MAT_POWDER_BURN

Material properties

Beta command

This command is in the beta stage and the format may change over time.

*MAT_POWDER_BURN
"Optional title"
mid, $\rho$, $E$, $\nu$, did
$C_v$, $\gamma$, $e_0$, $b$, fid, $T_i$, $p_i$, $t_i$
local, $A$, $B$, $n$

Parameter definition

Variable
Description
mid
Unique material identification number
$\rho$
Density
$E$
Young's modulus (optional)
default: not used
$\nu$
Posson's ratio (only used if $E \gt 0$)
did
Damage property command ID
$C_v$
Heat capacity
$\gamma$
Heat capacity ratio $(C_p/C_v)$
$e_0$
Combustion energy per unit mass
$b$
Nobel-Abel co-volume parameter
fid
Burn rate function ID
$T_i$
Ignition temperature
$p_i$
Ignition pressure
$t_i$
Surface heating parameter
local
Local burn rate flag
$A$
Initial yield strength
$B$
Hardening parameter
$n$
Hardening exponent

Description

This material command is used to model unburned propellant as rigid or elasto-plastic grains and its combustion products as gas lumped into an overlapping CFD grid. The grains are assumed rigid, unless $E \gt 0$.

If $E \gt 0$ then the flow stress is defined as:

$\displaystyle{ \sigma_y = A + B(\varepsilon_{eff}^p)^n }$

The pressure of the generated gases is defined as:

$\displaystyle{ p = \frac{\gamma-1}{1 - \rho b} e}$

where $\rho$ is the current gas density and $e$ is the current specific internal energy. Note that $b$ has the units $m^3/kg$.

By default (local=0) the burn rate is uniform for each grain. That is, the average pressure and temperature is calculated and used for all element faces on the grain. If local=1, then the local pressure and temperature define the local burn rate for each individual element face.

A grain ignites if the local gas pressure $p_{CFD} \geq p_i$ and the grain surface temperature $T_g \geq T_i$. The grain temperature evolves according to:

$\displaystyle{ \dot T_g = \frac{T_{CFD} - T_g}{t_i} }$

The command POWDER_BURN_IGNITE can also be used to ignite grains inside a specific region.

Example

Propellant burning inside a small cylinderical space

Idealized rings of propellant burning inside a cylindrical container. The inner ring is ignited by depositing hot gases at time zero, using CFD_GAS.

*UNIT_SYSTEM SI *PARAMETER # # geometry and grid Ri = 0.06, "Inflator radius" hi = 0.03, "Inflator height" ri = 0.005, "Inflator hole radius" wi = 0.005, "Inflator wall thickness" L = 0.2, "CFD domain size" dc = 0.0015, "CFD cell size" # # powder properties dens_p = 1800.0, "Powder density" Cv_p = 1200.0, "Heat capacity" g_p = 1.2, "Powder gamma Cp/Cv" e0_p = 2.0e6, "Chemical energy per unit mass" b = 0.0005, "Co-volume parameter" Ti = 600.0, "Ignition temperature" pi = 3.0e5, "Ignition pressure" ti = 1.0e-5, "Grain surface heating parameter" eta0 = 0.3, "Initial porosity" # # igniting gas dens_g = 10.0, "Igniting gas density" g_g = 1.3, "Igniting gas gamma (Cp/Cv)" e0_g = 1.0e7, "Igniting gas energy (per unit volume)" Cv_g = 1000.0, "Igniting gas heat capacity" # # --- TIME --- # *TIME 0.001 # # --- MESH --- # *COMPONENT_CYLINDER "Inflator - 1" 1, 1, 1, 6 0, 0, [-%wi], 0, 0, 0, [%Ri] *COMPONENT_PIPE "Inflator - 2" 2, 1, 1, 24, 1 0, 0, [-%wi], 0, 0, 0, [%Ri], [%Ri+%wi] *COMPONENT_PIPE "Inflator - 3" 3, 1, 5, 24, 1 0, 0, 0, 0, 0, [%hi], [%Ri], [%Ri+%wi] *COMPONENT_PIPE "Inflator - 4" 4, 1, 1, 24, 1 0, 0, [%hi], 0, 0, [%hi+%wi], [%Ri], [%Ri+%wi] *COMPONENT_PIPE "Inflator - 5" 5, 1, 1, 24, 4 0, 0, [%hi], 0, 0, [%hi+%wi], [%ri], [%Ri] *MERGE_DUPLICATED_NODES P, 1, P, 1, 0.0001 *COMPONENT_PIPE "Powder 1" 6, 2, 5, 24, 1 0, 0, 0, 0, 0, [1.0*%hi], [2*%Ri/10], [3*%Ri/10] *COMPONENT_PIPE "Powder 2" 7, 2, 5, 24, 1 0, 0, 0, 0, 0, [1.0*%hi], [5*%Ri/10], [6*%Ri/10] *COMPONENT_PIPE "Powder 3" 8, 2, 5, 24, 1 0, 0, 0, 0, 0, [1.0*%hi], [8*%Ri/10], [9*%Ri/10] # # --- MATERIAL --- # *MAT_RIGID "Inflator" 1, 7800.0 *MAT_POWDER_BURN 2, [%dens_p] [%Cv_p], [%g_p], [%e0_p], [%b], 100, [%Ti], [%pi], [%ti] 1 *FUNCTION "Burn rate" 100 0.3 * (p / 1.0e5)^0.5 # # --- PART --- # *PART "Inflator" 1, 1 "Powder" 2, 2 # # --- BC --- # *BC_MOTION "Inflator" 1 P, 1, XYZ, XYZ # # --- CFD --- # *CFD_DOMAIN 1 0, 0, [%dc], 1, 10 [-%L/2], [-%L/2], [-%wi], [%L/2], [%L/2], [%L] 1, 1, 1, 1, 1, 1 *CFD_GAS "Igniting gas" 1 USER, 1 [%dens_g], [%g_g], [%e0_g], [%Cv_g] *GEOMETRY_PIPE "Igniting gas domain" 1 0, 0, 0, 0, 0, [%hi], [%Ri/4] *CFD_STRUCTURE_INTERACTION "Inflator" 1 P, 1, 1 *CFD_STRUCTURE_INTERACTION "Powder" 2 P, 2, 1 *END