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Impact of various parameters on the CFD predictions of atrium smoke management systems.

Article Excerpt
INTRODUCTION

Computational Fluid Dynamics (CFD) models are becoming widespread in the design of smoke control and smoke management systems for large and geometrically complex spaces such as atria. This paper reviews general theoretical concepts used in CFD models, and discusses how they affect the results of the simulations. It also provides some guidance to users of CFD models on some basic but important parameters that affect the solutions.

CFD Modelling of Smoke Control in Atria

CFD modelling has been used to study the behaviour of fire, and it has been demonstrated that it can be used for the study of smoke movement [McGrattan and Forney 2006]. The CFD model, Fire Dynamics Simulator (FDS) developed by NIST (National Institute of Standards and Technology) [McGrattan et al. 2002] and used extensively in the design of fire protection systems, such as smoke control and smoke management systems, is used in this study.

FDS (Fire Dynamics Simulator)

FDS is a computational fluid dynamics (CFD) model of fire driven fluid flow, which solves numerically a form of the Navier-Stokes equations appropriate for low-speed, thermally-driven flow with an emphasis on smoke and heat transport from fires [McGrattan and Forney 2006]. The formulation of the equations and the numerical algorithm can be found in the Fire Dynamics Simulator -Technical Reference Guide [McGrattan et al. 2002]. A brief description of the main features of FDS is given in the following sections.

a. Hydrodynamic Model

* The fundamental conservation equations of mass, momentum and energy as well as the state equation for low Mach number compressible flows are:

[[partial derivative][rho]/[partial derivative]t] + [nabla]*[rho]u = (1)

[[partial derivative]([rho]u])/[partial derivative]t] + [nabla]*[rho]uu = -[nabla]p + [rho]g + [nabla]*[tau] (2)

[[partial derivative]([rho]h)/[partial derivative]t] + [nabla]*[rho]hu = [Dp/Dt] + q'- + [nabla]*k[nabla]T (3)

p = R[rho]T (4)

* Large Eddy Simulation

FDS uses a Large Eddy Simulation (LES) approach to model turbulence [McGrattan et al. 2002]. LES solves the large eddy motions using a set of filtered equations governing the three dimensional, time-dependent motions. Small eddies are modeled independently from the flow geometry.

* Direct Numerical Simulation

FDS has also the option to use a Direct Numerical Simulation (DNS) if the numerical grid is fine enough.

b. Combustion Model

To model combustion, FDS uses a mixture fraction method based on equilibrium chemistry. Since combustion reaction mechanisms are exceedingly complex or unknown, simplifying assumptions are adopted for combustion modeling. In this approach, the reaction is assumed to be infinitely fast, and concentrations of individual species are derived from the predicted mixture fraction distribution [McGrattan et al. 2002].

The mixture fraction is defined in relation to common reaction systems. Consider a simple combustion system involving a fuel (F), an oxidizer (O) and a reaction product (P), [v.sub.F]F + [[upsilon].sub.O]O [right arrow] P.

The mixture fraction, Z, is defined as

Z = [[[bar.[upsilon]][Y.sub.F] - ([Y.sub.O] - [Y.sub.O.sup.[infinity]]]/[[bar.[upsilon]][Y.sub.F.sup.I] + [Y.sub.O.sup.[infinity]]]] (5))

where

[bar.[upsilon]] = [[[upsilon].sub.O][M.sub.O]/[[upsilon].sub.F][M.sub.F]]

where [Y.sub.F.sup.I] is the fraction of fuel in the fuel stream, and [Y.sub.O] and [Y.sub.O.sup.[infinity]] are the fractions of oxygen and un-depleted fraction of oxygen in ambient air, respectively. [M.sub.O] and [M.sub.F] are molecular weights of the oxidizer and fuel respectively.

An advantage of the mixture fraction approach is its computational efficiency as it does not require the solution of a large number of species transport equations. For some atrium fire scenarios, such as pool fires in large atria, the mixture fraction model produces very good predictions. However, for small-scale, under-ventilated fires, the mixture...

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