International Journal of Computer Science and Intelligent Computing

DESIGN AND ANALYSIS OF ROTATING AEROFOIL BY USING MAGNUS EFFECT

A.Animhons1, Prof.A.Sankaran2, N.Maheswaran3 and S.Tamilselvan4 1,2,3,4 Department of Aeronautical Engineering, Hindusthan Institute of Technology, Coimbatore Abstract-In an aircraft there so many advanced techniques in the development of high speed airfoil. The lift of the main wing depends upon an aircraft with depends on selection of airfoil. In our project we introduce a simple rotating airfoil which creates a positive lift. However the study of a rotating airfoil to generate more lift, under a “kutta –joukowski” and “Magnus effect”. The main concept of Magnus effect could be applied only over symmetrical bodies like spinning ball or cylinder or disk. We analyzed that this effect can also be applied to symmetrical airfoil. This study will explain the condition and the design of such a wing using the rotating airfoil concept that will have high performance and high cruise speed. In our thesis we introduce rotating airfoil at leading edge instead of a rigid body airfoil. We carried out the rotating airfoil concept using the software Ansys CFD. From the analysis the concept of rotating airfoil gives an additional increment of lift than the rigid body airfoil. Keywords-Rotating Aerofoil, Magnus Effect, kutta-joukowski, Symmetrical Aerofoil, Ansys CFD

I. INTRODUCTION

A fixed-wing aircraft's wings, horizontal, and vertical stabilizers are built with airfoil-shaped cross sections, as are helicopter rotor blades. Airfoils are also found in propellers, fans, compressors and turbines. Sails are also airfoils, and the underwater surfaces of sailboats, such as the centerboard and keel, are similar in cross-section and operate on the same principles as airfoils. Swimming and flying creatures and even many plants and sessile organisms employ airfoils/hydrofoils: common examples being bird wings, the bodies of fish, and the shape of sand dollars. An airfoil-shaped wing can create down force on an automobile or other motor vehicle, improving traction. Any object with an angle of attack in a moving fluid, such as a flat plate, a building, or the deck of a bridge, will generate an aerodynamic force (called lift) perpendicular to the flow. Airfoils are more efficient lifting shapes, able to generate more lift (up to a point), and to generate lift with less drag. The Magnus effect is the force exerted on a rapidly spinning cylinder or sphere moving through air or another fluid in a direction at an angle to the axis of spin. This force is responsible for the swerving of balls when hit or thrown with spin. The kutta-joukowski theorem is a fundamental theorem of aerodynamics that can be used for the calculation of the lift of an airfoil, or of any two-dimensional bodies including circular cylinders, translating in a uniform fluid at constant speed large enough so that the flown seen in the body-fixed frame is steady and unseparated. The theorem relates the lift generated by an airfoil to the speed of the airfoil through the fluid, the density of the fluid, and the circulation. The circulation is defined as the line integral around a closed loop enclosing the airfoil, of the component of the velocity of the fluid tangent to the loop. Kutta-joukowski. It is named after the German Martin Wilhelm Kutta and the Russian Nikolai Zhukovsky Who first developed its key ideas in the early 20th century. Kutta-Joukowski theorem is an in viscid theory which for pressure and the lift is however a good approximation to real viscous flow for typical aerodynamic applications. Kutta-Joukowski theorem relates lift to circulation much like the Magnus effect relates side force (called Magnus effect) to rotation. However, circulation here is not induced by rotation of the airfoil but by some intrinsic mechanism described below. Due to the circulation, the flow of air in response to the presence of the airfoil can be treated as the superposition of a translational flow and a

DOI:10.21884/IJMTER.2017.4202.XQV6W 203 International Journal of Modern Trends in Engineering and Research (IJMTER) Volume 04, Issue 6, [June– 2017] ISSN (Online):2349–9745; ISSN (Print):2393-8161 rotating flow.This rotating flow is induced by joint effect of camber, angle of attack and sharp trailing edge of the airfoil and should not be confused with a vortex like a tornado encircling the cylinder or the wing of an airplane in flight. Seen from a distance large enough to the airfoil, this rotating flow may be regarded as induced by a line vortex (with the rotating line perpendicular to the two dimensional plane). In the derivation of the Kutta-Joukowski theorem the airfoil is usually mapped into a circular cylinder and Joukowski airfoil, but it holds true for general airfoils.

II. MOTIVATION

In an aircraft these are so many advance techniques in the development of high speed airfoil. The airfoil shape of a wing has always been design to generate lift. But few realized that a simple rotating cylinder (or) airfoil can also create a lift. These are variety of airfoils are used in aircraft wing. According to Magnus effect, this effect could be applied only over symmetrical bodies like spinning ball (or) cylinder (or) disk, which produces a lift so we are choosing a symmetric airfoil to generate a lift .Under the kutta-joukowski and Magnus effect the study of a rotating airfoil to generate more lift. Generally all the aircraft procedure lift, if we use a symmetric airfoil it will produce an additional lift to the aircraft.

III. CONFIGURATION STUDIED

Configuration of Aerofoil

IV. GRID GENERATION

Edge Sizing Grid Generation

@IJMTER-2017, All rights Reserved 204 International Journal of Modern Trends in Engineering and Research (IJMTER) Volume 04, Issue 6, [June– 2017] ISSN (Online):2349–9745; ISSN (Print):2393-8161 A grid is a small-sized geometrical shape that covers the physical domain, whose objective is to identify the discrete volumes or elements where conservation laws can be applied. Grid generation is the first process involved in computing numerical solutions to the equations that describe a physical process. The result of the solution depends upon the quality of grid. A well-constructed grid can improve the quality of solution whereas, deviations from the numerical solution can be observed with poorly constructed grid. The grid generation by algebraic methods is done by using known functions in one, two or three dimensions taking arbitrary shaped regions. The computational domain might not be rectangular one, but for the sake of simplicity, the domain is taken to be rectangular. The simplest procedure that may be used to produce boundary fitted computational mesh is the normalization transformation. Variation method includes a technique that minimizes grid smoothness, orthogonally and volume variation. This method forms mathematical platform to solve grid generation problems. In this method an alternative grid is generated by a new mesh after each iteration and computing the grid speed using backward difference method. This technique is a powerful one with a disadvantage that effort is required to solve the equations related to grid. Further work needed to be done to minimize the integrals that will reduce the CPU time. We must identify what information is required to identify the cell and all the neighbors of the cell in the computational mesh. We can choose to locate the arbitrary points anywhere we want for the unstructured grid. A point insertion scheme is used to insert the points independently and the cell connectivity is determined. This suggests that the point be identified as they are inserted. Logic for establishing new connectivity is determined once the points are inserted. Data that form grid point that identifies grid cell are needed. As each cell is formed it is numbered and the points are sorted. In addition the neighbor cell information is needed. A problem in solving partial differential equations using previous methods is that the grid is constructed and the points are distributed in the physical domain before details of the solution is known. So the grid may or may not be the best for the given problem. Adaptive methods are used to improve the accuracy of the solutions. The adaptive method is referred to as „h‟ method if mesh refinement is used, „r‟ method if the number of grid point is fixed and not redistributed and „p‟ if the order of solution scheme is increased in finite-element theory. The multi- dimensional problems using the equi-distribution scheme can be accomplished in several ways. The simplest to understand are the Poisson Grid Generators with control function based on the equi- distribution of the weight function with the diffusion set as a multiple of desired cell volume. The equi-distribution scheme can also be applied to the unstructured problem. The problem is the connectivity hampers if mesh point movement is very large. Steady flow and the time-accurate flow calculation can be solved through this adaptive method. The grid is refined and after a predetermined number of iteration in order to adapt it in a steady flow problem. The grid will stop adjusting to the changes once the solution converges. In time accurate case coupling of the Partial Differential Equations of the physical problem and those describing the grid movement is required.

V. BOUNDARY CONDITIONS

In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional constraints, called the boundary conditions. A solution to a boundary value problem is a solution to the differential equation which also satisfies the boundary conditions. Boundary value problems arise in several branches of physics as any physical differential equation will have them. Problems involving the wave equation, such as the determination of normal modes, are often stated as boundary value problems. A large class of important boundary value problems is the Sturm–Lowville problems. The analysis of these problems involves the Eigen functions of a operator. To be useful in applications, a boundary value problem should be well posed. This means that given the input to the problem there exist a unique solution, which depends continuously on the input. Much theoretical work in the field of partial differential equations is devoted to proving that boundary value problems arising from scientific and engineering applications are in fact well-posed. A boundary condition which specifies the value of the function itself is a Dirichlet boundary condition, or first-type boundary condition. For example, if one end of

@IJMTER-2017, All rights Reserved 205 International Journal of Modern Trends in Engineering and Research (IJMTER) Volume 04, Issue 6, [June– 2017] ISSN (Online):2349–9745; ISSN (Print):2393-8161 an iron rod is held at absolute zero, then the value of the problem would be known at that point in space. A boundary condition which specifies the value of the normal derivative of the function is a Neumann boundary condition, or second-type boundary condition. For example, if there is a heater at one end of an iron rod, then energy would be added at a constant rate but the actual temperature would not be known. If the boundary has the form of a curve or surface that gives a value to the normal derivative and the variable itself then it is a Cauchy boundary condition. Among the earliest boundary value problems to be studied is the Dirichlet problem, of finding the harmonic functions (solutions to Laplace's equation); the solution was given by the principle. Aside from the boundary condition, boundary value problems are also classified according to the type of differential operator involved. For an elliptic operator, one discusses elliptic boundary value problems. For a hyperbolic operator, one discusses hyperbolic boundary value problems. These categories are further subdivided into linear and various nonlinear types.

VI. CFD SIMULATION

Pressure contour of stationary airfoil Velocity contour of stationary airfoil

Pressure contour of rotating airfoil Pressure contour of rotating airfoil

Velocity contour of rotating airfoil Velocity contour of rotating airfoil

VII. CONCLUSION

• By comparing the results of stationary airfoil and rotating aero foil with various angles of attack found that the lift generated by the rotating aerofoil is more than the stationary airfoil. • By comparing the results of stationary airfoil and rotating aero foil with various angles of attack found that the drag generated by the rotating aerofoil is less than the stationary airfoil.

REFERENCES

[1] Seifert, J(2012); A review of the Magnus effect in aeronautics. Progress in Aerospace Sciences; vol 55: pp. 17–45. [2] Glauert, M.B,(1957);A boundary layer theorem with applications to rotating cylinders. J. Fluid Mech.; vol 2: pp. 89. [3] Mittal, S., Kumar, B., (2003): Flow past a rotating cylinder. Journal of Fluid Mechanics; vol 476: pp. 303-334. [4] Tokumaru, P., Dimotakis, P., (1991); Rotary oscillation control of a cylinder wake. J. Fluid mech; vol 224: pp77-90. [5] McKinney, W. and De Laurier, J., “The Wingmill: (1981) An Oscillating-Wing Windmill,” Journal of Energy, Vol. 5, No. 2, pp. 109-115. [6] Jones, K. D. and Platzer, M. F., (1997) “Numerical Computation of Flapping-Wing Propulsion and Power Extraction,” AIAA Paper No. 97 [7] Anderson, J. D., (1991) Fundamentals of Aerodynamics, 2nd edition, McGraw-Hill, Inc. New York, pp. 16-17.