Mechanical explosion problem

A clearer example of a normative orientation to knowledge can be seen in the section on the thermodynamics of mechanical explosions (Sandler, 2006, pp. 173-182). An example of a mechanical explosion is the result of the failure of an over-pressurised container of a given volume of air at room temperature and high pressure. The problem requires an estimate of the damage done by the explosion.

A crucial step in solving the problem is to define the ‘system’ and the ‘surroundings’, since there is an exchange in the energy between system and surroundings in the form of ‘work’ that the system performs on the surroundings in the explosion. This ‘work’ is the damage that needs to be calculated to solve the problem. In this case the expanding shock wave is defined as the system. The characteristics of an explosion allow the engineer to justify certain assumptions or idealisations made in order to solve the problem: firstly, explosions are so rapid that a

reasonable assumption is that there is insufficient time for heat or mass to transfer to or from the initial exploding body across its boundary. This means that the system can be treated as closed. The exploding matter expands extremely fast, creating a shock wave as the surrounding air is thrust away. The pressure outside the shockwave is ambient, but inside the shockwave the pressure is much higher than ambient pressure. This pressure differential is the cause of

damage during an explosion.

The shockwave front continues to travel outwards as a result of the rapid expansion of the gases inside the front. The rapidity of the expansion also allows the engineer to assume that the expansion occurs uniformly. As the volume expands, the pressure inside the shock front falls as predicted by gas laws. This process continues until the pressure inside the shockwave

eventually becomes equal to the ambient pressure and the final temperature of the gas is lower than the initial temperature.

Expanding shockwave Initial system boundary Ambient pressure

Uniform expansion

165 The description above with the associated idealising assumptions allows the engineering

student to treat the problem as a closed (no mass transfer to the surroundings), adiabatic (no heat transfer to the surroundings) system with a uniformly expanding boundary. It is then possible to derive a set of relatively simple equations, using the mass, energy and entropy balances from the First and Second Law of thermodynamics. Without going into detail on the mathematics, the following equations are derived:

Mass balance equation: No change in the mass: mfinal – minitial = 0 (closed system)

Entropy balance: Sfinal – Sinitial = Sgen where Sgen is the entropy generated across the shock wave.

Energy balance equation: The change in internal energy of the system is equal to the work done on the surroundings by the expanding boundary: Ufinal - Uinitial = W. This equation allows the

calculation of the work W done by the shockwave on the surroundings, which is the damage done in the explosion.

With the exception of Sgen, all of the thermodynamic properties of the system can be calculated

or read off detailed thermodynamics property tables. The amount of entropy generated across a shock wave, Sgen , is almost impossible to quantify, and so, to solve the problem, Sgen is neglected

(Sgen is set to zero):

…the only generation of entropy occurs across the shock wave. If we neglect this entropy generation, the work we compute will be somewhat too high. However, in safety

problems we prefer to be conservative and err on the side of overpredicting and energy release resulting from an explosion, since we are usually interested in estimating the maximum energy release and the maximum damage that could result. Further, we do not really have a good way of computing the amount of entropy generated during an explosion. Consequently, we will set the Sgen = 0… (Sandler, 2006, p. 175)

Sandler here uses a simplifying approximation to solve the problem. The calculation results in a somewhat inaccurate answer, but because the result overestimates the damage from the

explosion, it is an acceptable and cautious approach.

Furthermore, Sandler encourages students to compare the amount of work done by the system (i.e. the damage produced by the explosion) to the blast energy released in the (chemical) explosion of a mass of TNT. Sandler also points out that if the pressurised tank above contained a combustible substance (rather than air), there is a real danger that a secondary chemical explosion could occur when the expanding vapour-containing shock front comes into contact

166 with enough oxygen to ignite. This would obviously add to the devastation caused by the

explosion.

The normative concern that drives the problem-solving approach gives the knowledge mode as constitutive normativity, and the approximation made in order to arrive at the answer means that a secondary knowledge modality, idealisation, is present. The resulting approximation is justified by the safety concern for the physical circumstances under which the explosion takes place (mode physical realisability), and the typical industrial context of an overpressurised tank, identifies another secondary modality, specialisation, mode particulars.

Overall, the normative orientation of the knowledge in the chemical engineering textbook is less prominent and also more implicit than in the mechanical engineering text. In addition, no attention is paid to what could be called First Law efficiency of devices (there are some examples of Carnot efficiency and coefficients of performance of refrigeration cycles). Even in the explosion example discussed above a normative orientation is muted, apart from the

injunction to over-predict (rather than under-predict) the damage from an explosion: the safety concern is implicit, rather than explicit.

6.5

Chemistry