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Governing Equations of Fluid Mechanics and Heat Transfer
Published in Dale A. Anderson, John C. Tannehill, Richard H. Pletcher, Munipalli Ramakanth, Vijaya Shankar, Computational Fluid Mechanics and Heat Transfer, 2020
Dale A. Anderson, John C. Tannehill, Richard H. Pletcher, Munipalli Ramakanth, Vijaya Shankar
A shock wave is a very thin region in a supersonic flow, across which there is a large variation in the flow properties. Because these variations occur in such a short distance, viscosity and heat conductivity play dominant roles in the structure of the shock wave. However, unless one is interested in studying the structure of the shock wave, it is usually possible to consider the shock wave to be infinitesimally thin (i.e., a mathematical discontinuity) and use the Euler equations to determine the changes in flow properties across the shock wave. For example, let us consider the case of a stationary straight shock wave oriented perpendicular to the flow direction (i.e., a normal shock). The flow is in the positive x direction, and the conditions upstream of the shock wave are designated with a subscript 1, while the conditions downstream are designated with a subscript 2. Since a shock wave is a weak solution to the hyperbolic Euler equations, we can apply the theory of weak solutions, described in Section 4.4, to Equation 5.205. For the present discontinuity, this gives [E]=0
Applied Chemistry and Physics
Published in Robert A. Burke, Applied Chemistry and Physics, 2020
Secondary effects of an explosion are shock-wave modification, fire and shock-wave transfer. There are three ways that a shock wave can be modified: it may be reflected, focused or shielded. Reflection refers to the shock wave striking a solid surface and bouncing off. When a shock wave strikes a concave (curved) surface, the force of the shock wave is focused, or concentrated, on an object or small area once it bounces off the concave surface. This effect is similar to the principle behind satellite dishes. When a signal reaches a satellite dish from the satellite in space, the signal is focused on the electronic sensor protruding out of the front of the satellite dish. Shielding simply means that the shock wave encounters an object too substantial to be damaged by the wave, so the shock wave goes around the object or is absorbed by it. The area immediately behind the object provides a place of shelter from the shock wave. Fire and shock-wave transfer involves the transfer of the shock-wave energy and fire to other objects, causing fires and destruction.
Methods of generation of shock waves and measurement of gas-dynamic parameters in dynamic experiments
Published in G. I. Kanel′, Shock Waves in Solid State Physics, 2019
Each experimental point on the Hugoniot is determined from the results of measurements of two independent parameters of shock compression, as a rule, the velocity of the shock wave and the particle velocity behind the shock jump. The pressure, specific volume and specific internal energy of the shock-compressed substance are then calculated on the basis of the laws of conservation of mass, momentum and energy in the form (1.12), (1.13), (1.14). The velocity of the shock wave is determined directly by measuring the time it takes to travel a previously measured distance, usually the sample thickness of the material under study. The overwhelming majority of data on the shock compressibility of condensed media was obtained using the methods of measuring wave and mass velocities based on the use of electrocontact sensors or flare gas gaps.
The influence of flexible/rigid obstacle on flame propagation and blast injuries risk in gas explosion
Published in Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 2023
Shuwei Yu, Yulong Duan, Fengying Long, Hailin Jia, Jun Huang, Yunbing Bu, Lul Zheng, Xiaohua Fan
The reflected shock wave between the flame front and the obstacle forms a positive feedback mechanism with turbulent combustion, which is one of the reasons for the acceleration of the flame in the later stage of the obstacle. In Figure 9, after the flame passes through the obstacle, different vortex degrees appear on the flame front, which promotes the reaction intensity. In contrast, the obstacle reflects the shock wave in the same direction as the flame front, which accelerates the reaction speed between the vortex center and the flame front and further promotes the growth of the surface area of the flame front. In the case of flexible obstacles, the shock wave causes the elastic deformation of the obstacles, and the obstacles absorb part of the shock wave. The acceleration effect of the reflected pressure wave on the flame front caused by the deformation is smaller than that of rigid obstacles. The absorption of shock waves by flexible obstacles plays a positive role in reducing the indirect and direct damage caused by reflected shock waves.
Comparative study of pulsed laser-induced breakdown at a metal-liquid interface at two liquid temperatures using a beam-deflection probe
Published in Journal of Modern Optics, 2022
Arindom Phukan, Prahlad K. Baruah, Alika Khare, Arpita Nath
In this section, the velocity attained by the primary pressure transient while propagating through cold (T = 293 K) and hot (T = 353 K) waters is estimated. The peak considered for the analysis is the primary peak (denoted by *) originating from the nickel target plasma. As seen in Figure 5(i) and (ii), velocities of the primary peaks are attributed to shockwave velocities. The shock waves reach peak velocities close to ∼1.7 mm for cold water and at ∼2 mm for hot water, which corresponds to a region of multiple plasma formation. The maximum velocity reached by the shock wave while propagating through cold water was ∼1.8 km/s and in the case of propagation through hot water was ∼1.9 km/s. The fluctuations in velocity values are represented as absolute standard deviations. This increase in velocity is expected as the density of hot water is less than that of cold water.
Buckling mechanism of pillar rockbursts in underground hard rock mining
Published in Geomechanics and Geoengineering, 2018
When an explosive charge is initiated within a blast hole, reactions take place resulting in production of large amount of gases at very high temperature and pressure in a very short time. The gas pressure subjects rocks beyond the hole to vast stress and strain. This strain pulse travels away from the shot point in all directions, transmitting energy and attenuating in amplitude as it propagates outward. The rocks around the blast hole can be divided into crushed zone, fractured zone and seismic zone. The crushed zone does not exceed 3–7 radii, while fracture zone averages 120 borehole radii away and extends to 150 radii (Bhandari 1997), and the seismic zone is beyond 150 radii as shown in Figure 2. Correspondingly, stress waves around (borehole) rock blasting can be divided into a shock wave, a strong elastic wave and a seismic wave. The shock wave is a high-amplitude pressure pulse that travels at supersonic speeds. As it propagates from the blast hole, shock wave degenerates into strong elastic wave and then seismic wave with characteristic of reduction in amplitude and change in dominant frequency.