On the shock dynamics of weak converging shock waves in solid materials
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On the shock dynamics of weak converging shock waves in solid materials R. K. Anand1 Received: 19 July 2020 / Accepted: 4 November 2020 © Università degli Studi di Napoli "Federico II" 2020
Abstract We presented a geometrical shock dynamics model to predict the behavior of weak converging shock waves in solid materials. Taking into consideration Mie–Grüneisen equation of state the analytical solution is obtained for the flow behind the converging shock-front propagating in solids. The analytical formaluas are also obtained for the shock velocity, pressure, density, particle velocity, temperature, speed of sound, adiabatic bulk modulus, and change-in-entropy behind or across the weak converging shock wave. For this it was assumed that the medium is a homogeneous and isotropic, and the disturbances behind the front do not overtake the converging shock waves. The effects due to an increase in (i) the propagation distance from the axis or centre of convergence, (ii) the Grüneisen parameter, and (iii) the material parameter, are explored on the shock velocity and quantities in the shocked titanium, brass, tantalum, iron, stainless steel 304, aluminum 6061-T6 and OFHC copper. The geometrical shock dynamics model provided a clear picture of whether and how the properties of solids are affected due to the passage of converging shock inside the solid materials. Keywords Converging shock wave · Geometrical shock dynamics · Analytical solution · Solid materials Mathematics Subject Classification 35L67 · 58J45 · 74J40 · 76L05
1 Introduction In recent years there has been renewed interest in converging shock waves in nonideal materials. A high-speed train enters the tunnel and a micropressure wave (loud noise) occurs at the tunnel exit. This is due to compression wave generated by the
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R. K. Anand [email protected]; [email protected] Department of Physics, UGC Centre of Advanced Studies, University of Allahabad, Prayagraj 211002, India
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train entering the tunnel. The shock wave is a most basic hydrodynamic phenomenon in various branches of physics. If the surface area of a shock decreases with time, as happens with converging shock, the strength of the shock wave rapidly increases. The shock waves are usually generated by laser beam focusing, point explosions (nuclear explosion and detonation of solid explosives, solid and liquid propellants rocket motors), high pressure gas containers (chemical explosions), etc. The problem of converging shock waves in an ideal gas was first studied by Guderley [1], and also independently by Landau [2] and Stanukovich [3]. In cylindrical or spherical geometries, a converging shock wave is cumulatively strengthened towards the axis or center of convergence, and produces high pressure and temperature. The geometrical shock dynamics approach was developed by Chester [4], Chisnell [5] and Whitham [6] in the mid of 1960s. The methods of the three authors are quite different, however, their final results are the same. According to the geometrical shock dyna
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