Estimating In-Depth Radiative Propoerties of Carbon Composites (Fiber Form)

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.