# Surface Erosion Analysis for Thermal Insulation Materials of Graphite and Carbon-Carbon Composite
## 1 Introduction  
A rocket is a device that generates thrust through action and reaction forces. It uses fuel and oxidants to generate propulsion by combustion and emissions, and is mainly used for space exploration aircrafts, weapons and satellite launches. Examples include liquid-propellant, solid-propellant, nuclear propulsion, and laser propulsion rockets. Among them, solid-propellant rockets consist of a motor case, igniter, propellant, nozzle, insulator, and control and drive device. The nozzle is a very important component that generates thrust. However, since the nozzle is burnt in a high-temperature/high-pressure environment, it cannot be cooled, unlike the liquid-propellant rocket that circulates fuel around the nozzle. As a result, solid-propellant rockets experience erosion due to combustion gas [1].  
The nozzle throat of a rocket is a portion where the gas pressure and density are comparatively high, and the velocity of the gas becomes the speed of sound and the amount of heat transferred to the nozzle wall is significant. When erosion occurs on the nozzle throat of such a rocket, it affects the reaching height, reaching distance, and flight speed [1]. Therefore, one of the most important issues in nozzle design is to select or develop materials suitable for such environments that have durability against combustion gases of high temperature and pressure. Bulk-type graphite and carbon-carbon (C-C) composite materials have been mainly used for solid-propellant rocket nozzles. In particular, C-C composites are made by laminating multiple layers of carbon fibers and have recently been used because of their relatively strong thermal shock and mechanical strength compared to graphite.  
An oxy-acetylene torch test has been used for basic research and evaluation of erosion materials [2]. Many studies have been performed by [PERSON] and [PERSON] and other researchers to characterize erosion based on the thermochemical erosion model previously presented by [PERSON] and [PERSON] [3; 4]. This model consists of a chemical-controlled recession process and a diffusion-controlled recession process. However, the thermochemical erosion model alone has limits in fully understanding the erosion characteristics. In addition, there are few analyses of the improved erosion characteristics using a mechanical erosion model, including the friction factor, porosity, and characteristic exhaust velocity proposed by [PERSON] [5] in the thermochemical erosion model for graphite and C-C composite materials.  
In this study, the mechanical erosion model is considered with the thermochemical model for better analysis of erosion characteristics. The parameters required for the thermochemical erosion model of graphite and C-C composite materials were experimentally measured through the development of the erosion experimental system, and the main factors influencing the erosion were compared with the model. Additionally, the characteristics of mechanical erosion of graphite and C-C composite materials were investigated experimentally; more accurate erosion was predicted, and major factors influencing the mechanical erosion were analyzed.