Fig. 5 Comparison of numerical and steady-steady theory predictions for the grain surface heat flux variation within the incident compaction
wave profile for φL = 0.99 and up = 100 m/s. The numerical predictions are given for N = 4, 000, 8,000, 16,000, and 32,000 computational
nodes
scaling, pulse-like variations in heat flux are predicted within
the compaction waves. For example, a magnified view of the
heat flux profile within the incident compaction wave for this
simulation is shown in Fig. 5 for t ≈ 0.11ms following piston
impact. The flux within this profile typically peaks at the
location ofmaximum inelastic compaction rate, and vanishes
at the end of the compaction zone; the width of this pulse
defines the compaction zone width δ. Returning to Fig. 4f, it
seen that the predicted peak heat flux significantly increases
approximately from 158 to 586MW/m2 as the incident wave
encounters the loose material due to a rapid increase in the
inelastic compaction rate, before obtaining a steady value
of 357MW/m2 within the transmitted compaction wave. A
simple estimate for the grain scale temperature rise generated
by inelastic heating can be obtained by depositing the dissipated
energy E = 4π