University of Bristol

Transcription

1 Uniersity of Bristol AEROGUST Workshop 27 th - 28 th April 2017, Uniersity of Lierpool Presented by Robbie Cook and Chris Wales

2 Oeriew Theory Nonlinear strctral soler copled with nsteady aerodynamics Gst loads process for nonlinear aeroelastic systems Reslts WP2 recap of M18 reslts Uncertainty Qantification initial reslts Conclsions and next steps

3 Nonlinear Aeroelastic Framework Free-free geometrically-exact nonlinear beam code based on Hodges intrinsic beam formlation Linear strain-cratre/force-moment relationship Large beam deformations and rotations captre EOM Strain-Cratre/Velocity Relation Additional eqation reqired to satisfy free-free conditions Free-free elocity coples with second eqation aboe Allows for arbitrarily large rigid body rotations Linear finite-elements are sed to sole the strctral EOM Positions and orientations are obtained by integrating strains/cratres along the beam, or, elocities with time (parameterising rotations sing qaternions)

4 Nonlinear Aeroelastic Framework Aerodynamics from modified nsteady strip theory Leishman s indicial response method for nsteady effects (compressibility effects ignored) Spanwise lift distribtion from VLM Sectional AoA related to beam motion Linear relationship between AoA and lift (no stall) Fnded by the Static copled nonlinear strctral and aerodynamics eqations soled sing Newton-Raphson method Dynamic soltion obtained sing Newmark-β time-stepping soler Code erified against Nastran, other UoB codes, UCT, UMich Gst Loads Process for NL Aeroelastics Indstrial gst loads process can no longer be sed for NL system Large deformations may lead to RTC gsts exceeding a prely ertical or lateral gst RTC gsts cannot be calclated directly for NL system

5 Vertical gst s. angled gst on free-flying aircraft Θ=0 o Θ=60 o

6 Oeriew of Delierable 2.6 Nonlinear strctre with linear aerodynamics Analysis carried ot on UAV wing (test case 2) Baseline isn t flexible enogh for nonlinear effects to become important Flexible ariants created from the original baseline wing EI1,EI2,GJ redced niformly by a factor (no mass changes) A nmber of flexibility ariants are trimmed Wing cannot spport the aircraft mch below 15% of the baseline stiffness Flexibilities below 25% baseline show considerable difference compared to NASTRAN Little difference between corrected strip theory and VLM for the nonlinear reslts large deformations do not change the lift distribtions drastically WP2

7 Work Package 3: Oeriew of Delierable 3.10 Effects of ncertainty on the gst loads process Part of Task 3.3, addresses objecties To assess the impact of the nderlying assmptions of the crent loads process To inestigate methods to extend the applicability of the crrent process to highly flexible and innoatie strctres To deelop methods to inclde the ncertainty present in both the aerodynamic and strctral models within the crrent loads process and inestigate the impact on gst loads

8 Uncertainty Qantification of Aeroelastic System Need to define what system inpts are ncertain Enironmental ncertainties (air density, temperatre, etc.) Aircraft property ncertainties (stiffness properties, mass properties, etc.) Gst inpts themseles are assmed to be the known, EASA/FAA reglation deterministic inpt gsts Need to define reasonable inpt PDFs for the ncertain ariables Little information fond in literatre for what ales to se Initial reslts se a normal distribtion with 3σ limits at ±10% of the mean ales First set of reslts consider only an ncertain air density, with mean ale defined in the test case docment Polynomial Chaos Expansion techniqes are sed to determine how inpt ncertainties propagate throgh to the otpt loads ncertainties Static PCE reslts can be compared to a Monte Carlo simlation to obtain an exact reslt MCS of dynamic reslts reqires considerable comptation

9 Work Package 3: Oeriew of Delierable 3.10 Effects of ncertainty on the gst loads process UQ Analysis Aeroelastic Trim Analysis (Static)

10 MCS carried ot with 1000 trim cases at different air densities MSC PDF histograms for AoA compared to PCE PDFs calclated with 5 trim cases and 4 shape fnctions Good agreement to MCS from PCE sing fewer simlations Trim loads do not ary mch with air density 1000 simlation Monte Carlo exact soltion Polynomial Chaos emlation from sbset of reslts

11 Mean ales calclated from PCE ales match well with the ales calclated with the mean air density ales

12 Standard deiations appear to remain roghly constant for linear system regardless of flexibility Standard de increases in nonlinear system

13 Skewness and krtosis plots inclded as a first case indication of how normal the otpt distribtions are Small amont of skewness is seen for linear and nonlinear, and excess krtosis is low fairly normal otpt PDFs

14 Work Package 3: Oeriew of Delierable 3.10 Effects of ncertainty on the gst loads process UQ Analysis Aeroelastic Gst Analysis (Dynamic)

15 Oeriew of Delierable Effects of ncertainty on the gst loads process Wing is sbjected to a family of ertical 1-cosine gsts, with gst intensity and lengths defined by FAA/EASA certifications Nonlinear aeroelastic code compared to linearised code abot nderformed and trim geometries Incremental loads abot ndeformed geometry 1g loads added afterwards nder linear assmptions Nonlinear reslts obtained from the deformed trim geometry Loads time histories post-processed on linear and nonlinear reslts to look at trends WP2

16 RTC gst direction calclated from linear system abot trim geometry Een for stiff wings, the worst case gst is orientated away from prely ertical Can lead to loads increases 10% May be exacerbated by fixed-root assmptions

17 Baseline stiffness Fnded by the 15% baseline stiffness

18 Linear system oer-predicts shear, torsion and bending moments on stiffer wing Trend reersed for torqe at lower stiffness Axial and in-plane shear/bending are almost zero in linear

19 Standard deiation of the linear system otpt PDFs remains fairly constant for different flexibilities Standard de redces significantly for root shear, torqe and bending moment as aircraft gets more flexible Opposite trend as seen in trim AoA

20 Low skewness and excess krtosis for almost all cases seems to be a fairly normal otpt PDF One exception on 25% flexibility where the skewness is relatiely large

21 Conclsions Fnded by the PCE sed to recreate the PDFs of qantities of interest of an aeroelastic system s.t. air density ncertainties Comparison of linear to nonlinear systems Trim angle of attack ncertainty (std de) increases in nonlinear system as it becomes more flexible, bt remains fairly constant in linear Incremental gst loads ncertainty redces in nonlinear system as it becomes more flexible, bt remains fairly constant in linear Next steps Inclde more sorces of ncertainties in the analysis Strctral properties EI/GJ Mass properties Strctral damping Drag?

22 Work Package 2: Understanding Non-linearities in CFD Based Gst Simlations Part of Task 2.1, Non-linear Aerodynamics of Gst Using RANS Inestigation of predicted non-linear behaior sing Field and Split Velocity Methods WP2

23 Gst elocity is prescribed throghot domain Moing grid code modified The grid elocity set to mins the gst No grid displacement Soles for the total elocity mins the gst Gst not dissipated by large cells Does not inclde the interaction with the body Correct if: no body in domain; steady state change to niform flow throghot the domain Field Velocity Method 0 p y E p y y y y p x E x p x x x E t t t t t t t t t ˆ ˆ E p p E y x y x t t t t WP2

24 Gst elocity component is split from total Gst component prescribed Follow split throgh eqations Pressre not a fnction of gst component Moing grid code modified As FVM except Additional sorce terms Incldes the interaction with the body Split Velocity Method 34 ˆ ˆ E p E p 0 ˆ ˆ, ˆ ˆ 0 ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ s s s p E p y p E p x E t E m m y x p s s s y x t s m m E m ˆ ˆ ˆ ˆ ˆ ˆ, ˆ ˆ WP2

25 Split Velocity Methods Prescribed elocity approach incldes interaction of the gst with the body 1-cosine gst, transonic 2D aerofoil case Change in elocity de to gst Change in pressre de to gst

26 M=0.8 w=0.5c Δα=0.5 WP2

27 Gst elocity (m/s) Fnded by the Gst test case definition Case H ft, Mach 0.86 Maximm take off mass case Case H 8 Gst Length (m) Gst elocity (m/s) Eqialent AoA (degrees) Time (s)

28 NCRM case H reslts - rigid Fnded by the 30ft 150ft 350ft WP2

29 NCRM case H reslts - flexible Fnded by the 30ft 150ft 350ft WP2

30 Comparison between FVM and SVM srface pressres Case H gst length 30ft FVM SVM WP2

31 Difference in srface pressres between SVM and FVM Case H 30ft gst 350ft gst WP2

32 Work Package 3: Redced reliance on wind tnnel data The recreation of the indstrial gst loads process, sing CFD in place of experimental data Inestigation of the nderlying assmptions of the crrent indstrial gst loads process

33 Rapid Loads ealation stitched VLM components rapid & robst nsteady VLM High T-tail CFD or experiment Loads Database niersal correction process / matrices Target Strt braced Prop wash

34 Recreating the crrent indstrial loads process Steady state CFD Generate correction Matrices Wkk/F2jg NASTRAN Corrected DLM SOL 144/145 Post process Reslts Loads Enelope/Correlated Loads Strip wise lift moments extracted Correction matrices generated to match strip wise lift and moment Rn different gst and mass at corrected flight condition Loads extracted from NASTRAN monitor points

35 MSC NASTRAN time steps iteration steps Fnded by the Copling NASTAN to Ta MSC Nastran 1 Start initialize Mesh Deformation - IC TAU Sole Steady DLR Ta The copling matrix H is created sing NASTRAN and exported sing DMAP initializetime Spline Method f str = H sa f aero getwettednode Forces TAU Sole Unsteady aero = H as str Nastran FE Sole ptwettednode Displacements finalizetime Mesh Deformation Ta modified to allow ariable time stepping. Speeds p simlation by sing large time steps to conect gst to close to aircraft terminate Updated to allow rigid body motion as well End 1 MSC Software Deelopment Kit 2014 User's Gide

36 UVLM code 3 Parts Vortex ring elements on body Layer of bffer panels in the wake Vortex particles in the wake Rigid body motions Deformations Gst interactions

37 Cl Fnded by the UVLM correction process C 0 + C w w b + w w = AΓ P = SZA 1 wc 9.00E-01 Map CFD loads on to UVLM mesh Iterate correction matrices calclation de to interaction with wake 8.00E E E E E E E E E Angle of attack (deg) DLM DLM_corrected UVLM UVLM_corrected CFD

38 Nasa Common Research Model FEM condensed mass and stiffness from FERMAT strctral model DLM Mesh for wing and tail CFD mesh from 4 th Drag Prediction Workshop Only wing copled

39 Corrected DLM and UVLM for rigid geometry 30ft 150ft 350ft

40 Corrected DLM loads for flexible wing 30ft Root shear Root bending Root torqe 350ft

41 AIC Unsteady Correction Aeroelastic freqency response analysis in modal coordinates formlation: Mode Deformation Rigid Gst In the gst response analysis aailable in the Nastran soler these contribtions are linearly added to obtain the total aerodynamic loads. From this the idea that it is possible to correct once to match the rigid gst loads and the other to generate the aerodynamic load obtained from a mode shape deformation.

42 AIC Unsteady Correction Rigid Gst The aim of this correction approach is to match the integrated aerodynamic loads acting on the strctral nodes compted from the CFD code: where the right hand side term can be specialized for the corrected Doblet Lattice Method, as follow: A post mltiplication correction approach The downwash contribtion is a matrix defined as follow Defining the generalized aerodynamic inflence coefficient matrix relating the downwash to the aerodynamic loads on the monitor points, corresponding to the CFD strip being mentioned:

43 AIC Unsteady Correction Framework The time domain CFD gst response loads has been ealated for different redced freqency. For each of them the time history of the integrated loads of the ten strips along the wing has been compted. The inpt signal has been chosen long enogh to reach a stationary harmonic response. At this point a reference period has been selected, and an eqialent periodic signal has been reconstrcted. To obtain comparable reslts to the ones compted by the DLM the Forier Series has been sed to obtain the freqency domain loads. The correction factors hae been sed to pdate the AICs matrices compted in the gst response analysis.

44 1-COS Gst Response Analysis The main goal is to focs on the gst response analysis of interest in a design process: short medim large With a design gst elocity gien by : Mach nmber =

45 1-COS Gst Response: M=0.85, Short Gst Length

46 1-COS Gst Response: M=0.85, Medim Gst Length

47 1-COS Gst Response: M=0.85, Long Gst Length

48 Conclsions For gst lengths reqired for certifying 1-cosine gst loads the FVM and SVM prodce the same reslts DLM and UVLM both oer predict gst loads when corrected with prely steady data Using nsteady data the accracy of the corrected DLM can be greatly improed Next steps Apply improed DLM correction method to NCRM test case Test corrected UVLM copled to NASTRAN Use nsteady data to improe UVLM correction

49 The research leading to this work has receied fnding from the s Horizon 2020 research and innoation programme nder grant agreement nmber