A simplified model with lumped parameters for explosion venting simulation V.R. Feldgun * , Y.S. Karinski, D.Z. Yankelevsky National Building Research Institute, Technion City, Haifa 32000, Israel article info Article history: Received 14 February 2011 Received in revised form 3 August 2011 Accepted 9 August 2011 Available online 11 September 2011 Keywords: Explosion venting Protective cover Pressure relief Partially confined explosion abstract The paper presents a study aiming at simulation of some characteristics of an interior explosion within a room with an opening, that is initially closed by a heavy cover, and is gradually opened due to the pressures exerted by the explosion products. An effective simplified model of explosion venting due to separation of the protective cover has been developed. The developed model with lumped parameters is based on the Bernoulli equation and describes the quasi-stationary venting phase of the interior explosion. The initial internal gas pressure induced by the very short non-stationary phase is predicted by the developed approximate analytical formula, based on the full energy conservation law. The formula yields very good agreement with experimental data and with numerical analysis results. The simulation of the unsteady outflow from a cylindrical high-pressure vessel upon a sudden separation of the cover has shown that the developed simplified model yields the integral characteristics of the outflow process (such as a maximum cover’s velocity and displacement etc.) with reasonable accuracy. The proposed approach is demonstrated by the simulation of gas outflow from a chamber upon a sudden separation of the cover or upon a rectangular shutter rotation about a fixed line hinge. The analysis has been performed using the developed simplified approach and through simulations with AUTODYN. A good correspondence between both methods has been obtained. The effect of gravity on the protective cover velocity and displacement has been also examined. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction Explosion pressure venting, reduces the pressure buildup in an enclosed space due to an interior explosion, thus reducing the resulting structural damage of its envelope components [1e3]. The venting allows rapid release of the high explosive products (heated gases, flame, and burnt and non-burnt dust) from the closed space. By removal of heat energy and fuel from the explosion space, the rate of combustion is reduced and the development of high pressures causing destructive effects can be reduced accordingly. Full release of pressures due to a sufficiently large opening, generally provides the most effective venting. However, because of the protection require- ments both performance and functional as well as weather protec- tion aspects, only limited venting is generally feasible in practice. It is necessary to cover the vent openings with diaphragms or blowout disks, poppet-type closures, louvers, hinged panels, hinged windows with proper latches, scored glass panes, light sections in wall or roof surfaces, or other rapidly opening devices. Confined and partially confined explosions may occur by various reasons and their effects may be destructive [4]. The confined explosion effects depend on the geometrical parameters of the space where the explosion occurs (geometrical dimensions, the charge location, the locations and sizes of the openings etc) as well as on the charge characteristics. The complete typical confined explosions’ analysis aims at estimating the immediate local damages caused by the explosion, occurring shortly after the shock waves arrival at the structural components and may lead to further collapse of the entire structure [5,6]. Such an analysis may be performed either without coupling of the shock wave reflection with the elements’ response [7] or with coupling [8,9]. The time history of the blast load (pressure) acting on some element of a fully or partially confined space due to an interior explosion is signifi- cantly more complex than that occurring due to an external explosion [10e12]. This complexity is caused by the repetitive shock waves reflecting from the closed space faces (walls, ceiling, and floor) and by the openings which allow pressure relief [13]. Vented HE explosions have been studied theoretically [10,12,14e17] and experimentally [14,15,18e23]. Methods for pre- dicting blast loads due to exterior or interior explosions, as well as quasi-static pressure buildup, and venting times due to interior explosions are presented in [14]. The effective vented area ratio for a multi-walled structure with various sizes of venting areas in each wall was developed. * Corresponding author. Tel.: þ972 4 8292244; fax: þ972 4 8324534. E-mail address: aefeldgo@technion.ac.il (V.R. Feldgun). Contents lists available at SciVerse ScienceDirect International Journal of Impact Engineering journal homepage: www.elsevier.com/locate/ijimpeng 0734-743X/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijimpeng.2011.08.004 International Journal of Impact Engineering 38 (2011) 964e975