As the development behind the CPR method is ultimately purposed towards nuclear det- onation simulations, a Taylor-Sedov blast wave can be set as an appropriate benchmark case. This case encapsulates many characteristics of a high energy simulation including a shock wave with a large instant pressure magnitude. A Sedov blast wave simulation also reveals flaws in a simulation framework that may be triggered via large energy errors. A sample Sedov blast wave was generated using a energy source with a high energy density with a small volume was introduced to an axisymmetric simulation. A rectangular Cartesian grid was defined with a length of 10 m and a width of 5 m. The spherical explosive device was placed at (5.0,0) with a radius of 0.0875 m. The device contained 105 J and the entire control volume had an initial density of 1.0 kg/m3. Material properties were governed by the ideal gas equation [29]. A Pressure wave solution obtained at t = 0.1 s is given in Figure 6.3.
Figure 6.3 Sedov blast wave - pressure solution
At the beginning of the simulation (t = ∆t), a sudden pressure jump of 1012Pa was created. Due to this sudden pressure amplitude, the Eulerian solver seems to have accumulated a large energy error. The AUTODYN simulation was adjusted to ignore the energy error and proceed with the shock wave. Both pressure and density data was extracted along the line, x = 5. These curves were compared with the corresponding analytical solution.
(a) Pressure Solution (b) Density Solution
Figure 6.4 Sedov blast wave
The solutions obtained by the simulations (shown in Figure 6.4) were slightly different from the analytic solutions. Both analytical and numerically obtained pressure solutions demon- strated a slight difference in x location of the peak while density solutions had a slight under prediction. Such differences are possible due to large energy errors and other simulation in- stabilities. However, these issues will be fixed in the future research with CPR method by introducing limiters and other stabilization criterion.
6.2 Thermal and Whipple Shield Development
Both thermal and Whipple shields will be subjected to extensive material testing with the use of AUTODYN. Composites such as Nextel and Kevlar should be tested with accurate material parameters to ensure structural strength. The new grid based CPR method coupled with fragmentation dynamics will allow researchers to determine the average size of a frag- ment which is crucial in determining Whipple shield thicknesses. A new time dependent heat radiation scheme will be introduced to the current steady state algorithm using COMSOL, a commercial multi-physics software .
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