Estimation of the probability of two consecutive passages through resonance during the descent of an asymmetric rigid body in a rarefied atmosphere

A two-frequency nonlinear system of ordinary differential equations is considered. This system describes the perturbed motion of a rigid body with considerable asymmetry in a rarefied atmosphere. It is known that when the frequencies of this system of equations coincide, the phenomena of capture or passage through the principal resonance, which have a random nature, are possible. In this case, the probability of a passage through the resonance is calculated from the initial conditions on the separatrix. The objective of this study is to obtain an expression for estimating the probability of two consecutive passages through the resonance regions during the descent in the rarefied atmosphere of Mars of a rigid body with significant geometric and aerodynamic asymmetry.

Dependence of the amplitude of transverse oscillations of the axisymmetric UAV rotating around the longitudinal axis on the residual imbalance

The analysis of the relationship between residual imbalance of an axisymmetric cylindrical UAV, and the amplitude of its prevailing transverse oscillations during the flight. The residual imbalance of an UAV that rotates along the roll and its effect on the amplitude of the vehicle`s transverse oscillations in real flight are discussed and investigated. The total imbalance and the average imbalance of UAV were calculated on the basis of dynamic imbalance measurements in two planes. Flight data from twelve UAV launches was obtained for this dependence analysis. During angular velocity sensors signals processing an orientation algorithm with one quaternion equation was applied. Eiler-Krylov angles were obtained from the resulting orientation quaternion and an average and total imbalance influence on transverse oscillations amplitude was investigated. During the analysis of the tests held, it is possible to make a conclusion that transverse oscillations amplitude directly depends on the magnitude of residual imbalance. Transverse oscillations amplitude mostly depends on average imbalance (which is arithmetic average between imbalance magnitudes in every plane of measurement) and it depends less on total imbalance (which is geometric sum of imbalance vectors in every plane of measurement): average imbalance change from 100 g∙mm to 700 g∙mm caused transverse oscillations amplitude change from 0,5° to 2°. In some cases we will see spread of oscillations amplitude values up to ±1° relatively approximation line, this is due to other factors influence, besides imbalance, such as aerodynamic asymmetry. However, the tendency of oscillations amplitude increase with the increase of imbalance is preserved. The obtained results give us an explicit dependence of transverse oscillations amplitude of UAV from its dynamic imbalance in specific conditions of flight (velocity, type of trajectory and rotation velocity) and with specific UAV parameters (aerodynamic, mass-inertial and other parameters). Change of these parameters may cause change of specific quantitative parameters of obtained dependence, but its nature remains the same. The mass of the investigated UAV was approximately 15 kg, trajectory was ballistic, flight speed was transonic and subsonic, rotation velocity around longitudinal axis was 1..7 rounds per second.

Effects of Asymmetric Gas Distribution on the Instability of a Plane Power-Law Liquid Jet

As a kind of non-Newtonian fluid with special rheological features, the study of the breakup of power-law liquid jets has drawn more interest due to its extensive engineering applications. This paper investigated the effect of gas media confinement and asymmetry on the instability of power-law plane jets by linear instability analysis. The gas asymmetric conditions mainly result from unequal gas media thickness and aerodynamic forces on both sides of a liquid jet. The results show a limited gas space will strengthen the interaction between gas and liquid and destabilize the power-law liquid jet. Power-law fluid is easier to disintegrate into droplets in asymmetric gas medium than that in the symmetric case. The aerodynamic asymmetry destabilizes para-sinuous mode, whereas stabilizes para-varicose mode. For a large Weber number, the aerodynamic asymmetry plays a more significant role on jet instability compared with boundary asymmetry. The para-sinuous mode is always responsible for the jet breakup in the asymmetric gas media. With a larger gas density or higher liquid velocity, the aerodynamic asymmetry could dramatically promote liquid disintegration. Finally, the influence of two asymmetry distributions on the unstable range was analyzed and the critical curves were obtained to distinguish unstable regimes and stable regimes.

Aerodynamic Asymmetry Analysis of Unsteady Flows in Turbomachinery

A nonlinear harmonic balance technique for the analysis of aerodynamic asymmetry of unsteady flows in turbomachinery is presented. The present method uses a mixed time-domain/frequency-domain approach that allows one to compute the unsteady aerodynamic response of turbomachinery blades to self-excited vibrations. Traditionally, researchers have investigated the unsteady response of a blade row with the assumption that all the blades in the row are identical. With this assumption the entire wheel can be modeled using complex periodic boundary conditions and a computational grid spanning a single blade passage. In this study, the steady/unsteady aerodynamic asymmetry is modeled using multiple passages. Specifically, the method has been applied to aerodynamically asymmetric flutter problems for a rotor with a symmetry group of 2. The effect of geometric asymmetries on the unsteady aerodynamic response of a blade row is illustrated. For the cases investigated in this paper, the change in the diagonal terms (blade on itself) dominated the change in stability. Very little mode coupling effect caused by the off-diagonal terms was found.

The Effects of Aerodynamic Asymmetric Perturbations on Forced Response of Bladed Disks

Most of the existing mistuning research assumes that the aerodynamic forces on each of the blades are identical except for an interblade phase angle shift. In reality, blades also undergo asymmetric steady and unsteady aerodynamic forces due to manufacturing variations, blending, mis-staggered, or in-service wear or damage, which cause aerodynamically asymmetric systems. This paper presents the results of sensitivity studies on forced response due to aerodynamic asymmetry perturbations. The focus is only on the asymmetries due to blade motions. Hence, no asymmetric forcing functions are considered. Aerodynamic coupling due to blade motions in the equation of motion is represented using the single family of modes approach. The unsteady aerodynamic forces are computed using computational fluid dynamics (CFD) methods assuming aerodynamic symmetry. Then, the aerodynamic asymmetry is applied by perturbing the influence coefficient matrix in the physical coordinates such that the matrix is no longer circulant. Therefore, the resulting aerodynamic modal forces in the traveling wave coordinates become a full matrix. These aerodynamic perturbations influence both stiffness and damping while traditional frequency mistuning analysis only perturbs the stiffness. It was found that maximum blade amplitudes are significantly influenced by the perturbation of the imaginary part (damping) of unsteady aerodynamic modal forces. This is contrary to blade frequency mistuning where the stiffness perturbation dominates.

Aerodynamic Asymmetry Analysis of Unsteady Flows in Turbomachinery

A nonlinear harmonic balance technique for the analysis of aerodynamic asymmetry of unsteady flows in turbomachinery is presented. The present method uses a mixed time-domain/frequency-domain approach that allows one to compute the unsteady aerodynamic response of turbomachinery blades to self-excited vibrations. Traditionally, researchers have investigated the unsteady response of a blade row with the assumption that all the blades in the row are identical. With this assumption the entire wheel can be modeled using complex periodic boundary conditions and a computational grid spanning a single blade passage. In this study, the steady/unsteady aerodynamic asymmetry is modeled using multiple passages. Specifically, the method has been applied to aerodynamically asymmetric flutter problems for a rotor with a symmetry group of two. The effect of geometric asymmetries on the unsteady aerodynamic response of a blade row is illustrated. For the cases investigated in this paper, the change in the diagonal terms (blade on itself) dominated the change in stability. Very little mode coupling effect caused by the off-diagonal terms was found.

The Effects of Aerodynamic Asymmetric Perturbations on Forced Response of Bladed Disks

Most of the existing mistuning research assumes that the aerodynamic forces on each of the blades are identical except for an interblade phase angle shift. In reality, blades also undergo asymmetric steady and unsteady aerodynamic forces due to manufacturing variations, blending, mis-staggered blades or in-service wear or damage, which cause aerodynamically asymmetric systems. This paper presents the results of sensitivity studies on forced response due to aerodynamic asymmetry perturbations. The focus is only on the asymmetries due to blade motions. Hence, no asymmetric forcing functions are considered. Aerodynamic coupling due to blade motions in the equation of motion is represented using the single family of modes approach. The unsteady aerodynamic forces are computed using CFD methods assuming aerodynamic symmetry. Then, the aerodynamic asymmetry is applied by perturbing the influence coefficient matrix in the physical coordinates such that the matrix is no longer circulant. Therefore, the resulting aerodynamic modal forces in the traveling wave coordinates become a full matrix. These aerodynamic perturbations influence both stiffness and damping while traditional frequency mistuning analysis only perturbs the stiffness. It was found that maximum blade amplitudes are significantly influenced by the perturbation of the imaginary part (damping) of unsteady aerodynamic modal forces. This is contrary to blade frequency mistuning where the stiffness perturbation dominates.