A Level Set Approach for a Premixed Flame Based on a New Concept of Flame Speed

Abstract

In this paper we propose a new level set approach to describe not only a flame's surface but also to the flame's spatial distribution. First, we derived the mathematical formulation for a one-dimensional laminar premixed flame, where the steady flame has a finite thickness depending on the diffusion flux whose physical quantity such as temperature has a relation to index function G . Further, to investigate the relationship between the present model and Inage's model, we extracted the physical meaning from the energy equation. We also validated another important parameter, the heat reaction release rate using the modified G-equation. The analysis of the heat release term leads to the definition of local flame speed, describing the distribution in the flame thickness. We evaluated the distribution of local flame speed with scalar G based on the one-dimensional solutions of premixed flames obtained by the detailed chemical reaction GRI-Mech3.0 using CHEMKIN. For 4 CH /Air premixed fuel, we carried out a series of calculations with different fuel rates and inlet temperatures. Based on the linear distribution of local flame speed, the modified G-equation can again be certified as the hyperbolic tangent profile.

Mathematical study on the thickened interface model by viscosity solution of the level-set equation

“…To derive the level-set formulation from the conservation equation (Eq. ( 4)), Liu et al (2011) ). Oshima (2017) proposed an extended formulation to the three-dimensional problem with the surface curvature flow as…”

“…Ishida et al (2009) have verified a one-dimensional Allen-Cahn type equation, the most familiar model of the phase field approach, essentially to the same solution. Using an analogy of the two interface models by the level-set and phase field approaches, Liu and Oshima (2011) proposed a numerical model for a premixed combustion flame. Oshima (2016Oshima ( , 2017 later extended this model to a three-dimensional formultion for a viscosity solution of the level-set equation.…”

“…Following Liu and Oshima (2011), the physical behavior of an interface were considered here on the basis of a relation to the scalar conservation law expressed by…”

Propagation Velocity and Fractal Structure of Premixed Flame during Gas Explosion

“…e idea of Eq. ( 2) is based on the modi cation of the so-called G-equation proposed by Liu and Oshima (2011).…”

A novel approach for wall-boundary immersed flow simulation (proposal of modified Navier-Stokes equation)

“…In contrast, a level-set approach (Osher and Fedkiw, 2002) is a novel idea for treating the boundary surface, wherein the surface geometry is indirectly defined by an iso-contour of a continuous function derived using a level-set equation. It has been extensively investigated in mathematics (Chen et al, 1991), and applied to practical problems such as image processing (Li et al, 2011), 3D printing (Cacace et al, 2017, and simulations of interface problems, including a phase interface (Grave et al, 2020) and combustion flame (Liu and Oshima, 2011). Oshima (2016Oshima ( , 2017Oshima ( , 2022) investigated a viscosity solution for the level-set equation as laminated multiple iso-contours of an interface "region" with a finite thickness, instead of a single surface defined by the traditional level-set approach.…”