The Nonlinearity during Start-Oscillation of Thermo-Acoustic Instability in Rijke-Type Combustor

2011 ◽  
Vol 204-210 ◽  
pp. 1158-1161
Author(s):  
Guo Neng Li ◽  
Chen Yang Zang ◽  
Kai Li
Keyword(s):  
Acoustic Waves ◽  
Nonlinear Effects ◽  
Resonance Mode ◽  
Limit Cycle Oscillation ◽  
Main Resonance ◽  
Acoustic Instability ◽  
Short Period ◽  
Excited Oscillation ◽  
Cycle Oscillation ◽  
Pressure Perturbations

In order to study the nonlinearity during the start-oscillation of thermo-acoustic instability, an experimental setup was built. The growing process of nonlinearity during the start-oscillation of thermo-acoustic instability was captured and analyzed. Experimental results revealed that after a suitable resonance mode corresponding to the structural of the combustor was selected, the pressure perturbations inside the combustor grow in amplitude into a very large amplitude and self-excited oscillation in a very short period of time. Then, slowly, the nonlinear effects adjust the shapes of pressure waveforms and amplify the oscillations. Ultimately, a limit-cycle oscillation with smooth and uniform pressure waveforms was obtained, and the acoustic waves exhibit only the main resonance mode, damping other modes of instability.

Dynamics of a delayed competitive system affected by toxic substances with imprecise biological parameters

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5271-5293
Author(s):  
A.K. Pal ◽  
P. Dolai ◽  
G.P. Samanta
Keyword(s):  
Equilibrium Points ◽  
Stable Limit Cycle ◽  
Limit Cycle Oscillation ◽  
Toxic Substances ◽  
Stable Limit ◽  
Biological Parameters ◽  
Delay Model ◽  
Competitive System ◽  
Interval Numbers ◽  
Cycle Oscillation

In this paper we have studied the dynamical behaviours of a delayed two-species competitive system affected by toxicant with imprecise biological parameters. We have proposed a method to handle these imprecise parameters by using parametric form of interval numbers. We have discussed the existence of various equilibrium points and stability of the system at these equilibrium points. In case of toxic stimulatory system, the delay model exhibits a stable limit cycle oscillation. Computer simulations are carried out to illustrate our analytical findings.

scholarly journals Reducing parametric uncertainty in limit-cycle oscillation computational models

2017 ◽  
Vol 121 (1241) ◽  
pp. 940-969 ◽  
Author(s):  
R. Hayes ◽  
R. Dwight ◽  
S. Marques
Keyword(s):  
Limit Cycle ◽  
Computational Models ◽  
Structural Parameters ◽  
Parametric Uncertainty ◽  
Limit Cycle Oscillation ◽  
Posterior Distributions ◽  
Input Parameters ◽  
Data Points ◽  
Cycle Oscillation ◽  
True Values

ABSTRACTThe assimilation of discrete data points with model predictions can be used to achieve a reduction in the uncertainty of the model input parameters, which generate accurate predictions. The problem investigated here involves the prediction of limit-cycle oscillations using a High-Dimensional Harmonic Balance (HDHB) method. The efficiency of the HDHB method is exploited to enable calibration of structural input parameters using a Bayesian inference technique. Markov-chain Monte Carlo is employed to sample the posterior distributions. Parameter estimation is carried out on a pitch/plunge aerofoil and two Goland wing configurations. In all cases, significant refinement was achieved in the distribution of possible structural parameters allowing better predictions of their true deterministic values. Additionally, a comparison of two approaches to extract the true values from the posterior distributions is presented.

A weakly nonlinear framework to study shock–vorticity interaction

2022 ◽  
Vol 933 ◽  
Author(s):  
Pranav Thakare ◽  
Vineeth Nair ◽  
Krishnendu Sinha
Keyword(s):  
Numerical Simulations ◽  
Acoustic Waves ◽  
Significant Contribution ◽  
Interaction Analysis ◽  
Nonlinear Effects ◽  
Normal Shock ◽  
Linear Interaction ◽  
Weakly Nonlinear ◽  
High Incidence ◽  
Vorticity Generation

Linear interaction analysis (LIA) is routinely used to study the shock–turbulence interaction in supersonic and hypersonic flows. It is based on the inviscid interaction of elementary Kovásznay modes with a shock discontinuity. LIA neglects nonlinear effects, and hence it is limited to small-amplitude disturbances. In this work, we extend the LIA framework to study the fundamental interaction of a two-dimensional vorticity wave with a normal shock. The predictions from a weakly nonlinear framework are compared with high-order accurate numerical simulations over a range of wave amplitudes ( $\epsilon$ ), incidence angles ( $\alpha$ ) and shock-upstream Mach numbers ( $M_1$ ). It is found that the nonlinear generation of vorticity at the shock has a significant contribution from the intermodal interaction between vorticity and acoustic waves. Vorticity generation is also strongly influenced by the curvature of the normal shock wave, especially for high incidence angles. Further, the weakly nonlinear analysis is able to predict the correct scaling of the nonlinear effects observed in the numerical simulations. The analysis also predicts a Mach number dependent limit for the validity of LIA in terms of the maximum possible amplitude of the upstream vorticity wave.

scholarly journals Sound-wave instabilities in dilute plasmas with cosmic rays: implications for cosmic ray confinement and the Perseus X-ray ripples

2020 ◽  
Vol 493 (4) ◽  
pp. 5323-5335 ◽  
Author(s):  
Philipp Kempski ◽  
Eliot Quataert ◽  
Jonathan Squire
Keyword(s):  
Cosmic Rays ◽  
Thermal Plasma ◽  
Acoustic Waves ◽  
Cosmic Ray ◽  
High Energy ◽  
Density Fluctuations ◽  
Sound Waves ◽  
X Ray ◽  
Acoustic Instability ◽  
Anisotropic Viscosity

ABSTRACT Weakly collisional, magnetized plasmas characterized by anisotropic viscosity and conduction are ubiquitous in galaxies, haloes, and the intracluster medium (ICM). Cosmic rays (CRs) play an important role in these environments as well, by providing additional pressure and heating to the thermal plasma. We carry out a linear stability analysis of weakly collisional plasmas with CRs using Braginskii MHD for the thermal gas. We assume that the CRs stream at the Alfvén speed, which in a weakly collisional plasma depends on the pressure anisotropy (Δp) of the thermal plasma. We find that this Δp dependence introduces a phase shift between the CR-pressure and gas-density fluctuations. This drives a fast-growing acoustic instability: CRs offset the damping of acoustic waves by anisotropic viscosity and give rise to wave growth when the ratio of CR pressure to gas pressure is ≳αβ−1/2, where β is the ratio of thermal to magnetic pressure, and α, typically ≲1, depends on other dimensionless parameters. In high-β environments like the ICM, this condition is satisfied for small CR pressures. We speculate that the instability studied here may contribute to the scattering of high-energy CRs and to the excitation of sound waves in galaxy-halo, group and cluster plasmas, including the long-wavelength X-ray fluctuations in Chandra observations of the Perseus cluster. It may also be important in the vicinity of shocks in dilute plasmas (e.g. cluster virial shocks or galactic wind termination shocks), where the CR pressure is locally enhanced.

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