Science China Technological Sciences

, Volume 55, Issue 11, pp 3131–3141 | Cite as

Numerical simulation of parachute Fluid-Structure Interaction in terminal descent

Article

Abstract

A numerical simulation method for parachute Fluid-Structure Interaction (FSI) problem using Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm is proposed. This method could be used in both coupling computation of parachute FSI and flow field analysis. Both flat circular parachute and conical parachute are modeled and simulated by this new method. Flow field characteristics at various angles of attack are further simulated for the conical parachute model. Comparison with the space-time FSI technique shows that this method also provides similar and reasonable results.

Keywords

parachute Fluid-Structure Interaction (FSI) Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm vortex structure flowfield topological analysis 

Nomenclature

α

angle of attack

ρ

air density

V

velocity

V

velocity at the inflow boundary

Γϕ

generalized diffusion coefficient

Sϕ

generalized source term

p

static pressure

p

pressure at the inflow boundary

µ

molecular viscosity coefficient

µe

equivalent viscosity coefficient

Cp

pressure coefficient

ΔCp

the pressure coefficient difference between the inner and outer canopy

K

turbulent fluctuation kinetic energy

ɛ

turbulent energy dissipation rate

Re

Reynolds number

φ

an angle between the canopy axis and the normal line of meridian

ψ

apex angle of conical parachute

ω

the half angle between two contiguous planes E

ν, β, θ

angles (see Figure 5)

Rf*

dimensionless length of apex point of the cord line to the point on itself in unstretched gore state

σm*, σu*

dimensionless stress in canopy fabric in the longitudinal and latitudinal direction

k

shrink factor of canopy material

r*

dimensionless bulge radius of the canopy

T*

dimensionless force in cord line

xf*, zf*

dimensionless x and z coordinates of cord line in cylindrical coordinates

Eb, Ef

dimensionless elasticity modulus of canopy fabric and cord line

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Tezduyar T E. Stabilized finite element formulations for incompressible flow computations. Adv Appl Mech, 1992, 28: 1–44MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Tezduyar T E, Behr M, Liou J. A new strategy for finite element computations involving moving boundaries and interfaces—The Deforming-Spatial-Domain/Space-Time Procedure: I. The concept and the preliminary numerical tests. Computer Meth Appl Mech Eng, 1992, 94: 339–351MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Tezduyar T E, Behr M, Mittal S, et al. A new strategy for finite element computations involving moving boundaries and interfaces—The Deforming-Spatial-Domain/Space-Time Procedure: II. Computation of free-surface flows, two-liquid flows, and flows with drifting cylinders. Comput Meth Appl Mech Eng, 1992, 94: 353–371MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Mittal S, Tezduyar T E. A finite element study of incompressible flows past oscillating cylinders and airfoils. Int J Num Meth Fluids, 1992, 15: 1073–1118CrossRefGoogle Scholar
  5. 5.
    Mittal S, Tezduyar T E. Parallel finite element simulation of 3D incompressible flows-fluid-structure interactions. Int J Num Meth Fluids, 1995, 21: 933–953MATHCrossRefGoogle Scholar
  6. 6.
    Stein K, Benney R, Kalro V, et al. Parallel computation of parachute fluid-structure interactions. Proceedings of the 14th AIAA Aerodynamic Decelerator Technology Conference, San Francisco, AIAA-97-1505, 1997Google Scholar
  7. 7.
    Kalro V, Tezduyar T E. A parallel 3D computational method for fluid-structure interactions in parachute systems. Comput Meth Appl Mech Eng, 2000, 190: 321–332MATHCrossRefGoogle Scholar
  8. 8.
    Stein K, Benney R, Kalro V, et al. Parachute fluid-structure interactions: 3D computation. Comput Meth Appl Mech Eng, 2000, 190: 373–386MATHCrossRefGoogle Scholar
  9. 9.
    Tezduyar T E, Sathe S, Keedy R, et al. Space-Time Finite Element Techniques for computation of fluid-structure interactions. Comput Meth Appl Mech Eng, 2006, 195: 2002–2027MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Tezduyar T E, Sathe S. Modeling of fluid-structure interactions with the Space-Time Finite Elements: solution techniques. Int J Num Meth Fluids, 2007, 54: 855–900MathSciNetMATHCrossRefGoogle Scholar
  11. 11.
    Tezduyar T E, Sathe S, Pausewang J, et al. Air-fabric interaction modeling with the stabilized space-time FSI technique. Proceedings of the Third Asian-Pacific Congress on Computational Mechanics, Kyoto, CD-ROM, 2007Google Scholar
  12. 12.
    Tezduyar T E, Sathe S, Pausewang J, et al. Interface projection techniques for fluid-structure interaction modeling with moving-mesh methods. Comput Mech, published online, 2008, doi: 10.1007/s00466-008-0261-7Google Scholar
  13. 13.
    Tezduyar T E, Sathe S, Pausewang J, et al. Fluid-structure Interaction Modeling of Ringsail Parachutes. Comput Mech, published online, 2008, doi: 10.1007/s00466-008-0260-8Google Scholar
  14. 14.
    Kim Y, Peskin C S. 3-D parachute simulation by the immersed boundary method. Comput Fluids, 2009, 38: 1080–1090MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    Karagiozis K, Kamakoti R, Cirak F, et al. A computational study of supersonic disk-gap-band parachutes using Large-Eddy Simulation coupled to a structural membrane. J Fluids Struct, 2011, 27: 175–192CrossRefGoogle Scholar
  16. 16.
    Patankar S V. Numerical Heat Transfer and Fluid Flow. New York: Hemisphere Publishing, McGraw-Hill, 1980MATHGoogle Scholar
  17. 17.
    Zhu L C. An approximate approach to calculate drag, stress and deformation of inflated flat circular parachute (in Chinese). Land Technol, 1983, (1): 143–177, translated from the paper titled as Angenäherter Berechnung der Kräfte, Spannungen und Form des Ebenen Rundkappen-Fallschirms im gefüllten Zustand. DLR(FB) 71–98 Q (W) 0860Google Scholar
  18. 18.
    Suryanaranyana G K, Prabhu, A. Effect of natural ventilation on the boundary separation and near-wake vortex shedding characteristics of a sphere. Exp Fluids, 2000, 29: 582–591CrossRefGoogle Scholar
  19. 19.
    Tobak M, Peake D J. Topology of three-dimensional separated flows. Ann Rev Fluid Mech, 1982, 14: 61–85MathSciNetCrossRefGoogle Scholar
  20. 20.
    Sahu J, Cooper G, Benney R. 3-D parachute descent analysis using coupled CFD and structural codes. AIAA-95-1580, 1995Google Scholar
  21. 21.
    Coutanceau M. On the role of high order separation on the onset of the secondary instability of the circular cylinder wake boundary. C R Acad Sci Serie II, 1988, 306: 1259–1263Google Scholar
  22. 22.
    Bouard R, Coutanceau M. The early stage of development of the wake behind an impulsively started cylinder for 40<Re<104. J Fluid Mech, 1980, 101: 583–607CrossRefGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • YiHua Cao
    • 1
  • Kan Wan
    • 1
  • QianFu Song
    • 1
  • John Sheridan
    • 2
  1. 1.School of Aeronautical Science and EngineeringBeihang UniversityBeijingChina
  2. 2.Department of Mechanical and Aerospace Engineering, Faculty of EngineeringMonash UniversityMelbourneAustralia

Personalised recommendations