scholarly journals Weakly nonlinear analysis of thermoacoustic bifurcations in the Rijke tube

2016 ◽  
Vol 805 ◽  
pp. 523-550 ◽  
Author(s):  
Alessandro Orchini ◽  
Georgios Rigas ◽  
Matthew P. Juniper
Keyword(s):  
Dynamical Evolution ◽  
Hopf Bifurcations ◽  
Solvability Conditions ◽  
Rijke Tube ◽  
Nonlinear Dynamical ◽  
Weakly Nonlinear ◽  
The Cost ◽  
Fifth Order ◽  
Thermoacoustic Oscillations ◽  
Good Agreement

In this study we present a theoretical weakly nonlinear framework for the prediction of thermoacoustic oscillations close to Hopf bifurcations. We demonstrate the method for a thermoacoustic network that describes the dynamics of an electrically heated Rijke tube. We solve the weakly nonlinear equations order by order, discuss their contribution on the overall dynamics and show how solvability conditions at odd orders give rise to Stuart–Landau equations. These equations, combined together, describe the nonlinear dynamical evolution of the oscillations’ amplitude and their frequency. Because we retain the contribution of several acoustic modes in the thermoacoustic system, the use of adjoint methods is required to derive the Landau coefficients. The analysis is performed up to fifth order and compared with time domain simulations, showing good agreement. The theoretical framework presented here can be used to reduce the cost of investigating oscillations and subcritical phenomena close to Hopf bifurcations in numerical simulations and experiments and can be readily extended to consider, e.g. the weakly nonlinear interaction of two unstable thermoacoustic modes.

scholarly journals Perturbation solutions of fifth order oscillatory nonlinear systems

2011 ◽  
Vol 16 (2) ◽  
pp. 123-134
Author(s):  
M. Ali Akbar ◽  
Sk. Tanzer Ahmed Siddique
Keyword(s):  
Degrees Of Freedom ◽  
Nonlinear Differential Equations ◽  
Weakly Nonlinear ◽  
Physical Systems ◽  
Oscillatory Systems ◽  
Engineering Problems ◽  
Kbm Method ◽  
Fifth Order ◽  
Method Show ◽  
Good Agreement

Oscillatory systems play an important role in the nature. Many engineering problems and physical systems of fifth degrees of freedom are oscillatory and their governing equations are fifth order nonlinear differential equations. To investigate the solution of fifth order weakly nonlinear oscillatory systems, in this article the Krylov–Bogoliubov–Mitropolskii (KBM) method has been extended and desired solution is found. An example is solved to illustrate the method. The results obtain by the extended KBM method show good agreement with those obtained by numerical method.

scholarly journals Simulation of Thermal and Electric Field Distribution in Packaged Sausages Heated in a Stationary Versus a Rotating Microwave Oven

Foods ◽  
2021 ◽  
Vol 10 (7) ◽  
pp. 1622
Author(s):  
Wipawee Tepnatim ◽  
Witchuda Daud ◽  
Pitiya Kamonpatana
Keyword(s):  
Temperature Distribution ◽  
Electric Field ◽  
Three Dimensional ◽  
Development Stage ◽  
Microwave Oven ◽  
Computational Time ◽  
Plastic Package ◽  
Heating Uniformity ◽  
The Cost ◽  
Good Agreement

The microwave oven has become a standard appliance to reheat or cook meals in households and convenience stores. However, the main problem of microwave heating is the non-uniform temperature distribution, which may affect food quality and health safety. A three-dimensional mathematical model was developed to simulate the temperature distribution of four ready-to-eat sausages in a plastic package in a stationary versus a rotating microwave oven, and the model was validated experimentally. COMSOL software was applied to predict sausage temperatures at different orientations for the stationary microwave model, whereas COMSOL and COMSOL in combination with MATLAB software were used for a rotating microwave model. A sausage orientation at 135° with the waveguide was similar to that using the rotating microwave model regarding uniform thermal and electric field distributions. Both rotating models provided good agreement between the predicted and actual values and had greater precision than the stationary model. In addition, the computational time using COMSOL in combination with MATLAB was reduced by 60% compared to COMSOL alone. Consequently, the models could assist food producers and associations in designing packaging materials to prevent leakage of the packaging compound, developing new products and applications to improve product heating uniformity, and reducing the cost and time of the research and development stage.

A fifth-order multiple-scale solution for Hopf bifurcations

2004 ◽  
Vol 82 (31-32) ◽  
pp. 2723-2731 ◽  
Author(s):  
D. Dessi ◽  
F. Mastroddi ◽  
L. Morino
Keyword(s):  
Multiple Scale ◽  
Hopf Bifurcations ◽  
Fifth Order

Efficient Fatigue Testing of Tubular Joints

2015 ◽  
Author(s):  
P. Thibaux ◽  
J. Van Wittenberghe ◽  
E. Van Pottelberg ◽  
M. Van Poucke ◽  
P. De Baets ◽  
...  
Keyword(s):  
Finite Element ◽  
Fatigue Testing ◽  
Fatigue Loading ◽  
Tubular Joints ◽  
Testing Method ◽  
Out Of Plane ◽  
Resonance Principle ◽  
Tubular Joint ◽  
The Cost ◽  
Good Agreement

Tubular joints are intensively used in off-shore structures for shallow waters. Depending on the sea conditions and the type of structure, the design can be fatigue driven. This is particularly the case for off-shore wind turbines, where turbulences are generating a fatigue loading. Any improvement of the fatigue performance of the tubular joint would be beneficial to reduce the weight and the cost of the structure. To assess efficiently the fatigue resistance of the tubular joint, a testing method has been developed based on the resonance principle. The complete circumference of the welded joint can be loaded, successively in the in-plane and out-of-plane modes at a frequency close to 20Hz. Finite element computations were used to investigate the feasibility of the concept. Then, an X-node was made and successfully tested to investigate the stress distribution along the weld. The experimental results were compared with finite element computations, giving a good agreement.

scholarly journals Theoretical and Experimental Investigation of Two-to-One Internal Resonance in MEMS Arch Resonators

2018 ◽  
Vol 14 (1) ◽  
Author(s):  
Feras K. Alfosail ◽  
Amal Z. Hajjaj ◽  
Mohammad I. Younis
Keyword(s):  
Internal Resonance ◽  
Nonlinear Response ◽  
Multiple Scales ◽  
Hopf Bifurcations ◽  
Chaotic Motions ◽  
Different Types ◽  
Quadratic Nonlinearities ◽  
Multiple Scales Perturbation Method ◽  
Good Agreement ◽  
Perturbation Solutions

We investigate theoretically and experimentally the two-to-one internal resonance in micromachined arch beams, which are electrothermally tuned and electrostatically driven. By applying an electrothermal voltage across the arch, the ratio between its first two symmetric modes is tuned to two. We model the nonlinear response of the arch beam during the two-to-one internal resonance using the multiple scales perturbation method. The perturbation solution is expanded up to three orders considering the influence of the quadratic nonlinearities, cubic nonlinearities, and the two simultaneous excitations at higher AC voltages. The perturbation solutions are compared to those obtained from a multimode Galerkin procedure and to experimental data based on deliberately fabricated Silicon arch beam. Good agreement is found among the results. Results indicate that the system exhibits different types of bifurcations, such as saddle node and Hopf bifurcations, which can lead to quasi-periodic and potentially chaotic motions.

Stirring Effect on the Belousov-Zhabotinsky Oscillating Chemical Reactions in a Batch. Experimental and Modelling

2010 ◽  
Vol 65 (1-2) ◽  
pp. 132-140 ◽  
Author(s):  
Yevhen Yu. Kalishyn ◽  
Małgorzata Rachwalska ◽  
Peter E. Strizhak
Keyword(s):  
Kinetic Scheme ◽  
Hopf Bifurcations ◽  
Hydrodynamic Turbulence ◽  
Stirring Rate ◽  
Diffusion Controlled ◽  
Stirring Effect ◽  
Delayed Bifurcations ◽  
Diffusion Controlled Reaction ◽  
Transient Oscillations ◽  
Good Agreement

AbstractWe have studied the stirring effect on the time-delayed bifurcations of transient oscillations in the Belousov-Zhabotinsky (BZ) oscillating chemical reaction in a closed system. Experiments show that oscillations disappear through the time-delayed Hopf bifurcations, whose parameters depend on the stirring rate. The explanation of the stirring effect is based on the theories of diffusion-controlled reactions and hydrodynamic turbulence. We show that an increase of the stirring rate leads to an increase of the rate constant for the diffusion-controlled reaction. We propose a kinetic scheme that describes the effect observed in the experiments. A good agreement between the experimental data and the simulations is obtained.

On the evolution of a nonlinear Alfvén pulse

1999 ◽  
Vol 62 (2) ◽  
pp. 219-232 ◽  
Author(s):  
E. VERWICHTE ◽  
V. M. NAKARIAKOV ◽  
A. W. LONGBOTTOM
Keyword(s):  
Temporal Evolution ◽  
Transverse Velocity ◽  
Longitudinal Velocity ◽  
Initial Pulse ◽  
Weakly Nonlinear ◽  
Starting Position ◽  
Linearly Polarized ◽  
Nonlinear Plane ◽  
The Magnetic Field ◽  
Good Agreement

The temporal evolution of weakly nonlinear, plane, linearly polarized Alfvén pulses in a cold homogeneous plasma is investigated. A static initial pulse-like disturbance in transverse velocity produces two Alfvén pulses that travel in opposite directions along the magnetic field. The ponderomotive force of the two pulses produces a static shock in longitudinal velocity at the starting position. The travelling pulses form a shock front that is governed by the scalar Cohen–Kulsrud equation. We find good agreement between the analytical solutions we derive and the results from a fully nonlinear numerical MHD code.

scholarly journals Collisional Evolution of Galaxy Clusters: Fokker–Planck and N-body models

2003 ◽  
Vol 208 ◽  
pp. 449-450
Author(s):  
Koji Takahashi ◽  
Tomohiro Sensui ◽  
Yoko Funato ◽  
Junichiro Makino
Keyword(s):  
Power Law ◽  
Dynamical Evolution ◽  
Cluster Center ◽  
Combined Effects ◽  
Clusters Of Galaxies ◽  
Relative Importance ◽  
Self Consistent ◽  
The Common ◽  
Good Agreement ◽  
Fokker Planck

We investigate the dynamical evolution of clusters of galaxies in virial equilibrium by using Fokker–Planck models and self-consistent N-body models. In particular we focus on the growth of the common halos and the development of the central density cusps in the clusters. We find good agreement between the Fokker–Planck and N-body models. At the cluster center the cusp approximated by a power law, ρ(r) ∝ r-α (α ∼ 1), develops. We conclude that this shallow cusp results from the combined effects of two-body relaxation and tidal stripping. The cusp steepness α weakly depends on the relative importance of tidal stripping.

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