A Reduced Order Aerothermodynamic Modeling Framework for Hypersonic Aerothermoelasticity

Crowell, Andrew; McNamara, Jack J.; Kecskemety, Krista M.; Goerig, Trevor

doi:10.2514/6.2010-2969

Cited by 21 publications

(44 citation statements)

References 4 publications

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“…The aerothermal model used for calculation of the aerodynamic heat flux at the surface of the structure is based on that developed in recent work [23], in which both a POD basis and a surrogate-based function were constructed using Latin hypercube parameter space sampling. The models were generated by performing full-order CFD solutions at various points within the identified parameter space.…”

Section: Aerodynamicmentioning

confidence: 99%

Reduced-Order Aerothermoelastic Framework for Hypersonic Vehicle Control Simulation

Falkiewicz¹,

Cesnik²,

Crowell³

et al. 2011

AIAA Journal

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Hypersonic vehicle control system design and simulation require models that contain a low number of states. Modeling of hypersonic vehicles is complicated due to complex interactions between aerodynamic heating, heat transfer, structural dynamics, and aerodynamics. Although there exist techniques for analyzing the effects of each of the various disciplines, these methods often require solution of large systems of equations, which is infeasible within a control design and evaluation environment. This work presents an aerothermoelastic framework with reducedorder aerothermal, heat transfer, and structural dynamic models for time-domain simulation of hypersonic vehicles. Details of the reduced-order models are given, and a representative hypersonic vehicle control surface used for the study is described. The methodology is applied to a representative structure to provide insight into the importance of aerothermoelastic effects on vehicle performance. The effect of aerothermoelasticity on total lift and drag is found to result in up to an 8% change in lift and a 21% change in drag with respect to a rigid control surface for the four trajectories considered. An iterative routine is used to determine the angle of attack needed to match the lift of the deformed control surface to that of a rigid one at successive time instants. Application of the routine to different cruise trajectories shows a maximum departure from the initial angle of attack of 8%.corresponding to ith column of A C = correlation matrix c = modal coordinate of thermal proper orthogonal decomposition basis vector Cx = correlation model for kriging c p = specific heat at constant pressure d = structural modal coordinates, kriging sample point E = modulus of elasticity F = thermal load vector of full system in physical space f = generalized thermal load vector of reduced system in modal space F s = structural load vector of full system in physical space f s = generalized structural load vector of reduced system in modal space H i = coefficient matrices for integration of equations of motion h i = thickness of ith layer of thermal protection system K = thermal conductivity matrix of full system in physical space k = generalized thermal conductivity matrix of reduced system in modal space K G = geometric stiffness matrix K s = structural stiffness matrix k s = generalized stiffness matrix of reduced system in modal space k T = thermal conductivity of material K s = modified structural stiffness matrix L = aerodynamic lift, length M = thermal capacitance matrix of full system in physical space, Mach number m = generalized thermal capacitance matrix of reduced system in modal space M s = structural mass matrix of full system in physical space m s = generalized mass matrix of reduced system in modal space n = number of proper orthogonal decomposition snapshots n e = number of snapshots for kriging evaluation cases n k = number of kriging snapshots n s = number of structural parameters in reduced-order aerothermodynamic model n t = number of thermal parameters...

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Section: Aerodynamicmentioning

confidence: 99%

Reduced-Order Aerothermoelastic Framework for Hypersonic Vehicle Control Simulation

Falkiewicz¹,

Cesnik²,

Crowell³

et al. 2011

AIAA Journal

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“…12. The green blocks in the figure describe the process for generating a kriging-based aerothermal ROM developed by Crowell et al 36 and incorporated…”

Section: Aerothermoelastic Control Surface Rom Generationmentioning

confidence: 99%

“…The thermal and structural ROMs are then used in the aerothermal ROM generation process developed by Crowell et al 36 An added benefit to expressing the temperature distribution and deformation as a linear combination of modes is that it allows for parameterization of each in terms of a small number of design variables for the purpose of creating the aerothermal ROM. Bounds on the aerothermal ROM parameters are first established.…”

mentioning

confidence: 99%

Effect of Control Surface-Fuselage Inertial Coupling on Hypersonic Vehicle Flight Dynamics

Falkiewicz

Frendreis

Cesnik

2011

AIAA Atmospheric Flight Mechanics Conference

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A simulation framework is developed for assessing the effect of control surface inertial loads on hypersonic vehicle response. The framework is based on a partitioned, timemarching approach in which the fuselage and control surface equations of motion are integrated independently and forces/motion at the interface are exchanged between the two systems at pre-determined time intervals. This approach is advantageous in that it does not require direct coupling of the fuselage and control surface models, and therefore allows for the models to be of dissimilar form. Equations of motion for both the fuselage and control surface are presented and a formulation for coupling the two systems is outlined which includes iterations within each aeroelastic time step. The methodology is applied to a representative hypersonic vehicle elevator control surface model which includes aerothermoelastic effects and is attached to a single degree of freedom oscillator representing the fuselage. Results show that control surface inertial effects lead to a departure of the instantaneous control surface lift force by up to a factor of eight with respect to the static value. Investigation of the system response under a commanded change in control surface deflection angle shows that control surface inertia results in departure of the instantaneous control surface pitching moment by up to a factor of 500 with respect to the static value. Nomenclature B= body-fixed reference frame c = generalized damping matrix c p = specific heat d = control surface elastic modal coordinates E = modulus of elasticity, Earth-fixed reference frame F = physical load vector f = generalized load vector f i = fuselage ordinary natural frequencies g = gravitational acceleration H(t) = Heaviside step function H i = coefficient matrices in control surface integration scheme h = altitude h i = thickness of i-th layer of thermal protection system I i = coefficient matrices in fuselage integration scheme

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“…이 때문에 공 력, 구조 변형에 대한 축약모델(reduced-order model)을 구축하고, 이들을 통합하여 공탄성 혹 은 열공탄성(aerothermoelastics) 해석을 수행하는 방법론을 연구하고 있다 [1][2][3][4][5][6][7][8][9].…”

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“…한편, 미국의 McNamara 교수와 Cesnik 교수 연구팀은 Kriging 및 POD 기법을 적용하여 공 력, 구조, 열전달에 대한 축약모델 구축하고 [3][4][5][6][7], 이를 이용해 초음속 플러터해석을 수행한 바 있 다 [7][8][9]. 특히 이들은 초음속 비정상(unsteady) 표 면 압력 분포를 축약 계산하기 위해 피스톤 이론 을 적용하였다.…”

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A Quasi-Steady Method for Unsteady Flows over Surfaces with Structural Deformation

Kim¹,

Lee²,

Lee³

et al. 2017

Journal of the Korean Society for Aeronautical & Space Scie

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In this paper, we present and verify an aerodynamic reduced-order model (ROM) based on a quasi-steady flow method to reduce the computational cost of supersonic aeroelastic analysis. For supersonic flows, especially when the characteristic time scale of the flow is small compared to that of the structural motion, the unsteadiness of flow can be negligible, and quasi-steady solutions can be used instead of the unsteady solutions for the aeroelastic analysis. Kriging method is used to build the ROM of the aerodynamics. The surface solutions from the ROM are used as the boundary conditions for the structural analysis at each time-step. The ROM is validated against the unsteady solutions.

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A Reduced Order Aerothermodynamic Modeling Framework for Hypersonic Aerothermoelasticity

Cited by 21 publications

References 4 publications

Reduced-Order Aerothermoelastic Framework for Hypersonic Vehicle Control Simulation

Reduced-Order Aerothermoelastic Framework for Hypersonic Vehicle Control Simulation

Effect of Control Surface-Fuselage Inertial Coupling on Hypersonic Vehicle Flight Dynamics

A Quasi-Steady Method for Unsteady Flows over Surfaces with Structural Deformation

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