Uncertainty Quantification in Gust Loads Analysis of a ...
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Uncertainty Quantification in Gust Loads Analysis of a Highly Flexible Aircraft Wing 05 July 2017 1 IFASD, 25 th -28 th June 2017, Como, Italy Funded by the European Union IFASD 2017 25 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
Transcript of Uncertainty Quantification in Gust Loads Analysis of a ...
Uncertainty Quantification in Gust Loads
Analysis of a Highly Flexible Aircraft Wing
05 July 2017
1IFASD, 25th-28th June 2017, Como, Italy
Funded by the European Union
IFASD 201725th - 28th June 2017, Como
R. G. Cook , C. Wales, A. L. Gaitonde,
D. P. Jones and Jonathan Cooper
University of Bristol, Faculty of Engineering
05 July 2017
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• 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
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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
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• 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
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AeroGust Partners
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• 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?
Motivation for this Work
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Background
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Nonlinear Aeroelastic Framework
• Free-free geometrically-exact nonlinear beam code based on Hodges’ intrinsic beam formulation• Linear strain-curvature/force-moment relationship
• Large beam deformations and rotations captured
EOM
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)
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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
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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 (0o-360o in 30o
increments)
• total simulations -132
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• 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
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Uncertainty Quantification
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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
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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
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LHS could sample this problem
space, but it would still result in
a large number of simulations
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Test Case
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Generic UAV wing test case• Rectangular HAR UAV wing
• AR 12.5 (chord = 2m)
• No sweep/dihedral/twist
• Cantilever beam boundary conditions
• 55,000ft @ 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
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Results - Static
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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
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Root loads vs. stiffness factor• Biggest
difference between linand nonlinseen in root torque
• Nonlinear output uncertainties higher than linear output uncertainty
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Results - Dynamic
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Root loads envelope vs. stiffness factor
• Linear (undef) over-predicts some loads
• Nonlinear uncertainties reduce with flexibility, apart from root torque loads
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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
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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
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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
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• 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
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• PCE used to recreate the PDFs of quantities of interest of an aeroelasticsystem 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
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Conclusions
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The research leading to this work has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement number 636053.
