MAT_POWDER_BURN_POROUS
Material properties
Beta command
This command is in the beta stage and the format may change over time.
"Optional title"
mid, $\rho$, $E$, $\nu$
$C_v$, $\gamma$, $e_0$, $b$, fid, $T_i$, $p_i$, $t_i$
$\eta_0$, $A$, $B$, $n$
Parameter definition
Description
This command is used to model unburned propellant as an elasto-plastic porous material. Finite Elements using this model should be coupled to an overlapping CFD grid. As the propellant burns, generated combustion producs are mapped to the CFD grid. The pressure and temperature in the CFD grid control the burn rate of the powder.
The pressure of the generated gases is:
$\displaystyle{ p = \frac{\gamma-1}{1 - \rho_{CFD} b} e}$
where $\rho_{CFD}$ is the current gas density and $e$ is the specific internal energy. Note that $b$ has the units $m^3/kg$.
The powder ignites if the local gas pressure $p_{CFD} \geq p_i$ and the powder temperature $T_p \geq T_i$. The grain temperature evolves according to:
$\displaystyle{ \dot T_p = \frac{T_{CFD} - T_p}{t_i} }$
The coupling force (per unit volume) between gas (CFD) and the porous powder is:
$\displaystyle{ \mathbf{f} = (1 - \eta) \cdot \rho_{CFD} \cdot (C_1 + C_2 \vert \mathbf{v}_{rel} \vert) \cdot \mathbf{v}_{rel} }$
where $\eta$ is the current porosity, $\mathbf{v}_{rel}$ is the local relative velocity between the CFD cell and the overlapping element. Note that the coupling must be defined with the command CFD_STRUCTURE_INTERACTION.
The powder can be assigned a shear strength with the flow stress (J2):
$\displaystyle{ \sigma_y = A + B(\varepsilon_{eff}^p)^n }$
Example
Gas generator
A small container is filled with porous powder using MAT_POWDER_BURN_POROUS. Combustion products generated during the process are evacuated through a hole at the top. The gas flow resistance through the powder bed is controlled with CFD_STRUCTURE_INTERACTION.
