[american institute of aeronautics and astronautics 52nd aiaa/asme/asce/ahs/asc structures,...

American Institute of Aeronautics and Astronautics

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ASTE-P: Integrated and Multi-fidelity Modeling and Simulation

Tool for Aero-structure and Propulsion Dynamics

of Aerospace Vehicles

Drs. Patrick Hu1, Liping Xue2, Kan Ni2, Hongwu Zhao3

Advanced Dynamics Inc.(ADI), Lexington, KY, USA

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 dynam-

ics as well as more important interactions of these dynamics. All flight regimes from subson-

ic to hypersonic are covered. The interface of structural/control surface motion and vibra-

tion 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 simula-

tion 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 environ-

ment which is based upon reduced order models (ROM) and provides fast turn-around time,

and (3) top level of rapid design and optimization environment. This paper provides the

comprehensive validation and verification (V&V) of ASTE-P toolset recently done at Ad-

vanced Dynamics which resulted in over 600 pages report for over 40 benchmark test exam-ples that were selected from industry and academic research and design. The validation cas-

es presented in this paper indicate that the capability of ASTE-P is compatible or even more

powerful than the similar software that is currently available.

I. Introduction

HE development of modern transportation vehicles (i.e. high-speed train and aircraft) is driving the need to de-

velop advanced multi-disciplinary analysis methods and software design tools. Methods and software capability

for predicting aerodynamics, structural and control dynamics have been extensively developed during last dec-

ades. For example, for computational fluid dynamics (CFD) only there are tens types of software available in both commercial standard (i.e. Ansys-Fluent, Ansys-CFX, Start-CD, etc.) and in-house codes (Cart3D, Overflow,

CFL3D, Fun3D, etc.). The leading software for computational structural dynamics (CSD) includes Nastran, Ansys,

LS-Dyna among others. However, understanding and quantifying the coupling and interaction among these dynam-

ics still require development of advanced and accurate numerical methods and coupling algorithms guided by the

underlying physics. Therefore, the present paper for developing the full predictive capability of integrated Aero-

Servo-Thermo-Elasticity and Propulsion analysis and evaluation for transportation vehicles will have a great poten-

tial in supporting such vehicle evaluations and designs.

_______________________

1 Chief Scientist, Senior Member AIAA; 2 Principal Scientist, Member AIAA; 3Senior Scientist, Member AIAA

T

52nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference<BR> 19th4 - 7 April 2011, Denver, Colorado

AIAA 2011-2076

Copyright © 2011 by Advanced Dynamics Inc. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.


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It is well-established fact that a linear aerodynamic method, such as vortex-lattice and doublet-lattice based panel

method, is not suitable for compressible flows with shocks, and that a nonlinear aerodynamic method, such as

computational fluid dynamics (CFD) using Euler equations and Euler equations with boundary layer correction, is

not capable of predicting separated flows. For simplicity and computational efficiency, some of the current

software tools still use these methods or these methods with some nonlinear correction terms. Commercial codes

such as MSC/Aeroelasticity, ZAERO/ASE developed by ZONA Technology, Inc., and the STARS code developed by NASA are favored in current aeroelastic (AE)/aeroservoelastic (ASE) modeling and simulation because of the

integration with other analysis tools (e.g. NASTRAN for structures, MATLAB for controls). However, the fidelity

of computing the flight environment around a vehicle will strongly influence the forces (pressure and skin friction),

energy flux (conduction and radiation heat), and mass flux (ablation, if any) on the vehicle. These effects are

integrated over the complete vehicle configuration to determine the total aerodynamic forces (lift, drag, pitching

moment, control surface effectiveness) and the TPS sizing requirements for the vehicle. One of the objectives for

development of the ASTE-P software tool set is to enable a high-fidelity yet computationally-efficient capability for

simulating highly-nonlinear aerodynamics and structural dynamics and their interactions.

The significant innovation of the present work is the ASTE-P software tool set1-2 which enables accurate

integration and coupling of the fluid, structure and control field simulation in aeroelastic system with variable fidelity

options available at different analysis and design stages, resulting in significant time saving for aerospace vehicle

evaluations and designs. Moreover, the ASTE-P software tool set will be applicable to all flight regimes ranging from subsonic to hypersonic. The interface of structural/control surface motion and vibration modes with

aerodynamic flows is modeled using the powerful state-of-the-art CFD/CSD coupling algorithm and particle-based

methods (Material Point Method-MPM and Pure Particle Method-PPM)1-6 in a static and dynamic fluid-structure

interaction environment. By using the particle methods, the information between different field solvers passes

through momentum and energy exchange terms in conservation laws. Consequently, the overall accuracy will

maintain the same order as field solvers, being not compromised by information passing at interface that is typically

encountered by standard finite element based methods. The PPM/MPM is essentially a “mesh-free” and highly

parallelizable method which avoids dealing with the time-varying mesh distortions and boundary variations due to

structural deformations and/or control surface motions, thus being significantly more robust and computationally

efficient than other methods with moving-boundary and mesh-regeneration.

Full-coupled and full-order computational models based upon the Euler and Navier-Stokes fluid models and nonlinear structural models are computational extensive and generally take weeks or months to obtain the solution

for real engineering problems, and recent advances in rapid-solution techniques for such models – using the

harmonic balance (HB) or time periodic method7-14, and/or the expansion of the flow field and/or structure in terms

of proper orthogonal decomposition (POD) modes15-19– has made the use of such high fidelity models potentially

feasible for design and pretest evaluation studies of aerospace vehicles. See Refs. [9] and [20] for an overview of

these methods. The computational efficiency can be further enhanced by massive parallelization, in-situ residual

monitoring and computational steering. The ASTE-P tool set presented in this paper will encompass a detailed

evaluation capability that includes the full solution benefits of the powerful state-of-the-art CFD/CSD coupling

algorithm and the particle-based MPM/PPM method with full flight control system (FCS) definition, propulsion

module, fast evaluation environment and fast design and optimization environment.

Advanced Dynamics is dedicated to the development of Multi-disciplinary, Multi-physics, Multi-scale and

Multi-fidelity (4M) Analysis and Optimization (4MAO) modeling and simulation software tools21,22, including aero-elasticity (AE), aeroservoelasticity (ASE), aeroservothermoelasticity and propulsion (ASTE-P), as well as fluid dy-

namics, structural mechanics, system dynamics and control, multiphase flows and combustions, etc. The software

tools developed by Advanced Dynamics are variable-fidelity, thus the low-to-mid fidelity has fast turn-around time

for concept design, and the high-fidelity can be used for final design verification. The integrated tools can be rou-

tinely applied to realistic engineering design and physics-based real or near-real time modeling and simulation for

complex aerospace systems that are commonly researched and manufactured by NASA, U.S. Air Force, Navy and

Army, as well as major defense contractors such as Boeing, Lockheed Martin, Pratt Whitney, Rolls-Royce, General

Electric, General Dynamics and Textron, etc.

II. Integrated Software Configuration of ASTE-P Tool Set

The integrated software of ASTE-P tool set includes 3 levels of simulation and design environments with variable-fidelity computational models. The integrated software configuration is shown in Figure 1. The bottom level

is the high-fidelity and full-order simulation environment, which includes computational fluid dynamics (CFD) and


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thermal analysis component, the computational structural dynamics (CSD) component, propulsion component, flight

control component and particle method (MPM/PPM) component, as well as the multi-field interaction modeling and

simulation component. These components can be run independently for single field simulation and collaboratively

for multi-field interaction problems such as aeroelasticity (AE), aeroservoelasticity (ASE), aeroservothermoelasticity

and propulsion (ASTE-P) problems. The middle level is fast analysis and evaluation environment which has mid-to-

high fidelity in reduced order models (ROM), including Volterra ROM, HB and POD-ROM. These ROMs can provide fast turn-around time for vehicle analysis and evaluation, which is maybe tens to hundreds times faster than

the bottom level full-coupled and full-order modeling and simulation. The top level is fast design and optimization

environment which uses both the bottom level and the middle level simulation depending on the design stage. For

example, the middle level will be used in the conceptual and initial design, but the bottom level will be used for final

design verification. The integrated software also includes the visualization package for post-processing and the pre-

processing package of CGNS23 which reads the mesh generated by current popular grid generation packages such as

Gridgen, Hypermesh, etc. The main window of the ASTE-P 2.0 is shown in Figure 2.

Figure 1. The Integrated Software Configuration

of ASTE-P 2.0.

Figure 2. The Main Window of the ASTE-P 2.0

Tool Set.

III. Components of ASTE-P Tool Set and Computational Models

A. Computational Fluid Dynamics (CFD) The component of Computational Fluid Dynamics (CFD) includes high-fidelity Euler and Navier-Stokes based

methods. The Reynolds-averaged Navier-stokes (RANS) turbulence models include algebraic models, Spalart-

Allmaras one equation model, several k-epsilon and k-omega models, etc. In near future this CFD component will

include direct numerical simulation (DNS), Large-Eddy Simulation (LES) and Detached-Eddy Simulation (DES)

subcomponents. Both ideal as well as chemically and thermally equilibrium and non-equilibrium gas models are

included. The numerical algorithm includes grid-based finite-volume as well as particle-based MPM/PPM me-thods.

A.1. Grid Based Finite-Volume Solver The flow equations are discretized by a central difference or upwind finite-volume scheme on struc-

tured/unstructured or hybrid grids. A turbulence model is selected to close the flow equations in viscous cases. Simi-

larly, the velocities of cell faces should also be included in convective terms. The turbulence equations are solved

decoupled with basic flow equations. Multigrid acceleration is employed for fast convergence on the iteration at

pseudo time domain. Adaptive Mesh refinement (AMR) option is available in hybrid unstructured CFD solver.

A.2. Time Integral for Unsteady flow For the reason of computational efficiency, the code adopts the method in which the left-hand side is treated with

an implicit approximate-factorization method as steady-state simulations. The implicit derivatives are written as spatially first-order accurate, and therefore second-order temporal accuracy is forfeited for unsteady computations.

One method for recovering the desired accuracy is using sub-iterations. Thus “dual time stepping” strategy is intro-

duced in the ASTE-P tool set.


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B. Computational Structural Dynamics (CSD) Component ASTE-P-FE is the CSD (finite element based computational structural dynamics) solver in ASTE-P. ASTE-P-FE

component is built for the purpose of finite element (FE) analysis of structures including aircraft, marine and off-

shore structures, automotive, high-speed train, and civil engineering structures, etc. there are the following sub-

modules: 1) Static FE analysis;

2) Static FE nonlinear geometry analysis;

3) Structural dynamics FE analysis;

4) Structural dynamics FE nonlinear geometry analysis;

5) FE Aeroelasticity analysis;

6) FE thermal analysis;

7) FE thermal stress analysis.

8) High-Dimensional Harmonic Balance (HDHB) finite element (beam and plate elements finished).

Currently the basic FE element library has been established, which includes

1) 2D and 3D bar;

2) 2D and 3D beam (with different section areas);

3) plane (3-node, 4-node, 4-node iso-parameter); 4) plate bending (T-9 and R-12);

5) plate shell (3-node DKT and 4-node DKQ);

6) curved shell (quad-4 and quad-8) and

7) brick (iso-parameter 8-node, 20-node and 27-node).

The Component of CSD includes the finite-element and MPM models. The finite element models include all

components of aircraft structural system and subsystem components such as beam, plate, shell, bar as well as solid

element (8-nodes, 20 nodes and 27 nodes), etc. The theory of finite-element models is described in many literatures,

and will not repeat here. The implementation of the MPM method for both fluid and structural dynamics will be

presented in the sub-section D that will follow.

C. CFD/CSD Coupling Algorithm for Aeroelastic Simulation The aeroelastic system is a coupled nonlinear system that combines the CFD and CSD models. The CSD model

deforms driven by the aerodynamic force computed by the CFD model, while CFD model is disturbed by the struc-

tural deformation. The way of coupling these two models might be loose coupling or strong coupling.

For strong coupling, the two models are solved by some kind of iteration method to make them synchronous at

each time step. Figure 3(a) shows the solving procedure of a classic serial approach. Although strong coupling way

is more complicated, the time accuracy is not sensitive to the time step.

For loose coupling, in each time step, the two models are solved once separately. With the aerodynamic force

computed, the CSD model is advanced one step to obtain the new structural displacement. Then, according to the

displacement, the new grid is generated by the grid deforming module. Thus, the CFD model can be advanced in

real time domain in the new grid configuration. After that, the aerodynamic force of next time step can be computed.

Figure 3(b) shows two procedures of the loose coupling method. This loose coupling method is easy to implement.

However, the solving of ordinary differential equation for the CSD model needs the aerodynamic force of next time step which cannot be obtained in advance. Considering both time accuracy and robustness, an aerodynamic force

interpolation technique is introduced in the ASTE-P code.

For single-block grid, traditional transfinite interpolation (TFI) is a good choice for excellent efficiency because

only explicit algebraic computation is involved. For multi-block grid, if the deformation on the surfaces of each

block can be determined first, then TFI can still be used. In the presence of multiblocks of grids, Radial Base Func-

tion (RBF) approach is applied to determine the deforming displacements of a coarse background grid. Then in each

coarse element, TFI is used to compute the displacements of fine grid nodes. Because RBF only needs the data of

those nodes on the deforming surfaces and constrained surfaces but not the volume nodes and the connecting infor-

mation, the fine grid is actually split into a coarse grid logically, which means that no real coarse grid is generated,

stored and manipulated. And another advantage is that the splitting is independent on the interpolating points used in

RBF. Once the RBF interpolating coefficients are computed, the displacement on any node can be interpolated. It is different from the spring analog or FEM which can only determine the displacement of the specified coarse nodes.

The procedure of grid deforming is presented as follows:

(1) Choose some control points from the boundary surfaces of the grid as interpolating points of RBF;

(2) Construct RBF interpolator with those control points;


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(3) At each time step of an unsteady CFD simulation, update the RBF interpolator and the symmetry correcting

RBF interpolator if needed and compute the RBF coefficients;

(4) Compute the displacements on all edges: split each edge of the grid into segments, determine the displace-

ment of each unknown endpoint of each segment by the RBF interpolator, compute the displacements of

other nodes of the segment with TFI, and force all coincident nodes with the same displacements;

(5) Compute the displacements on all surfaces: split each surface of the grid into patches, determine the dis-placements of unknown corners of each patch with RBF, compute the displacements of other nodes of the

patch with TFI, and force all coincident nodes with the same displacements;

(6) Compute the displacements in all blocks: split each block of the grid into bricks, determine the displace-

ments of unknown corners of each brick with RBF, compute the displacement of other nodes of the brick

with TFI, and force all coincident nodes with the same displacements.

Figure 3. Schematic of Solving Procedure:

(a) Classic Serial Approach, and (b) a Loose Coupling Approach. D. Unified MPM Solver for both Fluid and Structural Dynamics The shape and size of flexible vehicles may change substantially during flight. This shape and size change may

result in a wide variety of changes to the mechanical properties of the structure, such as the stiffness of the vehicle

structure, and the aerodynamics of the vehicle as well. Therefore, traditional linear structural models and nonlinear

yet simple models cannot be used in order not to degrade solution accuracy. For finite element methods, significant

efforts are needed for grid re-generation and dealing with time-varying mesh distortions and boundary variations due

to structural deformations and/or motions. Finite element methods with transpiration boundary correction avoid

dealing with time-varying mesh distortions, but only allow for small deformations and/or motions (p-version FEM is

more adept at handling these large element distortions). Fortunately, particle-based methods provide an alternative

approach. Particle-based methods have many advantages over the traditional FEA-based methods; the advantages

include ease of handling arbitrarily large deformations and/or motions; ease of linking with a CAD database for complex geometries; and ease of modeling damages to the structure, etc.

Techniques developed and used at Advanced Dynamics Inc. (ADI) are the material point method (MPM) and

the pure particle method (PPM). They are both particle-based methods. MPM was originally developed for structural

dynamics with arbitrary deformation and/or material failure24,25. With significant development at ADI, it has been

extended for complex fluid-flows as well as for FSI and aeroelastic problems26-28. PPM has been developed recently

at ADI to take the advantages of pure particle method and forms an alternative for solving fluid and FSI problems in

ASTE-P tool set.

The MPM method is based on the particle-in-cell (PIC) method, where the fluids and/or solid materials in com-

putational domain are discretized into a collection of material points (particles) much like a computer image is

represented by pixels. As the dynamic analysis proceeds, the solution is tracked on the material points by updating

all required properties such as position, velocity, acceleration, stress state, etc. There are two variations to this ap-

proach; one in which a background mesh is employed to solve for the velocities (MPM) and another in which every-thing is solved entirely on the particles (PPM). The first variation leads to a mixed Eulerian-Lagrangian framework

and the latter is based purely on a Lagrangian framework. Since the particles can freely move and different particles

can interact with each other, we avoid dealing with time-varying mesh distortions and boundary variations due to

structural/control-surface deformations and/or motions. This results in the particle methods being significantly more

robust and computationally efficient than traditional FEM-based methods that are currently favored for

FSI/aeroelastic modeling and simulation.


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E. Propulsion Component The functionalities to be enabled by the propulsion component of ASTE-P is compatible to all the existing CFD

software available on marketing such as Fluent, CFX, STAR-CD, Fastran, and CFD++ as well as Phoenics, etc.

Although different CFD software has different classification of its combustion modules, the core combustion solver

of them are almost the same (except for Fastran and CFD++), the differences mainly lie in the specialization for

particular applications. In ASTE-P we use a general way to categorize our combustion modules, just like other CFD software did. According to the basic theory of combustion and the available combustion modules in popular CFD

software, ASTE-P covers the three typical combustion regimes: (1) non-premixed combustion; (2) premixed

combustion; (3) partially premixed combustion. Therefore, for most important applications of combustion solvers,

there are several important areas covered and included into ASTE-P tool set:

(1) Description of real mixtures. This part involves the governing system of chemical reacting flows and the

description of turbulent effects, including the RANS equations and LES equations.

(2) Turbulent-flame interactions. This topic refers to the study of three typical turbulent-flame interaction

regimes: the wrinkled regime, the corrugated regime and the thickened regime.

(3) Topological models. These include the research of flamelet models and the flame surface density model.

(4) Reactor models. This area is divided into three subzones: a) infinitely fast chemistry (like the equilibrium

reacting model in air chemistry); b) premixed combustions, such as the turbulent flame speed model, eddy

break-up model and bray-moss-libby model; c) non-premixed combustion, such as the conserved scalar equilibrium models.

(5) Finite rate chemistry. This topic involves the 4 principal subzones: a) premixed combustion which includes

coherent flame model and flamelets based on G-equation; b) non-premixed combustion which includes

flamelets based on conserved scalar, intrinsic Low Dimensional Manifolds (ILDM) and Conditional

Moment Closure (CMC); c) Linear Eddy Model; d) PDF Transport Model.

(6) Multiphase flow. This part is important for partially premixed combustion and focus on the transport

properties between particles of different phases and the devolatilization models of reactants.

F. Fast Analysis and Evaluation Environment The pretest evaluation and design of aircraft involves aerodynamics, structure dynamics, propulsion and control

dynamics, therefore is a comprehensive and multidisciplinary. The analysis and evaluation of this integrated system is very important for performance and stability analysis of aircraft. Particularly, the near-real or real time simulation

of these dynamics will provide the insight for the performance and safety of aircraft in the flight envelope before the

flight test. However, if the full-order CFD and CSD approaches are used, the large degree-of-freedom, nonlinear

fluid and structural system for the whole aircraft may take weeks or months to finish the computation and, thus are

computationally prohibitive. A reduced order model (ROM) that captures the dominant feature of the full system is

highly desired and extremely useful in practical simulation. In general, ROM analysis involves several steps: (1)

generation of training data (snapshots or time-histories of loading excited by prescribed inputs) by conducting full-

order simulations, (2) generation of the ROM model by utilizing methods such as eigenmode based methods and

system identification methods, and (3) deployment of the ROM model for the full-order system analysis. Different

approaches have been extensively investigated in the last few decades, including linearization about a nonlinear

steady-state condition, linear model fitting (such as the ARMA model), representation of the aeroelastic system in

terms of its eigenmodes, and linearized representation of a ROM for nonlinear aeroelastic/aeroservoelastic systems. The POD and Volterra29,30 ROM models are selected for use in present study.

The combination of high-fidelity models and the ROMs is the innovative idea of variable-fidelity modeling and

simulation. The ROM does not only facilitate the near-real or real time simulation, but also can be used at the initial

design stage so as to achieve fast turn-around time. On the other hand, the high-fidelity full-order and full-coupled

simulation can be used at the final design stage to verify and validate whether the design will meet the design

objective and the mission requirement. Although many studies have investigated aeroelastic phenomenon using

POD and Voltrra ROM, few have addressed the near-real or real time simulation, even for simple configuration and

trajectory. Advanced Dynamics pioneered the research in this field and explored the POD and Volterra ROM

approach towards real time simulation of the aeroservoelastic dynamics31.

G. Unique Features of ASTE-P Tool Set Compared with Similar Software There are 10 advantages of ASTE-P compared to existing CAE software such Fluent, CFX, Nastran and Ansys,

which include:

1) Integrated, user-friendly and self-contained all necessary components for multi-disciplinary analysis and

design of aerospace, automotives, marine ships and complex mechanical systems: CFD, CSD, FSI &AE,


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ASE, Propulsion, CAA, Material Database, Particle Methods and Post-processor. All modules can be

RUN and BOUGHT individually or jointly with other nodule(s).

2) Strong capability for solving nonlinear problems for fluid dynamics (i.e. shock, flow separation, high-

temperature gas dynamics), structural dynamics (i.e. crack, impact and penetration and arbitrary large de-

formations using particle-based methods) and coupled nonlinear fluid-structure interaction (FSI) and aero-

elasticity/Aeroservoelasticity (AE/ASE) (i.e. flutter/LCO, buffet). 3) Strong capability for solving fluid-structure interaction, aeroelasticity and aeroservoelasticity problems, the

CFD and CSD solvers are directly embedded into FSI/AE and ASE modules and no third party software is

need, both grid-based and particle-based approaches are available in FSI/AE and ASE modules for solving

viscous, large deformation and strong nonlinear problems.

4) Mesh generation is not needed for complex and or rotating geometry (i.e. full aircraft, rotating problems

such as rotor wake interacting with fuselage, turbine blade and disk) if particle method is used.

5) Faster turn-round time is guaranteed by using reduced order models (ROM) such as Proper Orthogonal De-

composition (POD), Volterra ROM (e.g. 2 hours coupled CFD/CSD simulation vs. 2 seconds for POD-

ROM for a flutter analysis of a typical 3D wing)

6) Higher numerical accuracy is achieved by incorporating most recent numerical algorithms in CFD and CSD

for high Mach number in ASTE-P (Mach number could be as high as 50) and incompressible flows with

velocity approach to 0, and multiphase flows with essentially no-upper limit for number of dispersed phas-es.

7) Simulation data is directly outputted for design optimization.

8) Strong capability for computing combustion and noise (for both subsonic and supersonic jets).

9) Independent pre- and post- processors for geometry modeling, mesh and particle generations and structural,

unstructural and particle data high-quality display and fast animation capability (e.g. fast vibration of struc-

tural component).

10) Comprehensive and user-friendly material database for user to choose and customize the materials types

and properties.

IV. Validation and Applications of ASTE-P Tool Set As a world leader for modeling and simulation software and consulting services, Advanced Dynamics clearly

understands the huge potential and high demands for ASTE-P tool set that can be robustly applied to complex fluid,

thermal, structural, propulsion and control dynamics and the interactions of all these dynamics. In June 2008, Ad-

vanced Dynamics was selected as one of the companies for NASA’s SBIR Infusion Assistance Program for transi-

tioning ASTE-P tool set to Phase III and commercial marketing, and 2010 Advanced Dynamics was actually enter-ing the Phase III transition for ASTE-P. The major NASA application of this ASTE-P tool set is the pretest evalua-

tion, modeling and simulation of wind tunnel and flight testing vehicles. The ASTE-P is a powerful tool for solving

subsonic rotary-wing and fixed wing aircraft, supersonics and hypersonics problems. In addition, because the

ASTE-P tool set is particularly efficient in modeling and simulation of multi-field interactions with complex confi-

guration, it should have much broader applications than current available tools such as Ansys-Fluent, Ansys-CFX,

and Nastran.

Moreover, Advanced Dynamics has established partnerships with the World’s leading aviation companies such

as Boeing, Bell Helicopter, Sikorsky Aircraft, AeroVironment, Inc., Rolls-Royce, Northrop Grumman, Honeywell

Engine & Air Management, Honeywell International Turbine Technology, etc. These companies expressed tre-

mendous interests for ASTE-P tool set, and believed that the advanced modeling and simulation software for multi-

disciplinary interactions can help aerospace engineers solve complex fluid, thermal, structural and control dynamics

and combustion problems, thus will provide excellent tool for their evaluations and designs of flight vehicles and engine components. In addition, the high-speed train and automotive industry companies may also significantly

benefit from this state-of-the-art modeling and simulation technology in the design of more economic and environ-

ment friendly vehicles.

In order for ASTE-P to be as a reliable and user-friendly tool, the validation and verification are very important

at current stage, and we have committed to this effort recently by testing ASTE-P over 40 benchmark testing cases

selected from industry and academic research and design, which resulted in over 600 pages validation and verifica-

tion report. The range of applications covers from aircraft to high-speed train in CFD, CSD, propulsion and acous-

tics as well as aeroelasticity/aeroservoelasticity and reduced order models. Due to the page limitation, this paper

only presents a small number of validation and verification cases, and in the later papers we will continue to present

the rest of the validation and verification for ASTE-P toolset.


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A. Validation of Aeroelastic/Aeroservoelastic Solver in ASTE-P

A.1 Flutter and LCO Prediction and Aeroservoelastic Modeling of AGARD 445.6 Wing The AGARD 445.6 wing test case, which was tested in the Transonic Dynamics Tunnel at NASA Langley Re-

search Center, has been widely used as a benchmark for evaluating aeroelastic simulations. The wing is a semimodel

that has a quarter-chord sweep angle of 450, a panel aspect ratio of 1.65, a taper ratio of 0.66 and NACA 65A004

airfoil cross section. The wing flutter speed index is defined as

f

UV

bα

ω µ

∞

=

where U∞ is the velocity of freestream, b is the half chord at wing root,

αω is the natural angular frequency of the

first uncoupled torsion mode, / ( )m vµ ρ= is the wing mass ratio, m is the mass of the wing, v is the volume related

to the wing, and ρ is density of the freestream. The flutter analysis selects the first four modes, which are identified

as the first bending, first torsional, second bending and second torsional modes, as shown in Figure 4.

(a) Mode 1, Frequency=9.4574Hz (b) Mode 2, Frequency=39.6986Hz

(c) Mode 3, Frequency=49.4515Hz (d) Mode 4, Frequency=95.1005Hz

Figure 4. Modal Shapes of AGARD Wing 445.6.

Presently, the flutter boundary is searched for zero angle of attack. For comparing with the experiment data, flut-

ter velocities under six freestream Mach numbers are searched, including 0.499, 0.678, 0.901, 0.96, 1.072 and 1.141.

To find a flutter point at one freestream Mach number M∞

, the freestream velocity U∞

and corresponding dynamic

pressure 2( ) / 2Uρ∞

are adjusted and the transient flows are calculated. If the transients of the generalized coordi-

nates do not grow or decay, then a flutter boundary point is obtained.

For viscous calculations, the Reynolds-averaged Navier-Stokes equations are solved based on thin shear layer

approximation. Jameson central scheme is used to discretize the convective terms. SST k-omega model is adopted to

simulate the turbulence transport, and 2-level multigrids are employed for accelerating the flow calculation.

Above all, the sensitivity to time step size of loose coupling algorithm is examined. Although displacement

curves are usually smooth and aerodynamic force interpolating possesses good time accuracy, obvious errors may

still be induced when using a large time step. Here the transient flows when 0.901M∞

= are selected as the inves-

tigation cases. Under this Mach number, the non-dimensional flutter velocity is 0.3548. Further, under this velocity,

the dynamic responses of four structural modes are calculated with different time step lengths. For inviscid calculations, Jameson central scheme is adopted to discretize the convective terms. No multigrid is

employed for acceleration.

According to the CFD/CSD coupling algorithm introduced in Section III, the flutter velocity boundaries for Eu-

ler, RANS and POD simulations under six freestream Mach numbers are found. The results are shown in Figure 5.

For comparison, the experiment data and the results of Duke University are also given. It’s obvious that the flutter

velocity boundaries calculated by the present code have a good agreement with the experiment result and the com-

putational results of Duke University. Taking the experiment result as the benchmark, the flutter boundary calcu-

lated by RANS equations are more accurate than that by Euler equations. This seems reasonable because the real


9

flow is always viscous. Note that the flutter boundary calculated by POD method almost coincides with that by Eu-

ler simulation. On the one hand, this may prove the reliability of POD method; on the other hand, this is because

POD algorithm uses the steady flow field calculated with Euler equations.

The flutter frequency ratio /f αω ω for Euler and RANS simulations under the same Mach numbers are also

found, where fω is the flutter frequency and

αω is the frequency of the first torsion mode. As shown in Figure 6,

the flutter frequency ratio calculated by ASTE-P has very good agreement with experimental measurement and the

results of Duke University, and the result from RANS simulation is closer to experimental data than from Euler si-

mulation. Several Snapshots of the wing flutter calculated by Euler model is presented in Figure 7. Even in large

deformation, the ASTE-P tool can robustly perform the calculation.

Figure 5. Flutter Velocity Boundary of AGARD

Wing 445.6.

Figure 6. Flutter Frequency Ratio of AGARD

Wing 445.6.

Figure 7. Snapshots of the Flutter Simulation for AGARD 445.6 Wing.

A.2 Free-play Induced Flutter and LCO Prediction of All-movable Tail Tested in Wright Air

Development Center (WADC) The structural model was obtained from WADC report32, and tatoal 19 cases with different free-play parameters

such as rotational frequencies and free-play angles were computed and compared with experimental measurements.

The agreement between the computational results and experimental measurements are very good in flutter speed and

flutter frequencies except 2-3 cases in which the experimental measurements may contaminated by some wind tunnel factors such the flow turbuence at the testing time. Due to the page limitation, we only provide 2 cases here for

illustration purpose. The Figures 8(a)-(b) show the structural dynamics model and Table 1 shows the comparision of

the computational results and experimental measurements. Figiures 9 (a)-(c) show the generalized modal

displacment, generalized modal velocity and phase plot, respectively. Figiures 9 (d)-(f) show the time history of lift


10

coeffcient, the rotational angle and rotatioal speed, respectively. The simulation clearliy demonstrates that the wing

runs into LCO and exhibits complex structural nonlinearity with free-play.

(a)

(b)

Figure 8. Structural Dynamics Model.

(a)

(b)

(c)

Time

Cl

1 2 3

-6

-4

-2

0

2

4

6

8

(d)

Time

Ro

ot

Ro

tati

on

An

gle

(De

g)

1 2 3-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

(e)

Time

Ro

ot

Ro

tati

on

Sp

ee

d

1 2 3-1

-0.5

0

0.5

1

(f)

Figure 9. The Computational Results for WADC Wing with Free-play Angle of 1.52 Degrees.

Table 1: The Comparison between Computational Results and Experimental Measurements.

Free-play Angle

(Degree)

Flutter Speed (m/s) Flutter Frequency (CPM)

Exp. Num. Error (%) Exp. Num. Error (%)

1.52 15.8 14.2 10.0 262 260 8.6

0.62 38.5 35.2 8.6 267 285 6.7

B. Validation of CFD Solver

B.1 2D Transonic RAE2822 Airfoil A 2D transonic RAE2822 airfoil was modeled using the hybrid grid CFD solver. The flow condition is: Mach

number is 0.725, Reynolds number is 6.5×106, and Angle-of-Attack is 2.92 deg. Figures 10(a)-b present the pressure


11

coefficient distribution over the surface of the airfoil and density contours, respectively. From these figures it can be

seen that ASTE-P captured all transonic flow features over an airfoil and obtained a very good agreement with

experimental measurement.

V1

V2

0 0.2 0.4 0.6 0.8 1

-1.5

-1

-0.5

0

0.5

1

1.5

2 Numerical

Experimental

Figure 10 (a). Pressure Coefficient

Distribution.

Figure 10(b). Density Contours.

(a)

Cp

z/L

-0.01 -0.005 0 0.005 0.01-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

NumericalExperimental

x/L=0.35

(b)

(c)

(d)

Figure 11. Simulation for ROBIN Helicopter Using Hybrid Grid CFD Solver in ASTE-P: (a) Helicopter

Body and Mesh, (b) Pressure Distribution on the Helicopter Body Surface, (c) Helicopter Rotor Wake and

Body Interaction, (d) The Pressure Oscillation on the Helicopter Body Surface.

B.2 Helicopter Rotor Body Interaction (ROBIN)

The ROBIN fuselage is first simulated without the influence of the rotor wake for inviscid flow, with Mach

number 0.121, 0 degree of attack angle and 1.2 degree of yaw angle. Figure 11(a) shows the unstructured mesh on

the body surface and computational domain. The total mesh cell number is about 2.0 million. Figure 11(b) shows

the pressure coefficient comparison with the experimental result at x/L=0.35. In general, the pressure on the ROBIN

body surface is well predicted. Then the rotor wake influence on the ROBIN body was simulated. The rotor wake

was first computed by Vortex Particle Method (VPM). Then the wake induced velocities inside the body of

computational domain was included in CFD simulation by using flux corrections at all cell faces of a control


12

volume. Since this is a four blade rotor, the rotor wake is periodic in each quarter revolution, the wake within a

quarter rotor revolution can be repeatedly used during the coupling simulation. Figure 11(c) shows the vorticity iso-

surface with value of 100. The rotor wake vorticity can be clearly observed above the ROBIN body. The rotor

wake interacts with the ROBIN body and causes the periodic pressure oscillation on the body surface. Figure 11(d)

shows the pressure time history at the location x/L=1.556, y/L=0.007 and z/L=0.073. It is obvious that the pressure

is oscillating with a period of 0.0075, which is a quarter revolution time of the rotor. The pressure oscillation phase and magnitude correlated well with the experimental result33.

B.3 High-Speed Train

For high-speed train, aerodynamic resistance is the main resistance during its moving. When speed reaches

200km/h, aerodynamic resistance is about 70 percent of its whole resistance, while reaches 300km/h, the number

will become 85~90 percent. For double container freight train, the number will be bigger. So it is very important to

study aerodynamic problem during moving of the high-speed train. The length of the train is 27.5 m, high is 4 m,

and width is 3.2 m, and the speed is 300km/h.

Figures 12 (a)-(b) show the pressure and velocity distribution over the train body and head, respectively, from

which we can see the compression wave of the air flow over the train head is very strong; Figures 12 (c)-(d) show

the velocity and streamline distribution in the train base and far away from the base, respectively; and Figures 12 (e)-(f) show the convergence history of the drag coefficient and the work rate done by the power for overcoming the

aerodynamic drag, without the friction drag between the wheels and the railway. The geometry of the high-speed

train is very complex and this test example examined the strong capability of the CFD solver in ASTE-P for

computing a flow passing over a complex geometry.


13

Time

Cd

0 0.001 0.002 0.003

0.02

0.04

0.06

Time

Dra

gW

ork

(N.m

/s)

0 0.001 0.002 0.003

2E+06

4E+06

6E+06

8E+06

1E+07

1.2E+07

Figure 12. High-speed Train Simulation Results.

C. Test Cases Using Particle Methods

C.1 Subsonic Flow past an AFA An Aluminum Fighter Aircraft (AFA) is used to test the code’s ability of particle methods for handling complex

geometries. The domain size used for this computation was 24x16x8 with 3 levels of grid refinement. The coarsest

background mesh has 10x80x40 points, which amounts to 9.5 million particles initially.

We performed two calculations, one corresponds to an angle of attack of 0 degree and one with 5 degrees. The

Mach number for both cases are 0.8. Plots pertaining to zero degree angle of attack are shown in Figure 13(a) and those pertaining to 5 degrees AOA are shown in Figure 13(b). We can clearly see the couple of counter-rotating

vortices over the wing tip region for the 5 degrees AOA case, which is consistent with the theory. This case shows

immense promise in the robustness of the particle solvers to deal with complex geometries.

(a)

(b)

Figure 13. Simulation of Particle Method for Complex Geometry: (a) Pressure Distribution on the Aircraft

Surface and Surrounding Fluid and (b) Streamline past AFA at 5 Degrees Angle of Attack

C.2 Flow past Vibrating AGARD 445.6 This example is used to demonstrate the fluid-structure interaction capability of the particle methods in ASTE-P.

In this simulation, the standard 3D AGARD 445.6 wing is used as the object subject to translation and twisting

degrees of freedom placed in fresstream condition at Mach 0.7. The root of the AGARD wing is fixed and the

remaining of the wing is subject to a first bending type translation motion and a linearly varying twist along the

span of the wing. The wing shapes at the maximum and minimum deflection points is shown in Figure 14(a). The

surface pressure contours at these deflection points are depicted in Figure14 (b)-(c) at two different times. As can

be seen from the figures, the pressures are quite different as the wing undergoes deformation. This case was

selected to show that the particle method can handle large deformation in the 3D sense as well.


14

(a)

(b)

(c)

Figure 14. (a) AGARD 445.6 Deflection Depicting Maximum and Minimum Deflection Shapes; (b) Surface

Pressure Contours at the Maximum, and (c) Minimum (Right) Deflection Points.

D. Finite Element Solver Validation We will demonstrate the ASTEP-FE capability using a real aircraft 3D wing model. Figure 15(a) shows the FE

model of the wing and the deformation under a loading condition. What follows, we will show that the results of modal analysis, static analysis, and structural dynamics analysis of this wing model by using ASTE-P-FE agree very

well with the result of MSC/Nastran.

D.1 Mode Comparison Table 2 shows the modal analysis of this wing model. The first ten modes computed by ASTE-P-FE are nearly

the same with those computed by MSC/Nastran.

Table 2. Modal Analysis

Mode NO. Nastran ASTE-P error

1 23.780 23.839 -0.25% 2 60.732 61.041 -0.51% 3 78.768 79.018 -0.32% 4 149.877 151.330 -0.97% 5 169.399 170.071 -0.40% 6 219.499 220.602 -0.50% 7 280.037 281.689 -0.59% 8 302.030 303.740 -0.57% 9 415.517 417.932 -0.58%

10 449.486 452.316 -0.63%

D.2 Nodal Response Comparison

Because there are a large number of nodes in this wing model, only nodes of number 1-200 are selected to be

presented in the Figure 15(b).

For structural dynamics FE analysis, herein only the time-dependent displacement history of node 1521 is

presented in Figure 15(c).

(a)


15

(b)

(c)

Figure 15. FE Modeling of a 3D Aircraft Wing: (a) Wing Model and Deformation under a Loading

Condition; (b) Comparison with Nastran for Static Response, and (c) Comparison with Nastran for

Dynamic Response

V. Conclusions

All validation and verification cases presented in this paper are in good agreement with experimental measure-

ments and other computational results, which indicates that: (1) the ASTE-P tool set is compatible with the current

state-of-the-art software where the traditional FVM and FEM based approaches are utilized, and (2) the fully devel-

oped ASTE-P tool set will be very powerful for modeling, simulation, evaluation and design of various aerospace

vehicles, marine ships, high-speed trains, automotives and complex mechanical systems. The release of ASTE-P

enables (1) the accurate and efficient prediction of nonlinear FSI/Aeroelastic problems using an integrated CFD and

CSD solvers and (2) robust particle methods for analysis and design for complex configurations. The middle level

ROM models of fast analysis and evaluation environment can provide a reasonable good computational fidelity and

fast turn-around time compared to the bottom level high-fidelity and full order simulation environment. The top lev-el rapid design and optimization environment provides the convenient way for engineers to directly access the simu-

lation data in the middle and bottom levels for their design and evaluation purposes.

Acknowledgement This work was partially supported by National Aeronautics and Space Administration SBIR Phase I contract

NNX07CA39P, Phase II contract No. NNX08CA39C, and Phase III Contract No. NND10AM05P, Mr. Marty

Brenner was the COTR. This work was also partially supported by US Navy STTR Phase I contract No. N68335-

10-C-0411 with Dr. Peter Attar and Dr. Prakash Vedula at University of Oklahoma as the University Partner, Mr.

Madan Kittur was the Technical Monitor. Many thanks should be given to Dr. Earl Dowell at Duke University for

his great help during the development of ASTE-P in these years. Also, many thanks should be given to Brian

Froist, Brent Whiting and Dale Pitt for their strong support on Advanced Dynamics Inc. in recent years. Any opinions, findings, conclusions, or recommendation expressed here are those of the authors and do not necessarily

reflect the views of the funding agencies and our University and Industry partners.


16

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[american institute of aeronautics and astronautics 52nd aiaa/asme/asce/ahs/asc structures,...

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