Numerical simulations of gas explosion using Porosity Distributed Resistance approach Part −1: Validation against small-scale experiments

Abstract

A new model, PDRFOAM, has been developed for the prediction of gas explosions in congested plant. It uses the PDR approach to model the effect of small-scale obstacles, e.g., pipes and vessels on flame propagation and on explosion overpressure. While the effects of large obstacles i.e., that is the large scales are explicitly resolved. The equations for mass, momentum, enthalpy and Favre-averaged regress variable are solved. In addition, porosity modified standard k-ε turbulence model and the transport equations for the flame wrinkling parameter are solved. The model PDRFOAM, is built as a new application in OpenFOAM, suite of models. OpenFOAM is an open-source CFD package of routines for solution of systems of partial differential equations.In addition, to the PDRFOAM model, the CADPDR program was developed which generates various fields (volume blockage, area blockages, surface area, sub-grid drag and turbulence generation parameters) needed by PDRFOAM. CADPDR needs as input obstacle files that list coordinates and dimension of the obstacles e.g. pipes and vessels. The PDRFOAM code solves porosity-modified momentum and continuity equations with sub-grid source terms. The combustion model in PDRFOAM is based on flame area transport. The turbulent burning velocity correlation used is based on Markstein and Karlowitz number. Flame area generation due to the folding of the flame around obstacles is explicitly modelled.This paper presents the formulation of PDRFOAM and validation of the PDRFOAM code against three series of small- and medium-scale experiments i.e., ERGOS, MERGE and Buxton S-Series experiments. A total of more than 150 experiments were used for validation which includes variation in blockage ratio, grid pitch, size of the congested region, equivalence ratio, confinement, partial fill, obstacle diameter, different obstacle shapes and three different fuels. The model is compared against flame position, flame speed as a function of time and maximum overpressure obtained from experiments. Simulations predict the experimental trends of increase in overpressure with increase in blockage ratio, laminar burning velocity, partial fill of the gas cloud, size of the congested region, confinement, grid pitch and obstacle diameter. It also predicts the trends of increase in overpressure with increase in equivalence ratio, variation of maximum overpressure with ignition location, change in obstacle shape and obstacle configuration. The maximum overpressure predicted by simulations (see Fig. 1) is in general within the uncertainty of a factor of two.