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Unsteady Aerodynamic Vortex Lattice of Moving Aircraft

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Unsteady Aerodynamic Vortex Lattice of Moving Aircraft Unsteady Aerodynamic Vortex Lattice of Moving Aircraft September 30, 2011 Master thesis Supervisors: Author: Arthur Rizzi Enrique Mata Bueso Jesper Oppelstrup Aeronautical and Vehicle engineering department, KTH, Kungliga Tekniska H¨ogskolan SE-100 44 Stockholm, Sweden Contents 1 Introduction 1 1.1 CEASIOM............................................1 1.2 TORNADO, a brief overview..................................3 1.3 Linear Aerodynamics.......................................5 1.3.1 Steady Aerodynamics..................................6 1.3.2 Quasi-steady Aerodynamics...............................7 1.3.3 Unsteady Aerodynamics.................................7 2 Vortex Lattice Method9 2.1 Basics of fluid dynamics.....................................9 2.1.1 Kinematic concepts................................... 10 2.1.2 The Continuity Equation................................ 10 2.1.3 Bernoulli equation.................................... 11 2.2 Potential Flow Theory...................................... 11 2.2.1 Kelvin's circulation theorem............................... 11 2.2.2 Helmholtz theorems................................... 12 2.2.3 Kutta-Joukowsky theorem................................ 12 2.2.4 Boundary conditions................................... 13 2.2.5 Biot-Savart's Law.................................... 13 2.2.6 Horseshoe vortex..................................... 14 2.2.7 Vortex Rings....................................... 15 2.3 Classical Vortex Lattice Method................................ 15 2.4 Unsteady VLM, theoretical background............................ 17 3 ABSOLUT, the Computational Method 21 3.1 Code Structure.......................................... 22 3.2 Preprocessor........................................... 22 3.2.1 Inputs........................................... 23 3.2.2 Discretization....................................... 23 3.2.3 Lattice meshing...................................... 25 3.2.4 Airfoil........................................... 26 3.3 Processor, the solver....................................... 27 3.3.1 Kinematics........................................ 27 3.3.2 Influence coefficients and boundary conditions..................... 29 3.3.3 Forces and Moments................................... 29 3.3.4 Stability derivatives................................... 30 3.3.5 Wake treatment..................................... 30 3.3.6 Singularities in the solution............................... 32 4 Code Validation 33 4.1 Deflected Flap.......................................... 33 4.2 Sudden acceleration....................................... 34 4.3 Heaving motion.......................................... 35 4.4 Flapping flap........................................... 36 4.5 Bending wing........................................... 36 i Contents Contents 4.6 Discussion of results....................................... 37 5 Wind tunnel tests 39 5.1 F12 configuration......................................... 39 5.1.1 Steady results....................................... 40 5.1.2 Unsteady results..................................... 43 5.2 TCR-C15 configuration..................................... 43 5.2.1 Steady results....................................... 44 5.2.2 Unsteady results..................................... 47 5.3 Agreement between ABSOLUT and the experimental results................ 47 6 Conclusions 49 7 Acknowledgments 51 A Code structure 55 B Some remarks on the DLR-F12 tests 57 C Future work 59 C.1 C functions............................................ 59 C.2 Gust field............................................. 59 C.3 Aircraft propeller......................................... 59 C.4 Flexible wing........................................... 59 C.5 Aeroelasticity........................................... 59 ii Nomenclature D Aerodynamic drag. L Lift force. T Thrust. W Weight of the flying body. ∆pij Pressure on a panel of the lifting surface. c¯ Mean aerodynamic chord of the aircraft. V1 Free stream velocity. Γ Circulation. l Lift per unit width. C Velocity of the aircraft in the inertial system of reference V Velocity vector of the free-stream in the inertial system of reference Ω Angular frequency. Θ Rate angles vector ρ Air density. bref Span of the main wing of the aircraft. Also called reference span. g Gravity constant (9:81m=s2). k Reduced frequency k = Ωc 2V1 p Pressure. u Velocity of the aircraft in X-direction in the inertial frame of reference v Velocity of the aircraft in Y-direction in the inertial frame of reference w Velocity of the aircraft in Z-direction in the inertial frame of reference z Altitude. c¯ Mean aerodynamic chord of the aircraft. iii Contents Contents iv List of Figures 1.1 Overview of the different modules of CEASIOM........................2 1.2 Tornado's different views of the B-52..............................4 1.3 Vortex sling vs horseshoe vortex, [21]..............................4 1.4 Stall limit in a lift-angle of attack curve............................5 1.5 Compressibility effects on the drag according to Potential Flow theory...........6 1.6 Reference system according to CEASIOM definitions [8]...................6 2.1 Boundary layer velocity profile.................................9 2.2 Fixed and moving systems of reference, [15]........................... 10 2.3 Cross section of a stream tube.................................. 10 2.4 Stream tube............................................ 10 2.5 Representation of Kelvin's theorem............................... 12 2.6 Kutta-Joukowski......................................... 13 2.7 Kutta assumption for the wake shape near the trailing edge................. 13 2.8 Physical problem and mathematical model for a horseshoe vortex, [1]............ 14 2.9 Vortex ring definition...................................... 15 2.10 Classical vortex-lattice method, [35]............................... 16 2.11 Kinematics of the aircraft motion, [16].............................. 17 3.1 Unsteady Vortex lattice method for vortex rings....................... 21 3.2 Flow chart of the code...................................... 22 3.3 Flow chart of the Preprocessor................................. 23 3.4 Planform view of the main semi-wing of a B-747 model................... 23 3.5 Planform view of X31 VLM model discretized......................... 25 3.6 Lattice meshing for steady conditions............................. 25 3.7 Profile definition......................................... 26 3.8 Coordinates of X31-W1 airfoil.................................. 26 3.9 Wing's partition of the TCR-C15 VLM model......................... 27 3.10 Flow chart of solver....................................... 27 3.11 Wind's reference system according to CEASIOM definitions [8]............... 28 3.12 Flat wake for steady case, α = 25◦................................ 30 3.13 Rigid rings' wake after a sudden acceleration of a flat plate with k = 3, see section 3.3.6.. 31 3.14 Deformable rings' wake after a sudden acceleration of a flat plate with k = 0........ 31 4.1 Flat plate wing with swept back Λ = 35◦ ............................ 33 4.2 Pressure distribution for a deflection of 5.73° ......................... 34 4.3 Lift coefficient for sudden acceleration of a flatplate...................... 34 4.4 Lift coefficient for heaving motion of a flatplate at k = 0:5.................. 35 4.5 Chβ for a wing with an oscillatory flap............................. 36 4.6 Pressure distributions for an oscillating wing......................... 37 5.1 F12 model in wind tunnel.................................... 40 5.2 Lift coefficient variation for a sweep in α ............................ 40 5.3 Drag coefficient variation for a sweep in α ........................... 41 5.4 Pitch moment coefficient variation for a sweep in α ...................... 41 v List of Figures List of Figures 5.5 Lateral force coefficient variation for a sweep of the sideslip angle β ............. 42 5.6 Roll moment coefficient variation for a sweep of the sideslip angle β ............ 42 5.7 Yaw moment coefficient variation for a sweep of the sideslip angle β ............ 42 5.8 TCR general configuration.................................... 44 5.9 Normal force coefficient vs angle of attack at V1 = 40 m=s ................. 45 5.10 Pitch coefficient vs angle of attack at V1 = 40 m=s ...................... 45 5.11 Lateral force coefficient variation for a sweep of the sideslip angle β ............. 46 5.12 Roll moment coefficient variation for a sweep of the sideslip angle β ............ 46 5.13 Yaw moment coefficient variation for a sweep of the sideslip angle β ............ 46 ◦ 5.14 Lift coefficient variation with time for TCR-C15 in oscillatory pitch motion at α0 = 0 , ∆α = 3◦ and f = 1 Hz...................................... 47 5.15 Comparison between the TCR configuration and the DLR-F12............... 48 A.1 Code structure.......................................... 56 vi List of Tables 4.1 Sudden acceleration data.................................... 35 4.2 Heaving motion data....................................... 35 4.3 Flapping flap data........................................ 36 4.4 Bending wing data........................................ 37 5.1 Comparison of fundamental geometrical data of F12..................... 39 ◦ ◦ 5.2 Results for pitch motion test on F12 model for α0 = 0 , ∆α = 4:52 and f = 3 Hz .... 43 ◦ ◦ 5.3 Results for roll motion test on F12 model for α0 = 6 , ∆φ = 4:86 and f = 3 Hz ..... 43 ◦ ◦ 5.4 Results for yaw motion test on F12 model for α0 = 6 , ∆β = 4:32 and f = 3 Hz ....
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