Formation of Shock Wave

One assumes that a discontinuous flow occurs between regions 1 and 2, as shown in Fig. 1.2. The flow is also assumed to be one-dimensional and in a steady state, and not subject to a viscous force, an external force, or a chemical reaction. 

Using Eq. (1.25), the temperature ratio in regions 2 and 1 is represented by the Mach number in 2 and 1 according to 

Combining Eqs. (1.33) and (1.34), the Mach number relationship in the upstream 1 and downstream 2 is obtained as 

The solution expressed by Eq. (1.36) indicates that there is no discontinuous flow between the upstream 1 and the downstream 2. However, the solution given by Eq. (1.37) indicates the existence of a discontinuity of pressure, density, and temperature between 1 and 2. This discontinuity is called a normal shock wave , which is set-up in a flow field perpendicular to the flow direction. Discussions on the structures of normal shock waves and supersonic flow fields can be found in the relevant monographs. 

Substituting Eq. (1.37) into Eq. (1.33), one also obtains the temperature ratio as 

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Ultrasonic irradiation of a liquid leads to the generation of cavitation phenomenon which comprised of unique reaction fields in addition to physical and mechanical effects the formation of micro-meter sized bubbles, formation of bubbles with high temperature and high pressure conditions, formation of shock waves, and strong micro-stirring effects are produced. Table 5.1 shows representative ultrasound techniques to synthesize inorganic and metal nanoparticles and nanostructured materials. 

The compressed air introduced from the atmosphere through the air-intake is termed ram air , and the associated pressure is termed ram pressure . Ram pressure is built-up when the airflow velocity is decelerated in flow fields. The air-intake is designed as an aerodynamic tool to obtain maximum ram pressure.lh Air-intakes are designed to decelerate supersonic flow to subsonic flow by the formation of shock waves in front of them. The combustor in which the fuel gas is burned with the ram air is termed a ramburner . 

A zone of combustion, accompanied by a build-up of the pressure, developed in the wake of the shock front. This led sometimes to a) smooth acceleration of the latter until detonation was established b) formation of shock waves which overtook the front and caused deton or c) decay of the initial shock without deton. Compn and pressure limits were observed beyond which... 

Radius-time diagram of the formation of shock waves by the detonation of a spherical charge, log (1 / x) scale Fig 37... 

Earnshaw was the first to note that an acoustic wave of arbitrary form can propagate without deformation (so that all states propagate with the same velocity, i.e., steadily) only in the case of a linear relation between the pressure and specific volume. Actually, the adiabatic relation between the pressure and volume is not linear, and this is the reason for the deformation of acoustic waves, discovered by Poisson and Stokes and studied by Riemann, which leads to the formation of shock waves. 

The phenomenon of shock waves in gases seems to have been first predicted by Riemann in 1860 and analyzed quantitatively by Chapman, Jouguet, and then, from a kinetic point of view, Becker, who presented a very picturesque model for the formation of shock waves. 

Plasma formed as a result of the electrical breakdown at high pressure facilitates neck break, formation of a new bubble, and, probably, formation of shock waves and cumulative jets. 

The static reading on a Pitot tube is accurate to 0.5% for Mach numbers up to 0.5. For Mach numbers befween the values of 0.5 to 0.7 the accuracy increases to 1.5%. Above a Mach number of 0.7 fhe error can increase as much as 10% due to the formation of shock waves on and around the tip of the probe. Above a Mach number of 1.0 both the total and static readings vary significantly for the actual values [27]. The Mach number in the above example is calculated as follows ... 

Since the Mach number in this example is less than 0.7 we would not expect any error from formation of shock waves around the probe. 

Though the detonation pressure is not as high as brisant explosives, the reaction time of detonation is longer. Followed by the explosion products impacting the surrounding media and the formation of shock waves, the action time of positive pressure is much longer than the condensed explosives. This is the key feature of explosion from liquid explosives. Figure 2.30 is the explosion of 3,000 g liquid explosive. 

At a high Reynolds number, the drag coefficient shows an increase with Mach number reaching a maximum value for light supersonic flow. This increase is due to the formation of shock waves on the particle and the attendant wave drag (essentially form drag). Mach number effects become significant for a Mach number of 0.6, which is the critical Mach number, that is, when sonic flow first occurs on the sphere. 

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... 

In an elegant study of shock waves in dilute N2Os/Ar mixtures, Schott and Davidson278 have measured the low-pressure limit of the rate coefficient for pure N205 decomposition, /c42, by monitoring N03 and N02 formation behind the shock front. By subsequently following the decay of N03 they were able also to compute values of k30 and k43. These values, however, should be accepted with caution since there was some difficulty in separating the individual contributions of steps (30) and (43) to the total rate of N03 destruction. However, their rate... 

Fig. D-2 shows the shock-wave formation at a supersonic diffuser composed of a divergent nozzle. Three types of shock wave are formed at three different back-pressures downstream of the diffuser. When the back-pressure is higher than the design pressure, a normal shock wave is set up in front of the divergent nozzle and the flow velocity becomes a subsonic flow, as shown in Fig. D-2 (a). Since the streamline bends outwards downstream of the shock wave, some air is spilled over from the air-intake. The cross-sectional area upstream of the duct becomes smaller than the cross-sectional area of the air-intake, and so the efficiency of the diffuser is reduced. The subsonic flow velocity is further reduced and the pressure is increased in the divergent part of the diffuser.

He states that in the last few decades, Russian scientists have been studying with considerable success such questions as the propagation of shock waves, effects of explosions in complex media, effects of a powerful explosion in a nonhomogeneous atmosphere and at-great heights, formation and propagation of shock waves in shallow water, at the surface of a liquid, and in two-phase media. 

Under the title "Distant Effect of Detonation , Dr G.R. Loehr [PicArsn Translation No 5 (1956)1 translated from the German the paper by A. Haid entitled "Die Fernwirkung von Detonationen in Explosivstoffe 3, 139-44 (1955). The paper deals with the following subjects a) Formation of a compression shock wave b) Properties of shock waves c) Destructive effect of shock waves... 

Under the title "Formation of Pressure Wave , Cook (Ref 53, p 324) related the pressure rise in the front of an ait "shock wave to the point at which the initial air shock wave from unconfined charges is obliterated by the emerging gas cloud of the products of detonation. His table 13.3 (our Table 2) presents some selected thermodynamic data computed by R. Becker for air shocks relating, among other quan-... 

Cook (1958), Ionization in Shock Waves (pp 153-58) Thermal Effects of Shock Waves in Solids (213-16) Stability of a Shock Wave in an Inert Solid (216) Chapter 13. Shock Waves in Gaseous and Condensed Media, which includes Mechanism of Formation and Propagation of Shock Waves in Air and Water (322-24) Formation of Pressure Wave (324-26) Propagation of Pressure Wave in... 

Fig 32 The Separated Charge Arrangement and a Sketch of Shock Wave Positions at the Point of Mach Wave Formation... 

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