About 50 - 60 % of the total energy released by a nuclear explosion in air is converted into a blast wave [1]. When the burst point is not too high above the ground, a significant mass of dust and sand is lofted and entrained into the blast flow fields. Detailed computation of lofting effect is important since this dust may carry adsorbed fission products to large distances. In circumstances where dust is being lofted, the shock wave propagates in a heavy air-particles suspension rather than in a pure air. Constitutive characteristics of the suspension have a major effect on the wave propagation [2]. Thus, in computational modeling of the blast wave several phases have to be accounted for (air, dust, sand etc.), including inter-phase coupling effects. The lofting phenomenon is then modeled by boundary conditions based on an extended boundary layer theory that takes into account lofting of sand particles into the air flow [3, 4].
A sweep-up model [5] was incorporated in a 2-phase GRP scheme, aimed at calculating the flow field due to high speed wind blowing over a flat sandy surface. It has been observed that particle saltation takes place at wind velocities higher than some threshold. The sweep-up regime starts at a velocity about an order of magnitude higher than the threshold value, where the turbulent drag force can overcome the gravitational free fall. Gaj and Small [5] provide an approximate expression for the vertical dust mass flux lofted by the wind, as a function of wind velocity and air density.
The GRP hydrodynamic method [6] has been extended to treat a gas-particles suspension, assuming dynamic (velocity) and thermodynamic (temperature) equilibrium. The modified scheme was applied to calculate flows with dust lofting from the ground. The boundary conditions for such flows are formulated in terms of a sweep-up model. This equilibrium approximation is based on the assumption that the gas-particle relaxation time is much smaller than all other time scales of the flow field. The equilibrium suspension is then treated as a (single-phase) compressible fluid. Taking an ideal gas EOS for air, the suspension EOS is also an ideal gas with a load-dependent adiabatic index given by [7]
γ=1+(γair-1) / [1+γairδα/(1-α)]
where α≡ρdust/ρtotal is the dust mass fraction and δ≡Cdust/CP,air is the heat capacities ratio.
The modified GRP code was used to calculate spatial and temporal distribution of lofted dust either by a nuclear burst, or by a steady high speed wind. We present and discuss several cases of blast waves with lofted dust distributions obtained by our calculations for a variety of yield and HOB values.
[1] Glasstone and P.J. Dolan, The Effects of Nuclear Weapons. UOD & DOE, 1977.
[2] E. Needham. Blast Waves. Springer, 2010.
[3] Mirels, Blowing model for turbulent boundary layer dust ingestion. AIAI Journal, 22:1582–1589, 1984.
[4] Hartenboum, Lofting of particulates by a high speed wind. Technical report, Applied Theory, Inc., 1971.
[5] A. Gaj and R.D. Small, Target Area Operating Conditions - Dust Lofting from Natural Surfaces. Technical Report, Pacific-Syerra Research Corporation, 1991.
[6] Ben-Artzi and J. Falcovitz, Generalized Riemann Problems in Computational Fluid Dynamics. Cambridge University Press, 2003.
[7] Rudinger, Fundamentals of Gas-Particle Flow. Elsevier, 1980.
