Purdue Aeroelasticity AAE 556 Aeroelasticity Lecture 15 Finite element subsonic aeroelastic models I like algebra Algebra is my friend. Purdue Aeroelasticity

Lift computation idealizations Purdue Aeroelasticity

Purdue Aeroelasticity Everything you wanted to know about aerodynamics but were afraid to ask Lift per unit length l(y) changes along the span of a 3-D wing The 2-D lift curve slope is not the same as the 3-D lift curve slope Lift curve slope in degrees e = Oswald’s efficiency factor Purdue Aeroelasticity

Purdue Aeroelasticity Lift Purdue Aeroelasticity

Aerodynamic strip theory Wing is sub-divided into a set of small spanwise strips The lift and pitching moment on each strip is modeled as if the strip had infinite span There is no aerodynamic interaction There is limited or no aerodynamic influence between elements Purdue Aeroelasticity

Purdue Aeroelasticity Paneling methods The wing is replaced by a thin surface This surface is replaced by a finite number of elements or panels with aerodynamic features such as singularities There is an aerodynamic influence coefficient matrix with interactive elements Purdue Aeroelasticity

Strip theory gives different results Source: G. Dimitriadis, University of Liege Purdue Aeroelasticity

Purdue Aeroelasticity Background Gray and Schenk NACA TN-3030 1952 Adapted for composites 1978 Purdue Aeroelasticity

Paneling - idealization requirements and limitations Purdue Aeroelasticity

Panel aero model finding the lift distribution pi=rVGi Purdue Aeroelasticity

Lifting line wing model Horseshoe vortices with varying strength bound at 1/4 chord points Downwash matching points at 3/4 chord trailing vortices extending to infinity The wing can be unswept or have non-constant chord Purdue Aeroelasticity

Purdue Aeroelasticity Panel aerodynamics interacts because of downwash (angle of attack) matching Each horseshoe vortex creates a flow field around it. The 3/4 chord downwash is affected by every other vortex on the wing. The vortex strengths must be adjusted so that all conditions are satisfied. Vortex influence decays with distance Purdue Aeroelasticity

Aerodynamic relationship Solving for vortex strengths allow us to approximate the lift distribution wing Relationship between local angle of attack and segment lift values. Purdue Aeroelasticity

Aero matrix equation development Matrix is square, but not symmetrical ai=arigid + qstructural + acontrol Matrix elements are functions of wing planform geometry 2D lift curve slope Purdue Aeroelasticity

Structural idealization Purdue Aeroelasticity

Each panel has its own FBD and panel geometry Purdue Aeroelasticity

Purdue Aeroelasticity Put them all together to get the static equilibrium equations – this is where the aeroelastic interaction occurs local angles lift on each element dynamic pressure Purdue Aeroelasticity

Purdue Aeroelasticity Wing Geometry Purdue Aeroelasticity

Purdue Aeroelasticity Flexible and Rigid lift distributions (M=0.5) areas under each curve are equal Purdue Aeroelasticity

Flexible and Rigid lift distribution (M=0.6) Purdue Aeroelasticity

Rigid and flexible roll effectiveness (pb/2V) MRev= 0.55 Purdue Aeroelasticity

Rigid wing and flexible wing Purdue Aeroelasticity

Divergence Mach number Divergence Mach No. = 0.590 Purdue Aeroelasticity

Purdue Aeroelasticity Summary Use of bound vortices creates a math model that can predict subsonic high aspect ratio wing lift distribution. This model has been incorporated into a MATLAB code that you will use to do some homework exercises to calculate divergence, lift effectiveness and control effectiveness. You will compare the trends previously derived Purdue Aeroelasticity