Global stability analysis of the double Tsuji burner

• Grant number: 22/14361-4
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• Effective date (Start): April 01, 2023
• Effective date (End): March 31, 2024
• Field of knowledge: Engineering - Mechanical Engineering
• Principal Investigator: Leandro Franco de Souza
• Grantee: Matheus de Padua Severino
• Supervisor: Daniel Rodríguez Álvarez
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Research place: Universidad Politécnica de Madrid (UPM), Spain
• Associated to the scholarship: 21/10689-2 - Coupling between hydrodynamic instabilities and buoyant diffusion flames with drastic shape variation, BP.DR

Abstract

The peculiar characteristics of the double Tsuji burner allow it to be a base configuration for fundamental studies and even practical applications. Notably, by providing flames with continuous geometric variation from the counterflow mode to the coflow mode. This study is part of the analysis proposed in the PhD project (FAPESP 2021/10689-2) for the double Tsuji burner. In particular, in this sub-project, a global stability analysis will be performed, which will provide stability/instability conditions of this configuration in the scope of a linear stability analysis (LST). Neither the basic state nor the perturbations dynamics can be described exactly (analytically). Therefore, a numerical solver will be used to obtain the base flow. It is based on the asymptotic form of the balance equations at a low Mach number and for an infinitely fast reaction (the flame surface approximation). Finite volumes discretize the physical domain on fully staggered grids, and the solution is iteratively approximated by the artificial compressibility method. For the global stability analysis, the physical domain is described mathematically by a two-dimensional non-homogeneous domain extended periodically in the third (longitudinal) direction. Then, a decomposition into temporal normal modes allows the derivation of a system of equations, and the respective boundary conditions, for the perturbations dynamics. If the perturbations attenuate (amplify), the system is stable (unstable). The global stability analysis code will be verified by solving cases available in the literature. In addition, the numerical solver will be used, comparing the amplification rates with those provided by the linear analysis. Physical validation of the mathematical model will be possible, in the future, through experimental data provided by the "Grupo de Mecânica de Fluidos Reativos (INPE)". (AU)