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