Reflection of Shock Wave

If the angle of incidence is between regular and extreme, the so-called extreme regular reflection takes place 

In the so-called Mach reflection, the incident and reflected waves do not intersect on the ground but at some point above the ground. The lower portions of the incident and reflected waves fuse into one wave which is known as the Mach stem, M, (also known as Mach shock or Mach bridge). 

The point of intersection of I, R M is known as the triple point, TP. The resulting existence of the above three waves, causes a density discontinuity. The surface of this discontinuity, known as slipstream, S, represents a stream line for the flow relative to the intersection. Between this and the reflecting surface is the region of high pressure, known as Mach region here the pressure is approx twice that behind the incident wave. The top of this pressure region, the triple point, travels away from the reflected surface. As pressure and impulse appear to have their maximum values just above and below the triple point, respectively, the region of maximum blast effect is approximately that of the triple point 

Spark photography with shadowgraph, schlieren and interferometer techniques (such as described in. Vol 2 of Encycl, under CAMERAS) showed that density is uniform in zones I-TP-M and I-TP-R, but not in the zone R-TP-M, which includes the Mach region. The Mach shock M appears to be followed by rarefaction. Above the slipstream there is an angular variation of density so that, if measured at points farther and farther behind R, the density first rises to a maximum and then falls again For more detailed description of Mach waves etc, see Refs 2a, 3, 4, 5, 6, 7 and 8 Refs 1) Anon, Military Explosives , TM9-1910 (1955), PP 74-5 2) Dunkle s 

Sullabus (1957-1958), pp91-2 315 2a) Baum, Stanyukovich 3c She khter (1959), p 327 (Volna Makha) 3) J. Sternberg, Triple Shock Intersections , Physics of Fluids 2(2), 179-206(1959) 4) E.A. 

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FIG. 2.2. Reflection of shock waves, (a) Shock wave in denser medium. 

Spalling. In explosives technology implies the breaking off of a scab of material from a free face as a result of the reflection of shock waves (see p. 135). 

Reflection of Shock Waves from Rigid Barriers... 

Figure 2.38 gives the reflection of shock waves when they meet the vertical rigid unlimited walls. If the incident waves are one-dimensional steady ones, the refection waves are also one-dimensional steady waves. The parameters of air are Po) To, Po 0 = 0 before being bothered and the parameters of incident wave fronts are, Pq, Pi, Ti, and Vi. Because the wall is absolutely rigid, the air particles close to the wall are in a stationary state before reflection. When shock waves meet the rigid wall, the air particles near the wall produce the reflection waves with velocity/speed D2. The direction of reflection waves is the opposite of incident waves. The parameters of reflection wave fronts are P2, P2, P2 vi = 0 because of the rigidity of the wall. 

Fig. 2.38 The reflection of shock waves in semienclosed space when liquid explosives explode...

Fig. 2.40 The oblique reflection of shock waves on rigid surfaces/walls [21]...

The oblique reflection of shock waves occurs when the incident air shock waves have an angle 7 with the surface of a barrier. The angle 2 between the reflected waves and the surface of barrier may not be equal to 1. Di and D2 are the transportation velocities of incident waves and reflected waves. Because of reflection, the velocity component vertical to the surface equals zero (Fig. 2.40). 

White, D.R., An Experimental Survey of the Mach Reflection of Shock Waves, Technical Rept. II-IO, Department of Physics, Princeton Univ., Princeton, NJ, 1951. 

Hornung, H. (1988) Regular and Mach reflection of shock waves. Ann. Rev. Fluid Mech. 18 33-58. 

Understanding such interaction is important both in predicting the amplitudes of shock waves transmitted across interfaces (in the case where the equations of state of all materials are known), and in determining release isentropes or reflected Hugoniots (when measurement of the equation of state is needed). Consider first a shock wave in material A being transmitted to a... 

The pressure vessel under consideration in this subsection is spherical and is located far from surfaces that might reflect the shock wave. Furthermore, it is assumed that the vessel will fracture into many massless fragments, that the energy required to mpture the vessel is negligible, and that the gas inside the vessel behaves as an ideal gas. The first consequence of these assumptions is that the blast wave is perfectly spherical, thus permitting the use of one-dimensional calculations. Second, all energy stored in the compressed gas is available to drive the blast wave. Certain equations can then be derived in combination with the assumption of ideal gas behavior. 

Fig. 9.6 Schematic representation of shock wave propagation and the generation of a reflected expansion wave within a solid wall.

Fig. D-5 shows an external compression air-intake designed for optimized use at Mach number 2.0. Fig. D-6 shows a set of computed airflows of an external compression air-intake designed for use at Mach number 2.0 (a) critical flow, (b) sub-critical flow, and (c) supercritical flow. The pressures at the bottom wall and the upper wall along the duct flow are also shown. Two oblique shock waves formed at two ramps are seen at the tip of the upper surface of the duct at the critical flow shown in Fig. D-6 (a). The reflected oblique shock wave forms a normal shock wave at the bottom wall of the throat of the internal duct. The pressure becomes 0.65 MPa, which is the designed pressure. In the case of the subcritical flow shown in Fig. D-6 (b), the shock-wave angle is increased and the pressure downstream of the duct becomes 0.54 MPa. However, some of the airflow behind the obhque shock wave is spilled over towards the external airflow. Thus, the total airflow rate becomes 68% of the designed airflow rate. In the case of the supercritical flow shown in Fig. D-6 (c), the shock-wave angle is decreased and the pressure downstream of the duct becomes 0.15 MPa, at which the flow velocity is stiU supersonic.

Normal Reflection of Shock and Rarefaction Waves (82-4) Types of Interaction (86) Normal Reflection of Rarefaction (86-7) Normal Refraction of Shock and Rarefaction Waves (87-8) Head-on Collisions (88-9) Oblique Intersections (89 90) Oblique Interactions (90-1) Spherical Shock Waves (97-8) Distinction Between Shock and Detonation Fronts (163-66) Application to Solid Explosives (166-68) Principle of Similarity and Its Application to Shock Waves (307-10) Effects of Ionization in the Shock Front (387-90)... 

A feature of shock waves not yet considered is that there is inevitably a low pressure or rarefaction wave produced at the diaphragm at the same time as the shock wave. This moves initially in the opposite direction from the shock wave but is reflected by the back wall of the tube, and so eventually follows the main shock wave down the tube. Relative to laboratory coordinates this rarefaction wave travels with the local velocity of sound in the gas. This is considerably less than that of the shock wave because of the substantially lower temperature, but superimposed on it is the flow motion of the driver gas towards the low-pressure region. This has the result that the rarefaction wave tends to catch up with the shock wave. Because of the simplifications it allows, it is convenient to make the measurements on the shocked gas before the rarefaction arrives. This consideration is an important one in deciding on the relative positions of the diaphragm and observation points, and on the relative lengths of the high- and low-pressure areas . For a reason considered below, measurements are also sometimes made after the shock wave has been reflected from the front wall, but before the rarefaction wave has arrived. Such a situation is only used where absolutely necessary because it is now felt that the shock front is significantly distorted on reflection. 

All containers are made of mild steel. The magnitude of the shock wave associated with the explosive detonation increases by convergence of shock wave due to the reduction of cross section area and reflection on the conical wall of the water tank. The pressure level and shock duration can be easily controlled by adjusting the mass and detonation velocity of explosive and the conical angle of the water container. 

Fig. 2. a) radial inward shock phase b) reflected shock phase of plasma focus, and c) formation of shock wave driven by CS inward motion... 

Reflection of Shock and Explosion Waves from Surfaces Covered with Layers of Polyurethane Foam... 

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