Effective Surface Recession Laws for the Physico‐Chemical Ablation of C/C Composite Materials

The thermostructural parts which have to suffer the most severe temperatures in a rocket nozzle or in a Thermal Protection System for atmospheric re-entry are frequently Carbon/Carbon composites. They principally undergo physico-chemical ablation by oxidation and sublimation. Fibers, matrices and interphases have marked differences in their ablation resistance, which usually leads to typical surface roughness features. A comprehensive study of the relations between material parameters, physicochemical conditions, and the surface recession leads to the possibility to reproduce numerically any surface roughness pattern. In addition, the effective recession rates are provided by the approach, in transient and steady states. In this work, we discuss the results of this modeling approach with an emphasis on the « composite laws » that can be inferred from them, as a practical design tool for the engineer. For instance, a « weakest-link » law has been put forward: it is shown in what physicochemical regime such an assumption is true. Extensions to other regimes are also provided. INTRODUCTION Materials for atmospheric re-entry body protection are mostly ablative Thermal Protection Systems (TPS); among them, carbon/carbon (C/C) and carbon/phenolic resin (C/R) composites are of common use, because of their excellent compromise between thermal, thermochemical and mechanical properties. The principle of thermal protection is that an appreciable amount of the received heat flux is converted into an outwards mass flux through endothermic processes, like sublimation and chemical etching: this induces surface recession. Surface roughening then appears: this unavoidable phenomenon has several consequences of importance in the case of atmospheric re-entry. First, it increases the chemically active surface of the wall; and second, it contributes to the laminar-to-turbulent transition in the surrounding flow. Both of these modifications to the physico-chemistry lead to an increase in heat transfer, resulting in an acceleration of the surface recession. The TPS thickness design has to account for this rather strong effect. Another space technology application for the same class of materials is the fabrication of rocket nozzle throats and inner parts. Here again, the acquisition of surface roughness during rocket launch is a critical issue, not because of the laminar-to-turbulent transition, but principally because of its impact on surface recession velocity, and on the possibility of triggering mechanical erosion. For both applications, if general phenomenological tendencies are predictable, the understanding of the interaction between the flow and the material has to be improved. One of the key points of ablative material design is the understanding of the relation between the global effective recession rate of the composite and the individual recession rates of its constituents. In the past years, a large effort has been made at modeling ablation from a material point of view. The observation of the material morphology at all scales has led to the conclusion that morphological features of the surfaces were linked to the contrast between constituents, as well as to the reaction/diffusion (interfacial/bulk transfer) ratio. A modeling study has been designed and performed; its results have largely confirmed the first hypotheses. Analytical models have also been exploited for a better understanding of the role of the parameters. In addition to the successful results on morphology reproduction, there is also another interesting output of the study, which is the prevision of effective ablation resistances (or reactivities) from the constituent individual properties. The aim of this paper is to summarize and discuss these results, which can be presented as “composite laws”. The document is organized as follows. A first part will recall the essentials of the approach, and the main results on morphology. Second, the effective laws will be presented for initial (flat) surfaces, then steady-state surfaces, and, finally, transient surfaces. A final discussion will conclude the document. MODELLING METHODS From the morphological study, it appears that the modeling of the roughness onset on ablative composites should feature the following elements: (i)Surface recession, under the action of oxidation or of sublimation. The surface recession velocity at any point depends on surface orientation, and on the rate of mass transfer. This latter quantity is a function of surface temperature and of local concentration of reactant gas or the local partial pressure of sublimed species, compared to the equilibrium value, e.g. through a Knudsen-Langmuir relationship. (ii)The local gas concentration is attained by solving a mass balance equation featuring consumption or production by the surface, and transport in the bulk of the gas phase. (iii)Similarly, the local surface temperature is evaluated by a heat balance equation featuring transport in the solid gas phases, as well as interfacial heat consumption. (iv)When necessary, the chemical reactivity will be a function of space, in order to translate the possible material heterogeneity. Point (i) is modeled by a Hamilton-Jacobi equation which describes the propagation of the surface under the action of a Hamiltonian which depends a priori on surface concentration and temperature. Points (ii) and (iii) may be modeled by transport equations for gas species and temperature; gas-phase transport should feature diffusion (possibly multi-component), and convection. This last element requires knowledge of the gas phase velocity field, in possibly turbulent flow conditions, which may be extremely difficult to obtain in a realistic fashion. A first model has been built using a set of rather restrictive assumptions: Isothermal conditions. This is suited to two kinds of situations: (1) isothermal oxidation tests; (2) micro-scale simulations where it appears that temperature differences across a characteristic roughness feature length are small enough to be neglected. Gas transport is restricted to the pure diffusion of a single species between the surface and a gas source (or sink) located at a large enough distance above the surface; at this place, it is considered that convection ensures the constancy of gas concentration. The relation between source concentration and source-to-surface distance may be obtained through a boundary-layer analysis. The criterion for the choice of the source-to-surface distance is based on a perturbation analysis argument, which shows that it can be as small as a few times the transverse characteristic length of the roughness pattern. Surface gas transfer is first order. It can be shown that oxidation and sublimation follow the same formalism in these conditions, as far as convection is not concerned. Even though this model looks extremely restrictive, it has the merit of being easily tractable and of capturing the essentials of the bulk transport/interfacial transfer competition. It has been possible to perform 3D simulations based on this model on rather large meshes. Also, some interesting analytical results have been produced.