General Airfoil Research Articles

Effect of number of blades in ducted turbine system on kinetic energy extraction from chimney flue gases – benchmarking with wind energy system

A multi-blade ducted wind turbine, also called the diffuser augmented wind turbine (DAWT) has a good wind energy conversion effect over the traditional wind turbine. The market potential for energy recovery from the chimney flue gases made it necessary to explore the possibility of extraction of the energy from flue gases using the DAWT. The duct is a converging-diverging nozzle with the turbineblades located at the throat. In general 3 or more number of blades is frequently used to maximize the energy conversion to the bladetorque. The effect of number of blades on the power extraction by the energy recovery ducted turbine has been studied in this paper. A CFD-based simulation study has been carried out. The results so obtained have been benchmarked with the published data for the results for the ducted turbines for wind power generation. The general airfoil NACA4420, NACA4416 and NACA4412 were adopted to produce various composite profiles for turbine-blade. The large number of blades appears to provide the sufficient blade areas for the conversion of energy of flue gases to the turbine-rotor torque. On other hand the more number of blades also increases the blockage to the flue gases, resulting in increased back-flow. This paper presents the variation of power coefficient (CP) and torque coefficient (CT) with respect to the tip speed ratio (λ) for different number of blades, and varying blade geometry.

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

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 proposed methodology, the aeroacoustic transfer function of a generic airfoil profile is computed by the boundary element method. The effects of the airfoil leading-edge thickness on the inflow turbulence are accounted for by a turbulence spectrum based on the rapid distortion theory. This research shows that the turbulence distortion plays a significant role on the predicted noise levels. Compared with the von Kármán model for isotropic turbulence, the rapid distortion theory predicts reduced noise levels at high frequencies and increased noise levels at low frequencies. This paper also shows that the spanwise-varying inflow, here represented by a linearly changing condition, contributes to raising the noise levels when compared to the similar uniform inflow case. This research confirms that the finite airfoil thickness decreases the airfoil-gust lift response, consequently reducing the noise levels. This observation is more pronounced for microphones positioned downstream of the airfoil and for high frequencies.

Vortex force map method for viscous flows of general airfoils

In a previous paper, an inviscid vortex force map approach was developed for the normal force of a flat plate at arbitrarily high angle of attack and leading/trailing edge force-producing critical regions were identified. In this paper, this vortex force map approach is extended to viscous flows and general airfoils, for both lift and drag forces due to vortices. The vortex force factors for the vortex force map are obtained here by using Howe’s integral force formula. A decomposed form of the force formula, ensuring vortices far away from the body have negligible effect on the force, is also derived. Using Joukowsky and NACA0012 airfoils for illustration, it is found that the vortex force map for general airfoils is similar to that of a flat plate, meaning that force-producing critical regions similar to those of a flat plate also exist for more general airfoils and for viscous flow. The vortex force approach is validated against NACA0012 at several angles of attack and Reynolds numbers, by using computational fluid dynamics.

Reduced-Order Techniques for Sensitivity Analysis and Design Optimization of Aerospace Systems

This work proposes a new method for using reduced-order models in lieu of high-fidelity analysis during the sensitivity analysis step. Reduced-order models are developed using a combination of proper orthogonal decomposition and radial basis functions. Interpolation using reduced-order models based on proper orthogonal decomposition is compared against normal optimization on a general airfoil shape optimization problem. The interpolation procedure does not require additional high-fidelity evaluations to construct new reduced-order models. The errors associated with the reduced-order models themselves as well as the gradients calculated from them are compared. The effects of each approach on the overall optimization paths, times, and function counts are also examined.

Lock-in of elastically mounted airfoils at a 90° angle of attack

Reducing vortex-induced vibration (VIV) of elastically mounted cylinders has applications to petroleum, nuclear, and civil engineering. One simple method is streamlining the cylinder into an airfoil shape. However, if flow direction changes, an elastic airfoil could experience similar oscillations with even more drag. To better understand a general airfoil's response, three elastically mounted airfoil shapes are tested at a 90° angle of attack in a 3ft by 4ft wind tunnel. The shapes are a NACA 0018, a sharp leading- and trailing-edge (sharp–sharp) model, and a round leading- and trailing-edge (round–round) model. Mass-damping ranges from 0.96 to 1.44. For comparison to canonical VIV research, a cylinder is also tested. Since lock-in occurs near Rec=125×103, the models are also tested with a trip strip. The NACA 0018 and sharp–sharp configuration show nearly identical responses. The cylinder and round–round airfoil have responses five to eight times larger. Thus, the existence of a single sharp edge is sufficient to greatly reduce VIV at 90° angle of attack. Whereas the cylinder and round–round maximum response amplitudes are similar, cylinder lock-in occurs over a velocity range three times larger than the round–round. The tripped cylinder and round–round models' response is attenuated by 70% compared to their respective clean configurations. Hysteresis is only observed in the circular cylinder and round–round models. Hotwire data indicates the clean cylinder has a unique vortex pattern compared to the other configurations.

Aerodynamic Optimization of Airfoils Using Adaptive Parameterization and Genetic Algorithm

A new method for airfoil shape parameterization is presented, and its influences on the optimum design and convergence of the evolutionary optimization process are investigated. An online adaptive method is used that alters the airfoil parametric function during the process of optimization. A geometric inverse design is carried out, and the capability of the method for producing general airfoil shapes is assessed. The performance of the method is then evaluated by aerodynamic shape optimization. The result indicates that the proposed method improves the optimum design airfoil significantly. In addition, it reduces the total number of flow solver calls, which consequently reduces the required computational time.

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

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.

Influence of Optimization Algorithm on Airfoil Shape Optimization of Aircraft Wings

Computational fluid dynamics (CFD) is one of the computer-based solution methods which are more widely employed in aerospace engineering. The computational power and time required to carry out the analysis increases as the fidelity of the analysis increases. Aerodynamic shape optimization has become a vital part of aircraft design in the recent years. The Method of search algorithms or 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), Particle Swarm Optimization (PSO) etc., are more widely employed to solve the aerodynamic shape optimization problems. In addition to the optimization method, the geometry parameterisation becomes an important factor to be considered during the aerodynamic shape optimization process. 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, Hicks- Henne Bump function, PARSEC etc. 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 Particle Swarm optimization Algorithm which is one kind of Non-Traditional Optimization technique to optimize the aerodynamic characteristics of a general airfoil for specific conditions. An aerodynamic shape optimization problem is formulated for NACA 2411 airfoil and solved using the method of Particle Swarm Optimization for 5.0 deg angle of attack. A MATLAB program has been developed to implement PARSEC, Panel Technique, and PSO 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 has been calculated using panel method. NACA 2411 airfoil has been generated using PARSEC and optimized for 5.0 deg angle of attack using PSO Algorithm. The results show that the particle swarm optimization scheme is more effective in finding the optimum solution among the various possible solutions.

Influence of Search Algorithms on Aerodynamic Design Optimisation of Aircraft Wings

The Method of search algorithms or optimisation algorithms is one of the most important parameters which will strongly influence the fidelity of the solution during an aerodynamic shape optimisation problem. Nowadays various optimisation methods such as Genetic Algorithm (GA), Simulated Annealing (SA), Particle Swarm Optimisation (PSO) etc., are more widely employed to solve the aerodynamic shape optimisation problems. In addition to the optimisation method, the geometry parameterisation becomes an important factor to be considered during the aerodynamic shape optimisation process. Since the reduction in the number of design parameters is one of the most important requirements for the aerodynamic shape optimisation problem, it becomes important to mathematically describe the airfoil geometry with minimum number of design parameters. 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 optimisation algorithms. It is also demonstrated that the estimation of a suitable optimisation scheme for a given optimisation problem. An aerodynamic shape optimisation problem is formulated for NACA 0012 airfoil and solved using the methods of Particle Swarm Optimisation and Genetic Algorithm for 5.0 deg angle of attack. The results show that the particle swarm optimisation scheme is more effective in finding the optimum solution among the various possible solutions. It is also found that the PSO shows more exploitation characteristics as compared to the GA which is considered to be more effective explorer.

Application of Nontraditional Optimization Techniques for Airfoil Shape Optimization

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.

Optimized Nonuniform Rational B-Spline Geometrical Representation for Aerodynamic Design of Wings

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

On the construction and calculation of optimal nonlifting critical airfoils

Numerical calculations are carried out in the hodograph plane to construct optimal critical airfoil shapes and the flow about them. These optimal airfoil shapes give the highest free-stream Mach numberM ∞ for a given thickness ratio δ and tail angle θ t (nonlifting) for which the flow is nowhere supersonic. A relationship betweenM ∞ and δ for various θ t is given. Analytical and numerical solutions to the same problem are found on the basis of transonic small-disturbance theory. These results provide a limiting case asM ∞ →1, δ → 0 and agree well with the calculations of the full problem. Using a numerical method to calculate the flow about general (subsonic) airfoils, a comparison is made between the critical free-stream Mach numbers for some standard airfoil shapes and the optimal free stream Mach number of the corresponding δ and θ t . A significant increase in the critical free-stream Mach number is found for the optimal airfoils.

Transonic flow around the leading edge of a thin airfoil with a parabolic nose

Transonic potential flow around the leading edge of a thin two-dimensional general airfoil with a parabolic nose is analysed. Asymptotic expansions of the velocity potential function are constructed at a fixed transonic similarity parameter (K) in terms of the thickness ratio of the airfoil in an outer region around the airfoil and in an inner region near the nose. These expansions are matched asymptotically. The outer expansion consists of the transonic small-disturbance theory and it second-order problem, where the leading-edge singularity appears. The inner expansion accounts for the flow around the nose, where a stagnation point exists. Analytical expressions are given for the first terms of the inner and outer asymptotic expansions. A boundary value problem is formulated in the inner region for the solution of a uniform sonic flow about an infinite two-dimensional parabola at zero angle of attack, with a symmetric far-field approximation, and with no circulation around it. The numerical solution of the flow in the inner region results in the symmetric pressure distribution on the parabolic nose. Using the outer small-disturbance solution and the nose solution a uniformly valid pressure distribution on the entire airfoil surface can be derived. In the leading terms, the flow around the nose is symmetric and the stagnation point is located at the leading edge for every transonic Mach number of the oncoming flow and shape and small angle of attack of the airfoil. The pressure distribution on the upper and lower surfaces of the airfoil is symmetric near the edge point, and asymmetric deviations increase and become significant only when the distance from the leading edge of the airfoil increases beyond the inner region. Good agreement is found in the leading-edge region between the present solution and numerical solutions of the full potential-flow equations and the Euler equations.

Conformal grid generation for multielement airfoils

Abstract : This paper describes recently-developed conformal mapping techniques applicable to cases involving general multielement airfoils having any number of airfoil elements. Each technique can be considered as a purely geometric construction or, equivalently, as a network a streamlines and potential-lines of an auxiliary potential-flow solution. The nonuniqueness of such solutions ensures the existence of a wide variety of conformal grid types, each having different point-spacing characteristics. A chronicle is given of the search for the type of grid most suitable for solving the inviscid compressible flow equations using a distributed-source field-panel approach. Examples are shown for grids involving up to four airfoil elements.

7 - Risk Associations in the Thrombotic Disorders

Reducing vortex-induced vibration (VIV) of elastically mounted cylinders has applications to petroleum, nuclear, and civil engineering. One simple method is streamlining the cylinder into an airfoil shape. However, if flow direction changes, an elastic airfoil could experience similar oscillations with even more drag. To better understand a general airfoil's response, three elastically mounted airfoil shapes are tested at a 90° angle of attack in a 3 ft by 4 ft wind tunnel. The shapes are a NACA 0018, a sharp leading- and trailing-edge (sharp–sharp) model, and a round leading- and trailing-edge (round–round) model. Mass-damping ranges from 0.96 to 1.44. For comparison to canonical VIV research, a cylinder is also tested. Since lock-in occurs near Rec=125×103, the models are also tested with a trip strip. The NACA 0018 and sharp–sharp configuration show nearly identical responses. The cylinder and round–round airfoil have responses five to eight times larger. Thus, the existence of a single sharp edge is sufficient to greatly reduce VIV at 90° angle of attack. Whereas the cylinder and round–round maximum response amplitudes are similar, cylinder lock-in occurs over a velocity range three times larger than the round–round. The tripped cylinder and round–round models' response is attenuated by 70% compared to their respective clean configurations. Hysteresis is only observed in the circular cylinder and round–round models. Hotwire data indicates the clean cylinder has a unique vortex pattern compared to the other configurations.

A Digital-Analog Machine Tool Control System

The research objectives of the Lewis Flight Propulsion Laboratory of the National Advisory Committee for Aeronautics include fundamental investigations of aircraft flight propulsion systems. A portion of the research deals with the experimental investigation of the optimum design parameters of the blades of compressor and turbine rotors. In the conduct of this program a series of rotors must be constructed on which the blade shapes have been systematically varied. Problems involved in the fabrication of these experimental blades are similar to those encountered in the fabrication of three dimensional cams. The blades (figure 1) have a general airfoil cross section and in many cases present a high degree of longitudinal twist and taper. Usual production techniques for their manufacture cannot be used at the Lewis laboratory because there are relatively few blades of a given design. The required expenditure of time and personnel to fabricate a single set of experimental blades was such that a program was undertaken to study the problem of automatizing a machine tool in such a manner that complete blades might be automatically fabricated directly from their original mathematical descriptions.