Pressure wave propagation

Water Hammer When hquid flowing in a pipe is suddenly decelerated to zero velocity by a fast-closing valve, a pressure wave propagates upstream to the pipe inlet, where it is reflected a pounding of the hne commonly known as water hammer is often produced. For an instantaneous flow stoppage of a truly incompressible fluid in an inelastic pipe, the pressure rise would be infinite. Finite compressibility of the flmd and elasticity of the pipe limit the pressure rise to a finite value. The Joukowstd formula gives the maximum pressure... 

Figure 3.64 Measured and calculated pressure wave propagation velocity in air-water mixtures at 25 psia. (From Henry et al., 1969. Copyright 1969 by Plenum Publishing, New York. Reprinted with permission.)... 

High-frequency pressure oscillations (10-100 Hz) related to time required for pressure wave propagation in system Low-frequency oscillations (-1 Hz) related to transit time of a mass-continuity wave Occurs close to film boiling... 

Henry, R. E., 1970, Pressure Wave Propagation in Two-Phase Mixtures, AIChE Chem. Eng. Prog. Symp. Ser. 66(102) 1-10. (3)... 

A pressure wave propagating in air is called a blast wave because the pressure wave is followed by a strong wind. A shock wave or shock front results if the pressure front has an abrupt pressure change. A shock wave is expected from highly explosive materials, such as TNT, but it can also occur from the sudden rupture of a pressure vessel. The maximum pressure over ambient pressure is called the peak overpressure. 

The speed uw with which a small pressure wave propagates through a fluid can be shown [Shapiro (1953)] to be related to the compressibility of the fluid dp/dP by equation 6.65 ... 

Assuming that the pressure wave propagates through the fluid polytropi-cally, then the equation of state is... 

In practice, small pressure waves (such as sound waves) propagate virtually isentropically. The reasons for this are that, being a very small disturbance, the change is almost reversible and, by virtue of the high speed, there is very little heat transfer. Thus the speed of sound c is equal to the speed at which a small pressure wave propagates isentropically, so from equation 6.69... 

A simple interpretation of this choking condition is as follows. The gas flows as a result of the pressure difference P — P2. When the gas speed reaches the speed at which a pressure wave propagates relative to the gas, any pressure wave generated will be unable to travel upstream but will remain stationary relative to the pipe. Thus, if the pressure in the reservoir into which the gas discharges is reduced below Pw, the fact cannot be transmitted upstream and so the flow rate will not change. 

If the valve is closed more quickly, the pressure rise will be correspondingly greater. It might be thought that if the valve were closed instantly the pressure rise would be infinite. This is not the case. When a valve is closed suddenly, a pressure wave propagates upstream at approximately the speed of sound in the fluid and only the fluid through which the pressure wave has passed is decelerated thus the pressure rise is finite because the speed of sound is finite. 

In the free field, the blast wave from an explosion travels at or above the acoustic speed for the propagating medium. TM 5-1300 provides plots of shock front velocity vs. scaled distance for high energy TNT explosives. There are no similar plots available for pressure wave propagation. However, for design purposes it can be conservatively assumed that a pressure wave travels at the same velocity as a shock wave. In the low pressure range, and for normal atmospheric conditions, the... 

The pressure wave propagating through the premixed LNG and water collapses the vapor film surrounding the LNG. Intimate liquid-liquid contact occurs and, since the interface temperature is above T i, rapid heat transfer and vaporization occur. The time scale of the vaporization is comparable to that of the trigger step. Propagation and escalation then result. 

There are inherent phenomena associated with gas-solid flows. Such phenomena are of considerable interest to a wide spectrum of process applications involving gas-solid flows and can be exemplified by erosion, attrition, pressure-wave propagation, flow instability, and gas-solid turbulence modulation. 

The propagation of pressure waves such as acoustic wave, shock wave, and Prandtl-Meyer expansion through a gas-solid suspension is a phenomenon associated primarily with the transfer of momentum although certain processes of energy transfer such as kinetic energy dissipation and heat transfer between gas and solids almost always occur. Typical applications of the pressure wave propagation include the measurements of the solids concentration and flow rate by use of acoustic devices as well as detonation combustion such as in a rocket propellant combustor or in the barrel of a gun. 

Flg.3 presents numerical predictions of the strain histories in the bottle at two different positions - 25 and 50 mm from the base. As soon as the bottle hits the floor, a compressive pressure wave is generated and starts to travel towards the top of the bottle, deforming the bottle wall. As expected, the position nearest to the base (25 mm) is first reached by the pressure wave, followed by the position further away, i.e. pressure wave propagation can be observed by the time delay between strain histories at different positions. The process is very similar to the water-hammer phenomena in pipelines, and is characterised by a slnusoid-llke wave. The high frequency oscillations superimposed on the main signal are due to natural oscillation of the bottle. 

Similar behaviour, pressure wave propagation characterised by the time delay between different positions, can also be seen in experimental results (Fig.4), which is opposed to the observations made by Reed et. al. [1]. Superimposed oscillations with higher frequency are also present in the trace. However, the longer low-pressure period can be seen in the experimental results just after 2 ms. This is due to cavitation that takes place during the experiment. In the numerical simulation, cavitation is not modelled, and pressure can drop below absolute zero. 

For optimizing pressure wave propagation FAE are ignited similar to nuclear-weapons in a defined distance above ground zero. So they often produce an atomic-mushroom-like smoke signature and blast characteristics making them look like mini Nukes . 

Whereas in the case of an explosion the pressure wave propagates at a subsonic rate, the speed of pressure propagation in the case of a detonation is much higher and lies in the supersonic range. At normal temperatures, a detonation will not be... 

SHOCK AND PRESSURE WAVE PROPAGATION IN NANO-ELUIDIC SYSTEMS... 

To what extent shock and pressure wave propagation occurs in nano-fluidic systems cannot be determined by classical simulation, nor has it been studied experimentally. If, in the future, such behavior were observed, a quantum mechanical treatment or some other method would be required for explanation. 

This value is of the order of the speed of sound in air (346 m s at 298 K). This makes sense because the sound waves, which are simultaneously density and pressure waves, propagate via molecular motion. 

Dynamic Acoustic oscillations High frequencies related to time required for pressure wave propagation in system -... 

A virtual boundary (interface) exists between a gas jet exhausting from a nozzle and the surrounding quiescent medium. Compression and/or expansion pressure waves propagating within the jet will undergo a reflection at the... 

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