The Application of Grid Fins on Missilesand Launch Vehicles

Quirijn Frederix

Supervisor: Prof. dr. ir. Eric Van den Bulck

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

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

Introduction

• Large variety of geometries

• Used since ‘60s, mostly military applications, currently shift to more civil applications

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

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

Literature study

Possible improvements

• Shape of web cross section

• Thickness web/frame

• Coarseness of lattice

• Swept-back grid fin

• Shape of web

Literature study

Algebraic methods

• Split flow in different regimeso Subsonic: Vortex lattice

theoryo Transsonic: choked

flow/normal shockso Supersonic: Oblique shocks

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

Dimensional analysis

• Goal: Determine the dimensonless parameters that influence the performance characteristics

• Neglect heat transfer and assume constant geometry

Dimensional analysis

• Force/moment coefficients independent of Reynolds number!

• Flow over wings is almost always turbulent

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

Linear cascade approximation

Approximation as individual wings

• Performance depends on spacing between the different elements or wings

Linear cascade approximation

Linear cascade method

• Outlet flow will not be exactly perpendicular to the plates!

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):

Linear cascade approximation

Linear cascade method

• Normal force of Falcon 9 grid fin as calculated by linear cascade method

Linear cascade approximation

Linear cascade method

• Comparison of both methods

Linear cascade approximation

Linear cascade method

• Influence of solidity

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

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

Comparison of grid fins and planar fins

Mass estimation

• Grid fins: 41kg

• Tapered wings: o Estimate thickness from strength coniderations:

t = 1.42cmo Mass = 30.18kg

• Normal force per kg: o Grid fins: 386.8N/kgo Tapered wings: 750.6N/kg

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)

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

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

Further research

• Validation of linear cascade methodo Compare with experiments/CFDo 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

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

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 regimeo Solidity parameter has a large influence

• Choice of grid fins by SpaceX is clear

Thank you for your attention!