Effect of small heat release and viscosity on thermal-diffusive instability

Area of Science:

• Chemical Engineering
• Combustion Science
• Fluid Dynamics

Background:

• The Zel'dovich-Frank-Kamenetskii (ZFK) model describes thermal reaction fronts, neglecting hydrodynamic flow.
• Two instabilities, cellular and oscillatory, arise from heat conduction and mass diffusion.
• Cellular instability has a positive real growth rate; oscillatory instability has a non-zero imaginary part.

Purpose of the Study:

• To investigate the effects of heat release and viscosity on cellular and oscillatory instabilities.
• To analyze the linear stability of thermal reaction fronts under varying conditions.
• To understand the asymptotic and numerical behavior of these instabilities.

Main Methods:

• Coupling mass-conservation and Navier-Stokes equations with the ZFK model.
• Asymptotic and numerical analysis for small heat release.
• Investigating the influence of Lewis and Prandtl numbers, and viscosity.

Main Results:

• Non-zero heat release widens the stable range of Lewis number for all wavenumbers.
• Increased Prandtl number stabilizes oscillatory instability.
• Viscosity destabilizes cellular instability at small wavenumbers but stabilizes it at moderate wavenumbers, defining a cut-off wavenumber.

Conclusions:

• Heat release and viscosity are critical factors in thermal reaction front stability.
• The interplay between heat release, viscosity, and hydrodynamic effects determines instability types and ranges.
• Understanding these phenomena is crucial for controlling reaction front propagation.