Uncertainty Quantification in Gust Loads Analysis of a Highly Flexible Aircraft Wing

Transcription

1 Uncertainty Quantification in Gust Loads Analysis of a Highly Flexible Aircraft Wing IFASD th - 28 th June 2017, Como R. G. Cook, C. Wales, A. L. Gaitonde, D. P. Jones and Jonathan Cooper University of Bristol, Faculty of Engineering 1

2 Introduction The AeroGust project Motivation Background Nonlinear Aeroelastic Formulation Gust Loads Process Uncertainty Quantification Polynomial Chaos Techniques Results Test Case Properties Static Results Dynamic Gust Loads Conclusions and Further Work 2

3 The AeroGust Project EU funded Horizon 2020 project Collaboration between industry and academia Inspiration from Flight Path 2050 Maintaining and extending industrial leadership Background Market trend for adoption of more flexible structures, novel design configurations and higher flight speeds Pushing limits of linear analyses Process relies on wind tunnel data from predicted cruise geometry Gust loads considered relatively late in design procedure design space limited Extension of aerospace technologies to wind turbine design 3

4 AeroGust Partners University of Bristol Institut National De Recherche En Informatique Et En Automatique (INRIA) Stichting Nationaal Lucht - En Ruimtevaartlaboratorium (NLR) Deutsches Zentrum für Luft- und Raumfahrt e.v. (DLR) University of Cape Town Numerical Mechanics Applications International SA (NUMECA) Optimad engineering s.r.l. University of Liverpool Airbus Defence and Space Dassault Aviation SA Piaggio Aero Industries SPA Valeol SAS 4

5 Motivation for this Work Understanding what effect structural nonlinearities have on aircraft loads compared to the traditional, industrial approach Particular focus on next-gen HARW and UAVs Large deformations Develop a nonlinear gust loads process and UQ approach which is rapid enough use in robust, automated design procedures Do nonlinearities lead to different optimal solutions to those found using a standard approach? 5

6 Background 6

7 Nonlinear Aeroelastic Framework Free-free geometrically-exact nonlinear beam code based on Hodges intrinsic beam formulation EOM Linear strain-curvature/force-moment relationship Large beam deformations and rotations captured Strain-Curvature/Velocity Relation Additional equation required to satisfy free-free conditions Free-free velocity couples with second equation above Allows for arbitrarily large rigid body rotations Linear finite-elements are used to solve the structural EOM Positions and orientations are obtained by integrating strains/curvatures along the beam, or, velocities with time (parameterising rotations using quaternions) 7

8 Nonlinear Aeroelastic Framework Aerodynamics from modified unsteady strip theory Leishman s indicial response method for unsteady effects (compressibility effects ignored) Spanwise lift distribution from VLM Sectional AoA related to beam motion Linear relationship between AoA and lift (no stall) Static coupled nonlinear structural and aerodynamics equations solved using Newton-Raphson method Dynamic solution obtained using Newmark-β time-stepping solver Code verified against Nastran, other UoB codes, UCT, UMich 8

9 Gust Loads Process for NL Aeroelastics Industrial gust loads process can no longer be used for NL system Large deformations may lead to RTC gusts exceeding a purely vertical or lateral gust RTC gusts cannot be calculated directly for NL system FAA/EASA regulations discrete gusts for 9,000m gust lengths considered (10m- 110m in 10m increments) gust directions (0 o -360 o in 30 o increments) total simulations

10 Uncertainty Quantification Need to define what system inputs are uncertain Environmental uncertainties (air density, temperature, etc.) Aircraft property uncertainties (stiffness properties, mass properties, etc.) Gust inputs themselves are assumed to be the known, EASA/FAA regulation deterministic input gusts Need to define reasonable input PDFs for the uncertain variables Little information found in literature for what values to use Initial results use a normal distribution with 3σ limits at ±10% of the mean values Air density, Young s modulus and shear modulus will be considered to be uncertain in this work 10

11 Uncertainty Quantification Methods Gust loads process can be expressed as a black-box-type block Aim of UQ is to determine how uncertainties in input variables propagate through the mapping linear vs. nonlinear gust processes MCS could be considered, but results in an unfeasibly large number of simulations Polynomial chaos expansion methods are used to reduce number of simulations Least squares fit of Hermite polynomials reduces number of simulations required 5 input samples for each 3 uncertain input results in 125 gust loads processes to run 11

12 Uncertainty Quantification Methods Gust loads process can be expressed as a black-box-type block Aim of UQ is to determine how uncertainties in input variables propagate through the mapping linear vs. nonlinear gust processes MCS could be considered, but results in an unfeasibly large number of simulations LHS could sample this problem space, but it would still result in a large number of simulations Polynomial chaos expansion methods are used to reduce number of simulations Least squares fit of Hermite polynomials reduces number of simulations required 5 input samples for each 3 uncertain input results in 125 gust loads processes to run 12

13 Test Case 13

14 Generic UAV wing test case Rectangular HAR UAV wing AR 12.5 (chord = 2m) No sweep/dihedral/twist Cantilever beam boundary conditions M0.5 flight case Flexible variants of the baseline case considered to accentuate nonlinearities Baseline wing behaves linearly Both E and G multiplied by some factor Below 50% baseline stiffness, significant tip shortening and large rotations can be seen 14

15 Results - Static 15

16 Angle of attack vs. stiffness factor Opposite trend seen in linear vs. nonlinear deterministic Mean UQ values match deterministic AoA uncertainty increases as wing becomes flexible 16

17 Root loads vs. stiffness factor Biggest difference between lin and nonlin seen in root torque Nonlinear output uncertainties higher than linear output uncertainty 17

18 Results - Dynamic 18

19 Root loads envelope vs. stiffness factor Linear (undef) over-predicts some loads Nonlinear uncertainties reduce with flexibility, apart from root torque loads 19

20 Root loads envelope vs. stiffness factor Uncertainties on baseline wing dominated by air density uncertainties stiffness uncertainties are negligible Relationship switches as the wing becomes more flexible 20

21 Worst case gust direction vs. stiffness factor Linear (undef) predicts vertical gust as worst case Linear (def) and nonlinear worst case gust angle increases with flexibility Large uncertainty on one case 21

22 Worst case gust direction vs. stiffness factor Linear (undef) predicts vertical gust as worst case Linear (def) and nonlinear worst case gust angle increases with flexibility Large uncertainty on one case 22

23 Large uncertainty in nonlinear torque prediction due to split in worst case Linear cases are clustered more closely Opposite trend seen in worst case gust length for torque Worst case soon exceeds EASA/FAA min/max gust length guidelines 23

24 Conclusions PCE used to recreate the PDFs of quantities of interest of an aeroelastic system s.t. air density, E and G uncertainties Comparison of linear to nonlinear systems Static uncertainties (std dev) increase in nonlinear system with flexibility uncertainties fairly constant in linear Gust loads uncertainty reduces in nonlinear system with flexibility also remains fairly constant in linear Not generally the case torque for most flexible case shows opposite trend Worst case gust cases sometimes exceed regulation guidelines Future Work Reduction of number of gust cases required via surrogate modelling, and look into sampling for PCE to make the whole approach more efficient and rapid Include ability to explore outside of regulation guidelines Funded by the 24

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