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.