Transient characteristics of dense gas dispersion. Part 1:: A depth-averaged numerical model

Abstract

A wind-tunnel validated, non-proprietary depth integrated numerical model is developed to calculate the behavior of heavy and cold gas clouds released into the atmosphere at ground level. The model (DENS20) is time dependent, quasi-three dimensional, and permits cloud heating from below and the entrainment of moist air. The model does not depend upon the Boussinesq assumption, but it does require the hydrostatic assumption. Model constants are set to fit a cross-section of data from wind-tunnel experiments on the transient and steady behavior of releases of heavy gases. Plume shape and concentration decay with distance and time are reproduced for comparative cases from the Porton Downs and China Lake field tests and the Colorado State University cold gas laboratory tests on dense gas behavior. T001 List of symbols B Plume width C Concentration mass fraction C f/2 Surface drag coefficient c p Specific heat capacity E Enthalpy g′ Gravitational constant Gr Grashof number, gβ( T a - T 0) H 0/ν a 2 H Plume height ( HS) Heavyside operator h s Surface heat transfer coefficient k Von Karman constant K See eqn. (8), section longitudinal momentum l b Bouyancy length scale L h, l H 2O See eqn. (9), latent heat of vaporization of water vapor M See eqn. (5), section lateral momentum, or molecular weight N See eqn. (6), section mass p Pressure P See eqn. (7), section mass fraction Pr Prandtl number Q See eqn. (9), section enthalpy, or plume source strength R See eqn. (5), plume density Re Reynolds number, ( g′ 0 H) 1/2 H/ν a Ri* Richardson number, ( g′ 0 H 0)/ u* 2 ( SG) Specific gravity t Time T Temperature, or time scale T* Dimensionless temperature, ( T-T 0)/( T a- T 0) u, U Velocity, velocity scale u* Friction velocity U T, W T Advection velocities at cloud top υ e, w e Entrainment velocities V g Gravity spread velocity χ Mole fraction concentration x,y,z Coordinates z 0 Surface roughness ν Kinematic viscosity ϱ Density α, β, Re T Constants Subscripts a Ambient air conditions m Maximum 0 Initial value or ground level R Reference value Superscripts Ensemble average