Adam J. Culler

Studies on Fluid-Thermal-Structural Coupling for Aerothermoelasticity in Hypersonic Flow

The field of aerothermoelasticity plays an important role in the analysis and optimization of airbreathing hypersonic vehicles, impacting the design of the aerodynamic, structural, control, and propulsion systems at both the component and multidisciplinary levels. This study aims to expand the fundamental understanding of hypersonic aerothermoelasticity by performing systematic investigations into fluid-thermal-structural coupling. A focus is on the targeted use of simplified coupling procedures in order to abate the computational effort associated with comprehensive aerothermoelastic analysis. Because of the fundamental nature of this work, the analysis is limited to cylindrical bending of a simply supported, von Karman panel. Multiple important effects are included in the analysis: namely, 1) mutual coupling between elastic deformation and aerodynamic heating, 2) transient arbitrary in-plane and through-thickness temperature distributions, and 3) the associated thermal stresses and material property degradations. It is found that including elastic deformations in the aerodynamic heating computations results in nonuniform heat flux, which produces nonuniform temperature distributions and material property degradations. This results in localized regions in which material temperature limits may be exceeded; it also impacts flutter boundary predictions and nonlinear flutter response. Additionally, the tradeoff between computational cost and accuracy is evaluated for aerothermoelastic analysis based on either quasi-static or time-averaged dynamic coupling. It is determined that these approaches offer substantial reductions in computational expense, with negligible loss of accuracy, for aerothermoelastic analysis over long-duration hypersonic trajectories.

Impact of Fluid-Thermal-Structural Coupling on Response Prediction of Hypersonic Skin Panels

DOI: 10.2514/1.J050617 The goal of the United States Air Force to field durable platforms capable of sustained hypersonic flight and responsive access to space depends on the ability to predict the response and the life of structures under combined aerothermal andaeropressure loading. However,current predictive capabilities are limitedfor these conditions due in part to the inability to seamlessly address fluid-thermal-structural interactions. This study aims to quantify the significance of a frequently neglected interaction, namely: the mutual coupling of structural deformation and aerodynamic heating, on response prediction. The quasi-static response of a carbon–carbon skin panel is investigated. It is found that the significance of this coupling depends largely on the in-plane boundary conditions, since increasing resistance to thermal expansion results in buckling and increasing deflections into the flow. Including these deformations in aerodynamic heating results in O10% increase in peak temperature and O100% increase in surface ply failure index for deflections O1% of panel length. In these cases, the locations of peaktemperaturesandstressesaresignificantlyaltered.Finally,neglectingdeformationsintheaeroheatinganalysis results in the prediction of snap-through for a gradual heating trajectory, whereas, inclusion leads to a higher mode dominated, dynamically stable response.

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

Fluid-Thermal-Structural Modeling and Analysis of Hypersonic Structures under Combined Loading

Accurate predictions of structural response and life in extreme environments are necessary to achieve the United States Air Force’ goals of affordable, reusable platforms capable of sustained hypersonic flight and responsive access to space. However, the predictive capability of current commercial software is limited for combined aerothermal and aeropressure loading due in part to the inability to seamlessly address multi-coupled, multi-scale fluid-thermal-structural interactions. This study aims to quantify the significance of a frequently neglected interaction, namely: the mutual (2-way) coupling of structural deformation and aerodynamic heating, on response prediction in hypersonic flow. In order to accomplish this objective, an additional focus is on the use of partitioned solution procedures to couple separate: fluid, thermal, and structural models. The response of a carbon-carbon hypersonic skin panel in Mach 12 flow is investigated. It is determined that the 2-way coupled quasi-static solution is converged for O(10) thermal time steps and O(10) deformation updates in aerodynamic heating computations within the characteristic thermal response time. Subsequently, it is shown that including the dependence of aerodynamic heating on structural deformation results in O(20%) increase in peak skin temperature and O(200%) increase in surface ply failure index for relatively modest peak displacement, O(2%) of panel length. Dynamic aeroelastic stability of the quasi-static response predictions is verified through the use of short-duration, transient dynamic response tests that use subiterations to converge the fluid-structural response. Additionally, a long-duration, staggered dynamic solution procedure is investigated. It is determined that the use of sequential cold restarts of the dynamic structural solution results in numerical errors that can alter the predicted response.

Thermal reduced order model adaptation to aero-thermo-structural interactions

The application of reduced order modeling (ROM) techniques to hypersonic structures has gained significant momentum in recent years owing to its ability to deliver accurate structural-thermal response predictions with reduced computational costs relative to full order methods. Accurate response prediction is dependent on the selection of an appropriate basis which is relatively straightforward for single discipline problems. For structural problems, the basis is comprised of the natural mode shapes of the structure and duals, which are modes constructed to capture the nonlinear membrane stretching effect. Similarly, eigenvectors of the generalized conductance-capacitance eigenvalue problem have been shown to provide an adequate basis for thermal ROMs. Selecting a basis for multidisciplinary problems may be significantly more difficult because of the unexpected behavior that may result from the interactions between the disciplines. It is proposed here that reduced order models first be developed as above on single discipline arguments, then be adapted, specifically their bases, to account for the interaction as the computations proceed. An adaptive model is most likely needed for the thermal problem, since the corresponding eigenvalues are more densely clustered than for the structural problem, resulting in significant contributions from more modes as the thermal loading conditions change. To investigate these concepts, a representative hypersonic panel is considered here and a thermal reduced order model of it is first developed and validated under single discipline conditions. The applicability of this basis to represent the temperature distribution resulting from a fully coupled aero-thermo-structural interaction is then assessed and a methodology to adapt the thermal basis is proposed and discussed.

Aerothermoelastic Modeling Considerations for Hypersonic Vehicles

The field of aerothermoelasticity plays 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. This study aims to expand the fundamental understanding of hypersonic aerothermoelasticity by performing systematic investigations into fluid-thermal-structural coupling, and also to develop frameworks, using innovative modeling strategies, for reducing the computational effort associated with aerothermoelastic analysis. Due to the fundamental nature of this work, the analysis is limited to cylindrical bending of a simply-supported, von K arm an panel. Multiple important effects are included in the analysis, namely: 1) arbitrary, nonuniform, in-plane and through-thickness temperature distributions, 2) material property degradation at elevated temperature, and 3) the effect of elastic deformation on aerodynamic heating. It is found that including elastic deformations in the aerodynamic heating computations results in reduced flight time to the onset of flutter. Additionally, the trade-off between computational cost and accuracy is evaluated for aerothermoelastic analysis based on either quasi-static or time-averaged dynamic fluid-thermal-structural coupling, as well as computational fluid dynamics based reduced-order modeling of the aerodynamic heat flux. It is determined that these approaches offer the potential for significant improvements in aerothermoelastic modeling in terms of efficiency and/or accuracy.

Control-oriented aerothermoelastic modeling approaches for hypersonic vehicles

The field of aerothermoelasticity is essential for control-oriented modeling of hypersonic vehicles due to a high degree of coupling between vehicle systems, as well as the presence of aerodynamic heating. In the present study, an efficient aerothermoelastic model is investigated in two ways. First, an approximate aerodynamic heating model is verified using Computational Fluid Dynamic flow analysis. Next, the model is used to gain insight into the degree of coupling between the aerothermal and aeroelastic systems. Results demonstrate that both material property degradation and two-way coupling are important for control-oriented aerothermoelastic modeling. Furthermore, quasi-static and dynamic average approaches for fluid-thermal-structural coupling offer an accurate and efficient approximation for implementing two-way coupling.

Panel response prediction through reduced order models with application to hypersonic aircraft

The present work is the culmination of a series of investigations by the authors on the construction and validation of structural, thermal, and coupled structural-thermal reduced order models (ROMs) for the prediction of the displacements and temperature fields on a representative panel of a hypersonic aircraft during a particular trajectory. The focus of the present paper is first on the development and validation of an efficient strategy for enriching the thermal ROM basis to reflect the temperature distribution induced by the structural deformations through changes of the aerodynamics. Next, the assembly of the thermal and structural ROM bases and the identification of their coefficients is revisited for both cases of constant and temperature dependent coefficient of thermal expansion. The coupled ROM predictions are finally compared to those obtained from full structural and thermal finite element models and it is seen that the ROMs perform overall very well over the large temperature change during the trajectory, from room temperature to 2300F. The only exception to the accuracy of the ROMs is a mode switching event occurring for one of the finite element models but not for the ROMs. This issue is under continued investigation. Background and Objectives There have been several attempts in the past to develop reusable, manned, hypersonic aircraft, but all attempts have so far been called off prior to accomplishing their goal. One of the challenges with developing such a vehicle has been the lack of accurate, predictive models [1]. Consider for example a panel of such a hypersonic vehicle. Its structural response is expected to be both highly nonlinear due to the extreme loading environment and the result of multidisciplinary interactions, involving aerodynamics, structural dynamics and heat transfer [26]. Further complicating the issue is the need to perform long duration analyses for fatigue life prediction. Taken together, these factors constitute a computational task that is extremely demanding even with current computational resources when utilizing full order analyses, i.e. finite element and CFD capabilities. As such, reduced order modeling has emerged as a promising tool to provide accurate structural-thermal predictions while reducing time and computational requirements for simulations. The consideration of nonlinear geometric effects in a reduced order model format has initially focused on isothermal conditions, e.g. see [7] for a recent extensive review. However, the inclusion of thermal effects with the temperature itself represented in a reduced order form has recently been developed and validated [8-12]. The structure considered here is a representative hypersonic panel of [2], see Fig. 1, of which structural and thermal finite element models were developed while the aerodynamic pressure and aerodynamic heating were modeled using piston theory and Eckert’s reference enthalpy method, respectively. The vehicle was accelerated from Mach 2 to Mach 12 over 300 seconds, while the dynamic pressure was held constant at 2,000 psf. The structural, thermal and aerodynamic solutions were marched in time in a process described in detail in [2]. Two different options for this time marching were considered: the one-way and two-way coupling scenarios. One-way coupling refers to an analysis in which the thermal problem is carried out in the absence of structural deformations. The temperature field is thus obtained directly from the aeroheating and heat conduction on the rigid structure, i.e. as a two-discipline (aerodynamics-thermal) problem. Then, the structural deformations are determined for the obtained temperatures distributions as the result of the interaction with the aerodynamics, i.e. another two-discipline problem (aerodynamics-structural). Two-way coupling refers to analyses in which the heating on the panel is influenced by the structural displacement through the aerodynamics, i.e. a three-discipline problem. It is this latter format that more closely resembles reality, and is the subject of the present reduced order model based investigation. Figure 1. Representative hypersonic ramp panel. The present work is the culmination of a series of investigations by the authors. A purely structural, isothermal reduced order model of the panel of Fig. 1 was first developed and validated using uniform static pressure loads and acoustic loading in [11]. Next, a basis for the thermal reduced order model was determined [12] that captures the temperature fields occurring in the one-way coupled trajectory analysis of [2]. The structural responses induced by these temperature distributions and an external loading were then determined using both Nastran and the reduced order models in [13]. A very good to excellent match of these two sets of responses demonstrated the applicability of the structural-thermal reduced order modeling to the one-way coupled scenario. The consideration of two-way coupling was initiated in [14] in which a methodology was proposed to construct a thermal basis for the two-way coupled temperature field. More specifically, an adaptive approach was presented in which a linear, auxiliary problem was utilized to obtain a very fast first estimate of the temperature fields resulting from the full interaction. Appropriate enrichments to the thermal basis were then determined from these Skin