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26 Background for Aeroshell Modelling Chapter 2
is the work of Matsuyama et al. [87] in 2003. Their work extended that of Sakai and Sawada by
including more sophisticated modelling for the details of radiating flow: a modern multi-band
model with on the order of 10 3 wavelength points was used for the spectral detail; and the
transport was calculated with the tangent-slab approximation, as well 2D and 3D ray-tracing
techniques. In order to perform a calculation of such complexity, the code was parallelised
by dividing the wavelength range between various processors. In total, 128 processors of an
SGI ORIGIN 2000 were used to perform the calculations. This example goes some way to
demonstrating that fully-coupled radiating flow field calculations are not yet available as a
quick calculation aid for design work.
In terms of entry into Titan, recent calculations have focused on a 3.75 m diameter, 70 degree
sphere cone geometry as a proposed aerocapture configuration. In 2003, Olejniczak et al. [88]
reported on calculations of a nonequilibrium flow field to which the radiation calculation was
applied as a post-processing step. For the spectral modelling, both a modern multi-band code
(LORAN [67]) and a detailed line-by-line code (NEQAIR96 [89]) code were used. In both cases,
the radiation transport was approximated by using the tangent-slab approach and a correc-
tion for surface curvature was included by applying a reduction factor of 0.8. The authors
acknowledged that the radiative heating estimate was conservative because of the uncoupled
calculation. Nevertheless, they concluded that radiative heating is a significant design issue
for a Titan aerocapture mission, with the peak radiative heating rate being up to five times
larger than the peak convective heating rate. The authors also found that the radiation field
was optically thin for all conditions of interest.
In 2005, Wright et al. [90] extended the analysis of Olejniczak et al. [88] by performing
fully coupled radiation flow field calculations for the same proposed Titan aerocapture vehicle.
Wright et al. made use of the fact that the radiation field was optically thin; they were able to
fully couple the flow field and radiation calculation because the radiation transport problem
was reduced to an emitting gas only. In an emitting gas only, no absorption is considered, and
thus the radiation problem becomes one of volumetric heat sinks in the flow field calculation.
The emissivity properties of the gas were calculated based on curve fits which were constructed
from NEQAIR calculations. Only the CN red and CN violet bands were included in the cal-
culation of radiative emission — previous analyses had shown that these bands dominate the
radiation for this flow field. Wright et al. found that the fully coupled calculations gave a net
radiative heating rate that was a factor of 2 reduction on the value given using the tangent-slab
approximation. Also, in the stagnation region, the peak radiative heating was 25% less using
the “emission only” model with a view factor calculation instead of the tangent-slab approxi-
mation. The authors recommended the use of their approach for optically thin gases, or even
just the optically thin portion of a given spectrum, for other atmospheric-entry problems.
2.3 Summary
In this chapter, an introduction to the blunt body problem has been provided with focus on the
pertinent high-temperature phenomena: chemical and thermal nonequilibrium, and radiating