## Grants and Contracts Details

### Description

1 Alignment and relevance to NASA
Perceived impact: It had been previously believed that the incoming radiative flux was either reflected at
the surface or absorbed within a 1 mm thickness of the surface [1]. Since most TPS are far thicker than this 1
mm absorption zone, the penetration of radiation within the heat shield has always been neglected. However,
a recent experimental study shows that spectral radiation can penetrate the ablator and affect the material
response over a significant depth, with higher intensity emissions penetrating deeper into the ablator [2].
Since shock layer radiation is dominated by single wavelength emissions, it is important to account for this
in-depth radiation inside TPS materials.
Proposed research: To capture the in-depth penetration of radiation into the material, we will explicitly
account for the microstructure of carbon composites (FiberForm) to determine the radiative properties that
are required to model radiation transport in TPS materials. In CFD and material response codes, the radiation model that is implemented is the P-1 model, which is an approximate solution of the radiative transport
equation that uses spherical harmonics. This model was chosen for its ease of integration, and its relative
accuracy for both optically thin and thick domains. The P-1 radiation model requires absorption, scattering,
and phase function coefficients as inputs. This research effort will provide the coefficients for the
P-1 model by simulating the transport of photons through the microstructures of FiberForm.
The proposed research will leverage a funded NASA ESI-18 effort (Panesi & Martin, 80NSSC19K0218) which
has a subtask on TPS radiation modeling. However, that effort proposed to implement a cruder model, with
properties obtained from the literature.
Current state-of-the-art: Theoretical work on a single fiber and fibrous medium shows that the radiative properties (coefficients) are a function of fiber orientations [3, 4]. The extinction (both absorption
and scattering) coefficients are largest for fibers oriented parallel to the boundaries, lowest if they are oriented
normal to the boundaries, and intermediate for random orientation. The scattering phase function coefficient
was also shown to be different for random and non-random fiber orientations. Therefore, the coefficients for
carbon-phenolic composites need to be obtained by accounting for the microstructure of the TPS material
(FiberForm).
Technical path: We will use a Monte Carlo Radiation (MCR) technique to obtain the radiative properties. MCR is similar to the direct simulation Monte Carlo method allowing us to use the Sparta code [5] as
the baseline starting point. A set of photon packets (modeled as particles) will interact with the microstructure for given incident intensity and wavelength. As the particles collide with the fibers, they can absorb,
scatter, or re-emit. The absorption, scatter, and re-emission coefficients on a single fiber (cylinders) depend
on the relative directions of the incident radiation and fiber orientation as well as the incident intensity [3].
The coefficients for a single fiber [3] will be used to quantify the in-depth/effective coefficients within the
TPS material. An example simulation is shown in Fig. 1, where photon packets collided with the fibers with
a fundamental extinction (absorption/scattering) coefficient of 0.1. The result shown in Fig. 1 provides the
in-depth penetration of radiative emission into the TPS material. This information can then be transferred
into material response codes that account for radiation modeling.
2 Detailed Approach
Task 1: Implementation of Scattering and Absorption Cross-Sections: Since photons have a wave-effect,
the interaction cross-sections can be greater than the geometric cross-sections. The existing cut-cell method
in Sparta will be extended to include this effect. The coefficients available on a single fiber (cylinder) [3] will
then be incorporated into the code as tabulated data/fit functions. Initial validation of the MCR code will
be performed using spectral reflectance data that is available for fiber materials composed of silica, alumina,
and silicon carbide, where the fiber radius ranges from 1-15 microns [4].
Task 2: Validation and Statistical Computations: The required radiative properties will be generated over
thousands of statistically representative microstructures for the desired wavelengths. This is an essential
step to quantify the variability that is observed in the microstructures of FiberForm. The microstructures
will be generated using FiberGen (or Otter, which is currently being used for a parallel effort on mechanical properties). The relevant information will be transferred into KATS-MR and will be easily portable to
other material response codes such as ICARUS or CHAR. It should be noted that CHAR already has a 1D
diffusion radiation model implemented. Detailed validation will be performed by comparing to experiments
from LHMEL facility, where the depth of char zone was measured for two different emission intensities [2].
Task 3: Coupled Radiation, Convection, and Conduction: Since the MCR code will use the Sparta platform, it can be easily interfaced with microscale simulations using DSMC that include in-depth penetration
of boundary layer gases, the expulsion of pyrolysis gases, and heat conduction through the microstructures.
This task will help us combine all energy transfer and chemical processes occurring within the microstructures of FiberForm. This will be greatly beneficial to look for failure modes in TPS materials when all
processes are occurring simultaneously, instead of examining isolated processes, which ignores the influence
of competing/complementary processes that can result in failure.

Status | Active |
---|---|

Effective start/end date | 6/1/20 → 5/31/24 |

### Funding

- National Aeronautics and Space Administration: $240,000.00

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