American Transactions on Engineering & Applied Sciences http://TuEngr.com/ATEAS Smooth Particle Hydrodynamics for Bird-Strike Analysis Using LS-DYNA Vijay K. Goyal a* , Carlos A. Huertas a , Thomas J. Vasko b a Department of Mechanical Engineering, University of Puerto Rico at Mayagüez, PR 00680, USA b Engineering Department, Central Connecticut State University, New Britain, CT 06050, USA A R T I C L E I N F O A B S T RA C T Article history: Received December 23, 2012 Received in revised form 24 February 2013 Accepted February 26, 2013 Available online March 04, 2013 Keywords: Finite element; Impact analysis; Bird-strike; Smooth-particle hydrodynamics. In this second of a three-paper sequence, we developed a standard work using the Smoothed Particle Hydrodynamic (SPH) approach in LS-DYNA and compared the results against those the Lagrangian model and available experimental results. First, the SPH model was validated against a one-dimensional beam centered impact’s analytical solution and the results are within 3% error. Bird-strike events were divided into three separate problems: frontal impact on rigid flat plate, 0 and 30 deg impact on deformable tapered plate. The bird model was modeled as a cylindrical fluid. We successfully identified the most influencing parameters when using SPH in LS-DYNA. The case for 0 deg tapered plate impact shows little bird-plate interaction because the bird is sliced in two parts and the results are within 5% difference from the test data available in the literature, which is an improvement over the Lagrangian model. Conclusion: The developed SPH approach is suitable for bird-strike events within 10% error. 2013 Am. Trans. Eng. Appl. Sci. 2013 American Transactions on Engineering & Applied Sciences. *Corresponding author (V. Goyal), Tel.: 1-787-832-4040 Ext. 2111; E-mail: [email protected]. 2013. American Transactions on Engineering & Applied Sciences. Volume 2 No. 2 ISSN 2229-1652 eISSN 2229-1660 Online Available at http://TuEngr.com/ATEAS/V02/083-107.pdf 83
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Smooth Particle Hydrodynamics for Bird-Strike …Bird-strike events have been studied using Lagrangian method in different finite element codes [8]. But we seek a model with a better
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American Transactions on Engineering & Applied Sciences
http://TuEngr.com/ATEAS
Smooth Particle Hydrodynamics for Bird-Strike Analysis Using LS-DYNA
Vijay K. Goyal a*, Carlos A. Huertas a, Thomas J. Vasko b
a Department of Mechanical Engineering, University of Puerto Rico at Mayagüez, PR 00680, USA b Engineering Department, Central Connecticut State University, New Britain, CT 06050, USA A R T I C L E I N F O
A B S T RA C T
Article history: Received December 23, 2012 Received in revised form 24 February 2013 Accepted February 26, 2013 Available online March 04, 2013 Keywords: Finite element; Impact analysis; Bird-strike; Smooth-particle hydrodynamics.
In this second of a three-paper sequence, we developed a standard work using the Smoothed Particle Hydrodynamic (SPH) approach in LS-DYNA and compared the results against those the Lagrangian model and available experimental results. First, the SPH model was validated against a one-dimensional beam centered impact’s analytical solution and the results are within 3% error. Bird-strike events were divided into three separate problems: frontal impact on rigid flat plate, 0 and 30 deg impact on deformable tapered plate. The bird model was modeled as a cylindrical fluid. We successfully identified the most influencing parameters when using SPH in LS-DYNA. The case for 0 deg tapered plate impact shows little bird-plate interaction because the bird is sliced in two parts and the results are within 5% difference from the test data available in the literature, which is an improvement over the Lagrangian model. Conclusion: The developed SPH approach is suitable for bird-strike events within 10% error.
2013 Am. Trans. Eng. Appl. Sci.
2013 American Transactions on Engineering & Applied Sciences.
*Corresponding author (V. Goyal), Tel.: 1-787-832-4040 Ext. 2111; E-mail: [email protected]. 2013. American Transactions on Engineering & Applied Sciences. Volume 2 No. 2 ISSN 2229-1652 eISSN 2229-1660 Online Available at http://TuEngr.com/ATEAS/V02/083-107.pdf
the interpolation and the SPH approximations for the equations of energy and mass conservation.
A general description of the SPH method was presented by Hut et al. [13]. The authors
presented applications of the method as well as information about the computational parameters for
the SPH method and the expectations for accelerating processing time with the implementation of
faster computers.
In this work, we attempt to create a standard work based on the SPH formulation by
identifying the most important influencing parameters in the bird-strike simulation and validate the
simulation with the test data and compare against the Lagrangian model previously developed
[1].
2. Impact Analysis The bird-strike events are considered as soft body impact in structural analysis because the
yield point of the bird is far smaller when compared with that of the target. Thus, the bird at the
impact can be considered as a fluid material. The soft body impact results in damage over a larger
area if compared with ballistic impacts. Let us understand the main equations involved in this
study.
2.1 A Continuum Approach Three major equations are solved by LS-DYNA to obtain the velocity, density, and pressure of
the fluid for a specific position and time. These equations are conservation of mass, conservation of
momentum, and constitutive relationship of the material and are essential to solve the soft body
impact problem (Cassenti [6]). The conservation of momentum can be stated as follows:
(1)
where P represents a diagonal matrix containing only normal pressure components, ρ the density,
and V the velocity vector. The conservation of mass per unit volume equation can be written as
follows:
(2)
86 Vijay K. Goyal, Carlos A. Huertas, and Thomas J. Vasko
The last equation is that of the constitutive relation and can be expressed in its general form as
follows:
(3)
2.2 SPH Approach Smooth Particle Hydrodynamics (SPH) formulation is a meshless Lagrangian technique used
to model the fluid equations of motion using a pseudo-particle interpolation method to compute
smooth hydrodynamic variables. Initially this method was used to simulate astrophysical
phenomenon, but recently it has been used to resolve other physics problems in continuum
mechanics, crash simulations, brittle and ductile fracture in solids. Due to the absence of a grid, this
method allows solving many problems that are hardly reproducible in other classical methods
discarding the problem of large mesh deformations or tangling. Another advantage of the SPH
method is that due to the absence of a mesh, problems with irregular geometry can be solved.
Figure 1: Integration cycle in time of the SPH computation process.
In this formulation, the fluid is represented as a set of moving particles, each one representing
an interpolation point, where all the fluid properties are known. Then, with a regular interpolation
function called smoothing length the solution of the desired quantities can be calculated for all the
particles. A real fluid can be modeled as many fluid particles provided that the particles are small
compared to the scale over which macroscopic properties of the fluid varies, but large enough to
contain many molecules so macroscopic properties can be defined sensibly. A large number of
particles are needed for the SPH calculations, since the continuum limit is recovered when the *Corresponding author (V. Goyal), Tel.: 1-787-832-4040 Ext. 2111; E-mail: [email protected]. 2013. American Transactions on Engineering & Applied Sciences. Volume 2 No. 2 ISSN 2229-1652 eISSN 2229-1660 Online Available at http://TuEngr.com/ATEAS/V02/083-107.pdf
Pratt & Whitney. The authors gratefully acknowledge the grant monitors for providing the
necessary computational resources and support for this work. The research presented herein is an
extension of the work presented at the 47th AIAA/ASME/ACE/AHS/ASC SDM Conference,
Rhode Island, May 2006, AIAA.
8. References [1] V. K. Goyal, C. A. Huertas, T. J. Vasko, 2013. Bird-Strike Modeling Based on the Lagrangian
Formulation Using LS-DYNA. Am. Trans. Eng. Appl. Sci. 2(2): 057-081. Available at: http://TuEngr.com/ATEAS/V02/057-081.pdf. Accessed: March 2013.
[2] J. Metrisin, B. Potter, Simulating Bird Strike Damage in Jet Engines, ANSYS Solutions 3 (4) (2001) 8–9.
[3] E. Parkes, “The permanent deformation of a cantilever strucks transversely at its tip”, in: Proceedings Roy. Soc. Lond., England, 1995.
[4] W. J. Stronge, T. Yu, Dynamic Models for Structural Plasticity, Springer-Verlag, London, Great Britain, 1993.
[5] W. Goldsmith, IMPACT: The Theory and Phisical Behaviour of Colliding Solids, Dover Publications, Mineola, New York, 2001.
[6] B. N. Cassenti, Hugoniot Pressure Loading in Soft Body Impacts.
[7] J. P. Barber, H. R. Taylor, J. S. Wilbeck, “Characterization of Bird Impacts on a Rigid Plate: Part 1”, Technical report AFFDL-TR-75-5, Air Force Flight Dynamics Laboratory, Wright-Patterson Air Force Base, OH (1975).
[8] E. Niering, Simulation of Bird Strikes on Turbine Engines.
[9] W. Moffat, Timothy J. and Cleghorn, “Prediction of Bird Impact Pressures and Damage Using MSC/DYTRAN”, in: Proceedings of ASME TURBOEXPO, Louisiana, 2001.
[10] N. F. Martin, Nonlinear Finite Element Analysis to Predict Fan Blade Impact Damage.
[11] J. Lacome, “Smooth Particle Hydrodynamics (SPH): A New Feature in LS-DYNA”, in: Proceedings of the 6th International LS-DYNA Users Conference, 2000.
[12] J. Lacome, Smooth Particle Hydrodynamics-Part II (2001) 6–11.
[13] L. H. Hut, P., G. Lake, S. M. J. Makino, T. Sterling, “Smooth Particle Hydrodynamics: Models, Applications, and Enabling Technologies”, in: Proceedings form the Workshop Presented by the Institute for Advance Study, Princeton., 1997.
[14] V. K. a. C. A. H. Goyal, “Robust Bird-Strike Modeling Using LS-DYNA”, in: Proceeding of
106 Vijay K. Goyal, Carlos A. Huertas, and Thomas J. Vasko
the 23th Southeastern Conference on Theoretical and Applied Mechanics Conference, Mayaguez, Puerto Rico., 2006.
[15] D. R. Bowman, G. J. Frank, “IBRG ARTIFICIAL BIRD PROJECT”, Work programmed and Schedule, United Kingdom (2000).
Dr. V. Goyal is an associate professor committed to develop a strong sponsored research program for aerospace, automotive, biomechanical and naval structures by advancing modern computational methods and creating new ones, establishing state-of-the-art testing laboratories, and teaching courses for undergraduate and graduate programs. Dr. Goyal, US citizen and fully bilingual in both English and Spanish, has over 17 years of experience in advanced computational methods applied to structures. He has over 15 technical publications with another three in the pipeline, author of two books (Aircraft Structures for Engineers and Finite Element Analysis) and has been recipient of several research grants from Lockheed Martin Co., ONR, and Pratt & Whitney.
C. Huertas completed his master’s degree at University of Puerto Rico at Mayagüez in 2006. Currently, his is back to his home town in Peru working as an engineer.
Dr. Thomas J. Vasko, Assistant Professor, joined the Department of Engineering at Central Connecticut State University in the fall 2008 semester after 31 years with United Technologies Corporation (UTC), where he was a Pratt & Whitney Fellow in Computational Structural Mechanics. While at UTC, Vasko held adjunct instructor faculty positions at the University of Hartford and RPI Groton. He holds a Ph.D. in M.E. from the University of Connecticut, an M.S.M.E. from RPI, and a B.S.M.E. from Lehigh University. He is a licensed Professional Engineer in Connecticut and he is on the Board of Directors of the Connecticut Society of Professional Engineers
Peer Review: This article has been internationally peer-reviewed and accepted for
publication according to the guidelines given at the journal’s website.
*Corresponding author (V. Goyal), Tel.: 1-787-832-4040 Ext. 2111; E-mail: [email protected]. 2013. American Transactions on Engineering & Applied Sciences. Volume 2 No. 2 ISSN 2229-1652 eISSN 2229-1660 Online Available at http://TuEngr.com/ATEAS/V02/083-107.pdf