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The Application of Grid Fins on Missiles and Launch Vehicles

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A study of grid fins is presented. Particular attention was given to the grid fins used on the Falcon 9 of SpaceX.

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The Application of Grid Fins on Missiles and Launch Vehicles

  1. 1. The Application of Grid Fins on Missiles and Launch Vehicles Quirijn Frederix Supervisor: Prof. dr. ir. Eric Van den Bulck
  2. 2. Table of contents • Introduction • Literature study • Dimensional analysis • Linear cascade approximation of grid fins • Comparison of grid fins and equivalent planar fins • Further research • Conclusion
  3. 3. Table of contents • Introduction • Literature study • Dimensional analysis • Linear cascade approximation of grid fins • Comparison of grid fins and equivalent planar fins • Further research • Conclusion
  4. 4. Introduction • Large variety of geometries • Used since ‘60s, mostly military applications, currently shift to more civil applications
  5. 5. Table of contents • Introduction • Literature study • Dimensional analysis • Linear cascade approximation of grid fins • Comparison of grid fins and equivalent planar fins • Further research • Conclusion
  6. 6. Literature study General characteristics Pros: • Can be folded • Higher αstall • Low hingemoment • Useful at high Mach numbers • Radius of curvature has negligible influence Cons: • Higher drag in transsonic region • Drop in normal force and pitch moment in transsonic region
  7. 7. Literature study Possible improvements • Shape of web cross section • Thickness web/frame • Coarseness of lattice • Swept-back grid fin • Shape of web
  8. 8. Literature study Algebraic methods • Split flow in different regimes o Subsonic: Vortex lattice theory o Transsonic: choked flow/normal shocks o Supersonic: Oblique shocks
  9. 9. Table of contents • Introduction • Literature study • Dimensional analysis • Linear cascade approximation of grid fins • Comparison of grid fins and equivalent planar fins • Further research • Conclusion
  10. 10. Dimensional analysis • Goal: Determine the dimensonless parameters that influence the performance characteristics • Neglect heat transfer and assume constant geometry
  11. 11. Dimensional analysis • Force/moment coefficients independent of Reynolds number! • Flow over wings is almost always turbulent
  12. 12. Table of contents • Introduction • Literature study • Dimensional analysis • Linear cascade approximation of grid fins • Comparison of grid fins and equivalent planar fins • Further research • Conclusion
  13. 13. Linear cascade approximation Approximation as individual wings • Performance depends on spacing between the different elements or wings
  14. 14. Linear cascade approximation Linear cascade method • Outlet flow will not be exactly perpendicular to the plates!
  15. 15. Linear cascade approximation Linear cascade method • Calculate deviation angle, δdev • Solidity is very important • Incompressible potential flow for linear cascade of flat plates (Kramer and Stanitz):
  16. 16. Linear cascade approximation Linear cascade method • Normal force of Falcon 9 grid fin as calculated by linear cascade method
  17. 17. Linear cascade approximation Linear cascade method • Comparison of both methods
  18. 18. Linear cascade approximation Linear cascade method • Influence of solidity
  19. 19. Table of contents • Introduction • Literature study • Dimensional analysis • Linear cascade approximation of grid fins • Comparison of grid fins and equivalent planar fins • Further research • Conclusion
  20. 20. Comparison of grid fins and planar fins Case Study: Falcon 9 grid fins • Loads at Max Q • Equate normal forces of grid fins and tapered wings • Cr = 0,995m, Ct = 0.497, b = 1.119m
  21. 21. Comparison of grid fins and planar fins Mass estimation • Grid fins: 41kg • Tapered wings: o Estimate thickness from strength coniderations: t = 1.42cm o Mass = 30.18kg • Normal force per kg: o Grid fins: 386.8N/kg o Tapered wings: 750.6N/kg
  22. 22. Comparison of grid fins and planar fins Axial force estimation • Calculate axial force at α = 0° and assume constant • Skin friction and pressure component Grid fins: • 3081N (432.5N friction, 2648.5N pressure) Tapered wings: • 292.3N (111.6N friction, 180.73N pressure)
  23. 23. Comparison of grid fins and planar fins Overview of comparison: • Grid fins have higher mass • Lower hinge moment • High drag/axial force not necessarily disadvantageous • Grid fins useful at high Mach numbers • Foldable • High stall angle
  24. 24. Table of contents • Introduction • Literature study • Dimensional analysis • Linear cascade approximation of grid fins • Comparison of grid fins and equivalent planar fins • Further research • Conclusion
  25. 25. Further research • Validation of linear cascade method o Compare with experiments/CFD o Compare with currently used methods • Grid fin/missile body interaction • Set up general formula for estimating performance characteristics in early design stages from database of coefficients • Structural analysis of grid fins
  26. 26. Table of contents • Introduction • Literature study • Dimensional analysis • Linear cascade approximation of grid fins • Comparison of grid fins and equivalent planar fins • Further research • Conclusion
  27. 27. Conclusion • Advantages/disadvantages and general characteristics of grid fins are well documented • Algebraic methods available • Performance characteristic seem independent of Reynolds number • Linear cascade approach can be applied to estimate performance in the subsonic regime o Solidity parameter has a large influence • Choice of grid fins by SpaceX is clear
  28. 28. Thank you for your attention!

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