Approximate estimation of the critical diameter in Koenen tests

1 Introduction

In order to obtain an Interim Hazard Classification and Transport Permit for a new energetic material, one requirement is the undertaking of the Koenen (or steel-sleeve) test. The Koenen test is used in particular for assessing transport safety [1], [2], [3], [4], [5]. In this test, the substance is loaded into a steel sleeve (internal diameter: 24 mm, length: 75 mm, wall thickness: 0.5 mm, V = 25 mL) up to a height of 1 mm beneath the top edge, and then the sleeve is closed with a nozzle plate (Figure 1). Nozzle plates are available with orifices of 1.0–20 mm. The steel sleeve is attached to the nozzle plate with a two-part threaded socket. It is then heated simultaneously by four burners (Figures 1 and 2). By varying the orifice diameters, the critical diameter can be determined. It is defined as being the diameter at which the pressure increase on burning and the subsequent explosion destroys the sleeve into at least four small splinters. The largest orifice diameter at which an explosion occurs is termed the “critical” or “limiting” diameter, and its value is used to classify the behavior of the sample when heated under confinement. A critical diameter (D_crit.) of 1 or 1.5 mm indicates that the substance has some thermal explosive properties, and 2 mm or more that it is “thermally sensitive” [2, 6].

Figure 1:

Performance of a Koenen (steel-sleeve) test.

Figure 2:

Typical results of a Koenen (steel-sleeve) test: (a) before test, (b) in test apparatus, (c) and (d) test result type “F”.

Taking into account the volume of 25 mL stated above, this means that for every Koenen test more than 25 g of a new energetic material are sacrificed. This is not only costly, but is also a safety concern if the new energetic material gets prepared manually. Therefore, it is of high interest to start with the “right” orifice in order not to waste too much material and equipment (steel-sleeves and nozzle plates). This paper provides a very rough method to estimate the expected critical diameters for new secondary explosives.

2 Results and discussion

Usually, the brisance is referred to as the shattering capability of a secondary (high) explosive, and is determined mainly by its detonation pressure [6]. According to H. Kast [6], the brisance value (B) is defined as the product of the loading density (ρ), the specific energy (F for “force of an explosive”) and the detonation velocity VoD:

The specific energy (“force”) of an explosive (F) on the other hand, can be calculated according to the general equation of state for gases:

In this study, we computed the detonation pressures (p_C–J; Chapman–Jouguet pressure (see ref. [6]), detonation velocities (VoD) and volume of detonation gases V⁰) of 25 secondary explosives for which experimental Koenen test parameters were available using the Explo5 code (Table 1).

While there is some correlation between the critical diameter in the Koenen test and the detonation pressure, as well as with the brisance, the best correlation was obtained by plotting the critical diameter against: ρ × pC−J2 × V⁰ × VoD (Table 1, Figure 3) which we now call the Koenen parameter K:

Figure 3:

Critical diameters D_crit. (Koenen test) plotted against K = ρ × pC−J2 × V⁰ × VoD.

From the above equation (see Figure 3), it is now possible to estimate the expected critical diameter in the Koenen test for secondary explosives as follows (values given in: ρ: kg m⁻³, p: kg m⁻¹ s⁻², V⁰: m³ kg⁻¹, VoD: m s⁻¹) (compare top of Table 1):

This correlation is not meant to replace a proper Koenen test, but rather, it is intended to act as an aid to know which orifice diameter to start testing with.

3 Computational details

All calculations were carried out with the thermochemical equilibrium code Explo5 (version 6.05.02) [11].