A Cost-Effective Model for Indoor Contaminant Simulation

A cost-effective numerical model has been developed which employs hp-adaptive finite elements to construct velocity fields and Lagrangian particles to predict contaminant dispersion patterns. The adaptive finite element method is based on both mesh enrichment (h-adaptation) and spectral order incensement (p-adaptation). The use of Lagrangian particles permits rapid visualization and assessment of contaminated areas within rooms and buildings. By coupling the model with AutoCAD/ProE drawings of a building, a domain model of offices on a floor including ventilation pathways can be readily implemented. Simulation results for contaminant transport in an office complex consisting of three rooms and an adjacent hallway are presented. A sequence of movies and results for various ventilation scenarios are available at web site: www.unlv.edu/NCACM/IAQ. INTRODUCTION Numerous investigators have conducted considerable research over many years to address issues dealing with indoor air quality [1-5]. Fast and accurate predictions of health effects, mitigation, and regulation of emissions are especially important when dealing with indoor air quality. This has become extremely important as a result of the increase in terrorist activities over the past few years. The finite element method (FEM), with its ability to easily deal with irregular geometries while employing the use of general-purpose algorithms, is especially attractive as a numerical method for simulating indoor contaminant transport. The use of adaptive FEM is even more attractive * Corresponding author for it can produce accurate results with less computational effort than conventional, fine mesh approaches. Generally, four main categories exist for adaptation: (1) h-adaptation, where the element sizes vary while the order of the shape functions are constant; (2) p-adaptation, where the element sizes are constant while the order of the shape functions increase to meet desired accuracy requirements; (3) r-adaptation, where spring analogy is used to redistribute the nodes in an existing mesh; (4) hp-adaptation, which is the combination of both h-and p-adaptation. Hp-adaptive schemes are among the best mesh-based schemes with the potential payoff of obtaining fast convergence rates. In this model, the hp-adaptive FEM is employed to construct indoor velocity fields. In Lagrangian methods, a large number of particles are used to approximate advection and dispersion instead of solving the PDE for concentration directly. In this model, a random walk/stochastic Lagrangian particle approach is applied. This scheme uses a general probability distribution for the random component of motion due to turbulent diffusion and generates Lagrangian particles that define the contaminant dispersion trajectories. Coupling the model with the ability to read AutoCAD/ProE drawings of a building, a domain model of offices on a floor including ventilation pathways can be quickly implemented. The Cad drawings permit the room and floor boundaries to be established while serving as a preload for the coarse mesh generation of the interior spaces. Coupling room sensors that would automatically trigger the model and set up appropriate response actions would allow immediate preventive measures to take affect. Simulation results for contaminant transport in an office complex consisting of three rooms and an adjacent hallway are presented. A sequence of movies and results for various ventilation scenarios can be accessed at web site: www.unlv.edu/NCACM/IAQ. MESH GENERATION The establishment of a suitable coarse mesh is very important. The first step in creating a valid mesh is to establish the domain boundaries, which is easily done by reading a Cad file. Generally mesh generation can be quite time consuming, especially for the FEM. Even though numerous commercial meshing software exists, it is usually hard to integrate them with other codes. In this study, the initial coarse mesh is generated using Gambit – a well known and easily obtained commercial code. Coupling the model with the ability to read AutoCad/ProE drawings, a separate mesh module integrates the output from Gambit with the hybrid numerical model for discretizing interior domains for indoor contaminant transport simulation. Meshing begins from the initial AutoCAD drawings for an office complex; in the following example, an interior domain consists of three rooms and an adjacent hallway. AutoCAD exports ACIS files, which are importable to Gambit. The configuration for the office complex is shown in Fig. 1. Figure 1 Office complex configuration After importing the ACIS file from AutoCAD, Gambit creates an initial coarse mesh. The mesh in this expel simulation consisted of 389 quadrilateral elements and 500 nodes, as shown in Fig. 2. Figure 2 Initial coarse meshes The meshing information from Gambit Neutral files is extracted after running the computer program “Mesh Converter” module. “Mesh Converter” is a bridge which connects the commercial meshing software to the hp-FEM codes. In order to minimize the bandwidth of the stiffness matrix in FEM, Quicksort Partitioning algorithms have been adopted [6]. NUMERICAL MODELS The governing equations used to describe indoor air flow and contaminant transport are based on the conservation of momentum and species transport: Conservation of Momentum ( ) V V V P V B t ρ μ ρ ∂ ⎛ ⎞ + ⋅∇ = −∇ +∇⋅ ∇ + ⎜ ⎟ ∂ ⎝ ⎠ (1) Species Transport ( ) ( ) m m m h m C VC k C S t ∂ +∇⋅ = ∇⋅ ∇ + ∂ C (2) Applying the Galerkin weighted residual method, and replacing the variables V and Cm with the trial functions: i i V( , t) N ( )V (t) =∑ x x (3) m i C ( , t) N ( )C (t) = mi ∑ x x (4) matrix equivalent forms for the integral expressions, Eq. 2 and Eq. 4, are obtained as: (5) V [M]{V} ([K] [A(V)]){V} C{p} {F } + + + = (6) m m m [M]{C } ([K] [A(V)]){C } {F } + + = C A Petrov-Galerkin scheme is employed to weight the advection terms in the momentum and species concentration equations: [ ] 2 e i i i h W N V N V α = + ⋅∇ (7)