Study for dynamically unstable motion of reentry capsule

Abe, Takashi; Sato, Syunichi; Matsukawa, Yutaka; Yamamoto, Kazuhiro; Hiraoka, Katsumi

doi:10.2514/6.2000-2589

Cited by 12 publications

(24 citation statements)

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“…This behavior was noted in the investigations of the hysteresis effects on dynamic stability by Beam and Hedstrom [3]. Figure 3 displays both experimental (extracted from rear pressure measurements) and computational data for the MUSES-C capsule from Abe [5] and computational data generated with the CFD tool LAURA for the Mars Exploration Rover (MER) and Viking configurations by Schoenenberger [7]. These data sets show the angle-of-attack dependence of the aftbody pitching moment.…”

Section: B Time-lagged Aftbody Pitching Moment Model 1 Form Of the mentioning

confidence: 87%

“…In the past decade, work has been conducted to investigate the possible means by which flow structures surrounding the blunt body can manifest into unsteady aftbody moments and, subsequently, oscillation divergence. Studies by Teramoto et al [4], Abe et al [5], and Schoenenberger [7] have shed light on and given credibility to this theory.…”

Section: Introductionmentioning

confidence: 91%

“…As in the studies of Abe et al [5] and Schoenenberger [7], the approach is based on separating the forebody and aftbody contributions to the total pitching moment of the body:…”

Section: B Time-lagged Aftbody Pitching Moment Model 1 Form Of the mentioning

confidence: 99%

“…1). Hysteresis in the pitching moment results in a net input of work to the system over each cycle and this influx of energy may be responsible for dynamic instabilities [3,5].…”

Section: Pitching Moment Hysteresis Of a Blunt Bodymentioning

confidence: 99%

“…Throughout the experimental history of dynamic stability investigations, it has been observed that the pitching moment often tends to exhibit a dependence on the direction of the pitching motion [3][4][5][6]. This hysteresis has been attributed to a phase lag between the forebody and aftbody pressure fields (and therefore, their corresponding contributions to the pitching moment).…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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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Section: B Time-lagged Aftbody Pitching Moment Model 1 Form Of the mentioning

confidence: 87%

Section: Introductionmentioning

confidence: 91%

“…As in the studies of Abe et al [5] and Schoenenberger [7], the approach is based on separating the forebody and aftbody contributions to the total pitching moment of the body:…”

Section: B Time-lagged Aftbody Pitching Moment Model 1 Form Of the mentioning

confidence: 99%

“…1). Hysteresis in the pitching moment results in a net input of work to the system over each cycle and this influx of energy may be responsible for dynamic instabilities [3,5].…”

Section: Pitching Moment Hysteresis Of a Blunt Bodymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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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Investigation of the dynamic stability of a capsule in multidisciplinary methods

Liu

Zhao

2012

Proceedings of the Institution of Mechanical Engineers, Part G:

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A preliminary exploration on active control methods of an unsteady reentry capsule with multi-disciplinary research methods, including computational fluid dynamics, flight mechanics and control technology, was implemented. The active control process of the dynamic instability of the capsule was studied with a simplified two-jet attitude control system. The effects of different control methods were analyzed and compared. With the pole placement method, the state of the capsule could transfer from the limit cycle vibration to the trim state by selecting appropriate control parameters corresponding to the different control efficiencies. The time of the capsule changing the limit cycle vibration and reaching a trim state, the deviation between the pitch angle and the equilibrium position and the maximum total pressure of the jet changed with different control parameters.

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Dynamic instability modeling on phase plane for thin aeroshell capsule with pitching motion at transonic speed

TAKASAWA,

FUJII,

HIRATA

et al. 2024

Mechanical Engineering Journal

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For sample return missions from deep space, a thin aeroshell capsule was proposed aimed at mitigating the aerodynamic heating during its reentry into the earth's atmosphere. The functional requirements of the capsule mandate that it aerodynamically decelerate sufficiently and land in the appropriate attitude without a parachute. To evaluate its motion attitude during transonic conditions in a wind tunnel, we employed the 1-degree of freedom (1-DOF) oscillation method. Furthermore, to predict its motion during an actual flight based on the wind tunnel test results, we examined the impact of the moment of inertia (MOI) on the motion. In all the MOI cases investigated, the limit cycle oscillation (LCO) was observed with a constant amplitude of angle. The variations in the MOI resulted in differences in the amplitude of the angle and time to reach the LCO. This study focused on the growth phase until the LCO and evaluated the characteristics on the phase plane. Consequently, a gradual approach to acceleration attributed to the static moment was observed in the growth history. A new modeling approach, centered on the nullcline during the growth phase, was adopted. Here, an approximation using a third-order function of angular velocity was applied to reproduce the nullcline obtained from the experiment. Upon non-dimensionalization of this model equation using the motion period, it was confirmed that the non-dimensional parameters were affected by the motion period, while this model focused solely on the growth phase. Furthermore, upon parameter tuning to replicate the amplitude of the angle and time to reach the LCO, and using these parameters, we predicted the impact of the MOI. The predicted results qualitatively reproduced larger MOI leading to larger amplitudes of angle and longer times to reach the LCO, which was consistent with the experimental results.

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Study for dynamically unstable motion of reentry capsule

Cited by 12 publications

References 0 publications

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

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

Investigation of the dynamic stability of a capsule in multidisciplinary methods

Dynamic instability modeling on phase plane for thin aeroshell capsule with pitching motion at transonic speed

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