Ongoing Fixed Wing Research within the NASA Langley Aeroelasticity Branch

The NASA Langley Aeroelasticity Branch is involved in a number of research programs related to fixed wing aeroelasticity and aeroservoelasticity. These ongoing efforts are summarized here, and include aeroelastic tailoring of subsonic transport wing structures, experimental and numerical assessment of truss-braced wing flutter and limit cycle oscillations, and numerical modeling of high speed civil transport configurations. Efforts devoted to verification, validation, and uncertainty quantification of aeroelastic physics in a workshop setting are also discussed. The feasibility of certain future civil transport configurations will depend on the ability to understand and control complex aeroelastic phenomena, a goal that the Aeroelasticity Branch is well-positioned to contribute through these programs

Summary Findings from the AVT-191 Project to Assess Sensitivity Analysis and Uncertainty Quantification Methods for Military Vehicle Design

A NATO symposium held in Greece in 2008 identified many promising sensitivity analysis and uncertainty quantification technologies, but the maturity and suitability of these methods for realistic applications was not clear. The NATO Science and Technology Organization, Task Group AVT-191 was established to evaluate the maturity and suitability of various sensitivity analysis and uncertainty quantification methods for application to realistic vehicle development problems. The program ran from 2011 to 2015, and the work was organized into four discipline-centric teams: external aerodynamics, internal aerodynamics, aeroelasticity, and hydrodynamics. This paper summarizes findings and lessons learned from the task group

Quantification of Model-Form, Predictive, and Parametric Uncertainties in Simulation-Based Design

Traditional uncertainty quantification techniques in simulation-based analysis and design focus upon on the quantification of parametric uncertainties-inherent natural variations of the input variables. This is done by developing a representation of the uncertainties in the parameters and then efficiently propagating this information through the modeling process to develop distributions or metrics regarding the output responses of interest. However, in problems with complex or newer modeling methodologies, the variabilities induced by the modeling process itself-known collectively as model-form and predictive uncertainty-can become a significant, if not greater source of uncertainty to the problem. As such, for efficient and accurate uncertainty measurements, it is necessary to consider the effects of these two additional forms of uncertainty along with the inherent parametric uncertainty. However, current methods utilized for parametric uncertainty quantification are not necessarily viable or applicable to quantify model-form or predictive uncertainties. Additionally, the quantification of these two additional forms of uncertainty can require the introduction of additional data into the problem-such as experimental data-which might not be available for particular designs and configurations, especially in the early design-stage. As such, methods must be developed for the efficient quantification of uncertainties from all sources, as well as from all permutations of sources to handle problems where a full array of input data is unavailable. This work develops and applies methods for the quantification of these uncertainties with specific application to the simulation-based analysis of aeroelastic structures

Efficient Uncertainty Quantification Applied to the Aeroelastic Analysis of a Transonic Wing

The application of a Point-Collocation Non-Intrusive Polynomial Chaos method to the uncertainty quantification of a stochastic transonic aeroelastic wing problem has been demonstrated. The variation in the transient response of the first aeroelastic mode of a three-dimensional wing in transonic flow due to the uncertainty in free-stream Mach number and angle of attack was studied. A curve-fitting procedure was used to obtain time-independent parameterization of the transient aeroelastic responses. Among the uncertain parameters that characterize the time-dependent transients, the damping factor was chosen for uncertainty quantification, since this parameter can be thought as an indicator for flutter. Along with the mean and the standard deviation of the damping factor, the probability of having flutter for the given uncertainty in the Mach number and the angle of attack has been also calculated. Besides the Point-Collocation Non-Intrusive Polynomial Chaos method, 1000 Latin Hypercube Monte Carlo simulations were also performed to quantify the uncertainty in the damping factor. The results obtained for various statistics of the damping factor including the flutter probability showed that an 8th degree Point-Collocation Non-Intrusive Polynomial Chaos expansion is capable of estimating the statistics at an accuracy level of 1000 Latin Hypercube Monte Carlo simulation with a significantly lower computational cost. In addition to the uncertainty quantification, the response surface approximation, sensitivity analysis, and reconstruction of the transient response via Non-Intrusive Polynomial Chaos were also demonstrated

Sizing and Topology Design of an Aeroelastic Wingbox Under Uncertainty

The goals of this work are to use a nested optimizer to conduct simultaneous sizing (inner level) and topology (outer level) design of a wingbox, considering uncertainties in the safety factors used to define the aeroelastic constraints. These uncertainties, propagated via sampling-driven polynomial chaos, are explicitly introduced at the inner level of the method, during gradient-based sizing optimization, resulting in a stochastic optimal sizing distribution. Measures of robustness in the total structural mass are then passed to the outer level, where a global optimizer evolves the topology parameters. The results demonstrate design choices needed to improve robustness in the face of uncertain safety factors, and the various physical mechanisms driving this process

Model-form and predictive uncertainty quantification in linear aeroelasticity

In this work, Bayesian techniques are employed to quantify model-form and predictive uncertainty in the linear behavior of an elastically mounted airfoil undergoing pitching and plunging motions. The Bayesian model averaging approach is used to construct an adjusted stochastic model from different model classes for time-harmonic incompressible flows. From a set of deterministic function approximations, we construct different stochastic models, whose uncertain coefficients are calibrated using Bayesian inference with regard to the critical flutter velocity. Results show substantial reductions in the predictive uncertainties of the critical flutter speed compared to non-calibrated stochastic simulations. In particular, it is shown that an efficient adjusted model can be derived by considering a possible bias in the random error term on the posterior predictive distributions of the flutter index

Plans for Aeroelastic Prediction Workshop

This paper summarizes the plans for the first Aeroelastic Prediction Workshop. The workshop is designed to assess the state of the art of computational methods for predicting unsteady flow fields and aeroelastic response. The goals are to provide an impartial forum to evaluate the effectiveness of existing computer codes and modeling techniques, and to identify computational and experimental areas needing additional research and development. Three subject configurations have been chosen from existing wind tunnel data sets where there is pertinent experimental data available for comparison. For each case chosen, the wind tunnel testing was conducted using forced oscillation of the model at specified frequencie

Reduced Order Modeling for Transonic Aeroservoelastic Control Law Development

As aircraft become more flexible, aeroelastic considerations become increasingly important and complex, particularly for transonic flight where nonlinearities in the flow render linear analysis tools less effective. In order to analyze these aeroelastic interactions between the fluid and the structure efficiently, reduced order models (ROMs) are sometimes generated from and used in place of computational fluid dynamics solutions. In this paper, several aerodynamic ROMs are generated and coupled with structural models to form aeroelastic ROMs. The aerodynamic ROMs generated here include the effects of control surface motion. Hence, the aeroelastic ROMs presented here are appropriate for use in aeroservoelastic applications and are intended to be used for aeroservoelastic control law development. These ROMs are used to simulate a number of test cases with and without control surface involvement. Results show that several of the ROMs generated in the paper are able to predict results similar to solutions of higher-order computational methods