J. Godelle, C. Letellier, G. Gouesbet, J. N. Le Toulouzan, G. Gréhan, C. Dumouchel, S. Leroux, J. B. Blaisot & M. Ledoux
Use of the theory of nonlinear dynamical systems to study the growth of perturbations in an excited water jet,
International Journal of Fluid Mechanics Research, 24 (1-3), 189-197, 1997.
An excited cylindrical water jet is studied by using a laser beam technique for jet shape characterizations. A laser sheet is scattered by a jet allowing to record highly-sampled time series to track the evolution of the jet diameter. With such a technique, the perturbation growth of an excited water jet is investigated from the needle to break-up. Time series are analyzed with tools borrowed to the theory of nonlinear dynamical systems. We then show that the growth of modes close to those predicted by the Rayleigh theory arises when the perturbations due to the exciting system have vanished.
B. Maheu, C. Letellier & B. Cheron
Nitrogen low pressure arc fluctuations,
High Temperature Material Processes, 1, 191-204, 1997. Online
A supersonic low pressure nitrogen plasma jet is studied by using tools from nonlinear dynamical systems theory like phase portraits. More conventional tools like Fourier spectra or time correlation coefficients are also used. We find (i) a low frequency evolution (due to the generator) in the electrodes potentials as well as in the intensity of nitrogen emission and (ii) high frequency fluctuations of electrodes potentials. Moreover, we show that the erosion of the anode affects the dynamics underlying the plasma jet and reduces the degrees of freedom of the system.
C. Letellier, L. Le Sceller, G. Gouesbet, F. Lusseyran, A. Kemoun & B. Izrar
Recovering deterministic behavior from experimental time series in a standard mixing reactor,
AIChE Journal, 43 (9), 2194-2202, 1997.
The velocity field in a standard mixing reactor with a Rushton impeller is analyzed by using techniques from the theory of nonlinear dynamical systems. It is shown that the dynamical behavior contains a quasi-periodic motion with three frequencies, fp, the frequency associated with the rotation of blades, fp/6, and a third frequency f’. Relying on an evaluation of the correlation dimension equal to 3.9, the phase space is likely to be at least four-dimensional. Moreover, a set of four ordinary differential equations is indeed automatically obtained by using a global vector field reconstruction technique, confirming the existence of a 4D-deterministic behavior contributing to the dynamics of the system.
C. Letellier, E. Ringuet, B. Maheu, J. Maquet & G. Gouesbet
Global vector field reconstruction of chaotic attractors from one unstable periodic orbit,
Entropie, 202/203, 147-153, 1997.
Abstract: All the information necessary to build a chaotic attractor may be retrieved from the knowledge of a single unstable periodic orbit. This statement is illustrated by achieving a global vector field reconstruction of the Rössler system from a period-1 orbit. Similarly, it is shown that an intermittent behaviour may be reconstructed by only knowing the laminar phases.
C. Letellier, S. Meunier-Guttin-Cluzel, G. Gouesbet, F. Neveu, T. Duverger & B. Cousyn,
Use of the nonlinear dynamical system theory to study cycle-to-cycle variations from spark ignition engine pressure data
SAE Technical Paper Series, 971640.
Abstract: Cycle-to-cycle variations in the pressure evolution within the cylinder of a spark ignition engine has long been recognized as a phenomenon of considerable importance. In this work, use of tools borrowed to the nonlinear dynamical system theory to investigate the time evolution of the cylinder pressure is explored. By computing a divergence rate between different pressure cycles versus crank angle, four phases during the combustion cycle are exhibited. These four phases may be identified with the four common phases evidenced by burn rate calculations. Starting from phase portraits and using Poincaré sections, we also study correlations between peak pressures, IMEP and the durations from ignition to appearance of a flame kernel. Accounting for the fact that, during the ignition phase of the combustion cycle, trajectories in a plane projection of the reconstructed phase portrait associated with cycles in the case of motored engine cannot be distinguished from trajectories corresponding to combustion cycles, we estimate the duration of the ignition phase without any prior assumption on the combustion processes. Fluctuations of ignition phase lengths have been found to be correlated with IMEP standard deviations.