The Application of Grid Fins on Missiles and Launch Vehicles
1. The Application of Grid
Fins on Missiles
and Launch Vehicles
Quirijn Frederix
Supervisor:
Prof. dr. ir. Eric Van den Bulck
2.
3.
4.
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. 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
7. Introduction
• Large variety of
geometries
• Used since ‘60s, mostly military applications, currently shift
to more civil applications
8. 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
9. 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
11. Literature study
Algebraic methods
• Split flow in different regimes
o Subsonic: Vortex lattice
theory
o Transsonic: choked
flow/normal shocks
o Supersonic: Oblique shocks
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. Dimensional analysis
• Goal: Determine the dimensonless
parameters that influence the
performance characteristics
• Neglect heat transfer and assume
constant geometry
15. 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
18. 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):
22. 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
23. 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
24. 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
25. 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)
26. 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
27. 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
28. 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
29. 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
30. 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
16% thin fin, 22% ocoarse fin
Fram thickness has larger effect
Swept fin: 12-13% decrease
- Wat is de reden om een dimensieloze analyse te doen? Story over explosies
In the case this parameter approaches 0, the blades will be far apart and the cascade will behave as the sum of the individual blades. If the parameter approaches infinity, the blades will be very close to each other such that the flow will be perfectly parallel to the blades and thus have a deviation angle equal to 0.
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
very linear behaviour, which is also observed in the literature. Furthermore, the function reaches a maximum around an angle of attack of about 45° and then starts to decrease again. From the literature, we know that grid fins exhibit this type of behaviour. However it is noted that the angle at which the grid fin will begin to stall might be lower than this maximum value as the method presented above does not take into account effect of seperation of the flow.
The curve of Mach number 0.9 will probably deviate somewhat from the real curve
Another very interesting observation that can be deduced from the figure, is the fact that at M = 0.4, the normal force slope predicted by the method of individual wings
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.
For low solidity values, the normal force will change a lot while at high values the change of normal force with solidity will be fairly small. This is easily explained by
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
Normal force geschat met linear cascade methode
Verschil kan nog groter zijn voor holle vinnen
Vertikale vinnen dragen ook bij tot normal force
Order of magnitude, altough in practice a couple times
