The Physics of Rubber Elasticity (J. Meixner)

The complex flow and wave pattern following an initially planar shock wave transmitted through a double-bend duct is studied experimentally and theoretically/numerically. Several different double-bend duct geometries are investigated in order to assess their effects on the accompanying flow and shock wave attenuation while passing through these ducts. The effect of the duct wall roughness on the shock wave attenuation is also studied. The main flow diagnostic used in the experimental part is either an interferometric study or alternating shadow–schlieren diagnostics. The photos obtained provide a detailed description of the flow evolution inside the ducts investigated. Pressure measurements were also taken in some of the experiments. In the theoretical/numerical part the conservation equations for an inviscid, perfect gas were solved numerically. It is shown that the proposed physical model (Euler equations), which is solved by using the second-order-accurate, high-resolution GRP (generalized Riemann problem) scheme, can simulate such a complex, time-dependent process very accurately. Specifically, all wave patterns are numerically simulated throughout the entire interaction process. Excellent agreement is found between the numerical simulation and the experimental results. The efficiency of a double-bend duct in providing a shock wave attenuation is clearly demonstrated.

Experimental and theoretical study of shock wave propagation through double-bend ducts

The paper describes new experimental results regarding the pressure fields in front of and inside granular layers of different materials during their collision with weak shock waves. A variety of waves result from the shock wave-granular layer interaction. The pressure behind the reflected wave from the material interface approaches the equilibrium value, P5, which would have been reached had the shock wave reflected from a solid end-wall.

Experimental investigation of the interaction between weak shock waves and granular layers

Shock wave interaction with cellular materials: Part I: analytical investigation and governing equations

A space-time smooth artificial viscosity method with wavelet noise indicator and shock collision scheme, Part 2: The 2-D case

The head-on collision between a normal shock wave, propagating into a quiescent gas, and a rubber-supported plate was investigated theoretically and experimentally. In the theoretical part, a physical model was developed for describing the collision process. Three different modes in which the rubber could be loaded, due to its collision with the incident shock wave, were studied. They are: uni-axial stress loading, bi-axial stress loading and uni-axial strain loading. In the first two modes the rubber can expand while carrying the shock-wave induced compressive load, and therefore can be treated as an incompressible medium. This is not the case in a uni-axial strain loading where the rubber cannot expand while carrying the shock-wave-induced load. The model developed was based on both the conservation equations and on an appropriate strain stress relation which describes the rubber behaviour under loading. The model was solved numerically for each of the above-mentioned loading modes. Experiments were conducted in a shock tube; the rubber response to its collision with normal shock wave was studied for the case of bi-axial stress loading. Pressures, in the gas, and stresses, in the rubber, were recorded by using piezoelectric pressure transducers; the shock-wave reflection, in the gas, and the rubber displacement and compression processes were recorded on successive shadowgraphs. Good agreement was found between the experimental and numerical results for the case of bi-axial stress loading. This agreement validates the model developed for the collision process and the reliability of the numerical scheme used for its solution.

Head-On Collision of Normal Shock Waves with a Rubber-Supported Wall

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Head-On Collision of Normal Shock Waves with a Rubber-Supported Wall