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  • Aeroelasticity and Structural Dynamics Research Laboratory

    Coupled Nonlinear Aeroelasticity and Flight Dynamics of Highly Flexible

    AircraftWeihua Su

    Assistant ProfessorDepartment of Aerospace Engineering and Mechanics

    The University of AlabamaTuscaloosa, AL

    Applied Modeling & Simulation Seminar Series NASA Ames Research Center

    Moffett Field, CAAug. 27, 2014

  • Aeroelasticity and Structural Dynamics Research Laboratory

    Overview

    Introduction Background Motivation

    Theoretical formulation Geometrically nonlinear beam Unsteady aerodynamics Flight dynamic modeling

    Numerical studies Concluding remarks Ongoing and future developments

    2

  • Aeroelasticity and Structural Dynamics Research Laboratory

    Aerodynamic Efficiency andWing Aspect-Ratio

    3

    F-22aAR = 2.36

    ETA (Germany)AR = 51.33

    B787-8AR = 11.08

    0

    1

    or ln WLR ED W

    Large wing aspect-ratio to achieve high aerodynamic efficiency

    High aerodynamic efficiency

  • Aeroelasticity and Structural Dynamics Research Laboratory

    What about Structural Design?

    U.S. Air Force Sensorcraft studies High-altitude, long-endurance Unmanned vehicles Sensor platform Very high fuel fractions (up to 60%)

    Very light structures Not necessarily carry fuel, but

    4

    AeroVironments Helios>24 hrs

    0

    1

    or ln WLR ED W

    Highly flexible aircraft

    Low structural weight fraction

    High-aspect-ratio wings

    +

  • Aeroelasticity and Structural Dynamics Research Laboratory

    Whats Challenging?

    Large wing deformation Linear solution might not be sufficient Nonlinear solution needed

    Coupling between wing oscillation and rigid-body motion Coupled transient response Body freedom flutter

    Other effects Low Reynolds flights Local transonic effects

    5

    Need an integral solution for nonlinear aeroelasticity + flight dynamics

  • Aeroelasticity and Structural Dynamics Research Laboratory

    Objectives

    Create a low-order aeroelastic and flight dynamic framework Effectively represent dynamic behavior of highly flexible vehicle Efficient solution Facilitate active aeroelastic tailoring and control studies

    Explore structural, aerodynamic, and control techniques to enhance flight efficiency and performance Reduce drag Reduce power consumption Suppress instability Reject air disturbance

    6

  • Aeroelasticity and Structural Dynamics Research Laboratory

    Coupled Nonlinear Aeroelasticity and Flight Dynamics

    7

    CoupledAeroelasticity &Flight Dynamics

    Reduced-order Wing bending / twist Airfoil camber d.o.f.

    Geometrically Nonlinear BeamGeometrically

    Nonlinear Beam

    Structural DynamicsStructural Dynamics

    Composites Active materials

    Cross-Sectional Analysis

    Cross-Sectional Analysis

    Solid Mechanics

    Solid Mechanics

    Potential flow theory 3-D corrections Stall models Gust/turbulence models

    Finite-State Inflow TheoryFinite-State

    Inflow Theory

    AerodynamicsAerodynamics

    Rigid-Body DynamicsRigid-Body Dynamics

    Flight Dynamics

    Flight Dynamics

    A simplified aeroelastic/flight dynamics simulation system

  • Aeroelasticity and Structural Dynamics Research Laboratory

    Reduced-Order Structural Modeling

    From 3D elastic problem to 2D beam cross-sectional analysis and 1D beam model

    Dimensional reduction using the Variational-Asymptotic Method: Active thin-walled solution (mid-line discretization) VABS (finite-element discretization) User defined stiffness constants

    8

    X YZX YZ

    11 12 13 14

    21 22 23 24

    31 32 33 34

    41 42 43 44

    x x

    x x

    y y

    z z

    F K K K KM K K K KM K K K K

    K K K KM

    Cross-Section Stiffness and Inertial Properties

  • Aeroelasticity and Structural Dynamics Research Laboratory

    Basic Coordinate Systems

    Global frame (G) Body frame (B) origin not

    necessary to be C.G. of vehicle Body frame motion variables

    Local beam frame (w) Auxiliary local frame (b)

    9

    B

    B

    B B

    B B

    B B

    B B

    pb

    p vb

    p vb

  • Aeroelasticity and Structural Dynamics Research Laboratory

    Strained-Based Geometrically Nonlinear Beam Formulation

    Geometrically nonlinear beam formulation[1]

    Four local strain degrees-of-freedom (): extension, twist, flatwise bending, and chordwise bending

    Constant-strain elements Capture large complex deformations with fewer

    elements computationally efficient Isotropic and anisotropic constitutive relations

    10

    [1] Su, W., and Cesnik, C.E.S., Strain-Based Geometrically Nonlinear Beam Formulation for Modeling Very Flexible Aircraft, International Journal of Solids and Structures, Vol. 48, No. 16-17, 2011, pp. 2349-2360. (doi: 10.1016/j.ijsolstr.2011.04.012)

    Sample element deformations with constant strain

    Strains () and body velocities ()are independent variables

  • Aeroelasticity and Structural Dynamics Research Laboratory

    Formulation Based on Principle of Virtual Work

    11

    0

    ( ) ( ) ( , , ) ( , , ) 0( ) ( ) ( , , ) ( , , ) 0 0

    0

    FF FB FF FB FFF

    BF BB BF BB B

    TT TF p F disthFF

    TTB pbhb

    M M C C RKM M C C Rb

    R JJ JKNg B F

    R JJ

    T TpM dist pt ptTT Tpbb b

    J JB M F M

    JJ J

    0ii

    W

    Equations of Motion

    Generalized Mass Generalized Damping Generalized Stiffness

    Generalized Force

    Internal VW External VW

    +

    Inertia force, internal strain, and strain rate Gravity loads, distributed loads, and point

    loads

  • Aeroelasticity and Structural Dynamics Research Laboratory

    Recovery of Nodal Displacement

    Solution of displacement-strain equation:

    Marching kinematics in complete aircraft

    12

    0( ) ( )0 0

    ( ) ( ) ( )

    ( ) A s s s G s

    h s A s h ss

    h s e h e h

    Prescribed root

    s0, h0

    s, h(t)

    B Frame

    B.C.

  • Aeroelasticity and Structural Dynamics Research Laboratory

    Unsteady Aerodynamics

    2-D Theodorsen-like unsteady aerodynamics (Peters et al., 94, 95)

    Glauert expansion of inflow velocityas function of inflow states, n

    Finite state differential equation is transformed to independent variables and

    13

    2 2 20 1

    2 2 2 20 4

    12 22

    1 28

    mc

    mc

    zl b z y d by b d bc yy y y

    m b b yz dy y b c y

    Inflow velocity

    01

    12 n nn

    b

    1 2 3 4 1 2 3E E z E E F F F

  • Aeroelasticity and Structural Dynamics Research Laboratory

    Finite-State Inflow Theory: Modifications

    Aerodynamic coefficient modifications based on XFoil (Re effects) or CFD calculations

    Compressibility accounted for by Prandtl-Glauert correction

    Spanwise aerodynamic corrections(3-D effects)

    Simplified stall model

    14

    Additional aerodynamic development in progress

  • Aeroelasticity and Structural Dynamics Research Laboratory

    Fixed region in space Amplitude distribution

    Peak at center and zero at boundary Possibly different distribution in East

    and North directions Smooth transition

    Time variation: 1-cosine withdifferent temporal durations

    Discrete Non-uniform Gust Model15

    2 21( , , ) 1 cos 2 cos sin2 c E Ng

    tA r t A A At

    00 0

    ( ) sin 1 , ( ) sin 1 , 02 2

    E Nn n

    E Nr rA r A r r rr r

  • Aeroelasticity and Structural Dynamics Research Laboratory

    Dryden Gust Model

    Gust PSD function

    m: Frequency component (rad/s) U0: Free stream velocity (m/s) Lw: Scale of turbulence (m), determined by altitude (m) Superposition of all frequency components with random phase

    16

    22

    0

    22

    00

    1 3

    ( )

    1

    w mw w

    w m

    w m

    LLU

    LUU

    22

    0

    22

    00

    2 1 12

    ( )

    1 4

    w mw w

    w m

    w m

    LLU

    LUU

    1

    ( ) ( ) cos( )w m m mm

    w t t

    MIL-F-8785C MIL-HDBK-1797

  • Aeroelasticity and Structural Dynamics Research Laboratory

    PSD and Time History of Gust Velocity

    Frequency band [0.1~6] Hz adjusted to obtain enough

    wing deformation Uniform spanwise distribution

    17

    w

    Power concentrated at the lowfrequency range

  • Aeroelasticity and Structural Dynamics Research Laboratory

    Flight Dynamics Modeling18

    The trajectory and orientation of a fixed body reference frame, B, at point O, which in general is not the aircrafts center of mass

  • Aeroelasticity and Structural Dynamics Research Laboratory

    Full Air Vehicle Model for Flight Simulations

    Elastic equations of motion

    Finite-state 2-D unsteady aerodynamics

    Body reference frame propagation

    19

    ( ) ( ) ( )M C , , K R , , , , , , ,ub

    1 2 3F F F

    Strains (4 by m structural d.o.f.)

    Body velocities (6 flight dynamic d.o.f.)

    Inflow states (N by m aerodynamic d.o.f.)

    Control inputs

    12

    0GBBP C

    Inertial velocities (6 d.o.f.)

    Frame orientation(4 quaternions)

  • Aeroelasticity and Structural Dynamics Research Laboratory

    Numerical Studies

    20

  • Aeroelasticity and Structural Dynamics Research Laboratory

    Flutter of Constrained Vehicle

    Similar to constrained wind-tunnel model (no body DOFs) Fixed root angle of attack (8 deg) Free stream velocity 1% higher than flutter speed

    21

    Coupled out-of-plan