Reflected pressure

Successive reflections of the pressure wave between the pipe inlet and the closed valve result in alternating pressure increases and decreases, which are gradually attenuated by fluid friction and imperfect elasticity of the pipe. Periods of reduced pressure occur while the reflected pressure wave is travehng from inlet to valve. Degassing of the liquid may occur, as may vaporization if the pressure drops below the vapor pressure of the liquid. Gas and vapor bubbles decrease the wave velocity. Vaporization may lead to what is often called liquid column separation subsequent collapse of the vapor pocket can result in pipe rupture. 

In Figure 3.8a, a plane shock wave is moving toward a rigid structure. As the incident wave encounters the front wall, the portion striking the wall is reflected and builds up a local, reflected overpressure. For weak waves, the reflected overpressure is slightly greater than twice the incident (side-on) overpressure. As the incident (side-on) overpressure increases, the reflected pressure multiplier increases. See Appendix C, Eq. (C-1.4). 

If the body is near a surface against which the blast wave can reflect (Figures C-2C and C-2D), the pressure P acting on the body equals the reflected pressure... 

In an enclosure, a peak for initial pressure ratio for a deflagration generally can exceed 8 1 of the initial pressure. The pressures may build to a ratio of 40 1 (reflected pressure) times the initial pressure when a detonation develops. This is the reason detonations can be so disastrous. Their final pressure, when built on a deflagration peak pressure as a base or initial pressure, can be extremely high. 

Figure 7-53. Detonation velocity, V, static pressure, Pg, and reflected pressure, Pp developed by detonation wave propagating through hydrogen-oxygen mixtures in a cylindrical tube at atmospheric pressure at 18°C. By permission, U.S. Bureau of Mines, Bulletin 627 [43].

The reflected pressure wave amplitude and impulse for shock waves associated with detonations are well documented, as shown in Figure A. 3 (Ref. 7, Volume II). Less information is available on reflected overpressure and impulse resulting from deflagration pressure waves. Reference 67 documents approaches for evaluating reflected overpressure from weaker blast pressure waves. Forbes (Ref. 71) suggests the following approximate relation to model the more complex relations in Reference 64 ... 

Reflected pressure Pressure experienced by an object facing a blast. 

It then gives a multiplier which yields the reflected pressure on the surface at this incidence angle, Pro- Figure 28 gives directly the Hopkinson-Cranz scaled reflected impulse irci, also given the incidence angle and peak side-on overpressure as inputs. By using these two curves, plots of variations of peak pressure and impulse over a wall surface can be estimated, for the first shock wave reflected from the surface. 

Figure 27. Reflected Pressure Coefficient Versus Angle of Incidence.

The loads from external near-surface burst explosions are based on hemispherical surface burst relationships. Peak pressure (P psi) and scaled. impulse Ci/W psi/lb ) are plotted vs. scaled distance (R/W ft/lb ). Roof and sidewall elements, side-on to the shock wave, see side-on loads (P and i ). The front wall, perpendicular to the shock wave, sees the much higher reflected shock wave loads (P and i ). An approximate triangular pressure-time relationship is shown in Figure 5a. The duration, T, is determined from the peak pressure and impulse by assuming a triangular load. Complete load calculations include dynamic loads on side-on elements, the effect of clearing times on reflected pressure durations, and load variations on structural elements due to their size and varying distance from the explosive source. 

BLAST ATTENTION. Shields used to provide protection from accidental detonation, are to be designed to prevent exposure of operating personnel to peak, positive incident pressures above 2.3 psi or peak positive normal reflected pressure above 5.0 psi. 

When the free field blast wave from an explosion strikes a surface, it is reflected. The effect of this blast wave reflection is that the surface will experience a pressure much more than the incident side-on value. The magnitude of the reflected pressure is usually determined as an amplifying ratio of the incident pressure ... 

The duration of the reflected pressure depends on the dimensions of the reflecting surface, up to a maximum time approximately equal to the positive phase duration of the incident blast wave. This upper limit corresponds to the total reflection of the entire blast wave without any diffraction around the edges of the reflecting surface. Further details of the duration are provided in Section 3,5.1,... 

Historical data from industrial explosions are hard to accurately quantify as these can only be approximated by back calculating from observed deformations of structures. Blast overpressures from vapor cloud explosions are especially difficult to quantify because they tend to be directional, come from multiple sources, and vary with site conditions. Additionally, there is less information available than for high explosives. In one company s review of five recent vapor cloud explosion incidents, as measured at a range of 200 to 1,000 feet (60 to 300 meters), peak reflected pressures in the range from 2 psi (14 kPa) with a 35 ms duration to 12 psi (83 kPa) with a 33 ms duration have occurred. These pressures correspond to side-on overpressures ranging from 1 psi (7 kPa) to 5.5 psi (38 kPa). An extensive list of this type of explosion data is included in Lenoir 1993. 

Pso558 Incident (side-on) Overpressure Pr = Reflected Pressure Pa = Averaged Overpressure Pb = Back-Face Overpressure... 

The downward force from the overpressure on the roof is applied simultaneously with the horizontal force from the peak reflected pressure on the front wall, However, the compensating effects of blast forces acting on the rear wall may be conservatively neglected. 

Furnish the same information relative to peak incident overpressure, peak reflected pressure, and blast load duration that has been used for the structural components. 

An overpressure-distance graph has been drawn in Fig. 7. Plotted as the ordinate is the reflected pressure in pascals. The Shell Pipeline results... 

Fig. 6.3. Reflected pressure amplitude and transmitted longitudinal and shear stress amplitudes at a fluid-solid interface (a) water-PMMA (b) water-fused silica (i) reflected wave in the fluid (ii) transmitted longitudinal wave (iii) transmitted shear...

Reflected Pressure. Reflected pressure increases the pressure on a rigid surface if the... 

Maximum reflected pressure (wave strikes surface head-on) 28 4100... 

If turns in a process line are necessary, two 45° bends or a long sweep elbow will greatly reduce reflected pressure compared with a single 90° elbow. 

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