An orthotropic material model is implemented in a three-dimensional material response code, and numerically studied for charring ablative material. Model comparison is performed using an iso-Q sample geometry. The comparison is presented using pyrolysis gas streamlines and time series of temperature at selected virtual thermocouples. Results show that orthotropic permeability affects both pyrolysis gas flow and thermal response, but orthotropic thermal conductivity essentially changes the thermal performance only. The pyrolysis gas flow is hypothesized to contribute to the thermal response of the material as it convects energy through the porous medium.
Nomenclature
A= face area of a control volume, m 2 A i = pre-exponential factor of solid component i, s −1 E i ∕R = activation energy of solid component i over universal gas constant, K E g = overall gas energy per unit volume, J∕m 3 or kg∕m s 2 E s = overall solid energy per unit volume, J∕m 3 or kg∕m s 2 Fo = Forcheimer number H = gas enthalpy, J∕kg K = material sample permeability, m 2 L = arc length; distance to the origin of Cartesian coordinate system,, kg∕m 2 s p = static pressure, Pa p w = sample surface pressure (p w 0 is the stagnation value), Pa q w = sample surface heat flux (q w 0 is the stagnation value), W∕m 2 S D = source term accounts for the energy loss in porous media flow, kg∕m s 3 T = temperature, K T react = reaction initiate temperature, K t = time, s V = volume of a control volume, m 3 Γ i = volume fraction of virgin solid composite i Δ = discretized term ϵ = small perturbations in numerical Jacobians calculation θ = rotation angle around z-axis (counterclockwise) λ = solid material thermal conductivity, W∕mK ρ g = overall density of pyrolysis gases, kg∕m 3 ρ s = overall solid density, kg∕m 3 ρ s i = density of solid component i, kg∕m 3 ϕ = porosity of material ψ i = phenomenological parameter of solid component i in reaction forumula ω = reaction rate of gas/solid species, kg∕m 3 s D = (D x , D y , D z ), diffusive source terms in momentum equations, Pa∕m F cond = (F cond;x , F cond;y , F cond;z ), conductive heat flux, W∕m 2 n = face normal direction P = vector of primitive variables Q = vector of conservative variables RHS = right-hand side of the linear system to be solved S = vector of source terms in a control volume u = (u, v, w), velocity components of Cartesian coordinates, m∕s F = convective flux through the face of a control volume F d = diffusive flux through the face of a control volume Subscripts c = char state of the material g = overall pyrolysis gas IP = in-plane orientation i = solid component i max, min = maximum and minimum values of boundary conditions s = overall solid TTT = through-the-thickness v = virgin state of the material w = sample surface wall x, y, z = components of Cartesian coordinate system
