Scaling parameters for vented gas and dust explosions

Results of experiments or calculations for vented explosions are usually presented by expressing a term containing the peak (reduced) pressure as a function of a vent parameter. In gas explosions, the reactivity of the system has been typically characterized through an effective burning velocity, u_f. In the case of dust explosions, a normalized peak rate of pressure rise, K(=V^1/3(dp/dt)_max), has been used instead. Depending on the chosen approach, comparisons between systems with the same “reactivity” take different meanings. In fact, correlation formulas resulting from these two approaches imply different scaling between important system parameters. In the case of a constant-u_f system, and for sufficiently large vent areas, the reduced pressure, Δp_r, is approximately proportional to the square of the peak unvented pressure, Δp_m. On the other hand, correlations developed for constant-K systems imply proportionality of Δp_r with Δp_m raised to a power between −5/3 and −1, with the exact value depending on the assumptions made on the shape of the pressure profile. While the ultimate resolution of the details of the scaling may require recourse to experiments, this theoretical analysis offers a tool for the planning of such experiments and for the interpretation of their results. The paper provides a discussion of these scaling issues with the help of predictions from an isothermal model of vented explosions.