Assessment of Uncertain External Store Aerodynamics Using mu-p Flutter Analysis

Heinze, Sebastian; Ringertz, Ulf; Borglund, Dan

doi:10.2514/1.39158

Cited by 11 publications

(9 citation statements)

References 6 publications

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“…The data number for auto regression is chosen as 1000 with the sample frequency of 200 Hz. The least square error decays quickly when the physical modes number is selected as [10][11][12][13][14][15]. Consequently the number of the mathematical calculation modes is chosen as 60-80.…”

Section: B Uncertainty Bound Estimation Based On the Time Response Datamentioning

confidence: 99%

“…According to the nominal aerodynamic calculation methods, reciprocal aerodynamic uncertainty types were presented in their work,. Notably, experiments conducted by Borglund provide test evidence for the robust flutter analysis method 10,11 . In Reference 10 , an uncertainty model for aerodynamic coefficient for a large aspect ratio wing was established, based on the lifting-line theory.…”

Section: Introductionmentioning

confidence: 96%

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Aeroelastic Wind Tunnel Test for Aerodynamic Uncertainty Model Validation

Dai¹,

Wu²,

Yang³

et al. 2012

53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference

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A half model of a scaled aircraft is designed and tested in the wind tunnel to validate the uncertainty model for unsteady pressure coefficient in the frequency domain. In the wind tunnel test, a step-swept test was conducted to obtain the model's frequency response function. Then a time-domain response test was performed with turbulence excitation to identify the aircraft's on-line poles. Based on the tested frequency response function or the on-line poles, the structured singular value (µ) method was applied to determine the aerodynamic uncertainty level under the model validation framework. Finally, the widely used µ analysis was again employed to analyze the worst-case flutter boundary, compared with the experimental flutter velocity. The experimental flutter velocity (30.5m/s) is in the range of the predicted robust flutter boundary (28.5m/s), in which parameters' uncertainties were taken into account in the numerical model. Experimental results validate that the uncertainty quantification theoretical frameworks incorporating experimental data can estimate the proper aerodynamic uncertainty level and predict a safe flutter boundary. The present results suggest that the time-response validation theoretical framework is more advantageous in robust stability analysis than the one upon the frequency response function validation. Nomenclature M= structural general mass matrix K = structural general stiffness matrix C = structural general damping matrix F q , F δ = the general aerodynamics due to modal motion and control surface displacement M c = coupling mass matrix of the control surface q = modal displacement vector δ = displacement vector of control surface S = diagonal matrix composed of area for each flat patch C p0 = nominal aerodynamic pressure coefficient δ cpi = the ith normalized pressure uncertainty variable in the uncertainty matrix ∆ cp w j,i = weighting coefficient for pressure uncertainty on each patch j for each mode i n = number of normal modes ω = frequency with the unit of rad/s na = total number of devised flat aerodynamic patches Ф p = the modal matrix of the pressure points on the aerodynamic patches W cpr , W cpl = the right and left weighting matrixes for pressure uncertainty due to modal motion W δcpr , W δcpl = the right and left weighting matrixes for pressure uncertainty due to aileron deflection ρ = flow density 2 V = flow velocity K 0 , = nominal generalized stiffness W k = the weighting matrix for stiffness uncertainty ∆ k = uncertainty matrix for stiffness ∆ cp , ∆ cpδ = uncertainty matrixes for pressure due to modal motion and aileron defleciton nδ = the size of ∆ cp C p10 = nominal pressure coefficient for uncertain aerodynamic patches nau = the number of uncertain aerodynamic patches 2 0 1 2 q V ρ = = free stream dynamic pressure Ф s = the modal vector at the location of wing tip accelerator P A = the transfer function for the aileron's actuator h(t) = impulse response function R i = the ith residual matrix for pole identification u = command input to the actuator y = accelerat...

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Section: B Uncertainty Bound Estimation Based On the Time Response Datamentioning
confidence: 99%

Section: Introductionmentioning
confidence: 96%

Aeroelastic Wind Tunnel Test for Aerodynamic Uncertainty Model Validation
Dai¹,
Wu²,
Yang³
et al. 2012
53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference
0
0
0
0
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“…18 Uncertainties such as in structural damping, mass distribution, flow boundary conditions, geometry, material properties and aerodynamics have been studied in prior works in literature. 17,19,20 Robustness analyses and uncertainty quantification form a recent topic with growing interest in aeroelasticity community. Borglund 21 performed a robust flutter analysis by considering uncertainties in aerodynamics and mass properties.…”

Section: Introductionmentioning
confidence: 99%

Robust Aeroelastic Design Optimization of Wing/Store Configurations Based on Flutter Criteria
Nikbay
¹

2012
12th AIAA Aviation Technology, Integration, and Operations (ATIO) Conference and 14th AIAA/ISSMO Multidisciplinary Analysis And
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We present a robust aeroelastic design optimization study for three dimensional wing/ store configurations by employing an analytical flutter analysis. The flutter solution uses Lagrange equations with energy terms where structural displacements are represented by assumed mode technique and aerodynamic loads are calculated by Theodorsen function. An in-house flutter code is developed parametrically in terms of design variables such as taper ratio, sweep angle, elastic axis location and material properties, and validated by using available reference data for well-known aeroelastic benchmark problems which are the Goland and AGARD 445.6 wing models. The flutter code is coupled with an optimization software to perform deterministic design optimization of the AGARD 445.6 clean wing and then further developed to enable flutter analysis and optimization of wing/store configurations. The aeroelastic modeling counts for both structural and aerodynamic effects of external masses while couple of different optimization strategies are applied to determine optimum store locations and wing design to maximize flutter speed. Finally, robustness criterion is implemented into aeroelastic optimization in the presence of structural uncertainties. These uncertainties are propagated by Monte Carlo Simulation (MCS) while 2 nd order Polynomial Chaos Expansion (PCE) is used through MCS to reduce the computational time. NomenclatureA Cross-sectional area, [m 2 ] aNon-dimensional length between elastic axis and center of mass a s Non-dimensional length between elastic axis of the store and mass center of the wing bHalf chord length, [m] b R Half chord length of reference station, [m] ea Elastic axis length from leading edge for clean wing ea i Elastic axis length from leading edge for external masses (i= 1 to n s ) E y Elasticity modulus in spanwise direction, [M P a] EI Bending stiffness, [N m 2 ] (EI) wing Bending stiffness of clean wing, [N m 2 ] (EI) store Bending stiffness of store, [N m 2 ] g Damping term g w Damping term for bending motion g θ Damping term for torsional motion G y Shear modulus in spanwise direction, [M P a] GJ Torsional stiffness, [N m 2 ] (GJ) wing Torsonal stiffness of clean wing, [N m 2 ] (GJ) store Torsional stiffness of store, [N m 2 ] I sz Total moment of inertia of store, [kgm 2 ] * Associate Professor,AIAA 2012-5455 þÿ C o p y r i g h t © 2 0 1 2 b y P 1 n a r A c a r . P u b l i s h e d b y t h e A m e r i c a n I n s t i t u t e o f A e r o n a u t i c s a n d A s t r o n a u t i c s , I n c . , w i t h p e r m i s s i o n . Downloaded by KUNGLIGA TEKNISKA HOGSKOLEN KTH on July 30, 2015 | http://arc.aiaa.org |

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“…9 Uncertainties such as in structural damping, mass distribution, flow boundary conditions, geometry, material properties and aerodynamics have been studied in prior works in literature. 8,10,11 Monte Carlo Simulation (MCS) is a frequently used method in uncertainty quantification in a stochastic framework however it becomes nonconvergent in computationally expensive problems. Marques 12 considers MCS, perturbation and interval analyses in stability calculation of Goland wing based on eigenvalues containing Euler aerodynamics effects.…”

Section: Introductionmentioning
confidence: 99%

Flutter Based Aeroelastic Optimization of an Aircraft Wing with Analytical Approach
Nikbay¹
2012
53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference
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We present an analytical flutter prediction methodology employing assumed mode technique for three dimensional wing and wing/store configurations. The flutter solution makes use of Lagrange formulation for aeroelastic modeling and Theodorsen function for aerodynamic load calculation. An in-house flutter code is developed and validated by using benchmark problems, next applied to Goland and AGARD 445.6 wing models. Flutter results in all cases are in excellent agreement with the reference data. The flutter code is further enhanced to enable aeroelastic optimization and uncertainty based flutter analysis of AGARD 445.6 wing/store configurations. Firstly, aeroelastic optimization study varying input parameters such as taper ratio, sweep angle, spanwise elasticity and shear modulus is performed to maximize flutter boundary of AGARD 445.6 wing and an optimum clean wing model is ascertained. Next, the structural effects of designated external masses are investigated for flutter of initial and optimized AGARD 445.6 wing models and optimum configurations of store placement are determined. Finally, structural randomness such as in spanwise elasticity and shear modulus of the wing are propagated through flutter analyses and this uncertainty quantification is applied to initial and optimum AGARD 445.6 clean wing models. Finally, for wing/store models, random parameters relevant to store masses, store load placements are added to material property uncertainties and similarly flutter boundary uncertainty is examined. In all analyses, uncertainty quantification is accomplished by Monte Carlo Simulation method with various Coefficient of Variation estimates.

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Assessment of Uncertain External Store Aerodynamics Using mu-p Flutter Analysis

Cited by 11 publications

References 6 publications

Aeroelastic Wind Tunnel Test for Aerodynamic Uncertainty Model Validation

Aeroelastic Wind Tunnel Test for Aerodynamic Uncertainty Model Validation

Robust Aeroelastic Design Optimization of Wing/Store Configurations Based on Flutter Criteria

Flutter Based Aeroelastic Optimization of an Aircraft Wing with Analytical Approach

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