at wind turbine applications, and secondly to test the two-dimensional Navier-Stokes solver EllipSys2D by comparing its results with experimental data. In the present work, the original two-dimensional results are compared with three-dimensional calculations as it was surmised that the two-dimensional assumption might be in some cases responsible for discrepancies between the numerical flow solution and the actual fluid flow, and thereby the incorrect prediction of airfoil characteristics. In addition, other features of the flow solver, such as transition and turbulence modelling, and their influence onto the numerical results are investigated. Conclusions are drawn regarding the evaluation of airfoil aerodynamic characteristics, as well as the use of the Navier-Stokes solver for fluid flow calculations in general. (au)

Simple Parametric Model for Airfoil Shape Description

Science.gov (United States)

Ziemkiewicz, David

2017-12-01

We show a simple, analytic equation describing a class of two-dimensional shapes well suited for representation of aircraft airfoil profiles. Our goal was to create a description characterized by a small number of parameters with easily understandable meaning, providing a tool to alter the shape with optimization procedures as well as manual tweaks by the designer. The generated shapes are well suited for numerical analysis with 2D flow solving software such as XFOIL.

A Numerical Study of Aerodynamic Performance and Noise of a Bionic Airfoil Based on Owl Wing

Directory of Open Access Journals (Sweden)

Xiaomin Liu

2014-08-01

Full Text Available Noise reduction and efficiency enhancement are the two important directions in the development of the multiblade centrifugal fan. In this study, we attempt to develop a bionic airfoil based on the owl wing and investigate its aerodynamic performance and noise-reduction mechanism at the relatively low Reynolds number. Firstly, according to the geometric characteristics of the owl wing, a bionic airfoil is constructed as the object of study at Reynolds number of 12,300. Secondly, the large eddy simulation (LES with the Smagorinsky model is adopted to numerically simulate the unsteady flow fields around the bionic airfoil and the standard NACA0006 airfoil. And then, the acoustic sources are extracted from the unsteady flow field data, and the Ffowcs Williams-Hawkings (FW-H equation based on Lighthill's acoustic theory is solved to predict the propagation of these acoustic sources. The numerical results show that the lift-to-drag ratio of bionic airfoil is higher than that of the traditional NACA 0006 airfoil because of its deeply concave lower surface geometry. Finally, the sound field of the bionic airfoil is analyzed in detail. The distribution of the A-weighted sound pressure levels, the scaled directivity of the sound, and the distribution of dP/dt on the airfoil surface are provided so that the characteristics of the acoustic sources could be revealed.

On the acoustic signature of tandem airfoils: The sound of an elastic airfoil in the wake of a vortex generator

International Nuclear Information System (INIS)

Manela, A.

2016-01-01

The acoustic signature of an acoustically compact tandem airfoil setup in uniform high-Reynolds number flow is investigated. The upstream airfoil is considered rigid and is actuated at its leading edge with small-amplitude harmonic pitching motion. The downstream airfoil is taken passive and elastic, with its motion forced by the vortex-street excitation of the upstream airfoil. The non-linear near-field description is obtained via potential thin-airfoil theory. It is then applied as a source term into the Powell-Howe acoustic analogy to yield the far-field dipole radiation of the system. To assess the effect of downstream-airfoil elasticity, results are compared with counterpart calculations for a non-elastic setup, where the downstream airfoil is rigid and stationary. Depending on the separation distance between airfoils, airfoil-motion and airfoil-wake dynamics shift between in-phase (synchronized) and counter-phase behaviors. Consequently, downstream airfoil elasticity may act to amplify or suppress sound through the direct contribution of elastic-airfoil motion to the total signal. Resonance-type motion of the elastic airfoil is found when the upstream airfoil is actuated at the least stable eigenfrequency of the downstream structure. This, again, results in system sound amplification or suppression, depending on the separation distance between airfoils. With increasing actuation frequency, the acoustic signal becomes dominated by the direct contribution of the upstream airfoil motion, whereas the relative contribution of the elastic airfoil to the total signature turns negligible.

On the acoustic signature of tandem airfoils: The sound of an elastic airfoil in the wake of a vortex generator

Energy Technology Data Exchange (ETDEWEB)

Manela, A. [Faculty of Aerospace Engineering, Technion - Israel Institute of Technology, Haifa 32000 (Israel)

2016-07-15

The acoustic signature of an acoustically compact tandem airfoil setup in uniform high-Reynolds number flow is investigated. The upstream airfoil is considered rigid and is actuated at its leading edge with small-amplitude harmonic pitching motion. The downstream airfoil is taken passive and elastic, with its motion forced by the vortex-street excitation of the upstream airfoil. The non-linear near-field description is obtained via potential thin-airfoil theory. It is then applied as a source term into the Powell-Howe acoustic analogy to yield the far-field dipole radiation of the system. To assess the effect of downstream-airfoil elasticity, results are compared with counterpart calculations for a non-elastic setup, where the downstream airfoil is rigid and stationary. Depending on the separation distance between airfoils, airfoil-motion and airfoil-wake dynamics shift between in-phase (synchronized) and counter-phase behaviors. Consequently, downstream airfoil elasticity may act to amplify or suppress sound through the direct contribution of elastic-airfoil motion to the total signal. Resonance-type motion of the elastic airfoil is found when the upstream airfoil is actuated at the least stable eigenfrequency of the downstream structure. This, again, results in system sound amplification or suppression, depending on the separation distance between airfoils. With increasing actuation frequency, the acoustic signal becomes dominated by the direct contribution of the upstream airfoil motion, whereas the relative contribution of the elastic airfoil to the total signature turns negligible.

Experimental verification of the new RISOe-A1 airfoil family for wind turbines

Energy Technology Data Exchange (ETDEWEB)

Dahl, K S; Fuglsang, P; Antoniou, I [Risoe National Lab., Roskilde (Denmark)

1999-03-01

This paper concerns the experimental verification of a new airfoil family for wind turbines. The family consist of airfoils in the relative thickness range from 15% to 30%. Three airfoils, Risoe-A1-18, Risoe-A1-21, and Risoe-A1-24 were tested in a wind tunnel. The verification consisted of both static and dynamic measurements. Here, the static results are presented for a Reynolds number of 1.6x10{sup 6} for the following airfoil configurations: smooth surface (all three airfoils) and Risoe-A1-24 mounted with leading edge roughness, vortex generators, and Gurney-flaps, respectively. All three airfoils have constant lift curve slope and almost constant drag coefficient until the maximum lift coefficient of about 1.4 is reached. The experimental results are compared with corresponding computational from the general purpose flow solver, EllipSys2D, showing good agreement. (au)

VISUALISASI DISTRIBUSI TEKANAN PADA AIRFOIL JOUKOWSKY

Directory of Open Access Journals (Sweden)

Eddy Maryonoto

2009-02-01

Full Text Available The goal of this research is to develop a computer based system that can beused to visualize pressure distribution on the Joukowsky's airfoil and streamlinespattern around the airfoil. The pressure on the airfoil is calculdted usingformulasderived from potensial theory. Visualization of pressure distribution implementedby using color gradation technique and coded b.v using Borland Delphi 6programming language. The result of the test shotus lhat lhe system has performedperfectly. Pressure dislribution on some kinds of JoukowslE's airfoil shapes andstresmlines pattern around the airfoils can be presenled and seen clearly byusing this visualization system, where the paltern of the pressure distribution onthe airfoil marked by color gradation.

Efficient solution of the non-linear Reynolds equation for compressible fluid using the finite element method

DEFF Research Database (Denmark)

Larsen, Jon Steffen; Santos, Ilmar

2015-01-01

An efficient finite element scheme for solving the non-linear Reynolds equation for compressible fluid coupled to compliant structures is presented. The method is general and fast and can be used in the analysis of airfoil bearings with simplified or complex foil structure models. To illustrate...

Theory of viscous transonic flow over airfoils at high Reynolds number

Science.gov (United States)

Melnik, R. E.; Chow, R.; Mead, H. R.

1977-01-01

This paper considers viscous flows with unseparated turbulent boundary layers over two-dimensional airfoils at transonic speeds. Conventional theoretical methods are based on boundary layer formulations which do not account for the effect of the curved wake and static pressure variations across the boundary layer in the trailing edge region. In this investigation an extended viscous theory is developed that accounts for both effects. The theory is based on a rational analysis of the strong turbulent interaction at airfoil trailing edges. The method of matched asymptotic expansions is employed to develop formal series solutions of the full Reynolds equations in the limit of Reynolds numbers tending to infinity. Procedures are developed for combining the local trailing edge solution with numerical methods for solving the full potential flow and boundary layer equations. Theoretical results indicate that conventional boundary layer methods account for only about 50% of the viscous effect on lift, the remaining contribution arising from wake curvature and normal pressure gradient effects.

Navier-Stokes calculations on multi-element airfoils using a chimera-based solver

Science.gov (United States)

Jasper, Donald W.; Agrawal, Shreekant; Robinson, Brian A.

1993-01-01

A study of Navier-Stokes calculations of flows about multielement airfoils using a chimera grid approach is presented. The chimera approach utilizes structured, overlapped grids which allow great flexibility of grid arrangement and simplifies grid generation. Calculations are made for two-, three-, and four-element airfoils, and modeling of the effect of gap distance between elements is demonstrated for a two element case. Solutions are obtained using the thin-layer form of the Reynolds averaged Navier-Stokes equations with turbulence closure provided by the Baldwin-Lomax algebraic model or the Baldwin-Barth one equation model. The Baldwin-Barth turbulence model is shown to provide better agreement with experimental data and to dramatically improve convergence rates for some cases. Recently developed, improved farfield boundary conditions are incorporated into the solver for greater efficiency. Computed results show good comparison with experimental data which include aerodynamic forces, surface pressures, and boundary layer velocity profiles.

Virtual incidence effect on rotating airfoils in Darrieus wind turbines

International Nuclear Information System (INIS)

Bianchini, Alessandro; Balduzzi, Francesco; Ferrara, Giovanni; Ferrari, Lorenzo

2016-01-01

Highlights: • Novel methods to reduce CFD results into 1D aerodynamic parameters. • Assessment of the virtual incidence (VI) effect on Darrieus VAWT blades. • It is shown that blades experience a virtual AoA variation with respect to theoretical expectations. • Real AoAs are calculated for different airfoils in motion and compared to BEM predictions. - Abstract: Small Darrieus wind turbines are one of the most interesting emerging technologies in the renewable energies scenario, even if they still are characterized by lower efficiencies than those of conventional horizontal-axis wind turbines due to the more complex aerodynamics involved in their functioning. In case of small rotors, in which the chord-to-radius ratios are generally high not to limit the blade Reynolds number, the performance of turbine blades has been suggested to be moreover influenced by the so-called “flow curvature effects”. Recent works have indeed shown that the curved flowpath encountered by the blades makes them work like virtually cambered airfoils in a rectilinear flow. In the present study, focus is instead given to a further effect that is generated in reason of the curved streamline incoming on the blades, i.e. an extra-incidence seen by the airfoil, generally referred to as “virtual incidence”. In detail, a novel computational method to define the incidence angle has been applied to unsteady CFD simulations of three airfoils in a Darrieus-like motion and their effective angles of attack have been compared to theoretical expectations. The analysis confirmed the presence of an additional virtual incidence on the airfoils and quantified it for different airfoils, chord-to-radius ratios and tip-speed ratios. A comparative discussion on BEM prediction capabilities is finally reported in the study.

Airfoil shape for a turbine nozzle

Science.gov (United States)

Burdgick, Steven Sebastian; Patik, Joseph Francis; Itzel, Gary Michael

2002-01-01

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.

Decomposing the aerodynamic forces of low-Reynolds flapping airfoils

Science.gov (United States)

Moriche, Manuel; Garcia-Villalba, Manuel; Flores, Oscar

2016-11-01

We present direct numerical simulations of flow around flapping NACA0012 airfoils at relatively small Reynolds numbers, Re = 1000 . The simulations are carried out with TUCAN, an in-house code that solves the Navier-Stokes equations for an incompressible flow with an immersed boundary method to model the presence of the airfoil. The motion of the airfoil is composed of a vertical translation, heaving, and a rotation about the quarter of the chord, pitching. Both motions are prescribed by sinusoidal laws, with a reduced frequency of k = 1 . 41 , a pitching amplitude of 30deg and a heaving amplitude of one chord. Both, the mean pitch angle and the phase shift between pitching and heaving motions are varied, to build a database with 18 configurations. Four of these cases are analysed in detail using the force decomposition algorithm of Chang (1992) and Martín Alcántara et al. (2015). This method decomposes the total aerodynamic force into added-mass (translation and rotation of the airfoil), a volumetric contribution from the vorticity (circulatory effects) and a surface contribution proportional to viscosity. In particular we will focus on the second, analysing the contribution of the leading and trailing edge vortices that typically appear in these flows. This work has been supported by the Spanish MINECO under Grant TRA2013-41103-P. The authors thankfully acknowledge the computer resources provided by the Red Española de Supercomputacion.

Airfoil shape for a turbine bucket

Science.gov (United States)

Hyde, Susan Marie; By, Robert Romany; Tressler, Judd Dodge; Schaeffer, Jon Conrad; Sims, Calvin Levy

2005-06-28

Third stage turbine buckets have airfoil profiles substantially in accordance with Cartesian coordinate values of X, Y and Z set forth Table I wherein X and Y values are in inches and the Z values are non-dimensional values from 0 to 0.938 convertible to Z distances in inches by multiplying the Z values by the height of the airfoil in inches. The X and Y values are distances which, when connected by smooth continuing arcs, define airfoil profile sections at each distance Z. The profile sections at each distance Z are joined smoothly to one another to form a complete airfoil shape. The X and Y distances may be scalable as a function of the same constant or number to provide a scaled up or scaled down airfoil section for the bucket. The nominal airfoil given by the X, Y and Z distances lies within an envelop of .+-.0.150 inches in directions normal to the surface of the airfoil.

Dichotomies for generalized ordinary differential equations and applications

Science.gov (United States)

Bonotto, E. M.; Federson, M.; Santos, F. L.

2018-03-01

In this work we establish the theory of dichotomies for generalized ordinary differential equations, introducing the concepts of dichotomies for these equations, investigating their properties and proposing new results. We establish conditions for the existence of exponential dichotomies and bounded solutions. Using the correspondences between generalized ordinary differential equations and other equations, we translate our results to measure differential equations and impulsive differential equations. The fact that we work in the framework of generalized ordinary differential equations allows us to manage functions with many discontinuities and of unbounded variation.

Uncertainty Quantification and Bifurcation Analysis of an Airfoil with Multiple Nonlinearities

Directory of Open Access Journals (Sweden)

Haitao Liao

2013-01-01

Full Text Available In order to calculate the limit cycle oscillations and bifurcations of nonlinear aeroelastic system, the problem of finding periodic solutions with maximum vibration amplitude is transformed into a nonlinear optimization problem. An algebraic system of equations obtained by the harmonic balance method and the stability condition derived from the Floquet theory are used to construct the general nonlinear equality and inequality constraints. The resulting constrained maximization problem is then solved by using the MultiStart algorithm. Finally, the proposed approach is validated, and the effects of structural parameter uncertainty on the limit cycle oscillations and bifurcations of an airfoil with multiple nonlinearities are studied. Numerical examples show that the coexistence of multiple nonlinearities may lead to low amplitude limit cycle oscillation.

Airfoil characteristics for wind turbines

Energy Technology Data Exchange (ETDEWEB)

Bak, C; Fuglsang, P; Soerensen, N N; Aagaard Madsen, H [Risoe National Lab., Roskilde (Denmark); Shen, Wen Zhong; Noerkaer Soerensen, J [Technical Univ. of Denmark, Lyngby (Denmark)

1999-03-01

Airfoil characteristics for use in the Blade Element Momentum (BEM) method calculating the forces on Horizontal Axis Wind Turbines (HAWT) are derived by use of systematic methods. The investigation and derivation of the airfoil characteristics are based on four different methods: 1) Inverse momentum theory, 2) Actuator disc theory, 3) Numerical optimisation and 4) Quasi-3D CFD computations. The two former methods are based on 3D CFD computations and wind tunnel measurements on a 41-m full-scale rotor with LM 19.1 blades. The derived airfoil characteristics show that the lift coefficient in stall at the tip is low and that it is high at the root compared to 2D airfoil characteristics. The use of these characteristics in aeroelastic calculations shows a good agreement in power and flap moments with measurements. Furthermore, a fatigue analysis shows a reduction in the loads of up to 15 % compared to a commonly used set of airfoil characteristics. The numerical optimisation is based on both the 3D CFD computations and measurements on a 41-m rotor with LM 19.1 and LM 19.0 blades, respectively. The method requires power and loads from a turbine and is promising since a set of lift and drag curves is derived that can be used to calculate mean values of power and loads. The lift in stall at the tip is low and at the root it is high compared to 2D airfoil characteristics. In particular the power curves were well calculated by use of the optimised airfoil characteristics. In the quasi-3D CFD computations, the airfoil characteristics are derived directly. This Navier-Stokes model takes into account rotational and 3D effects. The model enables the study of the rotational effect of a rotor blade at computing costs similar to what is typical for 2D airfoil calculations. The depicted results show that the model is capable of determining the correct qualitative behaviour for airfoils subject to rotation. The method shows that lift is high at the root compared to 2D airfoil

Self-induced vibrations of a DU96-W-180 airfoil in stall

DEFF Research Database (Denmark)

Skrzypinski, Witold Robert; Gaunaa, Mac; Sørensen, Niels N.

2014-01-01

This work presents an analysis of two-dimensional (2D) and three-dimensional (3D) non-moving, prescribed motion and elastically mounted airfoil computational fluid dynamics (CFD) computations. The elastically mounted airfoil computations were performed by means of a 2D structural model with two...... degrees of freedom. The computations aimed at investigating the mechanisms of both vortex-induced and stall-induced vibrations related to a wind turbine blade at standstill conditions. In this work, a DU96-W-180 airfoil was used in the angle-of-attack region potentially corresponding to stallinduced...... vibrations. The analysis showed significant differences between the aerodynamic stability limits predicted by 2D and 3D CFD computations. A general agreement was reached between the prescribed motion and elastically mounted airfoil computations. 3D computations indicated that vortex-induced vibrations...

Viscous-inviscid method for the simulation of turbulent unsteady wind turbine airfoil flow

Energy Technology Data Exchange (ETDEWEB)

Bermudez, L.; Velazquez, A.; Matesanz, A. [Thermal Engineering Area, Carlos III University of Madrid, Avd. Universidad 30, 28911 Leganes, Madrid (Spain)

2002-06-01

A Viscous-inviscid interaction method is presented that allows for the simulation of unsteady airfoil flow in the context of wind turbine applications. The method couples a 2-D external unsteady potential flow to a 2-D unsteady turbulent boundary layer. The separation point on the airfoil leeward side is determined in a self-consistent way from the boundary-layer equations, and the separated flow region is modelled independently. Wake shape and motion are also determined in a self-consistent way, while an unsteady Kutta condition is implemented. The method is able to deal with attached flow and light stall situations characterised by unsteady turbulent boundary-layer separation size up to 50% of the airfoil chord length. The results of the validation campaign show that the method could be used for industrial design purposes because of its numerical robustness, reasonable accuracy, and limited computational time demands.

Turbine airfoil to shround attachment

Science.gov (United States)

Campbell, Christian X; Morrison, Jay A; James, Allister W; Snider, Raymond G; Eshak, Daniel M; Marra, John J; Wessell, Brian J

2014-05-06

A turbine airfoil (31) with an end portion (42) that tapers (44) toward the end (43) of the airfoil. A ridge (46) extends around the end portion. It has proximal (66) and distal (67) sides. A shroud platform (50) is bi-cast onto the end portion around the ridge without bonding. Cooling shrinks the platform into compression (62) on the end portion (42) of the airfoil. Gaps between the airfoil and platform are formed using a fugitive material (56) in the bi-casting stage. These gaps are designed in combination with the taper angle (44) to accommodate differential thermal expansion while maintaining a gas seal along the contact surfaces. The taper angle (44) may vary from lesser on the pressure side (36) to greater on the suction side (38) of the airfoil. A collar portion (52) of the platform provides sufficient contact area for connection stability.

Generalization of Einstein's gravitational field equations

International Nuclear Information System (INIS)

Moulin, Frederic

2017-01-01

The Riemann tensor is the cornerstone of general relativity, but as is well known it does not appear explicitly in Einstein's equation of gravitation. This suggests that the latter may not be the most general equation. We propose here for the first time, following a rigorous mathematical treatment based on the variational principle, that there exists a generalized 4-index gravitational field equation containing the Riemann curvature tensor linearly, and thus the Weyl tensor as well. We show that this equation, written in n dimensions, contains the energy-momentum tensor for matter and that of the gravitational field itself. This new 4-index equation remains completely within the framework of general relativity and emerges as a natural generalization of the familiar 2-index Einstein equation. Due to the presence of the Weyl tensor, we show that this equation contains much more information, which fully justifies the use of a fourth-order theory. (orig.)

Generalization of Einstein's gravitational field equations

Energy Technology Data Exchange (ETDEWEB)

Moulin, Frederic [Ecole Normale Superieure Paris-Saclay, Departement de Physique, Cachan (France)

2017-12-15

The Riemann tensor is the cornerstone of general relativity, but as is well known it does not appear explicitly in Einstein's equation of gravitation. This suggests that the latter may not be the most general equation. We propose here for the first time, following a rigorous mathematical treatment based on the variational principle, that there exists a generalized 4-index gravitational field equation containing the Riemann curvature tensor linearly, and thus the Weyl tensor as well. We show that this equation, written in n dimensions, contains the energy-momentum tensor for matter and that of the gravitational field itself. This new 4-index equation remains completely within the framework of general relativity and emerges as a natural generalization of the familiar 2-index Einstein equation. Due to the presence of the Weyl tensor, we show that this equation contains much more information, which fully justifies the use of a fourth-order theory. (orig.)

Multiple piece turbine airfoil

Science.gov (United States)

Kimmel, Keith D; Wilson, Jr., Jack W.

2010-11-02

A turbine airfoil, such as a rotor blade or a stator vane, for a gas turbine engine, the airfoil formed as a shell and spar construction with a plurality of dog bone struts each mounted within openings formed within the shell and spar to allow for relative motion between the spar and shell in the airfoil chordwise direction while also forming a seal between adjacent cooling channels. The struts provide the seal as well as prevent bulging of the shell from the spar due to the cooling air pressure.

A generalized auxiliary equation method and its application to nonlinear Klein-Gordon and generalized nonlinear Camassa-Holm equations

International Nuclear Information System (INIS)

Yomba, Emmanuel

2008-01-01

With the aid of symbolic computation, a generalized auxiliary equation method is proposed to construct more general exact solutions to two types of NLPDEs. First, we present new family of solutions to a nonlinear Klein-Gordon equation, by using this auxiliary equation method including a new first-order nonlinear ODE with six-degree nonlinear term proposed by Sirendaoreji. Then, we apply an indirect F-function method very close to the F-expansion method to solve the generalized Camassa-Holm equation with fully nonlinear dispersion and fully nonlinear convection C(l,n,p). Taking advantage of the new first-order nonlinear ODE with six degree nonlinear term, this indirect F-function method is used to map the solutions of C(l,n,p) equations to those of that nonlinear ODE. As a result, we can successfully obtain in a unified way, many exact solutions

Analysis of jet-airfoil interaction noise sources by using a microphone array technique

Science.gov (United States)

Fleury, Vincent; Davy, Renaud

2016-03-01

The paper is concerned with the characterization of jet noise sources and jet-airfoil interaction sources by using microphone array data. The measurements were carried-out in the anechoic open test section wind tunnel of Onera, Cepra19. The microphone array technique relies on the convected, Lighthill's and Ffowcs-Williams and Hawkings' acoustic analogy equation. The cross-spectrum of the source term of the analogy equation is sought. It is defined as the optimal solution to a minimal error equation using the measured microphone cross-spectra as reference. This inverse problem is ill-posed yet. A penalty term based on a localization operator is therefore added to improve the recovery of jet noise sources. The analysis of isolated jet noise data in subsonic regime shows the contribution of the conventional mixing noise source in the low frequency range, as expected, and of uniformly distributed, uncorrelated noise sources in the jet flow at higher frequencies. In underexpanded supersonic regime, a shock-associated noise source is clearly identified, too. An additional source is detected in the vicinity of the nozzle exit both in supersonic and subsonic regimes. In the presence of the airfoil, the distribution of the noise sources is deeply modified. In particular, a strong noise source is localized on the flap. For high Strouhal numbers, higher than about 2 (based on the jet mixing velocity and diameter), a significant contribution from the shear-layer near the flap is observed, too. Indications of acoustic reflections on the airfoil are also discerned.

Acoustic radiation due to gust-airfoil and blade-vortex interactions

Energy Technology Data Exchange (ETDEWEB)

Agarwal, R.K. [Wichita State Univ., KS (United States). National Inst. for Aviation Research

2001-07-01

An accurate and efficient method for computing acoustic radiation due to gust-airfoil and blade-vortex interactions is developed. In these types of problems, sound is generated as a result of interaction between the unsteadiness in the flow and the body. The acoustic governing equations are derived by linearizing the compressible unsteady Euler equations about the steady mean flow. From these equations, the frequency domain acoustic equations are obtained assuming a single frequency disturbance. The equations are solved by employing a multi-stage Runge-Kutta finite-volume time-stepping scheme with a fourth-order compact spatial discretization. In the farfield, both the Giles' nonreflecting boundary condition and the perfectly matched layer (PML) absorbing boundary conditions are employed. This report describes the technical approach and shows the results calculated for the interactions. (orig.)

Second Stage Turbine Bucket Airfoil.

Science.gov (United States)

Xu, Liming; Ahmadi, Majid; Humanchuk, David John; Moretto, Nicholas; Delehanty, Richard Edward

2003-05-06

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, 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 bucket.

Third-stage turbine bucket airfoil

Science.gov (United States)

Pirolla, Peter Paul; Siden, Gunnar Leif; Humanchuk, David John; Brassfield, Steven Robert; Wilson, Paul Stuart

2002-01-01

The third-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 coordinates defining the airfoil profile at each distance Z. 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 bucket.

Transonic Airfoil Flow Simulation. Part I: Mesh Generation and Inviscid Method

Directory of Open Access Journals (Sweden)

Vladimir CARDOS

2010-06-01

Full Text Available A calculation method for the subsonic and transonic viscous flow over airfoil using thedisplacement surface concept is described. Part I presents a mesh generation method forcomputational grid and a finite volume method for the time-dependent Euler equations. The inviscidsolution is used for the inviscid-viscous coupling procedure presented in the Part II.

Exact solution for the generalized Telegraph Fisher's equation

International Nuclear Information System (INIS)

Abdusalam, H.A.; Fahmy, E.S.

2009-01-01

In this paper, we applied the factorization scheme for the generalized Telegraph Fisher's equation and an exact particular solution has been found. The exact particular solution for the generalized Fisher's equation was obtained as a particular case of the generalized Telegraph Fisher's equation and the two-parameter solution can be obtained when n=2.

Numerical study of unsteady flows past oscillating airfoils using direct zonal coupling method

International Nuclear Information System (INIS)

Zhang, F.; Khalid, M.

2005-01-01

A direct zonal coupling method was proposed for solving the flows past oscillating airfoils in this study. The entire computational domain was divided into inner and outer zones. The grid in the inner zone is moving with the oscillation of the airfoil, whereas the grid in the outer zone is artificially adjusted to the position consistent with the inner zone grid. The governing equations in the moving frame (the rotation potential energy is included) and those under the stationary frame were applied to inner and outer zones, respectively. By using this kind of treatment, the grid on the zonal interface is 1-to-1 matched. The coupling between the two zones is direct. Both the geometric and flow conservations are entirely satisfied. The NACA0012 and NLR7301 airfoils with oscillations were used as the test cases. The accuracy of the proposed method was demonstrated by the computational results compared with the experimental data.(author)

Conditional Stability of Solitary-Wave Solutions for Generalized Compound KdV Equation and Generalized Compound KdV-Burgers Equation

International Nuclear Information System (INIS)

Zhang Weiguo; Dong Chunyan; Fan Engui

2006-01-01

In this paper, we discuss conditional stability of solitary-wave solutions in the sense of Liapunov for the generalized compound KdV equation and the generalized compound KdV-Burgers equations. Linear stability of the exact solitary-wave solutions is proved for the above two types of equations when the small disturbance of travelling wave form satisfies some special conditions.

A strong viscous–inviscid interaction model for rotating airfoils

DEFF Research Database (Denmark)

Ramos García, Néstor; Sørensen, Jens Nørkær; Shen, Wen Zhong

2014-01-01

Two-dimensional (2D) and quasi-three dimensional (3D), steady and unsteady, viscous–inviscid interactive codes capable of predicting the aerodynamic behavior of wind turbine airfoils are presented. The model is based on a viscous–inviscid interaction technique using strong coupling between...... a boundary-layer trip or computed using an en envelope transition method. Validation of the incompressible 2D version of the code is carried out against measurements and other numerical codes for different airfoil geometries at various Reynolds numbers, ranging from 0.9 ⋅ 106 to 8.2 ⋅ 106. In the quasi-3D...... version, a parametric study on rotational effects induced by the Coriolis and centrifugal forces in the boundary-layer equations shows that the effects of rotation are to decrease the growth of the boundary-layer and delay the onset of separation, hence increasing the lift coefficient slightly while...

Airfoil optimization for unsteady flows with application to high-lift noise reduction

Science.gov (United States)

Rumpfkeil, Markus Peer

The use of steady-state aerodynamic optimization methods in the computational fluid dynamic (CFD) community is fairly well established. In particular, the use of adjoint methods has proven to be very beneficial because their cost is independent of the number of design variables. The application of numerical optimization to airframe-generated noise, however, has not received as much attention, but with the significant quieting of modern engines, airframe noise now competes with engine noise. Optimal control techniques for unsteady flows are needed in order to be able to reduce airframe-generated noise. In this thesis, a general framework is formulated to calculate the gradient of a cost function in a nonlinear unsteady flow environment via the discrete adjoint method. The unsteady optimization algorithm developed in this work utilizes a Newton-Krylov approach since the gradient-based optimizer uses the quasi-Newton method BFGS, Newton's method is applied to the nonlinear flow problem, GMRES is used to solve the resulting linear problem inexactly, and last but not least the linear adjoint problem is solved using Bi-CGSTAB. The flow is governed by the unsteady two-dimensional compressible Navier-Stokes equations in conjunction with a one-equation turbulence model, which are discretized using structured grids and a finite difference approach. The effectiveness of the unsteady optimization algorithm is demonstrated by applying it to several problems of interest including shocktubes, pulses in converging-diverging nozzles, rotating cylinders, transonic buffeting, and an unsteady trailing-edge flow. In order to address radiated far-field noise, an acoustic wave propagation program based on the Ffowcs Williams and Hawkings (FW-H) formulation is implemented and validated. The general framework is then used to derive the adjoint equations for a novel hybrid URANS/FW-H optimization algorithm in order to be able to optimize the shape of airfoils based on their calculated far

Second-stage turbine bucket airfoil

Science.gov (United States)

Wang, John Zhiqiang; By, Robert Romany; Sims, Calvin L.; Hyde, Susan Marie

2002-01-01

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.

Design of a family of new advanced airfoils for low wind class turbines

International Nuclear Information System (INIS)

Grasso, Francesco

2014-01-01

In order to maximize the ratio of energy capture and reduce the cost of energy, the selection of the airfoils to be used along the blade plays a crucial role. Despite the general usage of existing airfoils, more and more, families of airfoils specially tailored for specific applications are developed. The present research is focused on the design of a new family of airfoils to be used for the blade of one megawatt wind turbine working in low wind conditions. A hybrid optimization scheme has been implemented, combining together genetic and gradient based algorithms. Large part of the work is dedicated to present and discuss the requirements that needed to be satisfied in order to have a consistent family of geometries with high efficiency, high lift and good structural characteristics. For each airfoil, these characteristics are presented and compared to the ones of existing airfoils. Finally, the aerodynamic design of a new blade for low wind class turbine is illustrated and compared to a reference shape developed by using existing geometries. Due to higher lift performance, the results show a sensitive saving in chords, wetted area and so in loads in idling position

Generalized Fermat equations: A miscellany

NARCIS (Netherlands)

Bennett, M.A.; Chen, I.; Dahmen, S.R.; Yazdani, S.

2015-01-01

This paper is devoted to the generalized Fermat equation xp + yq = zr, where p, q and r are integers, and x, y and z are nonzero coprime integers. We begin by surveying the exponent triples (p, q, r), including a number of infinite families, for which the equation has been solved to date, detailing

A generalized simplest equation method and its application to the Boussinesq-Burgers equation.

Science.gov (United States)

Sudao, Bilige; Wang, Xiaomin

2015-01-01

In this paper, a generalized simplest equation method is proposed to seek exact solutions of nonlinear evolution equations (NLEEs). In the method, we chose a solution expression with a variable coefficient and a variable coefficient ordinary differential auxiliary equation. This method can yield a Bäcklund transformation between NLEEs and a related constraint equation. By dealing with the constraint equation, we can derive infinite number of exact solutions for NLEEs. These solutions include the traveling wave solutions, non-traveling wave solutions, multi-soliton solutions, rational solutions, and other types of solutions. As applications, we obtained wide classes of exact solutions for the Boussinesq-Burgers equation by using the generalized simplest equation method.

Root region airfoil for wind turbine

Science.gov (United States)

Tangler, James L.; Somers, Dan M.

1995-01-01

A thick airfoil for the root region of the blade of a wind turbine. The airfoil has a thickness in a range from 24%-26% and a Reynolds number in a range from 1,000,000 to 1,800,000. The airfoil has a maximum lift coefficient of 1.4-1.6 that has minimum sensitivity to roughness effects.

Airfoil selection methodology for Small Wind Turbines

DEFF Research Database (Denmark)

Salgado Fuentes, Valentin; Troya, Cesar; Moreno, Gustavo

2016-01-01

On wind turbine technology, the aerodynamic performance is fundamental to increase efficiency. Nowadays there are several databases with airfoils designed and simulated for different applications; that is why it is necessary to select those suitable for a specific application. This work presents...... a new methodology for airfoil selection used in feasibility and optimization of small wind turbines with low cut-in speed. On the first stage, airfoils data is tested on XFOIL software to check its compatibility with the simulator; then, arithmetic mean criteria is recursively used to discard...... underperformed airfoils; the best airfoil data was exported to Matlab for a deeper analysis. In the second part, data points were interpolated using "splines" to calculate glide ratio and stability across multiple angles of attack, those who present a bigger steadiness were conserved. As a result, 3 airfoils...

The 'generalized Balescu-Lenard' transport equations

International Nuclear Information System (INIS)

Mynick, H.E.

1990-01-01

The transport equations arising from the 'generalized Balescu-Lenard' collision operator are obtained and some of their properties examined. The equations contain neoclassical and turbulent transport as two special cases having the same structure. The resultant theory offers a possible explanation for a number of results not well understood, including the anomalous pinch, observed ratios of Q/ΓT on TFTR, and numerical reproduction of ASDEX profiles by a model for turbulent transport invoked without derivation, but by analogy with neoclassical theory. The general equations are specialized to consideration of a number of particular transport mechanisms of interest. (author). Letter-to-the-editor. 10 refs

Generalization of the Knizhnik-Zamolodchikov-equations

International Nuclear Information System (INIS)

Alekseev, A.Yu.; Recknagel, A.; Schomerus, V.

1996-09-01

In this letter we introduce a generalization of the Knizhnik-Zamolodchikov equations from affine Lie algebras to a wide class of conformal field theories (not necessarily rational). The new equations describe correlation functions of primary fields and of a finite number of their descendents. Our proposal is based on Nahm's concept of small spaces which provide adequate substitutes for the lowest energy subspaces in modules of affine Lie algebras. We explain how to construct the first order differential equations and investigate properties of the associated connections, thereby preparing the grounds for an analysis of quantum symmetries. The general considerations are illustrated in examples of Virasoro minimal models. (orig.)

Nonlinear aeroelastic behavior of compliant airfoils

International Nuclear Information System (INIS)

Thwapiah, G; Campanile, L F

2010-01-01

Since the beginning of aviation and up to the present time, airfoils have always been built as rigid structures. They are designed to fly under their divergence speed in order to avoid static aeroelastic instabilities and the resulting large deformations, which are not compatible with the typically low compliance of such airfoils. In recent years, research on airfoil morphing has generated interest in innovative ideas like the use of compliant systems, i.e. systems built to allow for large deformations without failure, in airfoil construction. Such systems can operate in the neighborhood of divergence and take advantage of large aeroelastic servo-effects. This, in turn, allows compact, advanced actuators to control the airfoil's deformation and loads, and hence complement or even replace conventional flaps. In order to analyze and design such compliant, active aeroelastic structures a nonlinear approach to static aeroelasticity is needed, which takes into account the effect of large deformations on aerodynamics and structure. Such an analytical approach is presented in this paper and applied to a compliant passive airfoil as the preliminary step in the realization of a piezoelectrically driven, active aeroelastic airfoil. Wind tunnel test results are also presented and compared with the analytic prediction. The good agreement and the observed behavior in the wind tunnel give confidence in the potential of this innovative idea

Nonlinear aeroelastic behavior of compliant airfoils

Science.gov (United States)

Thwapiah, G.; Campanile, L. F.

2010-03-01

Since the beginning of aviation and up to the present time, airfoils have always been built as rigid structures. They are designed to fly under their divergence speed in order to avoid static aeroelastic instabilities and the resulting large deformations, which are not compatible with the typically low compliance of such airfoils. In recent years, research on airfoil morphing has generated interest in innovative ideas like the use of compliant systems, i.e. systems built to allow for large deformations without failure, in airfoil construction. Such systems can operate in the neighborhood of divergence and take advantage of large aeroelastic servo-effects. This, in turn, allows compact, advanced actuators to control the airfoil's deformation and loads, and hence complement or even replace conventional flaps. In order to analyze and design such compliant, active aeroelastic structures a nonlinear approach to static aeroelasticity is needed, which takes into account the effect of large deformations on aerodynamics and structure. Such an analytical approach is presented in this paper and applied to a compliant passive airfoil as the preliminary step in the realization of a piezoelectrically driven, active aeroelastic airfoil. Wind tunnel test results are also presented and compared with the analytic prediction. The good agreement and the observed behavior in the wind tunnel give confidence in the potential of this innovative idea.

The aerodynamic design of an advanced rotor airfoil

Science.gov (United States)

Blackwell, J. A., Jr.; Hinson, B. L.

1978-01-01

An advanced rotor airfoil, designed utilizing supercritical airfoil technology and advanced design and analysis methodology is described. The airfoil was designed subject to stringent aerodynamic design criteria for improving the performance over the entire rotor operating regime. The design criteria are discussed. The design was accomplished using a physical plane, viscous, transonic inverse design procedure, and a constrained function minimization technique for optimizing the airfoil leading edge shape. The aerodynamic performance objectives of the airfoil are discussed.

Exact solutions of generalized Zakharov and Ginzburg-Landau equations

International Nuclear Information System (INIS)

Zhang Jinliang; Wang Mingliang; Gao Kequan

2007-01-01

By using the homogeneous balance principle, the exact solutions of the generalized Zakharov equations and generalized Ginzburg-Landau equation are obtained with the aid of a set of subsidiary higher-order ordinary differential equations (sub-equations for short)

New airfoils for small horizontal axis wind turbines

Energy Technology Data Exchange (ETDEWEB)

Giguere, P.; Selig, M.S. [Univ. of Illinois, Urbana, IL (United States)

1997-12-31

In a continuing effort to enhance the performance of small energy systems, one root airfoil and three primary airfoils were specifically designed for small horizontal axis wind turbines. These airfoils are intended primarily for 1-10 kW variable-speed wind turbines for both conventional (tapered/twisted) or pultruded blades. The four airfoils were wind-tunnel tested at Reynolds numbers between 100,000 and 500,000. Tests with simulated leading-edge roughness were also conducted. The results indicate that small variable-speed wind turbines should benefit from the use of the new airfoils which provide enhanced lift-to-drag ratio performance as compared with previously existing airfoils.

New solutions of Heun's general equation

International Nuclear Information System (INIS)

Ishkhanyan, Artur; Suominen, Kalle-Antti

2003-01-01

We show that in four particular cases the derivative of the solution of Heun's general equation can be expressed in terms of a solution to another Heun's equation. Starting from this property, we use the Gauss hypergeometric functions to construct series solutions to Heun's equation for the mentioned cases. Each of the hypergeometric functions involved has correct singular behaviour at only one of the singular points of the equation; the sum, however, has correct behaviour. (letter to the editor)

Fundamental equations for two-phase flow. Part 1: general conservation equations. Part 2: complement and remarks; Equations fondamentales des ecoulements diphasiques. Premiere partie: equations generales de conservation. Deuxieme partie: complements et remarques

Energy Technology Data Exchange (ETDEWEB)

Delhaye, J M [Commissariat a l' Energie Atomique, 38 - Grenoble (France). Centre d' Etudes Nucleaires

1968-12-01

This report deals with the general equations of mass conservation, of momentum conservation, and energy conservation in the case of a two-phase flow. These equations are presented in several forms starting from integral equations which are assumed initially a priori. 1. Equations with local instantaneous variables, and interfacial conditions; 2. Equations with mean instantaneous variables in a cross-section, and practical applications: these equations include an important experimental value which is the ratio of the cross-section of passage of one phase to the total cross-section of a flow-tube. 3. Equations with a local statistical mean, and equations averaged over a period of time: A more advanced attempt to relate theory and experiment consists in taking the statistical averages of local equations. Equations are then obtained involving variables which are averaged over a period of time with the help of an ergodic assumption. 4. Combination of statistical averages and averages over a cross-section: in this study are considered the local variables averaged statistically, then averaged over the cross-section, and also the variables averaged over the section and then averaged statistically. 5. General equations concerning emulsions: In this case a phase exists in a locally very finely divided form. This peculiarity makes it possible to define a volume concentration, and to draw up equations which have numerous applications. - Certain points arising in the first part of this report concerning general mass conservation equations for two-phase flow have been completed and clarified. The terms corresponding to the interfacial tension have been introduced into the general equations. The interfacial conditions have thus been generalized. A supplementary step has still to be carried out: it has, in effect, been impossible to take the interfacial tension into account in the case of emulsions. It was then appeared interesting to compare this large group of fundamental

Fundamental equations for two-phase flow. Part 1: general conservation equations. Part 2: complement and remarks; Equations fondamentales des ecoulements diphasiques. Premiere partie: equations generales de conservation. Deuxieme partie: complements et remarques

Energy Technology Data Exchange (ETDEWEB)

Delhaye, J.M. [Commissariat a l' Energie Atomique, 38 - Grenoble (France). Centre d' Etudes Nucleaires

1968-12-01

This report deals with the general equations of mass conservation, of momentum conservation, and energy conservation in the case of a two-phase flow. These equations are presented in several forms starting from integral equations which are assumed initially a priori. 1. Equations with local instantaneous variables, and interfacial conditions; 2. Equations with mean instantaneous variables in a cross-section, and practical applications: these equations include an important experimental value which is the ratio of the cross-section of passage of one phase to the total cross-section of a flow-tube. 3. Equations with a local statistical mean, and equations averaged over a period of time: A more advanced attempt to relate theory and experiment consists in taking the statistical averages of local equations. Equations are then obtained involving variables which are averaged over a period of time with the help of an ergodic assumption. 4. Combination of statistical averages and averages over a cross-section: in this study are considered the local variables averaged statistically, then averaged over the cross-section, and also the variables averaged over the section and then averaged statistically. 5. General equations concerning emulsions: In this case a phase exists in a locally very finely divided form. This peculiarity makes it possible to define a volume concentration, and to draw up equations which have numerous applications. - Certain points arising in the first part of this report concerning general mass conservation equations for two-phase flow have been completed and clarified. The terms corresponding to the interfacial tension have been introduced into the general equations. The interfacial conditions have thus been generalized. A supplementary step has still to be carried out: it has, in effect, been impossible to take the interfacial tension into account in the case of emulsions. It was then appeared interesting to compare this large group of fundamental

Close-loop Dynamic Stall Control on a Pitching Airfoil

Science.gov (United States)

Giles, Ian; Corke, Thomas

2017-11-01

A closed-loop control scheme utilizing a plasma actuator to control dynamic stall is presented. The plasma actuator is located at the leading-edge of a pitching airfoil. It initially pulses at an unsteady frequency that perturbs the boundary layer flow over the suction surface of the airfoil. As the airfoil approaches and enters stall, the amplification of the unsteady disturbance is detected by an onboard pressure sensor also located near the leading edge. Once detected, the actuator is switched to a higher voltage control state that in static airfoil experiments would reattach the flow. The threshold level of the detection is a parameter in the control scheme. Three stall regimes were examined: light, medium, and deep stall, that were defined by their stall penetration angles. The results showed that in general, the closed-loop control scheme was effective at controlling dynamic stall. The cycle-integrated lift improved in all cases, and increased by as much as 15% at the lowest stall penetration angle. As important, the cycle-integrated aerodynamic damping coefficient also increased in all cases, and was made to be positive at the light stall regime where it traditionally is negative. The latter is important in applications where negative damping can lead to stall flutter.

An exterior Poisson solver using fast direct methods and boundary integral equations with applications to nonlinear potential flow

Science.gov (United States)

Young, D. P.; Woo, A. C.; Bussoletti, J. E.; Johnson, F. T.

1986-01-01

A general method is developed combining fast direct methods and boundary integral equation methods to solve Poisson's equation on irregular exterior regions. The method requires O(N log N) operations where N is the number of grid points. Error estimates are given that hold for regions with corners and other boundary irregularities. Computational results are given in the context of computational aerodynamics for a two-dimensional lifting airfoil. Solutions of boundary integral equations for lifting and nonlifting aerodynamic configurations using preconditioned conjugate gradient are examined for varying degrees of thinness.

Study of airfoil trailing edge bluntness noise

DEFF Research Database (Denmark)

Zhu, Wei Jun; Shen, Wen Zhong; Sørensen, Jens Nørkær

2010-01-01

This paper deals with airfoil trailing edge noise with special focus on airfoils with blunt trailing edges. Two methods are employed to calculate airfoil noise: The flow/acoustic splitting method and the semi-empirical method. The flow/acoustic splitting method is derived from compressible Navier...... design or optimization. Calculations from both methods are compared with exist experiments. The airfoil blunt noise is found as a function of trailing edge bluntness, Reynolds number, angle of attack, etc....

Characterization of Oscillatory Lift in MFC Airfoils

OpenAIRE

Lang Jr, Joseph Reagle

2014-01-01

The purpose of this research is to characterize the response of an airfoil with an oscillatory morphing, Macro-fiber composite (MFC) trailing edge. Correlation of the airfoil lift with the oscillatory input is presented. Modal analysis of the test airfoil and apparatus is used to determine the frequency response function. The effects of static MFC inputs on the FRF are presented and compared to the unactuated airfoil. The transfer function is then used to determine the lift component du...

Turbine airfoil having near-wall cooling insert

Science.gov (United States)

Martin, Jr., Nicholas F.; Wiebe, David J.

2017-09-12

A turbine airfoil is provided with at least one insert positioned in a cavity in an airfoil interior. The insert extends along a span-wise extent of the turbine airfoil and includes first and second opposite faces. A first near-wall cooling channel is defined between the first face and a pressure sidewall of an airfoil outer wall. A second near-wall cooling channel is defined between the second face and a suction sidewall of the airfoil outer wall. The insert is configured to occupy an inactive volume in the airfoil interior so as to displace a coolant flow in the cavity toward the first and second near-wall cooling channels. A locating feature engages the insert with the outer wall for supporting the insert in position. The locating feature is configured to control flow of the coolant through the first or second near-wall cooling channel.

Hybrid Optimization for Wind Turbine Thick Airfoils

Energy Technology Data Exchange (ETDEWEB)

Grasso, F. [ECN Wind Energy, Petten (Netherlands)

2012-06-15

One important element in aerodynamic design of wind turbines is the use of specially tailored airfoils to increase the ratio of energy capture and reduce cost of energy. This work is focused on the design of thick airfoils for wind turbines by using numerical optimization. A hybrid scheme is proposed in which genetic and gradient based algorithms are combined together to improve the accuracy and the reliability of the design. Firstly, the requirements and the constraints for this class of airfoils are described; then, the hybrid approach is presented. The final part of this work is dedicated to illustrate a numerical example regarding the design of a new thick airfoil. The results are discussed and compared to existing airfoils.

An overview of NACA 6-digit airfoil series characteristics with reference to airfoils for large wind turbine blades

NARCIS (Netherlands)

Timmer, W.A.

2009-01-01

This paper investigates the NACA 63 and 64 6-digit series of airfoils tested in the NACA LTPT in view to verify the RFOIL calculated airfoil characteristics for high Reynolds numbers. Some anomalies in the zero-lift angles of 15% and 18% thick airfoils from these series are identified, both in the

The effects of NACA 0012 airfoil modification on aerodynamic performance improvement and obtaining high lift coefficient and post-stall airfoil

Science.gov (United States)

Sogukpinar, Haci

2018-02-01

In this study, aerodynamic performances of NACA 0012 airfoils with distinct modification are numerically investigated to obtain high lift coefficient and post-stall airfoils. NACA 0012 airfoil is divided into two part thought chord line then suction sides kept fixed and by changing the thickness of the pressure side new types of airfoil are created. Numerical experiments are then conducted by varying thickness of NACA 0012 from lower surface and different relative thicknesses asymmetrical airfoils are modified and NACA 0012-10, 0012-08, 0012-07, 0012-06, 0012-04, 0012-03, 0012-02, 0012-01 are created and simulated by using COMSOL software.

Airfoil shape for flight at subsonic speeds. [design analysis and aerodynamic characteristics of the GAW-1 airfoil

Science.gov (United States)

Whitcomb, R. T. (Inventor)

1976-01-01

An airfoil is examined that has an upper surface shaped to control flow accelerations and pressure distribution over the upper surface and to prevent separation of the boundary layer due to shock wave formulation at high subsonic speeds well above the critical Mach number. A highly cambered trailing edge section improves overall airfoil lifting efficiency. Diagrams illustrating supersonic flow and shock waves over the airfoil are shown.

Design and optimization of tidal turbine airfoil

Energy Technology Data Exchange (ETDEWEB)

Grasso, F. [ECN Wind Energy, Petten (Netherlands)

2012-03-15

To increase the ratio of energy capture to the loading and, thereby, to reduce cost of energy, the use of specially tailored airfoils is needed. This work is focused on the design of an airfoil for marine application. Firstly, the requirements for this class of airfoils are illustrated and discussed with reference to the requirements for wind turbine airfoils. Then, the design approach is presented. This is a numerical optimization scheme in which a gradient-based algorithm is used, coupled with the RFOIL solver and a composite Bezier geometrical parameterization. A particularly sensitive point is the choice and implementation of constraints .A section of the present work is dedicated to address this point; particular importance is given to the cavitation phenomenon. Finally, a numerical example regarding the design of a high-efficiency hydrofoil is illustrated, and the results are compared with existing turbine airfoils, considering also the effect on turbine performance due to different airfoils.

Design and optimization of tidal turbine airfoil

Energy Technology Data Exchange (ETDEWEB)

Grasso, F. [ECN Wind Energy, Petten (Netherlands)

2011-07-15

In order to increase the ratio of energy capture to the loading and thereby to reduce cost of energy, the use of specially tailored airfoils is needed. This work is focused on the design of an airfoil for marine application. Firstly, the requirements for this class of airfoils are illustrated and discussed with reference to the requirements for wind turbine airfoils. Then, the design approach is presented. This is a numerical optimization scheme in which a gradient based algorithm is used, coupled with RFOIL solver and a composite Bezier geometrical parameterization. A particularly sensitive point is the choice and implementation of constraints; in order to formalize in the most complete and effective way the design requirements, the effects of activating specific constraints are discussed. Particularly importance is given to the cavitation phenomenon. Finally, a numerical example regarding the design of a high efficiency, tidal turbine airfoil is illustrated and the results are compared with existing turbine airfoils.

Airfoil flow instabilities induced by background flow oscillations

Energy Technology Data Exchange (ETDEWEB)

Selerowicz, W.C.; Szumowski, A.P. [Technical Univ. Warsaw (Poland)

2002-04-01

The effect of background flow oscillations on transonic airfoil (NACA 0012) flow was investigated experimentally. The oscillations were generated by means of a rotating plate placed downstream of the airfoil. Owing to oscillating chocking of the flow caused by the plate, the airfoil flow periodically accelerated and decelerated. This led to strong variations in the surface pressure and the airfoil loading. The results are presented for two angles of attack, {alpha}=4 and {alpha}=8.5 , which correspond to the attached and separated steady airfoil flows, respectively. (orig.)

VISUALISASI DISTRIBUSI TEKANAN PADA AIRFOIL JOUKOWSKY

OpenAIRE

Eddy Maryonoto

2009-01-01

The goal of this research is to develop a computer based system that can beused to visualize pressure distribution on the Joukowsky's airfoil and streamlinespattern around the airfoil. The pressure on the airfoil is calculdted usingformulasderived from potensial theory. Visualization of pressure distribution implementedby using color gradation technique and coded b.v using Borland Delphi 6programming language. The result of the test shotus lhat lhe system has performedperfectly. Pressure disl...

Generalized heat-transport equations: parabolic and hyperbolic models

Science.gov (United States)

Rogolino, Patrizia; Kovács, Robert; Ván, Peter; Cimmelli, Vito Antonio

2018-03-01

We derive two different generalized heat-transport equations: the most general one, of the first order in time and second order in space, encompasses some well-known heat equations and describes the hyperbolic regime in the absence of nonlocal effects. Another, less general, of the second order in time and fourth order in space, is able to describe hyperbolic heat conduction also in the presence of nonlocal effects. We investigate the thermodynamic compatibility of both models by applying some generalizations of the classical Liu and Coleman-Noll procedures. In both cases, constitutive equations for the entropy and for the entropy flux are obtained. For the second model, we consider a heat-transport equation which includes nonlocal terms and study the resulting set of balance laws, proving that the corresponding thermal perturbations propagate with finite speed.

Some Remarks on Stability of Generalized Equations

Czech Academy of Sciences Publication Activity Database

Outrata, Jiří; Henrion, R.; Kruger, A.Y.

2013-01-01

Roč. 159, č. 3 (2013), s. 681-697 ISSN 0022-3239 R&D Projects: GA AV ČR IAA100750802; GA ČR(CZ) GAP201/12/0671 Institutional support: RVO:67985556 Keywords : Parameterized generalized equation * Regular and limiting coderivative * Constant rank CQ * Mathematical program with equilibrium constraints Subject RIV: BA - General Mathematics Impact factor: 1.406, year: 2013 http://library.utia.cas.cz/separaty/2013/MTR/outrata-some remarks on stability of generalized equations.pdf

Unsteady Aerodynamics of Deformable Thin Airfoils

OpenAIRE

Walker, William Paul

2009-01-01

Unsteady aerodynamic theories are essential in the analysis of bird and insect flight. The study of these types of locomotion is vital in the development of flapping wing aircraft. This paper uses potential flow aerodynamics to extend the unsteady aerodynamic theory of Theodorsen and Garrick (which is restricted to rigid airfoil motion) to deformable thin airfoils. Frequency-domain lift, pitching moment and thrust expressions are derived for an airfoil undergoing harmonic oscillations and def...

Study on Trailing Edge Ramp of Supercritical Airfoil

Science.gov (United States)

2016-03-30

China Abstract Trailing edge flow control method could improve the performance of supercritical airfoil with a small modification on the original...stall behaviour . As a result, the non-separation ramp could increase the thickness of airfoil, which benefits wing structure and aerodynamic...direction based on the original RAE2822 airfoil, which will thicken the airfoil. The interpolation is implemented as shown in Eqn. 1. This modification could

General heavenly equation governs anti-self-dual gravity

Energy Technology Data Exchange (ETDEWEB)

Malykh, A A [Department of Numerical Modelling, Russian State Hydrometeorlogical University, Malookhtinsky pr 98, 195196 St Petersburg (Russian Federation); Sheftel, M B, E-mail: andrei-malykh@mail.ru, E-mail: mikhail.sheftel@boun.edu.tr [Department of Physics, Bogazici University, 34342 Bebek, Istanbul (Turkey)

2011-04-15

We show that the general heavenly equation, suggested recently by Doubrov and Ferapontov (2010 arXiv:0910.3407v2 [math.DG]), governs anti-self-dual (ASD) gravity. We derive ASD Ricci-flat vacuum metric governed by the general heavenly equation, null tetrad and basis of 1-forms for this metric. We present algebraic exact solutions of the general heavenly equation as a set of zeros of homogeneous polynomials in independent and dependent variables. A real solution is obtained for the case of a neutral signature.

A novel numerical flux for the 3D Euler equations with general equation of state

KAUST Repository

Toro, Eleuterio F.; Castro, Cristó bal E.; Bok Jik, Lee

2015-01-01

Euler equations for ideal gases and its extension presented in this paper is threefold: (i) we solve the three-dimensional Euler equations on general meshes; (ii) we use a general equation of state; and (iii) we achieve high order of accuracy in both

Parameter study of simplified dragonfly airfoil geometry at Reynolds number of 6000.

Science.gov (United States)

Levy, David-Elie; Seifert, Avraham

2010-10-21

Aerodynamic study of a simplified Dragonfly airfoil in gliding flight at Reynolds numbers below 10,000 is motivated by both pure scientific interest and technological applications. At these Reynolds numbers, the natural insect flight could provide inspiration for technology development of Micro UAV's and more. Insect wings are typically characterized by corrugated airfoils. The present study follows a fundamental flow physics study (Levy and Seifert, 2009), that revealed the importance of flow separation from the first corrugation, the roll-up of the separated shear layer to discrete vortices and their role in promoting flow reattachment to the aft arc, as the leading mechanism enabling high-lift, low drag performance of the Dragonfly gliding flight. This paper describes the effect of systematic airfoil geometry variations on the aerodynamic properties of a simplified Dragonfly airfoil at Reynolds number of 6000. The parameter study includes a detailed analysis of small variations of the nominal geometry, such as corrugation placement or height, rear arc and trailing edge shape. Numerical simulations using the 2D laminar Navier-Stokes equations revealed that the flow accelerating over the first corrugation slope is followed by an unsteady pressure recovery, combined with vortex shedding. The latter allows the reattachment of the flow over the rear arc. Also, the drag values are directly linked to the vortices' magnitude. This parametric study shows that geometric variations which reduce the vortices' amplitude, as reduction of the rear cavity depth or the reduction of the rear arc and trailing edge curvature, will reduce the drag values. Other changes will extend the flow reattachment over the rear arc for a larger mean lift coefficients range; such as the negative deflection of the forward flat plate. These changes consequently reduce the drag values at higher mean lift coefficients. The detailed geometry study enabled the definition of a corrugated airfoil

Time-Dependent Effects of Glaze Ice on the Aerodynamic Characteristics of an Airfoil

Directory of Open Access Journals (Sweden)

Narges Tabatabaei

2018-01-01

Full Text Available The main objective of this study is to estimate the dynamic loads acting over a glaze-iced airfoil. This work studies the performance of unsteady Reynolds-averaged Navier-Stokes (URANS simulations in predicting the oscillations over an iced airfoil. The structure and size of time-averaged vortices are compared to measurements. Furthermore, the accuracy of a two-equation eddy viscosity turbulence model, the shear stress transport (SST model, is investigated in the case of the dynamic load analysis over a glaze-iced airfoil. The computational fluid dynamic analysis was conducted to investigate the effect of critical ice accretions on a 0.610 m chord NACA 0011 airfoil. Leading edge glaze ice accretion was simulated with flat plates (spoiler-ice extending along the span of the blade. Aerodynamic performance coefficients and pressure profiles were calculated and validated for the Reynolds number of 1.83 × 106. Furthermore, turbulent separation bubbles were studied. The numerical results confirm both time-dependent phenomena observed in previous similar measurements: (1 low-frequency mode, with a Strouhal number Sth≈0,013–0.02, and (2 higher frequency mode with a Strouhal number StL≈0,059–0.69. The higher frequency motion has the same characteristics as the shedding mode and the lower frequency motion has the flapping mode characteristics.

Airfoil characteristics for wind turbines

DEFF Research Database (Denmark)

Bak, C.; Fuglsang, P.; Sørensen, Niels N.

1999-01-01

Airfoil characteristics for use in the Blade Element Momentum (BEM) method calculating the forces on Horizontal Axis Wind Turbines (HAWT) are derived by use of systematic methods. The investigation and derivation of the airfoil characteristics are basedon four different methods: 1) Inverse momentum...... theory, 2) Actuator disc theory, 3) Numerical optimisation and 4) Quasi-3D CFD computations. The two former methods are based on 3D CFD computations and wind tunnel measurements on a 41-m full-scale rotorwith LM 19.1 blades. The derived airfoil characteristics show that the lift coefficient in stall...... to a commonly used set of airfoil characteristics. The numerical optimisation is based on both the 3D CFDcomputations and measurements on a 41-m rotor with LM 19.1 and LM 19.0 blades, respectively. The method requires power and loads from a turbine and is promising since a set of lift and drag curves is derived...

2D CFD Airfoil Analysis

Science.gov (United States)

Babb, Grace

2017-11-01

This work aims to produce a higher fidelity model of the blades for NASA's X-57 all electric propeller driven experimental aircraft. This model will, in turn, allow for more accurate calculations of the thrust each propeller can generate. This work uses computational fluid dynamics (CFD) to first analyze the propeller blades as a series of 11 differently shaped airfoils and calculate, among other things, the coefficients for lift and drag associated with each airfoil at different angles of attack. OpenFOAM-a C + + library that can be used to create series of applications for pre-processing, solving, and post-processing-is one of the primary tools utilized in these calculations. By comparing the data OpenFOAM generates about the NACA 23012 airfoil with existing experimental data about the NACA 23012 airfoil, the reliability of our model is measured and verified. A trustworthy model can then be used to generate more data and sent to NASA to aid in the design of the actual aircraft.

An Integrated Method for Airfoil Optimization

Science.gov (United States)

Okrent, Joshua B.

Design exploration and optimization is a large part of the initial engineering and design process. To evaluate the aerodynamic performance of a design, viscous Navier-Stokes solvers can be used. However this method can prove to be overwhelmingly time consuming when performing an initial design sweep. Therefore, another evaluation method is needed to provide accurate results at a faster pace. To accomplish this goal, a coupled viscous-inviscid method is used. This thesis proposes an integrated method for analyzing, evaluating, and optimizing an airfoil using a coupled viscous-inviscid solver along with a genetic algorithm to find the optimal candidate. The method proposed is different from prior optimization efforts in that it greatly broadens the design space, while allowing the optimization to search for the best candidate that will meet multiple objectives over a characteristic mission profile rather than over a single condition and single optimization parameter. The increased design space is due to the use of multiple parametric airfoil families, namely the NACA 4 series, CST family, and the PARSEC family. Almost all possible airfoil shapes can be created with these three families allowing for all possible configurations to be included. This inclusion of multiple airfoil families addresses a possible criticism of prior optimization attempts since by only focusing on one airfoil family, they were inherently limiting the number of possible airfoil configurations. By using multiple parametric airfoils, it can be assumed that all reasonable airfoil configurations are included in the analysis and optimization and that a global and not local maximum is found. Additionally, the method used is amenable to customization to suit any specific needs as well as including the effects of other physical phenomena or design criteria and/or constraints. This thesis found that an airfoil configuration that met multiple objectives could be found for a given set of nominal

Generalized differential transform method to differential-difference equation

International Nuclear Information System (INIS)

Zou Li; Wang Zhen; Zong Zhi

2009-01-01

In this Letter, we generalize the differential transform method to solve differential-difference equation for the first time. Two simple but typical examples are applied to illustrate the validity and the great potential of the generalized differential transform method in solving differential-difference equation. A Pade technique is also introduced and combined with GDTM in aim of extending the convergence area of presented series solutions. Comparisons are made between the results of the proposed method and exact solutions. Then we apply the differential transform method to the discrete KdV equation and the discrete mKdV equation, and successfully obtain solitary wave solutions. The results reveal that the proposed method is very effective and simple. We should point out that generalized differential transform method is also easy to be applied to other nonlinear differential-difference equation.

Generalized equations of gravitational field

International Nuclear Information System (INIS)

Stanyukovich, K.P.; Borisova, L.B.

1985-01-01

Equations for gravitational fields are obtained on the basis of a generalized Lagrangian Z=f(R) (R is the scalar curvature). Such an approach permits to take into account the evolution of a gravitation ''constant''. An expression for the force Fsub(i) versus the field variability is obtained. Conservation laws are formulated differing from the standard ones by the fact that in the right part of new equations the value Fsub(i) is present that goes to zero at an ultimate passage to the standard Einstein theory. An equation of state is derived for cosmological metrics for a particular case, f=bRsup(1+α) (b=const, α=const)

Solitonlike solutions of the generalized discrete nonlinear Schrödinger equation

DEFF Research Database (Denmark)

Rasmussen, Kim; Henning, D.; Gabriel, H.

1996-01-01

We investigate the solution properties oi. a generalized discrete nonlinear Schrodinger equation describing a nonlinear lattice chain. The generalized equation interpolates between the integrable discrete Ablowitz-Ladik equation and the nonintegrable discrete Schrodinger equation. Special interes...... nonlinear Schrodinger equation. In this way eve are able to construct coherent solitonlike structures of profile determined by the map parameters.......We investigate the solution properties oi. a generalized discrete nonlinear Schrodinger equation describing a nonlinear lattice chain. The generalized equation interpolates between the integrable discrete Ablowitz-Ladik equation and the nonintegrable discrete Schrodinger equation. Special interest...

New multiple soliton solutions to the general Burgers-Fisher equation and the Kuramoto-Sivashinsky equation

International Nuclear Information System (INIS)

Chen Huaitang; Zhang Hongqing

2004-01-01

A generalized tanh function method is used for constructing exact travelling wave solutions of nonlinear partial differential equations in a unified way. The main idea of this method is to take full advantage of the Riccati equation which has more new solutions. More new multiple soliton solutions are obtained for the general Burgers-Fisher equation and the Kuramoto-Sivashinsky equation

Quiet airfoils for small and large wind turbines

Science.gov (United States)

Tangler, James L [Boulder, CO; Somers, Dan L [Port Matilda, PA

2012-06-12

Thick airfoil families with desirable aerodynamic performance with minimal airfoil induced noise. The airfoil families are suitable for a variety of wind turbine designs and are particularly well-suited for use with horizontal axis wind turbines (HAWTs) with constant or variable speed using pitch and/or stall control. In exemplary embodiments, a first family of three thick airfoils is provided for use with small wind turbines and second family of three thick airfoils is provided for use with very large machines, e.g., an airfoil defined for each of three blade radial stations or blade portions defined along the length of a blade. Each of the families is designed to provide a high maximum lift coefficient or high lift, to exhibit docile stalls, to be relatively insensitive to roughness, and to achieve a low profile drag.

OUT Success Stories: Advanced Airfoils for Wind Turbines

Science.gov (United States)

Jones, J.; Green, B.

2000-08-01

New airfoils have substantially increased the aerodynamic efficiency of wind turbines. It is clear that these new airfoils substantially increased energy output from wind turbines. Virtually all new blades built in this country today use these advanced airfoil designs.

OUT Success Stories: Advanced Airfoils for Wind Turbines

International Nuclear Information System (INIS)

Jones, J.; Green, B.

2000-01-01

New airfoils have substantially increased the aerodynamic efficiency of wind turbines. It is clear that these new airfoils substantially increased energy output from wind turbines. Virtually all new blades built in this country today use these advanced airfoil designs

Airfoil nozzle and shroud assembly

Science.gov (United States)

Shaffer, J.E.; Norton, P.F.

1997-06-03

An airfoil and nozzle assembly are disclosed including an outer shroud having a plurality of vane members attached to an inner surface and having a cantilevered end. The assembly further includes a inner shroud being formed by a plurality of segments. Each of the segments having a first end and a second end and having a recess positioned in each of the ends. The cantilevered end of the vane member being positioned in the recess. The airfoil and nozzle assembly being made from a material having a lower rate of thermal expansion than that of the components to which the airfoil and nozzle assembly is attached. 5 figs.

METHOD FOR NUMERICAL MODELING OF UNSTEADY SEPARATED FLOW AROUND AIRFOILS MOVING CLOSE TO FLAT SCREEN

Directory of Open Access Journals (Sweden)

V. Pogrebnaya Tamara

2017-01-01

Full Text Available In this article an attempt is made to explain the nature of differences in measurements of forces and moments, which influence an aircraft at take-off and landing when testing on different types of stands. An algorithm for numerical simulation of unsteady separated flow around airfoil is given. The algorithm is based on the combination of discrete vortex method and turbulent boundary layer equations. An unsteady flow separation modeling has been used. At each interval vortex method was used to calculate the potential flow around airfoils located near a screen. Calculated pressures and velocities were then used in boundary layer calculations to determine flow separation points and separated vortex in- tensities. After that calculation were made to determine free vortex positions to next time step and the process was fulfilled for next time step. The proposed algorithm allows using numeric visualization to understand physical picture of flow around airfoil moving close to screen. Three different ways of flow modeling (mirror method, fixed or movable screens were tested. In each case the flow separation process, which determines pressure distribution over airfoil surface and influ- ences aerodynamic performance, was viewed. The results of the calculations showed that at low atitudes of airfoil over screen mirror method over predicts lift force compared with movable screen, while fixed screen under predicts it. The data obtained can be used when designing equipment for testing in wind tunnels.

Turbine airfoil to shroud attachment method

Science.gov (United States)

Campbell, Christian X; Kulkarni, Anand A; James, Allister W; Wessell, Brian J; Gear, Paul J

2014-12-23

Bi-casting a platform (50) onto an end portion (42) of a turbine airfoil (31) after forming a coating of a fugitive material (56) on the end portion. After bi-casting the platform, the coating is dissolved and removed to relieve differential thermal shrinkage stress between the airfoil and platform. The thickness of the coating is varied around the end portion in proportion to varying amounts of local differential process shrinkage. The coating may be sprayed (76A, 76B) onto the end portion in opposite directions parallel to a chord line (41) of the airfoil or parallel to a mid-platform length (80) of the platform to form respective layers tapering in thickness from the leading (32) and trailing (34) edges along the suction side (36) of the airfoil.

On Generalized Fractional Kinetic Equations Involving Generalized Bessel Function of the First Kind

Directory of Open Access Journals (Sweden)

Dinesh Kumar

2015-01-01

Full Text Available We develop a new and further generalized form of the fractional kinetic equation involving generalized Bessel function of the first kind. The manifold generality of the generalized Bessel function of the first kind is discussed in terms of the solution of the fractional kinetic equation in the paper. The results obtained here are quite general in nature and capable of yielding a very large number of known and (presumably new results.

BOOK REVIEW: Partial Differential Equations in General Relativity

Science.gov (United States)

Halburd, Rodney G.

2008-11-01

Although many books on general relativity contain an overview of the relevant background material from differential geometry, very little attention is usually paid to background material from the theory of differential equations. This is understandable in a first course on relativity but it often limits the kinds of problems that can be studied rigorously. Einstein's field equations lie at the heart of general relativity. They are a system of partial differential equations (PDEs) relating the curvature of spacetime to properties of matter. A central part of most problems in general relativity is to extract information about solutions of these equations. Most standard texts achieve this by studying exact solutions or numerical and analytical approximations. In the book under review, Alan Rendall emphasises the role of rigorous qualitative methods in general relativity. There has long been a need for such a book, giving a broad overview of the relevant background from the theory of partial differential equations, and not just from differential geometry. It should be noted that the book also covers the basic theory of ordinary differential equations. Although there are many good books on the rigorous theory of PDEs, methods related to the Einstein equations deserve special attention, not only because of the complexity and importance of these equations, but because these equations do not fit into any of the standard classes of equations (elliptic, parabolic, hyperbolic) that one typically encounters in a course on PDEs. Even specifying exactly what ones means by a Cauchy problem in general relativity requires considerable care. The main problem here is that the manifold on which the solution is defined is determined by the solution itself. This means that one does not simply define data on a submanifold. Rendall's book gives a good overview of applications and results from the qualitative theory of PDEs to general relativity. It would be impossible to give detailed

Wind turbine airfoil catalogue

DEFF Research Database (Denmark)

Bertagnolio, F.; Sørensen, Niels N.; Johansen, Jeppe

2001-01-01

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 solverEllipSys2D, as well as results from the panel...... method code XFOIL. Secondly, we are interested in validating the code EllipSys2D and finding out for which airfoils it does not perform well compared to the experiments, as well as why, when it does so. Theairfoils 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 forthe poor quality of the computational results for most of the considered airfoils. The transition model mechanism that leads...

Traveling wave behavior for a generalized fisher equation

International Nuclear Information System (INIS)

Feng Zhaosheng

2008-01-01

There is the widespread existence of wave phenomena in physics, chemistry and biology. This clearly necessitates a study of traveling waves in depth and of the modeling and analysis involved. In the present paper, we study a nonlinear reaction-diffusion equation, which can be regarded as a generalized Fisher equation. Applying the Cole-Hopf transformation and the first integral method, we obtain a class of traveling solitary wave solutions for this generalized Fisher equation

Two dimensional generalizations of the Newcomb equation

International Nuclear Information System (INIS)

Dewar, R.L.; Pletzer, A.

1989-11-01

The Bineau reduction to scalar form of the equation governing ideal, zero frequency linearized displacements from a hydromagnetic equilibrium possessing a continuous symmetry is performed in 'universal coordinates', applicable to both the toroidal and helical cases. The resulting generalized Newcomb equation (GNE) has in general a more complicated form than the corresponding one dimensional equation obtained by Newcomb in the case of circular cylindrical symmetry, but in this cylindrical case , the equation can be transformed to that of Newcomb. In the two dimensional case there is a transformation which leaves the form of the GNE invariant and simplifies the Frobenius expansion about a rational surface, especially in the limit of zero pressure gradient. The Frobenius expansions about a mode rational surface is developed and the connection with Hamiltonian transformation theory is shown. 17 refs

Advanced Airfoils Boost Helicopter Performance

Science.gov (United States)

2007-01-01

Carson Helicopters Inc. licensed the Langley RC4 series of airfoils in 1993 to develop a replacement main rotor blade for their Sikorsky S-61 helicopters. The company's fleet of S-61 helicopters has been rebuilt to include Langley's patented airfoil design, and the helicopters are now able to carry heavier loads and fly faster and farther, and the main rotor blades have twice the previous service life. In aerial firefighting, the performance-boosting airfoils have helped the U.S. Department of Agriculture's Forest Service control the spread of wildfires. In 2003, Carson Helicopters signed a contract with Ducommun AeroStructures Inc., to manufacture the composite blades for Carson Helicopters to sell

High-efficiency airfoil rudders applied to submarines

Directory of Open Access Journals (Sweden)

ZHOU Yimei

2017-03-01

Full Text Available Modern submarine design puts forward higher and higher requirements for control surfaces, and this creates a requirement for designers to constantly innovate new types of rudder so as to improve the efficiency of control surfaces. Adopting the high-efficiency airfoil rudder is one of the most effective measures for improving the efficiency of control surfaces. In this paper, we put forward an optimization method for a high-efficiency airfoil rudder on the basis of a comparative analysis of the various strengths and weaknesses of the airfoil, and the numerical calculation method is adopted to analyze the influence rule of the hydrodynamic characteristics and wake field by using the high-efficiency airfoil rudder and the conventional NACA rudder comparatively; at the same time, a model load test in a towing tank was carried out, and the test results and simulation calculation obtained good consistency:the error between them was less than 10%. The experimental results show that the steerage of a high-efficiency airfoil rudder is increased by more than 40% when compared with the conventional rudder, but the total resistance is close:the error is no more than 4%. Adopting a high-efficiency airfoil rudder brings much greater lifting efficiency than the total resistance of the boat. The results show that high-efficiency airfoil rudder has obvious advantages for improving the efficiency of control, giving it good application prospects.

Local vibrations and lift performance of low Reynolds number airfoil

Directory of Open Access Journals (Sweden)

TariqAmin Khan

2017-06-01

Full Text Available The 2D incompressible Navier-Stokes equations are solved based on the finite volume method and dynamic mesh technique is used to carry out partial fluid structure interaction. The local flexible structure (hereinafter termed as flexible structure vibrates in a single mode located on the upper surface of the airfoil. The Influence of vibration frequency and amplitude are examined and the corresponding fluid flow characteristics are investigated which add complexity to the inherent problem in unsteady flow. The study is conducted for flow over NACA0012 airfoil at 600≤Re≤3000 at a low angle of attack. Vibration of flexible structure induces a secondary vortex which modifies the pressure distribution and lift performance of the airfoil. At some moderate vibration amplitude, frequency synchronization or lock-in phenomenon occurs when the vibration frequency is close to the characteristic frequency of rigid airfoil. Evolution and shedding of vortices corresponding to the deformation of flexible structure depends on the Reynolds number. In the case of Re≤1000, the deformation of flexible structure is considered in-phase with the vortex shedding i.e., increasing maximum lift is linked with the positive deformation of flexible structure. At Re=1500 a phase shift of about 1/π exists while they are out-of-phase at Re>1500. Moreover, the oscillation amplitude of lift coefficient increases with increasing vibration amplitude for Re≤1500 while it decreases with increasing vibration amplitude for Re>1500. As a result of frequency lock-in, the average lift coefficient is increased with increasing vibration amplitude for all investigated Reynolds numbers (Re. The maximum increase in the average lift coefficient is 19.72% within the range of investigated parameters.

Estimation of supersonic fighter jet airfoil data and low speed aerodynamic analysis of airfoil section at the Mach number 0.15

Science.gov (United States)

Sogukpinar, Haci

2018-02-01

In this paper, some of the NACA 64A series airfoils data are estimated and aerodynamic properties are calculated to facilitate great understandings effect of relative thickness on the aerodynamic performance of the airfoil by using COMSOL software. 64A201-64A204 airfoils data are not available in literature therefore 64A210 data are used as reference data to estimate 64A201, 64A202, 64A203, 64A204 airfoil configurations. Numerical calculations are then conducted with the angle of attack from -12° to +16° by using k-w turbulence model based on the finite-volume approach. The lift and drag coefficient are one of the most important parameters in studying the airplane performance. Therefore lift, drag and pressure coefficient around selected airfoil are calculated and compared at the Reynolds numbers of 6 × 106 and also stalling characteristics of airfoil section are investigated and presented numerically.

BRST, generalized Maurer-Cartan equations and CFT

Energy Technology Data Exchange (ETDEWEB)

Zeitlin, Anton M. [Department of Mathematics, Yale University, 442 Dunham Lab, 10 Hillhouse Ave., New Haven, CT 06511 (United States); St. Petersburg Department of Steklov Mathematical Institute, Fontanka, 27, St. Petersburg 191023 (Russian Federation)]. E-mail: zam@math.ipme.ru

2006-12-25

The paper is devoted to the study of BRST charge in perturbed two-dimensional conformal field theory. The main goal is to write the operator equation expressing the conservation law of BRST charge in perturbed theory in terms of purely algebraic operations on the corresponding operator algebra, which are defined via the OPE. The corresponding equations are constructed and their symmetries are studied up to the second order in formal coupling constant. It appears that the obtained equations can be interpreted as generalized Maurer-Cartan ones. We study two concrete examples in detail: the bosonic nonlinear sigma model and perturbed first order theory. In particular, we show that the Einstein equations, which are the conformal invariance conditions for both these perturbed theories, expanded up to the second order, can be rewritten in such generalized Maurer-Cartan form.

Modeling and Grid Generation of Iced Airfoils

Science.gov (United States)

Vickerman, Mary B.; Baez, Marivell; Braun, Donald C.; Hackenberg, Anthony W.; Pennline, James A.; Schilling, Herbert W.

2007-01-01

SmaggIce Version 2.0 is a software toolkit for geometric modeling and grid generation for two-dimensional, singleand multi-element, clean and iced airfoils. A previous version of SmaggIce was described in Preparing and Analyzing Iced Airfoils, NASA Tech Briefs, Vol. 28, No. 8 (August 2004), page 32. To recapitulate: Ice shapes make it difficult to generate quality grids around airfoils, yet these grids are essential for predicting ice-induced complex flow. This software efficiently creates high-quality structured grids with tools that are uniquely tailored for various ice shapes. SmaggIce Version 2.0 significantly enhances the previous version primarily by adding the capability to generate grids for multi-element airfoils. This version of the software is an important step in streamlining the aeronautical analysis of ice airfoils using computational fluid dynamics (CFD) tools. The user may prepare the ice shape, define the flow domain, decompose it into blocks, generate grids, modify/divide/merge blocks, and control grid density and smoothness. All these steps may be performed efficiently even for the difficult glaze and rime ice shapes. Providing the means to generate highly controlled grids near rough ice, the software includes the creation of a wrap-around block (called the "viscous sublayer block"), which is a thin, C-type block around the wake line and iced airfoil. For multi-element airfoils, the software makes use of grids that wrap around and fill in the areas between the viscous sub-layer blocks for all elements that make up the airfoil. A scripting feature records the history of interactive steps, which can be edited and replayed later to produce other grids. Using this version of SmaggIce, ice shape handling and grid generation can become a practical engineering process, rather than a laborious research effort.

Integrated airfoil and blade design method for large wind turbines

DEFF Research Database (Denmark)

Zhu, Wei Jun; Shen, Wen Zhong

2013-01-01

This paper presents an integrated method for designing airfoil families of large wind turbine blades. For a given rotor diameter and tip speed ratio, the optimal airfoils are designed based on the local speed ratios. To achieve high power performance at low cost, the airfoils are designed...... with an objective of high Cp and small chord length. When the airfoils are obtained, the optimum flow angle and rotor solidity are calculated which forms the basic input to the blade design. The new airfoils are designed based on the previous in-house airfoil family which were optimized at a Reynolds number of 3...... million. A novel shape perturbation function is introduced to optimize the geometry on the existing airfoils and thus simplify the design procedure. The viscos/inviscid code Xfoil is used as the aerodynamic tool for airfoil optimization where the Reynolds number is set at 16 million with a free...

Integrated airfoil and blade design method for large wind turbines

DEFF Research Database (Denmark)

Zhu, Wei Jun; Shen, Wen Zhong; Sørensen, Jens Nørkær

2014-01-01

This paper presents an integrated method for designing airfoil families of large wind turbine blades. For a given rotor diameter and a tip speed ratio, optimal airfoils are designed based on the local speed ratios. To achieve a high power performance at low cost, the airfoils are designed...... with the objectives of high Cp and small chord length. When the airfoils are obtained, the optimum flow angle and rotor solidity are calculated which forms the basic input to the blade design. The new airfoils are designed based on a previous in-house designed airfoil family which was optimized at a Reynolds number...... of 3 million. A novel shape perturbation function is introduced to optimize the geometry based on the existing airfoils which simplifies the design procedure. The viscous/inviscid interactive code XFOIL is used as the aerodynamic tool for airfoil optimization at a Reynolds number of 16 million...

Inverse airfoil design method for low-speed straight-bladed Darrieus-type VAWT applications

Energy Technology Data Exchange (ETDEWEB)

Saeed, F. [King Fahd Univ. of Petroleum and Minerals, Dhahran (Saudi Arabia); Paraschivoiu, I.; Trifu, O. [Ecole Polytechnique, Montreal, PQ (Canada); Hess, M.; Gabrys, C. [Mariah Power Inc., Reno, NV (United States)

2008-07-01

Inverse airfoil design of a low-speed straight-bladed Darrieus-type vertical axis wind turbine (VAWT) can help improve aerodynamic performance and power output by eliminating undesirable flow field characteristics at very low Reynolds number. This study used an interactive inverse airfoil design method (PROFOIL) that allows specification of velocity and boundary-layer characteristics over different segments of the airfoil subject to constraints on the geometry (closure) and the flow field (far field boundary). Additional constraints were also considered to address pitching moment coefficient, thickness and the power output for a given tip-speed ratio. Performance analyses of the airfoil and the VAWT were carried out using state-of-the-art analyses codes XFOIL and CARDAAV, respectively. XFOIL is a panel method with a coupled boundary-layer scheme and is used to obtain the aerodynamic characteristics of resulting airfoil shapes. The final airfoil geometry is obtained through a multi-dimensional Newton iteration. The study showed that the strength of the method lies in the inverse design methodology whereas its weaknesses is in reliably predicting aerodynamic characteristics of airfoils at low Reynolds numbers and high angles of attack. A 10-15 per cent increase in the relative performance of the VAWT was achieved with this method. Although the results of the study showed that the method has great application potential for VAWTs in general, there is much room for improvement in flow analysis capabilities for low Re flows in reliably predicting post-stall aerodynamic characteristics. In the absence of such analysis capabilities, the authors suggested that the results should be viewed qualitatively and not quantitatively. 36 refs., 1 tab., 4 figs.

Experimental study of ice accretion effects on aerodynamic performance of an NACA 23012 airfoil

Directory of Open Access Journals (Sweden)

Sohrab Gholamhosein Pouryoussefi

2016-06-01

Full Text Available In this paper, the effects of icing on an NACA 23012 airfoil have been studied. Experiments were applied on the clean airfoil, runback ice, horn ice, and spanwise ridge ice at a Reynolds number of 0.6 × 106 over angles of attack from −8° to 20°, and then results are compared. Generally, it is found that ice accretion on the airfoil can contribute to formation of a flow separation bubble on the upper surface downstream from the leading edge. In addition, it is made clear that spanwise ridge ice provides the greatest negative effect on the aerodynamic performance of the airfoil. In this case, the stall angle drops about 10° and the maximum lift coefficient reduces about 50% which is hazardous for an airplane. While horn ice leads to a stall angle drop of about 4° and a maximum lift coefficient reduction to 21%, runback ice has the least effect on the flow pattern around the airfoil and the aerodynamic coefficients so as the stall angle decreases 2° and the maximum lift reduces about 8%.

Airfoil optimization for morphing aircraft

Science.gov (United States)

Namgoong, Howoong

Continuous variation of the aircraft wing shape to improve aerodynamic performance over a wide range of flight conditions is one of the objectives of morphing aircraft design efforts. This is being pursued because of the development of new materials and actuation systems that might allow this shape change. The main purpose of this research is to establish appropriate problem formulations and optimization strategies to design an airfoil for morphing aircraft that include the energy required for shape change. A morphing aircraft can deform its wing shape, so the aircraft wing has different optimum shapes as the flight condition changes. The actuation energy needed for moving the airfoil surface is modeled and used as another design objective. Several multi-objective approaches are applied to a low-speed, incompressible flow problem and to a problem involving low-speed and transonic flow. The resulting solutions provide the best tradeoff between low drag, high energy and higher drag, low energy sets of airfoil shapes. From this range of solutions, design decisions can be made about how much energy is needed to achieve a desired aerodynamic performance. Additionally, an approach to model aerodynamic work, which would be more realistic and may allow using pressure on the airfoil to assist a morphing shape change, was formulated and used as part of the energy objective. These results suggest that it may be possible to design a morphing airfoil that exploits the airflow to reduce actuator energy.

The generalized good cut equation

International Nuclear Information System (INIS)

Adamo, T M; Newman, E T

2010-01-01

The properties of null geodesic congruences (NGCs) in Lorentzian manifolds are a topic of considerable importance. More specifically NGCs with the special property of being shear-free or asymptotically shear-free (as either infinity or a horizon is approached) have received a great deal of recent attention for a variety of reasons. Such congruences are most easily studied via solutions to what has been referred to as the 'good cut equation' or the 'generalization good cut equation'. It is the purpose of this paper to study these equations and show their relationship to each other. In particular we show how they all have a four-complex-dimensional manifold (known as H-space, or in a special case as complex Minkowski space) as a solution space.

A complete second-order theory for the unsteady flow about an airfoil due to a periodic gust

Science.gov (United States)

Goldstein, M. E.; Atassi, H.

1976-01-01

A uniformly valid second-order theory is developed for calculating the unsteady incompressible flow that occurs when an airfoil is subjected to a convected sinusoidal gust. Explicit formulas for the airfoil response functions (i.e., fluctuating lift) are given. The theory accounts for the effect of the distortion of the gust by the steady-state potential flow around the airfoil, and this effect is found to have an important influence on the response functions. A number of results relevant to the general theory of the scattering of vorticity waves by solid objects are also presented.

First-stage high pressure turbine bucket airfoil

Science.gov (United States)

Brown, Theresa A.; Ahmadi, Majid; Clemens, Eugene; Perry, II, Jacob C.; Holiday, Allyn K.; Delehanty, Richard A.; Jacala, Ariel Caesar

2004-05-25

The first-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 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 coordinates defining the airfoil profile at each distance Z. 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 bucket.

Airfoil family design for large offshore wind turbine blades

Science.gov (United States)

Méndez, B.; Munduate, X.; San Miguel, U.

2014-06-01

Wind turbine blades size has scaled-up during last years due to wind turbine platform increase especially for offshore applications. The EOLIA project 2007-2010 (Spanish Goverment funded project) was focused on the design of large offshore wind turbines for deep waters. The project was managed by ACCIONA Energia and the wind turbine technology was designed by ACCIONA Windpower. The project included the design of a wind turbine airfoil family especially conceived for large offshore wind turbine blades, in the order of 5MW machine. Large offshore wind turbines suffer high extreme loads due to their size, in addition the lack of noise restrictions allow higher tip speeds. Consequently, the airfoils presented in this work are designed for high Reynolds numbers with the main goal of reducing blade loads and mantainig power production. The new airfoil family was designed in collaboration with CENER (Spanish National Renewable Energy Centre). The airfoil family was designed using a evolutionary algorithm based optimization tool with different objectives, both aerodynamic and structural, coupled with an airfoil geometry generation tool. Force coefficients of the designed airfoil were obtained using the panel code XFOIL in which the boundary layer/inviscid flow coupling is ineracted via surface transpiration model. The desing methodology includes a novel technique to define the objective functions based on normalizing the functions using weight parameters created from data of airfoils used as reference. Four airfoils have been designed, here three of them will be presented, with relative thickness of 18%, 21%, 25%, which have been verified with the in-house CFD code, Wind Multi Block WMB, and later validated with wind tunnel experiments. Some of the objectives for the designed airfoils concern the aerodynamic behavior (high efficiency and lift, high tangential coefficient, insensitivity to rough conditions, etc.), others concern the geometry (good for structural design

Airfoil family design for large offshore wind turbine blades

International Nuclear Information System (INIS)

Méndez, B; Munduate, X; Miguel, U San

2014-01-01

Wind turbine blades size has scaled-up during last years due to wind turbine platform increase especially for offshore applications. The EOLIA project 2007-2010 (Spanish Goverment funded project) was focused on the design of large offshore wind turbines for deep waters. The project was managed by ACCIONA Energia and the wind turbine technology was designed by ACCIONA Windpower. The project included the design of a wind turbine airfoil family especially conceived for large offshore wind turbine blades, in the order of 5MW machine. Large offshore wind turbines suffer high extreme loads due to their size, in addition the lack of noise restrictions allow higher tip speeds. Consequently, the airfoils presented in this work are designed for high Reynolds numbers with the main goal of reducing blade loads and mantainig power production. The new airfoil family was designed in collaboration with CENER (Spanish National Renewable Energy Centre). The airfoil family was designed using a evolutionary algorithm based optimization tool with different objectives, both aerodynamic and structural, coupled with an airfoil geometry generation tool. Force coefficients of the designed airfoil were obtained using the panel code XFOIL in which the boundary layer/inviscid flow coupling is ineracted via surface transpiration model. The desing methodology includes a novel technique to define the objective functions based on normalizing the functions using weight parameters created from data of airfoils used as reference. Four airfoils have been designed, here three of them will be presented, with relative thickness of 18%, 21%, 25%, which have been verified with the in-house CFD code, Wind Multi Block WMB, and later validated with wind tunnel experiments. Some of the objectives for the designed airfoils concern the aerodynamic behavior (high efficiency and lift, high tangential coefficient, insensitivity to rough conditions, etc.), others concern the geometry (good for structural design

Generalized Kutta–Joukowski theorem for multi-vortex and multi-airfoil flow (a lumped vortex model

Directory of Open Access Journals (Sweden)

Bai Chenyuan

2014-02-01

Full Text Available For purpose of easy identification of the role of free vortices on the lift and drag and for purpose of fast or engineering evaluation of forces for each individual body, we will extend in this paper the Kutta–Joukowski (KJ theorem to the case of inviscid flow with multiple free vortices and multiple airfoils. The major simplification used in this paper is that each airfoil is represented by a lumped vortex, which may hold true when the distances between vortices and bodies are large enough. It is found that the Kutta–Joukowski theorem still holds provided that the local freestream velocity and the circulation of the bound vortex are modified by the induced velocity due to the outside vortices and airfoils. We will demonstrate how to use the present result to identify the role of vortices on the forces according to their position, strength and rotation direction. Moreover, we will apply the present results to a two-cylinder example of Crowdy and the Wagner example to demonstrate how to perform fast force approximation for multi-body and multi-vortex problems. The lumped vortex assumption has the advantage of giving such kinds of approximate results which are very easy to use. The lack of accuracy for such a fast evaluation will be compensated by a rigorous extension, with the lumped vortex assumption removed and with vortex production included, in a forthcoming paper.

Lie symmetries of a generalized Kuznetsov-Zabolotskaya-Khoklov equation

OpenAIRE

Gungor, F.; Ozemir, C.

2014-01-01

We consider a class of generalized Kuznetsov--Zabolotskaya--Khokhlov (gKZK) equations and determine its equivalence group, which is then used to give a complete symmetry classification of this class. The infinite-dimensional symmetry is used to reduce such equations to (1+1)-dimensional PDEs. Special attention is paid to group-theoretical properties of a class of generalized dispersionless KP (gdKP) or Zabolotskaya--Khokhlov equations as a subclass of gKZK equations. The conditions are determ...

Acoustics of a Mixed Porosity Felt Airfoil

Science.gov (United States)

2016-06-06

NUWC-NPT Technical Report 12,212 6 June 2016 Acoustics of a Mixed Porosity Felt Airfoil Aren M. Hellum Undersea Warfare Weapons...Felt Airfoil 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) Aren M. Hellum 5.d PROJECT NUMBER 5e...existing literature. Geyer et al. [5] measured a sound reduction of 5 to 15 dB for airfoils made entirely of porous material. A 1973 patent

Dynamic stall study of a multi-element airfoil

Science.gov (United States)

Tung, Chee; Mcalister, Kenneth W.; Wang, Clin M.

1992-01-01

Unsteady flow behavior and load characteristics of a VR-7 airfoil with and without a slat were studied in the water tunnel of the Aeroflightdynamics Directorate, NASA Ames Research Center. Both airfoils were oscillated sinusoidally between 5 and 25 degrees at a Reynolds number of 200,000 to obtain the unsteady lift, drag and pitching moment data. A fluorescing dye was released from an orifice located at the leading edge of the airfoil for the purpose of visualizing the boundary layer and wake flow. The flow field and load predictions of an incompressible Navier-Stokes code based on a velocity-vorticity formulation were compared with the test data. The test and predictions both confirm that the slatted VR-7 airfoil delays both static and dynamic stall as compared to the VR-7 airfoil alone.

Wind turbine airfoil design method with low noise and experimental analysis

DEFF Research Database (Denmark)

Wang, Quan; Chen, Jin; Cheng, Jiangtao

2015-01-01

In order to study the noise characteristic of wind turbine airfoils, the airfoil optimal design mathematic model was built based on airfoil functional integrated theory and noise calculated model. The new optimized objective function of maximizing lift/drag to noise was developed on the design......, though there is a certain difference between the theory results and experiment data. Compared with NACA-64-618 airfoil, the CQU-DTU-B18 airfoil exhibits lower noise, which validates the feasibility of this design method. It is a guide to design wind turbine airfoil with lower noise and to reduce airfoil...

A Comparison between Linear IRT Observed-Score Equating and Levine Observed-Score Equating under the Generalized Kernel Equating Framework

Science.gov (United States)

Chen, Haiwen

2012-01-01

In this article, linear item response theory (IRT) observed-score equating is compared under a generalized kernel equating framework with Levine observed-score equating for nonequivalent groups with anchor test design. Interestingly, these two equating methods are closely related despite being based on different methodologies. Specifically, when…

Multi-symplectic Preissmann methods for generalized Zakharov-Kuznetsov equation

International Nuclear Information System (INIS)

Wang Junjie; Yang Kuande; Wang Liantang

2012-01-01

Generalized Zakharov-Kuznetsov equation, a typical nonlinear wave equation, was studied based on the multi-symplectic theory in Hamilton space. The multi-symplectic formulations of generalized Zakharov-Kuznetsov equation with several conservation laws are presented. The multi-symplectic Preissmann method is used to discretize the formulations. The numerical experiment is given, and the results verify the efficiency of the multi-symplectic scheme. (authors)

Development and testing of airfoils for high-altitude aircraft

Science.gov (United States)

Drela, Mark (Principal Investigator)

1996-01-01

Specific tasks included airfoil design; study of airfoil constraints on pullout maneuver; selection of tail airfoils; examination of wing twist; test section instrumentation and layout; and integrated airfoil/heat-exchanger tests. In the course of designing the airfoil, specifically for the APEX test vehicle, extensive studies were made over the Mach and Reynolds number ranges of interest. It is intended to be representative of airfoils required for lightweight aircraft operating at extreme altitudes, which is the primary research objective of the APEX program. Also considered were thickness, pitching moment, and off-design behavior. The maximum ceiling parameter M(exp 2)C(sub L) value achievable by the Apex-16 airfoil was found to be a strong constraint on the pullout maneuver. The NACA 1410 and 2410 airfoils (inverted) were identified as good candidates for the tail, with predictable behavior at low Reynolds numbers and good tolerance to flap deflections. With regards to wing twist, it was decided that a simple flat wing was a reasonable compromise. The test section instrumentation consisted of surface pressure taps, wake rakes, surface-mounted microphones, and skin-friction gauges. Also, a modest wind tunnel test was performed for an integrated airfoil/heat-exchanger configuration, which is currently on Aurora's 'Theseus' aircraft. Although not directly related to the APEX tests, the aerodynamics or heat exchangers has been identified as a crucial aspect of designing high-altitude aircraft and hence is relevant to the ERAST program.

Explicit Solutions for Generalized (2+1)-Dimensional Nonlinear Zakharov-Kuznetsov Equation

International Nuclear Information System (INIS)

Sun Yuhuai; Ma Zhimin; Li Yan

2010-01-01

The exact solutions of the generalized (2+1)-dimensional nonlinear Zakharov-Kuznetsov (Z-K) equation are explored by the method of the improved generalized auxiliary differential equation. Many explicit analytic solutions of the Z-K equation are obtained. The methods used to solve the Z-K equation can be employed in further work to establish new solutions for other nonlinear partial differential equations. (general)

Comparison of model propeller tests with airfoil theory

Science.gov (United States)

Durand, William F; Lesley, E P

1925-01-01

The purpose of the investigation covered by this report was the examination of the degree of approach which may be anticipated between laboratory tests on model airplane propellers and results computed by the airfoil theory, based on tests of airfoils representative of successive blade sections. It is known that the corrections of angles of attack and for aspect ratio, speed, and interference rest either on experimental data or on somewhat uncertain theoretical assumptions. The general situation as regards these four sets of corrections is far from satisfactory, and while it is recognized that occasion exists for the consideration of such corrections, their determination in any given case is a matter of considerable uncertainty. There exists at the present time no theory generally accepted and sufficiently comprehensive to indicate the amount of such corrections, and the application to individual cases of the experimental data available is, at best, uncertain. While the results of this first phase of the investigation are less positive than had been hoped might be the case, the establishment of the general degree of approach between the two sets of results which might be anticipated on the basis of this simpler mode of application seems to have been desirable.

Numerical Simulation of Unsteady Large Scale Separated Flow around Oscillating Airfoil

OpenAIRE

Isogai, Koji; 磯貝, 紘二

1991-01-01

Numerical simulations of dynamic stall phenomenon of NACA0012 airfoil oscillating in pitch near static stalling angle are performed by using the compressible Navier-Stokes equations. In the present computations, a TVD scheme and an algebraic turbulence model are employed for the simulations of the unsteady separated flows at Reynolds number of 1.1x105. The hysteresis loops of the unsteady pitching moment during dynamic stall are compared with the existing experimental data. The flow pattern a...

FLEET Velocimetry Measurements on a Transonic Airfoil

Science.gov (United States)

Burns, Ross A.; Danehy, Paul M.

2017-01-01

Femtosecond laser electronic excitation tagging (FLEET) velocimetry was used to study the flowfield around a symmetric, transonic airfoil in the NASA Langley 0.3-m TCT facility. A nominal Mach number of 0.85 was investigated with a total pressure of 125 kPa and total temperature of 280 K. Two-components of velocity were measured along vertical profiles at different locations above, below, and aft of the airfoil at angles of attack of 0 deg, 3.5 deg, and 7deg. Measurements were assessed for their accuracy, precision, dynamic range, spatial resolution, and overall measurement uncertainty in the context of the applied flowfield. Measurement precisions as low as 1 m/s were observed, while overall uncertainties ranged from 4 to 5 percent. Velocity profiles within the wake showed sufficient accuracy, precision, and sensitivity to resolve both the mean and fluctuating velocities and general flow physics such as shear layer growth. Evidence of flow separation is found at high angles of attack.

RANS Simulations of Aerodynamic Performance of NACA 0015 Flapped Airfoil

Directory of Open Access Journals (Sweden)

Sohaib Obeid

2017-01-01

Full Text Available An analysis of 2D subsonic flow over an NACA 0015 airfoil with a 30% trailing edge flap at a constant Reynolds number of 106 for various incidence angles and a range of flap deflections is presented. The steady-state governing equations of continuity and momentum conservation are solved combined with the realizable k-ε turbulence model using the ANSYS-Fluent code (Version 13.7, ANSYS, Inc., Canonsburg, PA, USA. The primary objective of the study is to provide a comprehensive understanding of flow characteristics around the NACA 0015 airfoil as a function of the angle of attack and flap deflection at Re = 106 using the realizable k-ε turbulence model. The results are validated through comparison of the predictions with the free field experimental measurements. Consistent with the experimental observations, the numerical results show that increased flap deflections increase the maximum lift coefficient, move the zero-lift angle of attack (AoA to a more negative value, decrease the stall AoA, while the slope of the lift curve remains unchanged and the curve just shifts upwards. In addition, the numerical simulations provide limits for lift increment Δ C l and Cl, max values to be 1.1 and 2.2, respectively, obtained at a flap deflection of 50°. This investigation demonstrates that the realizable k-ε turbulence model is capable of predicting flow features over an airfoil with and without flap deflections with reasonable accuracy.

Wind turbine airfoil catalogue

OpenAIRE

Bertagnolio, F.; Sørensen, Niels N.; Johansen, Jeppe; Fuglsang, P.

2001-01-01

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 solverEllipSys2D, as well as results from the panel method code XFOIL. Secondly, we are interested in validating the code EllipSys2D and finding out for which airfoils it does not perform well compared to the experiments, as well as why, when it does so...

Transonic Airfoil Flow Simulation. Part II: Inviscid-Viscous Coupling Scheme

Directory of Open Access Journals (Sweden)

Vladimir CARDOŞ

2010-09-01

Full Text Available A calculation method for the subsonic and transonic viscous flow over airfoil using the displacement surface concept is described. This modelling technique uses a finite volume method for the time-dependent Euler equations and laminar and turbulent boundary-layer integral methods. In additional special models for transition, laminar or turbulent separation bubbles and trailing edge treatment have been selected. However, the flow is limited to small parts of trailing edge-type separation. Comparisons with experimental data and other methods are shown.

Automatic computation and solution of generalized harmonic balance equations

Science.gov (United States)

Peyton Jones, J. C.; Yaser, K. S. A.; Stevenson, J.

2018-02-01

Generalized methods are presented for generating and solving the harmonic balance equations for a broad class of nonlinear differential or difference equations and for a general set of harmonics chosen by the user. In particular, a new algorithm for automatically generating the Jacobian of the balance equations enables efficient solution of these equations using continuation methods. Efficient numeric validation techniques are also presented, and the combined algorithm is applied to the analysis of dc, fundamental, second and third harmonic response of a nonlinear automotive damper.

An implicit spectral formula for generalized linear Schroedinger equations

International Nuclear Information System (INIS)

Schulze-Halberg, A.; Garcia-Ravelo, J.; Pena Gil, Jose Juan

2009-01-01

We generalize the semiclassical Bohr–Sommerfeld quantization rule to an exact, implicit spectral formula for linear, generalized Schroedinger equations admitting a discrete spectrum. Special cases include the position-dependent mass Schroedinger equation or the Schroedinger equation for weighted energy. Requiring knowledge of the potential and the solution associated with the lowest spectral value, our formula predicts the complete spectrum in its exact form. (author)

General particle transport equation. Final report

International Nuclear Information System (INIS)

Lafi, A.Y.; Reyes, J.N. Jr.

1994-12-01

The general objectives of this research are as follows: (1) To develop fundamental models for fluid particle coalescence and breakage rates for incorporation into statistically based (Population Balance Approach or Monte Carlo Approach) two-phase thermal hydraulics codes. (2) To develop fundamental models for flow structure transitions based on stability theory and fluid particle interaction rates. This report details the derivation of the mass, momentum and energy conservation equations for a distribution of spherical, chemically non-reacting fluid particles of variable size and velocity. To study the effects of fluid particle interactions on interfacial transfer and flow structure requires detailed particulate flow conservation equations. The equations are derived using a particle continuity equation analogous to Boltzmann's transport equation. When coupled with the appropriate closure equations, the conservation equations can be used to model nonequilibrium, two-phase, dispersed, fluid flow behavior. Unlike the Eulerian volume and time averaged conservation equations, the statistically averaged conservation equations contain additional terms that take into account the change due to fluid particle interfacial acceleration and fluid particle dynamics. Two types of particle dynamics are considered; coalescence and breakage. Therefore, the rate of change due to particle dynamics will consider the gain and loss involved in these processes and implement phenomenological models for fluid particle breakage and coalescence

Turbine airfoil with an internal cooling system having vortex forming turbulators

Science.gov (United States)

Lee, Ching-Pang

2014-12-30

A turbine airfoil usable in a turbine engine and having at least one cooling system is disclosed. At least a portion of the cooling system may include one or more cooling channels having a plurality of turbulators protruding from an inner surface and positioned generally nonorthogonal and nonparallel to a longitudinal axis of the airfoil cooling channel. The configuration of turbulators may create a higher internal convective cooling potential for the blade cooling passage, thereby generating a high rate of internal convective heat transfer and attendant improvement in overall cooling performance. This translates into a reduction in cooling fluid demand and better turbine performance.

Reversible airfoils for stopped rotors in high speed flight

International Nuclear Information System (INIS)

Niemiec, Robert; Jacobellis, George; Gandhi, Farhan

2014-01-01

This study starts with the design of a reversible airfoil rib for stopped-rotor applications, where the sharp trailing-edge morphs into the rounded leading-edge, and vice-versa. A NACA0012 airfoil is approximated in a piecewise linear manner and straight, rigid outer profile links used to define the airfoil contour. The end points of the profile links connect to control links, each set on a central actuation rod via an offset. Chordwise motion of the actuation rod moves the control and the profile links and reverses the airfoil. The paper describes the design methodology and evolution of the final design, based on which two reversible airfoil ribs were fabricated and used to assemble a finite span reversible rotor/wing demonstrator. The profile links were connected by Aluminum strips running in the spanwise direction which provided stiffness as well as support for a pre-tensioned elastomeric skin. An inter-rib connector with a curved-front nose piece supports the leading-edge. The model functioned well and was able to reverse smoothly back-and-forth, on application and reversal of a voltage to the motor. Navier–Stokes CFD simulations (using the TURNS code) show that the drag coefficient of the reversible airfoil (which had a 13% maximum thickness due to the thickness of the profile links) was comparable to that of the NACA0013 airfoil. The drag of a 16% thick elliptical airfoil was, on average, about twice as large, while that of a NACA0012 in reverse flow was 4–5 times as large, even prior to stall. The maximum lift coefficient of the reversible airfoil was lower than the elliptical airfoil, but higher than the NACA0012 in reverse flow operation. (paper)

Symmetries of the Euler compressible flow equations for general equation of state

Energy Technology Data Exchange (ETDEWEB)

Boyd, Zachary M. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Ramsey, Scott D. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Baty, Roy S. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

2015-10-15

The Euler compressible flow equations exhibit different Lie symmetries depending on the equation of state (EOS) of the medium in which the flow occurs. This means that, in general, different types of similarity solution will be available in different flow media. We present a comprehensive classification of all EOS’s to which the Euler equations apply, based on the Lie symmetries admitted by the corresponding flow equations, restricting to the case of 1-D planar, cylindrical, or spherical geometry. The results are conveniently summarized in tables. This analysis also clarifies past work by Axford and Ovsiannikov on symmetry classification.

Numerical optimization of circulation control airfoils

Science.gov (United States)

Tai, T. C.; Kidwell, G. H., Jr.; Vanderplaats, G. N.

1981-01-01

A numerical procedure for optimizing circulation control airfoils, which consists of the coupling of an optimization scheme with a viscous potential flow analysis for blowing jet, is presented. The desired airfoil is defined by a combination of three baseline shapes (cambered ellipse, and cambered ellipse with drooped and spiralled trailing edges). The coefficients of these shapes are used as design variables in the optimization process. Under the constraints of lift augmentation and lift-to-drag ratios, the optimal airfoils are found to lie between those of cambered ellipse and the drooped trailing edge, towards the latter as the angle of attack increases. Results agree qualitatively with available experimental data.

Assessment of the performance of various airfoil sections on power generation from a wind turbine using the blade element momentum theory

Energy Technology Data Exchange (ETDEWEB)

Chen, Xiaomin; Agarwal, Ramesh [Department of Mechanical Engineering and Materials Science, Washington University in St. Louis, Jolley Hall, Campus Box 1185, One Brookings Drive, St. Louis, Missouri, 63130 (United States)

2013-07-01

It is well established that the power generated by a Horizontal-Axis Wind Turbine (HAWT) is a function of the number of blades, the tip speed ratio (blade tip speed/wind free stream velocity) and the lift to drag ratio (CL /CD) of the airfoil sections of the blade. The airfoil sections used in HAWT are generally thick airfoils such as the S, DU, FX, Flat-back and NACA 6-series of airfoils. These airfoils vary in (CL /CD) for a given blade and ratio and therefore the power generated by HAWT for different blade airfoil sections will vary. The goal of this paper is to evaluate the effect of different airfoil sections on HAWT performance using the Blade Element Momentum (BEM) theory. In this study, we employ DU 91-W2-250, FX 66-S196-V1, NACA 64421, and Flat-back series of airfoils (FB-3500-0050, FB-3500-0875, and FB-3500-1750) and compare their performance with S809 airfoil used in NREL Phase II and III wind turbines; the lift and drag coefficient data for these airfoils sections are available. The output power of the turbine is calculated using these airfoil section blades for a given blade and ratio and is compared with the original NREL Phase II and Phase III turbines using S809 airfoil section. It is shown that by a suitable choice of airfoil section of HAWT blade, the power generated by the turbine can be significantly increased. Parametric studies are also conducted by varying the turbine diameter.

Symmetric airfoil geometry effects on leading edge noise.

Science.gov (United States)

Gill, James; Zhang, X; Joseph, P

2013-10-01

Computational aeroacoustic methods are applied to the modeling of noise due to interactions between gusts and the leading edge of real symmetric airfoils. Single frequency harmonic gusts are interacted with various airfoil geometries at zero angle of attack. The effects of airfoil thickness and leading edge radius on noise are investigated systematically and independently for the first time, at higher frequencies than previously used in computational methods. Increases in both leading edge radius and thickness are found to reduce the predicted noise. This noise reduction effect becomes greater with increasing frequency and Mach number. The dominant noise reduction mechanism for airfoils with real geometry is found to be related to the leading edge stagnation region. It is shown that accurate leading edge noise predictions can be made when assuming an inviscid meanflow, but that it is not valid to assume a uniform meanflow. Analytic flat plate predictions are found to over-predict the noise due to a NACA 0002 airfoil by up to 3 dB at high frequencies. The accuracy of analytic flat plate solutions can be expected to decrease with increasing airfoil thickness, leading edge radius, gust frequency, and Mach number.

A differential equation for the Generalized Born radii.

Science.gov (United States)

Fogolari, Federico; Corazza, Alessandra; Esposito, Gennaro

2013-06-28

The Generalized Born (GB) model offers a convenient way of representing electrostatics in complex macromolecules like proteins or nucleic acids. The computation of atomic GB radii is currently performed by different non-local approaches involving volume or surface integrals. Here we obtain a non-linear second-order partial differential equation for the Generalized Born radius, which may be solved using local iterative algorithms. The equation is derived under the assumption that the usual GB approximation to the reaction field obeys Laplace's equation. The equation admits as particular solutions the correct GB radii for the sphere and the plane. The tests performed on a set of 55 different proteins show an overall agreement with other reference GB models and "perfect" Poisson-Boltzmann based values.

Fundamental equations for two-phase flow. Part 1: general conservation equations. Part 2: complement and remarks

International Nuclear Information System (INIS)

Delhaye, J.M.

1968-12-01

This report deals with the general equations of mass conservation, of momentum conservation, and energy conservation in the case of a two-phase flow. These equations are presented in several forms starting from integral equations which are assumed initially a priori. 1. Equations with local instantaneous variables, and interfacial conditions; 2. Equations with mean instantaneous variables in a cross-section, and practical applications: these equations include an important experimental value which is the ratio of the cross-section of passage of one phase to the total cross-section of a flow-tube. 3. Equations with a local statistical mean, and equations averaged over a period of time: A more advanced attempt to relate theory and experiment consists in taking the statistical averages of local equations. Equations are then obtained involving variables which are averaged over a period of time with the help of an ergodic assumption. 4. Combination of statistical averages and averages over a cross-section: in this study are considered the local variables averaged statistically, then averaged over the cross-section, and also the variables averaged over the section and then averaged statistically. 5. General equations concerning emulsions: In this case a phase exists in a locally very finely divided form. This peculiarity makes it possible to define a volume concentration, and to draw up equations which have numerous applications. - Certain points arising in the first part of this report concerning general mass conservation equations for two-phase flow have been completed and clarified. The terms corresponding to the interfacial tension have been introduced into the general equations. The interfacial conditions have thus been generalized. A supplementary step has still to be carried out: it has, in effect, been impossible to take the interfacial tension into account in the case of emulsions. It was then appeared interesting to compare this large group of fundamental

RANS Based Methodology for Predicting the Influence of Leading Edge Erosion on Airfoil Performance

Energy Technology Data Exchange (ETDEWEB)

Langel, Christopher M. [Univ. of California, Davis, CA (United States). Dept. of Mechanical and Aerospace Engineering; Chow, Raymond C. [Univ. of California, Davis, CA (United States). Dept. of Mechanical and Aerospace Engineering; van Dam, C. P. [Univ. of California, Davis, CA (United States). Dept. of Mechanical and Aerospace Engineering; Maniaci, David Charles [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Wind Energy Technologies Dept.

2017-10-01

The impact of surface roughness on flows over aerodynamically designed surfaces is of interested in a number of different fields. It has long been known the surface roughness will likely accelerate the laminar- turbulent transition process by creating additional disturbances in the boundary layer. However, there are very few tools available to predict the effects surface roughness will have on boundary layer flow. There are numerous implications of the premature appearance of a turbulent boundary layer. Increases in local skin friction, boundary layer thickness, and turbulent mixing can impact global flow properties compounding the effects of surface roughness. With this motivation, an investigation into the effects of surface roughness on boundary layer transition has been conducted. The effort involved both an extensive experimental campaign, and the development of a high fidelity roughness model implemented in a R ANS solver. Vast a mounts of experimental data was generated at the Texas A&M Oran W. Nicks Low Speed Wind Tunnel for the calibration and validation of the roughness model described in this work, as well as future efforts. The present work focuses on the development of the computational model including a description of the calibration process. The primary methodology presented introduces a scalar field variable and associated transport equation that interacts with a correlation based transition model. The additional equation allows for non-local effects of surface roughness to be accounted for downstream of rough wall sections while maintaining a "local" formulation. The scalar field is determined through a boundary condition function that has been calibrated to flat plate cases with sand grain roughness. The model was initially tested on a NACA 0012 airfoil with roughness strips applied to the leading edge. Further calibration of the roughness model was performed using results from the companion experimental study on a NACA 63₃ -418 airfoil

Boundary layer development on turbine airfoil suction surfaces

Science.gov (United States)

Sharma, O. P.; Wells, R. A.; Schlinker, R. H.; Bailey, D. A.

1981-01-01

The results of a study supported by NASA under the Energy Efficient Engine Program, conducted to investigate the development of boundary layers under the influence of velocity distributions that simulate the suction sides of two state-of-the-art turbine airfoils, are presented. One velocity distribution represented a forward loaded airfoil ('squared-off' design), while the other represented an aft loaded airfoil ('aft loaded' design). These velocity distributions were simulated in a low-speed, high-aspect-ratio wind tunnel specifically designed for boundary layer investigations. It is intended that the detailed data presented in this paper be used to develop improved turbulence model suitable for application to turbine airfoil design.

Characterization of the Effect of Wing Surface Instrumentation on UAV Airfoil Performance

Science.gov (United States)

Ratnayake, Nalin A.

2009-01-01

Recently proposed flight research at NASA Dryden Flight Research Center (DFRC) has prompted study into the aerodynamic effects of modifications made to the surfaces of laminar airfoils. The research is focused on the high-aspect ratio, laminar-flow type wings commonly found on UAVs and other aircraft with a high endurance requirement. A broad range of instrumentation possibilities, such as structural, pressure, and temperature sensing devices may require the alteration of the airfoil outer mold line as part of the installation process. This study attempts to characterize the effect of installing this additiona1 instrumentation on key airfoil performance factors, such as transition location, lift and drag curves, and stall point. In particular, the general case of an airfoil that is channeled in the spanwise direction is considered, and the impact on key performance characteristics is assessed. Particular attention is focused on exploring the limits of channel depth and low-Reynolds number on performance and stall characteristics. To quantify the effect of increased skin friction due to premature transition caused by protruding or recessed instrumentation, two simplified, conservative scenarios are used to consider two potential sources of diaturbance: A) that leading edge alterations would cause linearly expanding areas (triangles) of turbulent flow on both surfaces of the wing upstream of the natural transition point, and B) that a channel or bump on the upper surface would trip turbulent flow across the whole upper surface upstream of the natural transition point. A potentially more important consideration than the skin friction drag increment is the change in overall airfoil performance due to the installation of instrumentation along most of the wingspan. To quantify this effect, 2D CFD simulations of the flow over a representative mid-span airfoil section were conducted in order to assess the change in lift and drag curves for the airfoil in the presence of

Generalized solutions of nonlinear partial differential equations

CERN Document Server

Rosinger, EE

1987-01-01

During the last few years, several fairly systematic nonlinear theories of generalized solutions of rather arbitrary nonlinear partial differential equations have emerged. The aim of this volume is to offer the reader a sufficiently detailed introduction to two of these recent nonlinear theories which have so far contributed most to the study of generalized solutions of nonlinear partial differential equations, bringing the reader to the level of ongoing research.The essence of the two nonlinear theories presented in this volume is the observation that much of the mathematics concernin

Alternate Solution to Generalized Bernoulli Equations via an Integrating Factor: An Exact Differential Equation Approach

Science.gov (United States)

Tisdell, C. C.

2017-01-01

Solution methods to exact differential equations via integrating factors have a rich history dating back to Euler (1740) and the ideas enjoy applications to thermodynamics and electromagnetism. Recently, Azevedo and Valentino presented an analysis of the generalized Bernoulli equation, constructing a general solution by linearizing the problem…

Research on improved design of airfoil profiles based on the continuity of airfoil surface curvature of wind turbines

DEFF Research Database (Denmark)

Chen, Jin; Cheng, Jiangtao; Shen, Wenzhong

2013-01-01

Aerodynamic of airfoil performance is closely related to the continuity of its surface curvature, and airfoil profiles with a better aerodynamic performance plays an important role in the design of wind turbine. The surface curvature distribution along the chord direction and pressure distributio...

Aeroacoustic Computations for Turbulent Airfoil Flows

DEFF Research Database (Denmark)

Shen, Wen Zhong; Zhu, Wei Jun; Sørensen, Jens Nørkær

2009-01-01

a NACA 0015 airfoil at a Mach number of 0.2 and a Reynolds number of 1.6 x 10(5) for different angles of attack. The flow solutions are validated by comparing lift and drag characteristics with experimental data. The comparisons show good agreements between the computed and measured airfoil lift...

Optimization design of airfoil profiles based on the noise of wind turbines

DEFF Research Database (Denmark)

Cheng, Jiangtao; Chen, Jin; Cheng, Jiangtao

2012-01-01

Based on design theory of airfoil profiles and airfoil self-noise prediction model, a new method with the target of the airfoil average efficiency-noise ratio of design ranges for angle of attack had been developed for designing wind turbine airfoils. The airfoil design method was optimized for a...

Generalized reduced MHD equations

International Nuclear Information System (INIS)

Kruger, S.E.; Hegna, C.C.; Callen, J.D.

1998-07-01

A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general toroidal configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Additionally, neoclassical closures and equilibrium shear flow effects are easily accounted for in this model. Equations for the inner resistive layer are derived which reproduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson

Generalized Callan-Symanzik equations and the Renormalization Group

International Nuclear Information System (INIS)

MacDowell, S.W.

1975-01-01

A set of generalized Callan-Symanzik equations derived by Symanzik, relating Green's functions with arbitrary number of mass insertions, is shown be equivalent to the new Renormalization Group equation proposed by S. Weinberg

Non-intrusive load characterization of an airfoil using PIV

Energy Technology Data Exchange (ETDEWEB)

Oudheusden, B.W. van; Scarano, F.; Casimiri, E.W.F. [Dept. of Aerospace Engineering, Delft Univ. of Tech., Delft (Netherlands)

2006-06-15

An assessment is made of the feasibility of using PIV velocity data for the non-intrusive aerodynamic force characterization (lift, drag and pitching moment) of an airfoil. The method relies upon the application of control-volume approaches in combination with the deduction of the pressure from the PIV experimental data, by making use of the momentum equation. First, the consistency of the method is verified by means of synthetic data obtained from CFD. Subsequently, the procedure was applied in an experimental investigation, in which the PIV approach is validated against standard pressure-based methods (surface pressure distribution and wake rake). (orig.)

On the non-stationary generalized Langevin equation

Science.gov (United States)

Meyer, Hugues; Voigtmann, Thomas; Schilling, Tanja

2017-12-01

In molecular dynamics simulations and single molecule experiments, observables are usually measured along dynamic trajectories and then averaged over an ensemble ("bundle") of trajectories. Under stationary conditions, the time-evolution of such averages is described by the generalized Langevin equation. By contrast, if the dynamics is not stationary, it is not a priori clear which form the equation of motion for an averaged observable has. We employ the formalism of time-dependent projection operator techniques to derive the equation of motion for a non-equilibrium trajectory-averaged observable as well as for its non-stationary auto-correlation function. The equation is similar in structure to the generalized Langevin equation but exhibits a time-dependent memory kernel as well as a fluctuating force that implicitly depends on the initial conditions of the process. We also derive a relation between this memory kernel and the autocorrelation function of the fluctuating force that has a structure similar to a fluctuation-dissipation relation. In addition, we show how the choice of the projection operator allows us to relate the Taylor expansion of the memory kernel to data that are accessible in MD simulations and experiments, thus allowing us to construct the equation of motion. As a numerical example, the procedure is applied to Brownian motion initialized in non-equilibrium conditions and is shown to be consistent with direct measurements from simulations.

Multiple solutions and stability of the steady transonic small-disturbance equation

Directory of Open Access Journals (Sweden)

Ya Liu

2017-09-01

Full Text Available Numerical solutions of the steady transonic small-disturbance (TSD potential equation are computed using the conservative Murman−Cole scheme. Multiple solutions are discovered and mapped out for the Mach number range at zero angle of attack and the angle of attack range at Mach number 0.85 for the NACA 0012 airfoil. We present a linear stability analysis method by directly assembling and evaluating the Jacobian matrix of the nonlinear finite-difference equation of the TSD equation. The stability of all the discovered multiple solutions are then determined by the proposed eigen analysis. The relation of stability to convergence of the iterative method for solving the TSD equation is discussed. Computations and the stability analysis demonstrate the possibility of eliminating the multiple solutions and stabilizing the remaining unique solution by adding a sufficiently long splitter plate downstream the airfoil trailing edge. Finally, instability of the solution of the TSD equation is shown to be closely connected to the onset of transonic buffet by comparing with experimental data.

Pitching Airfoil Boundary Layer Investigations

OpenAIRE

Raffel, Markus; Richard, Hugues; Richter, Kai; Bosbach, Johannes; Geißler, Wolfgang

2006-01-01

The present paper describes an experiment performed in a transonic wind tunnel facility where a new test section has been developed especially for the investigation of the unsteady flow above oscillating airfoils under dynamic stall conditions. Dynamic stall is characterized by the development, movement and shedding of one or more concentrated vortices on the airfoils upper surface. The hysteresis loops of lift-, drag- and pitching moment are highly influenced by these vortices. To understand...

Unsteady airfoil flows with application to aeroelastic stability

Energy Technology Data Exchange (ETDEWEB)

Johansen, Jeppe

1999-09-01

The present report describes numerical investigation of two-dimensional unsteady airfoil flows with application to aeroelastic stability. The report is divided in two parts. Part A describes the purely aerodynamic part, while Part B includes the aeroelastic part. In Part A a transition prediction algorithm based on a simplified version of the e{sup n} method is proposed. Laminar Boundary Layer instability data are stored in a database from which stability characteristics can be extracted by interpolation. Input to the database are laminar integral boundary layer parameters. These are computed from an integral boundary layer formulation coupled to a Navier-Stokes flow solver. Five different airfoils are considered at fixed angle of attack, and the flow is computed assuming both fully turbulent and transitional flow and compared with experimental data. Results indicate that using a transition model the drag prediction is improved considerably. Also the lift is slightly improved. At high angles of attack transition will affect leading edge separation which again will affect the overall vortex shedding. If the transition point is not properly predicted this will affect the whole hysteresis curve. The transition model developed in the present work showed more stable predictions compared to the empirical transition model. In Part B a simple three degrees-of-freedom (DOF) structural dynamics model is developed and coupled to the aerodynamics models from Part A. A 2nd order accurate time integration scheme is used to solve the equations of motion. Two airfoils are investigated. The aeroelastic models predict stable conditions well at low angle of attack. But at high angles of attack, and where unstable behaviour is expected, only the Navier-Stokes solver predict correct aeroelastic response. The semi-empirical dynamic stall model does not predict vortex shedding and moment correctly leading to an erroneous aerodynamic damping. (au) 5 tabs.; 55 ills., 52 refs.

Turbine blade having a constant thickness airfoil skin

Science.gov (United States)

Marra, John J

2012-10-23

A turbine blade is provided for a gas turbine comprising: a support structure comprising a base defining a root of the blade and a framework extending radially outwardly from the base, and an outer skin coupled to the support structure framework. The skin has a generally constant thickness along substantially the entire radial extent thereof. The framework and the skin define an airfoil of the blade.

Combinatorics of Generalized Bethe Equations

Science.gov (United States)

Kozlowski, Karol K.; Sklyanin, Evgeny K.

2013-10-01

A generalization of the Bethe ansatz equations is studied, where a scalar two-particle S-matrix has several zeroes and poles in the complex plane, as opposed to the ordinary single pole/zero case. For the repulsive case (no complex roots), the main result is the enumeration of all distinct solutions to the Bethe equations in terms of the Fuss-Catalan numbers. Two new combinatorial interpretations of the Fuss-Catalan and related numbers are obtained. On the one hand, they count regular orbits of the permutation group in certain factor modules over {{Z}^M}, and on the other hand, they count integer points in certain M-dimensional polytopes.

Damping element for reducing the vibration of an airfoil

Science.gov (United States)

Campbell, Christian X; Marra, John J

2013-11-12

An airfoil (10) is provided with a tip (12) having an opening (14) to a center channel (24). A damping element (16) is inserted within the opening of the center channel, to reduce an induced vibration of the airfoil. The mass of the damping element, a spring constant of the damping element within the center channel, and/or a mounting location (58) of the damping element within the center channel may be adjustably varied, to shift a resonance frequency of the airfoil outside a natural operating frequency of the airfoil.

A generalized Zakharov-Shabat equation with finite-band solutions and a soliton-equation hierarchy with an arbitrary parameter

International Nuclear Information System (INIS)

Zhang Yufeng; Tam, Honwah; Feng Binlu

2011-01-01

Highlights: → A generalized Zakharov-Shabat equation is obtained. → The generalized AKNS vector fields are established. → The finite-band solution of the g-ZS equation is obtained. → By using a Lie algebra presented in the paper, a new soliton hierarchy with an arbitrary parameter is worked out. - Abstract: In this paper, a generalized Zakharov-Shabat equation (g-ZS equation), which is an isospectral problem, is introduced by using a loop algebra G ∼ . From the stationary zero curvature equation we define the Lenard gradients {g j } and the corresponding generalized AKNS (g-AKNS) vector fields {X j } and X k flows. Employing the nonlinearization method, we obtain the generalized Zhakharov-Shabat Bargmann (g-ZS-B) system and prove that it is Liouville integrable by introducing elliptic coordinates and evolution equations. The explicit relations of the X k flows and the polynomial integrals {H k } are established. Finally, we obtain the finite-band solutions of the g-ZS equation via the Abel-Jacobian coordinates. In addition, a soliton hierarchy and its Hamiltonian structure with an arbitrary parameter k are derived.

Self-sustained Flow-acoustic Interactions in Airfoil Transitional Boundary Layers

Science.gov (United States)

2015-07-09

AFRL-AFOSR-VA-TR-2015-0235 Self-sustained flow-acoustic interactions in airfoil transitional boundary layers Vladimir Golubev EMBRY-RIDDLE...From - To)      01-04-2012 to 31-03-2015 4.  TITLE AND SUBTITLE Self-sustained flow-acoustic interactions in airfoil transitional boundary layers 5a...complementary experimental and numerical studies of flow-acoustic resonant interactions in transitional airfoils and their impact on airfoil surface

Supercritical Airfoil Coordinates

Data.gov (United States)

National Aeronautics and Space Administration — Rectangular Supercritical Wing (Ricketts) - design and measured locations are provided in an Excel file RSW_airfoil_coordinates_ricketts.xls . One sheet is with Non...

General Reducibility and Solvability of Polynomial Equations ...

African Journals Online (AJOL)

General Reducibility and Solvability of Polynomial Equations. ... Unlike quadratic, cubic, and quartic polynomials, the general quintic and higher degree polynomials cannot be solved algebraically in terms of finite number of additions, ... Galois Theory, Solving Polynomial Systems, Polynomial factorization, Polynomial Ring ...

General solutions of second-order linear difference equations of Euler type

Directory of Open Access Journals (Sweden)

Akane Hongyo

2017-01-01

Full Text Available The purpose of this paper is to give general solutions of linear difference equations which are related to the Euler-Cauchy differential equation \\(y^{\\prime\\prime}+(\\lambda/t^2y=0\\ or more general linear differential equations. We also show that the asymptotic behavior of solutions of the linear difference equations are similar to solutions of the linear differential equations.

Separation control of NACA0015 airfoil using plasma actuators

Science.gov (United States)

Harada, Daisuke; Sakakibara, Jun

2017-11-01

Separation control of NACA0015 airfoil by means of plasma actuators was investigated. Plasma actuators in spanwise intermittent layout on the suction surface of the airfoil were activated with spanwise phase difference φ = 0 or φ = π in the case of dimensionless burst frequencyF+ = 6 and F+ = 0.5 at Re = 6.3 ×104 . The lift and drag of the airfoil were measured using a two component force balance. The flow around the airfoil was measured by PIV analysis. In the condition of F+ = 6 and φ = π at around stall angle, which is 10 degrees, the lift-to-drag ratio was higher than that ofF+ = 6 and φ = 0 . Therefore, it was confirmed that aerodynamic characteristics of the airfoil improved by disturbances with temporal and spatial phase difference.

Design of advanced airfoil for stall-regulated wind turbines

Directory of Open Access Journals (Sweden)

F. Grasso

2017-07-01

Full Text Available Nowadays, all the modern megawatt-class wind turbines make use of pitch control to optimise the rotor performance and control the turbine. However, for kilowatt-range machines, stall-regulated solutions are still attractive and largely used for their simplicity and robustness. In the design phase, the aerodynamics plays a crucial role, especially concerning the selection/design of the necessary airfoils. This is because the airfoil performance is supposed to guarantee high wind turbine performance but also the necessary machine control capabilities. In the present work, the design of a new airfoil dedicated to stall machines is discussed. The design strategy makes use of a numerical optimisation scheme, where a gradient-based algorithm is coupled with the RFOIL code and an original Bezier-curves-based parameterisation to describe the airfoil shape. The performances of the new airfoil are compared in free- and fixed-transition conditions. In addition, the performance of the rotor is analysed, comparing the impact of the new geometry with alternative candidates. The results show that the new airfoil offers better performance and control than existing candidates do.

Airfoil characteristics for wind turbines

OpenAIRE

Bak, C.; Fuglsang, P.; Sørensen, Niels N.; Aagaard Madsen, Helge; Shen, W.Z.; Sørensen, Jens Nørkær

1999-01-01

Airfoil characteristics for use in the Blade Element Momentum (BEM) method calculating the forces on Horizontal Axis Wind Turbines (HAWT) are derived by use of systematic methods. The investigation and derivation of the airfoil characteristics are basedon four different methods: 1) Inverse momentum theory, 2) Actuator disc theory, 3) Numerical optimisation and 4) Quasi-3D CFD computations. The two former methods are based on 3D CFD computations and wind tunnel measurements on a 41-m full-scal...

A novel numerical flux for the 3D Euler equations with general equation of state

KAUST Repository

Toro, Eleuterio F.

2015-09-30

Here we extend the flux vector splitting approach recently proposed in (E F Toro and M E Vázquez-Cendón. Flux splitting schemes for the Euler equations. Computers and Fluids. Vol. 70, Pages 1-12, 2012). The scheme was originally presented for the 1D Euler equations for ideal gases and its extension presented in this paper is threefold: (i) we solve the three-dimensional Euler equations on general meshes; (ii) we use a general equation of state; and (iii) we achieve high order of accuracy in both space and time through application of the semi-discrete ADER methodology on general meshes. The resulting methods are systematically assessed for accuracy, robustness and efficiency on a carefully selected suite of test problems. Formal high accuracy is assessed through convergence rates studies for schemes of up to 4th order of accuracy in both space and time on unstructured meshes.

Measuring Lift with the Wright Airfoils

Science.gov (United States)

Heavers, Richard M.; Soleymanloo, Arianne

2011-01-01

In this laboratory or demonstration exercise, we mount a small airfoil with its long axis vertical at one end of a nearly frictionless rotating platform. Air from a leaf blower produces a sidewise lift force L on the airfoil and a drag force D in the direction of the air flow (Fig. 1). The rotating platform is kept in equilibrium by adding weights…

Compressor airfoil tip clearance optimization system

Science.gov (United States)

Little, David A.; Pu, Zhengxiang

2015-08-18

A compressor airfoil tip clearance optimization system for reducing a gap between a tip of a compressor airfoil and a radially adjacent component of a turbine engine is disclosed. The turbine engine may include ID and OD flowpath boundaries configured to minimize compressor airfoil tip clearances during turbine engine operation in cooperation with one or more clearance reduction systems that are configured to move the rotor assembly axially to reduce tip clearance. The configurations of the ID and OD flowpath boundaries enhance the effectiveness of the axial movement of the rotor assembly, which includes movement of the ID flowpath boundary. During operation of the turbine engine, the rotor assembly may be moved axially to increase the efficiency of the turbine engine.

Generalized Freud's equation and level densities with polynomial

Indian Academy of Sciences (India)

Home; Journals; Pramana – Journal of Physics; Volume 81; Issue 2. Generalized Freud's equation and level densities with polynomial potential. Akshat Boobna Saugata Ghosh. Research Articles Volume 81 ... Keywords. Orthogonal polynomial; Freud's equation; Dyson–Mehta method; methods of resolvents; level density.

New exact solutions to the generalized KdV equation with ...

Indian Academy of Sciences (India)

is reduced to an ordinary differential equation with constant coefficients ... Application to generalized KdV equation with generalized evolution ..... [12] P F Byrd and M D Friedman, Handbook of elliptic integrals for engineers and physicists.

Aero-elastic stability of airfoil flow using 2-D CFD

Energy Technology Data Exchange (ETDEWEB)

Johansen, J [Risoe National Lab., Roskilde (Denmark)

1999-03-01

A three degrees-of-freedom structural dynamics model has been coupled to a two-dimensional incompressible CFD code. The numerical investigation considers aero-elastic stability for two different airfoils; the NACA0012 and the LM 2 18 % airfoils. Stable and unstable configurations and limit cycle oscillations are predicted in accordance with literature for the first airfoil. An attempt to predict stall induced edge-wise vibrations on a wind turbine airfoil fails using this two-dimensional approach. (au)

Turbine airfoil with laterally extending snubber having internal cooling system

Science.gov (United States)

Scribner, Carmen Andrew; Messmann, Stephen John; Marsh, Jan H.

2016-09-06

A turbine airfoil usable in a turbine engine and having at least one snubber with a snubber cooling system positioned therein and in communication with an airfoil cooling system is disclosed. The snubber may extend from the outer housing of the airfoil toward an adjacent turbine airfoil positioned within a row of airfoils. The snubber cooling system may include an inner cooling channel separated from an outer cooling channel by an inner wall. The inner wall may include a plurality of impingement cooling orifices that direct impingement fluid against an outer wall defining the outer cooling channel. In one embodiment, the cooling fluids may be exhausted from the snubber, and in another embodiment, the cooling fluids may be returned to the airfoil cooling system. Flow guides may be positioned in the outer cooling channel, which may reduce cross-flow by the impingement orifices, thereby increasing effectiveness.

Generalized fractional Schroedinger equation with space-time fractional derivatives

International Nuclear Information System (INIS)

Wang Shaowei; Xu Mingyu

2007-01-01

In this paper the generalized fractional Schroedinger equation with space and time fractional derivatives is constructed. The equation is solved for free particle and for a square potential well by the method of integral transforms, Fourier transform and Laplace transform, and the solution can be expressed in terms of Mittag-Leffler function. The Green function for free particle is also presented in this paper. Finally, we discuss the relationship between the cases of the generalized fractional Schroedinger equation and the ones in standard quantum

Generalized reduced magnetohydrodynamic equations

International Nuclear Information System (INIS)

Kruger, S.E.

1999-01-01

A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-Alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Additionally, neoclassical closures and equilibrium shear flow effects are easily accounted for in this model. Equations for the inner resistive layer are derived which reproduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson. The equations have been programmed into a spectral initial value code and run with shear flow that is consistent with the equilibrium input into the code. Linear results of tearing modes with shear flow are presented which differentiate the effects of shear flow gradients in the layer with the effects of the shear flow decoupling multiple harmonics

Turbine airfoil with controlled area cooling arrangement

Science.gov (United States)

Liang, George

2010-04-27

A gas turbine airfoil (10) includes a serpentine cooling path (32) with a plurality of channels (34,42,44) fluidly interconnected by a plurality of turns (38,40) for cooling the airfoil wall material. A splitter component (50) is positioned within at least one of the channels to bifurcate the channel into a pressure-side channel (46) passing in between the outer wall (28) and the inner wall (30) of the pressure side (24) and a suction-side channel (48) passing in between the outer wall (28) and the inner wall (30) of the suction side (26) longitudinally downstream of an intermediate height (52). The cross-sectional area of the pressure-side channel (46) and suction-side channel (48) are thereby controlled in spite of an increasing cross-sectional area of the airfoil along its longitudinal length, ensuring a sufficiently high mach number to provide a desired degree of cooling throughout the entire length of the airfoil.

Aerodynamic loading on a cylinder behind an airfoil

Energy Technology Data Exchange (ETDEWEB)

Zhang, H.J.; Huang, L.; Zhou, Y. [Hong Kong Polytechnic University, Department of Mechanical Engineering, Kowloon (Hong Kong)

2005-05-01

The interaction between the wake of a rotor blade and a downstream cylinder holds the key to the understanding and control of electronic cooling fan noise. In this paper, the aerodynamic characteristics of a circular cylinder are experimentally studied in the presence of an upstream NACA 4412 airfoil for the cylinder-diameter-based Reynolds numbers of Re{sub d}=2,100-20,000, and the airfoil chord-length-based Reynolds numbers of Re{sub c}=14,700-140,000. Lift and drag fluctuations on the cylinder, and the longitudinal velocity fluctuations of the flow behind the cylinder were measured simultaneously using a load cell and two hot wires, respectively. Data analysis shows that unsteady forces on the cylinder increase significantly in the presence of the airfoil wake. The dependence of the forces on two parameters is investigated, that is, the lateral distance (T) between the airfoil and the cylinder, and the Reynolds number. The forces decline quickly as Tincreases. For Re{sub c}<60,000, the vortices shed from the upstream airfoil make a major contribution to the unsteady forces on the cylinder compared to the vortex shedding from the cylinder itself. For Re{sub c}>60,000, no vortices are generated from the airfoil, and the fluctuating forces on the cylinder are caused by its own vortex shedding. (orig.)

Analytical Solution of General Bagley-Torvik Equation

Directory of Open Access Journals (Sweden)

William Labecca

2015-01-01

Full Text Available Bagley-Torvik equation appears in viscoelasticity problems where fractional derivatives seem to play an important role concerning empirical data. There are several works treating this equation by using numerical methods and analytic formulations. However, the analytical solutions presented in the literature consider particular cases of boundary and initial conditions, with inhomogeneous term often expressed in polynomial form. Here, by using Laplace transform methodology, the general inhomogeneous case is solved without restrictions in boundary and initial conditions. The generalized Mittag-Leffler functions with three parameters are used and the solutions presented are expressed in terms of Wiman’s functions and their derivatives.

A generalized fractional sub-equation method for fractional differential equations with variable coefficients

International Nuclear Information System (INIS)

Tang, Bo; He, Yinnian; Wei, Leilei; Zhang, Xindong

2012-01-01

In this Letter, a generalized fractional sub-equation method is proposed for solving fractional differential equations with variable coefficients. Being concise and straightforward, this method is applied to the space–time fractional Gardner equation with variable coefficients. As a result, many exact solutions are obtained including hyperbolic function solutions, trigonometric function solutions and rational solutions. It is shown that the considered method provides a very effective, convenient and powerful mathematical tool for solving many other fractional differential equations in mathematical physics. -- Highlights: ► Study of fractional differential equations with variable coefficients plays a role in applied physical sciences. ► It is shown that the proposed algorithm is effective for solving fractional differential equations with variable coefficients. ► The obtained solutions may give insight into many considerable physical processes.

New solutions of Heun's general equation

Energy Technology Data Exchange (ETDEWEB)

Ishkhanyan, Artur [Engineering Center of Armenian National Academy of Sciences, Ashtarak (Armenia); Suominen, Kalle-Antti [Helsinki Institute of Physics, PL 64, Helsinki (Finland)

2003-02-07

We show that in four particular cases the derivative of the solution of Heun's general equation can be expressed in terms of a solution to another Heun's equation. Starting from this property, we use the Gauss hypergeometric functions to construct series solutions to Heun's equation for the mentioned cases. Each of the hypergeometric functions involved has correct singular behaviour at only one of the singular points of the equation; the sum, however, has correct behaviour. (letter to the editor)

On a generalized fifth order KdV equations

International Nuclear Information System (INIS)

Kaya, Dogan; El-Sayed, Salah M.

2003-01-01

In this Letter, we dealt with finding the solutions of a generalized fifth order KdV equation (for short, gfKdV) by using the Adomian decomposition method (for short, ADM). We prove the convergence of ADM applied to the gfKdV equation. Then we obtain the exact solitary-wave solutions and numerical solutions of the gfKdV equation for the initial conditions. The numerical solutions are compared with the known analytical solutions. Their remarkable accuracy are finally demonstrated for the gfKdV equation

Generalized Fokker-Planck equations for coloured, multiplicative Gaussian noise

International Nuclear Information System (INIS)

Cetto, A.M.; Pena, L. de la; Velasco, R.M.

1984-01-01

With the help of Novikov's theorem, it is possible to derive a master equation for a coloured, multiplicative, Gaussian random process; the coefficients of this master equation satisfy a complicated auxiliary integro-differential equation. For small values of the Kubo number, the master equation reduces to an approximate generalized Fokker-Planck equation. The diffusion coefficient is explicitly written in terms of correlation functions. Finally, a straightforward and elementary second order perturbative treatment is proposed to derive the same approximate Fokker-Planck equation. (author)

Aerodynamic shape optimization of Airfoils in 2-D incompressible flow

Science.gov (United States)

Rangasamy, Srinivethan; Upadhyay, Harshal; Somasekaran, Sandeep; Raghunath, Sreekanth

2010-11-01

An optimization framework was developed for maximizing the region of 2-D airfoil immersed in laminar flow with enhanced aerodynamic performance. It uses genetic algorithm over a population of 125, across 1000 generations, to optimize the airfoil. On a stand-alone computer, a run takes about an hour to obtain a converged solution. The airfoil geometry was generated using two Bezier curves; one to represent the thickness and the other the camber of the airfoil. The airfoil profile was generated by adding and subtracting the thickness curve from the camber curve. The coefficient of lift and drag was computed using potential velocity distribution obtained from panel code, and boundary layer transition prediction code was used to predict the location of onset of transition. The objective function of a particular design is evaluated as the weighted-average of aerodynamic characteristics at various angles of attacks. Optimization was carried out for several objective functions and the airfoil designs obtained were analyzed.

On the General Equation of the Second Degree

Indian Academy of Sciences (India)

IAS Admin

On the General Equation of the Second Degree. Keywords. Conics, eigenvalues, eigenvec- tors, pairs of lines. S Kesavan. S Kesavan works at the. Institute for Mathematical. Sciences, Chennai. His area of interest is partial differential equations with specialization in elliptic problems connected to homogenization, control.

Analytical Solution of General Bagley-Torvik Equation

OpenAIRE

William Labecca; Osvaldo Guimarães; José Roberto C. Piqueira

2015-01-01

Bagley-Torvik equation appears in viscoelasticity problems where fractional derivatives seem to play an important role concerning empirical data. There are several works treating this equation by using numerical methods and analytic formulations. However, the analytical solutions presented in the literature consider particular cases of boundary and initial conditions, with inhomogeneous term often expressed in polynomial form. Here, by using Laplace transform methodology, the general inhomoge...

Inviscid double wake model for stalled airfoils

International Nuclear Information System (INIS)

Marion, L; Ramos-García, N; Sørensen, J N

2014-01-01

An inviscid double wake model based on a steady two-dimensional panel method has been developed to predict aerodynamic loads of wind turbine airfoils in the deep stall region. The separated flow is modelled using two constant vorticity sheets which are released at the trailing edge and at the separation point. A calibration of the code through comparison with experiments has been performed using one set of airfoils. A second set of airfoils has been used for the validation of the calibrated model. Predicted aerodynamic forces for a wide range of angles of attack (0 to 90 deg) are in overall good agreement with wind tunnel measurements

Turbine airfoil with outer wall thickness indicators

Science.gov (United States)

Marra, John J; James, Allister W; Merrill, Gary B

2013-08-06

A turbine airfoil usable in a turbine engine and including a depth indicator for determining outer wall blade thickness. The airfoil may include an outer wall having a plurality of grooves in the outer surface of the outer wall. The grooves may have a depth that represents a desired outer surface and wall thickness of the outer wall. The material forming an outer surface of the outer wall may be removed to be flush with an innermost point in each groove, thereby reducing the wall thickness and increasing efficiency. The plurality of grooves may be positioned in a radially outer region of the airfoil proximate to the tip.

Travelling wave solutions of the generalized Benjamin-Bona-Mahony equation

International Nuclear Information System (INIS)

Estevez, P.G.; Kuru, S.; Negro, J.; Nieto, L.M.

2009-01-01

A class of particular travelling wave solutions of the generalized Benjamin-Bona-Mahony equation is studied systematically using the factorization technique. Then, the general travelling wave solutions of Benjamin-Bona-Mahony equation, and of its modified version, are also recovered.

Design of the LRP airfoil series using 2D CFD

DEFF Research Database (Denmark)

Zahle, Frederik; Bak, Christian; Sørensen, Niels N.

2014-01-01

This paper describes the design and wind tunnel testing of a high-Reynolds number, high lift airfoil series designed for wind turbines. The airfoils were designed using direct gradient- based numerical multi-point optimization based on a Bezier parameterization of the shape, coupled to the 2D...... Navier-Stokes flow solver EllipSys2D. The resulting airfoils, the LRP2-30 and LRP2-36, achieve both higher operational lift coefficients and higher lift to drag ratios compared to the equivalent FFA-W3 airfoils....

Design of the LRP airfoil series using 2D CFD

International Nuclear Information System (INIS)

Zahle, Frederik; Bak, Christian; Sørensen, Niels N; Vronsky, Tomas; Gaudern, Nicholas

2014-01-01

This paper describes the design and wind tunnel testing of a high-Reynolds number, high lift airfoil series designed for wind turbines. The airfoils were designed using direct gradient- based numerical multi-point optimization based on a Bezier parameterization of the shape, coupled to the 2D Navier-Stokes flow solver EllipSys2D. The resulting airfoils, the LRP2-30 and LRP2-36, achieve both higher operational lift coefficients and higher lift to drag ratios compared to the equivalent FFA-W3 airfoils

Nonlinear aerodynamics of two-dimensional airfoils in severe maneuver

Science.gov (United States)

Scott, Matthew T.; Mccune, James E.

1988-01-01

This paper presents a nonlinear theory of forces and moment acting on a two-dimensional airfoil in unsteady potential flow. Results are obtained for cases of both large and small amplitude motion. The analysis, which is based on an extension of Wagner's integral equation to the nonlinear regime, takes full advantage of the trailing wake's tendency to deform under local velocities. Interactive computational results are presented that show examples of wake-induced lift and moment augmentation on the order of 20 percent of quasi-static values. The expandability and flexibility of the present computational method are noted, as well as the relative speed with which solutions are obtained.

Considerations concering the generalization of the Dirac equations to unstable fermions

International Nuclear Information System (INIS)

Kniehl, Bernd A.; Sirlin, Alberto

2014-08-01

We discuss the generalization of the Dirac equations and spinors in momentum space to free unstable spin-1/2 fermions taking into account the fundamental requirement of Lorentz covariance. We derive the generalized adjoint Dirac equations and spinors, and explain the very simple relation that exists, in our formulation, between the unstable and stable cases. As an application of the generalized spinors, we evaluate the probability density. We also discuss the behavior of the generalized Dirac equations under time reversal.

General solution of Bateman equations for nuclear transmutations

International Nuclear Information System (INIS)

Cetnar, Jerzy

2006-01-01

The paper concerns the linear chain method of solving Bateman equations for nuclear transmutation in derivation of the general solution for linear chain with repeated transitions and thus elimination of existing numerical problems. In addition, applications of derived equations for transmutation trajectory analysis method is presented

On the pth moment stability of the binary airfoil induced by bounded noise

International Nuclear Information System (INIS)

Wu, Jiancheng; Li, Xuan; Liu, Xianbin

2017-01-01

Highlights: • We obtain finite pth moment Lyapunov exponent for binary airfoil subject to a bounded noise. • Based on perturbation approach and Green's functions method, second differential eigenvalue equation governing moment Lyapunov exponent is established. • The types of singular points are investigated. • The eigenvalue problem is solved analytically and numerically. • The effects of noise and system parameters on the moment Lyapunov exponent and the stochastic stability of the system are discussed. - Abstract: In the paper, the stochastic stability of the binary airfoil subject to the effect of a bounded noise is studied through the determination of moment Lyapunov exponents. The noise excitation here is often used to model a realistic model of noise in many engineering application. The partial differential eigenvalue problem governing the moment Lyapunov exponent is established. Via the Feller boundary classification, the types of singular points are discussed here, and for the system discussed, the singular points only exist in end points. The fundamental methods used are the perturbation approach and the Green's functions method. With these methods, the second-order expansions of the moment Lyapunov exponents are obtained, which are shown to be in good agreement with those obtained using Monte Carlo simulation. The effects of noise and system parameters on the moment Lyapunov exponent and the stochastic stability of the binary airfoil system are discussed.

Usage of Numerical Optimization in Wind Turbine Airfoil Design

Energy Technology Data Exchange (ETDEWEB)

Grasso, F. [ECN Wind Energy, Petten (Netherlands)

2011-01-15

One important key element in the aerodynamic design of wind turbines is the use of specially tailored airfoils to increase the ratio of energy capture to the loading and thereby to reduce the cost of energy. This work is focused on the design of a wind turbine airfoil by using numerical optimization. First, the requirements for this class of airfoils are illustrated and discussed in order to have an exhaustive outline of the complexity of the problem. Then the optimization approach is presented; a gradient-based algorithm is used, coupled with RFOIL solver and a composite Bezier geometrical parameterization. A particularly sensitive point is the choice and implementation of constraints; to formalize the design requirements in the most complete and effective way, the effects of activating specific constraints are discussed. Finally, a numerical example regarding the design of a high-efficiency airfoil for the outer part of a blade is illustrated, and the results are compared with existing wind turbine airfoils.

Airfoil shape for flight at subsonic speeds

Science.gov (United States)

Whitcomb, Richard T.

1976-01-01

An airfoil having an upper surface shaped to control flow accelerations and pressure distribution over the upper surface and to prevent separation of the boundary layer due to shock wave formulation at high subsonic speeds well above the critical Mach number. A highly cambered trailing edge section improves overall airfoil lifting efficiency.

Profile catalogue for airfoil sections based on 3D computations

DEFF Research Database (Denmark)

Bertagnolio, F.; Sørensen, Niels N.; Johansen, Jeppe

2006-01-01

This report is a continuation of the Wind Turbine Airfoil Catalogue [1] which objective was, firstly to provide a database of aerodynamic characteristics for a wide range of airfoil profiles aimed at wind turbine applications, and secondly to test thetwo-dimensional Navier-Stokes solver EllipSys2D...... and the actual fluid flow, and thereby the incorrect prediction of airfoil characteristics. In addition, other features of the flow solver, such astransition and turbulence modelling, and their influence onto the numerical results are investigated. Conclusions are drawn regarding the evaluation of airfoil...

Numerical simulation of airfoil trailing edge serration noise

DEFF Research Database (Denmark)

Zhu, Wei Jun; Shen, Wen Zhong

In the present work, numerical simulations are carried out for a low noise airfoil with and without serrated Trailing Edge. The Ffowcs Williams-Hawkings acoustic analogy is implemented into the in-house incompressible flow solver EllipSys3D. The instantaneous hydrodynamic pressure and velocity...... field are obtained using Large Eddy Simulation. To obtain the time history data of sound pressure, the flow quantities are integrated around the airfoil surface through the FW-H approach. The extended length of the serration is about 16.7% of the airfoil chord and the geometric angle of the serration...... is 28 degrees. The chord based Reynolds number is around 1.5x106. Simulations are compared with existing wind tunnel experiments at various angles of attack. Even though the airfoil under investigation is already optimized for low noise emission, numerical simulations and wind tunnel experiments show...

An Experimental Investigation of an Airfoil Traversing Across a Shear Flow

Science.gov (United States)

Hamedani, Borhan A.; Naguib, Ahmed; Koochesfahani, Manoochehr

2017-11-01

While the aerodynamics of an airfoil in a uniform approach flow is well understood, less attention has been paid to airfoils in non-uniform flows. An aircraft encounters such flow, for example, during landing through the air wake of an aircraft carrier. The present work is focused on investigating the fundamental aerodynamics of airfoils in such an environment using canonical flow experiments. To generate a shear approach flow, a shaped honeycomb block is employed in a wind tunnel setup. Direct force measurements are performed on a NACA 0012 airfoil, with an aspect ratio of 1.8, as the airfoil traverses steadily across the shear region. Measurements are conducted at a chord Reynolds number Rec 75k, based on the mean approach stream velocity at the center of the shear zone, for a range of airfoil traverse velocities and angles of attack (0 - 12 degree). The results are compared to those obtained for the same airfoil when placed statically at different points along the traverse path inside the shear zone. The comparison enables examination of the applicability of quasi-steady analysis in computing the forces on the moving airfoil. This work is supported by ONR Grant Number N00014-16-1-2760.

Genetic Algorithms in Wind Turbine Airfoil Design

Energy Technology Data Exchange (ETDEWEB)

Grasso, F. [ECN Wind Energy, Petten (Netherlands); Bizzarrini, N.; Coiro, D.P. [Department of Aerospace Engineering, University of Napoli ' Federico II' , Napoli (Italy)

2011-03-15

One key element in the aerodynamic design of wind turbines is the use of specially tailored airfoils to increase the ratio of energy capture to the loading and thereby to reduce cost of energy. This work is focused on the design of a wind turbine airfoil by using numerical optimization. Firstly, the optimization approach is presented; a genetic algorithm is used, coupled with RFOIL solver and a composite Bezier geometrical parameterization. A particularly sensitive point is the choice and implementation of constraints; in order to formalize in the most complete and effective way the design requirements, the effects of activating specific constraints are discussed. A numerical example regarding the design of a high efficiency airfoil for the outer part of a blade by using genetic algorithms is illustrated and the results are compared with existing wind turbine airfoils. Finally a new hybrid design strategy is illustrated and discussed, in which the genetic algorithms are used at the beginning of the design process to explore a wide domain. Then, the gradient based algorithms are used in order to improve the first stage optimum.

Load alleviation on wind turbine blades using variable airfoil geometry

Energy Technology Data Exchange (ETDEWEB)

Basualdo, S.

2005-03-01

A two-dimensional theoretical study of the aeroelastic behaviour of an airfoil has been performed, whose geometry can be altered using a rear-mounted flap. This device is governed by a controller, whose objective is to reduce the airfoil displacements and, therefore, the stresses present in a real blade. The aerodynamic problem was solved numerically by a panel method using the potential theory, suitable for modelling attached flows. It is therefore mostly applicable for Pitch Regulated Variable Speed (PRVS) wind turbines, which mainly operate under this flow condition. The results show evident reductions in the airfoil displacements by using simple control strategies having the airfoil position and its first and second derivatives as input, especially at the system's eigenfrequency. The use of variable airfoil geometry is an effective means of reducing the vibration magnitudes of an airfoil that represents a section of a wind turbine blade, when subject to stochastic wind signals. The results of this investigation encourage further investigations with 3D aeroelastic models to predict the reduction in loads in real wind turbines. (author)

Exact solutions of nonlinear generalizations of the Klein Gordon and Schrodinger equations

International Nuclear Information System (INIS)

Burt, P.B.

1978-01-01

Exact solutions of sine Gordon and multiple sine Gordon equations are constructed in terms of solutions of a linear base equation, the Klein Gordon equation and also in terms of nonlinear base equations where the nonlinearity is polynomial in the dependent variable. Further, exact solutions of nonlinear generalizations of the Schrodinger equation and of additional nonlinear generalizations of the Klein Gordon equation are constructed in terms of solutions of linear base equations. Finally, solutions with spherical symmetry, of nonlinear Klein Gordon equations are given. 14 references

Turbine airfoil having outboard and inboard sections

Science.gov (United States)

Mazzola, Stefan; Marra, John J

2015-03-17

A turbine airfoil usable in a turbine engine and formed from at least an outboard section and an inboard section such that an inner end of the outboard section is attached to an outer end of the inboard section. The outboard section may be configured to provide a tip having adequate thickness and may extend radially inward from the tip with a generally constant cross-sectional area. The inboard section may be configured with a tapered cross-sectional area to support the outboard section.

Design of the new Risoe-A1 airfoil family for wind turbines

Energy Technology Data Exchange (ETDEWEB)

Fuglsang, P; Dahl, K S [Risoe National Lab., Wind Energy and Atmospheric Physics Dept., Roskilde (Denmark)

1999-03-01

A new airfoil family for wind turbines was developed by use of a design method using numerical optimization and the flow solver, XFOIL. The results were evaluated with the Navier-Stokes solver EllipSys2D. The airfoil family constitutes 6 airfoils ranging in thickness from 15% to 30%. The airfoils were designed to have a maximum lift coefficient around 1.5 in natural conditions and high lift-drag ratios below maximum lift. Insensitivity to leading edge roughness was obtained by securing that transition from laminar to turbulent flow on the suction side occurred close to the leading edge just before stall. The airfoil family was designed for a 600 kW wind turbine and provides a basis for further enhancing the characteristics of airfoils for wind turbines and to tailor airfoils for specific rotor sizes and power regulation principles. (au) EFP-95; EFP-98. 16 refs.

Amiet theory extension to predict leading-edge generated noise in compact airfoils

NARCIS (Netherlands)

De Santana, Leandro Dantas; Schram, C.

2015-01-01

This paper extends the Amiet theory to frequencies where the airfoil can be considered a compact noise source. The original Amiet theory proposes to apply the Schwarzschild theorem in an iterative procedure, which generally leads to noise over-prediction at low-frequencies. To overcome this problem,

NUMERICAL INVESTIGATION OF TWO ELEMENT CAMBER MORPHING AIRFOIL IN LOW REYNOLDS NUMBER FLOWS

Directory of Open Access Journals (Sweden)

RAJESH SENTHIL KUMAR T.

2017-07-01

Full Text Available Aerodynamic performance of a two-element camber morphing airfoil was investigated at low Reynolds number using the transient SST model in ANSYS FLUENT 14.0 and eN method in XFLR5. The two-element camber morphing concept was employed to morph the baseline airfoil into another airfoil by altering the orientation of mean-line at 35% of the chord to achieve better aerodynamic efficiency. NACA 0012 was selected as baseline airfoil. NACA 23012 was chosen as the test case as it has the camber-line similar to that of the morphed airfoil and as it has the same thickness as that of the baseline airfoil. The simulations were carried out at chord based Reynolds numbers of 2.5×105 and 3.9×105. The aerodynamic force coefficients, aerodynamic efficiency and the location of the transition point of laminar separation bubble over these airfoils were studied for various angles of attack. It was found that the aerodynamic efficiency of the morphed airfoil was 12% higher than that of the target airfoil at 4° angle of attack for Reynolds number of 3.9×105 and 54% rise in aerodynamic performance was noted as Reynolds number was varied from 2.5×105 to 3.9×105. The morphed airfoil exhibited the nature of low Reynolds number airfoil.

Exact solutions of the one-dimensional generalized modified complex Ginzburg-Landau equation

International Nuclear Information System (INIS)

Yomba, Emmanuel; Kofane, Timoleon Crepin

2003-01-01

The one-dimensional (1D) generalized modified complex Ginzburg-Landau (MCGL) equation for the traveling wave systems is analytically studied. Exact solutions of this equation are obtained using a method which combines the Painleve test for integrability in the formalism of Weiss-Tabor-Carnevale and Hirota technique of bilinearization. We show that pulses, fronts, periodic unbounded waves, sources, sinks and solution as collision between two fronts are the important coherent structures that organize much of the dynamical properties of these traveling wave systems. The degeneracies of the 1D generalized MCGL equation are examined as well as several of their solutions. These degeneracies include two important equations: the 1D generalized modified Schroedinger equation and the 1D generalized real modified Ginzburg-Landau equation. We obtain that the one parameter family of traveling localized source solutions called 'Nozaki-Bekki holes' become a subfamily of the dark soliton solutions in the 1D generalized modified Schroedinger limit

Aerodynamic and aeroacoustic performance of airfoils with morphing structures

OpenAIRE

Ai, Qing; Azarpeyvand, Mahdi; Lachenal, Xavier; Weaver, Paul M.

2016-01-01

Aerodynamic and aeroacoustic performance of airfoils fitted with morphing trailing edges are investigated using a coupled structure/fluid/noise model. The control of the flow over the surface of an airfoil using shape optimization techniques can significantly improve the load distribution along the chord and span lengths whilst minimising noise generation. In this study, a NACA 63-418 airfoil is fitted with a morphing flap and various morphing profiles are considered with two features that di...

Airfoil gust response and the sound produced by airifoil-vortex interaction

Science.gov (United States)

Amiet, R. K.

1986-01-01

This paper contributes to the understanding of the noise generation process of an airfoil encountering an unsteady upwash. By using a fast Fourier transform together with accurate airfoil response functions, the lift-time waveform for an airfoil encountering a delta function gust (the indicial function) is calculated for a flat plate airfoil in a compressible flow. This shows the interesting property that the lift is constant until the generated acoustic wave reaches the trailing edge. Expressions are given for the magnitude of this constant and for the pressure distribution on the airfoil during this time interval. The case of an airfoil cutting through a line vortex is also analyzed. The pressure-time waveform in the far field is closely related to the left-time waveform for the above problem of an airfoil entering a delta function gust. The effects of varying the relevant parameters in the problem are studied, including the observed position, the core diameter of the vortex, the vortex orientation and the airfoil span. The far field sound varies significantly with observer position, illustrating the importance of non-compactness effects. Increasing the viscous core diameter tends to smooth the pressure-time waveform. For small viscous core radius and infinite span, changing the vortex orientation changes only the amplitude of the pressure-time waveform, and not the shape.

Wronskians, generalized Wronskians and solutions to the Korteweg-de Vries equation

International Nuclear Information System (INIS)

Ma Wenxiu

2004-01-01

A bridge going from Wronskian solutions to generalized Wronskian solutions of the Korteweg-de Vries (KdV) equation is built. It is then shown that generalized Wronskian solutions can be viewed as Wronskian solutions. The idea is used to generate positons, negatons and their interaction solutions to the KdV equation. Moreover, general positons and negatons are constructed through the Wronskian formulation. A few new exact solutions to the KdV equation are explicitly presented as examples of Wronskian solutions

Turbine airfoil fabricated from tapered extrusions

Science.gov (United States)

Marra, John J

2013-07-16

An airfoil (30) and fabrication process for turbine blades with cooling channels (26). Tapered tubes (32A-32D) are bonded together in a parallel sequence, forming a leading edge (21), a trailing edge (22), and pressure and suction side walls (23, 24) connected by internal ribs (25). The tapered tubes may be extruded without camber to simplify the extrusion process, then bonded along matching surfaces (34), forming a non-cambered airfoil (28), which may be cambered in a hot forming process and cut (48) to length. The tubes may have tapered walls that are thinner at the blade tip (T1) than at the base (T2), reducing mass. A cap (50) may be attached to the blade tip. A mounting lug (58) may be forged (60) on the airfoil base and then machined, completing the blade for mounting in a turbine rotor disk.

Generalized Friedmann-Robertson-Walker metric and redundancy in the generalized Einstein equations

International Nuclear Information System (INIS)

Kao, W.F.; Pen, U.

1991-01-01

A nontrivial redundancy relation, due to the differential structure of the gravitational Bianchi identity as well as the symmetry of the Friedmann-Robertson-Walker metric, in the gravitational field equation is clarified. A generalized Friedmann-Robertson-Walker metric is introduced in order to properly define a one-dimensional reduced problem which offers an alternative approach to obtain the gravitational field equations on Friedmann-Robertson-Walker spaces

CHARTS STRUTT-INCE FOR GENERALIZED MATHIEU EQUATION

Directory of Open Access Journals (Sweden)

R.I. Parovik

2012-06-01

Full Text Available We have investigated the solution of the generalized Mathieu equation. With the aid of diagrams Stratton-Ince built the instability region, the condition can occur when the parametric resonance.

General Navier–Stokes-like momentum and mass-energy equations

Energy Technology Data Exchange (ETDEWEB)

Monreal, Jorge, E-mail: jmonreal@mail.usf.edu

2015-03-15

A new system of general Navier–Stokes-like equations is proposed to model electromagnetic flow utilizing analogues of hydrodynamic conservation equations. Such equations are intended to provide a different perspective and, potentially, a better understanding of electromagnetic mass, energy and momentum behaviour. Under such a new framework additional insights into electromagnetism could be gained. To that end, we propose a system of momentum and mass-energy conservation equations coupled through both momentum density and velocity vectors.

General solution of the Bagley-Torvik equation with fractional-order derivative

Science.gov (United States)

Wang, Z. H.; Wang, X.

2010-05-01

This paper investigates the general solution of the Bagley-Torvik equation with 1/2-order derivative or 3/2-order derivative. This fractional-order differential equation is changed into a sequential fractional-order differential equation (SFDE) with constant coefficients. Then the general solution of the SFDE is expressed as the linear combination of fundamental solutions that are in terms of α-exponential functions, a kind of functions that play the same role of the classical exponential function. Because the number of fundamental solutions of the SFDE is greater than 2, the general solution of the SFDE depends on more than two free (independent) constants. This paper shows that the general solution of the Bagley-Torvik equation involves actually two free constants only, and it can be determined fully by the initial displacement and initial velocity.

Sealing apparatus for airfoils of gas turbine engines

Science.gov (United States)

Jones, R.B.

1998-05-19

An improved airfoil tip sealing apparatus is disclosed wherein brush seals are attached to airfoil tips with the distal ends of the brush seal fibers sealingly contacting opposing wall surfaces. Embodiments for variable vanes, stators and both cooled and uncooled turbine blade applications are disclosed. 17 figs.

Numerical simulation of the RISOe1-airfoil dynamic stall

Energy Technology Data Exchange (ETDEWEB)

Bertagnolio, F.; Soerensen, N. [Risoe National Lab., Wind Energy and Atmospheric Physics Dept., Roskilde (Denmark)

1997-12-31

In this paper we are concerned with the numerical computation of the dynamic stall that occur in the viscous flowfield over an airfoil. These results are compared to experimental data that were obtained with the new designed RISOe1-airfoil, both for a motionless airfoil and for a pitching motion. Moreover, we present some numerical computations of the plunging and lead-lag motions. We also investigate the possibility of using the pitching motion to simulate the plunging and lead-lag situations. (au)

Influence of transition on steady and unsteady wind-turbine airfoil aerodynamics

Science.gov (United States)

Paterson, Eric; Lavely, Adam; Vijayakumar, Ganesh; Brasseur, James

2011-11-01

Laminar-flow airfoils for large stall-regulated horizontal-axis wind turbines are designed to achieve a restrained maximum lift coefficient and a broad laminar low- drag bucket under steady flow conditions and at specific Reynolds numbers. Blind- comparisons of the 2000 NREL Unsteady Aerodynamics Experiment showed large discrepancies and illustrated the need for improved physics modeling. We have studied the S809 airfoil under static and dynamic (ramp-up, ramp-down, and oscillatory) conditions, using the four-equation transition model of Langtry and Menter (2009), which has been implemented as a library accessible by an OpenFOAM RANS solver. Model validation is performed using surface-pressure and lift/drag data from U. Glasgow (2009) and OSU (1995) wind tunnel experiments. Performance of the transition model is assessed by analyzing integrated performance metrics, as well as detailed surface pressure and pressure gradient, wall-shear stress, and boundary-layer profiles and separation points. Demonstration of model performance in the light- and deep-stall regimes of dynamic stall is an important step in reducing uncertainties in full 3D simulations of turbines operating in the atmospheric boundary layer. Supported by NSF Grant 0933647.

AirborneWind Energy: Airfoil-Airmass Interaction

OpenAIRE

Zanon , Mario; Gros , Sebastien; Meyers , Johan; Diehl , Moritz

2014-01-01

The Airborne Wind Energy paradigm proposes to generate energy by flying a tethered airfoil across the wind flow at a high velocity. While Airborne Wind Energy enables flight in higher-altitude, stronger wind layers, the extra drag generated by the tether motion imposes a significant limit to the overall system efficiency. To address this issue, two airfoils with a shared tether can reduce overall system drag. A study proposed in Zanon et al. (2013) confirms this claim by showing that, in the ...

Dynamic Stall Characteristics of Drooped Leading Edge Airfoils

Science.gov (United States)

Sankar, Lakshmi N.; Sahin, Mehmet; Gopal, Naveen

2000-01-01

Helicopters in high-speed forward flight usually experience large regions of dynamic stall over the retreating side of the rotor disk. The rapid variations in the lift and pitching moments associated with the stall process can result in vibratory loads, and can cause fatigue and failure of pitch links. In some instances, the large time lag between the aerodynamic forces and the blade motion can trigger stall flutter. A number of techniques for the alleviation of dynamic stall have been proposed and studied by researchers. Passive and active control techniques have both been explored. Passive techniques include the use of high solidity rotors that reduce the lift coefficients of individual blades, leading edge slots and leading edge slats. Active control techniques include steady and unsteady blowing, and dynamically deformable leading edge (DDLE) airfoils. Considerable amount of experimental and numerical data has been collected on the effectiveness of these concepts. One concept that has not received as much attention is the drooped-leading edge airfoil idea. It has been observed in wind tunnel studies and flight tests that drooped leading edge airfoils can have a milder dynamic stall, with a significantly milder load hysteresis. Drooped leading edge airfoils may not, however, be suitable at other conditions, e.g. in hover, or in transonic flow. Work needs to be done on the analysis and design of drooped leading edge airfoils for efficient operation in a variety of flight regimes (hover, dynamic stall, and transonic flow). One concept that is worthy of investigation is the dynamically drooping airfoil, where the leading edge shape is changed roughly once-per-rev to mitigate the dynamic stall.

OPTIMASI AIRFOIL MENGGUNAKAN PARTICLE SWARM DENGAN PARAMETERISASI CST (CLASS SHAPE TRANSFORMATION

Directory of Open Access Journals (Sweden)

Eva Hertnacahyani Herraprastanti

2017-11-01

Full Text Available Airfoil merupakan profil penampang yang diaplikasikan pada sarana transportasi maupun pembangkit energi sebagai penampang sudu turbin. Airfoil yang dirancang diharapkan menghasilkan gaya angkat (lift maksimal namun gaya hambat (drag seminimal mungkin. Tujuan penelitian 1 Validasi aerodinamika metode panel dengan Interaksi Viskos-Tak Viskos; 2 Analisis aerodinamika airfoil untuk menentukan koefisien lift dan drag; 3 Menerapkan metode optimasi Particle Swarm Optimization untuk mendapatkan geometri airfoil dengan rasio koefisien lift dan drag maksimum (CL/CD maks. Tahap pertama menentukan profil airfoil Class Shape Transformation (CST. Airfoil akan dianalisis menggunakan metoda panel selanjutnya diterapkan model aliran singularitas source dan doublet. Solusi yang diperoleh dari metode panel merupakan kondisi aliran yang dianggap tak viskos. Apabila sudut serang cukup tinggi solusi yang diperoleh dengan pendekatan tersebut sudah tidak akurat lagi. Untuk memperbaiki hasil maka diterapkan metode interaksi viskos-tak viskos kuasi simultan. Proses ini diulang sampai konvergensi dan diperoleh koefisien lift, dan drag. Dengan menggunakan optimasi Particle Swarm Optimization (PSO akan didapat profil airfoil dengan  koefisien lift dan drag maksimum. Namun apabila prosedur optimasi belum optimal, akan dilakukan update geometri, sampai didapat konvergensi. Kesimpulan penelitian :1 Metode panel dengan interaksi viskos tak viskos memberikan hasil yang cukup baik dan akurat, dengan rata-rata kesalahan dibawah 9.5%;  2 Semakin besar bilangan Reynold maka nilai CL/CD maksimum akan semakin tinggi; 3 Ketebalan (thickness dan camber maksimum cenderung meningkat dengan peningkatan bilangan Reynold; 4 Untuk airfoil CST optimasi dengan PSO memberikan hasil yang lebih baik.

Effects of Leading Edge Defect on the Aerodynamic and Flow Characteristics of an S809 Airfoil.

Science.gov (United States)

Wang, Yan; Zheng, Xiaojing; Hu, Ruifeng; Wang, Ping

Unexpected performance degradation occurs in wind turbine blades due to leading edge defect when suffering from continuous impacts with rain drops, hails, insects, or solid particles during its operation life. To assess this issue, this paper numerically investigates the steady and dynamic stall characteristics of an S809 airfoil with various leading edge defects. More leading edge defect sizes and much closer to practical parameters are investigated in the paper. Numerical computation is conducted using the SST k-ω turbulence model, and the method has been validated by comparison with existed published data. In order to ensure the calculation convergence, the residuals for the continuity equation are set to be less than 10-7 and 10-6 in steady state and dynamic stall cases. The simulations are conducted with the software ANSYS Fluent 13.0. It is found that the characteristics of aerodynamic coefficients and flow fields are sensitive to leading edge defect both in steady and dynamic conditions. For airfoils with the defect thickness of 6%tc, leading edge defect has a relative small influence on the aerodynamics of S809 airfoil. For other investigated defect thicknesses, leading edge defect has much greater influence on the flow field structures, pressure coefficients and aerodynamic characteristics of airfoil at relative small defect lengths. For example, the lift coefficients decrease and drag coefficients increase sharply after the appearance of leading edge defect. However, the aerodynamic characteristics could reach a constant value when the defect length is large enough. The flow field, pressure coefficient distribution and aerodynamic coefficients do not change a lot when the defect lengths reach to 0.5%c,1%c, 2%c and 3%c with defect thicknesses of 6%tc, 12%tc,18%tc and 25%tc, respectively. In addition, the results also show that the critical defect length/thickness ratio is 0.5, beyond which the aerodynamic characteristics nearly remain unchanged. In

Near-wall serpentine cooled turbine airfoil

Science.gov (United States)

Lee, Ching-Pang

2013-09-17

A serpentine coolant flow path (54A-54G) formed by inner walls (50, 52) in a cavity (49) between pressure and suction side walls (22, 24) of a turbine airfoil (20A). A coolant flow (58) enters (56) an end of the airfoil, flows into a span-wise channel (54A), then flows forward (54B) over the inner surface of the pressure side wall, then turns behind the leading edge (26), and flows back along a forward part of the suction side wall, then follows a loop (54E) forward and back around an inner wall (52), then flows along an intermediate part of the suction side wall, then flows into an aft channel (54G) between the pressure and suction side walls, then exits the trailing edge (28). This provides cooling matched to the heating topography of the airfoil, minimizes differential thermal expansion, revives the coolant, and minimizes the flow volume needed.

Generalized continuity equations from two-field Schrödinger Lagrangians

Science.gov (United States)

Spourdalakis, A. G. B.; Pappas, G.; Morfonios, C. Â. V.; Kalozoumis, P. A.; Diakonos, F. K.; Schmelcher, P.

2016-11-01

A variational scheme for the derivation of generalized, symmetry-induced continuity equations for Hermitian and non-Hermitian quantum mechanical systems is developed. We introduce a Lagrangian which involves two complex wave fields and whose global invariance under dilation and phase variations leads to a mixed continuity equation for the two fields. In combination with discrete spatial symmetries of the underlying Hamiltonian, the mixed continuity equation is shown to produce bilocal conservation laws for a single field. This leads to generalized conserved charges for vanishing boundary currents and to divergenceless bilocal currents for stationary states. The formalism reproduces the bilocal continuity equation obtained in the special case of P T -symmetric quantum mechanics and paraxial optics.

Generalized Path Analysis and Generalized Simultaneous Equations Model for Recursive Systems with Responses of Mixed Types

Science.gov (United States)

Tsai, Tien-Lung; Shau, Wen-Yi; Hu, Fu-Chang

2006-01-01

This article generalizes linear path analysis (PA) and simultaneous equations models (SiEM) to deal with mixed responses of different types in a recursive or triangular system. An efficient instrumental variable (IV) method for estimating the structural coefficients of a 2-equation partially recursive generalized path analysis (GPA) model and…

Classification of exact solutions to the generalized Kadomtsev-Petviashvili equation

International Nuclear Information System (INIS)

Pandir, Yusuf; Gurefe, Yusuf; Misirli, Emine

2013-01-01

In this paper, we study the Kadomtsev-Petviashvili equation with generalized evolution and derive some new results using the approach called the trial equation method. The obtained results can be expressed by the soliton solutions, rational function solutions, elliptic function solutions and Jacobi elliptic function solutions. In the discussion, we give a new version of the trial equation method for nonlinear differential equations.

Travelling Solitary Wave Solutions for Generalized Time-delayed Burgers-Fisher Equation

International Nuclear Information System (INIS)

Deng Xijun; Han Libo; Li Xi

2009-01-01

In this paper, travelling wave solutions for the generalized time-delayed Burgers-Fisher equation are studied. By using the first-integral method, which is based on the ring theory of commutative algebra, we obtain a class of travelling solitary wave solutions for the generalized time-delayed Burgers-Fisher equation. A minor error in the previous article is clarified. (general)

An Experimental Comparison Between Flexible and Rigid Airfoils at Low Reynolds Numbers

Science.gov (United States)

Uzodinma, Jaylon; Macphee, David

2017-11-01

This study uses experimental and computational research methods to compare the aerodynamic performance of rigid and flexible airfoils at a low Reynolds number throughout varying angles of attack. This research can be used to improve the design of small wind turbines, micro-aerial vehicles, and any other devices that operate at low Reynolds numbers. Experimental testing was conducted in the University of Alabama's low-speed wind tunnel, and computational testing was conducted using the open-source CFD code OpenFOAM. For experimental testing, polyurethane-based (rigid) airfoils and silicone-based (flexible) airfoils were constructed using acrylic molds for NACA 0012 and NACA 2412 airfoil profiles. Computer models of the previously-specified airfoils were also created for a computational analysis. Both experimental and computational data were analyzed to examine the critical angles of attack, the lift and drag coefficients, and the occurrence of laminar boundary separation for each airfoil. Moreover, the computational simulations were used to examine the resulting flow fields, in order to provide possible explanations for the aerodynamic performances of each airfoil type. EEC 1659710.

On the effect of leading edge blowing on circulation control airfoil aerodynamics

Science.gov (United States)

Mclachlan, B. G.

1987-01-01

In the present context the term circulation control is used to denote a method of lift generation that utilizes tangential jet blowing over the upper surface of a rounded trailing edge airfoil to determine the location of the boundary layer separation points, thus setting an effective Kutta condition. At present little information exists on the flow structure generated by circulation control airfoils under leading edge blowing. Consequently, no theoretical methods exist to predict airfoil performance under such conditions. An experimental study of the flow field generated by a two dimensional circulation control airfoil under steady leading and trailing edge blowing was undertaken. The objective was to fundamentally understand the overall flow structure generated and its relation to airfoil performance. Flow visualization was performed to define the overall flow field structure. Measurements of the airfoil forces were also made to provide a correlation of the observed flow field structure to airfoil performance. Preliminary results are presented, specifically on the effect on the flow field structure of leading edge blowing, alone and in conjunction with trailing edge blowing.

Partial Differential Equations in General Relativity

International Nuclear Information System (INIS)

Choquet-Bruhat, Yvonne

2008-01-01

General relativity is a physical theory basic in the modeling of the universe at the large and small scales. Its mathematical formulation, the Einstein partial differential equations, are geometrically simple, but intricate for the analyst, involving both hyperbolic and elliptic PDE, with local and global problems. Many problems remain open though remarkable progress has been made recently towards their solutions. Alan Rendall's book states, in a down-to-earth form, fundamental results used to solve different types of equations. In each case he gives applications to special models as well as to general properties of Einsteinian spacetimes. A chapter on ODE contains, in particular, a detailed discussion of Bianchi spacetimes. A chapter entitled 'Elliptic systems' treats the Einstein constraints. A chapter entitled 'Hyperbolic systems' is followed by a chapter on the Cauchy problem and a chapter 'Global results' which contains recently proved theorems. A chapter is dedicated to the Einstein-Vlasov system, of which the author is a specialist. On the whole, the book surveys, in a concise though precise way, many essential results of recent interest in mathematical general relativity, and it is very clearly written. Each chapter is followed by an up to date bibliography. In conclusion, this book will be a valuable asset to relativists who wish to learn clearly-stated mathematical results and to mathematicians who want to penetrate into the subtleties of general relativity, as a mathematical and physical theory. (book review)

Partial Differential Equations in General Relativity

Energy Technology Data Exchange (ETDEWEB)

Choquet-Bruhat, Yvonne

2008-09-07

General relativity is a physical theory basic in the modeling of the universe at the large and small scales. Its mathematical formulation, the Einstein partial differential equations, are geometrically simple, but intricate for the analyst, involving both hyperbolic and elliptic PDE, with local and global problems. Many problems remain open though remarkable progress has been made recently towards their solutions. Alan Rendall's book states, in a down-to-earth form, fundamental results used to solve different types of equations. In each case he gives applications to special models as well as to general properties of Einsteinian spacetimes. A chapter on ODE contains, in particular, a detailed discussion of Bianchi spacetimes. A chapter entitled 'Elliptic systems' treats the Einstein constraints. A chapter entitled 'Hyperbolic systems' is followed by a chapter on the Cauchy problem and a chapter 'Global results' which contains recently proved theorems. A chapter is dedicated to the Einstein-Vlasov system, of which the author is a specialist. On the whole, the book surveys, in a concise though precise way, many essential results of recent interest in mathematical general relativity, and it is very clearly written. Each chapter is followed by an up to date bibliography. In conclusion, this book will be a valuable asset to relativists who wish to learn clearly-stated mathematical results and to mathematicians who want to penetrate into the subtleties of general relativity, as a mathematical and physical theory. (book review)

Unsteady aerodynamic behavior of an airfoil with and without a slat

Science.gov (United States)

Tung, Chee; Mcalister, Kenneth W.; Wang, Clin M.

1993-01-01

Unsteady flow behavior and load characteristics of a 2D VR-7 airfoil with and without a leading-edge slat were studied in the water tunnel of the Aeroflightdynamics Directorate, NASA Ames Research Center. Both airfoils were oscillated sinusoidally between 5 and 25 deg at Re = 200,000 to obtain the unsteady lift, drag, and pitching moment data. A fluorescent dye was released from an orifice located at the leading edge of the airfoil for the purpose of visualizing the boundary layer and wake flow. The flowfield and load predictions of an incompressible Navier-Stokes code based on a velocity-vorticity formulation were compared with the test data. The test and predictions both confirm that the slatted VR-7 airfoil delays both static and dynamic stall as compared to the VR-7 airfoil alone.

Design analysis of vertical wind turbine with airfoil variation

Science.gov (United States)

Maulana, Muhammad Ilham; Qaedy, T. Masykur Al; Nawawi, Muhammad

2016-03-01

With an ever increasing electrical energy crisis occurring in the Banda Aceh City, it will be important to investigate alternative methods of generating power in ways different than fossil fuels. In fact, one of the biggest sources of energy in Aceh is wind energy. It can be harnessed not only by big corporations but also by individuals using Vertical Axis Wind Turbines (VAWT). This paper presents a three-dimensional CFD analysis of the influence of airfoil design on performance of a Darrieus-type vertical-axis wind turbine (VAWT). The main objective of this paper is to develop an airfoil design for NACA 63-series vertical axis wind turbine, for average wind velocity 2,5 m/s. To utilize both lift and drag force, some of designs of airfoil are analyzed using a commercial computational fluid dynamics solver such us Fluent. Simulation is performed for this airfoil at different angles of attach rearranging from -12°, -8°, -4°, 0°, 4°, 8°, and 12°. The analysis showed that the significant enhancement in value of lift coefficient for airfoil NACA 63-series is occurred for NACA 63-412.

Extraction of airfoil data using PIV and pressure measurements

DEFF Research Database (Denmark)

Yang, Hua; Shen, Wen Zhong; Sørensen, Jens Nørkær

2011-01-01

of the rotor. The extraction technique is verified by employing the derived airfoil characteristics as input to computations using the BEM technique and comparing the calculated axial and tangential forces to the measured data. The comparison also demonstrates that the used technique of determining the AOA...... airfoil data are compared to 2D data from wind tunnel experiments and XFOIL computations. The comparison suggests that the rotor is subject to severe 3D effects originating from the geometry of the rotor, and explains why the Blade Element Momentum technique with 2D airfoil data over‐predicts the loading......A newly developed technique for determining the angle of attack (AOA) on a rotating blade is used to extract AOAs and airfoil data from measurements obtained during the MEXICO (Model rotor EXperiments in COntrolled conditions) rotor experiment. Detailed surface pressure and Particle Image...

Numerical investigation of airfoils for small wind turbine applications

Directory of Open Access Journals (Sweden)

Natarajan Karthikeyan

2016-01-01

Full Text Available A detailed numerical investigation of the aerodynamic performance on the five airfoils namely Mid321a, Mid321b, Mid321c, Mid321d, and Mid321e were carried out at Reynolds numbers ranging from 0.5×105 to 2.5×105. The airfoils used for small wind turbines are designed for Reynolds number ranges between 3×105 and 5×105 and the blades are tend to work on off-design conditions. The blade element moment method was applied to predict the aerodynamic loads, power coefficient, and blade parameters for the airfoils. Based on the evaluate data, it was found that Mid321c airfoil has better lift to drag ratio over the range of Reynolds numbers and attained maximum power coefficient of 0.4487 at Re = 2×105.

A Generalized Halanay Inequality for Stability of Nonlinear Neutral Functional Differential Equations

Directory of Open Access Journals (Sweden)

Wansheng Wang

2010-01-01

Full Text Available This paper is devoted to generalize Halanay's inequality which plays an important rule in study of stability of differential equations. By applying the generalized Halanay inequality, the stability results of nonlinear neutral functional differential equations (NFDEs and nonlinear neutral delay integrodifferential equations (NDIDEs are obtained.

On global structure of general solution of the Chew-Sow equations

International Nuclear Information System (INIS)

Gerdt, V.P.

1981-01-01

The Chew-Low equations for static p-wave πN-scattering are considered. The equations are formulated in the form of a system of three nonlinear difference equations of the first order which have the general solution depending on three arbitrary periodic functions. An approach to the global construction of the general solution is suggested which is based on the series expansion in powers of one of the arbitrary functions C(ω) determining the structure of the invariant curve for the Chew-Low equations. It is shown that the initial nonlinear problem is reduced to the linear one in every order in C(ω). By means of solving the linear problem the general solution is found in the first-order approximation in C(ω) [ru

Aerodynamic sound of flow past an airfoil

Science.gov (United States)

Wang, Meng

1995-01-01

The long term objective of this project is to develop a computational method for predicting the noise of turbulence-airfoil interactions, particularly at the trailing edge. We seek to obtain the energy-containing features of the turbulent boundary layers and the near-wake using Navier-Stokes Simulation (LES or DNS), and then to calculate the far-field acoustic characteristics by means of acoustic analogy theories, using the simulation data as acoustic source functions. Two distinct types of noise can be emitted from airfoil trailing edges. The first, a tonal or narrowband sound caused by vortex shedding, is normally associated with blunt trailing edges, high angles of attack, or laminar flow airfoils. The second source is of broadband nature arising from the aeroacoustic scattering of turbulent eddies by the trailing edge. Due to its importance to airframe noise, rotor and propeller noise, etc., trailing edge noise has been the subject of extensive theoretical (e.g. Crighton & Leppington 1971; Howe 1978) as well as experimental investigations (e.g. Brooks & Hodgson 1981; Blake & Gershfeld 1988). A number of challenges exist concerning acoustic analogy based noise computations. These include the elimination of spurious sound caused by vortices crossing permeable computational boundaries in the wake, the treatment of noncompact source regions, and the accurate description of wave reflection by the solid surface and scattering near the edge. In addition, accurate turbulence statistics in the flow field are required for the evaluation of acoustic source functions. Major efforts to date have been focused on the first two challenges. To this end, a paradigm problem of laminar vortex shedding, generated by a two dimensional, uniform stream past a NACA0012 airfoil, is used to address the relevant numerical issues. Under the low Mach number approximation, the near-field flow quantities are obtained by solving the incompressible Navier-Stokes equations numerically at chord

The Effect of Aerodynamic Evaluators on the Multi-Objective Optimization of Flatback Airfoils

Science.gov (United States)

Miller, M.; Slew, K. Lee; Matida, E.

2016-09-01

With the long lengths of today's wind turbine rotor blades, there is a need to reduce the mass, thereby requiring stiffer airfoils, while maintaining the aerodynamic efficiency of the airfoils, particularly in the inboard region of the blade where structural demands are highest. Using a genetic algorithm, the multi-objective aero-structural optimization of 30% thick flatback airfoils was systematically performed for a variety of aerodynamic evaluators such as lift-to-drag ratio (Cl/Cd), torque (Ct), and torque-to-thrust ratio (Ct/Cn) to determine their influence on airfoil shape and performance. The airfoil optimized for Ct possessed a 4.8% thick trailing-edge, and a rather blunt leading-edge region which creates high levels of lift and correspondingly, drag. It's ability to maintain similar levels of lift and drag under forced transition conditions proved it's insensitivity to roughness. The airfoil optimized for Cl/Cd displayed relatively poor insensitivity to roughness due to the rather aft-located free transition points. The Ct/Cn optimized airfoil was found to have a very similar shape to that of the Cl/Cd airfoil, with a slightly more blunt leading-edge which aided in providing higher levels of lift and moderate insensitivity to roughness. The influence of the chosen aerodynamic evaluator under the specified conditions and constraints in the optimization of wind turbine airfoils is shown to have a direct impact on the airfoil shape and performance.

Generalized curvature and the equations of D=11 supergravity

Energy Technology Data Exchange (ETDEWEB)

Bandos, Igor A. [Departamento de Fisica Teorica, Universidad de Valencia and IFIC (CSIC-UVEG), 46100-Burjassot (Valencia) (Spain); Institute for Theoretical Physics, NSC ' Kharkov Institute of Physics and Technology' , UA-61108 Kharkov (Ukraine); Azcarraga, Jose A. de [Departamento de Fisica Teorica, Universidad de Valencia and IFIC (CSIC-UVEG), 46100-Burjassot (Valencia) (Spain)]. E-mail: j.a.de.azcarraga@ific.uv.es; Picon, Moises [Departamento de Fisica Teorica, Universidad de Valencia and IFIC (CSIC-UVEG), 46100-Burjassot (Valencia) (Spain); Department of Physics and Astronomy, University of Southern California, Los Angeles, CA 90089-2535 (United States); Varela, Oscar [Departamento de Fisica Teorica, Universidad de Valencia and IFIC (CSIC-UVEG), 46100-Burjassot (Valencia) (Spain); Michigan Center for Theoretical Physics, Randall Laboratory, Department of Physics, University of Michigan, Ann Arbor, MI 48109-1120 (United States)

2005-05-26

It is known that, for zero fermionic sector, {psi}{sub {mu}}{sup {alpha}}(x)=0, the bosonic equations of Cremmer-Julia-Scherk eleven-dimensional supergravity can be collected in a compact expression, Rab{alpha}{gamma}{gamma}b{gamma}{beta}=0, which is a condition on the curvature R{alpha}{beta} of the generalized connection w. In this Letter we show that the equation Rbc{alpha}{gamma}{gamma}abc{gamma}{beta}=4i((D-bar {psi}){sub bc}{gamma}{sup [abc{sub {beta}({psi}{sub d}{gamma}{sup d}]){sub {alpha}}), where D-bar is the covariant derivative for the generalized connection w, collects all the bosonic equations of D=11 supergravity when the gravitino is nonvanishing, {psi}{sub {mu}}{sup {alpha}}(x)<>0.

Geometrical effects on the airfoil flow separation and transition

KAUST Repository

Zhang, Wei; Cheng, Wan; Gao, Wei; Qamar, Adnan; Samtaney, Ravi

2015-01-01

We present results from direct numerical simulations (DNS) of incompressible flow over two airfoils, NACA-4412 and NACA-0012-64, to investigate the effects of the airfoil geometry on the flow separation and transition patterns at Re=104 and 10

Research on design methods and aerodynamics performance of CQUDTU-B21 airfoil

DEFF Research Database (Denmark)

Chen, Jin; Cheng, Jiangtao; Wen, Zhong Shen

2012-01-01

This paper presents the design methods of CQU-DTU-B21 airfoil for wind turbine. Compared with the traditional method of inverse design, the new method is described directly by a compound objective function to balance several conflicting requirements for design wind turbine airfoils, which based...... on design theory of airfoil profiles, blade element momentum (BEM) theory and airfoil Self-Noise prediction model. And then an optimization model with the target of maximum power performance on a 2D airfoil and low noise emission of design ranges for angle of attack has been developed for designing CQU......-DTU-B21 airfoil. To validate the optimization results, the comparison of the aerodynamics performance by XFOIL and wind tunnels test respectively at Re=3×106 is made between the CQU-DTU-B21 and DU93-W-210 which is widely used in wind turbines. © (2012) Trans Tech Publications, Switzerland....

Influences of surface temperature on a low camber airfoil aerodynamic performances

Directory of Open Access Journals (Sweden)

Valeriu DRAGAN

2016-03-01

Full Text Available The current note refers to the comparison between a NACA 2510 airfoil with adiabatic walls and the same airfoil with heated patches. Both suction and pressure sides were divided into two regions covering the leading edge (L.E. and trailing edge (T.E.. A RANS method sensitivity test has been performed in the preliminary stage while for the extended 3D cases a DES-SST approach was used. Results indicate that surface temperature distribution influences the aerodynamics of the airfoil, in particular the viscous drag component but also the lift of the airfoil. Moreover, the influence depends not only on the surface temperature but also on the positioning of the heated surfaces, particularly in the case of pressure lift and drag. Further work will be needed to optimize the temperature distribution for airfoil with higher camber.

A general comparison theorem for backward stochastic differential equations

OpenAIRE

Cohen, Samuel N.; Elliott, Robert J.; Pearce, Charles E. M.

2010-01-01

A useful result when dealing with backward stochastic differential equations is the comparison theorem of Peng (1992). When the equations are not based on Brownian motion, the comparison theorem no longer holds in general. In this paper we present a condition for a comparison theorem to hold for backward stochastic differential equations based on arbitrary martingales. This theorem applies to both vector and scalar situations. Applications to the theory of nonlinear expectat...

EUDP Project: Low Noise Airfoil - Final Report

DEFF Research Database (Denmark)

This document summarizes the scientific results achieved during the EUDP-funded project `Low-Noise Airfoil'. The goals of this project are, on one side to develop a measurement technique that permits the evaluation of trailing edge noise in a classical aerodynamic wind tunnel, and on the other side...... to develop and implement a design procedure to manufacture airfoil profiles with low noise emission. The project involved two experimental campaigns: one in the LM Wind Power wind tunnel, a classical aerodynamic wind tunnel, in Lunderskov (DK), the second one in the Virginia Tech Stability Wind Tunnel....... In particular, the so-called TNO trailing edge noise model could be significantly improved by introducing turbulence anisotropy in its formulation, as well as the influence of the boundary layer mean pressure gradient. This two characteristics are inherent to airfoil flows but were neglected in the original...

Experimental Investigation of Unsteady Aerodynamic Forces on Airfoil in Harmonic Translatory Motion

DEFF Research Database (Denmark)

Gaunaa, Mac; Sørensen, Jens Nørkær

2003-01-01

The present paper describes the main results from an experimental investigation of the unsteady aerodynamic forces on a NACA 0015 airfoil subject to 1-degree-of-freedom (DOF) harmonic translatory motion. The focus of the experimental investigations was to determine the factors that influence...... maximum lift for both stationary and moving airfoil configurations. The mean as well as the dynamic characteristics of the different stall levels were found to differ from each other. An investigation of the negative aerodynamically damped cases showed that the damping decrease as the reduced frequency...... is decreased. Comparison between the experimental data, 2D Navier-Stokes computations and two commonly used dynamic stall models reveal that all models failed to reproduce the dynamic characteristics of the flow for incidences above maximum lift, however the Navier-Stokes computations generally captured...

Prediction of unsteady airfoil flows at large angles of incidence

Science.gov (United States)

Cebeci, Tuncer; Jang, H. M.; Chen, H. H.

1992-01-01

The effect of the unsteady motion of an airfoil on its stall behavior is of considerable interest to many practical applications including the blades of helicopter rotors and of axial compressors and turbines. Experiments with oscillating airfoils, for example, have shown that the flow can remain attached for angles of attack greater than those which would cause stall to occur in a stationary system. This result appears to stem from the formation of a vortex close to the surface of the airfoil which continues to provide lift. It is also evident that the onset of dynamic stall depends strongly on the airfoil section, and as a result, great care is required in the development of a calculation method which will accurately predict this behavior.

Desirable airfoil features for smaller-capacity straight-bladed VAWT

Energy Technology Data Exchange (ETDEWEB)

Islam, Mazharul; Ting, D.S.-K.; Fartaj, Amir

2007-05-15

In the small scale wind turbine market, the simple straight-bladed Darrieus type vertical axis wind turbine (SB-VAWT) is very attractive for its simple blade design. A detailed aerodynamic performance analysis was conducted on a smaller capacity fixed-pitch SB-VAWT. Brief analyses of the main aerodynamic challenges of this type of wind turbine were first discussed and subsequently the authors conducted further literature survey and computational analysis to shortlist aerodynamic characteristics of a desirable airfoil for a self-starting and better performing SB-VAWT. The required geometric features of the desirable airfoil to achieve the short listed characteristics were also discussed. It has been found out that conventionally used NACA symmetric airfoils are not suitable for smaller capacity SB-VAWT. Rather, it is advantageous to utilize a high-lift and low-drag asymmetric thick airfoil suitable for low speed operation typically encountered by SB-VAWT. (author)

Airfoil

Science.gov (United States)

Ristau, Neil; Siden, Gunnar Leif

2015-07-21

An airfoil includes a leading edge, a trailing edge downstream from the leading edge, a pressure surface between the leading and trailing edges, and a suction surface between the leading and trailing edges and opposite the pressure surface. A first convex section on the suction surface decreases in curvature downstream from the leading edge, and a throat on the suction surface is downstream from the first convex section. A second convex section is on the suction surface downstream from the throat, and a first convex segment of the second convex section increases in curvature.

A Two Element Laminar Flow Airfoil Optimized for Cruise. M.S. Thesis

Science.gov (United States)

Steen, Gregory Glen

1994-01-01

Numerical and experimental results are presented for a new two-element, fixed-geometry natural laminar flow airfoil optimized for cruise Reynolds numbers on the order of three million. The airfoil design consists of a primary element and an independent secondary element with a primary to secondary chord ratio of three to one. The airfoil was designed to improve the cruise lift-to-drag ratio while maintaining an appropriate landing capability when compared to conventional airfoils. The airfoil was numerically developed utilizing the NASA Langley Multi-Component Airfoil Analysis computer code running on a personal computer. Numerical results show a nearly 11.75 percent decrease in overall wing drag with no increase in stall speed at sailplane cruise conditions when compared to a wing based on an efficient single element airfoil. Section surface pressure, wake survey, transition location, and flow visualization results were obtained in the Texas A&M University Low Speed Wind Tunnel. Comparisons between the numerical and experimental data, the effects of the relative position and angle of the two elements, and Reynolds number variations from 8 x 10(exp 5) to 3 x 10(exp 6) for the optimum geometry case are presented.

Numerical study comparing RANS and LES approaches on a circulation control airfoil

International Nuclear Information System (INIS)

Rumsey, Christopher L.; Nishino, Takafumi

2011-01-01

Highlights: → RANS compared with LES for circulation control airfoil. → RANS turbulence models need to account for streamline curvature. → RANS models yield higher lift than LES in spite of predicting similar jet separation. - Abstract: A numerical study over a nominally two-dimensional circulation control airfoil is performed using a large-eddy simulation code and two Reynolds-averaged Navier-Stokes codes. Different Coanda jet blowing conditions are investigated. In addition to investigating the influence of grid density, a comparison is made between incompressible and compressible flow solvers. The incompressible equations are found to yield negligible differences from the compressible equations up to at least a jet exit Mach number of 0.64. The effects of different turbulence models are also studied. Models that do not account for streamline curvature effects tend to predict jet separation from the Coanda surface too late, and can produce non-physical solutions at high blowing rates. Three different turbulence models that account for streamline curvature are compared with each other and with large eddy simulation solutions. All three models are found to predict the Coanda jet separation location reasonably well, but one of the models predicts specific flow field details near the Coanda surface prior to separation much better than the other two. All Reynolds-averaged Navier-Stokes computations produce higher circulation than large eddy simulation computations, with different stagnation point location and greater flow acceleration around the nose onto the upper surface. The precise reasons for the higher circulation are not clear, although it is not solely a function of predicting the jet separation location correctly.

Numerical study comparing RANS and LES approaches on a circulation control airfoil

Energy Technology Data Exchange (ETDEWEB)

Rumsey, Christopher L., E-mail: c.l.rumsey@nasa.gov [Computational AeroSciences Branch, NASA Langley Research Center, Hampton, VA 23681-2199 (United States); Nishino, Takafumi [Advanced Supercomputing Division, NASA Ames Research Center, Moffett Field, CA 94035-1000 (United States)

2011-10-15

Highlights: > RANS compared with LES for circulation control airfoil. > RANS turbulence models need to account for streamline curvature. > RANS models yield higher lift than LES in spite of predicting similar jet separation. - Abstract: A numerical study over a nominally two-dimensional circulation control airfoil is performed using a large-eddy simulation code and two Reynolds-averaged Navier-Stokes codes. Different Coanda jet blowing conditions are investigated. In addition to investigating the influence of grid density, a comparison is made between incompressible and compressible flow solvers. The incompressible equations are found to yield negligible differences from the compressible equations up to at least a jet exit Mach number of 0.64. The effects of different turbulence models are also studied. Models that do not account for streamline curvature effects tend to predict jet separation from the Coanda surface too late, and can produce non-physical solutions at high blowing rates. Three different turbulence models that account for streamline curvature are compared with each other and with large eddy simulation solutions. All three models are found to predict the Coanda jet separation location reasonably well, but one of the models predicts specific flow field details near the Coanda surface prior to separation much better than the other two. All Reynolds-averaged Navier-Stokes computations produce higher circulation than large eddy simulation computations, with different stagnation point location and greater flow acceleration around the nose onto the upper surface. The precise reasons for the higher circulation are not clear, although it is not solely a function of predicting the jet separation location correctly.

An Integrable Discrete Generalized Nonlinear Schrödinger Equation and Its Reductions

International Nuclear Information System (INIS)

Li Hong-Min; Li Yu-Qi; Chen Yong

2014-01-01

An integrable discrete system obtained by the algebraization of the difference operator is studied. The system is named discrete generalized nonlinear Schrödinger (GNLS) equation, which can be reduced to classical discrete nonlinear Schrödinger (NLS) equation. Furthermore, all of the linear reductions for the discrete GNLS equation are given through the theory of circulant matrices and the discrete NLS equation is obtained by one of the reductions. At the same time, the recursion operator and symmetries of continuous GNLS equation are successfully recovered by its corresponding discrete ones. (general)

A New Factorisation of a General Second Order Differential Equation

Science.gov (United States)

Clegg, Janet

2006-01-01

A factorisation of a general second order ordinary differential equation is introduced from which the full solution to the equation can be obtained by performing two integrations. The method is compared with traditional methods for solving these type of equations. It is shown how the Green's function can be derived directly from the factorisation…

Comparison of NACA 6-series and 4-digit airfoils for Darrieus wind turbines

Science.gov (United States)

Migliore, P. G.

1983-08-01

The aerodynamic efficiency of Darrieus wind turbines as effected by blade airfoil geometry was investigated. Analysis was limited to curved-bladed machines having rotor solidities of 7-21 percent and operating at a Reynolds number of 3 x 10 to the 6th. Ten different airfoils, having thickness-to-chord ratios of 12, 15, and 18 percent, were studied. Performance estimates were made using a blade element/momentum theory approach. Results indicated that NACA 6-series airfoils yield peak power coefficients as great as NACA 4-digit airfoils and have broader and flatter power coefficient-tip speed ratio curves. Sample calculations for an NACA 63(2)-015 airfoil showed an annual energy output increase of 17-27 percent, depending on rotor solidity, compared to an NACA 0015 airfoil.

General method for reducing the two-body Dirac equation

International Nuclear Information System (INIS)

Galeao, A.P.; Ferreira, P.L.

1992-01-01

A semi relativistic two-body Dirac equation with an enlarged set of phenomenological potentials, including Breit-type terms, is investigated for the general case of unequal masses. Solutions corresponding to definite total angular momentum and parity are shown to fall into two classes, each one being obtained by solving a system of four coupled first-order radial differential equations. The reduction of each of these systems to a pair of coupled Schroedinger-type equations is also discussed. (author)

Airfoils in Turbulent Inflow

DEFF Research Database (Denmark)

Gilling, Lasse

of resolved inflow turbulence on airfoil simulations in CFD. The detached-eddy simulation technique is used because it can resolve the inflow turbulence without becoming too computationally expensive due to its limited requirements for mesh resolution in the boundary layer. It cannot resolve the turbulence......Wind turbines operate in inflow turbulence whether it originates from the shear in the atmospheric boundary layer or from the wake of other wind turbines. Consequently, the airfoils of the wings experience turbulence in the inflow. The main topic of this thesis is to investigate the effect...... that is formed in attached boundary layers, but the freestream turbulence can penetrate the boundary layer. The idea is that the resolved turbulence from the freestream should mix high momentum flow into the boundary layer and thereby increase the resistance against separation and increase the maximum lift...

Computation of aerodynamic interference effects on oscillating airfoils with controls in ventilated subsonic wind tunnels

Science.gov (United States)

Fromme, J. A.; Golberg, M. A.

1979-01-01

Lift interference effects are discussed based on Bland's (1968) integral equation. A mathematical existence theory is utilized for which convergence of the numerical method has been proved for general (square-integrable) downwashes. Airloads are computed using orthogonal airfoil polynomial pairs in conjunction with a collocation method which is numerically equivalent to Galerkin's method and complex least squares. Convergence exhibits exponentially decreasing error with the number n of collocation points for smooth downwashes, whereas errors are proportional to 1/n for discontinuous downwashes. The latter can be reduced to 1/n to the m+1 power with mth-order Richardson extrapolation (by using m = 2, hundredfold error reductions were obtained with only a 13% increase of computer time). Numerical results are presented showing acoustic resonance, as well as the effect of Mach number, ventilation, height-to-chord ratio, and mode shape on wind-tunnel interference. Excellent agreement with experiment is obtained in steady flow, and good agreement is obtained for unsteady flow.

Thick airfoil designs for the root of the 10MW INNWIND.EU wind turbine

Science.gov (United States)

Mu≁oz, A.; Méndez, B.; Munduate, X.

2016-09-01

The main objective of the “INNWIND.EU” project is to investigate and demonstrate innovative designs for 10-20MW offshore wind turbines and their key components, such as lightweight rotors. In this context, the present paper describes the development of two new airfoils for the blade root region. From the structural point of view, the root is the region in charge of transmitting all the loads of the blade to the hub. Thus, it is very important to include airfoils with adequate structural properties in this region. The present article makes use of high-thickness and blunt trailing edge airfoils to improve the structural characteristics of the airfoils used to build this blade region. CENER's (National Renewable Energy Center of Spain) airfoil design tool uses the airfoil software XFOIL to compute the aerodynamic characteristics of the designed airfoils. That software is based on panel methods which show some problems with the calculation of airfoils with thickness bigger than 35% and with blunt trailing edge. This drawback has been overcome with the development of an empirical correction for XFOIL lift and drag prediction based on airfoil experiments. From the aerodynamic point of view, thick airfoils are known to be very sensitive to surface contamination or turbulent inflow conditions. Consequently, the design optimization takes into account the aerodynamic torque in both clean and contaminated conditions. Two airfoils have been designed aiming to improve the structural and the aerodynamic behaviour of the blade in clean and contaminated conditions. This improvement has been corroborated with Blade Element Momentum (BEM) computations.

Thick airfoil designs for the root of the 10MW INNWIND.EU wind turbine

International Nuclear Information System (INIS)

Muñoz, A; Méndez, B; Munduate, X

2016-01-01

The main objective of the “INNWIND.EU” project is to investigate and demonstrate innovative designs for 10-20MW offshore wind turbines and their key components, such as lightweight rotors. In this context, the present paper describes the development of two new airfoils for the blade root region. From the structural point of view, the root is the region in charge of transmitting all the loads of the blade to the hub. Thus, it is very important to include airfoils with adequate structural properties in this region. The present article makes use of high-thickness and blunt trailing edge airfoils to improve the structural characteristics of the airfoils used to build this blade region. CENER's (National Renewable Energy Center of Spain) airfoil design tool uses the airfoil software XFOIL to compute the aerodynamic characteristics of the designed airfoils. That software is based on panel methods which show some problems with the calculation of airfoils with thickness bigger than 35% and with blunt trailing edge. This drawback has been overcome with the development of an empirical correction for XFOIL lift and drag prediction based on airfoil experiments. From the aerodynamic point of view, thick airfoils are known to be very sensitive to surface contamination or turbulent inflow conditions. Consequently, the design optimization takes into account the aerodynamic torque in both clean and contaminated conditions. Two airfoils have been designed aiming to improve the structural and the aerodynamic behaviour of the blade in clean and contaminated conditions. This improvement has been corroborated with Blade Element Momentum (BEM) computations. (paper)

Aerodynamic Analysis of Trailing Edge Enlarged Wind Turbine Airfoils

DEFF Research Database (Denmark)

Xu, Haoran; Shen, Wen Zhong; Zhu, Wei Jun

2014-01-01

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 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...

New solutions of the generalized ellipsoidal wave equation

Directory of Open Access Journals (Sweden)

Harold Exton

1999-10-01

Full Text Available Certain aspects and a contribution to the theory of new forms of solutions of an algebraic form of the generalized ellipsoidal wave equation are deduced by considering the Laplace transform of a soluble system of linear differential equations. An ensuing system of non-linear algebraic equations is shown to be consistent and is numerically implemented by means of the computer algebra package MAPLE V. The main results are presented as series of hypergeometric type of there and four variables which readily lend themselves to numerical handling although this does not indicate all of the detailedanalytic properties of the solutions under consideration.

General method and exact solutions to a generalized variable-coefficient two-dimensional KdV equation

International Nuclear Information System (INIS)

Chen, Yong; Shanghai Jiao-Tong Univ., Shangai; Chinese Academy of sciences, Beijing

2005-01-01

A general method to uniformly construct exact solutions in terms of special function of nonlinear partial differential equations is presented by means of a more general ansatz and symbolic computation. Making use of the general method, we can successfully obtain the solutions found by the method proposed by Fan (J. Phys. A., 36 (2003) 7009) and find other new and more general solutions, which include polynomial solutions, exponential solutions, rational solutions, triangular periodic wave solution, soliton solutions, soliton-like solutions and Jacobi, Weierstrass doubly periodic wave solutions. A general variable-coefficient two-dimensional KdV equation is chosen to illustrate the method. As a result, some new exact soliton-like solutions are obtained. planets. The numerical results are given in tables. The results are discussed in the conclusion

Conservation form of the equations of fluid dynamics in general nonsteady coordinates

Science.gov (United States)

Zhang, H.; Camarero, R.; Kahawita, R.

1985-11-01

Many of the differential equations arising in fluid dynamics may be stated in conservation-law form. A number of investigations have been conducted with the aim to derive the conservation-law form of the Navier-Stokes equations in general nonsteady coordinate systems. The present note has the objective to illustrate a mathematical methodology with which such forms of the equations may be derived in an easier and more general fashion. For numerical applications, the scalar form of the equations is eventually provided. Attention is given to the conservation form of equations in curvilinear coordinates and numerical considerations.

Conservation form of the equations of fluid dynamics in general nonsteady coordinates

International Nuclear Information System (INIS)

Zhang, H.; Camarero, R.; Kahawita, R.

1985-01-01

Many of the differential equations arising in fluid dynamics may be stated in conservation-law form. A number of investigations have been conducted with the aim to derive the conservation-law form of the Navier-Stokes equations in general nonsteady coordinate systems. The present note has the objective to illustrate a mathematical methodology with which such forms of the equations may be derived in an easier and more general fashion. For numerical applications, the scalar form of the equations is eventually provided. Attention is given to the conservation form of equations in curvilinear coordinates and numerical considerations. 6 references

Aerodynamic characteristics of wind turbine blade airfoils at high angles-of-attack

NARCIS (Netherlands)

Timmer, W.A.

2010-01-01

Airfoil characteristics at deep stall angles were investigated. It appeared that the maximum drag coefficient as a function of the airfoil upwind y/c ordinate at x/c=0.0125 can be approximated by a straight line. The lift-drag ratios in deep stall of a number of airfoils with moderate lower surface

Sensitivity theory for general non-linear algebraic equations with constraints

International Nuclear Information System (INIS)

Oblow, E.M.

1977-04-01

Sensitivity theory has been developed to a high state of sophistication for applications involving solutions of the linear Boltzmann equation or approximations to it. The success of this theory in the field of radiation transport has prompted study of possible extensions of the method to more general systems of non-linear equations. Initial work in the U.S. and in Europe on the reactor fuel cycle shows that the sensitivity methodology works equally well for those non-linear problems studied to date. The general non-linear theory for algebraic equations is summarized and applied to a class of problems whose solutions are characterized by constrained extrema. Such equations form the basis of much work on energy systems modelling and the econometrics of power production and distribution. It is valuable to have a sensitivity theory available for these problem areas since it is difficult to repeatedly solve complex non-linear equations to find out the effects of alternative input assumptions or the uncertainties associated with predictions of system behavior. The sensitivity theory for a linear system of algebraic equations with constraints which can be solved using linear programming techniques is discussed. The role of the constraints in simplifying the problem so that sensitivity methodology can be applied is highlighted. The general non-linear method is summarized and applied to a non-linear programming problem in particular. Conclusions are drawn in about the applicability of the method for practical problems

Generalized Killing-Yano equations in D=5 gauged supergravity

International Nuclear Information System (INIS)

Kubiznak, David; Kunduri, Hari K.; Yasui, Yukinori

2009-01-01

We propose a generalization of the (conformal) Killing-Yano equations relevant to D=5 minimal gauged supergravity. The generalization stems from the fact that the dual of the Maxwell flux, the 3-form *F, couples naturally to particles in the background as a 'torsion'. Killing-Yano tensors in the presence of torsion preserve most of the properties of the standard Killing-Yano tensors - exploited recently for the higher-dimensional rotating black holes of vacuum gravity with cosmological constant. In particular, the generalized closed conformal Killing-Yano 2-form gives rise to the tower of generalized closed conformal Killing-Yano tensors of increasing rank which in turn generate the tower of Killing tensors. An example of a generalized Killing-Yano tensor is found for the Chong-Cvetic-Lue-Pope black hole spacetime [Z.W. Chong, M. Cvetic, H. Lu, C.N. Pope, (hep-th/0506029)]. Such a tensor stands behind the separability of the Hamilton-Jacobi, Klein-Gordon, and Dirac equations in this background.

A Note about the General Meromorphic Solutions of the Fisher Equation

Directory of Open Access Journals (Sweden)

Jian-ming Qi

2014-01-01

Full Text Available We employ the complex method to obtain the general meromorphic solutions of the Fisher equation, which improves the corresponding results obtained by Ablowitz and Zeppetella and other authors (Ablowitz and Zeppetella, 1979; Feng and Li, 2006; Guo and Chen, 1991, and wg,i(z are new general meromorphic solutions of the Fisher equation for c=±5i/6. Our results show that the complex method provides a powerful mathematical tool for solving great many nonlinear partial differential equations in mathematical physics.

Effects of Leading Edge Defect on the Aerodynamic and Flow Characteristics of an S809 Airfoil.

Directory of Open Access Journals (Sweden)

Yan Wang

Full Text Available Unexpected performance degradation occurs in wind turbine blades due to leading edge defect when suffering from continuous impacts with rain drops, hails, insects, or solid particles during its operation life. To assess this issue, this paper numerically investigates the steady and dynamic stall characteristics of an S809 airfoil with various leading edge defects. More leading edge defect sizes and much closer to practical parameters are investigated in the paper.Numerical computation is conducted using the SST k-ω turbulence model, and the method has been validated by comparison with existed published data. In order to ensure the calculation convergence, the residuals for the continuity equation are set to be less than 10-7 and 10-6 in steady state and dynamic stall cases. The simulations are conducted with the software ANSYS Fluent 13.0.It is found that the characteristics of aerodynamic coefficients and flow fields are sensitive to leading edge defect both in steady and dynamic conditions. For airfoils with the defect thickness of 6%tc, leading edge defect has a relative small influence on the aerodynamics of S809 airfoil. For other investigated defect thicknesses, leading edge defect has much greater influence on the flow field structures, pressure coefficients and aerodynamic characteristics of airfoil at relative small defect lengths. For example, the lift coefficients decrease and drag coefficients increase sharply after the appearance of leading edge defect. However, the aerodynamic characteristics could reach a constant value when the defect length is large enough. The flow field, pressure coefficient distribution and aerodynamic coefficients do not change a lot when the defect lengths reach to 0.5%c,1%c, 2%c and 3%c with defect thicknesses of 6%tc, 12%tc,18%tc and 25%tc, respectively. In addition, the results also show that the critical defect length/thickness ratio is 0.5, beyond which the aerodynamic characteristics nearly remain

An airloads theory for morphing airfoils in dynamic stall with experimental correlation

Science.gov (United States)

Ahaus, Loren A.

Helicopter rotor blades frequently encounter dynamic stall during normal flight conditions, limiting the applicability of classical thin-airfoil theory at large angles of attack. Also, it is evident that because of the largely different conditions on the advancing and retreating sides of the rotor, future rotorcraft may incorporate dynamically morphing airfoils (trailing-edge aps, dynamic camber, dynamic droop, etc.). Reduced-order aerodynamic models are needed for preliminary design and ight simulation. A unified model for predicting the airloads on a morphing airfoil in dynamic stall is presented, consisting of three components. First, a linear airloads theory allows for arbitrary airfoil deformations consistent with a morphing airfoil. Second, to capture the effects of the wake, the airloads theory is coupled to an induced ow model. Third, the overshoot and time delay associated with dynamic stall are modeled by a second-order dynamic filter, along the lines of the ONERA dynamic stall model. This paper presents a unified airloads model that allows arbitrary airfoil morphing with dynamic stall. Correlations with experimental data validate the theory.

Turbulence intensity measurement in the wind tunnel used for airfoil flutter investigation

Directory of Open Access Journals (Sweden)

Šidlof Petr

2017-01-01

Full Text Available The paper reports on hot wire turbulence intensity measurements performed in the entry of a suction-type wind tunnel, used for investigation of flow-induced vibration of airfoils and slender structures. The airfoil is elastically supported with two degrees of freedom (pitch and plunge in the test section of the wind tunnel with lateral optical access for interferometric measurements, and free to oscillate. The turbulence intensity was measured for velocities up to M = 0.3 i with the airfoil blocked, ii with the airfoil self-oscillating. Measurements were performed for a free inlet and further with two different turbulence grids generating increased turbulence intensity levels. For the free inlet and static airfoil, the turbulence intensity lies below 0.4%. The turbulence grids G1 and G2 increase the turbulence level up to 1.8% and 2.6%, respectively. When the airfoil is free to oscillate due to fluid-structure interaction, its motion disturbs the surrounding flow field and increases the measured turbulence intensity levels up to 5%.

Generalized nonlinear Proca equation and its free-particle solutions

Energy Technology Data Exchange (ETDEWEB)

Nobre, F.D. [Centro Brasileiro de Pesquisas Fisicas and National Institute of Science and Technology for Complex Systems, Rio de Janeiro, RJ (Brazil); Plastino, A.R. [Universidad Nacional Buenos Aires-Noreoeste, CeBio y Secretaria de Investigacion, Junin (Argentina)

2016-06-15

We introduce a nonlinear extension of Proca's field theory for massive vector (spin 1) bosons. The associated relativistic nonlinear wave equation is related to recently advanced nonlinear extensions of the Schroedinger, Dirac, and Klein-Gordon equations inspired on the non-extensive generalized thermostatistics. This is a theoretical framework that has been applied in recent years to several problems in nuclear and particle physics, gravitational physics, and quantum field theory. The nonlinear Proca equation investigated here has a power-law nonlinearity characterized by a real parameter q (formally corresponding to the Tsallis entropic parameter) in such a way that the standard linear Proca wave equation is recovered in the limit q → 1. We derive the nonlinear Proca equation from a Lagrangian, which, besides the usual vectorial field Ψ{sup μ}(vector x,t), involves an additional field Φ{sup μ}(vector x,t). We obtain exact time-dependent soliton-like solutions for these fields having the form of a q-plane wave, and we show that both field equations lead to the relativistic energy-momentum relation E{sup 2} = p{sup 2}c{sup 2} + m{sup 2}c{sup 4} for all values of q. This suggests that the present nonlinear theory constitutes a new field theoretical representation of particle dynamics. In the limit of massless particles the present q-generalized Proca theory reduces to Maxwell electromagnetism, and the q-plane waves yield localized, transverse solutions of Maxwell equations. Physical consequences and possible applications are discussed. (orig.)

Turbine Airfoil Leading Edge Film Cooling Bibliography: 1972–1998

Directory of Open Access Journals (Sweden)

D. M. Kercher

2000-01-01

Full Text Available Film cooling for turbine airfoil leading edges has been a common practice for at least 35 years as turbine inlet gas temperatures and pressures have continually increased along with cooling air temperatures for higher engine cycle efficiency. With substantial engine cycle performance improvements from higher gas temperatures, it has become increasingly necessary to film cool nozzle and rotor blade leading edges since external heat transfer coefficients and thus heat load are the highest in this airfoil region. Optimum cooling air requirements in this harsh environment has prompted a significant number of film cooling investigations and analytical studies reported over the past 25 years from academia, industry and government agencies. Substantial progress has been made in understanding the complex nature of leading edge film cooling from airfoil cascades, simulated airfoil leading edges and environment. This bibliography is a report of the open-literature references available which provide information on the complex aero–thermo interaction of leading edge gaseous film cooling with mainstream flow. From much of this investigative information has come successful operational leading edge film cooling design systems capable of sustaining airfoil leading edge durability in very hostile turbine environments.

Reduction of airfoil trailing edge noise by trailing edge blowing

International Nuclear Information System (INIS)

Gerhard, T; Carolus, T; Erbslöh, S

2014-01-01

The paper deals with airfoil trailing edge noise and its reduction by trailing edge blowing. A Somers S834 airfoil section which originally was designed for small wind turbines is investigated. To mimic realistic Reynolds numbers the boundary layer is tripped on pressure and suction side. The chordwise position of the blowing slot is varied. The acoustic sources, i.e. the unsteady flow quantities in the turbulent boundary layer in the vicinity of the trailing edge, are quantified for the airfoil without and with trailing edge blowing by means of a large eddy simulation and complementary measurements. Eventually the far field airfoil noise is measured by a two-microphone filtering and correlation and a 40 microphone array technique. Both, LES-prediction and measurements showed that a suitable blowing jet on the airfoil suction side is able to reduce significantly the turbulence intensity and the induced surface pressure fluctuations in the trailing edge region. As a consequence, trailing edge noise associated with a spectral hump around 500 Hz could be reduced by 3 dB. For that a jet velocity of 50% of the free field velocity was sufficient. The most favourable slot position was at 90% chord length

Numerical Simulation of Airfoil Aerodynamic Penalties and Mechanisms in Heavy Rain

Directory of Open Access Journals (Sweden)

Zhenlong Wu

2013-01-01

Full Text Available Numerical simulations that are conducted on a transport-type airfoil, NACA 64-210, at a Reynolds number of 2.6×106 and LWC of 25 g/m3 explore the aerodynamic penalties and mechanisms that affect airfoil performance in heavy rain conditions. Our simulation results agree well with the experimental data and show significant aerodynamic penalties for the airfoil in heavy rain. The maximum percentage decrease in CL is reached by 13.2% and the maximum percentage increase in CD by 47.6%. Performance degradation in heavy rain at low angles of attack is emulated by an originally creative boundary-layer-tripped technique near the leading edge. Numerical flow visualization technique is used to show premature boundary-layer separation at high angles of attack and the particulate trajectories at various angles of attack. A mathematic model is established to qualitatively study the water film effect on the airfoil geometric changes. All above efforts indicate that two primary mechanisms are accountable for the airfoil aerodynamic penalties. One is to cause premature boundary-layer transition at low AOA and separation at high AOA. The other occurs at times scales consistent with the water film layer, which is thought to alter the airfoil geometry and increase the mass effectively.

Generalized bootstrap equations and possible implications for the NLO Odderon

Energy Technology Data Exchange (ETDEWEB)

Bartels, J. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Vacca, G.P. [INFN, Sezione di Bologna (Italy)

2013-07-15

We formulate and discuss generalized bootstrap equations in nonabelian gauge theories. They are shown to hold in the leading logarithmic approximation. Since their validity is related to the self-consistency of the Steinmann relations for inelastic production amplitudes they can be expected to be valid also in NLO. Specializing to the N=4 SYM, we show that the validity in NLO of these generalized bootstrap equations allows to find the NLO Odderon solution with intercept exactly at one.

Influence of Thickness Variation on the Flapping Performance of Symmetric NACA Airfoils in Plunging Motion

Directory of Open Access Journals (Sweden)

Liangyu Zhao

2010-01-01

Full Text Available In order to investigate the impact of airfoil thickness on flapping performance, the unsteady flow fields of a family of airfoils from an NACA0002 airfoil to an NACA0020 airfoil in a pure plunging motion and a series of altered NACA0012 airfoils in a pure plunging motion were simulated using computational fluid dynamics techniques. The “class function/shape function transformation“ parametric method was employed to decide the coordinates of these altered NACA0012 airfoils. Under specified plunging kinematics, it is observed that the increase of an airfoil thickness can reduce the leading edge vortex (LEV in strength and delay the LEV shedding. The increase of the maximum thickness can enhance the time-averaged thrust coefficient and the propulsive efficiency without lift reduction. As the maximum thickness location moves towards the leading edge, the airfoil obtains a larger time-averaged thrust coefficient and a higher propulsive efficiency without changing the lift coefficient.

Enhancements to NURBS-Based FEA Airfoil Modeler: SABER

Science.gov (United States)

Saleeb, A. F.; Trowbridge, D. A.

2003-01-01

NURBS (Non-Uniform Rational B-Splines) have become a common way for CAD programs to fit a smooth surface to discrete geometric data. This concept has been extended to allow for the fitting of analysis data in a similar manner and "attaching" the analysis data to the geometric definition of the structure. The "attaching" of analysis data to the geometric definition allows for a more seamless sharing of data between analysis disciplines. NURBS have become a useful tool in the modeling of airfoils. The use of NURBS has allowed for the development of software that easily and consistently generates plate finite element models of the midcamber surface of a given airfoil. The resulting displacements can then be applied to the original airfoil surface and the deformed shape calculated.

Investigation of Airfoil Aeroacoustics with Blowing Control Mechanism

Directory of Open Access Journals (Sweden)

Baha ZAFER

2016-11-01

Full Text Available In this investigation, it is dealt with computational aero-acoustic analysis of an airfoil with jet blowing. The airfoil shape is selected as NACA0015 profile with jet blowing on upper surface. The calculations of analysis are done by using commercial finite volume solver. The k-ε turbulence model is used for the turbulence modeling and the Ffowcs Williams and Hawking acoustic analogy model is run for determination of acoustic data. The numerical results are compared with experimental data for computed Sound Pressure Level without jet blowing and well agreement is observed. In the case of jet blowing, the effects of different jet angle, velocity ratio and angle of attack on airfoil are investigated and noise levels of non jet cases and jet blowing cases are studied.

Airfoil design: Finding the balance between design lift and structural stiffness

International Nuclear Information System (INIS)

Bak, Christian; Gaudern, Nicholas; Zahle, Frederik; Vronsky, Tomas

2014-01-01

When upscaling wind turbine blades there is an increasing need for high levels of structural efficiency. In this paper the relationships between the aerodynamic characteristics; design lift and lift-drag ratio; and the structural characteristics were investigated. Using a unified optimization setup, airfoils were designed with relative thicknesses between 18% and 36%, a structural box height of 85% of the relative thickness, and varying box widths in chordwise direction between 20% and 40% of the chord length. The results from these airfoil designs showed that for a given flapwise stiffness, the design lift coefficient increases if the box length reduces and at the same time the relative thickness increases. Even though the conclusions are specific to the airfoil design approach used, the study indicated that an increased design lift required slightly higher relative thickness compared to airfoils with lower design lift to maintain the flapwise stiffness. Also, the study indicated that the lift-drag ratio as a function of flapwise stiffness was relatively independent of the airfoil design with a tendency that the lift-drag ratio decreased for large box lengths. The above conclusions were supported by an analysis of the three airfoil families Riso-C2, DU and FFA, where the lift-drag ratio as a function of flapwise stiffness was decreasing, but relatively independent of the airfoil design, and the design lift coefficient was varying depending on the design philosophy. To make the analysis complete also design lift and lift- drag ratio as a function of edgewise and torsional stiffness were shown

Generalized Sturmian Solutions for Many-Particle Schrödinger Equations

DEFF Research Database (Denmark)

Avery, John; Avery, James Emil

2004-01-01

The generalized Sturmian method for obtaining solutions to the many-particle Schrodinger equation is reviewed. The method makes use of basis functions that are solutions of an approximate Schrodinger equation with a weighted zeroth-order potential. The weighting factors are especially chosen so...

The general class of the vacuum spherically symmetric equations of the general relativity theory

International Nuclear Information System (INIS)

Karbanovski, V. V.; Sorokin, O. M.; Nesterova, M. I.; Bolotnyaya, V. A.; Markov, V. N.; Kairov, T. V.; Lyash, A. A.; Tarasyuk, O. R.

2012-01-01

The system of the spherical-symmetric vacuum equations of the General Relativity Theory is considered. The general solution to a problem representing two classes of line elements with arbitrary functions g 00 and g 22 is obtained. The properties of the found solutions are analyzed.

Aerodynamic Analysis of Trailing Edge Enlarged Wind Turbine Airfoils

International Nuclear Information System (INIS)

Xu, Haoran; Yang, Hua; Liu, Chao; Shen, Wenzhong; Zhu, Weijun

2014-01-01

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 × 10 6 . 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

New airfoil sections for straight bladed turbine

Science.gov (United States)

Boumaza, B.

1987-07-01

A theoretical investigation of aerodynamic performance for vertical axis Darrieus wind turbine with new airfoils sections is carried out. The blade section aerodynamics characteristics are determined from turbomachines cascade model. The model is also adapted to the vertical Darrieus turbine for the performance prediction of the machine. In order to choose appropriate value of zero-lift-drag coefficient in calculation, an analytical expression is introduced as function of chord-radius ratio and Reynolds numbers. New airfoils sections are proposed and analyzed for straight-bladed turbine.

New airfoil sections for straight bladed turbine

International Nuclear Information System (INIS)

Boumaza, B.

1987-07-01

A theoretical investigation of aerodynamic performance for vertical axis Darrieus wind turbine with new airfoils sections is carried out. The blade section aerodynamics characteristics are determined from turbomachines cascade model. The model is also adapted to the vertical Darrieus turbine for the performance prediction of the machine. In order to choose appropriate value of zero-lift-drag coefficient in calculation, an analytical expression is introduced as function of chord-radius ratio and Reynolds numbers. New airfoils sections are proposed and analyzed for straight-bladed turbine

The effect of variations in first- and second-order derivatives on airfoil aerodynamic performance

Directory of Open Access Journals (Sweden)

Penghui Yi

2017-01-01

Full Text Available The geometric factors which influence airfoil aerodynamic performance are attributed to variations in local first- and second-order curvature derivatives. Based on a self-developed computational fluid dynamics (CFD program called UCFD, the influence of local profile variations on airfoil aerodynamic performance in different pressure areas is investigated. The results show that variations in first- and second-order derivatives of the airfoil profiles can cause fluctuations in airfoil aerodynamic performance. The greater the variation in local first- and second-order derivatives, the greater the fluctuation amplitude of the airfoil aerodynamic coefficients. Moreover, at the area near the leading edge and the shock-wave position, the surface pressure is more sensitive to changes in first- and second-order derivatives. These results provide a reference for airfoil aerodynamic shape design.

Active Subspaces of Airfoil Shape Parameterizations

Science.gov (United States)

Grey, Zachary J.; Constantine, Paul G.

2018-05-01

Design and optimization benefit from understanding the dependence of a quantity of interest (e.g., a design objective or constraint function) on the design variables. A low-dimensional active subspace, when present, identifies important directions in the space of design variables; perturbing a design along the active subspace associated with a particular quantity of interest changes that quantity more, on average, than perturbing the design orthogonally to the active subspace. This low-dimensional structure provides insights that characterize the dependence of quantities of interest on design variables. Airfoil design in a transonic flow field with a parameterized geometry is a popular test problem for design methodologies. We examine two particular airfoil shape parameterizations, PARSEC and CST, and study the active subspaces present in two common design quantities of interest, transonic lift and drag coefficients, under each shape parameterization. We mathematically relate the two parameterizations with a common polynomial series. The active subspaces enable low-dimensional approximations of lift and drag that relate to physical airfoil properties. In particular, we obtain and interpret a two-dimensional approximation of both transonic lift and drag, and we show how these approximation inform a multi-objective design problem.

Airfoil noise prediction from 2D3C PIV data

NARCIS (Netherlands)

De Santana, Leandro Dantas; Schram, C.; Desmet, W.

2015-01-01

The noise emitted by incoming turbulence interacting with an airfoil has many technological applications, and has accordingly received much attention in the literature. While numerous developments are focused on the determination of the airfoil response to a given incoming gust, the characterization

Generally covariant Hamilton-Jacobi equation and rotated liquid sphere metrics

International Nuclear Information System (INIS)

Abdil'din, M.M.; Abdulgafarov, M.K.; Abishev, M.E.

2005-01-01

In the work Lense-Thirring problem on corrected Fock's first approximation metrics by Hamilton-Jacobi method considered. Generally covariant Hamilton-Jacobi equation had been sold by separation of variable method. Path equation of probe particle motion in rotated liquid sphere field is obtained. (author)

Holography and LDV techniques, their status and use in airfoil research

Science.gov (United States)

Johnson, D. A.; Bachalo, W. D.

1978-01-01

The measurement capabilities of laser velocimetry and holographic interferometry in transonic airfoil testing were demonstrated. Presented are representative results obtained with these two nonintrusive techniques on a 15.24 cm chord airfoil section. These results include the density field about the airfoil, flow angles in the inviscid flow and viscous flow properties including the turbulent Reynolds stresses. The accuracies of the density fields obtained by interferometry were verified from comparisons with surface pressure and laser velocimeter measurements.

Computation of viscous transonic flow about a lifting airfoil

Science.gov (United States)

Walitt, L.; Liu, C. Y.

1976-01-01

The viscous transonic flow about a stationary body in free air was numerically investigated. The geometry chosen was a symmetric NACA 64A010 airfoil at a freestream Mach number of 0.8, a Reynolds number of 4 million based on chord, and angles of attack of 0 and 2 degrees. These conditions were such that, at 2 degrees incidence unsteady periodic motion was calculated along the aft portion of the airfoil and in its wake. Although no unsteady measurements were made for the NACA 64A010 airfoil at these flow conditions, interpolated steady measurements of lift, drag, and surface static pressures compared favorably with corresponding computed time-averaged lift, drag, and surface static pressures.

Boundary Layer Control on Airfoils.

Science.gov (United States)

Gerhab, George; Eastlake, Charles

1991-01-01

A phenomena, boundary layer control (BLC), produced when visualizing the fluidlike flow of air is described. The use of BLC in modifying aerodynamic characteristics of airfoils, race cars, and boats is discussed. (KR)

NUMERICAL INVESTIGATION OF TWO ELEMENT CAMBER MORPHING AIRFOIL IN LOW REYNOLDS NUMBER FLOWS

OpenAIRE

RAJESH SENTHIL KUMAR T.; V. SIVAKUMAR; BALAJEE RAMAKRISHNANANDA; ARJHUN A.K, SURIYAPANDIYAN

2017-01-01

Aerodynamic performance of a two-element camber morphing airfoil was investigated at low Reynolds number using the transient SST model in ANSYS FLUENT 14.0 and eN method in XFLR5. The two-element camber morphing concept was employed to morph the baseline airfoil into another airfoil by altering the orientation of mean-line at 35% of the chord to achieve better aerodynamic efficiency. NACA 0012 was selected as baseline airfoil. NACA 23012 was chosen as the test case as it has the camber-line s...

Some new exact solutions of Jacobian elliptic function about the generalized Boussinesq equation and Boussinesq-Burgers equation

International Nuclear Information System (INIS)

Zhang Liang; Zhang Lifeng; Li Chongyin

2008-01-01

By using the modified mapping method, we find some new exact solutions of the generalized Boussinesq equation and the Boussinesq-Burgers equation. The solutions obtained in this paper include Jacobian elliptic function solutions, combined Jacobian elliptic function solutions, soliton solutions, triangular function solutions

Fractal diffusion equations: Microscopic models with anomalous diffusion and its generalizations

International Nuclear Information System (INIS)

Arkhincheev, V.E.

2001-04-01

To describe the ''anomalous'' diffusion the generalized diffusion equations of fractal order are deduced from microscopic models with anomalous diffusion as Comb model and Levy flights. It is shown that two types of equations are possible: with fractional temporal and fractional spatial derivatives. The solutions of these equations are obtained and the physical sense of these fractional equations is discussed. The relation between diffusion and conductivity is studied and the well-known Einstein relation is generalized for the anomalous diffusion case. It is shown that for Levy flight diffusion the Ohm's law is not applied and the current depends on electric field in a nonlinear way due to the anomalous character of Levy flights. The results of numerical simulations, which confirmed this conclusion, are also presented. (author)

EUDP project 'Low noise airfoil' - Final report

Energy Technology Data Exchange (ETDEWEB)

Bertagnolio, F. (ed.)

2012-06-15

This document summarizes the scientific results achieved during the EUDP-funded project 'Low-Noise Airfoil'. The goals of this project are, on one side to develop a measurement technique that permits the evaluation of trailing edge noise in a classical aerodynamic wind tunnel, and on the other side to develop and implement a design procedure to manufacture airfoil profiles with low noise emission. The project involved two experimental campaigns: one in the LM Wind Power wind tunnel, a classical aerodynamic wind tunnel, in Lunderskov (Denmark), the second one in the Virginia Tech Stability Wind Tunnel at the Aerospace and Ocean Engineering Department of Virginia Tech (Blacksburg, VA, USA), also a classical aerodynamic wind tunnel but equipped with an anechoic chamber that allow to perform acoustic measurements. On the theoretical side, the above experiments yield a series of model validations and improvements. In particular, the so-called TNO trailing edge noise model could be significantly improved by introducing turbulence anisotropy in its formulation, as well as the influence of the boundary layer mean pressure gradient. This two characteristics are inherent to airfoil flows but were neglected in the original approach. In addition, the experimental results are confronted to detailed Large Eddy Simulations of the airfoil flow giving more insight into the flow turbulence characteristics. The methodology which consists in measuring surface pressure spectra directly on the airfoil surface using flush-mounted microphones in order to evaluate far-field noise emission using additional theoretical results has been validated. This technique presents the advantage that it can easily be used in a classical aerodynamic wind tunnel and does not require the use of an anechoic facility. It was developed as a substitute to the original plan that consisted in measuring acoustic waves using hot-wire velocimetry. This last technique proved ineffective in the LM Wind

Numerical Investigation of an Oscillating Flat Plate Airfoil

Science.gov (United States)

Mohaghegh, Fazlolah; Janechek, Matthew; Buchholz, James; Udaykumar, Hs

2017-11-01

This research investigates the vortex dynamics of a plunging flat plate airfoil by analyzing the vorticity transport in 2D simulations. A horizontal airfoil is subject to a freestream flow at Re =10000. A prescribed vertical sinusoidal motion is applied to the airfoil. Smoothed Profile Method (SPM) models the fluid-structure interaction. SPM as a diffuse interface model considers a thickness for the interface and applies a smooth transition from solid to fluid. As the forces on the airfoil are highly affected by the interaction of the generated vortices from the surface, it is very important to find out whether a diffuse interface solver can model a flow dominated by vorticities. The results show that variation of lift coefficient with time agrees well with the experiment. Study of vortex evolution shows that similar to experiments, when the plate starts moving downward from top, the boundary layer is attached to the surface and the leading-edge vortex (LEV) is very small. By time, LEV grows and rolls up and a secondary vortex emerges. Meanwhile, the boundary layer starts to separate and finally LEV detaches from the surface. In overall, SPM as a diffuse interface model can predict the lift force and vortex pattern accurately.

Ice Roughness and Thickness Evolution on a Swept NACA 0012 Airfoil

Science.gov (United States)

McClain, Stephen T.; Vargas, Mario; Tsao, Jen-Ching

2017-01-01

Several recent studies have been performed in the Icing Research Tunnel (IRT) at NASA Glenn Research Center focusing on the evolution, spatial variations, and proper scaling of ice roughness on airfoils without sweep exposed to icing conditions employed in classical roughness studies. For this study, experiments were performed in the IRT to investigate the ice roughness and thickness evolution on a 91.44-cm (36-in.) chord NACA 0012 airfoil, swept at 30-deg with 0deg angle of attack, and exposed to both Appendix C and Appendix O (SLD) icing conditions. The ice accretion event times used in the study were less than the time required to form substantially three-dimensional structures, such as scallops, on the airfoil surface. Following each ice accretion event, the iced airfoils were scanned using a ROMER Absolute Arm laser-scanning system. The resulting point clouds were then analyzed using the self-organizing map approach of McClain and Kreeger to determine the spatial roughness variations along the surfaces of the iced airfoils. The resulting measurements demonstrate linearly increasing roughness and thickness parameters with ice accretion time. Further, when compared to dimensionless or scaled results from unswept airfoil investigations, the results of this investigation indicate that the mechanisms for early stage roughness and thickness formation on swept wings are similar to those for unswept wings.

Linearized propulsion theory of flapping airfoils revisited

Science.gov (United States)

Fernandez-Feria, Ramon

2016-11-01

A vortical impulse theory is used to compute the thrust of a plunging and pitching airfoil in forward flight within the framework of linear potential flow theory. The result is significantly different from the classical one of Garrick that considered the leading-edge suction and the projection in the flight direction of the pressure force. By taking into account the complete vorticity distribution on the airfoil and the wake the mean thrust coefficient contains a new term that generalizes the leading-edge suction term and depends on Theodorsen function C (k) and on a new complex function C1 (k) of the reduced frequency k. The main qualitative difference with Garrick's theory is that the propulsive efficiency tends to zero as the reduced frequency increases to infinity (as 1 / k), in contrast to Garrick's efficiency that tends to a constant (1 / 2). Consequently, for pure pitching and combined pitching and plunging motions, the maximum of the propulsive efficiency is not reached as k -> ∞ like in Garrick's theory, but at a finite value of the reduced frequency that depends on the remaining non-dimensional parameters. The present analytical results are in good agreement with experimental data and numerical results for small amplitude oscillations. Supported by the Ministerio de Economia y Competitividad of Spain Grant No. DPI2013-40479-P.

Analytical Solution of a Generalized Hirota-Satsuma Equation

Science.gov (United States)

Kassem, M.; Mabrouk, S.; Abd-el-Malek, M.

A modified version of generalized Hirota-Satsuma is here solved using a two parameter group transformation method. This problem in three dimensions was reduced by Estevez [1] to a two dimensional one through a Lie transformation method and left unsolved. In the present paper, through application of symmetry transformation the Lax pair has been reduced to a system of ordinary equations. Three transformations cases are investigated. The obtained analytical solutions are plotted and show a profile proper to deflagration processes, well described by Degasperis-Procesi equation.

Effects of finite aspect ratio on wind turbine airfoil measurements

DEFF Research Database (Denmark)

Kiefer, Janik; Miller, Mark A.; Hultmark, Marcus

2016-01-01

Wind turbines partly operate in stalled conditions within their operational cycle. To simulate these conditions, it is also necessary to obtain 2-D airfoil data in terms of lift and drag coefficients at high angles of attack. Such data has been obtained previously, but often at low aspect ratios...... and only barely past the stall point, where strong wall boundary layer influence is expected. In this study, the influence of the wall boundary layer on 2D airfoil data, especially in the post stall domain, is investigated. Here, a wind turbine airfoil is tested at different angles of attack and with two...

Experimental study of pitching and plunging airfoils at low Reynolds numbers

Energy Technology Data Exchange (ETDEWEB)

Baik, Yeon Sik; Bernal, Luis P. [University of Michigan, Department of Aerospace Engineering, Ann Arbor, MI (United States)

2012-12-15

Measurements of the unsteady flow structure and force time history of pitching and plunging SD7003 and flat plate airfoils at low Reynolds numbers are presented. The airfoils were pitched and plunged in the effective angle of attack range of 2.4 -13.6 (shallow-stall kinematics) and -6 to 22 (deep-stall kinematics). The shallow-stall kinematics results for the SD7003 airfoil show attached flow and laminar-to-turbulent transition at low effective angle of attack during the down stroke motion, while the flat plate model exhibits leading edge separation. Strong Re-number effects were found for the SD7003 airfoil which produced approximately 25 % increase in the peak lift coefficient at Re = 10,000 compared to higher Re flows. The flat plate airfoil showed reduced Re effects due to leading edge separation at the sharper leading edge, and the measured peak lift coefficient was higher than that predicted by unsteady potential flow theory. The deep-stall kinematics resulted in leading edge separation that led to formation of a large leading edge vortex (LEV) and a small trailing edge vortex (TEV) for both airfoils. The measured peak lift coefficient was significantly higher ({proportional_to}50 %) than that for the shallow-stall kinematics. The effect of airfoil shape on lift force was greater than the Re effect. Turbulence statistics were measured as a function of phase using ensemble averages. The results show anisotropic turbulence for the LEV and isotropic turbulence for the TEV. Comparison of unsteady potential flow theory with the experimental data showed better agreement by using the quasi-steady approximation, or setting C(k) = 1 in Theodorsen theory, for leading edge-separated flows. (orig.)

Integration of Airfoil Design during the design of new blades

Energy Technology Data Exchange (ETDEWEB)

Sartori, L.; Bottasso, L.; Croce, A. [Politecnico di Milano, Milan (Italy); Grasso, F. [ECN Wind Power, Petten (Netherlands)

2013-09-15

Despite the fact that the design of a new blade is a multidisciplinary task, often the different disciplines are combined together at later stage. Looking at the aerodynamic design, it is common practice design/select the airfoils first and then design the blade in terms of chord and twist based on the initial selection of the airfoils. Although this approach is quite diffused, it limits the potentialities of obtaining optimal performance. The present work is focused on investigating the benefits of designing the external shape of the blade including the airfoil shapes together with chord and twist. To accomplish this, a design approach has been developed, where an advanced gradient based optimization algorithm is able to control the shape of the blade. The airfoils described in the work are the NACA 4 digits, while the chord distribution and the twist distribution are described through Bezier curves. In this way, the complexity of the problem is limited while a versatile geometrical description is kept. After the details of the optimization scheme are illustrated, several numerical examples are shown, demonstrating the advantages in terms of performance and development time of integrating the design of the airfoils during the optimization of the blade.

Novel loop-like solitons for the generalized Vakhnenko equation

International Nuclear Information System (INIS)

Zhang Min; Ma Yu-Lan; Li Bang-Qing

2013-01-01

A non-traveling wave solution of a generalized Vakhnenko equation arising from the high-frequent wave motion in a relaxing medium is derived via the extended Riccati mapping method. The solution includes an arbitrary function of an independent variable. Based on the solution, two hyperbolic functions are chosen to construct new solitons. Novel single-loop-like and double-loop-like solitons are found for the equation

Quasisolutions of Inverse Boundary-Value Problem of Aerodynamics for Dense Airfoil Grids

Directory of Open Access Journals (Sweden)

A.M. Elizarov

2016-12-01

Full Text Available In the process of turbomachinery development, it is of great importance to accurately design impellers and select their blade shape. One of the promising approaches to solving this problem is based on the theory of inverse boundary-value problems in aerodynamics. It helps to develop methods for profiling airfoil grids with predetermined properties in the same way as it is done for isolated airfoils. In this paper, methods have been worked out to find quasisolutions of the inverse boundary-value problem in aerodynamics for a plane airfoil grid. Two methods of quasisolution have been described. The first “`formal” method is similar, in its essence, to the method used for construction of quasisolution for an isolated airfoil. It has been shown that such quasisolutions provide satisfactory results for grids having a sufficiently large relative airfoil pitch. If pitch values are low, this method is unacceptable, because “modified” velocity distribution in some areas is significantly different from the original one in this case. For this reason, areas with significant changes in the angle of the tangent line appear in the airfoil contour and the flow region becomes multivalent. To satisfy the conditions of solvability in the case of grids having a small airfoil pitch, a new quasisolution construction method taking into account the specifics of the problem has been suggested. The desired effect has been achieved due to changes in the weighting function of the minimized functional. The comparison of the results of construction of the new quasisolution with the results obtained by the “formal” method has demonstrated that the constructed airfoils are very similar when the pitch is large. In the case of dense grids, it is clear that preference should be given to the second method, as it brings less distortion to the initial velocity distribution and, thus, allows to physically find an actual airfoil contour.

Nonequilibrium Statistical Operator Method and Generalized Kinetic Equations

Science.gov (United States)

Kuzemsky, A. L.

2018-01-01

We consider some principal problems of nonequilibrium statistical thermodynamics in the framework of the Zubarev nonequilibrium statistical operator approach. We present a brief comparative analysis of some approaches to describing irreversible processes based on the concept of nonequilibrium Gibbs ensembles and their applicability to describing nonequilibrium processes. We discuss the derivation of generalized kinetic equations for a system in a heat bath. We obtain and analyze a damped Schrödinger-type equation for a dynamical system in a heat bath. We study the dynamical behavior of a particle in a medium taking the dissipation effects into account. We consider the scattering problem for neutrons in a nonequilibrium medium and derive a generalized Van Hove formula. We show that the nonequilibrium statistical operator method is an effective, convenient tool for describing irreversible processes in condensed matter.

Overview of results from 2D airfoil testing at Risoe

Energy Technology Data Exchange (ETDEWEB)

Fuglsang, P. [Risoe National Lab., Wind Energy and Atmospheric Physics Dept., Roskilde (Denmark)

1997-12-31

This paper gives an overview of the results from two dimensional airfoil testing at Risoe. A two dimensional testing method was recently developed where a test rig is inserted into an open jet flow in a wind tunnel of the close return loop type with an open test section. Pressure measurements provide the lift and drag forces. Both stationary flow and dynamic inflow from pitch motion are possible. The wind tunnel static pressure and total dynamic pressures were calibrated and wind tunnel boundary corrections were found. So far, the testing method was verified by comparison of NACA 63-215 airfoil measurements to numerical predictions and to measurements. Furthermore, the Risoe-1, FFA-W3-241, FFA-W3-301 and NACA 63-430 airfoils were measured. Different types of leading edge roughness and vortex generators were investigated. For all airfoils, good agreements with predictions were obtained on both pressure distribution and on lift coefficient. The drag coefficients were slightly higher than predicted. (eg) 10 refs.

Application of Nontraditional Optimization Techniques for Airfoil Shape Optimization

Directory of Open Access Journals (Sweden)

R. Mukesh

2012-01-01

Full Text Available The method of optimization algorithms is one of the most important parameters which will strongly influence the fidelity of the solution during an aerodynamic shape optimization problem. Nowadays, various optimization methods, such as genetic algorithm (GA, simulated annealing (SA, and particle swarm optimization (PSO, are more widely employed to solve the aerodynamic shape optimization problems. In addition to the optimization method, the geometry parameterization becomes an important factor to be considered during the aerodynamic shape optimization process. The objective of this work is to introduce the knowledge of describing general airfoil geometry using twelve parameters by representing its shape as a polynomial function and coupling this approach with flow solution and optimization algorithms. An aerodynamic shape optimization problem is formulated for NACA 0012 airfoil and solved using the methods of simulated annealing and genetic algorithm for 5.0 deg angle of attack. The results show that the simulated annealing optimization scheme is more effective in finding the optimum solution among the various possible solutions. It is also found that the SA shows more exploitation characteristics as compared to the GA which is considered to be more effective explorer.

Four-wall turbine airfoil with thermal strain control for reduced cycle fatigue

Science.gov (United States)

Cambell, Christian X

2013-09-17

A turbine airfoil (20B) with a thermal expansion control mechanism that increases the airfoil camber (60, 61) under operational heating. The airfoil has four-wall geometry, including pressure side outer and inner walls (26, 28B), and suction side outer and inner walls (32, 34B). It has near-wall cooling channels (31F, 31A, 33F, 33A) between the outer and inner walls. A cooling fluid flow pattern (50C, 50W, 50H) in the airfoil causes the pressure side inner wall (28B) to increase in curvature under operational heating. The pressure side inner wall (28B) is thicker than walls (26, 34B) that oppose it in camber deformation, so it dominates them in collaboration with the suction side outer wall (32), and the airfoil camber increases. This reduces and relocates a maximum stress area (47) from the suction side outer wall (32) to the suction side inner wall (34B, 72) and the pressure side outer wall (26).

Resummed memory kernels in generalized system-bath master equations

International Nuclear Information System (INIS)

Mavros, Michael G.; Van Voorhis, Troy

2014-01-01

Generalized master equations provide a concise formalism for studying reduced population dynamics. Usually, these master equations require a perturbative expansion of the memory kernels governing the dynamics; in order to prevent divergences, these expansions must be resummed. Resummation techniques of perturbation series are ubiquitous in physics, but they have not been readily studied for the time-dependent memory kernels used in generalized master equations. In this paper, we present a comparison of different resummation techniques for such memory kernels up to fourth order. We study specifically the spin-boson Hamiltonian as a model system bath Hamiltonian, treating the diabatic coupling between the two states as a perturbation. A novel derivation of the fourth-order memory kernel for the spin-boson problem is presented; then, the second- and fourth-order kernels are evaluated numerically for a variety of spin-boson parameter regimes. We find that resumming the kernels through fourth order using a Padé approximant results in divergent populations in the strong electronic coupling regime due to a singularity introduced by the nature of the resummation, and thus recommend a non-divergent exponential resummation (the “Landau-Zener resummation” of previous work). The inclusion of fourth-order effects in a Landau-Zener-resummed kernel is shown to improve both the dephasing rate and the obedience of detailed balance over simpler prescriptions like the non-interacting blip approximation, showing a relatively quick convergence on the exact answer. The results suggest that including higher-order contributions to the memory kernel of a generalized master equation and performing an appropriate resummation can provide a numerically-exact solution to system-bath dynamics for a general spectral density, opening the way to a new class of methods for treating system-bath dynamics

Design and Wind Tunnel Testing of a Thick, Multi-Element High-Lift Airfoil

DEFF Research Database (Denmark)

Zahle, Frederik; Gaunaa, Mac; Sørensen, Niels N.

2012-01-01

In this work a 2D CFD solver has been used to optimize the shape of a leading edge slat with a chord length of 30% of the main airfoil which was 40% thick. The airfoil configuration was subsequently tested in a wind tunnel and compared to numerical predictions. The multi-element airfoil was predi...

Unsteady effects in flows past stationary airfoils with Gurney flaps due to unsteady flow separations at low Reynolds numbers

Directory of Open Access Journals (Sweden)

Dan MATEESCU

2015-12-01

Full Text Available This paper presents the analysis of the unsteady flows past stationary airfoils equipped with Gurney flaps at low Reynolds numbers, aiming to study the unsteady behavior of the aerodynamic coefficients due to the flow separations occurring at these Reynolds numbers. The Gurney flaps are simple but very efficient lift-increasing devices, which due to their mechanical simplicity are of particular interest for the small size micro-air-vehicles (MAV flying at low speed and very low Reynolds number. The unsteady aerodynamic analysis is performed with an efficient time-accurate numerical method developed for the solution of the Navier-Stokes equations at low Reynolds numbers, which is second-order-accurate in time and space. The paper presents solutions for the unsteady aerodynamic coefficients of lift and drag and for the lift-to-drag ratio of several symmetric and cambered airfoils with Gurney flaps. It was found that although the airfoil is considered stationary, starting from a relatively small incidence (about 8 degrees the flow becomes unsteady due to the unsteadiness of the flow separations occurring at low Reynolds numbers, and the aerodynamic coefficients display periodic oscillations in time. A detailed study is presented in the paper on the influence of various geometric and flow parameters, such as the Gurney flap height, Reynolds number, airfoil relative thickness and relative camber, on the aerodynamic coefficients of lift, drag and lift-to-drag ratio. The flow separation is also studied with the aid of flow visualizations illustrating the changes in the flow pattern at various moments in time.

Linear Strength Vortex Panel Method for NACA 4412 Airfoil

Science.gov (United States)

Liu, Han

2018-03-01

The objective of this article is to formulate numerical models for two-dimensional potential flow over the NACA 4412 Airfoil using linear vortex panel methods. By satisfying the no penetration boundary condition and Kutta condition, the circulation density on each boundary points (end point of every panel) are obtained and according to which, surface pressure distribution and lift coefficients of the airfoil are predicted and validated by Xfoil, an interactive program for the design and analysis of airfoil. The sensitivity of results to the number of panels is also investigated in the end, which shows that the results are sensitive to the number of panels when panel number ranges from 10 to 160. With the increasing panel number (N>160), the results become relatively insensitive to it.

On the integrability of the generalized Fisher-type nonlinear diffusion equations

International Nuclear Information System (INIS)

Wang Dengshan; Zhang Zhifei

2009-01-01

In this paper, the geometric integrability and Lax integrability of the generalized Fisher-type nonlinear diffusion equations with modified diffusion in (1+1) and (2+1) dimensions are studied by the pseudo-spherical surface geometry method and prolongation technique. It is shown that the (1+1)-dimensional Fisher-type nonlinear diffusion equation is geometrically integrable in the sense of describing a pseudo-spherical surface of constant curvature -1 only for m = 2, and the generalized Fisher-type nonlinear diffusion equations in (1+1) and (2+1) dimensions are Lax integrable only for m = 2. This paper extends the results in Bindu et al 2001 (J. Phys. A: Math. Gen. 34 L689) and further provides the integrability information of (1+1)- and (2+1)-dimensional Fisher-type nonlinear diffusion equations for m = 2

Design of a 3 kW wind turbine generator with thin airfoil blades

Energy Technology Data Exchange (ETDEWEB)

Ameku, Kazumasa; Nagai, Baku M.; Roy, Jitendro Nath [Faculty of Mechanical Engineering, University of the Ryukyus, 1 Senbaru, Nishihara-cho, Okinawa 903-0213 (Japan)

2008-09-15

Three blades of a 3 kW prototype wind turbine generator were designed with thin airfoil and a tip speed ratio of 3. The wind turbine has been controlled via two control methods: the variable pitch angle and by regulation of the field current of the generator and examined under real wind conditions. The characteristics of the thin airfoil, called ''Seven arcs thin airfoil'' named so because the airfoil is composed of seven circular arcs, are analyzed with the airfoil design and analysis program XFOIL. The thin airfoil blade is designed and calculated by blade element and momentum theory. The performance characteristics of the machine such as rotational speed, generator output as well as stability for wind speed changes are described. In the case of average wind speeds of 10 m/s and a maximum of 19 m/s, the automatically controlled wind turbine ran safely through rough wind conditions and showed an average generator output of 1105 W and a power coefficient 0.14. (author)

Unsteady two-dimensional potential-flow model for thin variable geometry airfoils

DEFF Research Database (Denmark)

Gaunaa, Mac

2010-01-01

In the present work, analytical expressions for distributed and integral unsteady two-dimensional forces on a variable geometry airfoil undergoing arbitrary motion are derived under the assumption of incompressible, irrotational, inviscid flow. The airfoil is represented by its camber line...... in their equivalent state-space form, allowing for use of the present theory in problems employing the eigenvalue approach, such as stability analysis. The analytical expressions for the integral forces can be reduced to Munk's steady and Theodorsen's unsteady results for thin airfoils, and numerical evaluation shows...

Mathieu's Equation and its Generalizations: Overview of Stability Charts and their Features

DEFF Research Database (Denmark)

Kovacic, Ivana; Rand, Richard H.; Sah, Si Mohamed

2018-01-01

This work is concerned with Mathieu's equation - a classical differential equation, which has the form of a linear second-order ordinary differential equation with Cosine-type periodic forcing of the stiffness coefficient, and its different generalizations/extensions. These extensions include...... and features, and how it differs from that of the classical Mathieu's equation....

Exact solutions of the generalized Lane–Emden equations of the ...

Indian Academy of Sciences (India)

the mutual attraction of its molecules and subject to the classical laws of thermodynamics. This equation was proposed ... was investigated for first integrals by Leach [31]. Moreover, transformation properties of a more general Emden–Fowler equation were considered in Mellin et al [5]. A review paper by Wong [32] contains ...

Simulation of flow over double-element airfoil and wind tunnel test for use in vertical axis wind turbine

DEFF Research Database (Denmark)

Chougule, Prasad; Nielsen, Søren R.K.

2014-01-01

been made to utilize high lift technology for vertical axis wind turbines in order to improve power efficiency. High lift is obtained by double-element airfoil mainly used in aeroplane wing design. In this current work a low Reynolds number airfoil is selected to design a double-element airfoil blade...... for use in vertical axis wind turbine to improve the power efficiency. Double-element airfoil blade design consists of a main airfoil and a slat airfoil. Orientation of slat airfoil is a parameter of investigation in this paper and air flow simulation over double-element airfoil. With primary wind tunnel...... that there is an increase in the lift coefficient by 26% for single-element airfoil at analysed conditions. The CFD simulation results were validated with wind tunnel tests. It is also observe that by selecting proper airfoil configuration and blade sizes an increase in lift coefficient can further be achieved....

General Dirichlet Series, Arithmetic Convolution Equations and Laplace Transforms

Czech Academy of Sciences Publication Activity Database

Glöckner, H.; Lucht, L.G.; Porubský, Štefan

2009-01-01

Roč. 193, č. 2 (2009), s. 109-129 ISSN 0039-3223 R&D Projects: GA ČR GA201/07/0191 Institutional research plan: CEZ:AV0Z10300504 Keywords : arithmetic function * Dirichlet convolution * polynomial equation * analytic equation * topological algebra * holomorphic functional calculus * implicit function theorem * Laplace transform * semigroup * complex measure Subject RIV: BA - General Mathematics Impact factor: 0.645, year: 2009 http://arxiv.org/abs/0712.3172

Design of low noise airfoil with high aerodynamic performance for use on small wind turbines

Institute of Scientific and Technical Information of China (English)

Taehyung; KIM; Seungmin; LEE; Hogeon; KIM; Soogab; LEE

2010-01-01

Wind power is one of the most reliable renewable energy sources and internationally installed capacity is increasing radically every year.Although wind power has been favored by the public in general,the problem with the impact of wind turbine noise on people living in the vicinity of the turbines has been increased.Low noise wind turbine design is becoming more and more important as noise is spreading more adverse effect of wind turbine to public.This paper demonstrates the design of 10 kW class wind turbines,each of three blades,a rotor diameter 6.4 m,a rated rotating speed 200 r/min and a rated wind speed 10 m/s.The optimized airfoil is dedicated for the 75% spanwise position because the dominant source of a wind turbine blade is trailing edge noise from the outer 25% of the blade.Numerical computations are performed for incompressible flow and for Mach number at 0.145 and for Reynolds numbers at 1.02×106 with a lift performance,which is resistant to surface contamination and turbulence intensity.The objectives in the design process are to reduce noise emission,while sustaining high aerodynamic efficiency.Dominant broadband noise sources are predicted by semi-empirical formulas composed of the groundwork by Brooks et al.and Lowson associated with typical wind turbine operation conditions.During the airfoil redesign process,the aerodynamic performance is analyzed to reduce the wind turbine power loss.The results obtained from the design process show that the design method is capable of designing airfoils with reduced noise using a commercial 10 kW class wind turbine blade airfoil as a basis.Therefore,the new optimized airfoil showing 2.9 dB reductions of total sound pressure level(SPL) and higher aerodynamic performance are achieved.

Generalized internal long wave equations: construction, hamiltonian structure and conservation laws

International Nuclear Information System (INIS)

Lebedev, D.R.

1982-01-01

Some aspects of the theory of the internal long-wave equations (ILW) are considered. A general class of the ILW type equations is constructed by means of the Zakharov-Shabat ''dressing'' method. Hamiltonian structure and infinite numbers of conservation laws are introduced. The considered equations are shown to be Hamiltonian in the so-called second Hamiltonian structu

A new multi-symplectic scheme for the generalized Kadomtsev-Petviashvili equation

Science.gov (United States)

Li, Haochen; Sun, Jianqiang

2012-09-01

We propose a new scheme for the generalized Kadomtsev-Petviashvili (KP) equation. The multi-symplectic conservation property of the new scheme is proved. Back error analysis shows that the new multi-symplectic scheme has second order accuracy in space and time. Numerical application on studying the KPI equation and the KPII equation are presented in detail.

Peakons, solitary patterns and periodic solutions for generalized Camassa-Holm equations

International Nuclear Information System (INIS)

Zheng Yin; Lai Shaoyong

2008-01-01

This Letter deals with a generalized Camassa-Holm equation and a nonlinear dispersive equation by making use of a mathematical technique based on using integral factors for solving differential equations. The peakons, solitary patterns and periodic solutions are expressed analytically under various circumstances. The conditions that cause the qualitative change in the physical structures of the solutions are highlighted

Solution of the generalized Emden-Fowler equations by the hybrid functions method

International Nuclear Information System (INIS)

Tabrizidooz, H R; Marzban, H R; Razzaghi, M

2009-01-01

In this paper, we present a numerical algorithm for solving the generalized Emden-Fowler equations, which have many applications in mathematical physics and astrophysics. The method is based on hybrid functions approximations. The properties of hybrid functions, which consist of block-pulse functions and Lagrange interpolating polynomials, are presented. These properties are then utilized to reduce the computation of the generalized Emden-Fowler equations to a system of nonlinear equations. The method is easy to implement and yields very accurate results.

LES tests on airfoil trailing edge serration

International Nuclear Information System (INIS)

Zhu, Wei Jun; Shen, Wen Zhong

2016-01-01

In the present study, a large number of acoustic simulations are carried out for a low noise airfoil with different Trailing Edge Serrations (TES). The Ffowcs Williams-Hawkings (FWH) acoustic analogy is used for noise prediction at trailing edge. The acoustic solver is running on the platform of our in-house incompressible flow solver EllipSys3D. The flow solution is first obtained from the Large Eddy Simulation (LES), the acoustic part is then carried out based on the instantaneous hydrodynamic pressure and velocity field. To obtain the time history data of sound pressure, the flow quantities are integrated around the airfoil surface through the FWH approach. For all the simulations, the chord based Reynolds number is around 1.5x10 6 . In the test matrix, the effects from angle of attack, the TE flap angle, the length/width of the TES are investigated. Even though the airfoil under investigation is already optimized for low noise emission, most numerical simulations and wind tunnel experiments show that the noise level is further decreased by adding the TES device. (paper)

Travelling wave solutions of generalized coupled Zakharov–Kuznetsov and dispersive long wave equations

Directory of Open Access Journals (Sweden)

M. Arshad

Full Text Available In this manuscript, we constructed different form of new exact solutions of generalized coupled Zakharov–Kuznetsov and dispersive long wave equations by utilizing the modified extended direct algebraic method. New exact traveling wave solutions for both equations are obtained in the form of soliton, periodic, bright, and dark solitary wave solutions. There are many applications of the present traveling wave solutions in physics and furthermore, a wide class of coupled nonlinear evolution equations can be solved by this method. Keywords: Traveling wave solutions, Elliptic solutions, Generalized coupled Zakharov–Kuznetsov equation, Dispersive long wave equation, Modified extended direct algebraic method

Turbine airfoil manufacturing technology

Energy Technology Data Exchange (ETDEWEB)

Kortovich, C. [PCC Airfoils, Inc., Beachwood, OH (United States)

1995-12-31

The specific goal of this program is to define manufacturing methods that will allow single crystal technology to be applied to complex-cored airfoils components for power generation applications. Tasks addressed include: alloy melt practice to reduce the sulfur content; improvement of casting process; core materials design; and grain orientation control.

Anisotropic charged physical models with generalized polytropic equation of state

Energy Technology Data Exchange (ETDEWEB)

Nasim, A.; Azam, M. [University of Education, Division of Science and Technology, Lahore (Pakistan)

2018-01-15

In this paper, we found the exact solutions of Einstein-Maxwell equations with generalized polytropic equation of state (GPEoS). For this, we consider spherically symmetric object with charged anisotropic matter distribution. We rewrite the field equations into simple form through transformation introduced by Durgapal (Phys Rev D 27:328, 1983) and solve these equations analytically. For the physically acceptability of these solutions, we plot physical quantities like energy density, anisotropy, speed of sound, tangential and radial pressure. We found that all solutions fulfill the required physical conditions. It is concluded that all our results are reduced to the case of anisotropic charged matter distribution with linear, quadratic as well as polytropic equation of state. (orig.)

Monitoring pressure profiles across an airfoil with a fiber Bragg grating sensor array

Science.gov (United States)

Papageorgiou, Anthony W.; Parkinson, Luke A.; Karas, Andrew R.; Hansen, Kristy L.; Arkwright, John W.

2018-02-01

Fluid flow over an airfoil section creates a pressure difference across the upper and lower surfaces, thus generating lift. Successful wing design is a combination of engineering design and experience in the field, with subtleties in design and manufacture having significant impact on the amount of lift produced. Current methods of airfoil optimization and validation typically involve computational fluid dynamics (CFD) and extensive wind tunnel testing with pressure sensors embedded into the airfoil to measure the pressure over the wing. Monitoring pressure along an airfoil in a wind tunnel is typically achieved using surface pressure taps that consist of hollow tubes running from the surface of the airfoil to individual pressure sensors external to the tunnel. These pressure taps are complex to configure and not ideal for in-flight testing. Fiber Bragg grating (FBG) pressure sensing arrays provide a highly viable option for both wind tunnel and inflight pressure measurement. We present a fiber optic sensor array that can detect positive and negative pressure suitable for validating CFD models of airfoil profile sections. The sensing array presented here consists of 6 independent sensing elements, each capable of a pressure resolution of less than 10 Pa over the range of 70 kPa to 120 kPa. The device has been tested with the sensor array attached to a 90mm chord length airfoil section subjected to low velocity flow. Results show that the arrays are capable of accurately detecting variations of the pressure profile along the airfoil as the angle of attack is varied from zero to the point at which stall occurs.

Drag Coefficient of Water Droplets Approaching the Leading Edge of an Airfoil

Science.gov (United States)

Vargas, Mario; Sor, Suthyvann; Magarino, Adelaida Garcia

2013-01-01

This work presents results of an experimental study on droplet deformation and breakup near the leading edge of an airfoil. The experiment was conducted in the rotating rig test cell at the Instituto Nacional de Tecnica Aeroespacial (INTA) in Madrid, Spain. An airfoil model was placed at the end of the rotating arm and a monosize droplet generator produced droplets that fell from above, perpendicular to the path of the airfoil. The interaction between the droplets and the airfoil was captured with high speed imaging and allowed observation of droplet deformation and breakup as the droplet approached the airfoil near the stagnation line. Image processing software was used to measure the position of the droplet centroid, equivalent diameter, perimeter, area, and the major and minor axes of an ellipse superimposed over the deforming droplet. The horizontal and vertical displacement of each droplet against time was also measured, and the velocity, acceleration, Weber number, Bond number, Reynolds number, and the drag coefficients were calculated along the path of the droplet to the beginning of breakup. Results are presented and discussed for drag coefficients of droplets with diameters in the range of 300 to 1800 micrometers, and airfoil velocities of 50, 70 and 90 meters/second. The effect of droplet oscillation on the drag coefficient is discussed.

Generalized force in classical field theory. [Euler-Lagrange equations

Energy Technology Data Exchange (ETDEWEB)

Krause, J [Universidad Central de Venezuela, Caracas

1976-02-01

The source strengths of the Euler-Lagrange equations, for a system of interacting fields, are heuristically interpreted as generalized forces. The canonical form of the energy-momentum tensor thus consistently appears, without recourse to space-time symmetry arguments. A concept of 'conservative' generalized force in classical field theory is also briefly discussed.

Generalized Lorentz-Force equations

International Nuclear Information System (INIS)

Yamaleev, R.M.

2001-01-01

Guided by Nambu (n+1)-dimensional phase space formalism we build a new system of dynamic equations. These equations describe a dynamic state of the corporeal system composed of n subsystems. The dynamic equations are formulated in terms of dynamic variables of the subsystems as well as in terms of dynamic variables of the corporeal system. These two sets of variables are related respectively as roots and coefficients of the n-degree polynomial equation. In the special n=2 case, this formalism reproduces relativistic dynamics for the charged spinning particles

Turbine Airfoil Optimization Using Quasi-3D Analysis Codes

Directory of Open Access Journals (Sweden)

Sanjay Goel

2009-01-01

Full Text Available A new approach to optimize the geometry of a turbine airfoil by simultaneously designing multiple 2D sections of the airfoil is presented in this paper. The complexity of 3D geometry modeling is circumvented by generating multiple 2D airfoil sections and constraining their geometry in the radial direction using first- and second-order polynomials that ensure smoothness in the radial direction. The flow fields of candidate geometries obtained during optimization are evaluated using a quasi-3D, inviscid, CFD analysis code. An inviscid flow solver is used to reduce the execution time of the analysis. Multiple evaluation criteria based on the Mach number profile obtained from the analysis of each airfoil cross-section are used for computing a quality metric. A key contribution of the paper is the development of metrics that emulate the perception of the human designer in visually evaluating the Mach Number distribution. A mathematical representation of the evaluation criteria coupled with a parametric geometry generator enables the use of formal optimization techniques in the design. The proposed approach is implemented in the optimal design of a low-pressure turbine nozzle.

Numerical study of unsteady viscous flow past oscillating airfoil

Energy Technology Data Exchange (ETDEWEB)

Jin Yan; Yuan Xin [Tsinghua Univ., Dept. of Thermal Engineering, Beijing (China)

2001-07-01

Accurate simulation of the dynamic stall of an oscillating airfoil is of major importance to wing and wind turbine blade design. However, dynamic stall is complicated and influenced by many factors, such as geometry shape of the airfoil, reduced frequency, etc. The difficulties of simulation are both mathematical (numerical method) and physical (turbulence model). The present paper has introduced a new numerical method (new LU-type scheme and fourth-order higher resolution MUSCL TVD scheme) and q-{omega} turbulence modelling to calculate the unsteady flowfields of an oscillating NACA0015 airfoil. The test targets include attached flow, light-stall and deep-stall of the airfoil. The calculated results for attached flow and light-stall are in good agreement with those of experiments. The calculated results for deep-stall also show improvement, especially during the downstroke of the oscillation. However, there is still a significant difference between the results of calculation and experiment in the hysteresis curves of the drag coefficient. One reason is that the q-{omega} turbulence model still has limitations. Another is that the drag coefficient is difficult to measure and the experiments are not reliable. (Author)

Airfoil lance apparatus for homogeneous humidification and sorbent dispersion in a gas stream

Science.gov (United States)

Myers, Robert B.; Yagiela, Anthony S.

1990-12-25

An apparatus for spraying an atomized mixture into a gas stream comprises a stream line airfoil member having a large radius leading edge and a small radius trailing edge. A nozzle assembly pierces the trailing edge of the airfoil member and is concentrically surrounded by a nacelle which directs shielding gas from the interior of the airfoil member around the nozzle assembly. Flowable medium to be atomized and atomizing gas for atomizing the medium are supplied in concentric conduits to the nozzle. A plurality of nozzles each surrounded by a nacelle are spaced along the trailing edge of the airfoil member.

On the influence of airfoil deviations on the aerodynamic performance of wind turbine rotors

International Nuclear Information System (INIS)

Winstroth, J; Seume, J R

2016-01-01

The manufacture of large wind turbine rotor blades is a difficult task that still involves a certain degree of manual labor. Due to the complexity, airfoil deviations between the design airfoils and the manufactured blade are certain to arise. Presently, the understanding of the impact of manufacturing uncertainties on the aerodynamic performance is still incomplete. The present work analyzes the influence of a series of airfoil deviations likely to occur during manufacturing by means of Computational Fluid Dynamics and the aeroelastic code FAST. The average power production of the NREL 5MW wind turbine is used to evaluate the different airfoil deviations. Analyzed deviations include: Mold tilt towards the leading and trailing edge, thick bond lines, thick bond lines with cantilever correction, backward facing steps and airfoil waviness. The most severe influences are observed for mold tilt towards the leading and thick bond lines. By applying the cantilever correction, the influence of thick bond lines is almost compensated. Airfoil waviness is very dependent on amplitude height and the location along the surface of the airfoil. Increased influence is observed for backward facing steps, once they are high enough to trigger boundary layer transition close to the leading edge. (paper)

Modeling the Aerodynamic Lift Produced by Oscillating Airfoils at Low Reynolds Number

OpenAIRE

Khalid, Muhammad Saif Ullah; Akhtar, Imran

2014-01-01

For present study, setting Strouhal Number (St) as control parameter, numerical simulations for flow past oscillating NACA-0012 airfoil at 1,000 Reynolds Numbers (Re) are performed. Temporal profiles of unsteady forces; lift and thrust, and their spectral analysis clearly indicate the solution to be a period-1 attractor for low Strouhal numbers. This study reveals that aerodynamic forces produced by plunging airfoil are independent of initial kinematic conditions of airfoil that proves the ex...

The effect of acoustic forcing on an airfoil tonal noise mechanism.

Science.gov (United States)

Schumacher, Karn L; Doolan, Con J; Kelso, Richard M

2014-08-01

The response of the boundary layer over an airfoil with cavity to external acoustic forcing, across a sweep of frequencies, was measured. The boundary layer downstream of the cavity trailing edge was found to respond strongly and selectively at the natural airfoil tonal frequencies. This is considered to be due to enhanced feedback. However, the shear layer upstream of the cavity trailing edge did not respond at these frequencies. These findings confirm that an aeroacoustic feedback loop exists between the airfoil trailing edge and a location near the cavity trailing edge.

Cross-Validation of Numerical and Experimental Studies of Transitional Airfoil Performance

DEFF Research Database (Denmark)

Frere, Ariane; Hillewaert, Koen; Sarlak, Hamid

2015-01-01

The aerodynamic performance characteristic of airfoils are the main input for estimating wind turbine blade loading as well as annual energy production of wind farms. For transitional flow regimes these data are difficult to obtain, both experimentally as well as numerically, due to the very high...... sensitivity of the flow to perturbations, large scale separation and performance hysteresis. The objective of this work is to improve the understanding of the transitional airfoil flow performance by studying the S826 NREL airfoil at low Reynolds numbers (Re = 4:104 and 1:105) with two inherently different...

The General Traveling Wave Solutions of the Fisher Equation with Degree Three

Directory of Open Access Journals (Sweden)

Wenjun Yuan

2013-01-01

degree three and the general meromorphic solutions of the integrable Fisher equations with degree three, which improves the corresponding results obtained by Feng and Li (2006, Guo and Chen (1991, and Ağırseven and Öziş (2010. Moreover, all wg,1(z are new general meromorphic solutions of the Fisher equations with degree three for c=±3/2. Our results show that the complex method provides a powerful mathematical tool for solving a large number of nonlinear partial differential equations in mathematical physics.

New Generalized Hyperbolic Functions to Find New Exact Solutions of the Nonlinear Partial Differential Equations

Directory of Open Access Journals (Sweden)

Yusuf Pandir

2013-01-01

Full Text Available We firstly give some new functions called generalized hyperbolic functions. By the using of the generalized hyperbolic functions, new kinds of transformations are defined to discover the exact approximate solutions of nonlinear partial differential equations. Based on the generalized hyperbolic function transformation of the generalized KdV equation and the coupled equal width wave equations (CEWE, we find new exact solutions of two equations and analyze the properties of them by taking different parameter values of the generalized hyperbolic functions. We think that these solutions are very important to explain some physical phenomena.

Numerical solutions of the complete Navier-Strokes equations. no. 27

Science.gov (United States)

Hassan, H. A.

1996-01-01

This report describes the development of an enstrophy model capable of predicting turbulence separation and its application to two airfoils at various angles of attack and Mach numbers. In addition, a two equation kappa-xi model with a tensor eddy viscosity was developed. Plans call for this model to be used in calculating three dimensional turbulent flows.

Towards the general solution of the Yang-Mills equations

International Nuclear Information System (INIS)

Helfer, A.D.

1985-01-01

The author presents a new non-perturbative technique for finding arbitrary self-dual solutions to the Yang-Mills equations, and of describing massless fields minimally coupled to them. The approach uses techniques of complex analysis in several variables, and is complementary to Ward's: it is expected that a combination of the two techniques will yield general, non-self-dual solutions to the Yang-Mills equations. This has been verified to first order in perturbation theory

Generalized Ordinary Differential Equation Models.

Science.gov (United States)

Miao, Hongyu; Wu, Hulin; Xue, Hongqi

2014-10-01

Existing estimation methods for ordinary differential equation (ODE) models are not applicable to discrete data. The generalized ODE (GODE) model is therefore proposed and investigated for the first time. We develop the likelihood-based parameter estimation and inference methods for GODE models. We propose robust computing algorithms and rigorously investigate the asymptotic properties of the proposed estimator by considering both measurement errors and numerical errors in solving ODEs. The simulation study and application of our methods to an influenza viral dynamics study suggest that the proposed methods have a superior performance in terms of accuracy over the existing ODE model estimation approach and the extended smoothing-based (ESB) method.

Airfoil boundary layer separation and control at low Reynolds numbers

Energy Technology Data Exchange (ETDEWEB)

Yarusevych, S.; Sullivan, P.E. [University of Toronto, Department of Mechanical and Industrial Engineering, Toronto, ON (Canada); Kawall, J.G. [Ryerson University, Department of Mechanical and Industrial Engineering, Toronto, ON (Canada)

2005-04-01

The boundary layer separation on a NACA 0025 airfoil was studied experimentally via hot-wire anemometry and surface pressure measurements. The results provide added insight into periodic boundary layer control, suggesting that matching the excitation frequency with the most amplified disturbance in the separated shear layer is optimal for improving airfoil performance. (orig.)

Experimental Investigation of Aerodynamic Performance of Airfoils Fitted with Morphing Trailing Edges

OpenAIRE

Ai, Qing; Kamliya Jawahar, Hasan; Azarpeyvand, Mahdi

2016-01-01

The aerodynamic performance and wake development of a NACA 0012 airfoil fitted with morphing trailing edges were studied using experimental and computational techniques. The NACA 0012 airfoil was tested with morphing trailing edges having various camber profiles with the same trailing edge tip deflection. The aerodynamic force measurements for the airfoil were carried out for a wide range of chord-based Reynolds number and angles of attack with trailing edge deflection angle of β= 5◦ and 10◦....

S833, S834, and S835 Airfoils: November 2001--November 2002

Energy Technology Data Exchange (ETDEWEB)

Somers, D. M.

2005-08-01

A family of quiet, thick, natural-laminar-flow airfoils, the S833, S834, and S835, for 1 - 3-meter-diameter, variable-speed/variable-pitch, horizontal-axis wind turbines has been designed and analyzed theoretically. The two primary objectives of high maximum lift, relatively insensitive to roughness, and low profile drag have been achieved. The airfoils should exhibit docile stalls, which meet the design goal. The constraints on the pitching moment and the airfoils thicknesses have been satisfied.

S830, S831, and S832 Airfoils: November 2001-November 2002

Energy Technology Data Exchange (ETDEWEB)

Somers, D. M.

2005-08-01

A family of quiet, thick, natural-laminar-flow airfoils, the S830, S831, and S832, for 40 - 50-meter-diameter, variable-speed/variable-pitch, horizontal-axis wind turbines has been designed and analyzed theoretically. The two primary objectives of high maximum lift, relatively insensitive to roughness, and low profile drag have been achieved. The airfoils should exhibit docile stalls, which meet the design goal. The constraints on the pitching moment and the airfoils thicknesses have been satisfied.

Sketching the General Quadratic Equation Using Dynamic Geometry Software

Science.gov (United States)

Stols, G. H.

2005-01-01

This paper explores a geometrical way to sketch graphs of the general quadratic in two variables with Geometer's Sketchpad. To do this, a geometric procedure as described by De Temple is used, bearing in mind that this general quadratic equation (1) represents all the possible conics (conics sections), and the fact that five points (no three of…

General relativistic continuum mechanics and the post-Newtonian equations of motion

International Nuclear Information System (INIS)

Morrill, T.H.

1991-01-01

Aspects are examined of general relativistic continuum mechanics. Perfectly elastic materials are dealt with but not exclusively. The derivation of their equations of motion is emphasized, in the post-Newtonian approximation. A reformulation is presented based on the tetrad formalism, of Carter and Quintana's theory of general relativistic elastic continua. A field Lagrangian is derived describing perfect material media; show that the usual covariant conservations law for perfectly elastic media is fully equivalent to the Euler-Lagrange equations describing these same media; and further show that the equations of motion for such materials follow directly from Einstein's field equations. In addition, a version of this principle shows that the local mass density in curved space-time partially depends on the amount and distribution of mass energy in the entire universe and is related to the mass density that would occur if space-time were flat. The total Lagrangian was also expanded in an EIH (Einstein, Infeld, Hoffmann) series to obtain a total post-Newtonian Lagrangian. The results agree with those found by solving Einstein's equations for the metric coefficients and by deriving the post-Newtonian equations of motion from the covariant conservation law

Macro-Fiber Composite actuated simply supported thin airfoils

International Nuclear Information System (INIS)

Bilgen, Onur; Kochersberger, Kevin B; Inman, Daniel J; Ohanian, Osgar J III

2010-01-01

A piezoceramic composite actuator known as Macro-Fiber Composite (MFC) is used for actuation in the design of a variable camber airfoil intended for a ducted fan aircraft. The study focuses on response characterization under aerodynamic loads for circular arc airfoils with variable pinned boundary conditions. A parametric study of fluid–structure interaction is employed to find pin locations along the chordwise direction that result in high lift generation. Wind tunnel experiments are conducted on a 1.0% thick, 127 mm chord MFC actuated bimorph airfoil that is simply supported at 5% and 50% of the chord. Aerodynamic and structural performance results are presented for a flow rate of 15 m s −1 and a Reynolds number of 127 000. Non-linear effects due to aerodynamic and piezoceramic hysteresis are identified and discussed. A lift coefficient change of 1.46 is observed, purely due to voltage actuation. A maximum 2D L/D ratio of 17.8 is recorded through voltage excitation

Application of the Generalized Differential Quadrature Method in Solving Burgers' Equations

International Nuclear Information System (INIS)

Mokhtari, R.; Toodar, A. Samadi; Chegini, N.G.

2011-01-01

The aim of this paper is to obtain numerical solutions of the one-dimensional, two-dimensional and coupled Burgers' equations through the generalized differential quadrature method (GDQM). The polynomial-based differential quadrature (PDQ) method is employed and the obtained system of ordinary differential equations is solved via the total variation diminishing Runge-Kutta (TVD-RK) method. The numerical solutions are satisfactorily coincident with the exact solutions. The method can compete against the methods applied in the literature. (general)

Airfoil-shaped micro-mixers for reducing fouling on membrane surfaces

Science.gov (United States)

Ho, Clifford K; Altman, Susan J; Clem, Paul G; Hibbs, Michael; Cook, Adam W

2012-10-23

An array of airfoil-shaped micro-mixers that enhances fluid mixing within permeable membrane channels, such as used in reverse-osmosis filtration units, while minimizing additional pressure drop. The enhanced mixing reduces fouling of the membrane surfaces. The airfoil-shaped micro-mixer can also be coated with or comprised of biofouling-resistant (biocidal/germicidal) ingredients.

Fronts between hexagons and squares in a generalized Swift-Hohenberg equation

DEFF Research Database (Denmark)

Kubstrup, Christian; Herrero, H.; Pérez-García, C.

1996-01-01

Pinning effects in domain walls separating different orientations in patterns in nonequilibrium systems, are studied. Usually; theoretical studies consider perfect structures, but in experiments, point defects, grain boundaries, etc., always appear. The aim of this paper is to perform an analysis...... of the stability of fronts between hexagons and squares in a generalized Swift-Hohenberg model equation. We focus the analysis on pinned fronts between domains with different symmetries by using amplitude equations and by considering the small-scale structure in the pattern. The conditions for pinning effects...... and stable fronts are determined. This study is completed with direct simulations of the generalized Swift-Hohenberg equation. The results agree qualitatively with recent observations in convection and in ferrofluid instabilities....

A General Algorithm for Reusing Krylov Subspace Information. I. Unsteady Navier-Stokes

Science.gov (United States)

Carpenter, Mark H.; Vuik, C.; Lucas, Peter; vanGijzen, Martin; Bijl, Hester

2010-01-01

A general algorithm is developed that reuses available information to accelerate the iterative convergence of linear systems with multiple right-hand sides A x = b (sup i), which are commonly encountered in steady or unsteady simulations of nonlinear equations. The algorithm is based on the classical GMRES algorithm with eigenvector enrichment but also includes a Galerkin projection preprocessing step and several novel Krylov subspace reuse strategies. The new approach is applied to a set of test problems, including an unsteady turbulent airfoil, and is shown in some cases to provide significant improvement in computational efficiency relative to baseline approaches.

Wind Tunnel and Numerical Analysis of Thick Blunt Trailing Edge Airfoils

Science.gov (United States)

McLennan, Anthony William

Two-dimensional aerodynamic characteristics of several thick blunt trailing edge airfoils are presented. These airfoils are not only directly applicable to the root section of wind turbine blades, where they provide the required structural strength at a fraction of the material and weight of an equivalent sharp trailing edge airfoil, but are also applicable to the root sections of UAVs having high aspect ratios, that also encounter heavy root bending forces. The Reynolds averaged Navier-Stokes code, ARC2D, was the primary numerical tool used to analyze each airfoil. The UCD-38-095, referred to as the Pareto B airfoil in this thesis, was also tested in the University of California, Davis Aeronautical Wind Tunnel. The Pareto B has an experimentally determined maximum lift coefficient of 1.64 at 14 degrees incidence, minimum drag coefficient of 0.0385, and maximum lift over drag ratio of 35.9 at a lift coefficient of 1.38, 10 degrees incidence at a Reynolds number of 666,000. Zig-zag tape at 2% and 5% of the chord was placed on the leading edge pressure and suction side of the Pareto B model in order to determine the aerodynamic performance characteristics at turbulent flow conditions. Experimental Pareto B wind tunnel data and previous FB-3500-0875 data is also presented and used to validate the ARC2D results obtained in this study. Additionally MBFLO, a detached eddy simulation Navier-Stokes code, was used to analyze the Pareto B airfoil for comparison and validation purposes.

2D URANS simulation of aerodynamic loads on a pitching airfoil: Impact of computational parameters

NARCIS (Netherlands)

Geng, F.; Kalkman, I.M.; Suiker, A.S.J.; Blocken, B.J.E.

2017-01-01

A numerical study of aerodynamic loads on pitching airfoils using Computational Fluid Dynamics (CFD) is challenging due complicated airfoil-vortex interactions and the possible occurrence of dynamic stall. In the latter case the combination of boundary layer transitions and airfoil oscillations

Effects of relative thickness on aerodynamic characteristics of airfoil at a low Reynolds number

Directory of Open Access Journals (Sweden)

Ma Dongli

2015-08-01

Full Text Available This study focuses on the characteristics of low Reynolds number flow around airfoil of high-altitude unmanned aerial vehicles (HAUAVs cruising at low speed. Numerical simulation on the flows around several representative airfoils is carried out to investigate the low Reynolds number flow. The water tunnel model tests further validate the accuracy and effectiveness of the numerical method. Then the effects of the relative thickness of airfoil on aerodynamic performance are explored, using the above numerical method, by simulating flows around airfoils of different relative thicknesses (12%, 14%, 16%, 18%, as well as different locations of the maximum relative thickness (x/c = 22%, 26%, 30%, 34%, at a low Reynolds number of 5 × 105. Results show that performance of airfoils at low Reynolds number is mainly affected by the laminar separation bubble. On the premise of good stall characteristics, the value of maximum relative thickness should be as small as possible, and the location of the maximum relative thickness ought to be closer to the trailing edge to obtain fine airfoil performance. The numerical method is feasible for the simulation of low Reynolds number flow. The study can help to provide a basis for the design of low Reynolds number airfoil.

Design and verification of the Risø-B1 airfoil family for wind turbines

DEFF Research Database (Denmark)

Fuglsang, P.; Bak, C.; Gaunaa, M.

2004-01-01

This paper presents the design and experimental verification of the Risø-B1 airfoil family for MW-size wind turbines with variable speed and pitch control. Seven airfoils were designed with thickness-to-chord ratios between 15% and 53% to cover the entire span of a wind turbine blade. The airfoils...

FIA's volume-to-biomass conversion method (CRM) generally underestimates biomass in comparison to published equations

Science.gov (United States)

David. C. Chojnacky

2012-01-01

An update of the Jenkins et al. (2003) biomass estimation equations for North American tree species resulted in 35 generalized equations developed from published equations. These 35 equations, which predict aboveground biomass of individual species grouped according to a taxa classification (based on genus or family and sometimes specific gravity), generally predicted...

Improvement of airfoil trailing edge bluntness noise model

DEFF Research Database (Denmark)

Zhu, Wei Jun; Shen, Wen Zhong; Sørensen, Jens Nørkær

2016-01-01

In this article, airfoil trailing edge bluntness noise is investigated using both computational aero-acoustic and semi-empirical approach. For engineering purposes, one of the most commonly used prediction tools for trailing edge noise are based on semi-empirical approaches, for example, the Brooks......, Pope, and Marcolini airfoil noise prediction model developed by Brooks, Pope, and Marcolini (NASA Reference Publication 1218, 1989). It was found in previous study that the Brooks, Pope, and Marcolini model tends to over-predict noise at high frequencies. Furthermore, it was observed...

Computational methods for investigation of surface curvature effects on airfoil boundary layer behavior

Directory of Open Access Journals (Sweden)

Xiang Shen

2017-03-01

Full Text Available This article presents computational algorithms for the design, analysis, and optimization of airfoil aerodynamic performance. The prescribed surface curvature distribution blade design (CIRCLE method is applied to a symmetrical airfoil NACA0012 and a non-symmetrical airfoil E387 to remove their surface curvature and slope-of-curvature discontinuities. Computational fluid dynamics analysis is used to investigate the effects of curvature distribution on aerodynamic performance of the original and modified airfoils. An inviscid–viscid interaction scheme is introduced to predict the positions of laminar separation bubbles. The results are compared with experimental data obtained from tests on the original airfoil geometry. The computed aerodynamic advantages of the modified airfoils are analyzed in different operating conditions. The leading edge singularity of NACA0012 is removed and it is shown that the surface curvature discontinuity affects aerodynamic performance near the stalling angle of attack. The discontinuous slope-of-curvature distribution of E387 results in a larger laminar separation bubble at lower angles of attack and lower Reynolds numbers. It also affects the inherent performance of the airfoil at higher Reynolds numbers. It is shown that at relatively high angles of attack, a continuous slope-of-curvature distribution reduces the skin friction by suppressing both laminar and turbulent separation, and by delaying laminar-turbulent transition. It is concluded that the surface curvature distribution has significant effects on the boundary layer behavior and consequently an improved curvature distribution will lead to higher aerodynamic efficiency.

Aerodynamics of S809 Airfoil at Low and Transitional Reynolds Numbers

Science.gov (United States)

Carreras, Jaime J.; Laal-Dehghani, Nader; Gorumlu, Serdar; Mehdi, Faraz; Castillo, Luciano; Aksak, Burak; Sheng, Jian

2013-11-01

The S809 is a thick airfoil extensively used in wind turbine design applications and model studies in wind tunnel. With increased interests in reducing energy production cost and understanding turbulence and turbine interactions, scaled down models (Re ~103) are often used as an alternative to full scale field experimentation (Re >106). This Reynolds number discrepancy raises the issue of scaling for the airfoil performance from laboratory studies to field scale applications. To the best of our knowledge, there are no studies existing in literature to characterize the lift- and drag-coefficients of S809 airfoil at Re less than 3 ×105 . This study is to fill the deficit in the current state of knowledge by performing high resolution force measurements. The lift and drag measurements are carried out in Texas Tech Wind Tunnel Facility using an in-house developed dual-cell force balance. The configuration eliminates the large torque and torsion often accompanied by conventional mounts. This unique design allows us to reach a measurement accuracy of 0.02N (0.1%). Comparative studies are performed on a two-dimensional airfoil with a smooth- as well as a well-engineered surface covered by micro-pillar array to simulate the surface conditions of a real life airfoil.

Generalized Einstein’s Equations from Wald Entropy

Directory of Open Access Journals (Sweden)

Maulik Parikh

2016-03-01

Full Text Available We derive the gravitational equations of motion of general theories of gravity from thermodynamics applied to a local Rindler horizon through any point in spacetime. Specifically, for a given theory of gravity, we substitute the corresponding Wald entropy into the Clausius relation. Our approach works for all diffeomorphism-invariant theories of gravity in which the Lagrangian is a polynomial in the Riemann tensor.

Flow visualization over a thick blunt trailing-edge airfoil with base cavity at low Reynolds numbers using PIV technique.

Science.gov (United States)

Taherian, Gholamhossein; Nili-Ahmadabadi, Mahdi; Karimi, Mohammad Hassan; Tavakoli, Mohammad Reza

2017-01-01

In this study, the effect of cutting the end of a thick airfoil and adding a cavity on its flow pattern is studied experimentally using PIV technique. First, by cutting 30% chord length of the Riso airfoil, a thick blunt trialing-edge airfoil is generated. The velocity field around the original airfoil and the new airfoil is measured by PIV technique and compared with each other. Then, adding two parallel plates to the end of the new airfoil forms the desired cavity. Continuous measurement of unsteady flow velocity over the Riso airfoil with thick blunt trailing edge and base cavity is the most important innovation of this research. The results show that cutting off the end of the airfoil decreases the wake region behind the airfoil, when separation occurs. Moreover, adding a cavity to the end of the thickened airfoil causes an increase in momentum and a further decrease in the wake behind the trailing edge that leads to a drag reduction in comparison with the thickened airfoil without cavity. Furthermore, using cavity decreases the Strouhal number and vortex shedding frequency.

Measurement of tonal-noise characteristics and periodic flow structure around NACA0018 airfoil

Energy Technology Data Exchange (ETDEWEB)

Nakano, T.; Fujisawa, N. [Niigata University, Department Mechanical Engineering, Niigata (Japan); Lee, S. [Inha University, Department Mechanical Engineering, Incheon (Korea)

2006-03-15

The characteristics of tonal noise and the variations of flow structure around NACA0018 airfoil in a uniform flow are studied by means of simultaneous measurement of noise and velocity field by particle-image velocimetry to understand the generation mechanism of tonal noise. Measurements are made on the noise characteristics, the phase-averaged velocity field with respect to the noise signal, and the cross-correlation contour of velocity fluctuations and noise signal. These experimental results indicate that the tonal noise is generated from the periodic vortex structure on the pressure surface of the airfoil near the trailing edge of the airfoil. It is found that the vortex structure is highly correlated with the noise signal, which indicates the presence of noise-source distribution on the pressure surface. The vorticity distribution on the pressure surface breaks down near the trailing edge of the airfoil and forms a staggered vortex street in the wake of the airfoil. (orig.)

General relativistic Boltzmann equation, II: Manifestly covariant treatment

NARCIS (Netherlands)

Debbasch, F.; van Leeuwen, W.A.

2009-01-01

In a preceding article we presented a general relativistic treatment of the derivation of the Boltzmann equation. The four-momenta occurring in this formalism were all on-shell four-momenta, verifying the mass-shell restriction p(2) = m(2)c(2). Due to this restriction, the resulting Boltzmann

Vortex scale of unsteady separation on a pitching airfoil.

Science.gov (United States)

Fuchiwaki, Masaki; Tanaka, Kazuhiro

2002-10-01

The streaklines of unsteady separation on two kinds of pitching airfoils, the NACA65-0910 and a blunt trailing edge airfoil, were studied by dye flow visualization and by the Schlieren method. The latter visualized the discrete vortices shed from the leading edge. The results of these visualization studies allow a comparison between the dynamic behavior of the streakline of unsteady separation and that of the discrete vortices shed from the leading edge. The influence of the airfoil configuration on the flow characteristics was also examined. Furthermore, the scale of a discrete vortex forming the recirculation region was investigated. The non-dimensional pitching rate was k = 0.377, the angle of attack alpha(m) = 16 degrees and the pitching amplitude was fixed to A = +/-6 degrees for Re = 4.0 x 10(3) in this experiment.

An empirically-based model for the lift coefficients of twisted airfoils with leading-edge tubercles

Science.gov (United States)

Ni, Zao; Su, Tsung-chow; Dhanak, Manhar

2018-04-01

Experimental data for untwisted airfoils are utilized to propose a model for predicting the lift coefficients of twisted airfoils with leading-edge tubercles. The effectiveness of the empirical model is verified through comparison with results of a corresponding computational fluid-dynamic (CFD) study. The CFD study is carried out for both twisted and untwisted airfoils with tubercles, the latter shown to compare well with available experimental data. Lift coefficients of twisted airfoils predicted from the proposed empirically-based model match well with the corresponding coefficients determined using the verified CFD study. Flow details obtained from the latter provide better insight into the underlying mechanism and behavior at stall of twisted airfoils with leading edge tubercles.

Computational Investigations on the Effects of Gurney Flap on Airfoil Aerodynamics.

Science.gov (United States)

Jain, Shubham; Sitaram, Nekkanti; Krishnaswamy, Sriram

2015-01-01

The present study comprises steady state, two-dimensional computational investigations performed on NACA 0012 airfoil to analyze the effect of Gurney flap (GF) on airfoil aerodynamics using k-ε RNG turbulence model of FLUENT. Airfoil with GF is analyzed for six different heights from 0.5% to 4% of the chord length, seven positions from 0% to 20% of the chord length from the trailing edge, and seven mounting angles from 30° to 120° with the chord. Computed values of lift and drag coefficients with angle of attack are compared with experimental values and good agreement is found at low angles of attack. In addition static pressure distribution on the airfoil surface and pathlines and turbulence intensities near the trailing edge are present. From the computational investigation, it is recommended that Gurney flaps with a height of 1.5% chord be installed perpendicular to chord and as close to the trailing edge as possible to obtain maximum lift enhancement with minimum drag penalty.

Simulation of flow over double-element airfoil and wind tunnel test for use in vertical axis wind turbine

International Nuclear Information System (INIS)

Chougule, Prasad; Nielsen, Søren R K

2014-01-01

Nowadays, small vertical axis wind turbines are receiving more attention due to their suitability in micro-electricity generation. There are few vertical axis wind turbine designs with good power curve. However, the efficiency of power extraction has not been improved. Therefore, an attempt has been made to utilize high lift technology for vertical axis wind turbines in order to improve power efficiency. High lift is obtained by double-element airfoil mainly used in aeroplane wing design. In this current work a low Reynolds number airfoil is selected to design a double-element airfoil blade for use in vertical axis wind turbine to improve the power efficiency. Double-element airfoil blade design consists of a main airfoil and a slat airfoil. Orientation of slat airfoil is a parameter of investigation in this paper and air flow simulation over double-element airfoil. With primary wind tunnel test an orientation parameter for the slat airfoil is initially obtained. Further a computational fluid dynamics (CFD) has been used to obtain the aerodynamic characteristics of double-element airfoil. The CFD simulations were carried out using ANSYS CFX software. It is observed that there is an increase in the lift coefficient by 26% for single-element airfoil at analysed conditions. The CFD simulation results were validated with wind tunnel tests. It is also observe that by selecting proper airfoil configuration and blade sizes an increase in lift coefficient can further be achieved

Exact solitary and periodic wave solutions for a generalized nonlinear Schroedinger equation

International Nuclear Information System (INIS)

Sun Chengfeng; Gao Hongjun

2009-01-01

The generalized nonlinear Schroedinger equation (GNLS) iu t + u xx + β | u | 2 u + γ | u | 4 u + iα (| u | 2 u) x + iτ(| u | 2 ) x u = 0 is studied. Using the bifurcation of travelling waves of this equation, some exact solitary wave solutions were obtained in [Wang W, Sun J,Chen G, Bifurcation, Exact solutions and nonsmooth behavior of solitary waves in the generalized nonlinear Schroedinger equation. Int J Bifucat Chaos 2005:3295-305.]. In this paper, more explicit exact solitary wave solutions and some new smooth periodic wave solutions are obtained.

Dynamic Stall Vortex Formation of OA-209 Airfoil at Low Reynolds Number

OpenAIRE

Aung Myo Thu; Sang Eon Jeon; Yung Hwan Byun; Soo Hyung Park

2014-01-01

The unsteady flow field around oscillating OA-209 airfoil at a Reynolds number of 3.5×105 were investigated. Three different reduced frequencies were tested in order to see how it affects the hysteresis loop of an airfoil. At a reduced frequency of 0.05 the deep dynamic stall phenomenon was observed. Lift overshooting was observed as a result of dynamic stall vortex (DSV) shedding. Further investigation was carried out to find out the cause of DSV formation and shedding over airfoil. Particle...

Design and Experimental Validation of Thick Airfoils for Large Wind Turbines

DEFF Research Database (Denmark)

Hrgovan, Iva; Shen, Wen Zhong; Zhu, Wei Jun

2015-01-01