Low-Speed Aerodynamics of a Planetary Entry Capsule

Wang, Frank Y.; Karatekin, Özgür; Charbonnier, Jean-Marc

doi:10.2514/2.3498

Cited by 9 publications

(7 citation statements)

References 11 publications

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“…This result is con rmed by the simulations (see Figs. [12][13][14][15]. The results also show that, although the two subsystems are coupled in terms of frequency response, the motion of the parachute is generally limited in amplitude and highly damped.…”

Section: Analysis Of the Resultsmentioning

confidence: 82%

Validation of a Simulation Model for a Planetary Entry Capsule

Guglieri

Quagliotti

2003

Journal of Aircraft

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Subsonic static and oscillatory aerodynamic coef cients were measured at Politecnico di Torino for a planetary entry capsule model. The experimental data set was included in a mathematical model of payload-decelerator system, and the results of simulations were compared with ight-test data. The frequency-domain attitude response of the capsule was reproduced during the main parachutes' deployment, and discrepancies for the drogue opening phase were observed. The impact on simulations of atmospheric turbulence and asymmetries in the parachute suspension system was also considered. The results suggest that several factors may affect the delity of simulations such as correct modeling of suspension system geometry and exibility, parachute aerodynamics, accuracy of payload inertial data, and accurate matching of real ight external perturbations. The effect of some design parameters on capsule attitude dynamics was evaluated. The arti cial increase of capsule damping coef cients produced observable effects on attitude time histories for large perturbations of the aerodynamic derivatives only. The dynamic stability of the system is reduced for large increase of riser length and parachute added mass. Nomenclaturereference length (capsule diameter) F = elastic force I ay = added moment of inertia of the parachute I x ; I y ; I z ; I x z = mass moments of inertia K = elastic constant L = rolling moment L b = additional rolling moment due to bridles l = length M = pitching moment m = mass m ax ; m ay = axial and transverse added masses of the parachute N = yawing moment N b = additional yawing moment due to bridles p; q; r = angular rates (capsule) q 1 = dynamic pressure, ½V 2 =2 Re = Reynolds number, based on capsule diameter d S = reference area, ¼ d 2 =4 S P = parachute reference area s; y; h = Earth-xed axes [T BV ] = rotation matrix from s; y; h to x B ; y B ; z B ; f .Á; µ; Ã ) [T P V ] = rotation matrix from s; y; h to x P ; y P ; z P ; f .Á P ; µ P ; Ã P ) degli Abruzzi 24; quagliotti@polito.it.Senior Member AIAA.auxiliary body-xed longitudinal axes (origin at capsule theoretical apex) x B ; y B ; z B = body-xed axes (origin at capsule c.g.) x P ; y P ; z P = body-xed axes (origin at parachute c.g.) Y = lateral force Z = normal force ®;¯= angle of attack and sideslip (capsule) 1l = length increment ² = strain, 1l=l ¾ = total angle of attack (capsule) N ¾ = measurement accuracy of wind-tunnel data ¿; Â = angular displacement of the riser with respect to s; y; h (see Fig. 1) Á; µ ; Ã = Euler angles Á a = aerodynamic roll angle (capsule) Subscripts b = bridle CG = center of gravity (capsule) CP = center of gravity (parachute) g = gust P = parachute PA = parachute attach point P2 = point of con uence of riser and suspension lines r = riser s = suspension line 0 = reference condition 1, 2, 3 = vector components

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Section: Analysis Of the Resultsmentioning

confidence: 82%

Validation of a Simulation Model for a Planetary Entry Capsule

Guglieri

Quagliotti

2003

Journal of Aircraft

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“…This time-lag factor is akin to the reduced frequency parameter defined in many studies of dynamic stability [8,17,18], but the value of τ scales this parameter to account for variations in the length scale or the characteristic velocity. The hysteresis of the pitching motion and the subsequent oscillation growth of the vehicle are dependent on the factor τ, and its influence is discussed in following sections.…”

Section: Time Lagmentioning

confidence: 99%

“…2)[4]. Wang et al suggested a similar connection between the oscillation of a body and the motion of the rear stagnation point[8].…”

mentioning

confidence: 95%

Dynamic Stability Analysis of Blunt-Body Entry Vehicles Using Time-Lagged Aftbody Pitching Moments

Kazemba

Braun

Schoenenberger

et al. 2015

Journal of Spacecraft and Rockets

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This analysis defines an analytic model for the pitching motion of blunt bodies during atmospheric entry. The proposed model is independent of the pitch-damping sum coefficient present in the standard formulation of the equations of motion describing pitch oscillations of a decelerating blunt body, instead using the principle of a time-lagged aftbody moment as the forcing function for oscillation divergence. It is shown that the dynamic oscillation responses typical to blunt bodies can be produced using hysteresis of the aftbody moment in place of the pitch-damping coefficient. Four parameters, all with intuitive physical relevance, are introduced to fully define the aftbody moment and the associated time delay. The approach used in this investigation is shown to be useful in understanding the governing physical mechanisms for blunt-body dynamic stability and in guiding vehicle and mission design requirements. A validation case study using simulated ballistic range test data is conducted. From this, parameter identification is carried out through the use of a least-squares optimizing routine. Results show good agreement with the limited existing literature for the parameters identified, suggesting that the model proposed could be validated by a limited experimental ballistic range test series or with existing data. The trajectories produced by the identified parameters are found to match closely those from the Mars Exploration Rover ballistic range tests for a range of initial conditions. Nomenclature A = Euler-Cauchy angle-of-attack coefficientaerodynamic pitching moment slope coefficient d = aerodynamic reference diameter, m g = acceleration due to gravity, m∕s 2 h = altitude, m I yy = pitch axis mass moment of inertia, kg · m 2 l = characteristic length, m M = Mach number m = mass, kg N = number of simulated ballistic range shots R p = planet radius, m S = cross-sectional area, m 2 t = time, s t lag = lag time, s t − = time referenced by aftbody, s V = vehicle velocity, m∕s v = characteristic velocity, m∕s x c:g: = axial location of center of gravity α = angle of attack, rad β = parameter of aftbody moment Mach number dependence γ = flight-path angle, rad δ = phase-shift constant, rad ε = residual θ = pitch angle, rad μ = Euler-Cauchy oscillation growth exponent ν = Euler-Cauchy frequency coefficient ρ = atmospheric density, kg∕m 3 τ = lag time factor Subscripts eq = equivalent 0 = initial quantity ∞ = freestream Superscripts AB = aftbody contribution FB = forebody contribution * = reference value for aftbody moment curve

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“…Wang et al [59]- [61] studied the spectral characteristics of the flow structure at various locations around an Apollo capsule at low speed. Of particular interest were the oscillations of the rear stagnation point because of their possible influence on unsteady loads acting on the aftbody of the vehicle.…”

Section: Strouhal Number (Reduced Frequency Parameter)mentioning

confidence: 99%

Survey of Blunt Body Dynamic Stability in Supersonic Flow

Kazemba

Braun

Clark

et al. 2012

AIAA Atmospheric Flight Mechanics Conference

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This survey presents a comprehensive investigation of blunt body dynamic stability. An examination of the experimental, analytical, and computational methods for predicting dynamic stability characteristics, along with the deficiencies accompanying each method is presented. The observed influence of vehicle and environmental parameters on the resulting dynamic response is discussed. Additionally, the proposed physical mechanisms that may govern this complex phenomenon are introduced. There exists a vast amount of literature and test data that is continually growing with each mission. Compiling the observations of dynamic behavior acquired from various test geometries, environments, and techniques, as well as the proposed explanations to the observed trends, sheds light on the validity of the proposed physical mechanisms. This in turn guides future efforts to improve the experimental and computational prediction techniques and further the fundamental understanding of blunt body dynamic stability. NomenclatureA = Aerodynamic reference area, m 2 C D = Drag coefficient C L = Lift coefficient = Lift-curve slope = Pitching moment coefficient = Pitching moment slope = Pitch damping coefficient ̇ = Pitch damping sum CG = Center of gravity D = Reference diameter, m DOF = Degrees of freedom f = Oscillation frequency, Hz g = Acceleration due to gravity, m/s 2 h = Altitude, m I = Moment of inertia, kg-m 2 k = Reduced frequency parameter l = Characteristic length, m m = Mass, kg R = Radius from center of planet, m Sr, St = Strouhal number t = Time, s V = Velocity, m/s Greek α = Angle of attack, rad γ = Flight path angle, rad θ = Pitch angle, rad ξ = Dynamic stability parameter ρ = Atmospheric density, kg/m 3 ω = Angular velocity, rad/s Subscripts = Freestream condition

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Low-Speed Aerodynamics of a Planetary Entry Capsule

Cited by 9 publications

References 11 publications

Validation of a Simulation Model for a Planetary Entry Capsule

Validation of a Simulation Model for a Planetary Entry Capsule

Dynamic Stability Analysis of Blunt-Body Entry Vehicles Using Time-Lagged Aftbody Pitching Moments

Survey of Blunt Body Dynamic Stability in Supersonic Flow

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