PULSATING INSTABILITIES OF COMBUSTION WAVES IN A CHAIN-BRANCHING REACTION MODEL

2009 ◽  
Vol 19 (03) ◽  
pp. 873-887 ◽  
Author(s):  
V. V. GUBERNOV ◽  
A. V. KOLOBOV ◽  
A. A. POLEZHAEV ◽  
H. S. SIDHU ◽  
G. N. MERCER
Keyword(s):  
Activation Energy ◽  
Hopf Bifurcation ◽  
Combustion Wave ◽  
Traveling Wave ◽  
Lewis Number ◽  
Flame Speed ◽  
Traveling Wave Solution ◽  
Solution Branch ◽  
Combustion Waves ◽  
Parameter Values

In this paper we investigate the properties and linear stability of traveling premixed combustion waves and the formation of pulsating combustion waves in a model with two-step chain-branching reaction mechanism. These calculations are undertaken in the adiabatic limit, in one spatial dimension and for the case of arbitrary Lewis numbers for fuel and radicals. It is shown that the Lewis number for fuel has a significant effect on the properties and stability of premixed flames, whereas varying the Lewis number for the radicals has only qualitative (but not qualitative) effect on the combustion waves. We demonstrate that when the Lewis number for fuel is less than unity, the flame speed is unique and is a monotonically decreasing function of the dimensionless activation energy. Moreover, in this case, the combustion wave is stable and exhibits extinction for finite values of activation energy as the flame speed decreases to zero. However, for the fuel Lewis number greater than unity, the flame speed is a C-shaped and double valued function. The linear stability of the traveling wave solution was determined using the Evans function method. The slow solution branch is shown to be unstable whereas the fast solution branch is stable or exhibits the onset of pulsating instabilities via a Hopf bifurcation. The critical parameter values for the Hopf bifurcation and extinction are found and the detailed map for the onset of pulsating instabilities is determined. We show that a Bogdanov—Takens bifurcation is responsible for both the change in the behavior of the traveling wave solution near the point of extinction from unique to double valued type as well as for the onset of pulsating instabilities. We investigate the properties of the Hopf bifurcation and the emerging pulsating combustion wave solutions. It is demonstrated that the Hopf bifurcation observed in our present study is of supercritical type. We show that the pulsating combustion wave propagates with the average speed smaller than the speed of the traveling combustion wave and at certain parameter values the pulsating wave exhibits a period doubling bifurcation.

Period doubling and chaotic transient in a model of chain-branching combustion wave propagation

2010 ◽  
Vol 466 (2121) ◽  
pp. 2747-2769 ◽  
Author(s):  
Vladimir Gubernov ◽  
Andrei Kolobov ◽  
Andrei Polezhaev ◽  
Harvinder Sidhu ◽  
Geoffry Mercer
Keyword(s):  
Wave Propagation ◽  
Hopf Bifurcation ◽  
Combustion Wave ◽  
Period Doubling ◽  
Chaotic Regime ◽  
Bifurcation Parameter ◽  
Chain Branching ◽  
Combustion Waves ◽  
Combustion Wave Propagation ◽  
Parameter Values

The propagation of planar combustion waves in an adiabatic model with two-step chain-branching reaction mechanism is investigated. The travelling combustion wave becomes unstable with respect to pulsating perturbations as the critical parameter values for the Hopf bifurcation are crossed in the parameter space. The Hopf bifurcation is demonstrated to be of a supercritical nature and it gives rise to periodic pulsating combustion waves as the neutral stability boundary is crossed. The increase of the ambient temperature is found to have a stabilizing effect on the propagation of the combustion waves. However, it does not qualitatively change the behaviour of the travelling combustion waves. Further increase of the bifurcation parameter leads to the period-doubling bifurcation cascade and a chaotic regime of combustion wave propagation. The chaotic regime has a transient nature and the combustion wave extinguishes when the bifurcation parameter becomes sufficiently large. For Lewis numbers of fuel close to unity, the parameter regions where pulsating solutions exist become very close to each other and this makes it difficult to experimentally observe the period-doubling. It is shown that the average velocity of pulsating waves is less than the speed of the travelling wave for the same parameter values.

scholarly journals Non-adiabatic combustion waves for general Lewis numbers: wave speed and extinction conditions

2004 ◽  
Vol 46 (1) ◽  
pp. 1-16 ◽  
Author(s):  
A. C. McIntosh ◽  
R. O. Weber ◽  
G. N. Mercer
Keyword(s):  
Activation Energy ◽  
Heat Loss ◽  
Combustion Wave ◽  
Wave Speed ◽  
Energy Analysis ◽  
Lewis Number ◽  
Heat Losses ◽  
Combustion Waves ◽  
Wave Speeds ◽  
Oscillatory Instabilities

AbstractThis paper addresses the effect of general Lewis number and heat losses on the calculation of combustion wave speeds using an asymptotic technique based on the ratio of activation energy to heat release being considered large. As heat loss is increased twin flame speeds emerge (as in the classical large activation energy analysis) with an extinction heat loss. Formulae for the non-adiabatic wave speed and extinction heat loss are found which apply over a wider range of activation energies (because of the nature of the asymptotics) and these are explored for moderate and large Lewis number cases—the latter representing the combustion wave progress in a solid. Some of the oscillatory instabilities are investigated numerically for the case of a reactive solid.

Multiplicity of Premixed Flames Under the Effect of Heat Loss

2017 ◽  
Vol 9 (3) ◽  
Author(s):  
Eman Al-Sarairah ◽  
Chaouki Ghenai ◽  
Ahmed Hachicha
Keyword(s):  
Strain Rate ◽  
Heat Loss ◽  
Combustion Wave ◽  
Premixed Flames ◽  
Lewis Number ◽  
The Other ◽  
Premixed Flame ◽  
Two Dimensional ◽  
Combustion Waves ◽  
Loss Parameter

We investigate numerically the effect of heat loss and strain rate on the premixed flame edges encountered in a two-dimensional counterflow configuration for Lewis number higher than one. Under nonadiabatic conditions, multiple flame edges and multiple propagation speeds (positive and negative) are discussed. Different regions of multiple propagation speeds have been revealed ranging from two to four, depending on the value of the heat loss parameter and Damkohler number, which is inversely proportional to the strain rate. A combustion wave is modeled by connecting a strongly burning flame on one side of the burner to a weakly burning flame on the other side. These combustion waves are changing with increasing Dam number into flame edges with the fact that the strongly burning flame is the dominant.

scholarly journals Wave propagation in the Lorenz-96 model

2018 ◽  
Vol 25 (2) ◽  
pp. 301-314 ◽  
Author(s):  
Dirk L. van Kekem ◽  
Alef E. Sterk
Keyword(s):  
Hopf Bifurcation ◽  
Traveling Wave ◽  
Wave Number ◽  
Finite Limit ◽  
Stationary Waves ◽  
Double Hopf Bifurcation ◽  
Pitchfork Bifurcations ◽  
Lorenz 96 ◽  
Parameter Values ◽  
Dimension Parameter

Abstract. In this paper we study the spatiotemporal properties of waves in the Lorenz-96 model and their dependence on the dimension parameter n and the forcing parameter F. For F > 0 the first bifurcation is either a supercritical Hopf or a double-Hopf bifurcation and the periodic attractor born at these bifurcations represents a traveling wave. Its spatial wave number increases linearly with n, but its period tends to a finite limit as n → ∞. For F < 0 and odd n, the first bifurcation is again a supercritical Hopf bifurcation, but in this case the period of the traveling wave also grows linearly with n. For F < 0 and even n, however, a Hopf bifurcation is preceded by either one or two pitchfork bifurcations, where the number of the latter bifurcations depends on whether n has remainder 2 or 0 upon division by 4. This bifurcation sequence leads to stationary waves and their spatiotemporal properties also depend on the remainder after dividing n by 4. Finally, we explain how the double-Hopf bifurcation can generate two or more stable waves with different spatiotemporal properties that coexist for the same parameter values n and F.

Oscillatory Dynamics of P53 Network With Time Delays

2018 ◽  
Vol 21 (6) ◽  
pp. 411-419 ◽  
Author(s):  
Conghua Wang ◽  
Fang Yan ◽  
Yuan Zhang ◽  
Haihong Liu ◽  
Linghai Zhang
Keyword(s):  
Hopf Bifurcation ◽  
Cell Fate ◽  
Time Delays ◽  
Sustained Oscillation ◽  
Multiple Time ◽  
Cell Fate Decisions ◽  
Oscillatory Dynamics ◽  
Main Components ◽  
Parameter Values ◽  
P53 Network

Aims and Objective: A large number of experimental evidences report that the oscillatory dynamics of p53 would regulate the cell fate decisions. Moreover, multiple time delays are ubiquitous in gene expression which have been demonstrated to lead to important consequences on dynamics of genetic networks. Although delay-driven sustained oscillation in p53-based networks is commonplace, the precise roles of such delays during the processes are not completely known. Method: Herein, an integrated model with five basic components and two time delays for the network is developed. Using such time delays as the bifurcation parameter, the existence of Hopf bifurcation is given by analyzing the relevant characteristic equations. Moreover, the effects of such time delays are studied and the expression levels of the main components of the system are compared when taking different parameters and time delays. Result and Conclusion: The above theoretical results indicated that the transcriptional and translational delays can induce oscillation by undergoing a super-critical Hopf bifurcation. More interestingly, the length of these delays can control the amplitude and period of the oscillation. Furthermore, a certain range of model parameter values is essential for oscillation. Finally, we illustrated the main results in detail through numerical simulations.

scholarly journals Finite Element Study for Magnetohydrodynamic (MHD) Tangent Hyperbolic Nanofluid Flow over a Faster/Slower Stretching Wedge with Activation Energy

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 25
Author(s):  
Bagh Ali ◽  
Rizwan Ali Naqvi ◽  
Amna Mariam ◽  
Liaqat Ali ◽  
Omar M. Aldossary
Keyword(s):  
Activation Energy ◽  
Finite Element ◽  
Volume Fraction ◽  
Wedge Angle ◽  
Energy Parameter ◽  
Reliability And Validity ◽  
Lewis Number ◽  
Convergence Criteria ◽  
Convective Boundary ◽  
Differential Formulation

The below work comprises the unsteady flow and enhanced thermal transportation for Carreau nanofluids across a stretching wedge. In addition, heat source, magnetic field, thermal radiation, activation energy, and convective boundary conditions are considered. Suitable similarity functions use to transmuted partial differential formulation into the ordinary differential form, which is solved numerically by the finite element method and coded in Matlab script. Parametric computations are made for faster stretch and slowly stretch to the surface of the wedge. The progressing value of parameter A (unsteadiness), material law index ϵ, and wedge angle reduce the flow velocity. The temperature in the boundary layer region rises directly with exceeding values of thermophoresis parameter Nt, Hartman number, Brownian motion parameter Nb, ϵ, Biot number Bi and radiation parameter Rd. The volume fraction of nanoparticles rises with activation energy parameter EE, but it receded against chemical reaction parameter Ω, and Lewis number Le. The reliability and validity of the current numerical solution are ascertained by establishing convergence criteria and agreement with existing specific solutions.

scholarly journals Single peaked traveling wave solutions to a generalized μ-Novikov Equation

2020 ◽  
Vol 10 (1) ◽  
pp. 66-75
Author(s):  
Byungsoo Moon
Keyword(s):  
Linear Combination ◽  
Traveling Wave ◽  
Wave Solution ◽  
Traveling Wave Solutions ◽  
Traveling Wave Solution ◽  
Wave Solutions ◽  
Quadratic Nonlinearities ◽  
Novikov Equation

Abstract In this paper, we study the existence of peaked traveling wave solution of the generalized μ-Novikov equation with nonlocal cubic and quadratic nonlinearities. The equation is a μ-version of a linear combination of the Novikov equation and Camassa-Hom equation. It is found that the equation admits single peaked traveling wave solutions.

Periodic traveling-wave solution of the Sakuma-Nishiguchi equation

1996 ◽  
Vol 54 (19) ◽  
pp. 13484-13486 ◽  
Author(s):  
David R. Rowland ◽  
Zlatko Jovanoski
Keyword(s):  
Traveling Wave ◽  
Wave Solution ◽  
Traveling Wave Solution ◽  
Periodic Traveling Wave

The Effect of Lewis Number on Instantaneous Flamelet Speed and Position Statistics in Counter-Flow Flames With Increasing Turbulence

2017 ◽  
Author(s):  
Sean D. Salusbury ◽  
Ehsan Abbasi-Atibeh ◽  
Jeffrey M. Bergthorson
Keyword(s):  
Flame Front ◽  
Turbulence Intensity ◽  
High Speed ◽  
Rayleigh Scattering ◽  
Turbulent Flame ◽  
Lewis Number ◽  
Turbulent Flames ◽  
Flame Speed ◽  
Laminar Flames ◽  
Counter Flow

Differential diffusion effects in premixed combustion are studied in a counter-flow flame experiment for fuel-lean flames of three fuels with different Lewis numbers: methane, propane, and hydrogen. Previous studies of stretched laminar flames show that a maximum reference flame speed is observed for mixtures with Le ≳ 1 at lower flame-stretch values than at extinction, while the reference flame speed for Le ≪ 1 increases until extinction occurs when the flame is constrained by the stagnation point. In this work, counter-flow flame experiments are performed for these same mixtures, building upon the laminar results by using variable high-blockage turbulence-generating plates to generate turbulence intensities from the near-laminar u′/SLo=1 to the maximum u′/SLo achievable for each mixture, on the order of u′/SLo=10. Local, instantaneous reference flamelet speeds within the turbulent flame are extracted from high-speed PIV measurements. Instantaneous flame front positions are measured by Rayleigh scattering. The probability-density functions (PDFs) of instantaneous reference flamelet speeds for the Le ≳ 1 mixtures illustrate that the flamelet speeds are increasing with increasing turbulence intensity. However, at the highest turbulence intensities measured in these experiments, the probability seems to drop off at a velocity that matches experimentally-measured maximum reference flame speeds in previous work. In contrast, in the Le ≪ 1 turbulent flames, the most-probable instantaneous reference flamelet speed increases with increasing turbulence intensity and can, significantly, exceed the maximum reference flame speed measured in counter-flow laminar flames at extinction, with the PDF remaining near symmetric for the highest turbulence intensities. These results are reinforced by instantaneous flame position measurements. Flame-front location PDFs show the most probable flame location is linked both to the bulk flow velocity and to the instantaneous velocity PDFs. Furthermore, hydrogen flame-location PDFs are recognizably skewed upstream as u′/SLo increases, indicating a tendency for the Le ≪ 1 flame brush to propagate farther into the unburned reactants against a steepening average velocity gradient.

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