Numerical Prediction of Pitch Damping Stability Derivatives for Finned Projectiles

Abstract

The pitch damping dynamic stability derivatives were predicted for two basic finned projectiles using two distinct numerical techniques, namely, the transient planar pitching method and the steady lunar coning method. The dependence of these methods on various aerodynamic and numerical modeling parameters is presented. The accuracy of these methods is also compared to free-flight experimental data for Mach numbers in the range 0.5-4.5. Both numerical methods yielded comparable results, except for some transonic cases for one of the projectiles. Both methods provided poor comparisons with experimental data in the subsonic and low transonic regimes. However, the planar pitching method generally provided a better match with experiment than the coning method across the Mach number range. Nomenclature & Abbreviations ,= arbitrary force, moment = arbitrary force or moment coefficient = pitch damping force coefficient sum or PDF = pitch damping moment coefficient sum or PDM = pitching moment coefficient = pitching moment coefficient at zero angle of attack = pitching moment slope coefficient = pitching moment coefficient at zero angle of attack during planar pitching-up motion = pitching moment coefficient at zero angle of attack during planar pitching-down motion = normal force coefficient at zero angle of attack during planar pitching-up motion = normal force coefficient at zero angle of attack during planar pitching-down motion = side moment coefficient = side moment slope coefficient due to coning motion = Magnus moment coefficient due to coning motion = side force coefficient = side force slope coefficient due to coning motion = Magnus force coefficient due to coning motion = axial force at zero angle of attack = normal force slope coefficient = angle of attack/coning angle, rad or deg = mean angle of attack during planar pitching motion, rad or deg = time rate of change of angle of attack, rad/s = time rate of change pitch or pitch rate, rad/s = pitching amplitude, rad or deg 1 Aerospace Engineer, WMRD Flight Sciences Branch, vishal.a.bhagwandin.civ@mail.mil, AIAA Member. 2 Aerospace Engineer, WMRD Flight Sciences Branch, jubaraj.sahu.civ@mail.mil, AIAA Fellow. 2 = angular frequency of forced sinusoidal motion for planar pitching = pitching frequency, Hz = non-dimensional/reduced pitching frequency = time, s = period of pitch/roll cycle, s = transient global/physical timestep, s = global iterations per pitch cycle i = no. of inner iterations per global iteration = sine of angle of attack = cosine of angle of attack = angular coning/roll rate, rad/s = non-dimensional coning/roll rate M = freestream Mach number = freestream velocity, m/s D = projectile base diameter = 1 caliber, m = reference surface area = , m 2 = freestream density P S = static pressure T S = static temperature y+ = non-dimensional wall distance k = turbulent kinetic energy ε = turbulent dissipation rate aoa = angle of attack cal = caliber w.r.t. = with respect to ANF = Army-Navy Finner AFF = Air Force Finner CFD = computational fluid dynamics RAN...

Computational Investigation of Pitch Damping on Missile Geometries at High Angles of Attack

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“…[10][11][12][13][14]16 In this approach the geometry is forced to undergo a specified sinusoidal motion around the angle of attack of interest. The equations of motion for the forced oscillations are given in Eqns.…”

“…Owing to these uncertainties, correlating computational fluid dynamics (CFD) methods against these databases can be a daunting task. While several researchers have shown capability to estimate pitch damping values at low (< 10°) angles of attack, [5][6][7][8][9][10] to the authors' knowledge there has been little investigation into pitch damping values at very high angles of attack.…”

Computational Analysis of a Spinning Fin-Stabilized Projectile

“…11,12,13,14,15 In the current effort, the total normal force and pitching moment are assumed to have the functional dependence consistent with a linear force and moment expansion. When simplified for the case of planar pitching motion (i.e.…”

Numerical Prediction of Roll Damping and Magnus Dynamic Derivatives for Finned Projectiles at Angle of Attack

“…Current advances in the maneuverability of projectiles necessitate accurate dynamic stability predictions at high angles of attack. Most experimental 1-6 and numerical [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] studies have successfully demonstrated the ability to obtain the dynamic stability derivatives at zero angle of attack for a range of projectiles and flight conditions. This study seeks to extend current advanced numerical techniques to predict dynamic stability derivatives, in particular the roll damping and Magnus derivatives, at angles of attack up to 90° for fin-stabilized projectiles.…”