DOCSLIB.ORG

Explicit Kutta Condition Correction for Rotary Wing Flows A. D'alascio, A

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Explicit Kutta Condition Correction for Rotary Wing Flows A. D'alascio, A Transactions on Modelling and Simulation vol 18, © 1997 WIT Press, www.witpress.com, ISSN 1743-355X Explicit Kutta Condition Correction for Rotary Wing Flows A. D'Alascio, A. Visingardi, and P. Renzoni CIRA, Centra Italiano Ricerche Aerospaziali EMail: [email protected], [email protected], p.renzoni@cira. it Abstract An explicit correction to the Kutta condition applied to rotary wing potential flows is described. Indeed, the simple application of the classical steady Kutta condition, which ensures the uniqueness of the solution of the potential flow problems [1,2], is unable to guarantee a zero pressure jump at the blade trailing edge. Several investigations performed on this problem have indicated the presence of considerable non-zero pressure jumps for highly 3D flows (blade root and tip) [3] and for unsteady flows characterized by high reduced frequencies [4]. The application of a Kutta condition correction in CIRA's BEM code RAMSYS [3] has shown the ability to ensure a continuous pressure across the blade trailing edge. 1 Introduction The flow field around helicopter rotors is unsteady and highly three-dimensio- nal. A low frequency unsteadiness is induced in the flow by the relative motion between rotating and non-rotating components of the helicopter. The interaction between each main rotor blade with the wake of preceding blades is responsible for mid frequency unsteadiness whereas high frequency unsteadiness is generated by blade/tip vortex encounters. The rotor blades during their motion are subject to cross flows which make the flow field three-dimensional, expecially in the vicinity of the ro- Transactions on Modelling and Simulation vol 18, © 1997 WIT Press, www.witpress.com, ISSN 1743-355X 780 Boundary Elements tor blade root and tip. In addition, considering the role of the fuselage, its displacement effect distorts the onset flow further increasing the three- dimensionality of the flow field in the rotor disk. The rotor wake is deformed due to the presence of the fuselage which in turn alters the interaction pro- cess between rotor blades and their wake. In the numerical simulation of such complex flow fields the simple ap- plication of the classical steady Kutta condition has turned out to be unable to guarantee a zero pressure jump at the blade trailing edge. This pressure jump has shown to influence the whole pressure distribution on the blade, thus considerably altering the prediction of the aerodynamic loads. An explicit unsteady Kutta correction has been introduced in the CIRA computer code RAMSYS [3], based on Morino's boundary integral formulation, for the unsteady, incompressible aerodynamics of multi-body configurations in arbitrary rigid motion. The aim of this paper is to il- lustrate an algorithm of an unsteady Kutta correction by providing the necessary details about the structure of the algorithm itself, and to present some results relative to the application of this correction to the aerodynamic analysis of an oscillating airfoil and a helicopter rotor. 2 BEM formulation The formulation consists in the solution of Laplace's equation written in terms of the velocity potential <f> V^ = 0 Vx^^(f) (1) such that v = V<£. S(t) is a surface outside of which the flow is potential and consists of a surface SB surrounding the body geometry and a surface Sw surrounding the wake geometry. The boundary condition at infinity is that <j> — 0. The surface of the body is assumed to be impermeable hence |^ = v# • n where MB is the ve- locity of a point on the body. The wake is a surface of discontinuity which is not penetrated by the fluid and across which there is no pressure jump. The second wake condition implies that A0 remains constant following a wake point x*y, and equal to the value it had when XVK left the trailing edge. The value of A</> at the trailing edge is obtained by using the Kutta- Joukowski hypothesis that no vortex filament exists at the trailing edge; this implies that, at the trailing edge, the value of A</> on the wake and the value of A</> on the body are equal. Transactions on Modelling and Simulation vol 18, © 1997 WIT Press, www.witpress.com, ISSN 1743-355X Boundary Elements 781 The application of Green's function method to Eq.(l), yields the fol- lowing boundary-integral-representation for the velocity potential cf> E(x*)<Xx*,L) = /B + /w (2) with and representing respectively the contribution of the body and the wake. E(x*) is a domain function defined as zero inside S and unity elsewhere. The helicopter geometry and the wake are respectively discretised by M and N hyperboloidal quadrilateral panels on which the unknown velocity potential, the normal wash and the velocity potential jump are constant (zeroth-order formulation). Using the collocation method and setting the collocation points at the centroids of each element on the body geometry, the integral equation, Eq.(2), is replaced by an algebraic linear system of equations for the velocity potential </>: M M N Ek<t>k(t) = £ BfenVm(t) + £ Ckm4>m(t] + ]T F^A^(<) (3) 771=1 m = l n=l where 0, C, and F are respectively the body source, body doublet, and wake doublet influence coefficients. The system of linear Eqs.(3) can be written in matrix form as: A • </> = B - <0 + F - A0 (4) being Akm = EkSkm — Ckm with 8km representing the Kronecker function. A Conjugate Gradient Method (GMRES solver) is applied for the nu- merical solution of the problem. Once obtained the velocity potential <^(Z), the pressure coefficient Cpk(t) is computed, for each body panel k G [1,M], by applying the un- steady Bernoulli equation: = _-- + V* • V^ + v& • Vfa (5) *>e/ \ Ut * ) where V^e/ is the reference velocity and V& is the entrainment velocity of the panel k. Transactions on Modelling and Simulation vol 18, © 1997 WIT Press, www.witpress.com, ISSN 1743-355X 782 Boundary Elements 3 The unsteady Kutta condition problem The Kutta-Joukowski hypothesis that no vortex filament exists at the trail- ing edge is no longer sufficient for unsteady and/or highly three-dimensional fluid flows. Indeed the numerical validation of the RAMSYS code has shown that pressure jumps might occur at the blade trailing edge expecially for cases of helicopter rotors in forward flight and for highly unsteady flows on oscillating wings. Taking the idea of Kinnas and Hsin [5] an iterative procedure has been developed with which for each trailing-edge wake panel the pressure jump, computed by applying Bernoulli's equation for unsteady flows Eq.(6), has been explicitly set equal to zero, in order to impose a continuous pressure across the trailing edge. By denoting with A^_/ the difference between the values computed on the upper and lower body panels at the T.E. it is obtained: r^ 1 i = 0 (6) Indicating by NTE the number of trailing edge wake panels, NTE lin- earised equations are coupled, through the velocity potentials at the blade trailing edges, to the M Eqs.(3) of the algebraic system. A linearised ex- pression of the Eq. (6) is: . • V(<J . «_ at \ /t«, [ ot 2 (7) where 6 A<^ — A<$^~ — A<^, being A<^ = <&^— <&„ and j the preceding- iteration index; 2%, £ [1, A^^] is the wake T.E. panel index, and i^u and IM its neighbouring body panels on the T.E. upper and lower sides, Fig. 1. Figure 1: Discretisation stencil The time derivatives are evaluated with second-order accuracy. The right hand side of Eq.(7) is discretised, consistently with the expression of the pressure coefficient of Eq.(5), using a spline function chordwise and a Transactions on Modelling and Simulation vol 18, © 1997 WIT Press, www.witpress.com, ISSN 1743-355X Boundary Elements 783 central second-order discretisation function spanwise. The left hand side can be discretised using several schemes without changing the result of the iterative procedure, being the Bernoulli's equation written in terms of vari- ations of the velocity potential jump at the T.E.. Therefore the stencil influences the rate of convergence of the algorithm. In the RAMSYS code the term (V-f V<^'),^ is computed as the average of correspondent values on the upper and lower T.E. body panels, Fig. 1. A good rate of convergence has been obtained by imposing: (v + v^ = \ (v,,_ + v<. + v,,, + v<) where both V<^ and V</>^ are computed using the three neighbouring velocity potentials respectively in the panel centroids i^ and z&/, as shown in Fig. 1. Eq.(7) in the discretised form is written as: being cj = c^ w representing the over-relaxation factor set equal to 1.5. In matrix form: T' - 6 A^ = q^ (8) By coupling Eqs.(4) and (8), a new set of equations is obtained which is solved for a certain number of iterations. Convergence is reached when the maximum value of the trailing edge pressure coefficient jump is of the order of 10~^. In the RAMSYS code a number of iterations not greater than 5 are necessary to reach convergence. 4 Numerical validation The test cases performed are relative to an oscillating NACA 0012 airfoil and an isolated rotor in forward flight. In the first test case the pressure jump at the T.E. of the airfoil is due to the unsteadiness of the motion, while in the second case it is essentially due to the three-dimensional flow generated on the rotor blades. A comparison of the pressure coefficient distributions and the lift forces acting on both the airfoil and the rotor are computed by RAMSYS with and without the Kutta condition correction. 4.1 Oscillating airfoil This test case deals with a NACA 0012 airfoil, discretised by 60 panels, os- cillating about its quarter chord point at a reduced frequency k = ^j = 0.2 Transactions on Modelling and Simulation vol 18, © 1997 WIT Press, www.witpress.com, ISSN 1743-355X 784 Boundary Elements and with a pitching amplitude c*o = 10°.
Load more

Recommended publications
  • Clearing Certain Misconception in the Common Explanations of the Aerodynamic Lift
    Clearing certain misconception in the common explanations of the aerodynamic lift Clearing certain misconception in the common explanations of the aerodynamic lift Navinder Singh,∗ K. Sasikumar Raja, P. Janardhan Physical Research Laboratory, Ahmedabad, India. [email protected] October 30, 2018 Abstract Air travel has become one of the most common means of transportation. The most common question which is generally asked is: How does an airplane gain lift? And the most common answer is via the Bernoulli principle. It turns out that it is wrongly applied in common explanations, and there are certain misconceptions. In an alternative explanation the push of air from below the wing is argued to be the lift generating force via Newton’s law. There are problems with this explanation too. In this paper we try to clear these misconceptions, and the correct explanation, using the Lancaster-Prandtl circulation theory, is discussed. We argue that even the Lancaster-Prandtl theory at the zero angle of attack needs further insights. To this end, we put forward a theory which is applicable at zero angle of attack. A new length scale perpendicular to the lower surface of the wing is introduced and it turns out that the ratio of this length scale to the cord length of a wing is roughly 0.4930 ± 0.09498 for typical NACA airfoils that we analyzed. This invariance points to something fundamental. The idea of our theory is simple. The "squeezing" effect of the flow above the wing due to camber leads to an effective Venturi tube formation and leads to higher velocity over the upper surface of the wing and thereby reducing pressure according the Bernoulli theorem and generating lift.
    [Show full text]
  • How Do Wings Generate Lift? 2
    GENERAL ARTICLE How Do Wings Generate Lift? 2. Myths, Approximate Theories and Why They All Work M D Deshpande and M Sivapragasam A cambered surface that is moving forward in a fluid gen- erates lift. To explain this interesting fact in terms of sim- pler models, some preparatory concepts were discussed in the first part of this article. We also agreed on what is an accept- able explanation. Then some popular models were discussed. Some quantitative theories will be discussed in this conclud- ing part. Finally we will tie up all these ideas together and connect them to the rigorous momentum theorem. M D Deshpande is a Professor in the Faculty of Engineering The triumphant vindication of bold theories – are these not the and Technology at M S Ramaiah University of pride and justification of our life’s work? Applied Sciences. Sherlock Holmes, The Valley of Fear Sir Arthur Conan Doyle 1. Introduction M Sivapragasam is an We start here with two quantitative theories before going to the Assistant Professor in the momentum conservation principle in the next section. Faculty of Engineering and Technology at M S Ramaiah University of Applied 1.1 The Thin Airfoil Theory Sciences. This elegant approximate theory takes us further than what was discussed in the last two sections of Part 111, and quantifies the Resonance, Vol.22, No.1, ideas to get expressions for lift and moment that are remarkably pp.61–77, 2017. accurate. The pressure distribution on the airfoil, apart from cre- ating a lift force, leads to a nose-up or nose-down moment also.
    [Show full text]
  • Lecture 4: Panel Methods G. Dimitriadis Introduction
    Aerodynamics Lecture 4: Panel methods G. Dimitriadis Introduction • Until now we’ve seen two methods for modelling wing sections in ideal flow: –Conformal mapping: Can model only a few classes of wing sections –Thin airfoil theory: Can model any wing section but ignores the thickness. • Both methods are not general. • A more general approach will be presented here. 2D Panel methods • 2D Panel methods refers to numerical methods for calculating the flow around any wing section. • They are based on the replacement of the wing section’s geometry by singularity panels, such as source panels, doublet panels and vortex panels. • The usual boundary conditions are imposed: – Impermeability – Kutta condition Panel placement • Eight panels of length Sj • For each panel, sj=0-Sj. • Eight control (collocation) points (xcj,ycj) located in the middle of each panel. • Nine boundary points (xbj,ybj) • Normal and tangential unit vector on each panel, nj, tj • Vorticity (or source strength) on each panel j(s) (or j(s)) Problem statement • Use linear panels • Use constant singularity strength on each panel, j(s)=j (j(s)=j). • Add free stream U at angle . • Apply boundary conditions: – Far field: automatically satisfied if using source or vortex panels – Impermeability: Choose Neumann or Dirichlet. • Apply Kutta condition. • Find vortex and/or source strength distribution that will satisfy Boundary Conditions and Kutta condition. Panel choice • It is best to chose small panels near the leading and trailing edge and large panels in the middle: x 1 = ()cos +1 , = 0 2 c 2 Notice that now x/c 17 29 begins at 1, passes 16 30 through 0 and then goes 2 1 back to 1.
    [Show full text]
  • Explicit Role of Viscosity in Generating Lift
    AIAA JOURNAL Vol. 55, No. 11, November 2017 Technical Notes Explicit Role of Viscosity I. Introduction in Generating Lift HIS Note tries to elucidate the subtle but critical role of the fluid T viscosity in generating the aerodynamic lift. The viscous origin of the lift has not been widely understood or sufficiently highlighted Tianshu Liu∗ in the literature. In classical aerodynamics textbooks [1–4], the lift Western Michigan University, Kalamazoo, Michigan 49008 theory of an airfoil is usually developed based on the classical potential-flow theory, in which the Kutta–Joukowski (K-J) theorem and † ‡ is used as a key element in calculating the lift. However, the airfoil Shizhao Wang and Guowei He circulation in the K-J theorem cannot be automatically determined in Chinese Academy of Sciences, 100190 Beijing, the potential-flow framework alone because the vorticity cannot be People’s Republic of China physically generated in an inviscid flow. This fundamental difficulty is intrinsically related to D’Alembert’s paradox stating that the DOI: 10.2514/1.J055907 integrated pressure force of a body is zero in a steady inviscid irrotational incompressible flow [5,6]. To circumvent this problem, the Kutta condition is imposed at the airfoil trailing edge to determine Nomenclature the circulation. To a great extent, the success of the classical Cd = drag coefficient circulation theory in predicting the lift depends on the clever Cl = lift coefficient application of the Kutta condition and its generalized forms as the Cp = pressure coefficient phenomenological models of the viscous-flow effect on the lift c = chord length, m generation [7].
    [Show full text]
  • Joukowski Theorem for Multi-Vortex and Multi-Airfoil Flow (A
    CORE Metadata, citation and similar papers at core.ac.uk Provided by Elsevier - Publisher Connector Chinese Journal of Aeronautics, (2014),27(1): 34–39 Chinese Society of Aeronautics and Astronautics & Beihang University Chinese Journal of Aeronautics [email protected] www.sciencedirect.com Generalized Kutta–Joukowski theorem for multi-vortex and multi-airfoil flow (a lumped vortex model) Bai Chenyuan, Wu Ziniu * School of Aerospace, Tsinghua University, Beijing 100084, China Received 5 January 2013; revised 20 February 2013; accepted 25 February 2013 Available online 31 July 2013 KEYWORDS Abstract For purpose of easy identification of the role of free vortices on the lift and drag and for Incompressible flow; purpose of fast or engineering evaluation of forces for each individual body, we will extend in this Induced drag; paper the Kutta–Joukowski (KJ) theorem to the case of inviscid flow with multiple free vortices and Induced lift; multiple airfoils. The major simplification used in this paper is that each airfoil is represented by a Multi-airfoils; lumped vortex, which may hold true when the distances between vortices and bodies are large Vortex 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 out- side 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 demon- strate how to perform fast force approximation for multi-body and multi-vortex problems.
    [Show full text]
  • Kutta Condition
    SNS COLLEGE OF TECHNOLOGY (An Autonomous Institution) COIMBATORE–35 DEPARTMENT OF AERONAUTICAL ENGINEERING KUTTA CONDITION: The Kutta condition is a principle in steady-flow fluid dynamics, especially aerodynamics, that is applicable to solid bodies with sharp corners, such as the trailing edges of airfoils. A body with a sharp trailing edge which is moving through a fluid will create about itself a circulation of sufficient strength to hold the rear stagnation point at the trailing edge. In fluid flow around a body with a sharp corner, the Kutta condition refers to the flow pattern in which fluid approaches the corner from both directions, meets at the corner, and then flows away from the body. None of the fluid flows around the sharp corner. Prepared by Ms.X.Bernadette Evangeline AP/AERO 16AE208 AERODYNAMICS-I SNS COLLEGE OF TECHNOLOGY (An Autonomous Institution) COIMBATORE–35 DEPARTMENT OF AERONAUTICAL ENGINEERING The Kutta condition is significant when using the Kutta–Joukowski theorem to calculate the lift created by an airfoil with a sharp trailing edge. The value of circulation of the flow around the airfoil must be that value which would cause the Kutta condition to exist. In 2-D potential flow, if an airfoil with a sharp trailing edge begins to move with an angle of attack through air, the two stagnation points are initially located on the underside near the leading edge and on the topside near the trailing edge, just as with the cylinder. As the air passing the underside of the airfoil reaches the trailing edge it must flow around the trailing edge and along the topside of the airfoil toward the stagnation point on the topside of the airfoil.
    [Show full text]
  • A Kutta Condition Enforcing BEM Technology for Airfoil Aerodynamics
    Transactions on Modelling and Simulation vol 15, © 1997 WIT Press, www.witpress.com, ISSN 1743-355X A Kutta Condition Enforcing BEM Technology for Airfoil Aerodynamics G. lannelli*, C. Grille*, L. Tulumello* Department of Mechanical and Aerospace Engineering and Eng. Science, University of Tennessee, Knoxville, USA * Department of Mechanical and Aeronautical Engineering, University of Palermo, Italy Abstract An analytical perturbation stream function procedure is established for po- tential flows about lifting airfoils, which exactly enforces the fundamental Kutta condition. Using Green's identity, this formulation is transformed into an equivalent boundary integral equation. A boundary finite element discretization of this equation then yields a linear system for the efficient determination of the airfoil surface tangential velocity and associated lift 1 Introduction For many years boundary integral equation procedures, or panel methods, have been widely used for determining the potential flow field about com- plex aerodynamics configurations*. In the potential function procedure, the potential values are related to the boundary potentials and associated normal derivatives, whereas in the singularity procedure the local potential function value is expressed in terms of boundary sources, doublets and vor- tices of appropriate intensity. In either case, the reliability of the computed results critically depends on accurate boundary distributions of singularities or potentials. Furthermore, the Kutta condition, requiring the aft stagna- tion point to coincide with the trailing edge, must be adequately enforced. Several implementations of the potential function procedure indirectly en- force the Kutta condition. Conversely, the singularity method employs a trailing edge discretization node where the vanishing velocity condition can be enforced. Nevertheless, it has been reported that the substitution of the trailing edge integral equation with the vanishing velocity condition may lead to solution non-uniqueness.
    [Show full text]
  • AA200 Ch 11 Two-Dimensional Airfoil Theory Cantwell.Pdf
    CHAPTER 11 TWO-DIMENSIONAL AIRFOIL THEORY ___________________________________________________________________________________________________________ 11.1 THE CREATION OF CIRCULATION OVER AN AIRFOIL In Chapter 10 we worked out the force that acts on a solid body moving in an inviscid fluid. In two dimensions the force is F d = Φndlˆ − U (t) × Γ(t)kˆ (11.1) ρ oneunitofspan dt ∫ ∞ ( ) Aw where Γ(t) = !∫ UicˆdC is the circulation about the body integrated counter-clockwise Cw about a path that encloses the body. It should be stated at the outset that the creation of circulation about a body is fundamentally a viscous process. The figure below from Van Dyke’s Album of Fluid Motion depicts what happens when a viscous fluid is moved impulsively past a wedge. Figure 11.1 Starting vortex formation about a corner in an impulsively started incompressible fluid. 1 A purely potential flow solution would negotiate the corner giving rise to an infinite velocity at the corner. In a viscous fluid the no slip condition prevails at the wall and viscous dissipation of kinetic energy prevents the singularity from occurring. Instead two layers of fluid with oppositely signed vorticity separate from the two faces of the corner to form a starting vortex. The vorticity from the upstream facing side is considerably stronger than that from the downstream side and this determines the net sense of rotation of the rolled up vortex sheet. During the vortex formation process, there is a large difference in flow velocity across the sheet as indicated by the arrows in Figure 11.1. Vortex formation is complete when the velocity difference becomes small and the starting vortex drifts away carried by the free stream.
    [Show full text]
  • On the Circulation and the Position of the Forward Stagnation Point on Airfoils
    On the circulation and the position of the forward stagnation point on airfoils J. Meseguer (corresponding author), G. Alonso, A. Sanz-Andres and I. Perez-Grande IDR/UPM. EJ.S.I. Aeronauticos, Universidad Politecnica de Madrid, E-28040 Madrid, Spain E-mail: jmeseguer@idr. upm. es Abstract Lift and velocity circulation around airfoils are two aspects of the same phenomenon when airfoils are not stalled and the Kutta-Joukowski theorem applies. This theorem establishes a linear dependence between lift and circulation, which breaks when stalling occurs. As the angle of attack increases beyond this point, the circulation vanishes. Since the circulation determines to a great extent the position of the forward stagnation point on an airfoil, the measurement of this position is an easy and simple way to determine the circulation, which is of help in understanding the role of the latter in the generation of aerodynamic forces on airfoils. Keywords Kutta-Joukowski theorem; airfoil; stagnation point Introduction Wing profiles are aerodynamic devices which are designed to provide high values of the ratio lift/aerodynamic drag, lid. Airfoils are characterised by the camber line, the thickness distribution and the angle of attack. These streamlined two- dimensional bodies generally have a rounded leading edge and a wedged trailing edge, the latter being of paramount importance in generating lift. As is well known, due to the airfoil's shape, in normal operation the flow is accel­ erated on the airfoil's upper side and decelerated on its lower side. Hence, the pres­ sure decreases on the upper side and increases on the lower side, and thus a net force appears.
    [Show full text]
  • Chapter 1 Introduction to Fluid Flow
    CHAPTER 1 INTRODUCTION TO FLUID FLOW 1.1 INTRODUCTION Fluid flows play a crucial role in a vast variety of natural phenomena and man- made systems. The life-cycles of stars, the creation of atmospheres, the sounds we hear, the vehicles we ride, the systems we build for flight, energy generation and propulsion all depend in an important way on the mechanics and thermody- namics of fluid flow. The purpose of this course is to introduce students in Aeronautics and Astronautics to the fundamental principles of fluid mechanics with emphasis on the development of the equations of motion as well as some of the analytical tools from calculus needed to solve practically important problems involving flows in channels along walls and over lifting bodies. 1.2 CONSERVATION OF MASS Mass is neither created nor destroyed. This basic principle of classical physics is one of the fundamental laws governing fluid motion and is a good departure point for our introductory discussion. Figure 1.1 below shows an infinitesimally small stationary, rectangular control volume 6x6y6z through which a fluid is assumed to be moving. A control vol- ume of this type with its surface fixed in space is called an Eulerian control volume. The fluid velocity vector has components UUVW= (),, in the xxyz= (),, directions and the fluid density is l . In a general, unsteady, com- pressible flow, all four flow variables may depend on position and time. The law of conservation of mass over this control volume is stated as bjc 1.1 3/26/13 Conservation of mass ¨¬Rate of mass ¨¬Rate of mass ¨¬Rate of mass «««««« ««accumulation ««flow «« flow ©­= ©­– ©­(1.1) ««inside the control ««into the control ««out of the control «««««« ª®volume ª®volume ª®volume z lW z + 6z ()x +y6x,,+z6y + 6z W(x,y,z,t) lV y + 6y V(x,y,z,t) U U(x,y,z,t) lU x + 6x l()xyzt,,, lU x 6z y ()xyz,, lV lW y 6y z 6x x Figure 1.1 Fixed control volume in a moving fluid.
    [Show full text]
  • Unsteady Kutta Condition and Vortex-Sheet Generation
    XXIV ICTAM, 21-26 August 2016, Montreal, Canada UNSTEADY KUTTA CONDITION AND VORTEX-SHEET GENERATION Xi Xia1 and Kamran Mohseni ∗1;2 1Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL, USA 2Department of Electrical and Computer Engineering, University of Florida, Gainesville, FL, USA Summary Vortex method has been widely used for low-Reynolds-number flights as it reduces the computation domain from the entire flow field to only finite vortical structures. An essential challenge of the vortex method lies in the prediction of the vortex sheets separated from the solid body. To tackle this problem, this study extends the classical Kutta condition to unsteady situations based on the physical sense that flow cannot turn around a sharp edge. This unsteady Kutta condition can be readily applied to an airfoil with cusped trailing edge, where the forming vortex sheet is known to be tangential to the trailing edge. For a finite-angle trailing edge, previous studies indicate that the direction of the forming vortex sheet is ambiguous. Therefore, this study proposes a novel analytical formulation to determine the angle of the trailing-edge vortex sheet based on momentum conservation in the direction normal to the forming vortex sheet. INTRODUCTION Natural flies are observed to be superior than man-made aerial vehicles in terms of aerodynamic performance, especially the high lift-generation mechanisms. Early experimental investigations suggested that the existence of an attached leading edge vortex (LEV) contributes to enhanced lift generation for flapping wings [2]. To understand the fundamental mechanism of the LEV, recent analytical studies have been extensively focused on using vortex method (diagram shown in Fig.
    [Show full text]
  • Articulo Final Gabriel Heredia
    Inviscid, Incompressible CFD Solver with Coordinate Transformation for Aerodynamic Applications Gabriel A. Heredia Acevedo Master of Engineering in Mechanical Engineering Prof. José A. Pertierra Mechanical Engineering Department Polytechnic University of Puerto Rico Abstract Fluid mechanics is a complex field of purpose, a software tool was created using Matlab study with many modern design applications. that analyzes flow patterns over basic airfoils. Mechanical and aerospace engineers frequently The main idea behind this program is that if the have the need to analyze fluid flow patterns for flow speed distribution is obtained some distance practical design purposes ranging from a complete from the airfoil and afterwards, the pressure design to a validation of results. Physical concepts, distribution around the airfoil’s surface may also be such as conservation of mass, conservation of obtained. An incompressible, inviscid flow is used momentum, and conservation of energy are required to analyze the fluid flow patterns. A coordinate to fully describe any arbitrary flow pattern’s transformation technique is also employed to ensure characteristics. These concepts are required to that properties obtained at the airfoil’s body is compute pressure distribution, typically used in the obtained, given that this is the main area of interest design of airfoils and other arbitrary shapes, which for aerodynamic applications. are of main interest in the aerospace and naval industries. A tool was created that employs GOVERNING THEORY computational fluid dynamics techniques to provide The model used for the flow pattern analysis in solution for flow patterns over NACA four digit question is that of an incompressible, inviscid flow. airfoils.
    [Show full text]