Development and Validation of SACRAM: A Swiss Approach to the Computational Response of an Ablative Material

Future space exploration missions foresee high-speed entries into planetary atmospheres. These latter imply extreme thermal conditions to which the space vehicle is exposed to, and require an appropriate thermal protection system (TPS). The interest of the scientific community in modelling and testing of materials that compose the TPS has hence greatly increased over the past few years. Since a complete set of material properties is not available in open literature, it is difficult to numerically rebuild experiments. The inter-code comparison exercise proposed by the AF/SNL/NASA Ablation Workshop aims to give a baseline platform for ablation code calibration, with a complete set of material and gas properties. SACRAM 1.0 is a one-dimensional, finite-volume code that solves transient mass and energy continuity equations for a carbon-resin composite material that undergoes pyrolysis and charring. Mass loss is calculated integrating Arrhenius laws, with the hypothesis that all decomposed solid material is transformed into gas, and no closed pores appear. The solid mass conservation law translates therefore in a conservation of the porosity. Darcys law is used in the momentum conservation equation to determine gas velocity in the pores. Time integration is performed with an implicit method, and non-linarites are treated with NewtonRaphson iterations. Thermal non-equilibrium between gas and solid phases, formulation of pyrolysis gas as a multi-species entity and internal radiative heat transfer are under development and will be implemented in SACRAM version 2.0. SACRAM will also help to increase European scientific interest and activity in the field of ablation, where currently US presence in primary. In fact in the session dedicated to this exercise at the 4th AF/SNL/NASA Ablation Workshop (1-3 March 2011, Albuquerque, New Mexico), out of the fourteen research groups that presented their results, only two were from European countries

Parallel mesh adaptive techniques for complex flow simulation: geometry conservation

Dynamic mesh adaptation on unstructured grids, by localised refinement and derefinement, is a very efficient tool for enhancing solution accuracy and optimising computational time. One of the major drawbacks, however, resides in the projection of the new nodes created, during the refinement process, onto the boundary surfaces. This can be addressed by the introduction of a library capable of handling geometric properties given by a CAD (computer-aided design) description. This is of particular interest also to enhance the adaptation module when the mesh is being smoothed, and hence moved, to then reproject it onto the surface of the exact geometry

MATHICSE Technical Report : A continuation multi level Monte Carlo (C-MLMC) method for uncertainty quantification in compressible aerodynamics

In this work we apply the Continuation Multi-Level Monte Carlo (C-MLMC) algorithm proposed by [Collier et al, BIT 2014] to efficiently propagate operational and geometrical uncertainties in compressible aerodynamics numerical simulations. The key idea of MLMC is that one can draw MC samples simultaneously and independently on several approximations of the problem under investigations on a hierarchy of nested computational grids (levels). The expectation of an output quantity is computed as a sample average using the coarsest solutions and corrected by averages of the differences of the solutions of two consecutive grids in the hierarchy. By this way, most of the computational effort is transported from the finest level (as in a standard Monte Carlo approach) to the coarsest one. In the continuation algorithm (C-MLMC) the parameters that control the number of levels and realizations per level are computed on the y to further reduce the overall computational cost. The C-MLMC is applied to the quasi 1D convergent-divergent Laval nozzle and the 2D transonic RAE-2822 airfoil

Tomography-based radiative characterisation of decomposing carbonaceous heat shield materials

This work evaluates the changes in radiative properties of two decomposing carbonaceous porous materials, each composed of two semitransparent, homogeneous and isotropic phases. The understanding of the complex dependence of macroscopic optical behaviour on material microstructure, bulk phase properties and the wavelength of incoming radiation is paramount for modelling, design and optimisation of systems incorporating such media. Experimental and numerical techniques were combined to solve the homogenised radiative transfer equations using Monte Carlo ray tracing in the limit of geometrical optics. Effective radiative properties required by these equations were determined by Monte Carlo techniques using the exact 3D microstructures of the samples, obtained through high-resolution synchrotron computed tomography. This methodology is applied to medium density carbon phenolic and high density graphite reinforced polymer composite, each composed of semi-transparent solid and fluid phases. The extent of material decomposition is seen to affect the absorption behaviour of both samples. This effect is more obvious in the lower density carbon phenolic, where an 18% increase in absorptance is observed due to decomposition, compared to an increase of just 2% for the graphite. A library of absorption data is presented for use in continuum heat transfer modelling of similar chemically reacting macroporous carbon composites

Re-entry survival analysis and ground risk assessment of space debris considering by-products generation

[EN] Space debris that re-enter the Earth's atmosphere can be partially or fully ablated along the trajectory path after hitting the atmosphere layers, once these become denser (approximately below 82 km). This paper combines reentry survival analysis to by-product generation analyses according to specific trajectory analysis and different levels of modelling within the re-entry simulation tool. Particular attention is made on metallic alloy decomposition and metallic oxides formation from the debris' materials ablation. Generic alloys present within satellite constructions are considered. The flow field in the induced shock layer is considered to be in non-equilibrium and the trajectory tool is based on a 3DOF object-oriented approach. The by-product analyses give important information on emitted species in the atmosphere at different altitudes, and the risk of substances reaching the ground is evaluated as a function of the initial break-up altitude. The non-equilibrium atmospheric chemistry within the shock layer has a significant impact for the re-entry analysis.This work was supported by the Swiss Government Excellence Scholarship (ESKAS No. 2019.0535) awarded by Federal Commission for Scholarships (FCS). The collaboration with UPV was partially financed as part of an activity performed with TAS-I in the context of an ESA subcontract ARA, under ITT-A0/1-8558/16/NL/KML.Park, S.; Navarro-Laboulais, J.; Leyland, P.; Mischler, S. (2021). Re-entry survival analysis and ground risk assessment of space debris considering by-products generation. Acta Astronautica. 179:604-618. https://doi.org/10.1016/j.actaastro.2020.09.03460461817

MATHICSE Technical Report : Continuation Multi-Level Monte-Carlo method for Uncertainty Quantification in Turbulent Compressible Aerodynamics Problems modeled by RANS

In this technical report we apply the Continuation Multi Level Monte Carlo (C-MLMC) algorithm to efficiently propagate operating and geometric uncertainties in internal and external aerodynamic simulations modeled by RANS. In particular, we discuss the construction of suitable mesh hierarchies and test the C-MLMC algorithm on the 2D RAE-2822 transonic airfoil and the 3D NASA Rotor 37 affected by operating uncertaintie

MATHICSE Technical Report : A continuation-multilevel Monte Carlo evolutionary algorithm for robust aerodynamic shape design

The majority of problems in aircraft production and operation require decisions made in the presence of uncertainty. For this reason aerodynamic designs obtained with traditional deterministic optimization techniques seeking only optimality in a specific set of conditions may have very poor off-design performances or may even be unreliable. In this work, we present a novel approach for robust and reliability-based design optimization of aerodynamic shapes based on the combination of single and multi-objective Evolutionary Algorithms and a Continuation Multi Level Monte Carlo methodology to compute objective functions and constraints that involve statistical moments or statistical quantities such as quantiles, also called Value at risk, (VaR) and Conditional Value at Risk (CVaR) without relying on derivatives and meta-models. Detailed numerical studies are presente

Characterising Internal Heat Transfer in Thermal Protection Systems

Thermal protection systems (TPS) are employed for spacecraft to survive high temperature conditions during atmospheric re-entry. For space shuttle type re-entries, the use of ceramic tiles shield the payload from exposure to these high heat fluxes. Recent research into the use of low-density materials, such as alumina foams, brings its own scientific challenges, of which understanding internal heat transfer is one. To this end, the exact 3D geometry of their complex porous structures, before and after plasma torch heating, is obtained by tomography and used in direct pore-level simulations to numerically calculate their effective heat transfer properties. Morphological characterisation is conducted via two-point correlation functions and mathematical morphology operations. Porosity and hydraulic pore diameter are seen to increase from the pre-heating (virgin) to the post-heating (charred) sample. Collision-based Monte Carlo methods are then used for radiative heat transfer characterisation. A decrease in extinction coefficient is noted between the virgin and charred samples. Both samples exhibit a large backward scattering peak for diffusely reflecting surfaces

Continuation Multilevel Monte Carlo Evolutionary Algorithm for Robust Aerodynamic Shape Design

The majority of problems in aircraft production and operation require decisions made in the presence of uncertainty. For this reason, aerodynamic designs obtained with traditional deterministic optimization techniques seeking only optimality in a specific set of conditions may have very poor off-design performances or may even be unreliable. In this work, a novel approach for robust and reliability-based design optimization of aerodynamic shapes based on the combination of single- and multi-objective evolutionary algorithms and a continuation multilevel Monte Carlo methodology is presented, to compute objective functions and constraints that involve statistical moments or statistical quantities, such as quantiles, also called value at risk and conditional value at risk, without relying on derivatives and meta-models. Detailed numerical studies are presented for the RAE 2822 transonic airfoil design affected by geometrical and operational uncertainties

A Parallel Adaptive Newton-Krylov-Schwarz Method for 3D Compressible Inviscid Flow Simulations

A parallel adaptive pseudo transient Newton-Krylov-Schwarz (αΨNKS) method for the solution of compressible flows is presented. Multidimensional upwind residual distribution schemes are used for space discretisation, while an implicit time-marching scheme is employed for the discretisation of the (pseudo)time derivative. The linear system arising from the Newton method applied to the resulting nonlinear system is solved by the means of Krylov iterations with Schwarz-type preconditioners. A scalable and efficient data structure for the αΨNKS procedure is presented. The main computational kernels are considered, and an extensive analysis is reported to compare the Krylov accelerators, the preconditioning techniques. Results, obtained on a distributed memory computer, are presented for 2D and 3D problems of aeronautical interest on unstructured grids