Pankaj Wahi

Route to chaos for combustion instability in ducted laminar premixed flames

Complex thermoacoustic oscillations are observed experimentally in a simple laboratory combustor that burns lean premixed fuel-air mixture, as a result of nonlinear interaction between the acoustic field and the combustion processes. The application of nonlinear time series analysis, particularly techniques based on phase space reconstruction from acquired pressure data, reveals rich dynamical behavior and the existence of several complex states. A route to chaos for thermoacoustic instability is established experimentally for the first time. We show that, as the location of the heat source is gradually varied, self-excited periodic thermoacoustic oscillations undergo transition to chaos via the Ruelle-Takens scenario.

Bifurcation analysis of thermoacoustic instability in a horizontal Rijke tube

A bifurcation analysis of the dynamical behavior of a horizontal Rijke tube model is performed in this paper. The method of numerical continuation is used to obtain the bifurcation plots, including the amplitude of the unstable limit cycles. Bifurcation plots for the variation of nondimensional heater power, damping coefficient and the heater location are obtained for different values of time lag in the system. Subcritical bifurcation was observed for variation of parameters and regions of global stability, global instability and bistability are characterized. Linear and nonlinear stability boundaries are obtained for the simultaneous variation of two parameters of the system. The validity of the small time lag assumption in the calculation of linear stability boundary has been shown to fail at typical values of time lag of system. Accurate calculation of the linear stability boundary in systems with explicit time delay models, must therefore, not assume a small time lag assumption. Interesting dynamical behavior such as co-existing multiple attractors, quasiperiodic behavior and period doubling route to chaos have been observed in the analysis of the model. Comparison of the linear stability boundaries and bifurcation behavior from this reduced order model are shown to display trends similar to experimental data.

Bifurcations of Self-Excited Ducted Laminar Premixed Flames

Bifurcation analysis is performed on experimental data obtained from a simple setup comprising ducted laminar premixed conical flames in order to investigate the features of nonlinear thermoacoustic oscillations. It is observed that as the bifurcation parameter is varied, the system undergoes a series of bifurcations leading to characteristically different nonlinear oscillations. Through the application of nonlinear time series analysis to pressure and flame (CH * chemiluminescence) intensity time traces, these oscillations are characterized as periodic, aperiodic, or chaotic oscillations, and subsequently the nature of the obtained bifurcations is explained based on dynamical systems theory. Nonlinear interaction between the flames and the acoustic modes of the duct is clearly reflected in the high speed flame images acquired simultaneously with pressure time series.

Bifurcation and chaos in zero-Prandtl-number convection

We present a detailed bifurcation structure and associated flow patterns near the onset of zero-Prandtl-number Rayleigh-Benard convection. We employ both direct numerical simulation and a low-dimensional model ensuring qualitative agreement between the two. Various flow patterns originate from a stationary square observed at a higher Rayleigh number through a series of bifurcations starting from a pitchfork followed by a Hopf and finally a homoclinic bifurcation as the Rayleigh number is reduced to the critical value. Homoclinic chaos, intermittency, and crises are observed near the onset.

Full characterization of act-and-wait control for first-order unstable lag processes

Act-and-wait control is a special case of time-periodic control for systems with feedback delay, where the control gains are periodically switched on and off in order to stabilize otherwise unstable systems. The stability of feedback systems in the presence of time delay is a challenging problem. In this paper, we show that the act-and-wait type time-periodic control can always provide deadbeat control for first-order unstable lag processes with any (large but) fixed value of the time delay in the feedback loop. A full characterization of this act-and-wait controller with respect to the system and control parameters is given based on performance and robustness against disturbances.

Patterns and bifurcations in low–Prandtl-number Rayleigh-Bénard convection

We present a detailed bifurcation structure and associated flow patterns for low–Prandtl-number (P=0.0002, 0.002, 0.005, 0.02) Rayleigh-Benard convection near its onset. We use both direct numerical simulations and a 30-mode low-dimensional model for this study. We observe that low–Prandtl-number (low-P) convection exhibits similar patterns and chaos as zero-P convection (Pal P. et al., EPL, 87 (2009) 04003) namely squares, asymmetric squares, oscillating asymmetric squares, relaxation oscillations, and chaos. At the onset of convection, low-P convective flows have stationary 2D rolls and associated stationary and oscillatory asymmetric squares in contrast to zero-P convection where chaos appears at the onset itself. The range of Rayleigh number for which stationary 2D rolls exist decreases rapidly with decreasing Prandtl number. Our results are in qualitative agreement with results reported earlier.

A direct variational method for planning monotonically optimal paths for redundant manipulators in constrained workspaces

This paper proposes a path planner for serial manipulators with a large number of degrees of freedom, working in cluttered workspaces. Based on the variational principles, this approach involves formulating the path planning problem as constrained minimization of a functional representing the total joint movement over the complete path. We use modified boundary conditions at both ends of the trajectory to find more suitable start and end configurations. The concept of monotonic optimality is introduced in order to optimize the manipulator paths between the resulting end configurations. For obstacle avoidance, volume and proximity based penalizing schemes are developed and used. The presented planner uses a global approach to search for feasible paths and at the same time involves no pre-processing task. A variety of test cases have been presented to establish the efficacy of the presented scheme in providing good quality paths. The extent of advantage accruing out of the measures of free end-configurations and monotonic optimality are also analyzed quantitatively.

Investigating the dynamics of combustion-driven oscillations leading to lean blowout

The dynamics of combustion-driven thermoacoustic oscillations for a ducted laminar premixed flame has been investigated in lean equivalence ratio conditions. Combustion instability appears in the system as acoustic pressure and flame surface oscillations following a Hopf bifurcation. Further change in the control parameter leads to subsequent bifurcations, causing a rich dynamical behavior such as quasi-periodic and intermittent burst oscillations to appear in the system. During the burst oscillation phase, the system dynamics resembles the flame blowout phenomenon, which is of interest in practical combustion applications.

Analysis and control of friction-induced oscillations in a continuous system

We analyse and control friction-induced oscillations in a continuous system due to the drooping characteristics of the friction force. The model consists of a cantilever beam with an end mass that is in frictional contact with a rigid rotating disc. Time-delayed displacement feedback applied normal to the disc surface is used to control the vibrations. Linear stability analysis yields the stability boundary corresponding to the Hopf bifurcation point. Nonlinear analysis is performed to obtain conditions on the control parameters for which the nature of the bifurcation is subcritical such that these values can be avoided. The control parameters for effective quenching of the vibrations are obtained. An interesting regime of control parameters for which the system is stable for low and high velocities but unstable for intermediate velocities is also observed.

Dynamics of zero-Prandtl number convection near onset.

We present a detailed bifurcation scenario of zero-Prandtl number Rayleigh-Bénard convection using direct numerical simulations (DNS) and a 27-mode low-dimensional model containing the most energetic modes of DNS. The bifurcation analysis reveals a rich variety of convective flow patterns and chaotic solutions, some of which are common to that of the 13-mode model of Pal et al. [EPL 87, 54003 (2009)]. We also observed a set of periodic and chaotic wavy rolls in DNS and in the model similar to those observed in experiments and numerical simulations. The time period of the wavy rolls is closely related to the eigenvalues of the stability matrix of the Hopf bifurcation points at the onset of convection. This time period is in good agreement with the experimental results for low-Prandtl number fluids. The chaotic attractor of the wavy roll solutions is born through a quasiperiodic and phase-locking route to chaos.