The future of non-linear modelling of aeroelastic gust interaction

Transcription

1 The future of non-linear modelling of aeroelastic gust interaction C. J. A. Wales, C. Valente, R. G. Cook, A. L. Gaitonde, D. P. Jones, J. E. Cooper University of Bristol AVIATION, June 2018 Hyatt Regency Atlanta, Atlanta, Georgia

2 Outline Background Aerodynamic models DLM UVLM CFD Correction Methods Aeroelastic Coupling Results Generic UAV wing NASA CRM Generic UAV wing NASA CRM

3 Accuracy Funded by the Background Accurate gust loads modelling is essential for an optimal structural design. CFD-FEM analysis provide very accurate solutions, however the high cost make them too expensive to use for the numerous load cases required Gust Loads Simulations The current industrial standard for gust loads modelling is to use traditional potential flow models, due to there low cost. DLM* UVLM ROM CFD/FEM FSI Corrections are then applied to account for effects not included in the potential flow methods VLM DLM Computational Time

4 Corrections In industry DLM methods are corrected to match sectional loads typically from steady wind tunnel data. An unsteady correction method for DLM has been developed with the aim of increasing the accuracy of the loads estimation in the gust response analysis. UVLM aerodynamic model can be coupled with non linear structural model

5 DLM MSC.NASTRAN used for DLM calculations gust calculations Sol 146 Aeroelastic frequency response analysis in modal coordinates formulation: Mode Deformation Rigid Gust

6 UVLM code 3 Parts Vortex ring elements on body Layer of buffer panels in the wake Vortex particles in the wake Box method to speed up wake influence calculations Rigid body motions Deformations Gust interactions

7 UVLM code acceleration Calculating direct wake particle interaction is expensive O(n 2 ) Use octree data structure Particles far away agglomerated together to reduce number of particle interaction calculations required

8 8 CFD - Split Velocity Method Velocities are split into the prescribed gust components and the remaining velocity components Substituting into the Navier-Stokes equations and rearranging in terms of remaining velocity components leads to a set of equations similar to a moving mesh formulation plus source terms There are only gradients of the prescribed velocity in the source terms. Includes the interaction with the body Implemented in the Tau CFD solver u = u + u g v = v + v g w = w + w g Prescribed gust velocities Remaining velocity components Huntley, S., Jones, D., and Gaitonde, A. (2016). 2d and 3d gust response using a prescribed velocity method in viscous flows. In 46th AIAA Fluid Dynamics Conference, AIAA

9 DLM correction The loads on each DLM strip can be written as The aim is to correct the DLM so that it matches the loads from CFD Rewriting as F DLM = SA 1 w The difference between the uncorrected DLM and CFD can be written as Correction matrices can be solved for using a least squares approach F CFD = SA 1 Cw + C 0 F CFD = SA 1 I + ε w + C 0 F = SA 1 wε + C 0 Giesing, J., Kalman, T., and Rodden, W. P. (1976). Correction factory techniques for improving aerodynamic prediction methods. NASA CR

10 UVLM correction The UVLM equations can be written as Γ = Aw The loads on each UVLM strip can be written as F UVLM = SZΓ Appling the following correction matrices to the ULVM Γ = A(Cw + C 0 ) And equating the corrected UVLM to the CFD loads gives F CFD = SZA 1 Cw + SZA 1 C 0 This lead to the following equation for the correction factors F CFD = SZA 1 F = SZA 1 wε + SZC 0 I + ε w + SZA 1 C 0

11 UVLM correction process The corrected UVLM solves the following equations Γ = A(Cw + C 0 ) Where the downwash has two components w = w body + w wake The wake downwash depends on the strength of the shed vortex panels/particles. So the wake downwash changes with the correction matrices so the correction procedure has to be iterated

12 DLM Unsteady Correction Rigid Gust The sectional DLM loads on a due to the gust excitation can be written as F DLM = qw g PP ω Q(M, k)w(ω) The downwash contribution is a matrix defined as follow If the downwash is a sinusoidal gust excitation we can write F DLM = qw g Qw Applying a down wash correction so that the DLM matches a sinusoidal gust calculated with LFD F LFD = qw g QCw

13 DLM Unsteady Correction Rigid Gust Want the correction to be as close to the identity matrix as possible F LFD = qw g Q This simplifies to equation for the correction factor in terms of the difference between the uncorrected DLM and LFD I + ε ΔF = qw g Qwε At this point is possible to write a system where we decouple the real and imaginary parts ΔF Re = q Qw Re Qw Im ε Re ΔF Im Qw Im Qw Re ε Im Once the correction factors have been calculated, the AIC matrices in Nastran can be replaced with the corrected matrices. w

14 MSC NASTRAN time steps iteration steps Funded by the Aeroelastic Coupling Nastran coupled to external aerodynamic solvers through the OpenFSI interface Strong coupling used Nastran splining matrices used for the transfer of forces and displacements between the aerodynamic and structural meshes MSC Nastran Start initialize initializetime getwettednode Forces Spline Method Initial Mesh Deformation Tau/UVLM Solve to Steady State Tau/UVLM time step Tau/UVLM Nastran FE Solve putwettednode Displacements Mesh Deformation finalizetime terminate End Valente, C., Jones, D., Gaitonde, A., et al. (2015). Openfsi interface for strongly coupled steady and unsteady aeroelasticity. IFASD 2015, IFASD

15 Generic UAV Wing Unswept, untapered wing Span 25m Chord 2m Aerofoil NASA LRN 1015 Beam stick model for Structure Aircraft mass 7000kg

16 Generic UAV test cases Flight conditions Altitude 55000ft Mach 0.55 Rigid response The main goal is to focus on the gust response analysis of interest in a design process: With a design gust velocity given by : Aeroelastic response, wing clamped at root Gust Length (ft) Gust velocity (ft/s) Equivalent AoA (degrees) Steady DLM and UVLM corrections matching CFD at zero and two degrees DLM LFD correction at 19 reduced frequencies between and 4.000

17 Generic UAV gust response rigid 30ft 150ft 350ft

18 Generic UAV gust response rigid 30ft 150ft 350ft

19 Generic UAV gust response rigid 30ft 150ft 350ft

20 Generic UAV gust response aeroelastic 30ft 150ft 350ft

21 Generic UAV gust response aeroelastic 30ft 150ft 350ft

22 Generic UAV gust response aeroelastic 30ft 150ft 350ft

23 NASA Common Research Model NASA Common Research model, is a generic wide body aircraft[1] Span MAC 7m Structural model is a condensed beam stick version of the FERMAT structural model develop based on the NCRM[2] [1] J. C. Vassberg, M. A. DeHaan, S. M. Rivers, and R. A. Wahls. Development of a common research model for applied CFD validation studies, DPW4 website: [2] T. Klimmek. Development of a Structural Model of the CRM Configuration for Aeroelastic and Loads Analysis. In IFASD th International Forum on Aeroelasticity and Structural Dynamics, June 2013, Bristol, United Kingdom, 2013.

24 Gust velocity (m/s) Funded by the Generic UAV test cases Three 1-cosine gusts from certification requirements Gust Length (ft) Case H Gust velocity (ft/s) Equivalent AoA (degrees) Flight conditions Altitude 29995ft Mach 0.86 Rigid response Aeroelastic response, wing clamped at root Rigid aircraft free to move in pitch and heave Aeroelastic aircraft free to move in pitch and heave Time (s)

25 NCRM aerodynamics only 30ft 150ft 350ft

26 NCRM aerodynamics only 30ft 150ft 350ft

27 NCRM aerodynamics only 30ft 150ft 350ft

28 NCRM aeroelastic 30ft 150ft 350ft

29 NCRM aeroelastic 30ft 150ft 350ft

30 NCRM aeroelastic 30ft 150ft 350ft

31 NCRM rigid + pitch and heave 30ft 150ft 350ft

32 NCRM rigid + pitch and heave 30ft 150ft 350ft

33 NCRM aeroelastic + pitch and heave 30ft 150ft 350ft

34 NCRM aeroelastic + pitch and heave 30ft 150ft 350ft

35 Summary Corrections for DLM/UVLM using steady state data compared to CFD for rigid and flexible clamped configurations Rigid body simulations of NCRM, free in heave and pitch show that the NCRM enters a steady state climb after encountering larger gusts Unsteady CFD-based has the potential to improve DLM corrections used in the gust loads process

36 The research leading to this work has received funding from the s Horizon 2020 research and innovation programme under grant agreement number