Modelling of carbon-carbon composite ablation in rocket nozzles (7)

Two different woven architectures were compared (they will be referred to as A and B). As the description of such architectures by analytic means is complex and poorly realistic, the structure of the native composite was obtained using X-ray tomography with a voxel dimension of 20-20-20 μm3. The scans allow to recognize three phases: the yarns, the surrounding matrix and the pores. A region of 2-2-6mm3 was extracted from the whole scanned region. Such a volume contains a representative number of yarns. The initial structure of composite A is illustrated in the first picture of Fig.8.

Fig.8-3D-initial-and-ablated-morphologies-obtained-on-a-woven-composite

Fig.8-3D-initial-and-ablated-morphologies-obtained-on-a-woven-composite

The porosity was determined from the scans to be εA=10.4% and εB=9.7%. The final tortuosity for molecular diffusion in the vertical direction was determined from the scans as follows. A steady-state concentration field was computed using DiAbl3D by imposing an average vertical concentration gradient to the composite sample. This allows to calculate the effective diffusivity Deff  and, subsequently, the tortuosity, ηA and ηB. We found ηAA*Deff/D=15 and ηB=26. The obtained values show a good agreement with the values proposed by (47,48) for fibrous materials having a 3D structure. The ablative evolution of composite A is shown in Fig.8. As the composite has no stationary or even strictly periodic structure in the vertical direction the system does not reach a true steady-state profile. Nonetheless, the simulations have shown that after 0.2mm of recession, the thickness of the ablative front reaches a pseudo-steady state. At the studied temperatures, T=1850, 2300, 3000K, the associated Damkohler number defined with yarn properties takes the values Da=Kyarnlm/D=0.7, 1.1, 7. Under such conditions, the reactant is totally consumed in the first millimeters of the composite and does not penetrate deep inside the porous structure.

Fig.8 shows that, at the lowest temperature (T=1850K), the surface develops an important roughness. An estimation of the reaction front thickness was obtained using the maximum depth at which c=10-3co. The obtained values at this temperature are 1.1mm for composite A and only 0.7mm for composite B. So, gasification in composite B is limited to a thinner region than in the case of composite A. The obtained receding velocities are in the following ratio: Va|A/Va|B (T=1850K)=1.24. Under the chosen conditions, the ablation process occurs in a significant thickness of the porous material and is therefore influenced by the geometrcal structure of the porous domain. The explanation for the difference in behavior between sample A and sample B is that the penetration of the reactant is facilitated in the less tortuous material, which leads to a larger global reaction rate. When temperature increases, i.e., when Da increases, reaction occurs in a thinner domain. For instance, at T=3000K, which represents the temperature of the nozzle throat, the wall remains flat and the reaction front thickness is less than 60 μm for both composites. The difference of behavior between the two samples becomes negligible, as illustrated by the ablation velocity ratio value Va|A/Va|B (T=3000K)=1.02.

This study shows that at high temperature (T>2000K), the composite architecture plays a less significant role on its ablation behavior. When temperature reaches such values, ablation occurs only at the surface of the porous wall, even at the mesoscale.

In conclusion, the numerical simulations have shown the importance of the Damkohler number on the obtained morphologies. All other parameters remaining unchanged, a slower reaction rate leads to a higher roughness and an increase of the associated exposed surface.

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