Chaotic Behavior of the Biharmonic Dynamics System
Motion of a biharmonic system under action of small periodic force and small damped force is studied. The biharmonic oscillator is a physical system acting under a biharmonic force like . The article contains biharmonic oscillator analysis, phase space research, and analytic solutions for separatrixes. The biharmonic oscillator performs chaotic motion near separatrixes under small perturbations. Melnikov method gives analytical criterion for heteroclinic chaos in terms of system parameters. A transition from chaotic to regular motion of the biharmonic oscillator was found as the heteroclinic chaos can be removed by increasing the coefficient of a damping force. The analytical results obtained using Melnikov method have been confirmed by a good match with numeric research.
Dynamic stability of the HUYGENS probe at Mach 2.5
Abstract Atmospheric re-entry is a critical phase for space vehicles. Dynamic stability issues play a crucial role for the success of their mission. In the context of the HUYGENS probe entry into Titan's atmosphere, dynamic wind tunnel tests were achieved to address its behaviour. The probe is placed at an initial angle of attack of 4° in the wind tunnel and its spontaneous movement towards a possible equilibrium angle is measured. The unsteady flow simulations presented below intend to obtain a reliable prediction of dynamic stability for future re-entry vehicles. The FLUSEPA code was used to perform these numerical simulations. At first, an inviscid flow simulation has been performed at a Mach number of M = 2.5 , where the amplitude of the oscillations decreases although the probe should be dynamically stable. The frequency of the experimentally obtained oscillations is well predicted, however no damping has been found. So, the simulation was improved by the modelling of the turbulent effects. It enabled a proper prediction of the damping. Finally, the influence of the wind tunnel sting on the probe stability was numerically investigated. These results emphasize the importance of viscosity and turbulence effects for the prediction of dynamic stability or more generally for wake flows.
A two-equation turbulence model for compressible reacting flows
A two-equation turbulence model (k-epsilon) has been modified to model compressible reacting flows. A compressibility correction model based on modeling the dilatational terms in the Reynolds stress equations has been used. Computations are carried out using the Navier-Stokes solver SPARK which includes a finite rate chemistry model for hydrogen-air combustion. Initially, planar compressible mixing layers are simulated. Comparisons of the predictions with available experimental data and the predictions of a compressible Reynolds stress closure indicate that the model is well suited for the study of such flows. The decrease in the growth rate of the mixing layer with increasing convective Mach number is well predicted. The model is then tested on a three-dimensional supersonic flow problem where solid boundaries are present. An axisymmetric nonreacting mixing layer flow involving dissimilar gases is evaluated next using the model and the predictions are compared with available experimental data. Finally, two reacting turbulent flow configurations have been studied and comparison of predictions and experimental data has been done. The comparisons indicate that the model predicts the overall features of the test cases very well.