A model for predicting the behaviour of a compressible flow laden with shocks interacting with granular material has been developed and tested. The model consists of two sets of coupled Euler equations, one for the gas phase and the other for the granular phase. Drag, convective, heat transfer and non-conservative terms couple the two sets of governing equations. Intergranular stress acting on the grains is modelled using granular kinetic theory in dilute regimes where particle collisions are dominant and frictional-collisional pressure in dense regions where layers of granular material slide over one another. The two-phase granular-gaseous model, as a result, is valid from dilute to densely packed granular regimes. The solution of these nonlinearly coupled Euler equations is challenging due to the presence of the non-conservative nozzling and work terms. A numerical technique, based on Godunov's method, was designed for solving these equations. This method takes advantage of particle incompressibility to simplify the nozzling terms. It also uses the observation that a Riemann problem is valid in the region where gas can flow between particles and can be used to provide a physically accurate approximation of the non-conservative terms. The model and solution method are verified by comparisons to test problems involving granular shocks and two-phase shock-tube problems, and they are validated against experimental measurements of shock and dense particle-curtain interactions and transmitted oblique granular shocks.

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This paper explores a model for a nonlinear one-degree of freedom passive vibration isolator system, known as a smart engine mount. Nonlinearities are employed to analyze and possibly improve the behavior of the optimal linear mount. Nonlinear damping and stiffness rates of the isolator have interacting effects on the dynamic behavior of the mount. The frequency response of the system is obtained using the averaging perturbation method, and a parametric analysis shows that the effect of nonlinear stiffness rate on frequency response is opposite to that of the nonlinear damping rate. Stability of the steady state periodic response has also been analyzed. Jump avoidance criteria are introduced, and the conditions for jump avoidance are studied. Closed form solutions for the absolute acceleration and relative displacement frequency responses are derived, since they are essential to use of the RMS optimization method.

Multidimensional numerical simulations of an unconfined, homogeneous, chemically reactive gas were used to catalog interactions leading to the deflagration-to-detonation transition (DDT). The configuration studied was an infinitely long rectangular channel with regularly spaced obstacles containing a stoichiometric mixture of ethylene and oxygen, initially at atmospheric conditions and ignited in a corner with a small flame. The channel height is kept constant at 3200 µm and obstacle heights varied from 2560 µm to 160 µm to decrease the blockage ratio (br) from 0.8 to 0.05. The compressible reactive Navier-Stokes equations were solved by a high-order numerical algorithm on a locally adapting grid.The initially laminar flame develops into a turbulent flame with the creation of shocks, shock-flame interactions, shock-boundary layer interactions, a host of fluid and chemical-fluid instabilities, and DDT.Several different DDT mechanisms are observed as the br is reduced. For br in the range of 0.5 to 0.35, the shocks in the unburned material diffract over the obstacles and reflect against the channel wall, forming Mach stems that increase in strength with every obstacle traversed. Eventually, the Mach stem strength is sufficient for the unburned mixture to detonate after it reflects from an obstacle. For br outside of this range, DDT may occur either through Mach-stem reflection or through direct initiation due to shock focusing. Stochasticity of the turbulence leading to DDT in channels with low br is considered.