Danny D. Liu

Numerical investigation of transonic limit cycle oscillations of a two-dimensional supercritical wing

Abstract CFD-based aeroelastic computations are performed to investigate the effect of nonlinear aerodynamics on transonic limit cycle oscillation (LCO) characteristics of the NLR7301 airfoil section. It is found that the LCO solutions from Navier–Stokes computations deviate less from the experiment than an Euler solution but strongly depend on the employed turbulence model. The Degani–Schiff modification to the Baldwin–Lomax turbulence model provokes spurious vorticity spots causing multiple shocks which might be unphysical, while the Spalart–Allmaras turbulence model yields physically reasonable unsteady shocks. In the cases examined, smaller initial perturbations lead to larger LCO amplitudes and vice versa, in contradiction to what one might expect. The amplitude of the initial perturbation is also found to have an impact on the mean position of LCO. Also addressed in the paper are aspects of multiblock message passing interface (MPI) parallel computation techniques as related to the present problem.

RANDOM AEROELASTIC RESPONSE DUE TO STRONG HYPERSONIC UNSTEADY-WAVE/SHOCK INTERACTION WITH ACOUSTIC LOADS

This work provides a first report on a detailed investigation on the interaction between structural response of supersonic/hypersonic air vehicle panels and the shock they support in the presence of an impinging strong acoustic excitation. The physical model adopted here is of a flat, deformable panel of a wedge-shaped body in a two-dimensional supersonic/hypersonic flow with attached shock. The present effort utilizes a linearized, perturbed Euler, aerodynamics with both linear and nonlinear reduced order models of the panel response. Two broad problems are particularly considered that correspond to the system (aerodynamics and panel) being either self excited or subjected to the acoustic excitation. Accordingly, the present formulation permits the estimation of the panel flutter and its post flutter behavior both with and without the acoustic excitation.

ON THE NONLINEAR STRUCTURAL DAMPING MECHANISM OF THE WING/STORE LIMIT CYCLE OSCILLATION

Contrary to previously believed, our recent study along with factual observations of the F-16 have indicated that a nonlinear transonic aerodynamic (NL Aero) model cannot represent the sole mechanism for wing/store LCO. Rather, we found that a nonlinear structural damping (NSD) model based on dry friction, a largely overlooked component, would more likely be an individual or collective (with NL Aero) cause of LCO over much wider Mach ranges than transonic LCO. Additional rationales also suggest that priority should be given to NSD research instead of NL Aero investigations. Towards this end, two research plans are recommended, i.e. (1) Develop a LCO prediction methodology using simpler aerodynamics with NSD (2) Pursue the understanding of LCO using high level CFD with NSD Seven technical goals are proposed to address the basic research issues for plan (1) with particular emphasis on the identification of the Coulomb friction in the wing/store system. It is fmally recommended that the example cases set up by both plans should ultimately be validated with rigid F-16 wind-tunnel data yielding flutter and with F16 flight tests indicating LCO.

Nonlinear aeroelastic methodology for a membrane-on-ballute model with hypersonic bow shock

[Abstract] A nonlinear aeroelastic methodology for inflatable/ballute type structures has been successfully developed for, a heuristic case: a 2D membrane-on-wedge model, and an axisymmetric modeled ballute system (MBS), under hypersonic/supersonic shock waves. Specifically, the nonlinear structural ROM methodology ELSTEP/FAT is extended and validated (based on MSC.Nastran FEM model) to the membrane-on-wedge model and the axisymmetric MBS. The time-accurate GasKinetic BGKX methodology has been developed as the key aerodynamic solver. It has great advantages over current continuum CFD solvers with its solution robustness, one-step computation of pressure and heat flux, and broad range of Knudsen number for hypersonic applications. Nonlinear aerodynamic static deformations at various altitudes have been obtained through a tight coupling between the nonlinear structural ROM and the direct BGKX aerodynamic solver. An efficient aerodynamic ROM has been developed for the undeformed/deformed mean 2D/axisymmetric configurations using a system identification technique with staggered modal inputs. The aerodynamic ROM solutions are found to closely match the direct BGK solutions. ROM-ROM time-domain dynamic aeroelastic analyses reveal significant differences between analyses carried out around the undeformed configuration and around the deformed one. In particular, a decrease in altitude will increase the static deformations which lead to a stiffer behavior with respect to additional small perturbations. Accordingly, a decrease in altitude induces an increased stability, in contrary to aeroelastic solutions for the undeformed configuration. This fundamental observation demonstrates the need to perform tightly coupled steady aeroelastic analyses prior to any stability analysis.

Flutter Analysis with Structural Uncertainty by Using CFD- based Aerodynamic ROM

[Abstract] This paper presents a novel and efficient methodology for flutter analysis with structural uncertainty in conjunction with an expedient CFD-based aerodynamic reducedorder modeling. The non-parametric structural uncertainty approach allows one rapidly investigate the effects of uncertainty towards to the dynamic system in the case when not enough information about the structural uncertainty is available. With the structural equations represented in the modal space and the baseline structural modal shapes used for all the variations of the structure, one set of aerodynamic reduced-order-models that suit for all the structural variations become feasible and thus significantly reduce the computational expense. Specifically, ARMA models for the generalized aerodynamic forces are developed by using an Euler-based CFD solver. The aeroelastic governing equations are converted into the discrete state-space form, and thereafter can be conveniently linked with the aerodynamic ROMs. The flutter speed is then determined by examining the damping coefficient of the time responses of the modal coordinates. A heavy version of the Goland wing is analyzed as a numerical example to demonstrate the present methodology.

Impact of frictional structural nonlinearity in the presence of negative aerodynamic damping

The focus of this paper is on providing a first validation of the possible role of friction as a stabilization mechanism in post-flutter limit cycle oscillations (LCO). To this end, four structural lumped mass models exhibiting both friction and a negative dashpot modeling the unstable aerodynamics were considered and their response computed by numerical simulation, through an exact formulation, and by the harmonic balance method. Continuous slip and stick slip LCO motions were indeed obtained in a broad range of negative damping ratios thereby demonstrating the stabilization potential of friction. A detailed analysis of the LCO responses in the time and frequency domains was performed to provide a more in depth phenomenological perspective. Finally, a comparison of the prediction strategies validated the use of both the exact formulation and the harmonic balance method for this class of problems.

Neural net-based controller for flutter suppression using ASTROS with smart structures

Recent development of a smart structures module and its successful integration with a multidisciplinary design optimization software ASTROS* and an Aeroservoelasticity (ASE) module is presented. A modeled F-16 wing using piezoelectric (PZT) actuators was used as an example to demonstrate the integrated software capability to design a flutter suppression system. For an active control design, neural network based robust controller will be used for this study. A smart structures module is developed by modifying the existing thermal loads module in ASTROS* in order to include the effects of the induced strain due to piezoelectric (PZT) actuation. The thermal-PZT equivalence model enables the modifications of the thermal stress module to accommodate the smart structures module in ASTROS*. ZONA developed the control surface (CS)/PZT equivalence model principle, which ensures the interchangeability between the CS force input and the PZT force input to the ASE modules in ASTROS*. The results show that the neural net based controller can increase the flutter speed.

Nonlinear Aeroelastic Analysis for A Wrinkling Aeroshell/Ballute System

Nonlinear aeroelastic analyses have been performed for a modeled ballute system with wrinkling phenomena considered. Specifically, the explicit nonlinear finite element code, DYNA3D, is extended to include the modified Newtonian flow theory for providing hypersonic aerodynamic loading; and a higher fidelity CFD approach, gaskinetic Bhatnagar-Gross-Krook-Xu (BGKX) method, is currently under development and will be integrated with DYNA3D to render a tightly-coupled nonlinear aeroelastic analysis system. BGKX has broad applicability of wide range of Knudsen number from continuum to transition flow, and accurate solutions for real gas flow, crisp shocks resolutions and shockshock interactions, thus an ideal aerodynamic tool for hypersonic re-entry applications. DYNA3D’s feasibility on wrinkling modeling is carefully investigated through a rectangular membrane under simple shear and Buck’s experimental cone configuration under CF4 wind tunnel test. Thereafter, nonlinear aeroelastic analyses for the modeled ballute system (MBS) reveal that, at lower altitudes, the MBS has larger overall displacements due to the larger dynamic pressure. As the altitude gets lower, the wrinkling becomes more pronounced, and some secondary (smaller amplitude) wrinkles appear along with the primary ones. At higher altitude, the wrinkling is comparatively less evident. Dynamic characteristics around the statically deformed MBS configurations are studied from the restarting transient analysis after the nonlinear aeroelastic static analysis.

On Rocket Plume, Lunar Crater and Lunar Dust Interactions

This paper presents our recent progress on the investigations of rocket Plume-Crate interaction and Lunar/Martian Dust Interaction (PDI). PDI is a very challenging problem of complex flow/soil interactions, involved with multi-physics, multi-scales, multi-dimensions, and multi-species. We are developing hybrid computational fluid dynamics (CFD) package, with the direct simulation Monte Carlo (DSMC) and gaskinetic BGK method to simulate the lunar rarefied flowfield in an accurate and efficient manner. For dust liftoff/trajectory, we adopt discrete element method (DEM) to simulate single dust particle ejection, and the overlay method to move the dust particles in the flow field obtained by the DSMC and gaskinetic BGK method. Meanwhile two physical-based models employing DEM are under development as improved computational tools for the predictions of crater formulation/evolution.

Hypersonic Aerodynamics using BGK Approach for Oscillatory Membrane-on-Ballute with Bow Shock Wave

Gaskinetic BGK approach is preferable to handle the hypersonic- entry aerodynamics of inflatable decelerators or ballutes, because the peak dynamic pressure is likely to fall within the rarefied gasdynamic regime. We report here our recent development of such a BGK approach for inflatable aeroelastic applications. First, the gaskinetic flow solver BGKX is improved with grid deformation technique and the flux is modified to account for the grid velocity. Next, the improved time-accurate BGKX solver generates the steady/unsteady aerodynamics for a 2D membrane-on-wedge and an axisymmetric membrane-on-ballute models for nonlinear aeroelastic analysis. Furthermore the BGKX solver can yield readily in one step pressures as well as heat fluxes on an axisymmetric membrane-on-ballute model. The computed BGKX results are validated with results by other continuum CFD flow solvers in the continuum range and with available measured data. Finally BGKX is applied for the nonlinear static aeroelastic analysis to the membrane-on-wedge and membrane-on-ballute cases. The static deformation is obtained first which will serve as a base for the inflatable flutter analysis that follows.