1.1 Introduction
Carbon-based compounds are indispensable to aerospace application. Depending on the type of mission (Sub-Orbital or Super-Orbital), heat shields and wing leading edge components of hypersonic flight vehicles are made of compounds like graphite, Avcoat, Phenolic Impregnated Carbon Ablator (PICA) and Silicone Impregnated Reusable Ceramic Ablator (SIRCA) for shallow and deeper planetary missions. Many heat shield materials have been developed but this publication is limited to thermal verification of graphite through simulations at 1800 angle of attack. Slight changes in angle of attack can severely alter the activity of the re-entry capsule [1]. During atmospheric re-entry to earth, the spacecraft experience temperatures upwards of 15000C [2]. Some of the characteristics of a high speed Earth entry vehicle are: (1) entry velocity higher or equal to 11.7 km/s as against 7.5 km/s for the US Space Shuttle; (2) very high heat fluxes upwards of 10 MW/m2 and (3) heat loads in the range of 500 MJ/m2 [3] where the radiative part becomes very important. The effort in this publication is channelled to creating an efficient temperature distribution (using Joule or resistive or electric heating) which will be able to replicate re-entry temperatures of spherical heat shields. This methodology will enable the re-entry behaviour of heat shields to be critically examined using cold hypersonic flows. Example of a cold hypersonic wind tunnel is the Tunnel at the University of Southern Queensland (TUSQ), Australia. The TUSQ is a free piston compression Ludwieg tube facility capable of producing Mach 6 cold flow to a maximum temperature of 560K which is much lower than most re-entry temperatures (upwards of 2000K). Hence the relevance of Joule heating is to raise the experimental model to desired temperatures that will be able to replicate flight temperatures in a wind tunnel testing facility.
As electric current is applied to a graphite material, heat energy is generated at a rate proportional to the square of the applied current (I) and resistance (R) of the material. This heat energy generated through electrical method is called Joule heating according to Equation 1.1.
                                                                                                                                                   \(Heat\ flux\ \phi=I^2R\ eqn\ 1.1\)
The adopted methodology involve applying electric current to the centre of the spherical segment (which represents stagnation point) and allowed to spread out. This indicates a high energy density (due to small cross sectional area) at the centre and a low energy density (due to large cross sectional area) at the shoulder region shown in Fig.2.1 and 2.2. Since the cross sectional area continuously increases from being a point at the centre to being a big circle at the shoulder ends, it implies that for a fixed uniform thickness, the resistance at the centre is highest while that at the circumference is lowest according to Equation 1.2. Where \(\rho\) is the material’s resistivity, L is the distance along the path-length, and A is the cross sectional area.
                                                                                                                                        \(R\alpha\frac{L}{A}=\rho\frac{L}{A}\ eqn\ 1.2\)
Combining Eq.1.1 and 1.2 implies smaller cross sectional areas generate higher resistances, higher heating, and higher temperatures. This makes it possible for the adopted methodology to create re-entry prototype models with temperature fields hottest at the centre (stagnation point) and coldest at the shoulder ends. Between the highest and lowest temperature is the thermal distribution zone which is a function of the material’s thermal conductivity. Since temperature is one of the major factors affecting graphite oxidation [4-13], great care must be taken to ensure a proper distribution of temperature field to achieve good laboratory results replicating real re-entry missions.