Dynamic stability analysis of bodies of revolution in supersonic flow.

Abstract

A linearized characteristics method is presented for the dynamic stability analysis of bodies of revolution in supersonic flow. Using body-fixed coordinates, the first-order unsteady potential equation is solved by extending previous work by Sauer and Heinz and Erdmann and Oswatitsch to supersonic flow past slowly oscillating bodies of revolution. A simple numerical procedure is obtained which allows the analysis of pointed-nose bodies of arbitrary meridian profile including slope discontinuities (cone-cylinder bodies). Results are presented for the damping coefficient CM Q + dtfa for various body configurations as a function of Mach number and axis location. The range of validity of this approach is examined by comparison with other theoretical methods and experimental results. Nom enclature= normal force coefficient due to angular velocity C N6t = normal force coefficient due to time rate of change of angle of attack E (x, r] = complementary solution, Eq. (9) G(x, r} = zero angle-of-attack potential K(x, r) = angle-of-attack potential M = Mach number R(x\R'(x) = body radius and slope, respectively t = time u, v, w = velocity components in x, r, 6 directions, Eqs.(2) Xj r, 0 = cylindrical coordinates x g = center of oscillation a.= angle of attack 0 = (M 2 -1) 1/2 e = thickness ratio 7 = ratio of specific heats d = amplitude of oscillation $ 0 = cone semi-apex angle £, ?7 = characteristic coordinates £l(x, r, d, t) = velocity potential \(x, r) = out-of -phase potential 3?(x, r, 6, t) = perturbation potential

Oscillation of Supersonic Inflatable Aerodynamic Decelerators at Mars

“…23 Note that this rigid-body analysis does not capture the SIADaeroshell flex-interaction mode. Others have had success computing pitch-damping coefficients of slender and blunt entry vehicle configurations using code-level modifications to three-dimensional Navier-Stokes solvers 24 or linearized characteristics methods 25 . Despite the progress in computational methods for predicting pitch damping, the American Mars entry vehicle missions have all used experimental data collected from the Viking 26 , MER 18 , and MSL 7 entry vehicle aerodynamic test programs to populate their dynamic stability databases.…”