/MAT/LAW41 (LEE_TARVER)

The Lee-Tarver model is based on the assumption that the ignition starts at local hot spots in the passage of shock front and grows outward from these sites. The reaction rate is controlled by the pressure and the surface area as in a deflagration process.

Format

Definitions

Example (LX17)

#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  2. MATERIALS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/LAW41/1
LX17 (unit Mg-mm-s)
#              RHO_I               RHO_0
                1900                   0
#    Ireac
         2
#                 Ar                  Br                 R1r                 R2r                 R3r
       4930000000000       -166000000000                7.44                3.72           3.3337E-5
#                 Ap                  Bp                 R1p                 R2p                 R3p
        696000000000          2500000000                 4.4                 .94              4.3E-6
#                Cvr                 Cvp                  Eq
                2781                1000                .088
#     iter                           EPS               check
         0                             0                   0
#                rki                  ex                  ri
           100000000                   1                   4
#                rkg                  yg                  zg                 ex1
          1000000000                .371                   3                .191
#                  K                   X                 tol
                   0                   0                   0
#              grow2                 ex2                 yg2                 zg2
                   0                   1                   1                   1
#              ccrit               fmxig               fmxgr               fmngr
                   0                 .25                   1                 100
#                  G                  Ti
            75000000                 298
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

1. If f is the mass fraction of the products and p is the reduced pressure:
   Ireact = 1: "Ignition and growth" according to Lee/Tarver(1)

   $${\frac{df}{dt})}_i=r_{ki}\cdot {\left(1-f\right)}^{ex}\cdot {\left(\frac{\rho }{{\rho }_0}-1\right)}^{r_i}$$

   (2)

   $${\frac{df}{dt})}_g=r_{kg}\cdot {\left(1-f\right)}^{ex}\cdot f^{y_g}\cdot f^{z_g}$$
   Ireac = 2: "Ignition and growth" according to the formulation introduced in Dyna-2D(3)

   $${\frac{df}{dt})}_i=r_{ik}\cdot {\left(fmxig-f\right)}^{ex}\cdot {\left(\frac{\rho }{{\rho }_0}-1-ccrit\right)}^{r_i}$$

   (4)

   $${\frac{df}{dt})}_{g1}=gro{w}_1\cdot {\left(1-f\right)}^{ex1}\cdot f^{y_{g1}}\cdot P^{z_{g1}}$$

   (5)

   $${\frac{df}{dt})}_{g2}=gro{w}_2\cdot {\left(1-f\right)}^{ex2}\cdot f^{y_{g2}}\cdot P^{z_{g2}}$$
2. Coefficient grow₁ is initialized by r_kg
3. Coefficients y_g1 and z_g1 are respectively initialized by y_g and z_g.
4. Coefficients R₃ and $\omega$ are linked by the relation: $R_3=\omega C_{\nu }$
5. Coefficients fmxgr and fmngr are the limiters of the growth rate according to the mass fraction of products.
6. This material law is not compatible with ALE.
7. Heat of reaction $E_Q$ is supposed to be constant whatever the value of F is.
8. Reagent pressure and detonation products pressure are computed using a modified Jones-Wilkins-Lee equation of state:
   In terms of relative volume $v$ :(6)

   $$\mathrm{P}\left(v,T\right)=A{e}^{-R_{1}v}+B{e}^{-R_{2}v}+R_{3}Tv$$

   Where, $v=\frac{V}{V_0}$

   In terms of $\mu$ :(7)

   $$\mathrm{P}\left(\mu ,T\right)=A{e}^{-R_1/\left(1+\mu \right)}+B{e}^{-R_2/\left(1+\mu \right)}+R_{3}T/\left(1+\mu \right)$$

   Where, $\mu =\frac{\rho }{{\rho }_0}-1=\frac{1}{v}-1$ .