Navier-Stokes predictions of the individual components of the pitch-damping coefficient sum

Weinacht, Paul

doi:10.2514/6.1995-3458

Cited by 10 publications

(3 citation statements)

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“…Applying the chain rule of calculus and reformulating the integration variable in Eqn. (8) to time results in Eqn. (9).…”

Section: Forced Oscillation Approachmentioning

confidence: 97%

“…(5) into Eqn. (8). Applying the chain rule of calculus and reformulating the integration variable in Eqn.…”

Section: Forced Oscillation Approachmentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

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

McGowan

Kurzen

Nance

et al. 2012

30th AIAA Applied Aerodynamics Conference

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The capability of accurately estimating pitch damping values for missile-like geometries over a range of Mach numbers and at high angles of attack using state-of-the-art CFD techniques has been investigated. Toward this effort three geometries were examined: the Army-Navy Finner model, the extended Army-Navy Finner model, and the M823 research store. Pitch damping values are predicted using forced oscillation calculations performed with the RavenCFD Navier-Stokes flow solver. Additionally, pitch decay calculations and aerodynamic build-up methods are also employed using the RavenCFD solver. These methods are compared to both experimental results and AP09, a fast-running engineering tool. Pitch damping variations due to geometric changes, Mach number changes, and angle of attack changes are explored with each method. Overall, each CFD method exhibits an outstanding agreement with experiment and range data at the lower angles of attack. Both pitch decay and forced oscillation approaches provide good agreement for low-to-moderate angles. At angles of attack greater than 30 degrees, the forced oscillation approach provides the best agreement. Pitch damping variations at angles higher than 60-70 degrees for the Army-Navy Finner have been shown to be a peripheral effect of the extreme unsteadiness of the wake flow at these conditions. NomenclatureA = amplitude of oscillation k = reduced frequency c = chord C m = pitching moment coefficient ̇ = pitch damping sum = normal force coefficient = normal force curve slope d ref = reference length (typically missile diameter) FOA = Forced Oscillation Approach yy I = moment of inertia about the pitch axis k = reduced frequency, M = Mach number ncyc = number of points per cycle PD = Pitch Decay Approach 2 q = dynamic pressure, = reference area tp = time for given peak (used in pitch decay) t = time U ∞ = freestream velocity w = aerodynamic load = x-location of the i th missile panel (used in build-up approaches) xcg = x-location of the center of gravity xcp = x-location of the model center of pressure α = angle of attack α m = mean angle of attack α o = angle of attack amplitude α p = peak pitch angle (used in pitch decay) t = time step = width of the i th missile panel (used in build-up approaches)  = ratio of specific heats  = density  = angular frequency

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“…Applying the chain rule of calculus and reformulating the integration variable in Eqn. (8) to time results in Eqn. (9).…”

Section: Forced Oscillation Approachmentioning

confidence: 97%

“…(5) into Eqn. (8). Applying the chain rule of calculus and reformulating the integration variable in Eqn.…”

Section: Forced Oscillation Approachmentioning

confidence: 99%