Satoshi Kadowaki

THE INFLUENCE OF HYDRODYNAMIC INSTABILITY ON THE STRUCTURE OF CELLULAR FLAMES

The influence of hydrodynamic instability on the structure of two-dimensional (2D) and three-dimensional (3D) cellular flames is numerically investigated. The equation used is the compressible Navier–Stokes equation including a one-step irreversible chemical reaction. We superimpose an infinitesimal disturbance on the stationary plane flame and calculate the evolution of the disturbed flame front to obtain the relation between the growth rate and the wave number, i.e., the dispersion relation. With an increase in flame temperature, the growth rate increases since hydrodynamic instability becomes stronger. The unstable range normalized by the preheat zone thickness hardly changes, even though the flame temperature increases. The critical wave number, which corresponds to the maximum growth rate, is almost constant. Therefore, the normalized spacing between cells of the cellular flame is independent of the flame temperature. Moreover, we superimpose the disturbance with the critical wave number to investiga...

Instability of a deflagration wave propagating with finite Mach number

The hydrodynamic instability of a deflagration wave propagating with finite Mach number has been investigated. This paper deals with a wave front of deflagration as a surface of hydrodynamic discontinuity, and considers the pressure change through the wave front. The instability of the deflagration wave with respect to infinitesimal fluctuations is analyzed, and the relation between growth rates of fluctuations and their wave numbers (dispersion relation) is obtained. The obtained dispersion relation is consistent with the Darrieus–Landau solution when the Mach number is sufficiently small. Increased value of the Mach number causes larger pressure differences, and causes high growth rates compared with the results of Darrieus and Landau. Therefore, one should take account of the pressure change in the stability analysis of the deflagration wave propagating with considerably fast velocity.

The body-force effect on the cell formation of premixed flames

The body-force effect on the cell formation of premixed flames at Lewis number unity is investigated by two-dimensional (2-D) and three-dimensional (3-D), unsteady calculations of reactive flows. To investigate the body-force effect on intrinsic instability, the relation between the growth rate and the wave number, i.e., the dispersion relation, is obtained. When premixed flames are propagated downward (upward), the growth rate decreases (increases) and the unstable range narrows (widens) with an increase in acceleration. Positive growth rates induced by hydrodynamic and body-force effects form a cellular flame. To investigate the cell formation due to intrinsic instability, the disturbance with the linearly most unstable wavelength is superimposed on a planar flame. The superimposed disturbance evolves, and eventually a cellular flame front is formed. When the flame is propagated downward, the spacing between cells is almost constant and the cell depth becomes smaller as the acceleration increases. When the flame is propagated upward, on the other hand, the former becomes smaller and the latter becomes larger. In addition, the cell depth and flame-surface area of 3-D flames are larger than those of 2-D flames. This is caused by the difference in spacing between cells and disposition of cells.

Numerical Analysis on Instability of Cylindrical Flames

ABSTRACT Unsteady motions of 2-dimensional reactive flows have been simulated to investigate the hydrodynamic effect and the diffusive-thermal effect on the instability of freely expanding cylindrical flames. The numerical model includes compressibility, viscosity, heat conduction, molecular diffusion, one-step chemical reaction, and convection. We obtained the growth rates of disturbances superimposed on the cylindrical flames depending on their wave numbers. The results showed that the growth rates in the cylindrical flames are consistent with those in the plane flames for the case where the Lewis number is unity. Therefore, the hydrodynamic effect on the flame instability is independent of the mean curvature of the front. When the Lewis number is smaller/larger than unity, the growth rates in the cylindrical flames are lower/higher than those in the plane flames. It means that the instabilizing/stabilizing influence of the diffusive-thermal effect is less in the cylindrical flames than in the plane flames.

Flame velocity of cellular flames at low Lewis numbers

The flame velocity of cellular flames at low Lewis numbers is numerically studied, based on the compressible Navier-Stokes equation including a one-step chemical reaction. The flame velocity of a cellular flame is always larger than that of a plane flame and increases as the Lewis number becomes lower. When the Lewis number is unity, the flame velocity is proportional to the surface area. When the Lewis number is lower than unity, on the other hand, the increment of the flame velocity is greater than that of the surface area. The local flame velocity increases (decreases) at a convex (concave) flame front with respect to the unburned gas. The increase in the flame velocity at a convex flame front exceeds the decrease at a concave one, which is due to the Arrhenius nonlinearity. Thus, the flame-velocity increment is greater than the surface-area increment at Lewis numbers lower than unity.

Numerical study on the formation of cellular premixed flames at high Lewis numbers

Intrinsic instability and cell formation of premixed flames at high Lewis numbers (Le=1.0–3.0) are studied by two-dimensional, unsteady calculations of reactive flows. The relation between the growth rate and the wave number, i.e., the dispersion relation, is obtained to study intrinsic instability due to hydrodynamic and diffusive-thermal effects. The growth rate is positive at small wave numbers, and the marginal wave number separating stable and unstable ranges is found. The growth rate decreases and the unstable range narrows as the Lewis number becomes higher, since the diffusive-thermal effect has a stabilizing influence at Lewis numbers higher than unity. Positive growth rates caused by the hydrodynamic effect form a cellular flame. To study the formation of cellular flames, the disturbance with the linearly most unstable wave number is superimposed on a plane flame. The superimposed disturbance evolves, and eventually a cellular flame front is formed. The higher the Lewis number, the greater the c...

Numerical study on the instability of premixed plane flames in the three-dimensional field

The instability of premixed plane flames in the three-dimensional (3-D) field is investigated by means of the numerical simulation. We show numerically that infinitesimal disturbances superimposed on the flames grow exponentially with time, as predicted in the linear analysis, and obtain the growth rates of disturbances depending on the absolute values of the wave-number vectors. The growth rates of the 3-D flames are consistent with those of the two-dimensional (2-D) flames. The hydrodynamic effect has a destabilizing influence on the instability of flames, and the diffusive-thermal effect has a destabilizing/stabilizing influence for Le 1. Moreover, we produce the hexagonal cellular structure of the flame front not only for Le 1, where the spacing between cells in flames for Le 1. The spacing of the 3-D flames is 2√3 times as long as the cell size of the 2-D flames.

The lateral movement of the three-dimensional cellular flame at low Lewis numbers

Abstract The lateral movement of the three-dimensional (3-D) cellular flame at low Lewis numbers is numerically investigated. The equation used is the compressible Navier–Stokes equation including a one-step irreversible chemical reaction. We superimpose the hexagonal disturbance with the peculiar wave number on the stationary plane flame and calculate the evolution of the disturbed flame. When the Lewis number is unity, i.e., only the hydrodynamic effect has an influence on the flame instability, the stationary cellular flame is formed. When the Lewis number is lower than unity, i.e., the diffusive-thermal and hydrodynamic effects have an influence, the laterally moving cellular flame is formed. With a decrease in the Lewis number, the laterally moving velocity of the cell increases. The laterally moving velocity of the three-dimensional cellular flame is much larger than that of the two-dimensional (2-D) cellular flame. Because, the increment of local temperature at the convex flame front toward the unburned gas in the three-dimensional flame is great compared with that in the two-dimensional flame.

The Numerical Analysis of Cellular Premixed Flames Based on the Diffusive—Thermal and Navier—Stokes Equations

Unsteady calculations of two-dimensional (2—D) and three-dimensional (3—D) reactive flows are performed to investigate the hydrodynamic effect on the shape of cellular premixed flames at low Lewis numbers. The diffusive-thermal (D—T) and Navier-Stokes (N—S) equations, which contain a one-step irreversible chemical reaction, are employed. The D—T equation excludes the hydrodynamic effect caused by thermal expansion, since the constant-density approximation is used. The N—S equation, on the other hand, includes the hydrodynamic effect, since the compressibility of gases is taken into account. The hydrodynamic effect has a great influence on the flame instability and cellular-flame formation. The calculated growth rate based on the D—T equation is much smaller than that based on the N-S equation, and the obtained unstable range from the D—T equation is narrower. In addition, the calculated cell depth and flame length of a cellular flame based on the D—T equation are considerably smaller. Thus, it is necessary to include the hydrodynamic effect when studying the intrinsic instability of premixed flames and the shape of cellular-flame fronts.