Modelling of a One Dimensional Ablation Process with Char Formation

Abstract

We model an ablation process in an semi-infinite solid. The solid receives an external heat flux, which is kept constant during ablation. The process involves vapourisation of the virgin material and degradation of this material to another one. The thermal properties of the two materials can be different. However, the properties of both materials are independent of temperature. The fraction of material being vapourised per unit volume of the virgin solid is also kept constant throughout the process. In the model, we also assume an infinite chemical reaction rate. In other words, the ablation process takes place (and thus the secondary material is formed) instantaneously. In this paper, the second material will be referred to as char. Unlike pure ablation, in which regression rate always tends to a non-zero limit, the char forming model predicts it reaches a maximum and eventually tends to zero.

In the mathmatical model, a front fixing method is used to ‘fix’ the position of the moving boundary. An iterative method is used to evaluate the rate of char formation. A brief discussion on the method of solution is included.

In addition to the constant heat flux boundary condition, a convective heat loss and a radiative heat loss mechanism are also incorporated. Heat losses are important in real ablation. It has a significant effect on the mass loss rate (regression rate), and, in general, determines whether the ablation takes place. It is also interesting to note that the solutions for regression rate and for rate of char formation are qualitatively the same, with or without heat loss mechanisms present.

Keywords:

• Modelling
• ablation process
• heat flux