For the gas phase we solve the zero Mach number Navier-Stokes equations for a variable density gas, the energy equation, species equations and suitable chemical kinetics. We have assumed that all Lewis numbers are equal to unity, and use temperature dependent transport. Currently we use the simplest possible kinetic scheme: decomposition of the AP gases, and reaction between the AP decomposition gases and binder gases.
For the solid phase we initially ignore deformation, compressibility, etc, and hence only solve the unsteady heat equation with constant thermal properties. We do, however, allow for the different thermal and mechanical properties of the AP and binder (i.e., different thermal conductivity and density for AP and binder).
The connection conditions at the gas-solid phase interface include continuous mass flux and temperature, as well as mass flux conditions for the temperature and species. In the gas phase far field region away from the propellant surface all quantities have zero normal derivatives, and in the solid phase the temperature is held fixed deep into the solid.
The surface regresses normal to itself with a speed $r_b$ (>0), and we assume that $r_b$ is defined by simple pyrolysis laws, one for AP and one for the binder. The surface $\psi(x,y,z,t)=0$ is represented by the kinematic condition as shown in the figure to the left.
Here, $\vec{n}$ is a unit vector, normal to the surface, pointing into the gas. A level-set formulation is used in which the field variable $\psi(x,y,t)$ is evaluated, and the propellant surface is determined by the zero contour.
Instead of solving this kinematic equation directly, we first transform the physical space into a computational space where the surface is fixed in time and flat via the transformation $\psi=y-f(x,z,t)$. Then in the computational space a simple Hamilton-Jacobi equation for $f$ emerges, which is solved by using high-order WENO solvers.
T.L. Jackson (webmaster)
E-mail: tlj@csar.uiuc.edu
URL: www.csar.uiuc.edu/~tlj
Site Last Modified: February 1, 2003