On the verification and validation of a spring fabric for modeling parachute inflation

Abstract A mesoscale spring–mass model is used to mimic fabric surface motion. Through coupling with an incompressible fluid solver, the spring–mass model is applied to the simulation of the dynamic phenomenon of parachute inflation. A presentation of a verification and validation efforts is included. The present model is shown to be numerically convergent under the constraints that the summation of point masses is constant and that both the tensile stiffness and the angular stiffness of the spring conform with the material׳s Young modulus and Poisson ratio. Complex validation simulations conclude the effort via drag force comparisons with experiments.

[1]  H. Lomax,et al.  Thin-layer approximation and algebraic model for separated turbulent flows , 1978 .

[2]  M. Minion,et al.  Accurate projection methods for the incompressible Navier—Stokes equations , 2001 .

[3]  Zhiliang Xu,et al.  Front Tracking under TSTT , 2006 .

[4]  Lingling Wu,et al.  A simple package for front tracking , 2006, J. Comput. Phys..

[5]  Hervé Delingette,et al.  Triangular Springs for Modeling Nonlinear Membranes , 2008, IEEE Transactions on Visualization and Computer Graphics.

[6]  Xiao Ming,et al.  Study on transient aerodynamic characteristics of parachute opening process , 2007 .

[7]  Brian Fix,et al.  A TSTT integrated FronTier code and its applications in computational fluid physics , 2005 .

[8]  Tayfun E. Tezduyar,et al.  Modelling of fluid–structure interactions with the space–time finite elements: Solution techniques , 2007 .

[9]  Cédric Cochrane,et al.  A Flexible Strain Sensor Based on a Conductive Polymer Composite for in situ Measurement of Parachute Canopy Deformation , 2010, Sensors.

[10]  Vinod Kumar,et al.  The Road Ahead: A White Paper on the Development, Testing and Use of Advanced Numerical Modeling for Aerodynamic Decelerator Systems Design and Analysis , 2011 .

[11]  Charles S. Peskin,et al.  2-D Parachute Simulation by the Immersed Boundary Method , 2006, SIAM J. Sci. Comput..

[12]  Charles S. Peskin,et al.  3-D Parachute simulation by the immersed boundary method , 2009 .

[13]  D. Wilcox Turbulence modeling for CFD , 1993 .

[14]  Yan Li,et al.  Numerical Method of Fabric Dynamics Using Front Tracking and Spring Model , 2013 .

[15]  Eric Yu Tau A second-order projection method for the incompressible Navier-Stokes equations in arbitrary domains , 1994 .

[16]  Allen Van Gelder,et al.  Approximate Simulation of Elastic Membranes by Triangulated Spring Meshes , 1998, J. Graphics, GPU, & Game Tools.

[17]  Xiaolin Li,et al.  Robust Computational Algorithms for Dynamic Interface Tracking in Three Dimensions , 1999, SIAM J. Sci. Comput..

[18]  A. Chorin Numerical solution of the Navier-Stokes equations , 1968 .

[19]  Randall J. LeVeque,et al.  An Immersed Interface Method for Incompressible Navier-Stokes Equations , 2003, SIAM J. Sci. Comput..

[20]  Manley Butler,et al.  The design, development and testing of parachutes using the BAT Sombrero Slider , 1999 .

[21]  Jean Potvin,et al.  The Bi-model: Using CFD in simulations of slowly-inflating low-porosity hemispherical parachutes , 2011 .

[22]  Gustavo C. Buscaglia,et al.  A Note on the Numerical Treatment of the k-epsilon Turbulence Model* , 2001 .

[23]  Li Yu,et al.  The electrostatics of parachutes , 2007 .

[24]  Kenneth Desabrais,et al.  Vortex shedding in the near wake of a parachute canopy , 2005, Journal of Fluid Mechanics.

[25]  John Sheridan,et al.  Flow field and topological analysis of hemispherical parachute in low angles of attack , 2010 .

[26]  Yan Li,et al.  Simulation of parachute FSI using the front tracking method , 2013 .

[27]  Stefan Turek,et al.  On the implementation of the κ-ε turbulence model in incompressible flow solvers based on a finite element discretisation , 2007, Int. J. Comput. Sci. Math..

[28]  R. Winther,et al.  Numerical methods for incompressible viscous flow , 2002 .

[29]  Carl W. Peterson The Fluid Physics of Parachut Inflation , 1993 .

[30]  Leslie M. Smith,et al.  The renormalization group, the ɛ-expansion and derivation of turbulence models , 1992 .

[31]  M. Matyka Solution to two-dimensional Incompressible Navier-Stokes Equations with SIMPLE, SIMPLER and Vorticity-Stream Function Approaches. Driven-Lid Cavity Problem: Solution and Visualization , 2004, physics/0407002.