Liping Xue

Material Point Method Applied to Fluid-Structure Interaction (FSI)/Aeroelasticity Problems

The material point method (MPM) combined with adaptive mesh refinement (AMR) technique is applied to investigate complicated fluid-structure interactions (FSI) such as aircraft wing flutter and other aeroelastic problems. The advantage of MPM over traditional fluid-structure interaction (FSI) methods is its computational efficiency, accuracy and robustness. MPM avoids explicit discretization of convection terms in momentum equations and the fluid-structure interaction is realized by coupling the fluid and solid stress at the interface. The states of material points are updated through the solution on background Cartesian grid node which is fixed during the calculation, thus no mesh distortion problem needs to be dealing with in the case of large deformation. The dynamic AMR can effectively decrease the total number of background mesh nodes and material points for complicated FSI problems. Preliminary results indicate that MPM with dynamic AMR can be a powerful tool to simulate FSI/aeroelastic problems for aerial vehicles. A 3D MPM code (a part of ASTE-P toolset) has been developed at Advanced Dynamics Inc. (ADI) with the ability to model complex fluid-structure interaction (FSI) problems.

Unified Solver for Modeling and Simulation of Nonlinear Aeroelasticity and Fluid-Structure Interactions

In this work, Material Point Method (MPM) is extended and enhanced to solve both fluid and structural dynamics, leading to an innovative unified solver for modeling and simulation of nonlinear aeroelasticity and fluid-structure interactions. In this approach, the fluid and structure are discretized into material points, and a unified solver is used to solve both fluid and structural dynamics, but with different EOS. The fluid-structure interactions are modeled by momentum exchange at the interface via the computational background grid. To eliminate the numerical oscillations that are typically encountered by particle-based methods, a minmod-type slope limiter is adopted. The distortion of the material point distribution is solved by regularization. Adaptive multi-level mesh refinement algorithm is developed to capture the multi-scale physics such as shock waves as well as large and small eddies. To speed-up the calculation, parallelization is implemented. Several cases are presented to illustrate the potential of this methodology for modeling and simulation of nonlinear aeroelastcity and fluid-structure interactions.

Integrated Variable-Fidelity Tool Set for Modeling and Simulation of Aeroservothermoelasticity-Propulsion (ASTE-P) of Aerospace Vehicles from Subsonic to Hypersonic

Advanced Dynamics is under the way for development of an Integrated Variable-Fidelity Tool Set for Modeling and Simulation of Aeroservothermoelasticity-Propulsion (ASTE-P) Effects of Aerospace Vehicles Ranging from Subsonic to Hypersonic Flight. The ASTE-P software tool set is developed in the state-of-the-art and commercial standard and enables accurate integration and tight/loose coupling of the fluid, structural and control field simulation with variable fidelity options available. The ASTE-P software tool can be applicable to modeling and simulation of aerodynamics, structural dynamics, flight control and propulsion dynamics as well as more important interactions of these dynamics. All flight regimes from subsonic to hypersonic are covered. The interface of structural/control surface motion and vibration modes with fluid flows is modeled using either unified particle-based material point method (MPM) or FVM/FEM based tight/loose coupled fluid/structure solving algorithms. Three levels of simulation environments are included in ASTE-P tool set: (1) the bottom level of high-fidelity and full-order simulation environment, (2) middle level of fast analysis and evaluation environment which is based upon on reduced order models (ROM) and provides fast turn-around time, and (3) top level of rapid design and optimization environment. Moreover, various flight control systems (FCS) designs and simulations are encompassed in the fully developed ASTE-P software tool set. The test cases presented in this paper indicate that the functionalities of ASTE-P are compatible or even more efficient than the similar software that is currently available.

An Efficient POD/ROM Based Aeroelasticity Model

In this paper, an efficient reduced order model (ROM) for aeroelastic and aeroservoelastic modeling has been developed based upon proper orthogonal decomposition (POD). This model is validated by computing the flutter boundary and reduced frequency ratio of aeroelastic AGARD 445.6 wing and successfully applied to flutter/LCO simulation of an advanced fighter plane configuration. The numerical accuracy and efficiency of this POD/ROM is quantified by using the full-order and full-coupled CFD/CSD simulation, experimental measurements and other existing computational results. The initial study has demonstrated that the new approach is highly efficient and accurate, thus can be used to obtain computational solutions which are the most accurate with the current state of the art and to sufficiently and rapidly predict the behavior of aerospace vehicles. I. Introduction Eroelasticitic and aeroservoelastic dynamics of an aircraft involve aerodynamics, structure dynamics and control, therefore is a comprehensive and multidisciplinary research area. The analysis and evaluation of the aeroelastic and aeroservoelastic dynamics is very important for performance, control and stability analysis of aircraft. Many of the methods that have been developed over the years for simpler aeroelastic models that use, for example, doublet lattice aerodynamics can be adopted for this purpose. However, these models are based on potential flow theory and cannot capture the nonlinear system dynamics in transonic flight regime. High-fidelity model do exist, but if high-fidelity computational fluid dynamics (CFD) and computational structure dynamics (CSD) approaches are used, the large degree-of-freedom, nonlinear fluid and structural system may take days to weeks to finish the computation and, thus are cost prohibitive. Fortunately, reduced order model (ROM) that captures the dominant feature of the full system provides an alternative approach and is extremely useful for such purpose. Dowell and Hall 1 presented a comprehensive review of reduced order models, and in recent years Advanced Dynamics Inc. has developed such models and solvers in its commercial software ASTE-P 2,3 . In this paper we present POD based ROM model that is appropriate to high fidelity computational models for aeroelastic and aeroservoelastic modeling of aircraft. A. POD Methods The use of proper orthogonal decomposition (POD) to construct reduced-order models (ROM) for the highest fidelity computational fluid dynamics (CFD) codes, e.g. the Reynolds-Averaged Navier-Stokes(RANS) equations, has been demonstrated by Thomas, Dowell and Hall 1,5-6,13 and more recently by Lucia and Beran 4,7-8 , Slater and

Harmonic Balance Methodology for Meshless Particle-Based Methods

Two novel Time Reduced-Order Models (TROMs) for time-periodic problems, the High-Dimensional Harmonic Balance method and Harmonic Multiple Shooting method, are developed in the context of the meshless, particlebased methods. The use of such techniques can greatly reduce the computational time for problems that can be considered time-periodic, which is frequently observed in aeroelastic problems such as flutter, limit cycle oscillations (LCO), etc. These algorithms will be implemented into the comprehensive aeroservothermoelasticity and propulsion modeling and simulation tool - ASTE-P that has been developed by Advanced Dynamics Inc. One of the important modules for aeroelastic modeling and simulation in ASTE-P is based upon the particle-based method which can efficiently and accurately handle fluid-structural interactions with large structural deformation and/or motions. The results obtained for both ROMS of particle-based harmonic balance methods were found to be encouraging.

A Meshless Method for Aeroelastic Applications in ASTE-P Toolset

Advanced Dynamics has developed a comprehensive and integrated software toolset, ASTE-P, for mutidisciplinary, multiphysics, multiscale and multifidelity analysis and design optimization (4MAO) of aerospace vehicles, and the module of pure particle method (PPM) is one of the key modules in ASTE-P for fluid-structure interaction applications. PPM is similar to the Smooth Particle Hydrodynamic (SPH) method in a sense that the solutions are solved on the particles. But unlike SPH, instead of a kernel function, PPM uses least square technique to interpolate properties to the particles. PPM can handle complex fluid flows and it is also very convenient to treat the fluid-solid boundaries, thus making it a very powerful method for solving fluid-structure interaction and aeroelastic problems. In addition, a novel Reduced-Order Model (ROM) based on the Harmonic Balance (HB) methodology is developed in the context of the meshless, particle-based methods. The use of such techniques can greatly reduce the computational time for problems that can be considered time-periodic, which is frequently observed in aeroelastic problems such as flutter, limit cycle oscillations (LCO), etc. Such methods improve the robustness of the particle solver as well as making it computationally efficient.

High-fidelity Modeling and Simulation of Flutter/LCO for All-movable Horizontal Tail with Free-play

This paper presents the study of free-play induced flutter and limit-cycle oscillation (LCO) with high-fidelity numerical methods. An accurate FE model has been created for the all-movable horizontal tail. The structural characteristics of the model was tested and published in the prior paper, WADC-TR-54-53 (AD 39949). The time accurate aeroelastic solvers are used to study the flutter and nonlinear limit cycle oscillations (LCO) induced by a free play gap in the actuating mechanism at the root of the tail. The aeroelastic solver includes state-of-the-art CFD schemes that are formally higher-order time-accurate on moving grids, radial based function(RBF) algorithm is used for exchanging aerodynamic loading and structural deformation data at the fluid-structure interface. The computed flutter speed and flutter frequency are compared with the experimental data and good quantitative agreement between two data sets is achieved.

ASTE-P: Software Package for Multidisciplinary, Multiphysics, Multiscale and Multifidelity Analysis and Design (4MAO) of Aerospace Vehicles

Advanced Dynamics has developed an Integrated Variable-Fidelity Tool Set – ASTE-P for Modeling and Simulation of Aero-Servo-Thermo-Elasticity and Propulsion (ASTE-P) of Aerospace Vehicles Ranging from Subsonic to Hypersonic Flights. The ASTE-P software tool set is developed in the state-of-the-art and commercial standard and enables accurate integration and tight/loose coupling of the fluid, structural and control field simulation with variable fidelity options available. The ASTE-P software tool can be applicable to modeling and simulation of aerodynamics, structural dynamics, flight control and propulsion dynamics as well as more important interactions of these dynamics. All flight regimes from subsonic to hypersonic are covered. The interface of structural/control surface motion and vibration modes with fluid flows is modeled using either unified particle-based methods (MPM/PPM) or FVM/FEM based tight/loose coupled fluid/structure solving algorithms. The Euler and RANS based solvers enable the accurate prediction of nonlinear coupled fluid-structure problems in aeroelasticity and the embedded fluid and structural dynamics solvers make the software self-contained and not require the integration of two separate third-party fluid and structure solvers for aeroelastic modeling and simulation. Three levels of simulation environments are included in ASTE-P tool set: (1) the bottom level of high-fidelity and full-order simulation environment, (2) middle level of fast analysis and evaluation environment which is based upon reduced order models (ROM) and provides fast turn-around time, and (3) top level of rapid design and optimization environment. The test cases presented in this paper indicate that the functionalities of ASTE-P are compatible or even more efficient than the similar software that is currently available.

Particle-Based Methods with Least Squares Technique for Nonlinear Aeroelasticity and Fluid-Structure Interactions in ASTE-P Toolset

Advanced Dynamics has developed a comprehensive and integrated software toolset, ASTE-P, for mutidisciplinary, multiphysics, multiscale and multifidelity analysis and design optimization (4MAO) of aerospace vehicles, and the particle method module is one of the key modules in ASTE-P for fluid-structure interaction applications. The fluid-structure interaction is numerically challenging. In our implementation, two particle-based methods, the Material Point Method (MPM) and Pure Particle Method (PPM), are adopted to solve both fluid and structural dynamics, leading to innovative unified solvers for modeling and simulation of nonlinear aeroelasticity and fluid-structure interactions (FSI). Preliminary results indicate that the particle-based methods with least squares technique can be powerful tools to simulate nonlinear aeroelastic and FSI problems such as flow-induced flutter/LCO and buffeting, etc.

Modeling and Simulation of Multi-fidelity AE/ASE Dynamics with the Integrated and Variable-Fidelity Toolset - "ASTE-P"

Advanced Dynamics Inc. has developed an Integrated Variable-fidelity Toolset, “ASTEP”, for Modeling and Simulation of Aeroservothermoelasticity-Propulsion (ASTE-P) Effects of Aerospace Vehicles Ranging from Subsonic to Hypersonic Flight. “ASTE-P” was developed in the state-of-the-art and commercial standard and enables accurate integration and tight/loose coupling of the fluid, structural and control field simulation with variable fidelity options available. The ASE module of ASTE-P toolset has a comprehensive capability for modeling and simulation of multi-fidelity Aeroservoeastic (ASE) Dynamics of aerospace vehicles. The Multi-fidelity AE/ASE dynamics modeling and simulation environments in ASTE-P toolset include: (1) the high-fidelity and full-order AE/ASE dynamics modeling and simulation environment, (2) fast AE/ASE dynamics modeling and simulation environment that is based upon reduced order models (i.e., POD-ROM, VolterraROM, etc.). In ASTE-P, the CFD reduced order model (ROM) is coupled with flight dynamics and structural dynamics models to build the mathematical system model, which is in-turn imported into Matlab/Simulink to conduct various dynamic analyses, including stability, flutter/LCO, maneuver, ejection and gust. In this paper, several cases of AE/ASE dynamics modeling will be presented to illustrate the numerical procedure for multi-fidelity AE/ASE dynamics modeling and simulation, and the computational capability of ASTE-P for AE/ASE dynamics modeling and simulation will be demonstrated. Finally, the computational efficiency with the optional variable-fidelity will be discussed.