Aeroelasticity of a Helicopter Blade Using the Euler Equations

Introduction A CCIJRATE aeroelastic computations of helicopter rotor blades fL involve the use of high-fidelity fluids and structure models. Computing the flows that are dominated by shocks, waves, and blade-vortex interactions requires the use of three-dimensional (3-D) Euler/l.,lavier-Stokes (ENS) equations []. Because using the Navier-Stokes equations is computationally very expensive Il], the significantly less-expensive 3-D Euler (3DE) equations can be used for preliminary assessment of flow complexities such as shock waves and vortices. Reference [2] presented the first 3-D Fansonic aeroelastic computation of its kind for fixed wings by time-accurately OA) coupling the Euler flow equations of motion with the modal structural equations of motion. The work in [2] was based on the success of the original effort to TA couple 2-D unsteady potential flow equations with sfuctural equations, as reported in [3]. The current practice for aeroelastic computations of rotorcraft involves using precomputed displacements from rotorcraft comprehensive analysis methods [4] and iteratively correcting them in ad hoc fashion using loads from ENS or 3DE equations. Comprehensive analysis uses dependent parameters, such as measured thrust and aerodynamic lookup tables, to adjust the control angles for ENS computations [5]. The hybrid approach of combining comprehensive analysis with ENS/3DE, known as either loose coupling or delta coupling [4,5], is not mathematically valid [6], and it is not a correct procedure for time-dependent cases such as rotating blades [7]. The objective of this Note is to demonstrate the use of timeaccurate procedures for computing the aeroelasticiry of rotating blades in contrast with using existing hybrid methods. The aeroelastic responses are computed by TA integrating flow and structural equations following the procedure presented in [8]. Only independent flight parameters such as rotating speed, shaft angle, and conhol angles are used as input. This approach does not involve any tuning of the input parameters using lookup tables. Results are demonstrated for the isolated single blade ofa LIH-60A helicopter [9]. Fourier analysis is applied to compare data with flight tests.