Aerodynamic Analysis Of Grid Fins Using Analytical And Computational Methods
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Grid fins (lattice fins) are used as a lifting and control surface for highly manoeuvrable missiles. Grid fins also find their applications for air-launched submunitions. The main advantages are its low hinge moment requirement and good high angle of attack performance characteristics. Two dimensional analysis has been carried out using linear and shock-expansion theo- ries. The results indicate that above certain depth-to-height ratio, (called critical depth-to-height ratio,) the local normal force becomes negative due to shock reflection from the opposite side. Hence, depth (chord) for grid fin cell should not exceed a critical value. A prediction method has been developed for the estimation of aerodynamic character- istics of grid fin-body combinations at supersonic Mach numbers based on shock-expansion theory. Body upwash theory has been used for the effect of body; method of images has been used for carry-over forces onto the body. Empirical relation has been used for the modelling of separated body vortices and their effect on the leeward side fins. The method has been validated with experimental results for three configurations. The comparison is good for individual fin characteristics as well as overall characteristics for all the cases at higher supersonic Mach numbers. For lower supersonic Mach numbers at higher angles of attack, the prediction deviates from experiment. The reason for the deviation is due to shock detachment and shock reflection from opposite side, which is not modelled in the present method. Vortex lattice method has been used for prediction of linear aerodynamic character- istics of grid-fins at subsonic Mach numbers. Empirical relation based on trends from available experimental data has been used for the non-linear effect. The method has been validated with experimental results for several configurations without and with control surface deflections. The predicted aerodynamic characteristics compare well with experimental results for all the cases and the difference is within 15%. Based on the subsonic and supersonic analytical methods, a prediction code for the aerodynamic analysis of configuration with grid fins has been developed. Flow field computations inside isolated cells have been carried out using CFD code, PARAS-3D. Effects of depth-to-height ratio, web thickness, web leading edge angle and cell width-to-height ratio have been studied. Increase in thickness reduces the critical depth and increases the normal force. This increment in normal force is due to shock wave formation at the expansion side and its interaction with the opposite side. Effect of cell cross sectional shape has been studied using inviscid computation over isolated cells. Square, right triangular, equilateral triangular and hexagonal cross sections have been considered for this study. The normal force for square cell at zero roll is higher compared to 45 deg roll (diamond shape). Triangular cells show large variation in normal force with roll orientation due to large variation in projected area with roll angle. To compare the characteristics of different cross sectional cells, the normal force is normalised with respect to total internal web area. The comparison shows that the hexagonal cell gives maximum normal force and right triangular cell gives the minimum. Packaging efficiency of different cross sections is analysed by normalising the normal force with frontal area. The results show that triangular cells are preferred for packaging efficiency. Viscous flow computations over complete configuration have been carried out using FLUENT. GAMBIT has been used for geometry definition and grid generation. Hexahedral finite volumes are used to generate the grids including the nose region. Flow computations have been carried out at supersonic Mach numbers. To reduce the compu- tational time, Flow computations upto 0.5 calibre ahead of grid fin have been carried out with body-alone configuration. Flow over the fin-body section has been computed sep- arately taking the inlet pressure condition from the body-alone computed results. This procedure has reduced the grid size to around 1/5th and the computations converged faster due to imposition of converged solution at the pressure inlet. The computed results on the body show that the Flow separation occurs on the lee- ward side of the body and formation of separated vortices. The comparison of pressure distribution on the body with experiment is good. Flow computations over the fin-body section have been carried out at different Mach numbers and angles of attack. The computed normal force coefficient on the horizontal fin compares well with experimental data. Computations with fin deflection of -15 deg have also been carried out and the computed results are within 10% of the experimental data. Flow computations over another grid fin configuration have been carried out at dif- ferent roll angles. The comparison of individual fin force and overall normal force and pitching moment coefficients with experiment is good. The comparison demonstrates the capability of prediction methods as well as CFD in analysing aerodynamic performance of grid fin configurations.