Andrew R. Crowell

Approximate Modeling of Unsteady Aerodynamics for Hypersonic Aeroelasticity

DOI: 10.2514/1.C000190 Various approximations to unsteady aerodynamics are examined for the aeroelastic analysis of a thin doublewedge airfoil in hypersonic flow. Flutter boundaries are obtained using classical hypersonic unsteady aerodynamic theories: piston theory, Van Dyke’s second-order theory, Newtonian impact theory, and unsteady shock-expansion theory. The theories are evaluated by comparing the flutter boundaries with those predicted using computational fluid dynamics solutions to the unsteady Navier–Stokes equations. Inaddition, several alternative approaches to the classical approximations are also evaluated: two different viscous approximations based on effective shapes and combined approximate computational approaches that use steady-state computational-fluid-dynamics-based surrogatemodelsinconjunction withpistontheory.Theresultsindicatethat,with theexceptionof first-order piston theory and Newtonian impact theory, the approximate theories yield predictions between 3 and 17% of normalized root-mean-square error and between 7 and 40% of normalized maximum error of the unsteady Navier–Stokes predictions. Furthermore, the demonstrated accuracy of the combined steady-state computational fluid dynamics and piston theory approaches suggest that important nonlinearities in hypersonic flow are primarily due to steadystate effects. This implies that steady-state flow analysis may be an alternative to time-accurate Navier–Stokes solutions for capturing complex flow effects.

Reduced-Order Aerothermoelastic Framework for Hypersonic Vehicle Control Simulation

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, thesemethods 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 dynamicmodels 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. Themethodology 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 todifferent cruise trajectories shows a maximum departure from the initial angle of attack of 8%.

Model Reduction of Computational Aerothermodynamics for Hypersonic Aerothermoelasticity

A primary challenge for aerothermoelastic analysis in hypersonic flow is accurate and efficient computation of unsteady aerothermodynamic loads. This study examines two model reduction strategies with the goal to enable the use of computational fluid dynamics within a long time-record, dynamic, aerothermoelastic analysis. One approach seeks to exploit the quasi-steady nature of the flow by using steady-state computational fluid dynamics to capture primary flow features, and simple analytical approximations to account for unsteady effects. The second approach seeks to minimize the computational cost of steady-state computational fluid dynamics flow analysis using either kriging or proper orthogonal decomposition-based modeling techniques. These model reduction strategies are assessed, both individually and combined, in the context of a three-dimensional hypersonic control surface. Results computed over a wide range of operating conditions and reduced frequencies indicate that when combined, the considered approaches yield an aerothermodynamic model that is tractable within a dynamic aerothermoelastic analysis, and generally has less than 5% maximum error relative to computational fluid dynamics.

Uncertainty Propagation in Hypersonic Aerothermoelastic Analysis

This study sets the framework for uncertainty propagation in hypersonic aeroelastic and aerothermoelastic stability analyses. First, the aeroelastic stability of typical hypersonic control surface section is considered. Variability in the uncoupled natural frequencies of the system are modeled using beta probability distributions. Uncertainty is propagated to the

Robust and Efficient Treatment of Temperature Feedback in Fluid–Thermal–Structural Analysis

One of the primary challenges in the development of high-speed systems is accurate and efficient prediction of the aerodynamic heating, particularly for lightweight systems where there is a potential for strong coupling between the aerothermodynamic loads and the structural response. A novel approach is developed that corrects heat flux predictions from a pointwise dependency on surface temperature in order to account for surface temperature gradients. This enables efficient construction of a computational fluid dynamics surrogate for aerodynamic heating without a priori assumptions on the surface temperature profile while also accurately maintaining the critical feedback behavior of the surface temperature profile for a coupled fluid–thermal–structural analysis. The method is compared, in terms of accuracy and efficiency, with a hierarchy of approaches for aerodynamic heating prediction. Comparison cases include simple flat-plate heating, as well as shock impingements in two-dimensional and three-dimensi...

Modeling and Analysis of Shock Impingements on Thermo-Mechanically Compliant Surface Panels

Fluid-Thermal-Structural interactions play an important role in the development of high speed vehicles, impacting various sub-disciplines (i.e., aerodynamic, structural, material, propulsion, and control) at the micro, component and/or vehicle scales. This study focuses on the development of a partitioned fluid-thermal-structural procedure aimed at performing a long time record thermo-structural response prediction of surface panels subject to shock impingements. Specific modeling aspects essential to this are reduction of the computational aerothermodynamics to a tractable model, and partitioned timemarching of the fluid-thermal-structural problem. Additional factors considered are: 1) the movement of the shock impingement due to forced motion of a shock generator, 2) panel backpressure, 3) a 140dB random prescribed pressure load to account for pressure fluctuations associated with turbulent boundary layers, and 4) coupled vs. uncoupled fluid-thermal-structural analysis. Results indicate that quasistatic CFD analysis provides a promising means for generating an aerothermodynamic surrogate model. Differences between quasi-static and unsteady models were under 6% for both panel temperature rise and pressure loads for a forced motion analysis. Several studies using the fluid-thermal-structural model are performed, focusing on the differences between the coupled and uncoupled analyses, as well as the role of backpressure on the panel response. The effect of the backpressure to the direction of panel buckling is investigated, and the backpressure required to buckle the panel into the flow is predicted to be 10% of free stream higher for the uncoupled model than the coupled model. However, generally differences were minor between the coupled and uncoupled analysis. The inclusion of a 140 dB prescribed pressure load, meant to mimic the effect of turbulent boundary layer loadings, results in negligible temperature differences. However, both the shock motion and this load introduce large amplitude oscillations at the start of the response, followed by relatively small oscillations once the buckling amplitude of the panel becomes significant.

A Reduced Order Aerothermodynamic Modeling Framework for Hypersonic Aerothermoelasticity

The field of aerothermoelasticity will play an important role in the analysis and optimization of air-breathing hypersonic vehicles, impacting the design of the aerodynamic, structural, control, and propulsion systems at both the component and multi-disciplinary levels. One of the primary challenges for hypersonic aerothermoelastic analysis is accurate and efficient computation of the aerothermodynamics, where currently approaches are limited to either simple engineering level approximations or expensive Computational Fluid Dynamics (CFD). This study aims to fill the modeling gap between these two extremes using sophisticated reduced order modeling techniques to construct computationally efficient surrogates for CFD predictions of the hypersonic aerothermodynamics. Both Proper Orthogonal Decomposition (POD) and kriging approaches are considered and compared. In addition, two different sampling strategies are compared: a random one pass Latin Hypercube parameter space sampling and an adaptive sampling method based on an estimated mean squared error. The developed reduced order modeling framework is used to construct a CFD-based reduced order model for the three-dimensional aerothermodynamics over a hypersonic control surface. Input parameters include: freestream Mach number, altitude, angle-of-attack, side-slip angle, transient structural deformation, and spatio-temporally varying surface temperature. The developed reduced order models are compared to 500 full order CFD evaluation cases. Results illustrate that the developed ROMs require on the order of hundredths of a second to compute surface heat flux distributions and generally have less than 5% RMS error. However, a purely numerical “apparent” laminar to turbulent transition, which is highly nonlinear over the considered parameter space, regularly leads to 10 ‐ 20% L1 error in the surface heat flux.

Loosely Coupled Time-Marching of Fluid-Thermal-Structural Interactions

This study focuses on the development of a loosely coupled partitioned multi-physics time marching procedure for fluid-thermal-structural analysis using time-accurate high-fidelity models. The scheme is specifically formulated to maintain global second order temporal accuracy using implicit second order solvers for each discipline, and requires no subiterations between solvers. Furthermore, the scheme is designed to exploit disparities in time scales between the submodels through the use of multicycling, i.e. multiple fluid time steps between each structural step, and multiple structural steps between each thermal step. Preliminary verification of the scheme is carried out by coupling a CFD solver with thermal and structural solvers. A fluid-structural analysis with and without multicycling demonstrates the second order accuracy of structural displacements/velocities, and integrated pressure loads. A fluidthermal analysis is also performed, demonstrating second order accuracy of the temperature rise and integrated heat load in the absence of multicycling. However, currently the fluid-thermal time-marching is less than second order accurate with multicycling.

Computational Modeling for Conjugate Heat Transfer of Shock-Surface Interactions on Compliant Skin Panels

Aerothermal interactions play an important role in the analysis and optimization of high speed vehicles, impacting the design of the aerodynamic, structural, control, and propulsion systems at both the component and multi-disciplinary levels. This study aims to develop a CFD-FEM based partitioned aerothermal solver, for investigating the thermal response of surface panels subject to shock turbulent boundary layer interactions (STBLIs). The focus of the study is assessment of different time marching approaches for the partitioned conjugate heat transfer problem, and also the degree of coupling in STBLIs. An additional consideration is the potential for structural compliance in the system, which leads to a non-stationary shock impingement location. Preliminary results for the initial thermal response of a vibrating skin panel indicate that a one-way coupled and quasi-steady approximation yield similar panel temperatures to a fully unsteady, two-way coupled analysis. Furthermore, a static approximation, where the flow is predicted a priori without consideration of the surface motion, significantly under predicts the peak temperature rise and affected length of the panel.

Surrogate Based Reduced-Order Aerothermodynamic Modeling for Structural Response Prediction at High Mach Numbers

One of the primary challenges for hypersonic aerothermoelastic analysis of air-breathing hypersonic vehicles is accurate and efficient computation of the unsteady aerothermodynamic loads, where currently approaches are limited to either simple engineering level approximations or expensive Computational Fluid Dynamics. This study aims to fill the modeling gap between these two extremes by constructing computationally efficient surrogates for CFD predictions of the unsteady aerodynamic pressure loads. A novel aspect of the work is the use of steady-state CFD data for the surrogate, corrected for unsteady effects using piston-theory aerodynamics. Validation of the steady-state surrogate is achieved by comparing to 500 steady-state full order CFD cases. Results indicate that the surrogate generally has less than 1% RMS error. Comparison of the unsteady generalized aerodynamic forces computed using the corrected surrogate, third-order piston theory, unsteady Euler, and unsteady NavierStokes aerodynamics demonstrates that the developed surrogate method produces predictions superior to unsteady Euler solutions and piston theory, at a computational cost similar to that of piston theory. The surrogate is also implemented into a dynamic aerothermoelastic panel simultation, and compared with previous results using analytical approaches. The comparison reveals differences of over 100% in the onset time to flutter, and significantly altered post-flutter responses. The surrogate framework is found to enable a reasonably accurate, robust, and efficient method for incorporating CFD loads prediction, which would otherwise be impractical, into a long time-record aerothermoelastic analysis of structures for a complete hypersonic trajectory.