Hydrodynamics of thermal granular convection

A hydrodynamic theory is formulated for buoyancy-driven ("thermal") granular convection, recently predicted in molecular dynamic simulations and observed in experiment. The limit of a dilute flow is considered. The problem is fully described by three scaled parameters. The convection occurs via a supercritical bifurcation, the inelasticity of the collisions being the control parameter. The theory is expected to be valid for small Knudsen numbers and nearly elastic grain collisions.Comment: 4 pages, 4 EPS figures, some details adde

Secondary shock delay measurements from explosive trials

Following detonation of an explosive material, a series of rarefaction expansion waves collapse inwards from the interface between the explosive and the surrounding air. These rarefaction waves coalesce at the centre of the explosive and reflect as a shock wave. Whilst these successive shocks are small in magnitude compared to the primary shock and are often ignored, the inward reflected shock immediately following the primary shock wave, typically referred to as the ‘secondary shock’, is a noticeable feature on blast pressure histories and usually arrives after the beginning of the negative phase. This paper presents results from medium and large scale surface blast tests where accurate measurements of secondary shock delay (time after arrival of the primary shock) are obtained for various explosives at various scaled distances. A method is presented for adjusting the secondary shock delay time by the product of the velocity of detonation divided by the cube-root of the packing density of the explosive. The relationship between this new secondary shock delay parameter and scaled distance is then found to be consistent for all explosives considered. This gives a new empirical method for estimating the yield of an explosive, or determining the velocity of detonation, based only on measurements of the secondary shock delay

Onset of thermal convection in a horizontal layer of granular gas

The Navier-Stokes granular hydrodynamics is employed for determining the threshold of thermal convection in an infinite horizontal layer of granular gas. The dependence of the convection threshold, in terms of the inelasticity of particle collisions, on the Froude and Knudsen numbers is found. A simple necessary condition for convection is formulated in terms of the Schwarzschild's criterion, well-known in thermal convection of (compressible) classical fluids. The morphology of convection cells at the onset is determined. At large Froude numbers, the Froude number drops out of the problem. As the Froude number goes to zero, the convection instability turns into a recently discovered phase separation instability.Comment: 6 pages, 6 figures. An extended version. A simple and universal necessary criterion for convection presente