Overview of the CHarring Ablator Response (CHAR) Code

Abstract

JSC Engineering, Technology, and Science (JETS): Jacobs Technology and HX5, LLC An overview of the capabilities of the CHarring Ablator Response (CHAR) code is presented. CHAR is a one-, two-, and three-dimensional unstructured continuous Galerkin finite-element heat conduction and ablation solver with both direct and inverse modes. Additionally, CHAR includes a coupled linear thermoelastic solver for determination of internal stresses induced from the temperature field and surface loading. Background on the development process, governing equations, material models, discretization techniques, and numerical methods is provided. Special focus is put on the available boundary conditions including thermochemical ablation and contact interfaces, and example simulations are included. Finally, a discussion of ongoing development efforts is presented. Nomenclature α thermal diffusivity ( m 2 /sec) or coefficient of thermal expansion (K −1 ) or absorptivity α t , β t , γ t temporal finite-difference weights (sec −1 ) β extent of reaction also referred to as degree of char for volume fraction in virgin material γ P parameters for defining gas flow contact model stability ( m 2 /sec) and (sec) n unit normal vector κ permeability (m 2 ) λ Lamé's first parameter (Pa) or blowing reduction parameter R residual µ dynamic viscosity (Pa · sec) or Lamé's second parameters (Pa) ν Poisson's ratio Ω domain volume (m 3 ) φ porosity * Applied Aeroscience and CFD Branch 1 of 37 American Institute of Aeronautics and Astronautics Downloaded by MONASH UNIVERSITY on June 23, 2016 | http://arc.aiaa.org | This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States. AIAA Aviation ψ basis function ρ density ( kg /m 3 ) ρ e u e C H heat transfer film coefficient ( kg /m 2 ·sec) σ Stefan-Boltzmann constant ( W /m 2 ·K 4 ) or stress (Pa) σ P gas flow contact model stability parameter ( m /sec) and ( sec /m) σ T thermal contact model stability parameter ( W /m 2 ·K) τ shear stress (Pa) α coefficient of thermal expansion tensor (K −1 ) σ shear stress tensor (Pa) ε mechanical strain tensor C rotation matrix to shift coordinate reference framẽ K stiffness tensor (Pa) κ permeability tensor (m 2 ) k thermal conductivity tensor ( W /m·K) ε emissivity A element face area (m 2 ) b Klinkenberg parameter (Pa) B non-dimensional mass flux C specific heat ( J /kg·K) C H convective heat transfer Stanton number DE discretization error E activation energy ( J /kg) or Young's modulus (Pa) e o total internal energy ( J /kg) H convective heat transfer coefficient ( Wpre-exponential factor (sec −1 ) or roughness height (m) or thermal conductivity ( W /m·K) k + non-dimensional roughness height m reaction order N number of nodes nc number of components P pressure (Pa) p temporal order of accuracy q spatial order of accuracyfunction y effective mass fractions in solid DoF acronym for degree of freedom PDE acronym for partial differential equation TC abbreviation for thermocouple TPS acronym for thermal protection...

Computation of Effective Permeability for Porous Carbon Composites

“…Flow through TPS materials are computed by solving the combined solid-gas momentum transport equations. Historically, the momentum transport equations have been formulated as either surface models, one-dimensional volume averaged models [6,7], and more recently have been formulated as two/three-dimensional volume averaged models [8][9][10][11][12][13][14][15][16]. Such volume-averaged approaches [17] for momentum transport require model closure, in this case, the effective permeability of the material.…”

Development and Verification of Enclosure Radiation Capabilities in the CHarring Ablator Response (CHAR) code

“…The third candidate is the perpendicular to w, or ξ 3 = −e (1) , e (0) T . Because the box and segment are symmetric, we use Algorithm 1.…”

“…CHAR is a 1D/2D/3D material thermal response code which solves general heat transfer problems on decomposing charring ablators as well as non-decomposing, non-charring TPS materials, in serial or parallel. The general governing equations being solved in CHAR are briefly outlined in this section for completeness; however, a more complete description can be found in [1].…”

Inverse Heat Conduction Methods in the CHAR Code for Aerothermal Flight Data Reconstruction

“…It is implemented in the C++ programming language and is built on the libMesh library 26 . A more complete description can be found in references 27,28 .…”