Thermodynamic and Gasdynamic Aspects of a Boiling Liquid Expanding Vapour Explosion

Abstract

The risk of explosion due to rupture of a tank filled with pressurized liquefied gas (PLG) is one of the risks to be considered in the context of studies on tunnel safety. When a vessel containing liquid well above its boiling point at normal atmospheric pressure fails catastrophically a Boiling Liquid Expanding Vapour Explosion (BLEVE) can occur. A vessel containing a liquefied gas can rupture due to the consequences of mechanical impact and or external fire. Because at ambient pressure the thermodynamic equilibrium state of LPG is the gaseous state, after the sudden depressurisation caused by the vessel rupture a rapid vapourisation takes place possibly leading to blast waves propagating in the surroundings and possibly damaging the tunnel wall and tunnel structure. The topics of investigation in this thesis are the rapid vapourisation, immediately following rapid depressurisation, and the creation of an overpressure close to the tank. These phenomena can be described using thermodynamics and fluid dynamics. The objective of the investigation was to formulate and solve a physicsbased model that can be used to predict whether or not a BLEVE will occur and to predict the strength of the shock waves when a BLEVE occurs. In order to create an adequate model for BLEVE simulation the following steps were taken. An appropriate simplified formof the conservation equations of mass,momentum and energy was formulated. The flowof the rapidly vapourising liquid was described by the Equal-Velocity-Unequal-Temperature (EVUT) formulation of the Euler equations for two-phase flow. The flow of the surrounding air was described by the single phase Euler equations. In order to have to possibility to study in detail the coupling of thermodynamic and gas dynamic phenomena the flow was restricted to be one-dimensional. This is adequate to represent local phenomena in the direction orthogonal to a PLG/air interface or global phenomena in a tunnel geometry. Because of the short time scale of the phenomena to be described it can be assumed that there is no mass transfer at the interface between the two-phase liquid+vapour region and the air region (the contact face). A numerical scheme for the solution of the model equations of two-fluid two-phase compressible flow was formulated. Because of the restriction to one-dimensional flow the method of characteristics could be selected as solution algorithm. It was solved by the particle-path algorithm, both in the single phase region and the two phase region. An advanced cubic equation of state (EOS) was chosen to describe the relations between the relevant thermodynamic variables. The domain of application of the EOS was extended to the description of metastable states, such as superheated liquid, occurring during a BLEVE. Models were formulated for mass, momentum and heat transfer between liquid and vapour phase. Two types of heat and mass transfer models were used: a qualitative model based on the concept of a relaxation time, and a quantitative model using the concepts and formalism of non-equilibrium thermodynamics (NET). To describe the initiation of the rapid vapourisation a homogeneous nucleation model was used. The transfer models provide the source terms due to vapourisation appearing in the momentum and energy equations of the EVUT Euler equations. The two models developed in this way, the TUD-RT model when a relaxation time is used, and the TUD-NET model, when non-equilibrium thermodynamics is used,were solved for scenario’s of starting from different initial temperature and pressure of propane. The role of the TUD-RT model is mainly to demonstrate the dependence of shock strength on several parameters, but is cannot be a predictive model because the relaxation time has to be assumed. The TUD-NET model on the other hand can be expected to be predictive because it incorporates the fundamental physical phenomena in the vapourising liquid. The simulations by the TUD-NET model reveal that homogeneous bubble nucleation is the trigger of BLEVE. For each PLG, there is a minimal pressure needed for BLEVE, below which homogeneous bubble nucleation will not occur. In case of a BLEVE, the shock is mainly generated by PLG close to the PLG-air contact face and once the shock is generated, it will propagate along the tunnel in a pace faster than the expansion of the rest PLG mixture. Hence the vapourisation of the rest of the PLG has no direct influence on the shock generated in the surrounding air. But it will contribute to the dynamic pressure of the expanding two-phase PLG mixture. Both the impact of the shock in air and of the impact of the expanding two-phase mixture can lead to damage to the tunnel wall or objects in the tunnel. Compared to another simulation model using the EVUT Euler equations - the Pinhasi et al. model - , the TUD-NET model offers the following advantages i) a predictive model for homogeneous bubble nucleation is included. This makes it possible to predict the onset of BLEVE in an accident involving PLG tank rupture; ii) the interfacial fluxes model is based on non-equilibrium thermodynamics taking both the chemical driven force and the thermal driven force for the interfacial heat and mass transfer into account. Compared to a simpler simulation model - the TNO model -, the TUD-NET model predicts weaker shock blast and the dynamic impact of the two-phase mixture than the TNO model confirming the role of the TNO model as the most conservative model for BLEVE simulation. The combination of the simulation tools developed in this study with simulation tools for tank rupture and tunnel response provide a comprehensive simulation tool for estimating the consequences of PLG tank rupture in a tunnel. Implementation of the TUD-NET model in a numerical solver of the three-dimensional Euler equations is needed for further validation of the model and for application to analysis of real BLEVE events, and is recommended.