ID#: 41
Abstract Title: Concept of the Limit of Existence of 2-D Steady-State Structure of Fuel Liquid Film under Flame Propagation
Session Title: Poster Session I
Session Date: 7/31/01
Session Start Time: 2:50 PM
Contributing Author: Sharypov, O.V.
Organization: Institute of Thermophysics SB RAS
Country: Russia
Authors: Oleg V. Sharypov, Konstantin A. Medvedko
Short Abstract: Two-dimensional steady-state structure of the flow in fuel liquid film on heat conductive substrate under combustion wave propagation is theoretically studied in the framework of hydrodynamic approach. Physical mechanisms of the structure forming are analyzed. It is shown that the important role belongs to thermocapillary effect. The conclusion that two- dimensional regime is possible only when the value of temperature gradient at the film surface is low enough is substantiated. The critical condition governing the transition to three- dimensional regime is derived. This condition means the balance between the velocity of the flow (induced for example by gravitation) and the velocity induced by thermocapillarity. If the temperature gradient exceeds certain critical value then the zone with reverse flow would appear according to 2-D model. In the previous works we suppose that such regime could not exist because of its instability relatively to 3-D perturbations. Indeed, the experiments with flowing liquid films upon immovable local heat source (without combustion wave) confirm the conclusion about the transition to 3-D regular flow structure when the temperature gradient is high enough. The first part of the paper is devoted to modeling 2-D film structure in critical regime. The second part of the paper deals with generalization of the problem to the case of heat source, moving with constant speed. This statement of the problem includes the flame propagation. Mathematical formulation of this problem allows us to conclude that existence of 2-D solution in this case is limited by the same condition. If the temperature gradient is more than critical then 2-D film structure would not exist. This concept substantiated at the present work explains the phenomena experimentally observed in liquid films under local heating.