Heat Transfer Modeling of a Charring Material Using

An isoconversional modeling approach has been considered in the modeling of heat transfer and pyrolysis in a charring material. The isoconversional approach is appealing due to the use of only a single reacting component as opposed to the multicomponent model typically used. This reduces the number of required field variables which reduces numerical demands in large multi-dimensional models. In this study, isoconversional parameters have been reduced from available test data for a generic ablative material. The results were evaluated by implementing the approach into a onedimensional ablation heat transfer program and modeling the thermal and decomposition response of a charring material subjected to an elevated surface temperature. The results were compared to the same modeling using a traditional multi-component Arrhenius approach. Modeling outputs showed that the two methods produced very similar results when proper care was taken in the tabulated parameters of the isoconversional model which is susceptible to variations in supporting test data and insufficient table resolution. The results of this study indicate that the isoconversional model provides a viable alternative to the widely used multi-component approach. * Senior Technical Fellow, Thermal and Aerothermal Analysis, ATK Aerospace Group, UT40-252, P.O. Box 707, Brigham City, UT, 84302. (435) 863-2492, (435) 863-6223 fax, [email protected] † Graduate Research Assistant, Stanford University Distribution A: Approved for Public Release; Distribution Unlimited. PA Case Number: 15273 2 Introduction Ablative materials are commonly used in aerospace components such as rocket motor insulation and thermal protection systems of re-entry vehicles. These materials ablate at the surface due to thermochemical convective interaction with reactive boundary gases [1]. In addition, these materials often lose mass as they pyrolyze (char) internally, causing pyrolysis gases to escape through the porous char structure. As a result, accurate modeling of ablation heat transfer often requires submodels to capture the extent and effects of in-depth charring. Various models are available that include pyrolysis submodels. Notably the Charring Material Thermal Response and Ablation (CMA) [2] program has been available for decades, along with various derivatives of that program. Recently, the Insulation Thermal Response and Ablation Code (ITRAC) [3] has been made available for general modeling of ablative insulators. Both the CMA and ITRAC programs are one-dimensional and provide multi-component Arrhenius submodels to account for in-depth charring. The multi-component model has provided a successful modeling approach for some time, primarily within the framework of one-dimensional codes. However, with recent developments of advanced multi-dimensional codes such as the Heat Transfer and Erosion Analysis Program (Hero) [4,5], models with hundreds of thousands and even millions of elements are common, putting high demand on computational power. Successful reduction of computational expense in the numerical model is therefore of great value, and that is the primary impetus behind the work described here. For typical ablation heat transfer modeling in aerospace applications, three primary field variables are solved for within the ablative material. These variables are PA Case Number: 15273 3 temperature T, internal pore pressure P, and degree-of-char (or extent-of-reaction). With the multi-component model, the extent-of-reaction is quantified as a combination of individual component reactions i, typically three, with a field solution for each. A lessknown approach for modeling reaction kinetics is available that requires only a single overall extent-of-reaction . Use of this approach in the modeling of a charring material would therefore provide a reduction in the number of field variables, thereby reducing numerical demand. The approach, referred to as an “isoconversional” method [6], is described below following a review of the familiar multi-component model. Degree-of-Char (Extent-of-Reaction) Models The extent of material pyrolysis can be quantified using an overall extent-ofreaction based on the bulk density of the decomposing solid related to densities in the fully-virgin and fully-charred conditions and . The relationship is [3]