High-Lewis Number Premixed Gas Instability

ABSTRACT:

A system is excitable if a stimulus above a critical threshold can trigger a transient excursion away from the systems steady-state, only to return at a later time. Such systems are encountered in biology, fluid mechanics, material science and a number of chemical processes. Perhaps, the Belousov-Zhabotinsky (BZ) is the most widely studied excitable and spontaneously oscillatory chemical system. During the past thirty years, it has become the focus of unprecedented study among chemists and mathematicians and is an elegant display of nonlinear self-organization in autocatalytic chemical reactions. Moreover, the ease with which one can repeat the original experiments of Belousov and Zhabotinsky has contributed to its widespread popularity and use as a model of spontaneous chemical oscillations and waves.

While most oscillating reactions have been observed in liquid-phase, isothermal systems, some gas-phase oscillators have also been observed. Original observations happened in freely-propagating and burner-stabilized premixed gas combustion. It suggested that the patterns are a manifestation of the high-Lewis number (Le) diffusive-thermal instability, yet more recent evidence showing the patterns exist in burner-stabilized flames using propane-air and butane-air premixtures that have a Le near one raises doubt that the high-Le diffusive-thermal instability is the driving mechanism. It is perhaps possible since the critical Lewis number for onset of instability is expected to decrease with increasing heat loss from spatially-independent, nonadiabatic diffusive-thermal linear stability analyses. At the same time, a recent simple kinetic study with diffusive transport predicts that a premixed flame can develop target and spiral waves for Le<1 and Le≥1 provided the system is excitable. While excitable models have successfully been used to predict rotating spiral waves and target patterns in a wealth of systems that exhibit such instabilities, combustion reactions are not clearly excitable since the reactants are continuously depleted and the products do not regenerate the reactants, i.e., combustion reactions are one-off reactions. To this end, Panfilov and co-workers and Yuan have developed a refined model that refutes the importance of excitability and instead suggests that the instabilities depend on several parameters, including the Le, Zeld'ovich (Ze), and the burned to the unburned gas densities (s = r_b/r_u).

(1) To clarify and quantify the role of diffusive fluxes of heat and species, i.e., Lewis number, on the stability, onset, temporal evolution, and interaction of target and spiral wave patterns in burner-stabilized and freely-propagating flames.

(2) To systematically explore and isolate the roles of Zel’dovich number, density ratio, mixture stoichiometry, pressure, initial gas temperature, and heat loss on the burner-stabilized and freely-propagating premixed gas flames.

(3) To determine if these waves are physically propagating waves via transport mechanisms or simply phase waves.

(4) To quantify the species and temperature distributions for burner-stabilized test conditions in the flame and post flame regions.

Simulations:

Recent numerical work in our lab is using the two-step Sal’nikov model to explore the interaction of wave fronts induced by multiple oscillatory centers as observed in the reported experimental observations.

A representative case for different initial conditions (different initial concentrations) in the two oscillatory centers is shown in Fig. 2. This behavior is reminiscent of that observed experimentally by Pearlman shown in Fig. 3.

Fig 2: Temperature distribution for two spatial oscillatory centers with non-identical parameters.

In the above, domain size is 2x2, grid spacing, h=0.04; time associated with frames 1-6 are: (a) 0.163, 0.167, 0.170, 0.173, 0.179, 0.198s

Two spatial oscillatory centers with different initial concentration on the surface α_initial,left=0.245 ,α_{initial,right}=0.25.

Times associated with frames 1-4 of a downwardly-propagating are 0.313, 0.317, 0.322 and 0.328s, respectively.

Experiments:

McKenna Burner experiment results:

Fig 10: Proposed experimental setup in the lower pressure camber.

These numerical and experimental studies will provide an improved understanding of the roles of diffusive fluxes of heat and species, hydrodynamic effects, heat loss, and chemical kinetics on the onset and dynamics of the flame patterns.

With quantitative data and a clear understanding of the mechanism and controlling parameters, one may eventually develop an active method to control such premixed flame instabilities or perhaps even exploit them for useful purposes.

1. Ma, Y. and Pearlman, H. (2006) “Target and Rotating Spiral Waves in Premixed Gas Combustion,” The 31^st International Symposium on Combustion, Work-in-Progress Poster Section, Heidelberg, Germany.
2. Foster, M., Ma, Y. and Pearlman, H. et al. (2006) “Premixed Combustion Research at Drexel University,” The Eighth Annual Research Day of Drexel University, Philadelphia, PA.
3. Ma, Y. and Pearlman, H. (2005) “Two-dimensional Modeling Studies of Pattern Formation in Premixed Gas Flames,” The Fourth Joint Meeting of the U.S. Sections of the Combustion Institute, Philadelphia, PA.
4. Pearlman, H. “Target and spiral wave patterns in premixed gas combustion,” The Royal Society of Chemistry: Faraday Transactions 93 (0), 1-4 (1997).
5. Pearlman, H.
6. Pearlman, H. “Excitability in Premixed Gas Combustion: Nonlinear Dynamics and Pattern Formation in Combustion,” The Fourth SIAM Conference on Application of Dynamical System, Snowbird, Utah, May 18-22, 1997.

CONTACT: 

Howard Pearlman
3141 Chestnut St., MEM department, Philadelphia, PA, 19104
215-895-1373
hp37 at drexel.edu

Yi Ma
Philadelphia, PA, 19104
215-895-0581
ym49 at drexel.edu