Stevens T. Chan

A MODIFIED FINITE ELEMENT METHOD FOR SOLVING THE TIME-DEPENDENT, INCOMPRESSIBLE NAVIER-STOKES EQUATIONS. PART 1: THEORY*

Beginning with the Galerkin finite element method and the simplest appropriate isoparametric element for modelling the Navier-Stokes equations, the spatial approximation is modified in two ways in the interest of cost-effectiveness: the mass matrix is ‘lumped’ and all coefficient matrices are generated via 1-point quadrature. After appending an hour-glass correction term to the diffusion matrices, the modified semi-discretized equations are integrated in time using the forward (explicit) Euler method in a special way to compensate for that portion of the time truncation error which is intolerable for advection-dominated flows. The scheme is completed by the introduction of a subcycling strategy that permits less frequent updates of the pressure field with little loss of accuracy. These techniques are described and analysed in some detail, and in Part 2 (Applications), the resulting code is demonstrated on three sample problems: steady flow in a lid-driven cavity at Re ≤ 10,000, flow past a circular cylinder at Re ≤ 400, and the simulation of a heavy gas release over complex topography.

A review of recent field tests and mathematical modelling of atmospheric dispersion of large spills of Denser-than-air gases

Large-scale spills of hazardous materials often produce gas clouds which are denser than air. The dominant physical processes which occur during dense-gas dispersion are very different from those recognized for trace gas releases in the atmosphere. Most important among these processes are stable stratification and gravity flow. Dense-gas flows displace the ambient atmospheric flow and modify ambient turbulent mixing. Thermodynamic and chemical reactions can also contribute to dense-gas effects. Some materials flash to aerosol and vapor when released and the aerosol can remain airborne, evaporating as it moves downwind, causing the cloud to remain cold and dense for long distances downwind. Dense-gas dispersion models, which include phase change and terrain effects have been developed and are capable of simulating many possible accidental releases. A number of large-scale field tests with hazardous materials such as liquefied natural gas (LNG), ammonia (NH3), hydrofluoric acid(HF) and nitrogen tetroxide(N2O4) have been performed and used to evaluate models. The tests have shown that gas concentrations up to ten times higher than those predicted by trace gas models can occur due to aerosols and other dense-gas effects. A methodology for model evaluation has been developed which is based on the important physical characteristics of dense-gas releases.

Flow around a Complex Building: Comparisons between Experiments and a Reynolds-Averaged Navier–Stokes Approach

Abstract An experiment investigating flow around a single complex building was performed in 2000. Sonic anemometers were placed around the building, and two-dimensional wind velocities were recorded. An energy-budget and wind-measuring station was located upstream to provide stability and inflow conditions. In general, the sonic anemometers were located in a horizontal plane around the building at a height of 2.6 m above the ground. However, at the upwind wind station, two levels of the wind were measured. The resulting database can be sampled to produce mean wind fields associated with specific wind directions such as 210°, 225°, and 240°. The data are available generally and should be useful for testing computational fluid dynamical models for flow around a building. An in-house Reynolds-averaged Navier–Stokes approach was used to compare with the mean wind fields for the predominant wind directions. The numerical model assumed neutral flow and included effects from a complex array of trees in the vicin...

Flow around a complex building: Experimental and large-eddy simulation comparisons

A field program to study atmospheric releases around a complex building was performed in the summers of 1999 and 2000. The focus of this paper is to compare field data with a large-eddy simulation (LES) code to assess the ability of the LES approach to yield additional insight into atmospheric release scenarios. In particular, transient aspects of the velocity and concentration signals are studied. The simulation utilized the finite-element method with a high-fidelity representation of the complex building. Trees were represented with a canopy term in the momentum equation. Inflow and outflow conditions were used. The upwind velocity was constructed from a logarithmic law fitted to velocities obtained on two levels from a tower equipped with a 2D sonic anemometer. A number of different kinds of comparisons of the transient velocity and concentration signals are presented—direct signal versus time, spectral, Reynolds stresses, turbulent kinetic energy signals, and autocorrelations. It is concluded that the LES approach does provide additional insight, but the authors argue that the proper use of LES should include consideration of cost and may require an increased connection to field sensors; that is, higher-resolution boundary and initial conditions need to be provided to realize the full potential of LES.

Simulation of LNG vapour spread and dispersion by finite element methods1

Abstract Two finite element models, one based on solving the time-dependent, two-dimensional conservation equations of mass, momentum, and energy, with buoyancy effects included via the Boussinesq approximation, the other based on solving the otherwise identical set of equations except using the hydrostatic assumption, are described and used to predict some aspects of the vapour dispersion phenomena associated with LNG spills. A number of controlled numerical experiments, representing a reasonable expected range of LNG spill scenarios and atmospheric conditions, have been carried out. Based on a comparison of the results obtained with these finite element models, some data regarding the applicability and limitations of the hydrostatic assumption for predicting LNG vapour spread and dispersion are established.

A Study of Heavy Gas Effects on the Atmospheric Dispersion of Dense Gases

The atmospheric dispersion of a large, heavier-than-air gas release is affected by several physical phenomena that either do not occur or are unimportant in neutrally buoyant and trace gas releases. These include turbulence damping due to stable density stratification of the heavy gas cloud, alteration of the ambient velocity field due to gravity flow and the source momentum flux in a large release and, for cold gas releases, the effects of heat flow from the ground on cloud buoyancy and turbulence. Furthermore, the time scale of interest for a particular heavy gas release may differ considerably from the long term dose concerns associated with typical atmospheric pollutants. For example, in combustible gases releases, one is concerned with the instantaneous concentration, while in a toxic gas release one might be concerned about doses over minutes to hours. In order to make meaningful predictions of the size and duration of the hazardous concentration region from a large, heavy gas release, all of the significant physical phenomena need to be included and the appropriate concentration averaging time needs to be used.