Positive phase

The RF field is applied in such a way that one pair of opposed rods has the positive phase applied and the other pair has the negative phase apphed. 

An RF field is applied to the rings. The positive phase is applied to every other ring and the negative phase to the remaining intervening rings. Such an ion guide is called an ion tunnel. 

The magnitudes of symmetrical and non-symmetrical fault currents, under different conditions of fault and configurations of faulty circuits, can be determined from Table 13.5, where Z] = Positive phase sequence impedance, measured under symmetrical load conditions. The following values may be considered ... 

Table 13.6 Approximate negative and 2ero phase sequence impedances compared to positive phase sequence impedances...

Note The impedances marked on Figure 13.1.6 refer to positive phase. sequence impedances only. Faults that are non-symmelrical alone... 

Making a detailed estimate of the full loading of an object by a blast wave is only possible by use of multidimensional gas-dynamic codes such as BLAST (Van den Berg 1990). However, if the problem is sufficiently simplified, analytic methods may do as well. For such methods, it is sufficient to describe the blast wave somewhere in the field in terms of the side-on peak overpressure and the positive-phase duration. Blast models used for vapor cloud explosion blast modeling (Section 4.3) give the distribution of these blast parameters in the explosion s vicinity. 

The upper half of Figure 3.9 represents how a spherical explosive charge of diameter d produces a blast wave of side-on peak overpressure P and positive-phase duration r" " at a distance R from the charge center. Experimental observations show that an explosive charge of diameter Kd produces a blast wave of identical side-on peak overpressure p and positive-phase duration Kt at a distance KR from the charge center. (This situation is represented in the lower half of Figure 3.9.) Consequently,... 

The positive-phase duration of the blast wave from a vapor cloud explosion is in the range of 100 and 300 ms. 

Once the energy quantities E and the initial blast strengths of the individual equivalent fuel-air charges are estimated, the Sachs-scaled blast side-on overpressure and positive-phase duration at some distance R from a blast source can be read from the blast charts in Figure 4.24 after calculation of the Sachs-scaled distance ... 

The real blast side-on overpressure and positive-phase duration can be calculated from the Sachs-scaled quantities ... 

Explosively Dispersed Vapor Cloud Explosions (Giesbrecht et al. 1981). The Giesbrecht et al. (1981) model is based on a series of small-scale experiments in which vessels of various sizes (0.226-10001) containing propylene were ruptured. (See Section 4.1.2, especially Figure 4.5.) Flame speed, maximum overpressure, and positive-phase duration observed in explosively dispersed clouds are represented as a function of fuel mass. 

TNT blast is, however, a poor model for a gas explosion blast. In particular, the shape and positive-phase duration of blast waves induced by gas explosions are poorly represented by TNT blast. Nevertheless, TNT-equivalency methods are satisfactory, so long as far-field damage potential is the major concern. 

If, on the other hand, a vapor cloud s explosive potential is the starting point for, say, advanced design of blast-resistant structures, TNT blast may be a less than satisfactory model. In such cases, the blast wave s shape and positive-phase duration must be considered important parameters, so the use of a more realistic blast model may be required. A fuel-air charge blast model developed through the multienergy concept, as suggested by Van den Berg (1985), results in a more realistic representation of a vapor cloud explosion blast. 

TNT-equi valency methods express explosive potential of a vapor cloud in terms of a charge of TNT. TNT-blast characteristics are well known fiom empirical data both in the form of blast parameters (side-on peak overpressure and positive-phase duration) and of corresponding damage potential. Because the value of TNT-equiva-lency used for blast modeling is directly related to damage patterns observed in major vapor cloud explosion incidents, the TNT-blast model is attractive if overall damage potential of a vapor cloud is the only concern. 

If, on the other hand, blast modeling is a starting point for structural analysis, the TNT-blast model is less satisfactory because TNT blast and gas explosion blast differ substantially. Whereas a TNT charge produces a shock wave of very high amplitude and short duration, a gas explosion produces a blast wave, sometimes shockless, of lower amplitude and longer duration. In structural analysis, wave shape and positive-phase duration are important parameters these can be more effectively predicted by techniques such as the multienergy method. 

Figure 7.2b. Sachs-scaled positive-phase duration of blast from a hemispherical fuel-air charge.

The nondimensionalized side-on peak overpressures and their respective positive-phase durations can be transformed into real values for side-on peak overpressures and positive-phase durations by calculating ... 

TABLE 7.5a. Side-On Peak Overpressure and Positive-Phase Duration of Blast Produced by Charge I (E = 6870 MJ, Strength Number 7)... 

TABLE 7.5b. Side-On Peak Overpressure and Positive-Phase Duration ... 

Blast effects. The side-on peak overpressures and positive-phase durations of blast waves produced by the respective charges for any selected distance, R, can be found by calculating separately for each charge... 

The earliest tables were compiled from data collected from nuclear weapon tests, in which very high yield devices produced sharp-peaked shock waves with long durations for the positive phase. However, these data are used for other types of blast waves as well. Caution should be exercised in application of these simple criteria to buildings or structures, especially for vapor cloud explosions, which can produce blast waves with totally different shapes. Application of criteria from nuclear tests can, in many cases, result in overestimation of structural damage. 

Positive phase That portion of a blast wave whose pressure is above ambient. 

The gauge records eimbient pressure Pq. At arrival time ta, the pressure rises quite abruptly (discontinuously, in an ideal wave) to a peak value Pj + Pq. The pressure then decays to ambient in total time tg + T+, drops to a partial vacuum of amplitude Pj, and eventually returns to Po in total time tg + T+ + T. The quantity P is usually termed the peak side-on overpressure, or merely the peak overpressure. The portion of the time history above initial ambient pressure is called the positive phase, of duration T+. That portion below Po, of amplitude Ps and duration T, is called the negative phase. 

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