The influence of roll angles on unsteady aerodynamics in a canard-configured missile

Abstract

During the initial stage of vertical launch, a missile may exhibit an uncertain roll angle (ϕ) and a high angle of attack (α). This study focuses on examining the impact of roll angle variations on the flow field and the unsteady aerodynamics of a canard-configured missile at α = 75°. Simulations were performed using the validated k-ω SST turbulence model. The analysis encompasses the temporal development of vortices, the oscillatory characteristics of the lateral force, and the fluctuation of kinetic energy distribution within the framework of proper orthogonal decomposition (POD). The results indicate that the flow field surrounding the canard-configured missile is characterized by inconsistent shedding cycles of Kármán-like and canard-separated vortices. A distinct transition zone is identified between these vortices, where vortex tearing and reconnection phenomena occur. With increasing roll angles from 0° to 45°, there is an observed shift in the dominant frequency of the lateral force from the higher frequency associated with Kármán-like vortex shedding to the lower frequency of canard vortex shedding. The shedding frequency of Kármán-like vortices corresponds to the harmonics of the canard vortex shedding frequency, indicative of a higher-order harmonic resonance. The frequency of the lateral force is observed to decrease with an increase in roll angle, except in configurations lacking distinct canard-separated vortices, which are characterized by a “+” shape. The POD analysis reveals that the majority of the fluctuation energy is concentrated in the oscillations and shedding of the canard-separated vortices, leading to pressure fluctuations that are primarily observed on the canard and the downstream region of the canard.

Keywords

large angle of attack / roll angle / unsteady separated flow / power spectral density / properorthogonal decomposition

References

[1] Dexter P, Hunt B. The effect of roll angle on the flow over a slender body of revolution at high angles of attack. Paper presented at: AIAA 19th Aerospace Sciences Meeting;January 12-15, 1981;St. Louis, Missouri, U.S.A.

[2] Qi Z, Zong S, Wang Y. Bi-stable asymmetry on a pointed-nosed slender body at a high angle of attack. J Appl Phys. 2021;130(2):024703(2021).

[3] Degani D, Tobak M. Experimental study of controlled tip disturbance effect on flow asymmetry. Phys Fluids A. 1992;4(12):2825-2832.

[4] Zhai J, Zhang W, Gao QC, Zhang YH, Ye ZY. Side force control on slender body by vortex generators. Chinese J Theor Appl Mech. 2014;46(2):308-312.

[5] Zhao L, Wang Y, Qi Z. Investigation of periodic characteristics of perturbed flow over a slender body. Heliyon. 2023;9(5):e16194.

[6] Zong S, Wang Y, Qi Z. Structural control of asymmetric forebody vortices over a slender body. Phys Fluids (1994). 2021;33(11):117111(2021).

[7] Maynes D, Gebert GA. High-angle-of-attack aerodynamics of a missile geometry at low speed. J Spacecr Rockets. 1999;36(5):772-774.

[8] Thomson KD, Morrison DF. The spacing, position and strength of vortices in the wake of slender cylindrical bodies at large incidence. J Fluid Mech. 1971;50(4):751-783.

[9] Zeiger MD, Telionis DP, Vlachos PP. Unsteady separated flows over three-dimensional slender bodies. Prog Aerosp Sci. 2004;40(4-5):291-320.

[10] Wang G, Liang X. Multi-vortex flow over a slender body of revolution at high incidence. J Hydrodyn A. 2005;20(1):118-123.

[11] Degani D. Development of nonstationary side forces along a slender body of revolution at incidence. Phys Rev Fluids. 2022;7(124101):124101.

[12] Ericsson LE. Vortex unsteadiness on slender bodies at high incidence. J Spacecr Rockets. 1987;24(4):319-326.

[13] Ijaz H, Ma BF. Unsteady vortex flows around a hemisphere–cylinder body with turbulent separation. Phys Fluids. 2022;34(7):077105.

[14] Ma B, Huang Y, Liu T. Low-frequency unsteadiness of vortex wakes over slender bodies at high angle of attack. Chin J Aeronaut. 2014;27(4):772-780.

[15] Degani D, Zilliac GG. Experimental study of nonsteady asymmetric flow around an ogive-cylinder at incidence. AIAA J. 1990;28(4):642-649.

[16] Ayoub A, Karamcheti K. An experiment on the flow past a finite circular cylinder at high subcritical and supercritical Reynolds numbers. J Fluid Mech. 1982;118(1):1-26.

[17] Karn PK, Das S, Kumar P. Effect of ring on the flow unsteadiness of slender body at α=50. J Braz Soc Mech Sci Eng. 2023;45(3):173.

[18] Ma BF, Wang B, Deng XY. Effects of Reynolds numbers on wing rock induced by forebody vortices. AIAA J. 2017;55(9):2980-2991.

[19] Xu S, Deng X. Effects of angle of attack on wing rock motion induced by the flows over slender body with low swept wing. Sci China Phys Mech Astron. 2015;58(4):67-74.

[20] Ma BF, Huang Y, Deng XY. Dynamic responses of asymmetric vortices over slender bodies to a rotating tip perturbation. Exp Fluids. 2016;57(4):54.

[21] Wang F, Liu J, Qin H, Song Y, Chen L, Hu J. Unsteady aerodynamic characteristics of slender body at extra-wide angle-of-attack range. Aerosp Sci Technol. 2021;110:106477.

[22] Menter FR. Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J. 1994;32(8):1598-1605.

[23] Menter FR. Zonal Two Equation k-w Turbulence Models for Aerodynamic Flows. Paper presented at: 23rd Fluid Dynamics, Plasmadynamics, and Lasers Conference; July 6-9, 1993;Orlando, FL, U.S.A.

[24] Boussinesq J. Essai sur la théorie des eaux courantes. lmpr. nationale; 1877.

[25] Achenbach E. Distribution of local pressure and skin friction around a circular cylinder in cross-flow up to Re =5 ×10⁶. J Fluid Mech. 1968;34(4):625-639.

[26] Fage A, Falkner VM. Further experiments on the flow around a circular cylinder (Report No.1369). HM Stationery Office. 1931.

[27] Giedt WH. Effect of turbulence level of incident air stream on local heat transfer and skin friction on a cylinder. J Aeronaut Sci. 1951;18(11):725-730.

[28] Haase W, Braza M, Revell A. DESider–a European effort on hybrid RANSLES modelling: results of the European-Union Funded Project. Spring Science & Business Media; 2009.

RIGHTS & PERMISSIONS

2024 The Authors. International Journal of Mechanical System Dynamics published by John Wiley & Sons Australia, Ltd on behalf of Nanjing University of Science and Technology.