Multi-Disciplinary Design of a Grid Fin for a Generic High Speed Missile June 2020 Report By: Shakunt Tambe CID: 01196160 Supervisor: Dr. Paul Bruce Imperial College London Second Marker: Dr. David Hayes MBDA Missile Systems, UK Submitted to Imperial College London in partial fulfilment of the requirements for the Degree of Master of Engineering in Aeronautical Engineering Department of Aeronautics Imperial College London South Kensington SW7 2AZ Blank Page Abstract The use of grid fins for high speed missiles has recently seen a resurgence in interest. This project investigates the aerodynamic performance and the inevitable trade-offs that must be made for producibility of a low drag grid fin that is more competitive with traditional planar fins. By adopting a three-stage computational approach, CFD studies were carried out to characterise the effect on aerodynamic performance from altering local geometrical parameters such as the leading and trailing edge sharpness, thickness to chord ratio, chord to span ratio and 3D modifications such as the effect of brazed joints and tapered trailing edges. For the geometry of a Vympel R-77 grid fin, the importance of the leading edge sharpness and overall thickness to chord ratio was significant in achieving an optimum lift to drag ratio. Flow choking at the supersonic design point (Mach 3) was not found to be of concern and a periodicity in performance is analysed by developing a generalised model of the shock structure and underlying flow physics. Superior performance was typically observed at smaller angles of incidence resulting from greater pressure differences between the upper and lower surfaces of the grid fin cell. The effects of 3D modifications, particularly brazing at the joints, resulted in up to a 33% performance degradation, prompting suggestions for alternative approaches. Lastly, preliminary heating estimates from theory, empirical methods and CFD were compared which can additionally inform future material choices and producibility decisions. i Acknowledgements Dr Paul Bruce has not only provided an outstanding level of project supervision and guidance but also an impeccable standard of teaching during my time at Imperial; his lectures have been some of the most enjoyable, clearly delivered and of course engaging topics that I have studied. I am grateful to Dr Bruce for firstly taking on this project, and then sharing his incredible knowledge, passion and invaluable advice throughout, without which completing this project would never have been possible. I would also like to express a huge thank you to Dr David Hayes, Jeff Thornton, Jeremy Murgatroyd and the rest of the team at MBDA who have allowed me the unique opportunity to complete this project and provided extremely helpful feedback and guidance. Thanks also to Prof. Denis Doorly for providing an amazing level of support through personal tutorial sessions over the past four years at Imperial which have certainly helped me to overcome the challenges of this degree. ii Contents List of Figures ............................................. v List of Tables .............................................. vi Nomenclature ............................................. vii 1 Introduction ............................................. 1 1.1 Motivation............................................ 1 2 Background and Literature Review ............................... 2 2.1 Missile Configurations .................................... 2 2.2 Applications of Grid Fins................................... 3 2.2.1 Vympel R-77 ..................................... 3 2.2.2 SpaceX Falcon 9 ................................... 4 2.2.3 Orion Launch Abort Vehicle............................. 4 2.2.4 Producibility of Existing Designs........................... 5 2.3 Drag Reduction through Geometry Modification....................... 6 2.4 Leading and Trailing Edge Geometry............................. 9 2.5 Full Body CFD Studies.................................... 9 2.6 Unit Grid Fin Method..................................... 10 2.7 Theoretical Methods ...................................... 11 2.8 Flowfield around Grid Fins................................... 11 3 Computational Approach ..................................... 12 3.1 Key Objectives ........................................ 12 3.2 Flight Conditions ....................................... 12 3.3 Configuration and Vympel R-77 Geometry.......................... 12 3.4 Three Stage Approach..................................... 13 3.4.1 Stage 1 - Single Flat Plate............................... 13 3.4.2 Stage 2 - Two Flat Plates............................... 14 3.4.3 Stage 3 - Unit Grid Fin (3D) ............................. 14 3.4.4 Benefits of the Three Stage Approach ........................ 15 4 Single Flat Plate .......................................... 16 4.1 Simulation Setup ....................................... 16 4.2 Mesh Convergence ...................................... 17 4.3 Aerodynamic Forces ..................................... 17 4.4 Validating Results....................................... 18 4.4.1 Identifying the Sources of Drag ........................... 19 4.5 Higher Angles of Incidence.................................. 20 4.6 Effect of Thickness to Chord Ratio............................... 21 4.7 Effect of Removing Leading or Trailing Edge Taper...................... 21 4.8 Summary of Findings from a Single Flat Plate........................ 22 5 Two Flat Plates ........................................... 23 5.1 Simulation Setup ....................................... 23 5.2 Small Angles of Incidence .................................. 23 5.2.1 Detailed Analysis of Varying Chord to Span Ratio.................. 24 5.3 Higher Angles of Incidence.................................. 27 iii 5.4 Mach Number Variation.................................... 28 5.5 Summary and Limitations of the Two Flat Plates Analysis.................. 29 6 Unit Grid Fin ............................................ 30 6.1 Simulation Setup ....................................... 30 6.2 Mesh Convergence ....................................... 31 6.3 Aerodynamic Forces ...................................... 31 6.3.1 Validation....................................... 33 6.3.2 Transonic Performance................................ 34 6.3.3 Vortical Structures .................................. 35 6.4 Effects of 3D Geometry Modifications............................ 36 6.4.1 Aerodynamic Performance.............................. 36 7 Heating Estimates ......................................... 38 7.1 Theoretical and Empirical Methods.............................. 38 7.2 Results............................................. 38 8 Conclusion ............................................. 39 8.1 Summary ........................................... 39 8.2 Producibility and Further Work................................ 40 References ................................................ 41 Appendices ............................................... 46 A Vympel R-77 Missile ........................................ 46 B Grid Fin Drawing (Vympel R-77) ................................. 47 C Drag Reduction through Geometry Modification ........................ 48 D Flight Conditions and Prism Layer Parameters ......................... 49 E Shock Expansion Theory for a Single Flat Plate ......................... 50 F STAR-CCM+ Settings for CFD Simulations ........................... 52 F.1 Single Flat Plate........................................ 52 F.2 Two Flat Plates ........................................ 53 F.3 Unit Grid Fin ......................................... 54 G Wall Coordinates .......................................... 55 G.1 Single Flat Plate........................................ 55 G.2 Two Flat Plates ........................................ 56 G.3 Unit Grid Fin ......................................... 57 H UGF 3D Geometry Modifications ................................. 58 I Calculation of Heating Estimates ................................. 60 iv List of Figures 1 A Russian R-77 missile with tail mounted grid fins [1]. .................... 1 2 Canard, wing, tail and split-canard control missile configurations, each shown with grid fins.2 3 Falcon 9 with grid fins mounted at the top of the first stage [22]. .............. 4 4 Four, body folding titanium grid fins on the first stage of the SpaceX Falcon 9 launch vehicle [29]............................................... 5 5 Swept grid fins at the base of a scale model of the NASA Orion LAV [28].......... 5 6 Local sweep applied to individual grid fin cell members [31]................. 6 7 A folded sheet metal and mandrel curing approach to producing grid fins as given in [32].. 6 8 Flowfield structure around a single grid fin cell at different speeds [37]............ 7 9 A schematic of the flow approaching a blunt, unswept grid fin cell and a 30° sharp swept cell [41]............................................... 8 10 Section and edge variations in [48]............................... 9 11 Flow structure and SBLI between a grid fin and the missile body at M = 3, α = 0° [40]. 10 12 Surface pressure distribution showing the grid fin wake interacting with the aft missile body at M = 2:5, α = 5° [4]..................................... 10 13 Representation of a unit grid fin within a lattice framework [53]. .............. 10 14 A simplified drawing of the R-77 grid fin geometry showing a top and right view with key geometrical parameters labelled. A full drawing is provided in AppendixB. 13 15 Stage