The Integral Dense-gas Dispersion Model (IDDM) and comparison with Jack Rabbit II data

Abstract

The Integral Dense-gas Dispersion Model (IDDM) is presented and used to predict the maximum concentrations and spread of a dense-gas cloud from a short-term release. IDDM is based on integrated conservation equations and includes spreading due to source momentum and density effects, cloud-top air entrainment, height changes with time, and wind transport. The equations are solved numerically but some useful analytical results are found showing the dependence of cloud radius and height on source conditions, entrainment, and time. IDDM comparisons with the Jack Rabbit (JR) II experiments are made for two smooth-terrain Trials (6, 7) and one with a Mock Urban Array (MUA) of Conex containers (Trial 1). For the smooth-terrain cases, predicted concentrations (C) follow the observed JR II data trends with distance x, and for x>1 km are consistent with a -5/3 empirical correlation. In the near field, analytical results for C show excellent agreement with the IDDM numerical solution. For Trial 1, an internal boundary layer (IBL) model is added to obtain the modified winds, friction velocity, and IBL depth due to the MUA. With the IBL and a mean depth (10 m) included, IDDM concentrations agree with the data. Over all Trials (1,6,7), IDDM exhibits good statistical performance with 83% of the predictions within a factor of 2 of the observations. An elliptical horizontal cloud geometry is added to estimate the lateral cloud width given an anisotropy ratio (ani) of along-wind (x) to lateral (y) cloud width. With constant ani (=3), the agreement between predicted and observed width is good with a geometric mean (GM) of predicted-to-observed width of 1.02 and a geometric standard deviation (GSD) of 1.35. However, with a trial-specific ani (=0.5−3) and longitudinal wind shear included, the mean model agreement (GM) is about the same, but the model-data scatter is reduced to a GSD of ≃1.1.