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Fram thickness has larger effect

Swept fin: 12-13% decrease

Other factors that are of principal importance in determining the deviation angle are the camber angle and chord angle. Increasing these values will increase the deviation

Angle.

Assumption slechts goed tot ongeveer M = 0.3

The curve of Mach number 0.9 will probably deviate somewhat from the real curve

is roughly a factor 2 larger than the one predicted by the linear cascade method. At M = 0.8, however, this factor seems to be increased up to about 3.

the fact that for high solidity, the situation approaches the case where the flow leaves the grid fin is perfectly parallel with the internal web.

Trade-off: weight vs normal force

Vertikale vinnen dragen ook bij tot normal force

- 1. The Application of Grid Fins on Missiles and Launch Vehicles Quirijn Frederix Supervisor: Prof. dr. ir. Eric Van den Bulck
- 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. 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. Introduction • Large variety of geometries • Used since ‘60s, mostly military applications, currently shift to more civil applications
- 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. 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. Literature study Possible improvements • Shape of web cross section • Thickness web/frame • Coarseness of lattice • Swept-back grid fin • Shape of web
- 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. 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. Dimensional analysis • Goal: Determine the dimensonless parameters that influence the performance characteristics • Neglect heat transfer and assume constant geometry
- 11. Dimensional analysis • Force/moment coefficients independent of Reynolds number! • Flow over wings is almost always turbulent
- 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. Linear cascade approximation Approximation as individual wings • Performance depends on spacing between the different elements or wings
- 14. Linear cascade approximation Linear cascade method • Outlet flow will not be exactly perpendicular to the plates!
- 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. Linear cascade approximation Linear cascade method • Normal force of Falcon 9 grid fin as calculated by linear cascade method
- 17. Linear cascade approximation Linear cascade method • Comparison of both methods
- 18. Linear cascade approximation Linear cascade method • Influence of solidity
- 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. 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. 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. 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. 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. 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. 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. 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. 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. Thank you for your attention!

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