http://www.aertia.com

ZAERO

de Zona Technology

ZAERO es una arquitectura de software orientada a sistemas de vuelo para el calculo de condiciones aeroelasticas. El producto ha sido desarrollado por la empresa ZONA Technology, Inc.

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ABOUT ZAERO




THE ZAERO SOFTWARE SYSTEM / ARCHITECTURE

Main Features :

  • High Fidelity Geometry module to model full aircraft with stores/nacelles [1]
  • Flight regimes that cover all Mach numbers including transonic/hypersonic ranges [14]
  • Unified Mach AIC matrices as archival data entities for repetitive structural design/analysis [3]
  • Matched/non-matched point flutter solutions using K / P-K / g methods with true damping [5]
  • Built-in Flutter Mode Tracking procedure with structural parametric sensitivity analysis [13],[8]
  • State space Aeroservoelastic (ASE) analysis with continuous gust for SISO/MIMO control system [6]
  • Trim analysis for static aeroelasticity/flight loads [7]
  • Dynamic Loads Analysis including transient maneuver loads (MLOADS), ejection loads (ELOADS), and discrete gust loads (GLOADS) [8], [9], [10]
  • Nonlinear Flutter Analysis for open/closed loop system using discrete time-domain state space approach (NLFLTR) [18].
  • 3D Spline module provides accurate FEM/Aero displacements and forces transferal [2]
  • Modal Data Importer to process all NASTRAN/FEM modal output [4]
  • Dynamic Memory and Database Management Systems establish subprogram modularity [9]
  • Open architecture allows user direct access to data entities [10]
  • Bulk Data Input minimizes user learning curve while relieving user input burden [12]
  • Provides graphic display capability of aerodynamic models, CP?s, flutter modes and flutter curves with PATRAN/TECPLOT/EXCEL, etc. [16]
  • Executive control allows massive flutter/ASE/TRIM/Dynamics Loads inputs and solution outputs [17]
  • NASLINK module to export ZAERO aerodynamic data to MSC.NASTRAN [19]


The main body of the ZAERO system is comprised of eight modules and the ZONA Database Management (ZDM) system. The modules are:

[1] High-Fidelity Geometry (HFG) [4] Modal Data Importer [7] Gust
[2] 3-D Spline [5] Flutter [8] Sensitivity
[3] Unified AIC (UAIC) [6] Aeroservoelasticity (ASE)


ZAERO UAIC MODULE


ZONA7U ZONA7 ZTAIC ZONA6
ZAERO/UAIC Module



ZONA51 in MSC/NASTRAN


For nearly one and a half decades, ZONA Technology, Inc. (ZONA) has been directing its R&D effort towards the development of viable unsteady aerodynamic methods for aeroelastic applications. The first ZONA software product for supersonic lifting surface unsteady aerodynamics is the ZONA51 code, which is the outgrowth from the Harmonic Gradient Method (HGM) developed by Chen and Liu in 1985 (Ref 1). In early 1991, ZONA reached an agreement with the MacNeal-Schwendler Corporation (MSC) to provide a new set of unsteady aerodynamic methods as the Aeroelastic Option II for MSC/NASTRAN. Today, ZONA51 is the industrial standard method for supersonic lifting surface unsteady aerodynamics in MSC/NASTRAN ? Aero Option II with over 120 users worldwide.

ZONA Aerodynamic Codes

  • ZONA6 generates steady/unsteady subsonic aerodynamics for wing-body/aircraft configurations with external stores/nacelles including body wake effects.
  • ZTAIC generates unsteady transonic (modal) AIC?s using externally-provided steady mean pressures.
  • ZONA7 generates steady/unsteady supersonic aerodynamics for wing-body/aircraft configurations with external stores/nacelles (formerly ZONA51 for lifting surfaces).
  • ZONA7U generates unified hypersonic and supersonic steady/unsteady aerodynamics for wing-body/aircraft configurations with external stores/nacelles.

UAIC in ZAERO


Further development of these ZONA codes in recent years led to the present developed product: the ZAERO software system. A Unified Mach number AIC (UAIC) module is created to include all ZONA unsteady aerodynamics codes listed above. The functionality of the UAIC module is to provide the needed AIC matrix according to the flight condition input for any given Mach numbers.

ZONA6: SUBSONIC UNSTEADY AERODYNAMICS


FUNCTIONALITY
  • Generates steady/unsteady subsonic aerodynamics for wing-body/aircraft configurations with external stores/nacelles including the body-wake effect.
MAIN FEATURES
  • Any combinations of planar/nonplanar lifting surfaces with arbitrary bodies including fuselage+stores+tip missiles.
  • Higher-order panel formulation for lifting surfaces than the Doublet Lattice Method (DLM). First case below shows the ZONA6 robustness over DLM.
  • High-order paneling allows high-fidelity modeling of complex aircraft with arbitrary stores/tip missile arrangement. Second case below shows a solution improvement.
70 Degree Delta Wing (M=0.8, k=0.5, ho=0.35cr) Ref 10

  • Robust ZONA6 solutions are in contrast to the breakdown of the DLM solutions
  • High-order formulation of ZONA6 requires little care in paneling
70 Degree Delta Wing


NLR Wing-Tiptank-Pylon-Store, Ref 9

  • No. of Wing Aero Boxes=90, Tiptank Aero Boxes=264, Store Aero Boxes=216
  • ZONA6 shows improvement over NLR?s predicted results

ZTAIC: TRANSONIC UNSTEADY AERODYNAMICS USING TRANSONIC EQUIVALENT STRIP METHOD


FUNCTIONALITY
  • Generates unsteady transonic modal AIC using externally-provided steady mean pressure.

MAIN FEATURES

  • While using steady pressure input (provided by measurement or CFD):
    • grid generation is not required
    • the correct unsteady shock strength and position are ensured

  • The modal AIC of ZTAIC as an archival data entity allows:
    • repetitive aeroelastic analysis and structures design.
    • the ease of application of the K / g methods for flutter analysis.

  • Readily integrated with ZONA6 as a unified subsonic/transonic AIC method for complex aircraft configurations.
    • Additional input to ZONA6 amounts to only the provided steady pressure data.


AGARD Standard 445.6 Wing Refs 12,17

  • Steady pressure input provided by CAPTSD
  • Good agreement with test data
  • At subsonic speed, ZTAIC results approach that of ZONA6, as expected
  • ZTAIC predicts the transonic flutter dip
AGARD Standard 445.6 Wing


Lessing Wing in First-Bending Oscillation (M=0.9, k=0.13, n=0.5 x span) Ref 12

  • Used Lessing?s test data as the steady pressure input
  • Thus yields correct unsteady shock position and magnitude

Lessing Wing in First-Bending Oscillation

ZTRAN: TRANSONIC UNSTEADY AERODYNAMICS USING OVERSET FIELD-PANEL METHOD


FUNCTIONALITY
  • Generates unsteady transonic AIC matrix that has the same form as AIC of ZONA6/ZONA7.
MAIN FEATURES
  • ZTRAN solves the time-linearized transonic small disturbance equations using overset field-panel method.
  • The surface box modeling is identical to that of ZONA6. Only a few additional input parameters are required to generate the volume cells.
  • The variant coefficients in the time-linearized transonic small disturbance equation are interpolated from the Computational Fluid Dynamics (CFD) steady solutions.
  • The overset field-panel scheme allows the modeling of complex configurations without extensive field panel generation efforts.

Lessing Wing in First-Bending Oscillation

Lessing Wing in First-Bending Oscillation


Unsteady Pressure Validations

Unsteady Pressure Validations


Flutter Validations

Flutter Validations

ZONA7: SUPERSONIC UNSTEADY AERODYNAMICS

FUNCTIONALITY
  • Generates steady/unsteady supersonic aerodynamics for wing-body/aircraft configurations with external stores/nacelles
MAIN FEATURES
  • Any combinations of planar/nonplanar lifting surfaces with arbitrary bodies including fuselage+stores+tip missiles.
  • Panel formulation for lifting surface is identical to that of ZONA51 ? now the industrial standard method for supersonic flutter analysis in MSC/NASTRAN.
  • High-order paneling allows high-fidelity modeling of complex aircraft with arbitrary stores/tip missile arrangement.

NACA Wing-Body (xo=0.35cr, Ref 4) Ref 15

NACA Wing-Body





ZONA7

WING + BODY
WING ONLY
BODY ONLY

TEST DATA

R = 1.18 x 106
R = 1.89 x 106

ZONA7U: HYPERSONIC UNSTEADY AERODYNAMICS

FUNCTIONALITY
  • Generates unified hypersonic and supersonic steady/unsteady aerodynamics for wing-body/aircraft configurations with external stores/nacelles.
MAIN FEATURES
  • Nonlinear thickness effects of ZONA7U yields good agreement with Euler solution and test data.
  • Steady solutions approach linear and Newtonian limits.
  • Confirms hypersonic Mach independent principle.
  • Results/formulation are superior to Unsteady Linear Theory and Piston Theory.
  • ZONA7U usually results in more conservative flutter boundaries than other methods.
  • Unified with ZONA7 and is therefore applicable to all Mach numbers > 1.0.
  • Additional input to ZONA7 amounts to only wing root and tip sectional profile thickness.
70 Degree Delta Wing Ref 13

  • Thickness effect apparent at higher M
  • Thus, it yields more conservative flutter boundaries
70 Degree Delta Wing


Rectangular Wing with Wedge Profile (M=4.0, sigma=15, xo=0.25c) Ref 13

  • ZONA7U solution compares well with Euler solution over a wide frequency range
  • Piston Theory and Linear Theory (ZONA7) yield inferior results by comparison
Rectangular Wing with Wedge Profile

ZSAP: SONIC ACCELERATION POTENTIAL PANEL METHOD

FUNCTIONALITY
  • Generates steady/unsteady aerodynamics at sonic speed (M = 1.0) for wing-body/aircraft configurations with external stores/nacelles.
MAIN FEATURES
  • Any combinations of planar/nonplanar lifting surfaces with arbitrary bodies including fuselage+stores+tip missiles.
  • Compute the steady/unsteady aerodynamics at exactly Mach one.
  • Paneling scheme is identical to that of ZONA6/ZONA7, i.e. ZSAP shares the same aerodynamic model as ZONA6/ZONA7.
  • Computational time is on the same order.






  • Canard-Wing configuration in Canard Pitch Motion about its Mid-Chord.
  • Lift on Wing is mainly induced by the oscillatory wake from Canard.
  • Real and Imaginary parts of Lift (Re(Q12) & Im(Q12)) at M=1.0 are contrasted with that of the Subsonic Lifting Surface Method (ZONA6) at M=0.99 and the Supersonic Lifting Surface Method (ZONA7) at M=1.01.
  • ZONA6 and ZONA7 require large number of Boxes for solution convergence.







  • AGARD standard 445.6 Weakened Wing (in Air) and Solid Wing (in Freon 12)
  • Comparison of Flutter Speed Index and Flutter Frequency Ratio with TDT wind tunnel measurements

ZTAW: AIC CORRECTION METHODS

FUNCTIONALITY
  • Generates a corrected AIC matrix to match the given set of forces/moments or unsteady pressures.
MAIN FEATURES
  • The AIC correction module computes the AIC weighting matrix using a ZONA Transonic AIC Weighting (ZTAW) method that adopts a successive kernel expansion procedure.
  • The ZTAW method is an improved AIC correction method over the previous correction methods such as the force/moment correction method by Giesing et al and the downwash weighting matrix (DWM) method by Pitt and Goodman. With in-phase pressures obtained by wind-tunnel measurement or CFD, ZTAW yields accurate out-of-phase and higher frequency pressures resulting in well-correlated aeroelastic solutions whereas the previous method yield erroneous out-of-phase pressure in terms of shock jump behavior.
  • Four methods are incorporated in ZTAW: the steady downwash weighting matrix method, the unsteady downwash weighting matrix method, the steady force correction matrix method, and the unsteady force correction matrix method.

Unsteady Pressure Validations
Unsteady Pressure Validations


Flutter Validations
Flutter Validations

HIGH-FIDELITY GEOMETRY (HFG) MODULE



The HFG module is capable of modeling any full aircraft configuration with stores and/or nacelles. A complex aircraft configuration can be represented by the HFG module by means of wing-like and body-like definitions. Any modifications to the HFG module, such as input geometry enhancements, will have minimal impact on other general modules.


Wing-like components include:

wings, tails, pylons, launchers store fins, etc.
Body-like components include:

fuselage, underwing stores, missile bodies, etc.


3D SPLINE MODULE



The 3D Spline module establishes the displacement/force transferal between the structural Finite Element Method (FEM) model and the ZAERO aerodynamic model. It consists of four spline methods that jointly assemble a spline matrix. These four spline methods include:

(a) Thin Plate Spline;
(b) Infinite Plate Spline;
(c) Beam Spline; and
(d) Rigid Body Attachment methods.
The spline matrix provides the x, y and z displacements and slopes in three dimensions at all aerodynamic grids.




NACA L51F07 Wing-Body Configuration with Three Structural Modes
FEM MODEL AERODYNAMIC MODEL
Rigid Body Pitch Mode
First Wing Bending Mode
First Body Bending Mode
NACA L51F07 Wing-Body Configuration with Three Structural Modes.


ZONA DYNAMIC MEMORY AND DATABASE MANAGEMENT SYSTEM



The ZONA Dynamic Memory and Database Management System (ZDM) consists of the following five parts:

  • Matrix Entity Manager
    The matrix entity manager is designed to store and retrieve very large, often sparse, matrices. It minimizes disk storage requirements while allowing algorithms to be developed that can perform matrix operations of virtually unlimited size.

  • Relational Entity Manager
    Relational entities are essentially tables. Each relation has data stored in rows (called entries) and columns (called attributes). Each attribute is given a descriptive name, a data type, and constraints on the values that the attributes may assume (i.e. integer, real or character data). These definitions are referred to as the schema of the relation.

  • Unstructured Entity Manager
    There are many times that a software module requires temporary, or scratch, disk space while performing tasks. The data generated within these tasks are generally "highly-local" and, due to the modular nature of the software, are not be passed through arguments to other modules within the system. To effectively accommodate the transfer of this type of data, ZDM supports an unstructured database entity type composed of "records" that may contain any arbitrary collection of data.

  • Dynamic Memory Manager
    The dynamic memory manager consists of a suite of utility routines to allocate and release blocks of dynamic memory. The Dynamic Memory Manager provides the capability of developing an engineering software system which allows operations to be performed on data that would normally exceed the size of available memory.

  • Engineering Utility Modules
    Engineering utility modules contain a pool of routines that perform operations on matrix database entities. These operations include matrix decomposition, eigenvalue solver, matrix multiplication, matrix partitioning/merging, etc. These routines first check the property of a given matrix and then select the appropriate numerical technique to perform a particular matrix operation.

BULK DATA INPUT



ZAERO utilizes the bulk data input format, similar to that of NASTRAN and ASTROS. This type of input format has the advantage of:

(a) minimizing the user learning curve;
(b) relieving user input burden; and
(c) automated input error detection.
An example of this type of input format is shown below. Flow charts are also shown demonstrating some of the ZAERO bulk data interdependencies.



Example of ZAERO Bulk Data Input Format :

1

2

3

4

5

6

7

8

9

10

CAERO7

WID

LABEL

ACOORD

NSPAN

NCHORD

LSPAN

ZTAIC

PAFOIL7

CONT

CONT

XRL

YRL

ZRL

RCH

LRCHD

ATTCHR

CONT

CONT

XTL

YTL

ZTL

TCH

LTCHD

ATTCHT


CAERO7

101

WING

8

5

4

20

0

0

ABC

+BC

0.0

0.0

0.0

1.0

10

4

DEF

+EF

0.0

1.0

0.0

1.0

11

0


Flow Charts of ZAERO Bulk Interconnection


GRAPHIC DISPLAY


ZAERO allows for the graphic interface with commercialized graphic packages. Graphical data in output files containing the aerodynamic model, unsteady p ressures (CP), interpolated structural modes and flutter modes can be displayed via PATRAN or TECPLOT. V-g and V-f diagrams can be displayed via typical X-Y plotting packages. An example of the F-16 aerodynamic model with external stores and the resulting V-g and V-f diagrams are shown below.


Unsteady aerodynamic Model

V-G and V-F Diagrams

Animated Flutter Mode

Verification of Spline

Unsteady Pressure Display

Transient Response

FLUTTER MODULE


The ZAERO flutter module contains two flutter solution techniques: the K-method and the g-method. The g-method is ZONA's newly developed flutter solution method (Ref 20) that generalizes the K-method and the P-K method for true damping prediction. Ref 20 shows that the P-K method is only valid at the conditions of zero damping, zero frequency, or linear varying generalized aerodynamic forces (Q) with respect to reduced frequency. In fact, if Q is highly nonlinear, it is shown that the P-K method may produce unrealistic roots due to its inconsistent formulation.

The flutter module has a built-in atmospheric table as an option to perform matched-point flutter analysis. Sensitivity analysis with respect to the structural parameters is also included in the g-method.



Three Degrees of Freedom Airfoil at M=0.0 (MSC/NASTRAN HA145 Test Case)
  • A non-zero frequency "dynamic divergence speed" is well predicted by the g-method, the P-K method and the transient method (a time-domain method).
  • Both the g-method and the transient method capture two aerodynamic lag roots which are absent in the P-K method solution.
  • The frequency vs. velocity (V-f) diagrams of the g-method and the transient method are in good agreement. The frequency of the free-free plunge mode computed by the P-K method remains zero. This results in poor correlation in the V-f diagram with the g-method and transient method.


SENSITIVITY ANALYSIS WITH RESPECT TO STRUCTURAL PARAMETERS


ZAERO provides analytical sensitivities of flutter parameters (frequencies and damping) with respect to structural design variables. Using the same set of generalized coordinates, such as the normal modes of a baseline structure, massive sensitivities can be computed without returning to the finite-element model.

Symbolically, the analytical sensitivity can be expressed as :


which is the sensitivity of damping of the j-th mode ( yj ) with respect to the i-th design variable ( vi ).
which is the sensitivity of flutter reduced frequency of the j-th mode ( kj ) with respect to the i-th design variable ( vi ).


where A and B can be derived using the orthogonality of the right and left eigenvectors of the flutter equation. Computing A and B requires additional structural information from the finite element code; the derivatives of the stiffness matrices and the mass matrices with respect to the design variables. These matrices are imported from the finite element code through a bulk data input card DMIG.


STATIC AEROELASTIC / TRIM MODULE


Performs the static aeroelastic/trim analysis for solving the trim system and computing the flight loads.


Unsteady aerodynamic Model

V-G and V-F Diagrams
F-18 at 4-G Pull-Up Maneuver at Mach 1.2 and Altitude = 10,000 ft.
MAIN FEATURES
  • It employs the modal approach for solving the trim system of the flexible aircraft. The modal approach formulates a reduced-order trim system that can be solved with much less computer time than the so-called ?direct method?.
  • It is capable of dealing with the determined trim system as well as the over-determined trim system (more unknowns than the trim equations). The solutions of the over-determined trim system are obtained by using an optimization technique which minimizes a user-defined objective function while satisfying a set of constraint functions.
  • For a symmetric configuration (symmetric about the x-z plane), it requires only the modeling of one half of the configuration even for the asymmetric flight conditions.
  • It generates the flight loads on both sides of the configuration in terms of forces and moments at the structural finite element grid points in terms of NASTRAN FORCE and MOMENT bulk data cards for subsequent detailed stress analysis.

AEROSERVOELASTICITY (ASE) Module


The ASE software developed by Prof. Moti Karpel of Technion ? Israel Institute of Technology is integrated in the ZAERO software system as shown below.





Main Features of the ASE Module :
  • Rational-function approximation of the unsteady aerodynamic coefficient matrices
  • State-space MIMO formulation
  • Modular linear control modeling of most-general architecture
  • Open- and closed-loop flutter analysis
  • Open-closed gain and phase margins
  • Input and output singular values
  • Augmentation of continuous-gust dynamics
  • Structural gust response in statistical terms
  • Fixed-modes parametric studies
  • Sensitivity of flutter and control margins with respect to structural and control variables

RATIONAL-FUNCTION APPROXIMATION OF THE UNSTEADY AERODYNAMICS



The unsteady aerodynamic force coefficient matrices are approximated by a rational matrix function in the Laplace domain. The approximation formula is either the classic Roger?s formula

where p is the non-dimensional Laplace variable p = sb / V, or the more general minimum-state formula

that results with significantly less subsequent aerodynamic states per desired accuracy.

The approximation roots are selected by the user or determined by the code based on the frequency range of the input matrices. A direct least-square solution is used for Roger?s approximation, and a non-linear least-square is used for the minimum-state approximation.

A physical-weighting algorithm may be used to weight the data terms according to aeroelastic measures of importance.





AEROELASTIC STATE-SPACE MODEL



The generalized structural matrices and the aerodynamic approximation coefficient matrices are used to construct the time-domain state-space equation of motion of the open-loop aeroelastic system excited by control-surface motion,

where

where is the vector of generalized displacements, is the vector of aerodynamic lag states, and is the vector of control-surface deflection commands. The system output vector may include structural displacements, velocities and accelerations.

Augmentation of control actuators of at least third order yields the plant equations

where includes aeroelastic and actuator states and is the vector of actuator inputs.


CONTROL SYSTEM MODEL



The control system is modeled as an interconnection of four types of basic control elements:
  • Single-Input-Single-Output (SISO) elements defined by s-domain transfer functions
  • Multi-Input-Multi-Output (MIMO) elements defined by individual state-space matrices that may be imported from external control synthesis codes.
  • Junction elements (JNC) which are actually zero-order elements connecting some inputs with some outputs by .
  • Variable control gains which form the control gain matrix when the system is closed. Control margins, singular values and sensitivity analyses are performed with respect to these gains.




THE ASE MODEL



The plant and control models are interconnected by the following scheme:





Stability analyses of open- and closed-loop systems are based on system eigenvalues. Sensitivity computations are based on analytical expressions.

CONTINUOUS GUST RESPONSE



  • Gust filters are designed to represent Dryden?s and Von Karman?s power spectral density functions of atmospheric gust velocities.
  • Augmentation of a gust filter yields dynamic equations with random white-noise excitation process,

  • Mean-square response parameters are obtained by solving the Lyapunov equation

and then calculating the output covariance matrix

  • Similar expressions are used for the sensitivity of the response values to structural and control variables.

TRANSIENT MANEUVER LOADS



The transient maneuver loads module performs the transient maneuver loads analysis due to the pilot input command.





Idealized Forward Swept Wing Test Case (ZAERO and P-Transform correlate well while the quasistatic method does not due to low-frequency approximation)


MAIN FEATURES

  • It is formulated in the state space form for either the open loop or closed loop system. The rigid body degrees of freedom are transformed into the airframe states so that the sub-matrices associated with the airframe states in the state space matrices are in the same definition with those of the flight dynamics.
  • It allows the users to replace the program-computed sub-matrices associated with the airframe states by those supplied by the flight dynamic engineers. This can ensure that the time response of the airframe states is in close agreement with those of the flight dynamic analysis.
  • It computes the time histories of the maneuver loads of flexible airframe in the presence of control system. These maneuver loads include the time histories of component loads, grid point loads, etc. Based on these time histories of loads, the user can identify the critical maneuver load conditions.
  • It outputs the transient maneuver loads at each time step in terms of NASTRAN FORCE and MOMENT bulk data cards either by the mode displacement method or the mode acceleration method for subsequent detailed stress analysis.

TRANSIENT EJECTION LOADS



The transient ejection loads module performs the transient ejection loads analysis due to store separation.

Aircraft Response due to Ejection Force (x 5)




Advanced Fighter Test Case (ZAERO versus Flight Test)


MAIN FEATURES

  • It allows multiple store ejections (in sequential scheduling) while the aircraft is maneuvering due to pilot input commands.
  • It accounts for the effects of the sudden reduction in aircraft weight due to the separation of the stores from the aircraft.
  • It is formulated in the state-space form for either an open-loop or closed-loop system.
  • It outputs the transient loads at each time step in terms of NASTRAN FORCE and MOMENT bulk data cards either by the mode displacement method or the mode acceleration method for subsequent detailed stress analysis.

TRANSIENT DISCRETE AND CONTINUOUS GUST LOADS



The transient discrete gust loads module performs a transient response analysis of an aircraft structure when the aircraft encounters a discrete gust.

2-D Thin Airfoil Subjected to a Sharp-Edged Gust

Comparison Between Sear?s Function and the Gust Forces Computed by ZONA6

Comparison Between Wagner?s Function and ZAERO State-Space Equations

Comparisons Between ZAERO Results and Analytical Solution for a 2-D Airfoil Encountering Sharp-Edged Gust

Validation of the Discrete Gust Module with 2-D Classical Theory
(Excellent agreement is seen while NASTRAN fails to provide satisfactory results)



MAIN FEATURES

  • It includes various options for defining the discrete gust profile such as one-minus-cosine, sine, sharp-edged gust, and arbitrary gust profiles for discrete gust and Dryden?s or Von Karman?s gust spectrum for continuous gust.
  • For the discrete gust analysis, it includes three options to model the gust profile; the frequency-domain approach, the state-space approach, and the hybrid approach where the discrete gust loads are obtained by inverse Fouier transform and the system matrix by state-space formulation.
  • Its state space equations provide accurate displacement time history thereby circumventing the unreasonably large displacement response problem of the Fourier transform method in NASTRAN.
  • It outputs the transient loads at each time step in terms of NASTRAN FORCE and MOMENT bulk data cards either by the mode displacement method or the mode acceleration method for subsequent detailed stress analysis.

NONLINEAR FLUTTER MODULE



The nonlinear flutter module is a simulation tool for the transient response of open/closed-loop aeroelastic systems that include (1) nonlinear structures (2) nonlinear control system (3) large-amplitude unsteady aerodynamics (externally imported from other CFD code).
3 d.o.f. Airfoil with Free-Play




Excellent Agreement with Analytical and Experimental Results



MAIN FEATURES

  • Nonlinearities can be specified as a function of multiple user defined nonlinear parameters such as displacements, velocities, accelerations, element forces, modal values and control system outputs.
  • Discrete time-domain state space equations at each distinct value of the nonlinear parameters are pre-computed. During the time-integration computation, updated state-space equations are obtained by interpolation.
  • It outputs the NASTRAN FORCE and MOMENT bulk data cards at a given time step for subsequent stress analysis.

NASLINK Module



Exports the ZAERO Aerodynamic data to MSC.Nastran.

Unsteady aerodynamic Model

Excellent Agreement with Analytical and Experimental Results



MAIN FEATURES

  • It automatically creates a directory to store the AIC matrices, spline matrix, control surface modes, aerodynamics geometry, and load modes for component loads.
  • The user can user MSC.Nastran solution 144 for static aeroelastic analysis, solution 145 for aerodynamic flutter, solution 146 for aeroelastic response or solution 200 for design optimization but using ZAERO unsteady aerodynamics.

ZAERO VALIDATION

F-16 MA41 Limit Cycle Oscillation (LCO)

  • F-16 MA41 configuration experiences LCO from Mach 0.6 to 1.0 while the MA43 configuration is free from LCO.
  • ZAERO (ZONA6 linear method) predicts a hump mode damping curve that falls within 1-2% damping (M=0.6 to 1.0) for the MA41 configuration while the MA43 case falls below 1%.
  • The onset of LCO as predicted by ZAERO correlates very well with flight data.
Case MA41 LCO Occurred
at M = 0.6 ? 1.0 in Flight

LAU-129 Launcher
Case MA43
No LCO Occurred in Flight

16S210 Launcher
F-16 Case MA41 and Case MA43 Configurations


ZAERO Flutter Solutions of F-16 Case MA41 at M = 0.6, 0.8, 0.9 and 1.2

ZAERO Flutter Solutions of F-16 Case MA43 at M = 0.6, 0.8, 0.9 and 1.2

ZAERO VALIDATION

F-18 Limit Cycle Oscillation (LCO)

  • ZAERO transonic unsteady aerodynamic method (ZTAIC) is used to perform a flutter analysis.
  • Steady pressure input to ZTAIC is obtained by the CFL3D Navier-Stokes solver.
  • Unstable damping of Case 1 approximately ranges from M = 0.85 to 1.0 with a frequency of 5.6 Hz which correlates very well with the flight test data.
  • Similarly, good correlation is found for Case 2 (LCO region at M>0.9 with frequency 8.8 Hz)


Two F-18/Store LCO Configurations

ZAERO Flutter Solution of F/A-18 LCO Case 1 (at Altitude = 0 kft)

ZAERO Flutter Solution of F/A-18 LCO Case 2 (at Altitude = 0 kft)




2004, Aertia, S.L.