6.10.3 Velocity
At the very early stages of the expansion the particle velocity profile shows the
general outward movement of the air at the shock front and the subsequent reversal
in the flow direction as the rapid outward expansion exhausts the air within the
sphere’s interior (Fig. 6.16). The formation of multiple internal shocks is shown in
Fig. 6.17 as previously observed in the case of the pressure profile. At late stages as
Fig. 6.8a Pressure as a function of normalized radius is shown during the early stages of the
expansion of the isothermal sphere at the times indicated. For the numerical procedure the following
parameters apply; Δλ ¼ 0.000457, λ s ¼ 0.0457,κ ¼ 1.2, Δτ ¼ 2 Â 10
À6 and γ ¼ 1.4
6.10 Results of the Numerical Integration for the Expanding Sphere
305
At the very early stages of the expansion the particle velocity profile shows the
general outward movement of the air at the shock front and the subsequent reversal
in the flow direction as the rapid outward expansion exhausts the air within the
sphere’s interior (Fig. 6.16). The formation of multiple internal shocks is shown in
Fig. 6.17 as previously observed in the case of the pressure profile. At late stages as
Fig. 6.8a Pressure as a function of normalized radius is shown during the early stages of the
expansion of the isothermal sphere at the times indicated. For the numerical procedure the following
parameters apply; Δλ ¼ 0.000457, λ s ¼ 0.0457,κ ¼ 1.2, Δτ ¼ 2 Â 10
À6 and γ ¼ 1.4
6.10 Results of the Numerical Integration for the Expanding Sphere
305