Three Dimensional Flow Simulations with the Finite Element Technique over a Multi-Stage Rocket

Aerodynamic flow simulations over the first Brazilian satellite launch vehicle, VLS, during its first-stage flight are presented. The three dimensional compressible flow is modeled by the Euler equations and a Taylor-Galerkin finite element method with artificial dissipation is used to obtain the numerical solution. Transonic and supersonic results for zero angle-of-attack are presented and compared to available experimental results. The influence of mesh refinement and artificial dissipation coeffcient on the transonic flow results are discussed. The results obtained for the supersonic simulations present good agreement with experimental data. The transonic simulation results capture the correct trends but they also indicate that this flight condition requires more refined meshes.

[1]  Burton Wendroff,et al.  On the stability of difference schemes , 1962 .

[2]  J. Donea A Taylor–Galerkin method for convective transport problems , 1983 .

[3]  Edson Basso,et al.  CHIMERA SIMULATIONS OF VISCOUS FLOWS OVER A COMPLEX SATELLITE LAUNCHER CONFIGURATION , 2001 .

[4]  O. Zienkiewicz,et al.  Finite elements and approximation , 1983 .

[5]  P. Lax,et al.  Systems of conservation laws , 1960 .

[6]  O. C. Zienkiewicz,et al.  Finite element methods for second order differential equations with significant first derivatives , 1976 .

[7]  S. Giuliani,et al.  A simple method to generate high-order accurate convection operators for explicit schemes based on linear finite elements , 1981 .

[8]  Jaime Peraire,et al.  The computation of three-dimensional flows using unstructured grids , 1991 .

[9]  Thomas J. R. Hughes,et al.  Finite element methods for first-order hyperbolic systems with particular emphasis on the compressible Euler equations , 1984 .

[10]  P. Lax,et al.  Difference schemes for hyperbolic equations with high order of accuracy , 1964 .

[11]  O. Zienkiewicz,et al.  Finite element Euler computations in three dimensions , 1988 .

[12]  O. C. Zienkiewicz,et al.  An ‘upwind’ finite element scheme for two‐dimensional convective transport equation , 1977 .

[13]  I. St. Doltsinis,et al.  Hermes space shuttle: exploration of reentry aerodynamics , 1989 .

[14]  R. F. Warming,et al.  Diagonalization and simultaneous symmetrization of the gas-dynamic matrices , 1975 .

[15]  O. C. Zienkiewicz,et al.  An adaptive finite element procedure for compressible high speed flows , 1985 .

[16]  J. Steger,et al.  Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methods , 1981 .

[17]  Edson Basso,et al.  THREE DIMENSIONAL FLOW SIMULATIONS OVER A COMPLETE SATELLITE LAUNCHER WITH A CLUSTER CONFIGURATION , 2000 .

[18]  J. Azevedo,et al.  A numerical study of turbulent afterbody flows including a propulsive jet , 1999 .