Front velocity

At times it is necessary to have a feel for overpressure as it relates to shock front velocity [49]. (See Figure 7-60). Note especially that for a reasonable detonation velocity the peak overpressure could be in the range of 700 to 1000 psi and when referenced to Figure 7-60, the extent of industrial damage would be catastrophic. The use of scaled distance is illustrated in Ref. [41]. 

Figure 7-60. Shock front velocity as a function of peak overpressure at sea ievel. By permission, Report HNDM-1110-1 -2, U.S. Army Corps of Engineers, 1977, Huntsviiie, AL [49].

Ml is the liquid velocity and is the front velocity relative to the liquid, is the liquid length domain and L is the total channel length. Reprinted from Peles et al. (2001) with permission... 

Beckmann, J., Korber, C.H., Rau, G., Hubei, A., Carvalho, E.G. (1990). Redefining cooling rate in terms of ice front velocity and thermal gradient First evidence of relevance to freezing injury of lymphocytes. Cryobiol. 27,279-287. 

The solvent front velocity U from Equation 4.2 is given by differentiation of Equation 4.1 ... 

Equation (7.5) Indicates that the velocity constant should increase linearly with the average particle size. The solvent front velocity should be larger for coarse-particle layers than for fine-particle layers which is. in good agreement with experimental observations [27]. Also, from equation (7.5) we see that the velocity constant depends linearly on the ratio of the surface tension of the solvent to its viscosity and that solvents which maximize this ratio (and not just optimize one of the parameters) are preferred for TLC [8,30]. The contact angle for... 

Tapered plates, prepared with a gradual increase in thiclcness of the layer from 0.3 nm to 1.7 am, can be used to improve resolution of the sample [215]. On the tapered layer the solvent front velocity decreases as the thickness of the layer increases. This results in the formation of a negative velocity gradient in the direction of solvent migration. As a result the lower portion of a zone moves faster than the top portion, keeping each component focused as a narrow band. Plates with concentrating zones are useful for optimizing sample application. 

The surfactant retention tests were performed in the porous medium at 43° C in sandpack (Sor = 0) saturated with brine (See composition in Table I). The injection flow rate used in these tests (2 cm3/h) corresponds to a front velocity of 30 to 40 cm/day. 

Particle velocity, u Shock front velocity, U Dynamic pressure q = p u /2... 

We will now estimate the front velocity using the method of Guy (1984). Let us consider, in one dimension, the conservation of element i in a rock column (x = xt to x = x2) of unit section which contains a propagating front at the time-dependent position s(t). The discontinuity is handled by breaking the column at s = s(t). The amount of element i in the rock column only changes by fluid exchange through both ends of the column, hence... 

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... 

Stationary, traveling wave solutions are expected to exist in a reference frame attached to the combustion front. In such a frame, the time derivatives in the set of equations disappear. Instead, convective terms appear for transport of the solid fuel, containing the unknown front velocity, us. The solutions of the transformed set of equations exist as spatial profiles for the temperature, porosity and mass fraction of oxygen for a given gas velocity. In addition, the front velocity (which can be regarded as an eigenvalue of the set of equations) is a result from the calculation. The front velocity and the gas velocity can be used to calculate the solid mass flux and gas mass flux into the reaction zone, i.e., msu = ps(l — e)us and... 

The raw data of the thermocouples consist of the temperature as a function of time (Fig. 8.9, left). In the raw data, the passing of the conversion front can be observed by a rapid increase in temperature. Because the distance between the thermocouples is known, the velocity of the conversion front can be determined. The front velocity can be used to transform the time domain in Fig. 8.9 (left) to the spatial domain. The resulting spatial flame profiles can be compared with the spatial profiles resulting from the model. The solid mass flux can also be plotted as a function of gas mass flow rate. The trend of this curve is similar to the model results (Fig. 8.9, right). 

Further, that dividing contaminant input rate by the working differential loading we get the rate of utilization of molecular sieve per unit time. That quantity without specific reference to a front velocity can be a convenient design parameter as demonstrated in Section 9.5. 

The detonation wave is a combination of a shock and combustion front, and has a constant width on the time-distance plot. Passage thru the intermediate state would require the attainment of extremely high peak pressure, and of wave-front velocities above the CJ value. Oppenheim quotes (Ref 3, p 476) some exptl evidence of these phenomena... 

In the overdriven state, the observed propagation velocity of the combustion front was found to be much higher than the steady-state velocity of spherical detonation. The overdriven state exists for only a short time, and the combustion front velocity then drops rapidly to the steady-state value. The rate at which this exceedingly high velocity decreases was found by experiment to be inversely proportional to the induction distance... 

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