Bird Strike Aeromag Paper
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Transcript of Bird Strike Aeromag Paper
S. RamaprasadCenter of Excellence, Aerospace and Defence,
Satyam Computer Services Private Limited,
Bangalore 560100
Simulation of Bird Strike on Aero Structures Using Explicit Finite element Methods
A Bird Strike is a collision between a bird and a aircraft. It is serious
threat to aircraft flight safety and has caused a number of accidents with
human causalities. According to Federal Aviation Regulation wildlife
strikes like the bird hit has caused the civil aviation industry considerable
costs and resulted in significant reduction of flight downtime hours. An
aircraft must show compliance with “continued safe flight and landing”
requirements following specified types of high-energy bird impact. Hence
it is now imperative to design aircraft components capable of withstanding
these impacts
To obtain certification from the FAA, an aircraft must be able to land after
an impact with a 4 pound bird at any point in the aircraft. For new jet
engines designs, the FAA certification requires more tests for medium and
large bird ingestion. For the medium or flocking bird requirement, an
engine must be capable of operating for five minutes with less than 25%
thrust loss after impacting several 1.5 pound or 2.5 pound birds. For the
large bird ingestion test, the engine must be able to withstand a 6 pound or
8 pound bird and achieve safe shutdown. As a consequence the aviation
authorities require that none of the vital, forward facing elements of
aircraft structures should fail as a result of bird strike. These requirements
have serious effect on the production cost, as each new design must
incorporate the value of the full-scale testing. However, significant
savings can be achieved in the design and manufacture of elements of
aircraft structures by employing the state-of-the-art predictive modeling
techniques thus ensuring that the very first full-scale bird strike
certification tests are successful. Presently, major improvements are
expected in minimizing the consequences of bird ingestion into aircraft
engines and bird strike against leading edges of wing structures. Recent
advances in measurement instrumentation and computing have allowed
for the investigation of a wider spectrum of physical phenomena
surrounding bird strike impact on aircraft structures. Accordingly, the
ability to predict accurately the observed mechanisms of soft body impact
and to provide information on the magnitude and distribution of surface
pressures during such events becomes vital and hence pre-requisites to
reliable design of aircraft structures. Numerical simulation tools based on
the finite element method have reached such level of maturity that these
can be used confidently for dimensioning of structural elements subjected
to normal service loads. However, the ability to assess the behavior of
bird-like soft-bodied projectiles and to predict the integrity of structures
subjected to such loading to simulate the observed large deformations and
erosion of soft-bodied projectiles needs to be carried out with adequate
accuracy.
This article describes different simulation strategies to arrive at a robust
methodology for an accurate assessment of the bird impact event. This
model must be able to reproduce both impact and loads generated in a
bird-strike event. A good approximation for the model is the finite
element method because of its ability to analyze complex geometries,
material and load non-linearity, and study the interaction between the
bird and the target. Various finite element methods are used to model the
impact phenomena. Typically explicit finite element codes like LS-Dyna
are used to study the bird impact event. Explicit formulation of the finite
element method allows us to accommodate nonlinear effects involving
both geometric and material nonlinearity. LS Dyna is a general purpose
explicit finite element program used to analyze the nonlinear dynamic
response of three-dimensional structures. It includes an automated contact
analysis capability and error-checking features which gives the
opportunity to solve complex crash and impact problems. LS-DYNA
simulation results have been consistently correlated with experimental
data which give high confidence in using the program as an accurate
simulation tool.
The transient dynamic equation of motion for describing the motion of the
shell is given by
,
(1)
In the above equations, the Finternal is contributed by stiffness terms while
Fcontact is derived by a suitably chosen contact interaction algorithm. There
are many different contact algorithm which could be chosen, however the
frequently used contact algorithm is a surface to surface contact
interaction . The contact algorithm allows us to calculate the force
generated at the interface between the target and the Bird. Belytschko
Tsay formulation is predominantly used for shell modeling for
determining the dynamic response and Hourglass control is invoked to
achieve better accuracy of the results.
Due to the conditional stability of the explicit time integration scheme, the
time step calculation plays a very important role for its performance.
Larger time steps decrease the computational effort for solving the
problem, but if a limit called critical time step, tcr, is exceeded the
solution rapidly diverges. To be able to efficiently use, the well known
expression for the critical time step
, (2)
a simple estimate of the highest natural frequency max is required. In LS
DYNA the simple effective calculation of time step is carried out using
the characteristic length of the element and the sound speed
There are typically three different methods used for simulation of the bird
impact event. These are the Lagrangian method, Arbitrary Lagrangian
Eulerian formulation, and the Smooth Particle Hydrodynamics.
Lagrangian Approach: When the Lagrangian solver is used, grid points
are fixed to locations on the body being analyzed. Elements of material
are created by connecting the grid points together, and the collection of
elements produces a mesh. As the body deforms, the grid points move
with the material and the elements distort. The Lagrangian solver is,
therefore, calculating the motion of elements of constant mass This is
contrary to Eulerian approach where the grid points are fixed in space and
the elements are simply partitions of the space defined by connected grid
points. Numerical problems due to element distortions limit the
applicability of Lagrangian description of motion when modeling large
deformation process. On the other hand the Eulerian decription in which
the material flows through a mesh fixed in space can completely avoid
mesh distortion problems. The Eulerian approach though is not devoid of
instabilities and its applicability is limited by the dissipation and
dispersion problems associated with the fluxing of mass across element
boundaries. The Bird is usually modeled as Hexahedron elements while
the target could be modeled either as brick or shell elements. Graded mesh
shall be used with finer mesh used near the impact zone. To simulate the
residual stresses in the radial direction, cross-section near the impact zone
will have sufficient element density. Sufficient iterations in terms of mesh
density needs to be carried out to achieve convergence of computed
residual stresses. For the purpose of simulation, two parts shall be created
one for the Bird and another for the target. Cowper Symonds strain rate
parameters or different stress strain curves for different strain rates must
be supplied to capture the strain rate effects accurately. Necessary
boundary conditions shall be specified using the *BOUNDARY_SPC
control card. Impacting body’s velocity can input directly using the
*INITIAL_VELOCITY control card. The height between the Bird and the
target shall be maintained very small for solid elements. For shell element
modeling the height shall be maintained at marginally higher than the
average thickness of the Bird and the target thickness.
The contact interaction between the Bird and the Target can be defined
using the *CONTACT_NODES_TO_SURFACE for solid to solid
interaction and *CONTACT_SURFACE_TO_SURFACE for solid to
shell interaction. The time for analysis should be carried out for sufficient
length of time to get the correlation accurately for the deformation under
impact. Hour glass control shall be exercised to remove all zero energy
modes and to ensure the model reproduces the correct rigid body motions.
Augmented Lagrangian Eulerian Approach is known as the ALE
Formulation: An Alternative to Lagrangian approach is a method known
as ALE Formulation. In this formulation a portion of the structure (usually
a projectile or impactor) is modeled with an Eulerian mesh which can only
accept volume mesh and the active space also called void needs to be
meshed (with volume mesh )as well with different materials properties
from the impactor. The projectile or the impactor are decribed by Eulerian
mesh because the Lagrangian decription is not suited to model them as
they undergo large deformations. The computational cost of this method is
quite high since these meshes have to span the entire active space
covering all Lagrangian structures which is usually the targets. This
method shall require an Eulerian Lagrangian Coupling algorithm to
combine its motion with Lagrangian parts of the model. Here the target
shall be modeled with either Lagrangian solid or shell meshes. Finer mesh
shall be used near the zone of impact. The Bird and the space between the
Bird and the Target shall be modeled with an Eulerian solid mesh. The Air
space shall cover the entire Target as well as the Bird. For assigning
section properties to Eulerian mesh the *SECTION_PROPERTY_ALE
card should be used. Different contact method (Penalty and Constraint)
can be employed to assess the convergence of results. A standard ALE
formulation shall be employed for the simulation. Hour glass control shall
be exercised to remove all zero energy modes and to ensure the model
reproduces the correct rigid body motions. Appropriate material model
should be employed to model the Target for the simulation. The coupling
between the Lagrangian and Eulerian Mesh shall be established using the
*CONSTRAINED_LAGRANGE_IN_SOLID control card. The surface
of the Eulerian Mesh representating the Bird should be assigned as the
master set and the plate surface of the target shall be represented as the
slave set. The Contact interaction between the plate (modeled as solid
element) and the gelatin (Eulerian mesh) shall be defined using the control
card *CONTACT_NODES_TO_SURFACE control card, while for the
Target (modeled as a shell element) and the Bird, the contact interaction
shall be defined using the *CONTACT_SURFACE_TO_SURFACE
control card. Analysis can be carried out assuming zero friction during the
contact interaction. The density for both the Bird and the void mesh shall
be specified using the Material control card *MAT_NULL. The density
for the Void mesh shall be prescribed as the Air density If the Target is
modeled with a shell formulation, the *SECTION_SOLID control card
shall be used to specify the shell thickness for the Target elements.
Meshless methods like Smooth Particle Hydrodynamics (SPH): SPH
is a meshless lagrangian numerical technique used to model the fluid
equations of motion. SPH has proved to be useful in certain class of
problems where large mesh distortions occur such as high velocity
impact, crash simulations or compressible fluid dynamics. With the
SPH technique, both the structure and fluid can be modeled using a
Lagrangian approach. The SPH technique utilizes a meshless
Lagrangian method to represent fluids. In the SPH method, the fluid
material is treated as particles that have their masses smoothed in
space. Coupling between the SPH grid points and the structural
model is accomplished through normal contact definitions. The
projectile/ or Bird in this case shall be numerically represented by
few thousand (4000-5000) SPH particles. While the target shall be
modeled using solid or shell elements. The SPH particles shall be
assigned material properties, hence will have dual function i.e
approximation points and material components. These particles are
capable of moving in space, carry all computed information, and thus
form the computational frame for solving the partial differential
equations describing the conservation laws. The particles indicate the
gradation of the SPH particles. Because the SPH model is
represented by a group of elements or small spheres, and is not
continuous along the whole space they are occupying, it is necessary
to calculate the physical properties for each element by taking into
account that each element should have the same bird density. It is
also important to highlight that the sum of masses of all small
elements or spheres must be equal to the mass of the bird. The
following equation shows how the lumped mass for each SPH
element is calculated:
Lumped mass =
Note that the number of nodes is equal to the number SPH elements.
The *MAT_NULL shall be assigned to the SPH particles since they
are used to represent the gelatin. The constant for smoothing shall be
taken as 1.2 unless advised otherwise. The contact interaction type
shall be varied between Surface to Surface and Node to surface to
both the simulation involving target meshed with solids and shells.
In the all the fore-mentioned studies, Bird should be modeled using
elastic-plastic-hydrodynamic material model with polynomial
equation of state. For the Eulerian Mesh representing the Bird, the
equations of state coefficients (C1, C2,..CN) are supplied using the
*EOS_TABULATED control card for the Bird part.
Material Models: In all types of impact analysis it is not possible to
correlate the analytical results with experiments unless we use an
appropriate material model. The material model should be able to capture
the stain rate effects appropriate. For all the tree types of simulation
problem an appropriate material model depending on the target material
shall be employed. Usually for isotropic material for simulation of soft
body impact on a hard target the Material model 24 is predominantly
used. This material model can be chosen using the
*MAT_PIECEWISE_LINEAR_PLASTICITY control card in LS DYNA.
This is piecewise linear plasticity material model which can accommodate
strain rate effects by any of the following three options, Strain rate may be
accounted for by using the Cowper Symondsmodel which scales the yield
stress with the factor
Where C and p are called the Cowper Symonds strain
rate parameters to be defined by the user. These
values could be supplied on the material card
parameter list.
1. .For complete generality a complete load curve
defining b which scales the yield stress may be
supplied.
2. The most popular method is to supply different stress
strain curves for different strain rates.
The appropriate material model for the bird material is *MAT_NULL
material model.
Hour Glass Control: Hourglass energy is often a problem with the
reduced element formulations used in explicit analysis codes. Controlling
the hourglass energy is done by using *CONTROL_HOURGLASS or
*HOURGLASS. Option 2 (default viscous hourglass control) is typically
used for this type of analysis. Viscous control is recommended for high
velocity deformations.
Conclusions
Robust methodology for Bird impact simulation must be established in
order to achieve acceptable test correlation without which it is not
possible to get FAA Certification to ensure that Aircraft Flight safety is
not impaired under a Bird strike event. .Three Simulation techniques using
a Explicit finite element code LS DYNA for the predictive modeling of
bird impact on Aerospace structures has been discussed in this article. The
relative advantages and disadvantages of each method have been
elaborated. Details on the modeling aspects using each method are
explained.