Skip to main content
SpringerLink
Log in

Numerical simulations of three-dimensional flow over a multi-stage rocket using finite volumes

  • Technical Paper
  • Published:
Journal of the Brazilian Society of Mechanical Sciences and Engineering Aims and scope Submit manuscript

Abstract

The paper discusses the results obtained using an in-house developed finite volume code for three-dimensional, unstructured, adaptive meshes to simulate inviscid and viscous flows. A fully explicit, second-order accurate, five-stage, Runge–Kutta time-stepping scheme is used to perform the time march of the flow equations. Two different forms for flux calculation on the volume faces are implemented. The first one is a centered scheme which requires the addition of artificial dissipation terms. The other form for flux calculation is based on the van Leer flux-vector splitting scheme. The boundary conditions are set using Riemann invariants. The implementation uses a cell-centered, face-based data structure. The Spalart and Allmaras turbulence model is implemented to simulate viscous flows at high Reynolds numbers. In order to enhance the quality of the results, h-refinement routines are implemented in the code to adapt the original mesh. These routines are able to handle tetrahedra, hexahedra, triangular base prisms and quadrilateral base pyramids. A sensor based on density gradients selects the elements to be refined. The paper presents simulation results obtained for the Brazilian Satellite Launcher. The simulations using the adaptive mesh refinement routines are performed for inviscid flows. The paper also presents simulations of transonic and supersonic turbulent viscous flows over the vehicle.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28
Fig. 29
Fig. 30
Fig. 31
Fig. 32
Fig. 33
Fig. 34

Similar content being viewed by others

References

  1. Anderson WK, Thomas JL, van Leer B (1986) Comparison of finite volume flux vector splittings for the Euler equations. AIAA J 24(9):1453–1460

    Article  Google Scholar 

  2. Antunes AP, Basso E, Azevedo JLF (2001) Chimera simulations of viscous flows over a complex satellite launcher configuration. AIAA Paper No. 2001–2475, Proceedings of the 19th AIAA applied aerodynamics conference, Anaheim, CA

  3. Azevedo JLF (1992) On the development of unstructured grid finite volume solvers for high speed flows. Report NT-075-ASE-N/92, Instituto de Aeronáutica e Espaço, São José dos Campos, SP, Brazil

  4. Azevedo JLF, Figueira da Silva LF, Strauss D (2010) Order of accuracy study of unstructured grid finite volume upwind schemes. J Braz Soc Mech Sci Eng 32(1):78–93

    Article  Google Scholar 

  5. Azevedo JLF, Korzenowski H (2009) An assessment of unstructured grid finite volume schemes for cold gas hypersonic flow calculations. J Aerospace Technol Manag 1(2):135–152

    Article  Google Scholar 

  6. Basso E, Antunes AP, Azevedo JLF (2000) Three dimensional flow simulations over a complete satellite launcher with a cluster configuration. AIAA Paper No. 2000–4514, Proceedings of the 18th AIAA applied aerodynamics conference, Denver, CO

  7. Bigarella EDV, Azevedo JLF (2005) Numerical study of turbulent flows over launch vehicle configurations. J Spacecraft Rock 42(2):266–280

    Article  Google Scholar 

  8. Chakravarthy SR (1983) Euler equations, implicit schemes and boundary conditions. AIAA J 21(5):699–706

    Article  MathSciNet  MATH  Google Scholar 

  9. Hirsch C (1988) Numerical computation of internal and external flows, Volume 1: fundamentals of numerical discretization. Wiley, New York

  10. Jameson A, Mavriplis D (1986) Finite volume solution of the two-dimensional Euler equations on a regular triangular mesh. AIAA J 24(4):611–618

    Article  MATH  Google Scholar 

  11. Jameson A, Schmidt W, Turkel E (1981) Numerical solution of the Euler equations by finite volume methods using Runge–Kutta time-stepping schemes. AIAA Paper No. 81–1259, 14th AIAA fluid and plasma dynamics conference, Palo Alto, CA

  12. Korzenowski H, Figueira da Silva LF, Azevedo JLF (1997) Unstructured adaptive grid flow simulations of inert and reactive gas mixtures. In: Proceedings of the 14th Brazilian congress of mechanical engineering—COBEM 97, Bauru, SP, Brazil

  13. Lomax H, Pulliam TH, Zingg DW (2001) Fundamentals of computational fluid dynamics. Springer, Berlin

    Book  MATH  Google Scholar 

  14. Long L, Khan M, Sharp HT (1991) A massively parallel three-dimensional Euler/Navier-Stokes method. AIAA J 29(5):657–666

    Article  Google Scholar 

  15. Mavriplis DJ (1988) Multigrid solution of the two-dimensional Euler equations on unstructured triangular meshes. AIAA J 26(7):824–831

    Article  MATH  Google Scholar 

  16. Mavriplis DJ (1990) Accurate multigrid solutions of the Euler equations on unstructured and adaptive meshes. AIAA J 28(2):213–221

    Article  Google Scholar 

  17. Menter FR (2009) Review of the shear–stress transport turbulence model experience from an industrial perspective. Int J Comput Fluid Dyn 23(4):305–316

    Article  MATH  Google Scholar 

  18. Menter FR, Grotjans H (1998) Application of advanced turbulence models to complex industrial flows. Adv Fluid Mech

  19. Moraes P, Neto AA (1990) Aerodynamic experimental investigation of the Brazilian satellite launch vehicle (VLS). In: Proceedings of the 3rd Brazilian thermal science meeting. 1: 211–215

  20. Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical recipes in C: the art of scientific computing. Cambridge University Press, Cambridge

    Google Scholar 

  21. Pulliam TH, Steger JL (1980) Implicit finite-difference simulations of three-dimensional compressible flow. AIAA J 18(2):159–167

    Article  MATH  Google Scholar 

  22. Scalabrin LC, Azevedo JLF (2004) Adaptive mesh refinement and coarsening for aerodynamic flow simulations. Int J Numer Meth Fluids 45(10):1107–1122

    Article  MATH  Google Scholar 

  23. Scalabrin LC, Azevedo JLF, Teixeira PRF, Awruch AM (2002) Three dimensional flow simulations with the finite element technique over a multi-stage rocket. AIAA Paper No. 2002–0408, 40th AIAA aerospace sciences meeting and exhibit, Reno, NV

  24. Spalart PR, Allmaras SR (1992) A one-equation turbulence model for aerodynamic flows. AIAA Paper No. 92–0439, 30th AIAA aerospace sciences meeting and exhibit, Reno, NV

  25. Steger JL, Warming RF (1981) Flux vector splitting of the inviscid gasdynamic equations with application to finite difference methods. J Comput Phys 40(2):263–293

    Article  MathSciNet  MATH  Google Scholar 

  26. Strauss D, Azevedo JLF (1999) A numerical study of turbulent afterbody flows including a propulsive jet. AIAA Paper No. 99–3190, Proceedings of the 17th AIAA applied aerodynamics conference, Norfolk, VA, pp 654–664

  27. Strauss D, Azevedo JLF (2002) Unstructured multigrid simulation of turbulent launch vehicle flows including a propulsive jet. AIAA Paper No. 2002–2720, Proceedings of the 20th AIAA applied aerodynamics conference, St. Louis, MO

  28. Swanson RC, Radespiel R (1991) Cell centered and cell vertex multigrid schemes for the Navier–Stokes equations. AIAA J 29(5):697–703

    Article  Google Scholar 

  29. van Leer B (1982) Flux-vector splitting for the Euler equations. Lect Notes Phys 170:507–512

    Article  Google Scholar 

Download references

Acknowledgments

The authors would like to acknowledge Conselho Nacional de Desenvolvimento Científico e Tecnológico, CNPq, which partially supported the work under the Research Grants No. 312064/2006-3 and No. 471592/2011-0. Fundação de Amparo à Pesquisa do Estado de São Paulo, FAPESP, has also provided partial support for the present work under Project No. 2004/16064-9 and, more recently, under FAPESP Grant No. 2011/12493-6. Such support is greatly appreciated. The authors are further indebted to Centro Nacional de Supercomputação, CESUP/UFRGS, and to Núcleo de Atendimento em Computação de Alto Desempenho, NACAD-COPPE/UFRJ, which have provided the computational resources used for the present simulations.

Author information

Authors and Affiliations

  1. Embraer S.A., Av. Brigadeiro Faria Lima, 2170, São José dos Campos, SP, 12227-901, Brazil

    Leonardo Costa Scalabrin

  2. Departamento de Ciência e Tecnologia Aeroespacial, Instituto de Aeronáutica e Espaço, DCTA/IAE/ALA, São José dos Campos, SP, 12228-903, Brazil

    João Luiz F. Azevedo

Authors
  1. Leonardo Costa Scalabrin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. João Luiz F. Azevedo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Leonardo Costa Scalabrin.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Scalabrin, L.C., Azevedo, J.L.F. Numerical simulations of three-dimensional flow over a multi-stage rocket using finite volumes. J Braz. Soc. Mech. Sci. Eng. 38, 1–20 (2016). https://doi.org/10.1007/s40430-015-0330-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40430-015-0330-8

Keywords

Search

Navigation