Aerodynamics. High-Lift Devices
|
|
- Elijah Young
- 6 years ago
- Views:
Transcription
1 High-Lift Devices Devices to increase the lift coefficient by geometry changes (camber and/or chord) and/or boundary-layer control (avoid flow separation - Flaps, trailing edge devices - Slats, leading edge devices
2 High-Lift Devices Flaps Flat plate deflected at the trailing edge for zero angle of attack Loading distribution for an ideal fluid flowing around a flat plate with a deflected trailing edge C l > 0 due to the camber introduced by the trailing edge deflection. Adverse pressure gradients lead to flow separation
3 High-Lift Devices Flaps Flat plate deflected at the trailing edge for zero angle of attack or Separation at the flap corner Boundary-layer separation reduces the stall angle of attack. Boundary-layer control may avoid the reduction of the stall angle of attack
4 Plain flap High-Lift Devices Flaps a) Clean configuration b) Deflected flap
5 Plain flap High-Lift Devices Flaps Boundary-layer separation reduces the stall angle of attack
6 Flap split High-Lift Devices Flaps Simple deflection of a plate. Increase of C l is similar to plain flap, but there is a significant increase of C d compared to the plain flap
7 Slotted flap Aerodynamics High-Lift Devices Flaps Boundary-layer control at the trailing edge. Separation delayed by blowing at the region of adverse pressure gradient on the upper side of the flap
8 Fowler flap High-Lift Devices Flaps Boundary-layer control similar to the slotted flap. Increase of C l due to growth of the chord length C l L L = r = r 1 2 ρ V c 1 2 ρ V c f cf c = C 2 2 lf cf c
9 Lift coefficient Aerodynamics High-Lift Devices Flaps Fowler flap Slotted flap Plain flap Basic airfoil (no flaps)
10 High-Lift Devices Flaps Lift and drag coefficients
11 High-Lift Devices Leading edge slats Boundary-layer control at the suction peak close to the airfoil leading edge a) Basic section: separation bubble at the leading edge b) Deflected leading edge
12 High-Lift Devices Leading edge slats Boundary-layer control at the suction peak close to the airfoil leading edge Slot at the leading edge
13 High-Lift Devices Examples Fowler flap with double slot
14 High-Lift Devices Examples Deflection of high-lift devices in different flight configurations
15 High-Lift Devices Examples
16 Aerodynamic Appendages Spoiler
17 Aerodynamic Appendages
18 Aerodynamics For a steady, irrotational and incompressible flow around an airfoil it is possible to define a velocity potential function, φ, that satisfies the Laplace equation r r φ = 0 and the following boundary conditions r r φ φ n = = vw em S n r r φ = V para r
19 r r φ φ n = = vw on S n r r φ = V for r - V r is the velocity of the incoming flow assumed to be uniform v w - is the normal velocity component on the body surface that is equal to 0 for an impermeable surface
20 The velocity potencial function, φ, is split (linear problem) in to the velocity potential of the uniform incoming flow, φ, and the pertubation potential, Φ, that represents the effect of the airfoil φ = φ + Φ φ is known and Φ is defined by a superficial distribution of sources/sinks lines of intensity σ(q)
21 If the mathematical model contains only a uniform flow and sources/sinks distributions it has no circulation, Γ=0. Therefore, it can not satisfy the Kutta condition
22 The circulation required to satisfy the Kutta condition is introduced by the velocity potential of a purely circulatory flow, φ Γ
23 The circulatory flow (function φ Γ ), can be defined with superficial and/or interior line vortices distributions
24 The circulation introduced depends on a constant, γ o, that must be determined to satisfy the Kutta condition
25 The velocity induced by the vortex distribution at a point P is designated by V r γ, where V r o Γ Γ is the velocity induced by the vortex distribution with γ o =1
26 Aerodynamics The normal velocity component at any point P of the airfoil surface is obtained from φ, Φ e φ Γ and it satisfies the following equation σ 2 ( P) 1 [ ln( r( P, q) )] σ ( q) ds + ( V ) + γ ov np = vwp + Γ S 2π np - r(p,q) stands for the distance between point P and a point q on the airfoil surface - n r P is the (external) normal vector to the airfoil surface at point P r r r
27 ( P) σ 2 1 S 2π n r r V np r r γ V n v o w P Γ P P [ ln( r( P, q) )] σ ( q) ds Self-induction Normal velocity component induced by the superficial distribution of source/sinks lines Normal velocity component induced by the uniform incoming flow Normal velocity component induced by the circulatory flow Normal velocity component at point P
28 σ 2 ( P) 1 [ ln( r( P, q) )] σ ( q) ds + ( V ) + γ ov np = vwp + Γ S 2π np r r r The application of the boundary conditions on the airfoil surface leads to a Fredholm integral equation of the second kind that defines the intensity σ(q) of the line sources/sinks distribution
29 σ 2 ( P) 1 [ ln( r( P, q) )] σ ( q) ds + ( V ) + γ ov np = vwp + Γ S 2π np r r r The constant γ o is determined by the application of the Kutta condition. At the velocity at the trailing edge must be finite, i.e. the dividing streamline must be aligned with the bisector of the trailing edge angle
30 σ 2 ( P) Aerodynamics 1 [ ln( r( P, q) )] σ ( q) ds + ( V ) + γ ov np = vwp + Γ S 2π np The panel method transforms the Fredholm integral equation of the second kind into a system of algebraic equations that as a straighforward numerical solution. There are two types of approximations required: 1. Geometric representation of the airfoil shape 2. Piecewise (panels) definition of σ(q) r r r
31 Geometric discretization - The airfoil is described by n flat elements (panels) defined by boundary points. When n the approximate geometry converges to the exact shape of the airfoil Boundary points Control points
32 Approximation of σ(q) - For each flat element (panel), the intensity of the source/sinks lines remains constant. When n the approximate description of σ(q) tends to a continuous (exact) distribution Boundary points Control points
33 Boundary conditions - The boundary conditions (specification of the normal velocity component) are satisfied at the midpoint of each panel (control point). When n the boundary conditions are satisfied for the complete airfoil Boundary points Control points
34 Aerodynamics The discretization process leads to the following system of algebraic equations (n (n+1)): n A + r r ( V V ) r ijσ j + γ o ni = vw with 1 i n Γ j= 1 - Unknowns: n values of σ and γ o, total of n+1 - Equations: n control points to impose the normal component of the velocity The n+1 equation is the Kutta condition i i
35 Aerodynamics The discretization process leads to the following system of algebraic equations (n (n+1)): n A + r r ( V V ) r ijσ j + γ o ni = vw with 1 i n Γ j= 1 i - A ij is the influence coefficients matrix that define the normal velocity component induced at point i by a line source distribution of intensity one in panel j. - Analogously, the matrix B ij is defined for the tangential velocity component i
36 The influence coefficients matrices, A ij e B ij, are exclusively dependent on the airfoil geometry and can be easily determined in the local reference frames of the elements (panels) - Calculation of A ij and B ij 1. Transform the coordinates x,y to a reference frame with the horizontal axis aligned with panel j and the vertical axis aligned with the external normal of the (approximate) airfoil
37 - Calculation of A ij and B ij 2. Determine the induced velocity in the local reference frame V V x y = = 1 2π 1 2π L L E E 0 2 xe ζ dζ r ye dζ r 0 2 L is the length of E panel j
38 E L is the length of panel j ( ) = + + = e E e e e y e E e e e x y L x y x V y L x y x V arctg arctg 2 1 ln π π - Calculation of A ij and B ij 2. Determine the induced velocity in the local reference frame
39 - Calculation of A ij and B ij 3. Project the velocity vector obtained in the local reference frame of panel j to a reference frame with the horizontal axis aligned with panel i and with the vertical axis aligned with the external normal of the (approximate) airfoil at panel i
40 Aerodynamics There are several alternatives to impose the Kutta condition numerically: 1. Equal velocity (pressure) at the two control points of the panels that define the trailing edge 2. Equal velocity (pressure) at the trailing edge for extrapolations of the velocity based on the nearby control points 3. Define an extra control point downstream of the trailing edge and impose that the velocity normal to the bisector of the trailing edge is equal to zero
41 Aerodynamics Any of the previous alternatives leads to the extra algebraic equation that determines γ o and consequently Γ 1. Simple implementation, numerically robust and sufficiently accurate for reasonable panel sizes at the trailing edge (cosine distribution of boundary points along the chord) 2. The extra equation only remains linear for linear extrapolations. In that case, differences to the previous option are not significant
42 Any of the previous alternatives leads to the extra algebraic equation that determines γ o and consequently Γ 3. The distance of the extra control point to the trailing edge is ambiguous. Too small distances lead to numerical difficulties and too large distances to a loss of accuracy. Ideal distance depends on the local geometry of the airfoil (camber and trailing edge angle)
43 Theoretically, any superficial or interior vortex distribution may be used to satisfy the Kutta condition Numerical experiments show that superficial or internal vortex distributions lead to different results. Although the value of Γ may be correct, there are alternatives that lead to an incorrect pressure distribution at the trailing edge
44 Linear along the mean line Constant on the surface Parabolic on the surface Analytic solution Numerical solutions
45 s m Aerodynamics - is the distance to the trailing edge measured along the mean line panels - m is the number of mean line panels ( m = n 2) - is the length of the mean line panels l m Vortex distribution along de mean line of the airfoil with an intensity given by γ = γ s o 0,4 m (constant γ s o 0,4 m i in each panel) Boundary points Control points Mean line boundary points
46 Vortex distribution along de mean line of the airfoil with an intensity given by γ = γ s o 0,4 m (constant γ s o 0,4 m i in each - The total circulation around the airfoil is given by Γ = panel) L m m γds = γ o 0 i= 1 s 0,4 m i l Boundary points Control points Mean line boundary points m i
47 σ j and γ o are determined from the solution of the system of n+1 algebraic equations The tangential velocity components at the control points are given by n r r v B ( V V ) r t = ijσ j + + γ o Γ ti with 1 i n i j= 1 - t r i is the unit vector tangent to panel i i
48 The pressure coefficient is defined by p p C p = r 2 2 ρ V 1 In irrotational, incompressible flow (Bernoulli equation) r 2 1 V C p = r V
49 At the control points n Aerodynamics r v = 0 V = v i t i C p = 1 vt r i V 2
50 Aerodynamics Determination of the forces - There are two alternatives to determine the lift coefficient: Kutta-Joukowski equation (circulation) or integration of the surface pressure distribution - For an ideal fluid, the drag coefficient is zero. However, the numerical solution will only respect this result when the number of panels tends to infinity. The drag coefficient obtained from the integration of the surface pressure distribution is a useful measure of the discretization error/uncertainty
51 - Lift coefficient Aerodynamics Determination of the forces C l = 2Γ r V c ou C l = C y cos ( α ) C sen( α ) x
52 - Drag coefficient Aerodynamics Determination of the forces C = C cos + d x ( α ) C sen( α ) y
53 = = = = + + n i pf pf p p y n i pf pf p p x c x x C c x d C C c y y C c y d C C i i i i i i For flat panels and C p determined at the control points Determination of the forces
54 Aerodynamics Including viscous effects - Viscosity originates boundary-layers on the upper and lower surfaces of the airfoil (and a wake). The streamlines of the external are displaced δ * as a consequence of this viscous region of the flow - Boundary-layer calculations to determine δ* require the knowledge of the pressure gradient, which depends on the displacement thickness,δ *. Therefore, the solution procedure must be iterative (not possible if there is flow separation)
55 Including viscous effects - Two possible alternatives: 1. Define an aerodynamic shape of the airfoil adding the displacement thickness to the airfoil geometry (geometry change) 2. Keep the airfoil geometry fixed and introduce the δ * effect with a transpiration velocity, v w, at the airfoil surface
56 Aerodynamics Including viscous effects - Two possible alternatives: 1. Change of geometry implies the re-calculation of influence coefficients matrics everry iteration 2. Fixed geometry implies a fixed matrix of coefficients for the linear system that can be factorized. Introduction of the δ * effect corresponds to a simple change of the right-hand side
57 Including viscous effects - Determination of the transpiration velocity = y v v dy 0 y - From the continuity equation v = y u 0 x dy
58 Including viscous effects - Determination of the transpiration velocity = y u v dy 0 x - Adding and subtracting the external velocity to the boundary-layer U e = v 0 y x U e U e 1 u U e dy
59 ( ) * δ δ e e e e e y e e e U dx d x U v dy U u U dx d x U v dy U u U U x v + = + = = Including viscous effects - Determination of the transpiration velocity
60 Including viscous effects - Determination of the transpiration velocity U e d v = + U e δ x dx ( *) - The first term is of inviscid nature and the second one include the boundary-layer effect, so d v w = U e δ dx ( *)
61 ASA2D program ASA2D is a computer code for the numerical calculation of the aerodynamic characteristics of airfoils in steady, incompressible flows at small angles of attack (no flow separation) Weak viscous-inviscid interaction method that can not handle flow separation Iterative solution procedure with fixed geometry and transpiration velocity to include viscous effects in the ideal fluid solution
62 ASA2D program Adopted methods - Ideal fluid flow (potential flow) - Boundary-layer (viscous flow) Thwaites s method (laminar regime) Head s method (turbulent regime) Instantaneous transition at a point
63 Adopted methods Aerodynamics ASA2D program - Boundary-layer (viscous flow) Correlations H Re and R for the determination x e R θ e x of the transition point Wake influence neglected - Boundary-layer separation for laminar flow is assumed to be a transition criterion to turbulent flow
64 ASA2D program Determination of forces and moments - Lift coefficient, C l Kutta-Joukowski equation (circulation) Integration of the pressure distribution
65 ASA2D program Determination of forces and moments - Drag coefficient, C d Integration of pressure and wall shear-stress on the airfoil surface Squire & Young formula C d 2 = θbf e c r V r V bf H bf e θ bf i r V r V bf H bfi 2 + 5
66 ASA2D program Determination of forces and moments - Pitching moment relative to the airfoil centre coefficient Integration of pressure distribution
1. Fluid Dynamics Around Airfoils
1. Fluid Dynamics Around Airfoils Two-dimensional flow around a streamlined shape Foces on an airfoil Distribution of pressue coefficient over an airfoil The variation of the lift coefficient with the
More informationLifting Airfoils in Incompressible Irrotational Flow. AA210b Lecture 3 January 13, AA210b - Fundamentals of Compressible Flow II 1
Lifting Airfoils in Incompressible Irrotational Flow AA21b Lecture 3 January 13, 28 AA21b - Fundamentals of Compressible Flow II 1 Governing Equations For an incompressible fluid, the continuity equation
More informationMestrado Integrado em Engenharia Mecânica Aerodynamics 1 st Semester 2012/13
Mestrado Integrado em Engenharia Mecânica Aerodynamics 1 st Semester 212/13 Exam 2ª época, 2 February 213 Name : Time : 8: Number: Duration : 3 hours 1 st Part : No textbooks/notes allowed 2 nd Part :
More informationMasters in Mechanical Engineering Aerodynamics 1 st Semester 2015/16
Masters in Mechanical Engineering Aerodynamics st Semester 05/6 Exam st season, 8 January 06 Name : Time : 8:30 Number: Duration : 3 hours st Part : No textbooks/notes allowed nd Part : Textbooks allowed
More informationGiven the water behaves as shown above, which direction will the cylinder rotate?
water stream fixed but free to rotate Given the water behaves as shown above, which direction will the cylinder rotate? ) Clockwise 2) Counter-clockwise 3) Not enough information F y U 0 U F x V=0 V=0
More informationMasters in Mechanical Engineering. Problems of incompressible viscous flow. 2µ dx y(y h)+ U h y 0 < y < h,
Masters in Mechanical Engineering Problems of incompressible viscous flow 1. Consider the laminar Couette flow between two infinite flat plates (lower plate (y = 0) with no velocity and top plate (y =
More informationLaminar Flow. Chapter ZERO PRESSURE GRADIENT
Chapter 2 Laminar Flow 2.1 ZERO PRESSRE GRADIENT Problem 2.1.1 Consider a uniform flow of velocity over a flat plate of length L of a fluid of kinematic viscosity ν. Assume that the fluid is incompressible
More informationCopyright 2007 N. Komerath. Other rights may be specified with individual items. All rights reserved.
Low Speed Aerodynamics Notes 5: Potential ti Flow Method Objective: Get a method to describe flow velocity fields and relate them to surface shapes consistently. Strategy: Describe the flow field as the
More informationSPC Aerodynamics Course Assignment Due Date Monday 28 May 2018 at 11:30
SPC 307 - Aerodynamics Course Assignment Due Date Monday 28 May 2018 at 11:30 1. The maximum velocity at which an aircraft can cruise occurs when the thrust available with the engines operating with the
More informationChapter 6: Incompressible Inviscid Flow
Chapter 6: Incompressible Inviscid Flow 6-1 Introduction 6-2 Nondimensionalization of the NSE 6-3 Creeping Flow 6-4 Inviscid Regions of Flow 6-5 Irrotational Flow Approximation 6-6 Elementary Planar Irrotational
More informationINSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) Dundigal, Hyderabad
INSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) Dundigal, Hyderabad - 500 043 AERONAUTICAL ENGINEERING TUTORIAL QUESTION BANK Course Name : LOW SPEED AERODYNAMICS Course Code : AAE004 Regulation : IARE
More informationDepartment of Mechanical Engineering
Department of Mechanical Engineering AMEE401 / AUTO400 Aerodynamics Instructor: Marios M. Fyrillas Email: eng.fm@fit.ac.cy HOMEWORK ASSIGNMENT #2 QUESTION 1 Clearly there are two mechanisms responsible
More information1. Introduction, tensors, kinematics
1. Introduction, tensors, kinematics Content: Introduction to fluids, Cartesian tensors, vector algebra using tensor notation, operators in tensor form, Eulerian and Lagrangian description of scalar and
More informationInviscid & Incompressible flow
< 3.1. Introduction and Road Map > Basic aspects of inviscid, incompressible flow Bernoulli s Equation Laplaces s Equation Some Elementary flows Some simple applications 1.Venturi 2. Low-speed wind tunnel
More informationSyllabus for AE3610, Aerodynamics I
Syllabus for AE3610, Aerodynamics I Current Catalog Data: AE 3610 Aerodynamics I Credit: 4 hours A study of incompressible aerodynamics of flight vehicles with emphasis on combined application of theory
More informationLecture 7 Boundary Layer
SPC 307 Introduction to Aerodynamics Lecture 7 Boundary Layer April 9, 2017 Sep. 18, 2016 1 Character of the steady, viscous flow past a flat plate parallel to the upstream velocity Inertia force = ma
More informationPEMP ACD2505. M.S. Ramaiah School of Advanced Studies, Bengaluru
Two-Dimensional Potential Flow Session delivered by: Prof. M. D. Deshpande 1 Session Objectives -- At the end of this session the delegate would have understood PEMP The potential theory and its application
More informationV (r,t) = i ˆ u( x, y,z,t) + ˆ j v( x, y,z,t) + k ˆ w( x, y, z,t)
IV. DIFFERENTIAL RELATIONS FOR A FLUID PARTICLE This chapter presents the development and application of the basic differential equations of fluid motion. Simplifications in the general equations and common
More informationFundamentals of Fluid Dynamics: Ideal Flow Theory & Basic Aerodynamics
Fundamentals of Fluid Dynamics: Ideal Flow Theory & Basic Aerodynamics Introductory Course on Multiphysics Modelling TOMASZ G. ZIELIŃSKI (after: D.J. ACHESON s Elementary Fluid Dynamics ) bluebox.ippt.pan.pl/
More informationFlight Vehicle Terminology
Flight Vehicle Terminology 1.0 Axes Systems There are 3 axes systems which can be used in Aeronautics, Aerodynamics & Flight Mechanics: Ground Axes G(x 0, y 0, z 0 ) Body Axes G(x, y, z) Aerodynamic Axes
More informationBOUNDARY LAYER FLOWS HINCHEY
BOUNDARY LAYER FLOWS HINCHEY BOUNDARY LAYER PHENOMENA When a body moves through a viscous fluid, the fluid at its surface moves with it. It does not slip over the surface. When a body moves at high speed,
More informationLab Reports Due on Monday, 11/24/2014
AE 3610 Aerodynamics I Wind Tunnel Laboratory: Lab 4 - Pressure distribution on the surface of a rotating circular cylinder Lab Reports Due on Monday, 11/24/2014 Objective In this lab, students will be
More informationActive Control of Separated Cascade Flow
Chapter 5 Active Control of Separated Cascade Flow In this chapter, the possibility of active control using a synthetic jet applied to an unconventional axial stator-rotor arrangement is investigated.
More informationDesign of a Droopnose Configuration for a Coanda Active Flap Application. Marco Burnazzi and Rolf Radespiel
Design of a Droopnose Configuration for a Coanda Active Flap Application Marco Burnazzi and Rolf Radespiel Institute of Fluid Mechanics, Technische Universität Braunschweig, 38108 Braunschweig, Germany
More informationCOMPUTATIONAL SIMULATION OF THE FLOW PAST AN AIRFOIL FOR AN UNMANNED AERIAL VEHICLE
COMPUTATIONAL SIMULATION OF THE FLOW PAST AN AIRFOIL FOR AN UNMANNED AERIAL VEHICLE L. Velázquez-Araque 1 and J. Nožička 2 1 Division of Thermal fluids, Department of Mechanical Engineering, National University
More informationFluid Mechanics Prof. T. I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay
Fluid Mechanics Prof. T. I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay Lecture No. # 35 Boundary Layer Theory and Applications Welcome back to the video course on fluid
More informationLecture-4. Flow Past Immersed Bodies
Lecture-4 Flow Past Immersed Bodies Learning objectives After completing this lecture, you should be able to: Identify and discuss the features of external flow Explain the fundamental characteristics
More informationUNIT IV BOUNDARY LAYER AND FLOW THROUGH PIPES Definition of boundary layer Thickness and classification Displacement and momentum thickness Development of laminar and turbulent flows in circular pipes
More informationANALYSIS OF HORIZONTAL AXIS WIND TURBINES WITH LIFTING LINE THEORY
ANALYSIS OF HORIZONTAL AXIS WIND TURBINES WITH LIFTING LINE THEORY Daniela Brito Melo daniela.brito.melo@tecnico.ulisboa.pt Instituto Superior Técnico, Universidade de Lisboa, Portugal December, 2016 ABSTRACT
More informationA comparison of velocity and potential based boundary element methods for the analysis of steady 2D flow around foils
A comparison of velocity and potential based boundary element methods for the analysis of steady 2D flow around foils G.B. Vaz, L. E a, J.A.C. Falcao de Campos Department of Mechanical Engineering, Institute
More informationAE301 Aerodynamics I UNIT B: Theory of Aerodynamics
AE301 Aerodynamics I UNIT B: Theory of Aerodynamics ROAD MAP... B-1: Mathematics for Aerodynamics B-: Flow Field Representations B-3: Potential Flow Analysis B-4: Applications of Potential Flow Analysis
More informationFluid Mechanics II 3 credit hour. External flows. Course teacher Dr. M. Mahbubur Razzaque Professor Department of Mechanical Engineering BUET 1
COURSE NUMBER: ME 323 Fluid Mechanics II 3 credit hour External flows Course teacher Dr. M. Mahbubur Razzaque Professor Department of Mechanical Engineering BUET 1 External flows The study of external
More informationFluid Dynamics: Theory, Computation, and Numerical Simulation Second Edition
Fluid Dynamics: Theory, Computation, and Numerical Simulation Second Edition C. Pozrikidis m Springer Contents Preface v 1 Introduction to Kinematics 1 1.1 Fluids and solids 1 1.2 Fluid parcels and flow
More informationCOURSE ON VEHICLE AERODYNAMICS Prof. Tamás Lajos University of Rome La Sapienza 1999
COURSE ON VEHICLE AERODYNAMICS Prof. Tamás Lajos University of Rome La Sapienza 1999 1. Introduction Subject of the course: basics of vehicle aerodynamics ground vehicle aerodynamics examples in car, bus,
More informationAn Internet Book on Fluid Dynamics. Joukowski Airfoils
An Internet Book on Fluid Dynamics Joukowski Airfoils One of the more important potential flow results obtained using conformal mapping are the solutions of the potential flows past a family of airfoil
More informationGiven a stream function for a cylinder in a uniform flow with circulation: a) Sketch the flow pattern in terms of streamlines.
Question Given a stream function for a cylinder in a uniform flow with circulation: R Γ r ψ = U r sinθ + ln r π R a) Sketch the flow pattern in terms of streamlines. b) Derive an expression for the angular
More informationAerodynamics. Professor: Luís Eça
Aerodynamics Professor: Luís Eça Program 1. Introduction Aerodynamical forces. Flow description. Dependent variables and physical principles that govern the flow Program 2. Incompressible, Viscous Flow
More informationShape Optimization of Low Speed Airfoils using MATLAB and Automatic Differentiation. Christian Wauquiez
Shape Optimization of Low Speed Airfoils using MATLAB and Automatic Differentiation Christian Wauquiez Stockholm 2000 Licentiate s Thesis Royal Institute of Technology Department of Numerical Analysis
More informationDrag Computation (1)
Drag Computation (1) Why drag so concerned Its effects on aircraft performances On the Concorde, one count drag increase ( C D =.0001) requires two passengers, out of the 90 ~ 100 passenger capacity, be
More informationIncompressible Flow Over Airfoils
Chapter 7 Incompressible Flow Over Airfoils Aerodynamics of wings: -D sectional characteristics of the airfoil; Finite wing characteristics (How to relate -D characteristics to 3-D characteristics) How
More informationAerodynamics. Professor: Luís Eça
Professor: Luís Eça 1. Introduction Aerodynamical forces. Flow description. Dependent variables and physical principles that govern the flow 2. Incompressible, Viscous Flow Analytical solutions of the
More informationFLUID MECHANICS. Chapter 9 Flow over Immersed Bodies
FLUID MECHANICS Chapter 9 Flow over Immersed Bodies CHAP 9. FLOW OVER IMMERSED BODIES CONTENTS 9.1 General External Flow Characteristics 9.3 Drag 9.4 Lift 9.1 General External Flow Characteristics 9.1.1
More informationAerodynamics. Lecture 1: Introduction - Equations of Motion G. Dimitriadis
Aerodynamics Lecture 1: Introduction - Equations of Motion G. Dimitriadis Definition Aerodynamics is the science that analyses the flow of air around solid bodies The basis of aerodynamics is fluid dynamics
More informationSome Basic Plane Potential Flows
Some Basic Plane Potential Flows Uniform Stream in the x Direction A uniform stream V = iu, as in the Fig. (Solid lines are streamlines and dashed lines are potential lines), possesses both a stream function
More informationAerodynamic force analysis in high Reynolds number flows by Lamb vector integration
Aerodynamic force analysis in high Reynolds number flows by Lamb vector integration Claudio Marongiu, Renato Tognaccini 2 CIRA, Italian Center for Aerospace Research, Capua (CE), Italy E-mail: c.marongiu@cira.it
More informationUnsteady Viscous-Inviscid Interaction Technique for Wind Turbine Airfoils. PhD Thesis
Unsteady Viscous-Inviscid Interaction Technique for Wind Turbine Airfoils PhD Thesis Néstor Ramos García DCAMM Special Report no. S7 April MEK-PHD -4 Unsteady Viscous-Inviscid Interaction Technique for
More informationThe E80 Wind Tunnel Experiment the experience will blow you away. by Professor Duron Spring 2012
The E80 Wind Tunnel Experiment the experience will blow you away by Professor Duron Spring 2012 Objectives To familiarize the student with the basic operation and instrumentation of the HMC wind tunnel
More informationIran University of Science & Technology School of Mechanical Engineering Advance Fluid Mechanics
1. Consider a sphere of radius R immersed in a uniform stream U0, as shown in 3 R Fig.1. The fluid velocity along streamline AB is given by V ui U i x 1. 0 3 Find (a) the position of maximum fluid acceleration
More informationMomentum (Newton s 2nd Law of Motion)
Dr. Nikos J. Mourtos AE 160 / ME 111 Momentum (Newton s nd Law of Motion) Case 3 Airfoil Drag A very important application of Momentum in aerodynamics and hydrodynamics is the calculation of the drag of
More informationChapter 9 Flow over Immersed Bodies
57:00 Mechanics of Fluids and Transport Processes Chapter 9 Professor Fred Stern Fall 009 1 Chapter 9 Flow over Immersed Bodies Fluid flows are broadly categorized: 1. Internal flows such as ducts/pipes,
More informationAA210A Fundamentals of Compressible Flow. Chapter 1 - Introduction to fluid flow
AA210A Fundamentals of Compressible Flow Chapter 1 - Introduction to fluid flow 1 1.2 Conservation of mass Mass flux in the x-direction [ ρu ] = M L 3 L T = M L 2 T Momentum per unit volume Mass per unit
More informationLift Enhancement on Unconventional Airfoils
Lift Enhancement on nconventional Airfoils W.W.H. Yeung School of Mechanical and Aerospace Engineering Nanang Technological niversit, North Spine (N3), Level 2 50 Nanang Avenue, Singapore 639798 mwheung@ntu.edu.sg
More informationAerodynamics. Airfoils Kármán-Treftz mapping. The exponent k defines the internal angle of the trailing edge, τ, from. ( k)
z = b Aerodynamics Kármán-Treftz mapping ( ζ + b) + ( ζ b) ( ζ + b) ( ζ b) The eponent defines the internal angle of the trailing edge, τ, from ( ) τ = π = = corresponds to the Jouowsi mapping z z + b
More informationE80. Fluid Measurement The Wind Tunnel Lab. Experimental Engineering.
Fluid Measurement The Wind Tunnel Lab http://twistedsifter.com/2012/10/red-bull-stratos-space-jump-photos/ Feb. 13, 2014 Outline Wind Tunnel Lab Objectives Why run wind tunnel experiments? How can we use
More informationContents. I Introduction 1. Preface. xiii
Contents Preface xiii I Introduction 1 1 Continuous matter 3 1.1 Molecules................................ 4 1.2 The continuum approximation.................... 6 1.3 Newtonian mechanics.........................
More informationAirfoils and Wings. Eugene M. Cliff
Airfoils and Wings Eugene M. Cliff 1 Introduction The primary purpose of these notes is to supplement the text material related to aerodynamic forces. We are mainly interested in the forces on wings and
More informationWings and Bodies in Compressible Flows
Wings and Bodies in Compressible Flows Prandtl-Glauert-Goethert Transformation Potential equation: 1 If we choose and Laplace eqn. The transformation has stretched the x co-ordinate by 2 Values of at corresponding
More informationExplicit algebraic Reynolds stress models for internal flows
5. Double Circular Arc (DCA) cascade blade flow, problem statement The second test case deals with a DCA compressor cascade, which is considered a severe challenge for the CFD codes, due to the presence
More informationAll that begins... peace be upon you
All that begins... peace be upon you Faculty of Mechanical Engineering Department of Thermo Fluids SKMM 2323 Mechanics of Fluids 2 «An excerpt (mostly) from White (2011)» ibn Abdullah May 2017 Outline
More informationTHE EFFECT OF INTERNAL ACOUSTIC EXCITATION ON THE AERODYNAMIC CHARACTERISTICS OF AIRFOIL AT HIGH ANGLE OF ATTACKE
Vol.1, Issue.2, pp-371-384 ISSN: 2249-6645 THE EFFECT OF INTERNAL ACOUSTIC EXCITATION ON THE AERODYNAMIC CHARACTERISTICS OF AIRFOIL AT HIGH ANGLE OF ATTACKE Dr. Mohammed W. Khadim Mechanical Engineering
More informationUnsteady Aerodynamic Vortex Lattice of Moving Aircraft. Master thesis
Unsteady Aerodynamic Vortex Lattice of Moving Aircraft September 3, 211 Master thesis Author: Enrique Mata Bueso Supervisors: Arthur Rizzi Jesper Oppelstrup Aeronautical and Vehicle engineering department,
More informationAE 2020: Low Speed Aerodynamics. I. Introductory Remarks Read chapter 1 of Fundamentals of Aerodynamics by John D. Anderson
AE 2020: Low Speed Aerodynamics I. Introductory Remarks Read chapter 1 of Fundamentals of Aerodynamics by John D. Anderson Text Book Anderson, Fundamentals of Aerodynamics, 4th Edition, McGraw-Hill, Inc.
More informationOffshore Hydromechanics Module 1
Offshore Hydromechanics Module 1 Dr. ir. Pepijn de Jong 4. Potential Flows part 2 Introduction Topics of Module 1 Problems of interest Chapter 1 Hydrostatics Chapter 2 Floating stability Chapter 2 Constant
More informationHow Do Wings Generate Lift?
How Do Wings Generate Lift? 1. Popular Myths, What They Mean and Why They Work M D Deshpande and M Sivapragasam How lift is generated by a moving wing is understood satisfactorily. But the rigorous explanation
More informationThin airfoil theory. Chapter Compressible potential flow The full potential equation
hapter 4 Thin airfoil theory 4. ompressible potential flow 4.. The full potential equation In compressible flow, both the lift and drag of a thin airfoil can be determined to a reasonable level of accuracy
More informationComplex functions in the theory of 2D flow
Complex functions in the theory of D flow Martin Scholtz Institute of Theoretical Physics Charles University in Prague scholtz@utf.mff.cuni.cz Faculty of Transportation Sciences Czech Technical University
More informationR09. d water surface. Prove that the depth of pressure is equal to p +.
Code No:A109210105 R09 SET-1 B.Tech II Year - I Semester Examinations, December 2011 FLUID MECHANICS (CIVIL ENGINEERING) Time: 3 hours Max. Marks: 75 Answer any five questions All questions carry equal
More informationGeneral Solution of the Incompressible, Potential Flow Equations
CHAPTER 3 General Solution of the Incompressible, Potential Flow Equations Developing the basic methodology for obtaining the elementary solutions to potential flow problem. Linear nature of the potential
More informationTheory of turbo machinery. Chapter 3
Theory of turbo machinery Chapter 3 D cascades Let us first understand the facts and then we may seek the causes. (Aristotle) D cascades High hub-tip ratio (of radii) negligible radial velocities D cascades
More informationBoundary-Layer Theory
Hermann Schlichting Klaus Gersten Boundary-Layer Theory With contributions from Egon Krause and Herbert Oertel Jr. Translated by Katherine Mayes 8th Revised and Enlarged Edition With 287 Figures and 22
More informationApplied Fluid Mechanics
Applied Fluid Mechanics 1. The Nature of Fluid and the Study of Fluid Mechanics 2. Viscosity of Fluid 3. Pressure Measurement 4. Forces Due to Static Fluid 5. Buoyancy and Stability 6. Flow of Fluid and
More informationPEMP ACD2501. M.S. Ramaiah School of Advanced Studies, Bengaluru
Aircraft Aerodynamics Session delivered by: Mr. Ramjan Pathan 1 Session Objectives At the end of this session students would have understood Basics of Fluid Mechanics Definition of fluid, Fluid flow applications
More informationMath 575-Lecture Failure of ideal fluid; Vanishing viscosity. 1.1 Drawbacks of ideal fluids. 1.2 vanishing viscosity
Math 575-Lecture 12 In this lecture, we investigate why the ideal fluid is not suitable sometimes; try to explain why the negative circulation appears in the airfoil and introduce the vortical wake to
More informationTME225 Learning outcomes 2018: week 1
J. TME225 Learning outcomes 2018 360 J TME225 Learning outcomes 2018 Note that the questions related to the movies are not part of the learning outcomes. They are included to enhance you learning and understanding.
More informationDepartment of Energy Sciences, LTH
Department of Energy Sciences, LTH MMV11 Fluid Mechanics LABORATION 1 Flow Around Bodies OBJECTIVES (1) To understand how body shape and surface finish influence the flow-related forces () To understand
More informationDAY 19: Boundary Layer
DAY 19: Boundary Layer flat plate : let us neglect the shape of the leading edge for now flat plate boundary layer: in blue we highlight the region of the flow where velocity is influenced by the presence
More informationDay 24: Flow around objects
Day 24: Flow around objects case 1) fluid flowing around a fixed object (e.g. bridge pier) case 2) object travelling within a fluid (cars, ships planes) two forces are exerted between the fluid and the
More informationDetailed Outline, M E 320 Fluid Flow, Spring Semester 2015
Detailed Outline, M E 320 Fluid Flow, Spring Semester 2015 I. Introduction (Chapters 1 and 2) A. What is Fluid Mechanics? 1. What is a fluid? 2. What is mechanics? B. Classification of Fluid Flows 1. Viscous
More informationAn alternative approach to integral equation method based on Treftz solution for inviscid incompressible flow
An alternative approach to integral equation method based on Treftz solution for inviscid incompressible flow Antonio C. Mendes, Jose C. Pascoa Universidade da Beira Interior, Laboratory of Fluid Mechanics,
More informationROAD MAP... D-1: Aerodynamics of 3-D Wings D-2: Boundary Layer and Viscous Effects D-3: XFLR (Aerodynamics Analysis Tool)
AE301 Aerodynamics I UNIT D: Applied Aerodynamics ROAD MAP... D-1: Aerodynamics o 3-D Wings D-2: Boundary Layer and Viscous Eects D-3: XFLR (Aerodynamics Analysis Tool) AE301 Aerodynamics I : List o Subjects
More informationFundamentals of Airplane Flight Mechanics
David G. Hull Fundamentals of Airplane Flight Mechanics With 125 Figures and 25 Tables y Springer Introduction to Airplane Flight Mechanics 1 1.1 Airframe Anatomy 2 1.2 Engine Anatomy 5 1.3 Equations of
More informationHigh Speed Aerodynamics. Copyright 2009 Narayanan Komerath
Welcome to High Speed Aerodynamics 1 Lift, drag and pitching moment? Linearized Potential Flow Transformations Compressible Boundary Layer WHAT IS HIGH SPEED AERODYNAMICS? Airfoil section? Thin airfoil
More informationTHE VORTEX PANEL METHOD
THE VORTEX PANEL METHOD y j m α V 4 3 2 panel 1 a) Approimate the contour of the airfoil by an inscribed polygon with m sides, called panels. Number the panels clockwise with panel #1 starting on the lower
More informationA. Bottaro, D. Venkataraman & F. Negrello Università di Genova, Italy
A. Bottaro, D. Venkataraman & F. Negrello Università di Genova, Italy A. Bottaro, D. Venkataraman & F. Negrello & G. Tadmor Università di Genova, Italy Focus on passive actuators, what works, why it does,
More informationPart 3. Stability and Transition
Part 3 Stability and Transition 281 Overview T. Cebeci 1 Recent interest in the reduction of drag of underwater vehicles and aircraft components has rekindled research in the area of stability and transition.
More informationFLIGHT DYNAMICS. Robert F. Stengel. Princeton University Press Princeton and Oxford
FLIGHT DYNAMICS Robert F. Stengel Princeton University Press Princeton and Oxford Preface XV Chapter One Introduction 1 1.1 ELEMENTS OF THE AIRPLANE 1 Airframe Components 1 Propulsion Systems 4 1.2 REPRESENTATIVE
More informationa) Derive general expressions for the stream function Ψ and the velocity potential function φ for the combined flow. [12 Marks]
Question 1 A horizontal irrotational flow system results from the combination of a free vortex, rotating anticlockwise, of strength K=πv θ r, located with its centre at the origin, with a uniform flow
More informationDetailed Outline, M E 521: Foundations of Fluid Mechanics I
Detailed Outline, M E 521: Foundations of Fluid Mechanics I I. Introduction and Review A. Notation 1. Vectors 2. Second-order tensors 3. Volume vs. velocity 4. Del operator B. Chapter 1: Review of Basic
More informationBLUFF-BODY AERODYNAMICS
International Advanced School on WIND-EXCITED AND AEROELASTIC VIBRATIONS OF STRUCTURES Genoa, Italy, June 12-16, 2000 BLUFF-BODY AERODYNAMICS Lecture Notes by Guido Buresti Department of Aerospace Engineering
More informationChapter 9. Flow over Immersed Bodies
Chapter 9 Flow over Immersed Bodies We consider flows over bodies that are immersed in a fluid and the flows are termed external flows. We are interested in the fluid force (lift and drag) over the bodies.
More informationFLUID MECHANICS. Atmosphere, Ocean. Aerodynamics. Energy conversion. Transport of heat/other. Numerous industrial processes
SG2214 Anders Dahlkild Luca Brandt FLUID MECHANICS : SG2214 Course requirements (7.5 cr.) INL 1 (3 cr.) 3 sets of home work problems (for 10 p. on written exam) 1 laboration TEN1 (4.5 cr.) 1 written exam
More informationAeroelasticity. Lecture 7: Practical Aircraft Aeroelasticity. G. Dimitriadis. AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7
Aeroelasticity Lecture 7: Practical Aircraft Aeroelasticity G. Dimitriadis AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 7 1 Non-sinusoidal motion Theodorsen analysis requires that
More informationACD2503 Aircraft Aerodynamics
ACD2503 Aircraft Aerodynamics Session delivered by: Prof. M. D. Deshpande 1 Aims and Summary PEMP It is intended dto prepare students for participation i i in the design process of an aircraft and its
More informationFundamentals of Aerodynamics
Fundamentals of Aerodynamics Fourth Edition John D. Anderson, Jr. Curator of Aerodynamics National Air and Space Museum Smithsonian Institution and Professor Emeritus University of Maryland Me Graw Hill
More informationNumerical Simulation of Unsteady Aerodynamic Coefficients for Wing Moving Near Ground
ISSN -6 International Journal of Advances in Computer Science and Technology (IJACST), Vol., No., Pages : -7 Special Issue of ICCEeT - Held during -5 November, Dubai Numerical Simulation of Unsteady Aerodynamic
More informationVORTEX METHOD APPLICATION FOR AERODYNAMIC LOADS ON ROTOR BLADES
EWEA 2013: Europe s Premier Wind Energy Event, Vienna, 4-7 February 2013 Figures 9, 10, 11, 12 and Table 1 corrected VORTEX METHOD APPLICATION FOR AERODYNAMIC LOADS ON ROTOR BLADES Hamidreza Abedi *, Lars
More informationPPT ON LOW SPEED AERODYNAMICS B TECH IV SEMESTER (R16) AERONAUTICAL ENGINEERING. Prepared by Dr. A. Barai. Mr. N. Venkata Raghavendra
PPT ON LOW SPEED AERODYNAMICS B TECH IV SEMESTER (R16) AERONAUTICAL ENGINEERING Prepared by Dr. A. Barai Professor Mr. N. Venkata Raghavendra Associate Professor INSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous)
More informationAERODYNAMICS STUDY NOTES UNIT I REVIEW OF BASIC FLUID MECHANICS. Continuity, Momentum and Energy Equations. Applications of Bernouli s theorem
AERODYNAMICS STUDY NOTES UNIT I REVIEW OF BASIC FLUID MECHANICS. Continuity, Momentum and Energy Equations. Applications of Bernouli s theorem UNIT II TWO DIMENSIONAL FLOWS Complex Potential, Point Source
More informationChapter 9 Flow over Immersed Bodies
57:00 Mechanics of Fluids and Transport Processes Chapter 9 Professor Fred Stern Fall 014 1 Chapter 9 Flow over Immersed Bodies Fluid flows are broadly categorized: 1. Internal flows such as ducts/pipes,
More informationFUNDAMENTALS OF AERODYNAMICS
*A \ FUNDAMENTALS OF AERODYNAMICS Second Edition John D. Anderson, Jr. Professor of Aerospace Engineering University of Maryland H ' McGraw-Hill, Inc. New York St. Louis San Francisco Auckland Bogota Caracas
More information