Experimental and theoretical study on near-floor flame spread along a thin solid

A method how to determine parameters arising in a smoldering evolution equation by image segmentation for experiment's movies

“…where u r = 1000 [mm/s] is the reference oxidizer velocity at which the spread velocity without heat loss becomes zero, D th = 168.8808917 [mm 2 /s] is the thermal diffusivity,l 0 = D th /u r [mm], β = 10 is the Zel'dovich number and m = 7.557354925776 is the weighted density ratio of the gas to the solid phases. These data hat can be calculated from [5].…”

“…Moving boundary problems have attracted many researchers and been extensively studied in the fields of not only applied mathematics but also physics such as combustion and fire research. In recent studies, spreading flame/smoldering fronts along a sheet of paper were tracked experimentally (see Figure 1 and [5]), and numerically (see Figure 2 and [4]) by applying the Kuramoto-Sivashinsky (KS in short) equation [3,7,12]. The purpose of this paper is to detect the fronts from two dimensional experimental images, and to determine the "real" values of the parameters that appear in the KS equation.…”

“…Therefore, the shape is thoroughly determined by the normal velocity V only and we can choose the value of W according to our convenience. The following equation is a version of the KS equation for gas combustion [3], which is also a model equation for flame/smoldering fronts along a sheet of paper [4,5]:…”

Convergence of a finite difference scheme for the Kuramoto--Sivashinsky equation defined on an expanding circle

“…Step 0-1 Set the initial values R 0 and U 0 i := u(σ i , 0); Step 0-2 Set the initial values for (12) such that V 0 Newton := v 0 = ∂u 0 ∂σ ;…”

“…In recent years, the behavior of the flame front during the smoldering combustion on a thin solid (e.g. a sheet of paper) has been vigorously studied both experimentally ( [12,22,28,36,37,38,39]) and mathematically ( [10,13,14,16,17,18,19,20,21]) aspects. The Kuramoto-Sivashinsky (KS) equation ( [23,32]), which is a well-known mathematical model of gaseous combustion, has been applied to research on smoldering combustion ( [12,13,14,20]).…”